General Relativity & Quantum Mechanics

[BigApplePi]

This thread is an outgrowth of Re: Transhumanist 'party... and I thought it would be better served to bring it over here with a new thread. Agent Intellect has discussed this to a modest extent but that is dormant at present.

For convenience I will comment in blue.

The problem how to effectively let GR and QM work together is not clearly resolved yet, but one of the main reasons is that quantum field theory is itself very hard to handle anyway. A lot of work had to be done to make quantum electrodynamics, and the problem with gravitation is just one step harder. Still, it is not just plain contradictory. Indeed, there is loop quantum gravity which is a proposal how to reconcile them, but it is a hard subject of study.
I should think there is no surprise they don't work well together as GR deals with the universe as a whole while QM deals with the very small. If gravity at large exerts such as small force relative to other forces, then measuring its influence would be subject to experimental difficulties. At least that is my impression of the issue.

I think it is just a bit cynical and antirational to say that both theories don't logically go together.
Well they certainly seem to go together in this universe of ours.

There is some truth in it of course, but the way it is presented in popular books is, in my sense, grossly exaggerated.
I'd even say the difficulty to reconcile them seems to me rather pointless to mention, and only interests specialists. I don't see the point to worry about this problem of how to reconcile both theories. I see it just as a technical difficulty, while "in spirit" they go together well, through the least action principle.
A reconciliation would be of interest to novice amateurs as myself and the general public as well.

I did not invest myself in the hard part of quantum theory. I just know the basics (non-relativistic theory with hilbert spaces, and some intuitive understanding of the link between quantified fields and feynman diagrams, which provide the wave-particle duality). I don't know enough technical details to even figure out where trouble is with quantum gravity.
I guess we'll have to live with that. I have the equivalent of a Master's Degree in math but never got to Hilbert Spaces or Tensor Analysis really.

Anyway, both theories are wonderful and complementary. And even if someday the problem of reconciliation will be solved, I don't think it will make any difference: people will continue to learn GR and QM the same way, and the solution of how they are indeed compatible, will only interest a few specialists.
I'm so glad you are interested in this field. May I run some questions or comments by you?

In conclusion:
- You did not tell whether you know GR and QM or not
Only from basic popular works. I know enough to ask questions. Asking Qs is what I do.

- The remark that there remains a little problem to solve between them, is rather pointless in this discussion; all it can bring is to serve some sort of religious antiscientific propaganda. It does not substract anything to the wonderful interest in knowing these theories, nor their relevance to the understanding of our universe.

So, to the question "Have you been able to see those two put together? Is that logical?" the right meaningful reply to give is: Have you been able to see what the so-called "logical incompatibility" between GR and QM consist of, in the way specialists did face it ? Were you even aware that it is NOT that QM depended on any assumption of flat space-time, nor that gravitation would be of fundamentally different nature than the other interactions, but it is much more subtle than this ?
If ever you did study this, does it trouble you as for the relevance of these theories ?
I am very much interested in understanding this, at least intuitively. I understand String Theory is only in its infancy and is undergoing change.

Well this is trivial. Nobody could ever learn the currently known laws of physics without going on the way through tons of mathematical models of other sorts of universes with different laws than those of our universe.
You mean the laws of our universe are as arbitrary as the postulates in a mathematical system?

 

[spoirier]

"I should think there is no surprise they don't work well together as GR deals with the universe as a whole while QM deals with the very small."

Well, such a remark is very naive. In fact, the true issue of what makes trouble in the quantum treatment of gravity, is something that is very hard to explain to the general public, but I'll try.

" then measuring its influence would be subject to experimental difficulties."

Measurement difficulties is one thing, but here it is about theoretical difficulties, which is something else.
Yes, the measurement difficulty also has an impact, in that it does not let us a way to experiment the things which we did not theoretically understand.

"A reconciliation would be of interest to novice amateurs as myself and the general public as well."

Sorry I can't agree to take this seriously. I don't see the sense to pretend being interested in how goes the connection (conflict or reconciliation) between 2 theories that you did care to learn and understand in the first place.
If you want to be serious about being interested in the issues of theoretical physics, you should focus on learning these theories that are currently established, rather than staying like... cows watching trains pass by (uh, this is a usual French metaphor, I don't know in English...).

Then you may discover that, as compared to the state of ignorance in physics that the general public is, what is "known" (by physicists, but ignored by the public) can be appreciated as more interesting than what physicists are still searching for.

I'm not bringing any new idea of reconciliation between GR and QM. I'm just trying to express what has already been obvious for physicists since a very long time, but that they often just forgot to point out in popularization books.

Roughly, we can say the principles and concepts seem okay at first to start the study of quantum gravity. Namely, if we compare general relativity with classical electrodynamics, and we consider the framework of quantum field theory in which we wish to treat those interactions (we wish to quantize them), they don't seem to be of such a different nature that one could bet before effectively trying, that this work can succeed with the one (giving quantum electrodynamics) but fail with the other. Indeed they are both expressed in terms of the least action principle, and any classical theory expressed in such terms can naturally be "quantized", rewritten as a formula of quantum theory.
The problem is: this formula can have a mathematical sense (have a solution that can be computed), or not (indeed it is a habbit for physicists to work with formulas that make no mathematical sense, and process them until it does yields results and predictions...). So, the try is processed in the same way, starting with similar formulas. But the study of this formula works for electrodynamics, but fails (or it is not clear how to interpret it) for gravitation. Some divergences appear and it seems unclear how to handle them : if we try the methods that were successful for other interactions, it does not work for gravity anymore. Some divergences remain, and even worsen.
The method used for quantum electrodynamics is renormalization.
Namely, letting the physical constants vary depending on the scale of resolution. Indeed, the consequences of electrodynamics computed with a given scale of space resolution, can agree with those computed from another scale of space resolution, only if applied to different values of the physical constants. It's because a given scenario of particle interactions described at a given resolution, can only agree with a combination of different scenarios at a thinner resolution, as some particles appear there for only a very short time and thus can't be taken into account as this lifetime is shorter than the resolution (the thinner a situation is analysed, the manier particles it probably contains, something like a fractal, but a quantum one...).

Now this renormalization works for quantum electrodynamics, but fails with gravitation. The thinner the scale of resolution, the more unknowns in the description, failing to make predictions.

But, is it such a big difference ? Even for the standard model, which is supposedly renormalizable (if I remember well), computations are already so hard that they hardly converge in practice (they could only be made up to a satisfactory precision to be checked experimentally, but would diverge if processed further, or maybe it depends in the way the computation is made; indeed it is awfully complex, requiring the most powerful supercomputers to compute as "elementary" things as the mass of the proton).

Anyway, it is clear that gravitation has a community of essence with other interactions, so that that, just like them, it can be expressed as a particle (the graviton), even if this name of "particle" is quite misleading to the general public who does not understand what this wave-particle duality actually means from a mathematical viewpoint.
And it is also clear that the graviton is a boson with spin 2 (unlike all other known elementary bosons, which have spin 0 or 1).

"I guess we'll have to live with that. I have the equivalent of a Master's Degree in math but never got to Hilbert Spaces or Tensor Analysis really."

I know well Hibert spaces and Tensor analysis.

"Only from basic popular works. I know enough to ask questions. Asking Qs is what I do."

Great. As for me I am not an expert in theoretical physics and I have no solution to the problems that experts are facing, but I think I know enough to be able to answer most questions that can be raised by the general public, like experts would answer or so. So you can ask me your questions and I'll try to answer.

I have an intuitive understaning of what renormalization is about, but I did not learn how to make effective computations there.
I know that the problem with quantum gravity is about renormalization just because I read reports from experts mentioning this. I could not check it myself mathematically.

"You mean the laws of our universe are as arbitrary as the postulates in a mathematical system?"

Well, we cannot exactly say this, as we don't know what will be the right unifying theory describing our physical universe, that physicists are trying to discover. So we can't tell yet how unique it will be.

However, what we can tell is that the currently known form of the laws of physics, is made of different aspects (types of interactions), each of which forms a theory in its own right. And these specific interaction types that were picked up and put together to form the standard model, were taken in a seemingly arbitrary way from a quite larger general set of possible particles and interactions in the framework of quantum field theory.

Or we can also study interactions in the framework of classical physics, which is an approximation of the quantum one.
This framework of classical physics (as well as quantum field theory) can be applied to space-times of arbitrary dimensions. We know no good reason why the space-time has signature (3,1) (= 3 space dimensions + 1 time dimension) except out of the anthropic principle.
Indeed, the same theories of classical physics can easily be applied to arbitrary dimensions.

Classical Electrodynamics can be applied to any dimensions of space and time, and any dimension of electric charges (though, if we want charges to be carried by particles rather than strings or branes, charges should have dimension 1). But in signature (n,1), the force will necessarily vary as R^(1-n).
General relativity can also be applied to a space-time with any dimension at least 3, and it will also act like a force varying like R^(1-n), except at dimension 3 (i.e. n=2 space dimensions, for a total dimension n+1 = 3) where it does not look like a force (it cannot attract things together).

Therefore, dimension 3+1 is the only case where gravitation can let 2 bodies orbit each other: there would be no gravitational attraction in 2+1 dimension, and there is no possible stability of orbits in dimension 4+1 or higher.

Moreover, for the same reason (but treated with quantum theory), atoms could not be stable in dimension 4+1 or higher (they would collapse down to the nucleus).

In the course of initiation to quantum field theory I had attended, it was presented the phi^4 interaction as a theoretical example to show the general structure of things (the wave-particle duality, how feynman diagrams emerge from quantum fields), while (I think) there is no phi^4 interaction in the standard model. So, many types of interaction can be introduced...

 

[spoirier]

In fact, the main aspects of the situation are already explained in the wikipedia article of quantum gravity:

Historically, the most obvious way of combining the two (such as treating gravity as simply another particle field) ran quickly into what is known as the renormalization problem(...)
Indeed, the first quantum-mechanical corrections to graviton-scattering and Newton's law of gravitation have been explicitly computed (although they are so astronomically small that we may never be able to measure them). In fact, gravity is in many ways a much better quantum field theory than the Standard Model, since it appears to be valid all the way up to its cutoff at the Planck scale. (By comparison, the Standard Model is expected to start to break down above its cutoff at the much smaller scale of around 1000 GeV.) While confirming that quantum mechanics and gravity are indeed consistent at reasonable energies, it is clear that near or above the fundamental cutoff of our effective quantum theory of gravity (the cutoff is generally assumed to be of order the Planck scale), a new model of nature will be needed. Specifically, the problem of combining quantum mechanics and gravity becomes an issue only at very high energies, and may well require a totally new kind of model.
(...)
contrary to the popular claim that quantum mechanics and general relativity are fundamentally incompatible, one can demonstrate that the structure of general relativity essentially follows inevitably from the quantum mechanics of interacting theoretical spin-2 massless particles (called gravitons).
(...)
Quantum field theory on curved (non-Minkowskian) backgrounds, while not a full quantum theory of gravity, has shown many promising early results. In an analagous way to the development of quantum electrodynamics in the early part of the 20th century (when physicists considered quantum mechanics in classical electromagnetic fields), the consideration of quantum field theory on a curved background has led to predictions such as black hole radiation.

 

[BigApplePi]

03-22-10 by BAP in red.

"I should think there is no surprise they don't work well together as GR deals with the universe as a whole while QM deals with the very small."
Well, such a remark is very naive. In fact, the true issue of what makes trouble in the quantum treatment of gravity, is something that is very hard to explain to the general public, but I'll try
Welcome to the general public. I make no pretense I am not naive.

" then measuring its influence would be subject to experimental difficulties."
Measurement difficulties is one thing, but here it is about theoretical difficulties, which is something else.
Yes, the measurement difficulty also has an impact, in that it does not let us a way to experiment the things which we did not theoretically understand.

"A reconciliation would be of interest to novice amateurs as myself and the general public as well."
Sorry I can't agree to take this seriously. I don't see the sense to pretend being interested in how goes the connection (conflict or reconciliation) between 2 theories that you did care to learn and understand in the first place.
Pretend? You just met me. You don't know my motives, but that's okay.

If you want to be serious about being interested in the issues of theoretical physics, you should focus on learning these theories that are currently established, rather than staying like... cows watching trains pass by (uh, this is a usual French metaphor, I don't know in English...).
Epistemology (the nature of knowing) is a branch of philosophy. I am serious about what I want to know but am not after depth of knowledge at a professional level or anything close to that. Cows? Think of a small boy who sees trains, wonders about their power, where they go and what they carry. It is an honor to speak to someone who does have knowledge of such a subject and a difficult one at that.

Then you may discover that, as compared to the state of ignorance in physics that the general public is, what is "known" (by physicists, but ignored by the public) can be appreciated as more interesting than what physicists are still searching for.

I'm not bringing any new idea of reconciliation between GR and QM. I'm just trying to express what has already been obvious for physicists since a very long time, but that they often just forgot to point out in popularization books.

Roughly, we can say the principles and concepts seem okay at first to start the study of quantum gravity. Namely, if we compare general relativity with classical electrodynamics, and we consider the framework of quantum field theory in which we wish to treat those interactions (we wish to quantize them), they don't seem to be of such a different nature that one could bet before effectively trying, that this work can succeed with the one (giving quantum electrodynamics) but fail with the other. Indeed they are both expressed in terms of the least action principle, and any classical theory expressed in such terms can naturally be "quantized", rewritten as a formula of quantum theory.
The problem is: this formula can have a mathematical sense (have a solution that can be computed), or not (indeed it is a habbit for physicists to work with formulas that make no mathematical sense, and process them until it does yields results and predictions...). So, the try is processed in the same way, starting with similar formulas. But the study of this formula works for electrodynamics, but fails (or it is not clear how to interpret it) for gravitation. Some divergences appear and it seems unclear how to handle them : if we try the methods that were successful for other interactions, it does not work for gravity anymore. Some divergences remain, and even worsen.
The method used for quantum electrodynamics is renormalization.
Namely, letting the physical constants vary depending on the scale of resolution. Indeed, the consequences of electrodynamics computed with a given scale of space resolution, can agree with those computed from another scale of space resolution, only if applied to different values of the physical constants. It's because a given scenario of particle interactions described at a given resolution, can only agree with a combination of different scenarios at a thinner resolution, as some particles appear there for only a very short time and thus can't be taken into account as this lifetime is shorter than the resolution (the thinner a situation is analysed, the manier particles it probably contains, something like a fractal, but a quantum one...).

Now this renormalization works for quantum electrodynamics, but fails with gravitation. The thinner the scale of resolution, the more unknowns in the description, failing to make predictions.

But, is it such a big difference ? Even for the standard model, which is supposedly renormalizable (if I remember well), computations are already so hard that they hardly converge in practice (they could only be made up to a satisfactory precision to be checked experimentally, but would diverge if processed further, or maybe it depends in the way the computation is made; indeed it is awfully complex, requiring the most powerful supercomputers to compute as "elementary" things as the mass of the proton).
I have no comments at this time.

Anyway, it is clear that gravitation has a community of essence with other interactions, so that that, just like them, it can be expressed as a particle (the graviton), even if this name of "particle" is quite misleading to the general public who does not understand what this wave-particle duality actually means from a mathematical viewpoint.
And it is also clear that the graviton is a boson with spin 2 (unlike all other known elementary bosons, which have spin 0 or 1).

"I guess we'll have to live with that. I have the equivalent of a Master's Degree in math but never got to Hilbert Spaces or Tensor Analysis really."

I know well Hibert spaces and Tensor analysis.

"Only from basic popular works. I know enough to ask questions. Asking Qs is what I do."

Great. As for me I am not an expert in theoretical physics and I have no solution to the problems that experts are facing, but I think I know enough to be able to answer most questions that can be raised by the general public, like experts would answer or so. So you can ask me your questions and I'll try to answer.
I have three questions but I'll ask just two for now and see how it goes. I'm not so much looking for answers. That wouldn't be fair to you, but rather an acknowledgment of the questions.

One thing I have to say. That is popular works I've seen don't explain the physical experiments in many cases. That is, they make many unexplained statements, such as -- "This is a particle; we are shooting ONE particle; nothing exceeds the speed of light, the Planck's constant is this size, charge, spin." That tends to stop me right in my tracks. It stops me because I don't want to accept what is not explained. I don't want to go to the next step based on what may not be valid.

Question #1.
The Heisenberg principle. Isn't the reason why position and velocity can't be fixed within certain limits because photons are being used for the measurement? If we could be more refined than photons, couldn't we do better?

For your amusement I will give you theoretical limits not on the micro scale, but on the macro scale:
(A) Suppose I show you a still photograph. We can't tell precisely where objects shown are moving even if they appear to leave a trail.
(B) If I show you a moving object, we can't tell it's position in time precisely because it's moving.
Results can be obtained but they are no better than the instruments used to measure them. We need not go to the quantum scale.


Question #2.
In the double slit experiment where they are shooting photons (or electrons I forget which), they claim the resulting wave pattern is due to some "random" behavior of the particle where the particle is two places at once ... or some such explanation like that. That appears to be nonsense to me. Although they say they are firing one particle at a time, why can't they be wrong and this is a "wave-particle" instead. A wave particle would go through both slots at one shot and give rise to the interference wave pattern.

Question 3. Later.

I have an intuitive understanding of what renormalization is about, but I did not learn how to make effective computations there.
I know that the problem with quantum gravity is about renormalization just because I read reports from experts mentioning this. I could not check it myself mathematically.

"You mean the laws of our universe are as arbitrary as the postulates in a mathematical system?"
Well, we cannot exactly say this, as we don't know what will be the right unifying theory describing our physical universe, that physicists are trying to discover. So we can't tell yet how unique it will be.

However, what we can tell is that the currently known form of the laws of physics, is made of different aspects (types of interactions), each of which forms a theory in its own right. And these specific interaction types that were picked up and put together to form the standard model, were taken in a seemingly arbitrary way from a quite larger general set of possible particles and interactions in the framework of quantum field theory.
I guess we'll have to live with that for now.

Or we can also study interactions in the framework of classical physics, which is an approximation of the quantum one.
This framework of classical physics (as well as quantum field theory) can be applied to space-times of arbitrary dimensions. We know no good reason why the space-time has signature (3,1) (= 3 space dimensions + 1 time dimension) except out of the anthropic principle.
Indeed, the same theories of classical physics can easily be applied to arbitrary dimensions.

Classical Electrodynamics can be applied to any dimensions of space and time, and any dimension of electric charges (though, if we want charges to be carried by particles rather than strings or branes, charges should have dimension 1). But in signature (n,1), the force will necessarily vary as R^(1-n).
What is R^(1-n)? R=? A negative exponent?
Since you mention "charge", that is really

Question #3.
What is "charge"? We know it exists as anyone who has picked up a magnet knows. But what IS IT, not mathematically, but physically? It makes no sense that anything could act at a distance without some unusual dimensionality. It is intuitively impossible to imagine inside 3-4 dimensions. Am I wrong here?

I may have more to say about this and an answer in another context later. It has been discussed on the forum.

General relativity can also be applied to a space-time with any dimension at least 3, and it will also act like a force varying like R^(1-n), except at dimension 3 (i.e. n=2 space dimensions, for a total dimension n+1 = 3) where it does not look like a force (it cannot attract things together).

Therefore, dimension 3+1 is the only case where gravitation can let 2 bodies orbit each other: there would be no gravitational attraction in 2+1 dimension, and there is no possible stability of orbits in dimension 4+1 or higher.

Moreover, for the same reason (but treated with quantum theory), atoms could not be stable in dimension 4+1 or higher (they would collapse down to the nucleus).
That is over my head.

In the course of initiation to quantum field theory I had attended, it was presented the phi^4 interaction as a theoretical example to show the general structure of things (the wave-particle duality, how feynman diagrams emerge from quantum fields), while (I think) there is no phi^4 interaction in the standard model. So, many types of interaction can be introduced...
Maybe later. I'm really interested in Questions 1 to 3 first because they seem foundational.

 

[spoirier]

One thing I have to say. That is popular works I've seen don't explain the physical experiments in many cases. That is, they make many unexplained statements, such as -- "This is a particle; we are shooting ONE particle; nothing exceeds the speed of light, the Planck's constant is this size, charge, spin." That tends to stop me right in my tracks. It stops me because I don't want to accept what is not explained. I don't want to go to the next step based on what may not be valid.

I think you are asking too much. Physics took the work of thousands of researchers for many years to be established, through very large numbers of experiments. Verifications are much too many to be listed and explained, and always confirmed the same theories.
If the progress had been poor, made many predictions contradicted by experience, and if many phenomena remained unexplained, it would make sense to question previous claims, to suspect that the current interpretations of some experiments may not be valid, and would require further checking.
But this is not the case. The overwhelming set of verifications ensures that the current knowledge is right. Claims are valid because they have been checked to be valid by many ways, though newbies are not in a position to understand how.

If you think that learning physics as it is now is already hard for you, well, learning the whole list of all necessary experiments to justify it, would be even harder, and it may stick you to an impression that everything is so strange and escapes any possible understanding.
In my sense, the best understanding comes from mathematical definitions of how things are, from which you can logically deduce how they behave. It may first look strange, but then you can see the consistency.

Well, I may also agree with you that possibly a number of works hardly explain anything, not just for the experimental checking, but also are not careful to explain what they are talking about, even mathematically. So, they may let you no ground for understanding by any means. As for me, when I write maths and physics texts, I try to be as clear as possible, more than many things I could read elsewhere.

Question #1.
The Heisenberg principle. Isn't the reason why position and velocity can't be fixed within certain limits because photons are being used for the measurement? If we could be more refined than photons, couldn't we do better?

No, it does not matter of whether we use photons or anything else. The simultaneous data of the position and velocity of a particle below the limit of the Heisenberg inequalities, would make no physical sense, would not describe any possible reality. Simutaneous data of positions and velocities can only describe classical particles, the way balls look like in everyday life. But it is a different sort of reality that quantum theory deals with (well the same reality, but which cannot be described in the naive way)

In the double slit experiment where they are shooting photons (or electrons I forget which),

Anything. It has also been done with fullerene.

they claim the resulting wave pattern is due to some "random" behavior of the particle where the particle is two places at once ...

Uh ? this sounds like an unclear description. What did they precisely say ? Anyway it may be hopeless to expect a fine description in words, to satisfyingly express the concepts of quantum theory.

why can't they be wrong and this is a "wave-particle" instead

Electrons and photons are wave-particles just the same as fullerene or anything else is.

R= distance to the center.
In our universe, the space dimension is n=3, thus the force is in 1/R2.

But what IS IT, not mathematically, but physically?

Sorry, but in my view, which follows logical positivism and its " verifiability criterion of meaning" there is not such a thing as a physical nature of things beyond the mathematical theory that gives predictions.
Still I may have answers if you explain your question in more details, like this:

It makes no sense that anything could act at a distance

According to known laws of physics, nothing acts at a distance. Charges interact with fields, and fields propagate. (Well the situation is more complex with the EPR paradox, but...)

without some unusual dimensionality. It is intuitively impossible to imagine inside 3-4 dimensions. Am I wrong here?

Sorry what is your question ?

 

[BigApplePi]

spoirier. If I'm going to ask questions, I'm going to need better phrasing. You are right about that. Asking the right question gets one half-way there and I'm not ready. I will limit what I ask unless you feel differently.

"I think you are asking too much. Physics took the work of thousands of researchers for many years to be established"
I'm beginning to agree.

Question 4.
"As for me, when I write maths and physics texts"
I want to ask what you've written or even better, what your profession is but guess that might be too private for this board. I once had the opportunity to talk to a professor whose intention was to write a popular book on quantum physics but I muffed it. I have the feeling he would have given me similar answers to yours but am not sure. I don't recall his name but if you like I can look it up and you could tell me if you've heard of him.

Question 3.
What is "charge", not mathematically, but physically? You reply, "there is not such a thing as a physical nature of things beyond the mathematical theory." What? Mathematics is rearranged tautologies of symbols with psychological foundations in the real world. Mathematics is symbols, not the real world. My intuition says there is a real world out there whether we call it energy, matter, change, or interaction but something is out there. Do I need more background before I dare to ask what "charge" could be?

Question 5. This might be a more practical question though I don't know if I can get it across. Nuclear physicists are searching for truth. Are they searching more through mathematics or in the real world via experiment? I understand we can use mathematics as a template for the real world and then be pleased when the real world matches up. I understand that mathematics can then be used to extrapolate further into the real world, make conjectures and then try to see if the real world findings can be refined. But I say that taking pleasure in the results of mathematical conjectures is a psychological one, at best an art and at worst intellectual wheel spinning.* In the end it is the real world that is to be discovered if that is our inclination and that should not be forgotten.

Am I too unprepared to ask a question in this area or receive any answer? If quantum mechanics is going to violate ordinary intuition I cannot allow that to stand without overpowering it with a higher intuition.

Question 6. I heard or read somewhere that Schrodinger's equation or forms thereof is where most of nuclear physicists spend their time. Does that make any sense? This question is not as important as question 5.

*I chose not to use the word "masturbation."

 

[Agent Intellect]

Perhaps I can attempt to field some of these questions:

Question 3.
What is "charge", not mathematically, but physically? You reply, "there is not such a thing as a physical nature of things beyond the mathematical theory." What? Mathematics is rearranged tautologies of symbols with psychological foundations in the real world. Mathematics is symbols, not the real world. My intuition says there is a real world out there whether we call it energy, matter, change, or interaction but something is out there. Do I need more background before I dare to ask what "charge" could be?

Charge is a fundamental 'property' of stuff - it's essentially an axiom of reality. Asking what charge is is similar to asking "what is movement?" or "what is electron made out of?" It can't really be answered without referencing itself - movement is when something is moving, an electron is made out of electron (it doesn't break down any further than that).

Spoiler

Wikipedia has it defined: "More abstractly, a charge is any generator of a continuous symmetry of the physical system under study. When a physical system has a symmetry of some sort, Noether's theorem implies the existence of a conserved current. The thing that "flows" in the current is the "charge", the charge is the generator of the (local) symmetry group. This charge is sometimes called the Noether charge."

I assume you are asking this because of a previous discussion on how a field can cause different charged particles to be attracted or repelled, where a Gauge boson "hits" an electron and causes it to move toward the charged object? A Gauge boson is what's called a virtual particle, it's a quantized "particle" (which is a deceptive word in quantum mechanics) of a Gauge field. Once again, in this instance, classical analogies fail to describe the actual phenomenon.

Spoiler

Wikipedia describes the difference between Classical and Quantum fields:

Quantum mechanics, in its most general formulation, is a theory of abstract operators (observables) acting on an abstract state space (Hilbert space), where the observables represent physically-observable quantities and the state space represents the possible states of the system under study. Furthermore, each observable corresponds, in a technical sense, to the classical idea of a degree of freedom. For instance, the fundamental observables associated with the motion of a single quantum mechanical particle are the position and momentum operators

and

. Ordinary quantum mechanics deals with systems such as this, which possess a small set of degrees of freedom.
(It is important to note, at this point, that this article does not use the word "particle" in the context of wave–particle duality. In quantum field theory, "particle" is a generic term for any discrete quantum mechanical entity, such as an electron or photon, which can behave like classical particles or classical waves under different experimental conditions.)


A quantum field is a quantum mechanical system containing a large, and possibly infinite, number of degrees of freedom. This is not as exotic a situation as one might think (e.g., in an infinite-dimensional vector space, a vector is just a function as ordinary as f(x) = x^2; which is, of course, familiar territory). A classical field contains a set of degrees of freedom at each point of space; for instance, the classical electromagnetic field defines two vectors — the electric field and the magnetic field — that can in principle take on distinct values for each position r. When the field as a whole is considered as a quantum mechanical system, its observables form an infinite (in fact uncountable) set, because r is continuous.


Furthermore, the degrees of freedom in a quantum field are arranged in "repeated" sets. For example, the degrees of freedom in an electromagnetic field can be grouped according to the position r, with exactly two vectors for each r. Note that r is an ordinary number that "indexes" the observables; it is not to be confused with the position operator

encountered in ordinary quantum mechanics, which is an observable. (Thus, ordinary quantum mechanics is sometimes referred to as "zero-dimensional quantum field theory", because it contains only a single set of observables.)


It is also important to note that there is nothing special about r because, as it turns out, there is generally more than one way of indexing the degrees of freedom in the field

This is an interesting article on Quantum Field Theory and this gives a bit of background on the inception of the theory (if you are interested in further reading).

Question 5. This might be a more practical question though I don't know if I can get it across. Nuclear physicists are searching for truth. Are they searching more through mathematics or in the real world via experiment? I understand we can use mathematics as a template for the real world and then be pleased when the real world matches up. I understand that mathematics can then be used to extrapolate further into the real world, make conjectures and then try to see if the real world findings can be refined. But I say that taking pleasure in the results of mathematical conjectures is a psychological one, at best an art and at worst intellectual wheel spinning.* In the end it is the real world that is to be discovered if that is our inclination and that should not be forgotten.

Most of quantum theory can only be understood mathematically, but that doesn't mean it "happens" as mathematics. The problem stems from people like you (and me) demanding classical analogues for quantum phenomenon when there are none. Even using words like "wave" and "particle" are deceiving, as particle mainly denotes that it is quantized, and wave refers to probability amplitudes , when to laymen like you and I we want to picture little balls and ocean waves when thinking about the mechanics of quantum phenomenon - this is not how things on the quantum scale actually work, so the only way to understand whats happening in reality at this scale is through mathematics (which I admittedly am no good at, so I'm sure I'm in the same boat as you when I am left unsatisfied by the available explanations on these phenomenon).

Am I too unprepared to ask a question in this area or receive any answer? If quantum mechanics is going to violate ordinary intuition I cannot allow that to stand without overpowering it with a higher intuition.

Being that you have a background in math, I would say that you could probably teach yourself a lot about quantum mechanics. You are unprepared, since you demand classical, humanly intuitive explanations and analogues for something that is not humanly intuitive and doesn't have any direct analogue to the world we are used to living in.

Question 6. I heard or read somewhere that Schrodinger's equation or forms thereof is where most of nuclear physicists spend their time. Does that make any sense? This question is not as important as question 5.

Schrodinger's equation:

Spoiler

Is used a lot in chemistry (or, at least, that's where I encountered it). It describes the atomic orbitals of atoms.

 

[spoirier]

I had a few more thoughts to explain the Heisenberg inequalities.

The naive arguments, saying that the measurement of position of electrons by light is limited because of the photons'energies, finally sums up saying that the Heisenberg inequalities for electrons are due to those for photons. But this does not solve anything because these inequalities are the same for electrons, photons and anything, and don't depend on the means of measurement.
They are due to the wave-particle duality, which is also the same for everything. The wave nature of electrons is manifested in the orbitals in atoms.
We just can't describe electrons as classical waves (where 1 wave = many particles) in the way we do for the light made of electromagnetic waves, as electrons are fermions while classical wave behaviour is only possible for bosons.

I have only been teaching maths at university for 1 year but it did not happen very well so I'm not offcially working these times. In fact I can't integrate in the system, so let's just say I'm a free man. I started to write cleaner presentations of maths and physics subjects, taking them from the start, a rather top-down approach with a lot of explanation of what everything really means (in terms of mathematical structures...). You can check on my website what it is about, though I actually did most of it only in French for now.

Sorry I'll try to answer other questions another time.

 

[BigApplePi]

Hi AI. Glad you are here because I wanted you to meet spoirier. I sent you an email to that effect but don't know if you saw it. I will read your messages momentarily but may not reply now if I'm not ready.

 

[BigApplePi]

Charge is a fundamental 'property' of stuff - it's essentially an axiom of reality. Asking what charge is is similar to asking "what is movement?" or "what is electron made out of?" It can't really be answered without referencing itself - movement is when something is moving, an electron is made out of electron (it doesn't break down any further than that).

Spoiler

Wikipedia has it defined: "More abstractly, a charge is any generator of a continuous symmetry of the physical system under study. When a physical system has a symmetry of some sort, Noether's theorem implies the existence of a conserved current. The thing that "flows" in the current is the "charge", the charge is the generator of the (local) symmetry group. This charge is sometimes called the Noether charge."

I haven't read beyond Question 3 (What is charge?) yet because I want to respond to what you said before I get distracted by those links. I'm willing to bet those links don't answer the below but if I'm wrong feel free to tell me I'm ornery and an #@*&# INTP.

I will accept an axiom of reality like "motion." Motion I recognize as change. But not charge which appears to interact with other charges. It has an outward or inward affect. That I can't accept as fundamental. It seems to cause motion without being motion. Also I will not dismiss an electron either. I won't dismiss something which when interacting with another electron emits a photon. That says an electron is not fundamental. I think spoirier alluded to it being a wavi-particle. I want to know what is the possibility of that. Does it have an inside and an outside? Does it have a center emitting waves continually? Is it spherical? Does it exist with a "strong" center or a "weak" one? (I haven't the word to describe what I mean by strong/weak), does it rotate? Does it pulsate?

Okay I've taken a quick look at those links. I get the impression they are trying to describe physical reality in terms of those math'l systems like Lie algerbras, fields, "gauge" things, all kinds of groups. They name some particles but don't explain their properties so I can't tell what's going on. I'm going to guess that if they conjecture these particles the must know or have in mind what their properties should be but are sure hiding it from the likes of me. What do you think? I tend to be dismissive if they are describing complex events rather than the basic nature of wavi-particles. Perhaps underneath I'm asking about String Theory without really knowing if that's what I'm asking. Can't tell at this point.

 

[Agent Intellect]

Charge is motion, in a sense - or, at least, the propensity of a charged particle to move in a certain field.

Spoiler

In physics, an electric field is a field of force with a field strength equal to the force per unit charge at that point. Basically, it is a field in which a charge experiences a force.

The strength of the field at a given point is defined as the force that would be exerted on a positive test charge of +1 coulomb placed at that point; the direction of the field is given by the direction of that force. Electric fields contain electrical energy with energy density proportional to the square of the field amplitude. The electric field is to charge as gravitational acceleration is to mass and force density is to volume.

(source)

I'm sure someone can correct me (and I hope they do if I'm wrong) but the way I understand it is that charge is as fundamental as mass. For two charged particles to interact via their electromagnetic field is similar to two objects interacting via their mass (why should two objects bounce off each other and exert an equal and opposite reaction?).

 

[BigApplePi]

AI. I am thinking about your responses to those questions plus dabbling in the links. I wrote a response which I lost but just as well. Need time to mull things over.

 

[spoirier]

"Mathematics is symbols, not the real world."

What do you mean by "the real world" ? How can any concept be more about "the real world" than another concept, except for how well they can express the right predictions ? And a prediction is something mathematically expressed.
We can know the world through our senses. I don't know whether it is possible to see directly the world as it is based on out of body experiences, but as long as your soul remains inside your body, all you can know about the world is made of information through senses, thus consists of a set of mathematical connections between observations. Not directly the world as it is. So basically, it is pointless to expect anything else from physics than a precise definition of connections between observations.
However, don't worry: this mathematical expression of the laws of physics is quite meaningful. Maybe you can't see it because you are not familiar enough with it. But in fact, the mathematical understanding turns out to be quite more deep and meaningful than the naive one. It is just necessary to grow up intellectually and revise the nature of your expectations and the ground of your understanding.

Physics is not an unstructured set of arbitrary postulates. It has a strong self-consistency, even if we still wish to do better.

For the most general concept of charge, the least action principle needs to be understood first. And, well, the main example of charge is the electric one. For this, the question is not "what is charge" but "how to understand electromagnetism". Well, it's a very interesting subject, that would deserve to be done better than in the usual way with the Maxwell's equations, but I'm afraid this forum is not the right place for it.

But somehow I already gave a piece of answer about charges, did you not pay attention ? I wrote: charges don't act at a distance. Charges interact with fields, and fields propagate.

I'm afraid what you are willing to accept as an axiom of reality is the wrong one: motion is not a primitive concept. Indeed, motion is relative. Whenever you have motion of a particle, you can as well say that there is no motion by changing viewpoint. Well, more precisely when considering the Heisenberg inequalities, when you have a nonzero average speed, another frame will describe the same by a zero average speed.

"I won't dismiss something which when interacting with another electron emits a photon"

What ? Even alone, an electron is surrounded with an electric field (virtual photons).

"That says an electron is not fundamental."
?
The concept of electron can be seen as something fundamental, although it gathers the concept of spin 1/2 massive particle with an electric charge.

No, charge is not motion. There can be motion without charge.

Sorry I'll continue another time.

 

[spoirier]

Are they searching more through mathematics or in the real world via experiment?

Both. Some are searching the mathematical aspects, others are experimenting. Well I don't know the proportion but I think that further research in both is equally essential.

In the end it is the real world that is to be discovered if that is our inclination and that should not be forgotten.

I'd say that on the one hand for mathematicians, physics is a source of inspiration to discover some mathematical worlds. On the other hand, for physicists, what is to be discovered through experimentation, is the specification of which mathematical theory is the right one that properly describes our universe.

Does it have an inside and an outside? Does it have a center emitting waves continually?

No, the electron does not have an inside and an outside (at least not as far as we know). No, it does not have a center. No, it does not "emit" waves.
The wave is not in the electron nor produced by the electron. The wave is in the property of the question whether the electron is present or absent at every possible position (little volume). It is not a specific property of the electron, but a general property of the question of whatever there can be at any place.

So, for every space position (little volume) we have the question what is there: an electron ? a proton ? another nucleus ? nothing ? several things ? a fullerene ? and so on.
Most often there is not a unique true answer but a complex combination of several answers. But not even a specific combination in itself, as this combination of answers for each little volume, is in quantum correlation (like with the EPR paradox) with the ones for all other volumes.

In the general case, we can obtain a specific complex combination of possibilities for one place only as dependent on what has been observed everywhere else, provided the situation everywhere else has indeed been observed, which in fact is usually not the case. This is why the movement of a single electron appears as a wavefunction: it specifies the complex amplitude of presence of the electron in one place that would be obtained if the rest of the space has been observed as empty (with phase given by the amplitude of presence in such a case, and modulus reflecting the probability for this observation of emptiness everywhere else to have taken place).

This is valid only because emptiness of the rest of the space is a unique well-defined state. If there can be several particles in the space, as necessarily happens in quantum field theory (=when non-relativistic approximation is no more valid) then the situation becomes much trickier to imagine.

For example if we know that we have one electron in a volume, and we divide it into subvolumes, then the possible presence of the electron inside a subvolume is quantumly correlated with its absence from other subvolumes. But if subvolumes are smaller than the Compton wavelength of the electron (where relativistic effects come to dominate), then we can observe an electron's presence in more places than there globally were many electrons, provided that we also find positrons in other subvolumes, so that the total number (difference between the numbers of electrons and positrons) remains equal to the total number of electrons that was given in the whole volume.

 

[Agent Intellect]

For the most general concept of charge, the least action principle needs to be understood first. And, well, the main example of charge is the electric one. For this, the question is not "what is charge" but "how to understand electromagnetism". Well, it's a very interesting subject, that would deserve to be done better than in the usual way with the Maxwell's equations, but I'm afraid this forum is not the right place for it.

For the least action principle of charge, would that be taking the least action of a virtual photon in the electric field then? That makes sense to me, so I'd be grateful if you could correct me if I'm wrong.

Also, if you know of a website or something for "how to understand electromagnetism" I'd be willing to read it.

I'm afraid what you are willing to accept as an axiom of reality is the wrong one: motion is not a primitive concept. Indeed, motion is relative. Whenever you have motion of a particle, you can as well say that there is no motion by changing viewpoint. Well, more precisely when considering the Heisenberg inequalities, when you have a nonzero average speed, another frame will describe the same by a zero average speed.

I guess the motion thing was my doing. I was using motion as an analogy of how one would describe something to someone. If someone asked "what is motion?" one would probably answer "a change in position" and if someone asked "what's a change in position" one would probably answer "motion". As an everyday analogue, it's fundamental enough that it can really only be explained tautologically. As far as I understand charge (which admittedly isn't very far) it's the same in it can't really be broken down (ie, into "things that cause charge to exist" just as we can't say "this is why things are able to move") any further in order to explain it.

 

[BigApplePi]

I guess the motion thing was my doing. I was using motion as an analogy of how one would describe something to someone. If someone asked "what is motion?" one would probably answer "a change in position" and if someone asked "what's a change in position" one would probably answer "motion". As an everyday analogue, it's fundamental enough that it can really only be explained tautologically. As far as I understand charge (which admittedly isn't very far) it's the same in it can't really be broken down (ie, into "things that cause charge to exist" just as we can't say "this is why things are able to move") any further in order to explain it.

Motion? I want to see it even more basically, no tautology. I start with the existence of an observer. That is quite an assumption -- existence. I exist in time and space or somewhere somehow. What does motion require? Not one object only, for one can't tell it is moving without another for comparison. Are two objects enough? If they appear to be in motion, is that enough for a definition? As an observer when I see those two objects, that forms a triangle. Suppose I drop that idea. Just observe any triangle. When it changes its shape, that defines motion. Is this the answer? Maybe not as we still need the observer to say the triangle is changing shape. That makes four, or enough for three-dimensional space. Does this continue or have I made an error in thinking? If it continues 4,5,6,... we have to define an entire conscious existence before we can conjecture what motion is. This makes sense psychologically, but does it make sense without sentience?

Unfortunately I don't have time at the moment to think about these things. Hang in there guys a few days. I have to work on taxes. There is e-motion involved.

 

[BigApplePi]

"Mathematics is symbols, not the real world."

What do you mean by "the real world" ? How can any concept be more about "the real world" than another concept, except for how well they can express the right predictions ? And a prediction is something mathematically expressed.
We can know the world through our senses. I don't know whether it is possible to see directly the world as it is based on out of body experiences, but as long as your soul remains inside your body, all you can know about the world is made of information through senses, thus consists of a set of mathematical connections between observations. Not directly the world as it is. So basically, it is pointless to expect anything else from physics than a precise definition of connections between observations.

Let me see what I can say in the short time I have and hope later to get back to this.

The real world emerges via our senses. This emergence requires growing from an unaware baby to consciousness. Mathematics is too big a jump to have answers to go from this "real" world to math. First we form abstractions and store them in our brain. Many tools beyond our senses are employed. "Secondary" senses. We form models in our brain. Mathematics collects models, self-consistent we hope. (Didn't Godel say there is a limit to this?). We share mathematics among ourselves. The models of mathematics give the appearance of reality, but that is only conjecture. We have to experience feedback: math to tools to senses to the reality of the physical world and back to tools to math in a cycle.

Addition: I left out that this "real world" exists in our imagination but because we share our imagination with others and the results appears to be self-consistent, we assume what we have in our imagination is "out there", fixed, doesn't go away and is separate from us.

 

[spoirier]

I must correct the misunderstanding:

Least action principle = classical (non-quantum) physics (including general relativity). More precisely the expression "least action" is abusive, in fact it is stationary action (= the first derivative of the action with respect to any modification of the scenario cancels).

In quantum physics, the same concept of action is used, but managed another way. The action is no more required to be stationary, but scenarii of any action S contribute with a factor exp(iS/hbar) . Those near stationary action interfere constructively with their neighbours (variations of S < hbar), and those far from stationary action (variations of S > hbar) interfere destructively with their neigbours.

So, mixing the expression "least action" with concepts of quantum theory in the same sentence, makes no sense.

The expression "the least action of a virtual photon" especially makes no sense either. A photon could be approximated into a classical particle if we forget its wavy behaviour. As a classical particle it can be described using the least action principle. But the behaviour of virtual photons is no way close to the one of a classical particle obeying the least action principle. Instead, what can be described by the least action principle for interactions, is the classical field of interaction (not expressed as particles).

If we want to stay simple, what is charge: it is the ability for a particle to interact with a field.
Let's take an intuitive example: the scalar field in 2-dimensional space defined by the altitude function on a surface of water. An insect can stay on the water. The weight of the insect is a charge that bends the surface of the water, thus modifying the field of surface's altitude around itself.
This field would be massless (long range) if we were in a zero-gravity environment. But the effect of the gravity on the field, is the precise definition of a massive field, that makes a short-range interaction (= that decreases exponentially with distance). Indeed, 2 insects close to each other walking on water, have a short-range attraction to each other through their weight that bends the water surface.

Don't try to imagine this interaction as an exchange of virtual bosons that would look like particles. The expression of interactions in terms of virtual particles, is so abstract that it can only be misleading for the imagination of anyone who does not master quantum physics.

In order to explain what short-range has to do with mass of interactive boson:

A spatial short-range is described by an exponential decrease of the field with distance. But from space lengths to time lengths the ratio is imaginary (square root of a negative number). The exponential of an imaginary variable, is an oscillation (exp(ix)=cos x + i sin x).
And this oscillation in time is the wavy expression of the mass of a particle in relativistic quantum physics.

As in quantum theory there is no difference between a field and a type of particle, so the same concept of charge, as an interaction between a particle and a field, can as well be described in terms of ability for 2 particles to collide: this is the cross-section of collision (uh, I did not check how this may depend on relative speed). Or in terms of interaction between 2 fields...

If you want to understand motion as physicists understand it, you are still very far.
Forget about time. Space-time is not space and time. Rather, it is a 4-dimensional space with a pseudo-euclidean geometry. A classical particle appears as a stretched elastic there. The definition of "motion" between 2 particles, is that these stretched elastics are not parallel.

 

[BigApplePi]

Comments in blue, but also the message on Heisenberg below.

I must correct the misunderstanding:

Least action principle = classical (non-quantum) physics (including general relativity). More precisely the expression "least action" is abusive, in fact it is stationary action (= the first derivative of the action with respect to any modification of the scenario cancels).

In quantum physics, the same concept of action is used, but managed another way. The action is no more required to be stationary, but scenarii of any action S contribute with a factor exp(iS/hbar) . Those near stationary action interfere constructively with their neighbours (variations of S < hbar), and those far from stationary action (variations of S > hbar) interfere destructively with their neigbours.

So, mixing the expression "least action" with concepts of quantum theory in the same sentence, makes no sense.

The expression "the least action of a virtual photon" especially makes no sense either. A photon could be approximated into a classical particle if we forget its wavy behaviour. As a classical particle it can be described using the least action principle. But the behaviour of virtual photons is no way close to the one of a classical particle obeying the least action principle. Instead, what can be described by the least action principle for interactions, is the classical field of interaction (not expressed as particles).

If we want to stay simple, what is charge: it is the ability for a particle to interact with a field.
That sounds promising.

Let's take an intuitive example: the scalar field in 2-dimensional space defined by the altitude function on a surface of water. An insect can stay on the water. The weight of the insect is a charge that bends the surface of the water, thus modifying the field of surface's altitude around itself.
Does the insect depress the surface at 90 degrees, that is straight down?

This field would be massless (long range) if we were in a zero-gravity environment. But the effect of the gravity on the field, is the precise definition of a massive field, that makes a short-range interaction (= that decreases exponentially with distance). Indeed, 2 insects close to each other walking on water, have a short-range attraction to each other through their weight that bends the water surface.
How so attraction to each other if they depress the surface at 90 degrees?

Don't try to imagine this interaction as an exchange of virtual bosons that would look like particles. The expression of interactions in terms of virtual particles, is so abstract that it can only be misleading for the imagination of anyone who does not master quantum physics.

In order to explain what short-range has to do with mass of interactive boson:

A spatial short-range is described by an exponential decrease of the field with distance. But from space lengths to time lengths the ratio is imaginary (square root of a negative number). The exponential of an imaginary variable, is an oscillation (exp(ix)=cos x + i sin x).
And this oscillation in time is the wavy expression of the mass of a particle in relativistic quantum physics.
This may be saying something here. Is the particle behaving like a wave?

As in quantum theory there is no difference between a field and a type of particle, so the same concept of charge, as an interaction between a particle and a field, can as well be described in terms of ability for 2 particles to collide:
Interesting statement.
this is the cross-section of collision (uh, I did not check how this may depend on relative speed). Or in terms of interaction between 2 fields...

If you want to understand motion as physicists understand it, you are still very far.
Forget about time. Space-time is not space and time. Rather, it is a 4-dimensional space with a pseudo-euclidean geometry. A classical particle appears as a stretched elastic there. The definition of "motion" between 2 particles, is that these stretched elastics are not parallel.
Are you talking E-four space? Cute.

I believe it was Agent Intellect who displayed this link some time ago. I made the mistake of glossing over it. This is what I might have addressed earlier as it has always bothered me. Heisenberg Uncertainty.
http://en.wikipedia.org/wiki/Uncertainty_principle

Is the "particle" presented here one ellipsoidal pulse call a wave packet? Maybe I'm not reading correctly but why not call the position the center of the thing? Is that diagram illustrating multiple wave packets radiating outward? If so can't they get the momentum of the thing? Mass*velocity? Where is the mass supposed to be located: in the entire pulse or anywhere along the wave line in the diagram? Take the entire pulse and you have the momentum of "something."

Or rephrasing the question, how does an electron relate to this "wave packet"? Is this wave packet to be accepted as true or is it a conjecture? Are all envelopes of this wave packet the same (length, frequency and amplitude? The same distance between packets? Or is each answer to these questions, random?

A more advanced question is about an electron's supposed angular momentum. Is this angular momentum due to circling the nucleus (as the moon does the Earth) or does it spin as it goes around the nucleus? I'm not sure I'm ready to know before the "wave packet"'s meaning is more clear.

 

[Architectonic]

Maybe I'm not reading correctly but why not call the position the center of the thing?

Well for starters the expected value for a given wavefunction is not necessarily at the centre of the thing.
http://en.wikipedia.org/wiki/Expectation_value_(quantum_mechanics)
see also: http://en.wikipedia.org/wiki/Wave_function and http://en.wikipedia.org/wiki/Probability_amplitude
Secondly, the boundary values of the 'wavepacket' are ultimately arbitrary, though one may use statistical bounds as a guide.

A more advanced question is about an electron's supposed angular momentum. Is this angular momentum due to circling the nucleus (as the moon does the Earth) or does it spin as it goes around the nucleus? I'm not sure I'm ready to know before the "wave packet"'s meaning is more clear.

You have to stop projecting classical analogies onto quantum mechanics. It is often meaningless to compare the two.

http://en.wikipedia.org/wiki/Angular_momentum#Angular_momentum_in_quantum_mechanics
Most interesting is the idea of intrinsic angular momentum. This is analogous to the earth spinning on its axis, yet in Quantum mechanics, this idea of physically spinning on its axis becomes meaningless. If you are interested, it is worth following through the theoretical proof of the existence of half integer spin (of fermions).

Note, I am talking about QM, rather than QFT, but walking before running..

 

[BigApplePi]

Well for starters the expected value for a given wavefunction is not necessarily at the centre of the thing.
http://en.wikipedia.org/wiki/Expectation_value_(quantum_mechanics)
see also: http://en.wikipedia.org/wiki/Wave_function and http://en.wikipedia.org/wiki/Probability_amplitude
Secondly, the boundary values of the 'wavepacket' are ultimately arbitrary, though one may use statistical bounds as a guide.



You have to stop projecting classical analogies onto quantum mechanics. It is often meaningless to compare the two.

http://en.wikipedia.org/wiki/Angular_momentum#Angular_momentum_in_quantum_mechanics
Most interesting is the idea of intrinsic angular momentum. This is analogous to the earth spinning on its axis, yet in Quantum mechanics, this idea of physically spinning on its axis becomes meaningless. If you are interested, it is worth following through the theoretical proof of the existence of half integer spin (of fermions).

Note, I am talking about QM, rather than QFT, but walking before running..

Architectonic. I failed to prioritize what I'll call suggestions over priorities in getting questions answered.

From what I've read that I understand, classical explanations (classical language that is) will apply in a micro sense to quantum mechanics. Quantum mechanics doesn't compare directly with the macro levels of classical physics. That is because behavior at the quantum level is different.

The most important thing I want straightened out is the Heisenberg Principle. I want to know what they're talking about. Chuck those links unless the answer can be lifted from them. Those links only talk QM. I want English. Where is the particle? Is it the wave packet itself or is it along the tracing of the wave? The answer to that can be given in English and I have the feeling it is known what they intend. Forget classical versus quantum. I want English!

 

[Agent Intellect]

Architectonic. I failed to prioritize what I'll call suggestions over priorities in getting questions answered.

From what I've read that I understand, classical explanations (classical language that is) will apply in a micro sense to quantum mechanics. Quantum mechanics doesn't compare directly with the macro levels of classical physics. That is because behavior at the quantum level is different.

The most important thing I want straightened out is the Heisenberg Principle. I want to know what they're talking about. Chuck those links unless the answer can be lifted from them. Those links only talk QM. I want english. Where is the particle? Is it the wave packet itself or is it along the tracing of the wave? The answer to that can be given in english and I have the feeling it is known what they intend. Forget classical versus quantum. I want English!

I've explained this to you before, so I'll just copy and paste what I said:

If the probability amplitude of an electron or photon (or any particle, really) is spread out:

We can know the momentum of the particle, but not it's position (it's positions probability distribution is evenly spread out over a large distance).

But if the probability amplitude is 'collapsed' into wave packets:

We know it's position better (the higher amplitudes is where the particle is more likely to be; the lower amplitudes is where it's less likely to be) but we don't know it's momentum as accurately.

So, if

is position
And

is momentum
Then

With h being Planck's Constant.

Addendum: The important thing to remember is that in QM, a wave is a probability distribution, not like an ocean wave. To project QM onto classical analogue, think of it this way (remember this will be an imperfect analogue): where you are sitting right now, while holding still, the probability that you are in front of your computer is very high. Now, if you began moving walking, then within a certain time frame, we could only measure you being in front of your computer for a small amount of that time - your probability is "spread out" between your computer and wherever you walked during the time in which we measured your position.

So, when you are sitting in front of your computer, we know where you are, but not what your momentum is. When you start walking, we can measure your momentum, but we can't pinpoint a precise position for where you are at any given instant.

Of course, this analogue breaks down because the wave nature of quantum mechanics is always present, whereas for you in classical mechanics, we can say for sure when you are at a certain position.

The wavelength for an object can be calculated using:

Where P = momentum (often written m*v for this equation) and h = Planck's constant.

Spoiler

Relativistic version of

Example:
What is the wavelength of a ball, with mass 156g, thrown at a speed of 35 m/s? Planck's constant, h = 6.626x10^-34 J*s?

The speed of the ball is insignificant compared to the speed of light, therefore the wavelength is given by λ = h/mv.
Using this equation:
λ = h/mv, we have λ = 6.626x10^-34 J*s / (0.156 kg * 35 m/s) = 1.21x10^-34 m (wavelength)

This wavelength is far too small to be measured - hence, we don't see these quantum effects on the classical level.

 

[spoirier]

I did not care to mention, but as you ask: no, in the example of bending the water surface, we must keep the approximation that the angle is small, thus far from 90 degrees.
If you want to include the first correction (second order with respect to the angle), this translated into admitting vertices with 4 edges (self-interaction of the boson) in Feynman diagrams. For the next correction (4th order) this includes vertices with 6 edges, and so on.

"Is the particle behaving like a wave?"

Yes, particles behave like waves in the time dimension, with frequency mc2/h. But these waves do not really oscillate. Somehow phase varies at this frequency, but anyway phase is something relative that depends on a separate convention at each point of space-time. So nothing really becomes different in itself along one period. Indeed, if an electron is considered to be in an electrostatic potential, then its frequency is defined to reflect its total energy (mass energy + potential energy of the charge in the electric potential). But you know, the electric potential is only defined up to an arbitrary additive constant ! therefore the electron's frequency will arbitrarily depend on your convention for the potential.

Only when you have an electron-positron pair, the frequency will become "real", able to produce gamma rays...

One more hint:
You hope for clarification ? sorry you'll see things may be harder than you expected, but...
A classical particle is a point moving in the 3-dimensional space.
2 classical particles can be represented by 3 coordinates each, thus 6 coordinates total. They can be formalized as a point moving in a 6-dimensional space.

A quantum system of 2 particles ? Just take the 6-dimensional space where the system of 2 particles was represented as 1 moving point. Then replace this point by 1 wave.
So it is a wave in a 6-dimensional space.

And so on: a n-particles quantum system is formalized by 1 wave in a 3n-dimensional space.
Good luck figuring this out.

 

[Architectonic]

Architectonic. I failed to prioritize what I'll call suggestions over priorities in getting questions answered.

I assume you mean they compare on a macro level, but not a micro level..

The thing is that for me the mathematics makes it far more easily to communicate than explaining it purely in English. To me it doesn't make much sense to approach Heisenberg's uncertainty theorem until you understand the physics which it applies to. Likewise, Schrödinger's equation looks kind of arbitrary until you understand the
eigenvalue problem. Interestingly, AI stated the formula in such form.

How much mathematics do you know? Linear algebra? Integral calculus? Vector calculus?
Are you familiar with the usual statistical concepts - standard deviation, expected value, variance, probability density?

I guess I will attempt a sort of plug and play explanation.

The Copenhagen interpretation is an interpretation of quantum mechanics. A key feature of quantum mechanics is that the state of every particle is described by a wavefunction, which is a mathematical representation used to calculate the probability for it to be found in a location or a state of motion. According to this interpretation, the act of measurement causes the calculated set of probabilities to "collapse" to the value defined by the measurement. This feature of the mathematical representations is known as wavefunction collapse.

http://en.wikipedia.org/wiki/Copenhagen_interpretation

We will let our wavefunction = ψ(position,time)

Note that Fourier showed us that any periodic function can be reduced to a sum of sines and cosines (or equivalently a complex exponential via Euler)

Now as stated, we don't actually have a particle, but rather a probability amplitude, where we would expect an interaction could occur.

Now analogous to a probability density, this is given by |ψ(x)|^2

Or equivalently,

in 3d (also analogous to probability density)

To get the probability at a given point, you would solve for specific limits, and substitute that given point in.

Also not that if you definitely expect a particle to exist, then

(in 1d and the equivalent in 3d)
This is the normalisation condition and allows you to solve for a normalisation constant.

(also remember, if ψ is complex, then ψ^2 implies multiplying it by its conjugate)

To determine the value of an observable (eg momentum, or position) which are analogous to expected values in statistics, we need to introduce an operator for that particular observable and solve.

The position operator Q is given by:

For momentum, the operator P is given by:

For position in a 1D case, the expected value is given by:

(the p(x) is obviously the probability density, and if you are wondering what the other part is, its stated in Dirac Bra-ket notation)

Likewise for momentum:

In AIs example, the delta X, delta p can also have a statistical interpretation - sigma x, sigma p.

Also note that in AI's example, the wave function is arbitrary - it doesn't necessarily represent a real particle. To determine a real wave function, you must do some real physics - either measure one, or create a physical model.
The theoretical approach is to solve the eigenvalue problem for a real case.

This is the Schrödinger equation, where E represents the energy operator and H represents the Hamiltonian operator.

We then have the following expanded equation.

The ∇^2 is just the Laplace operator which is analogous to the second derivative, only for vectors.
The V(r) is the potential energy.

Which leads us to everyone's favourite illustration, which still isn't real but happens to be a nice example.

The particle in a box:

http://en.wikipedia.org/wiki/Particle_in_a_box (note the diagrams!)

On an interesting note, if you use this approach where there happens to be an infinite (eg an infinitely high barrier due to a delta function), something peculiar happens - the probability distribution still occurs on the other side of the barrier. Which is to say Quantum tunnelling can occur.

Unfortunately, you will have to be a bit more familiar with the formalisation/notation of QM to understand the proof of the Uncertainty principle, the derivation in my textbook isn't really any clearer than the one on Wikipedia. It is quite neat if you go through it though.

(equations from Wikipedia links previously mentioned)

 

[BigApplePi]

No dice.
I've explained this to you before, so I'll just copy and paste what I said:
While the electron is very fast, I am very sloooo.

I do NOT accept probabilities. Probability = ignorance. That's my point.
God does not shoot crap and I don't take crap unless very stressed.

If I were to say: If you are a gorilla, then you roam the jungle and I can tell your velocity, that's fine.
If the probability amplitude of an electron or photon (or any particle, really) is spread out:

We can know the momentum of the particle, but not it's position (it's positions probability distribution is evenly spread out over a large distance).
If I were to say you are a tree, then I can tell your position, that's fine.
But if the probability amplitude is 'collapsed' into wave packets:

We know it's position better (the higher amplitudes is where the particle is more likely to be; the lower amplitudes is where it's less likely to be) but we don't know it's momentum as accurately.

So, if

is position
And

is momentum
Then

Is the electron "spread out" or "collapsed"? Which is it or is it BOTH? You cannot be a gorilla AND a tree -- or is the quantum physicist saying BOTH? I think Herr Heisenberg got lost in the jungle one day and is now praying to the Planck god to save him because he didn't know where he was.

With h being Planck's Constant.

Addendum: The important thing to remember is that in QM, a wave is a probability distribution, not like an ocean wave. To project QM onto classical analogue, think of it this way (remember this will be an imperfect analogue): where you are sitting right now, while holding still, the probability that you are in front of your computer is very high. Now, if you began moving walking, then within a certain time frame, we could only measure you being in front of your computer for a small amount of that time - your probability is "spread out" between your computer and wherever you walked during the time in which we measured your position.

So, when you are sitting in front of your computer, we know where you are, but not what your momentum is. When you start walking, we can measure your momentum, but we can't pinpoint a precise position for where you are at any given instant.

Let's try something in between a gorilla and a tree. A bee. A bee always stays near the hive. So one knows the bee's motion and it's position at the same time.

Unlike the bee, I think I'm being told we can't tell what kind of wave an electron is. Just because we can't tell by observation doesn't mean the wave doesn't exist. Saying we can't measure position and velocity because we don't know what something is, is a tautology.

Of course, this analogue breaks down because the wave nature of quantum mechanics is always present, whereas for you in classical mechanics, we can say for sure when you are at a certain position.

The wavelength for an object can be calculated using:

Where P = momentum (often written m*v for this equation) and h = Planck's constant.

Spoiler

Relativistic version of

Example:
What is the wavelength of a ball, with mass 156g, thrown at a speed of 35 m/s? Planck's constant, h = 6.626x10^-34 J*s?

The speed of the ball is insignificant compared to the speed of light, therefore the wavelength is given by λ = h/mv.
Using this equation:
λ = h/mv, we have λ = 6.626x10^-34 J*s / (0.156 kg * 35 m/s) = 1.21x10^-34 m (wavelength)

This wavelength is far too small to be measured - hence, we don't see these quantum effects on the classical level.

.

 

[BigApplePi]

It may take me a couple weeks to settle down with this. Unfortunately I'm trying to do too many things at once: Taxes, address leaks in my apartment ceiling, plant the garden, edit Adymus's Cognitive Functions, watch the stock market, meet with a new group, and more.

Your link here looks promising: Wikipedia when I get the chance to look at it. Meanwhile I think what I want is an admission that probability is a cop out or is another word for "we don't know and can't tell." From what we do know we can measure and do mathematics and experiment and play with it and get results. This doesn't say what lies underneath for me.

I have one year of grad school math where I taught calculus to freshmen. I have a nodding acquaintance with statistics. When I studied eigenvalues long ago I had no idea what they were for and was too shy to ever ask. Analysis and topology were my favorites but I never took them anywhere.

I don't know what those operators Hamilton and LaPlace are but they don't sound much like new mathematics to me.

I assume you mean the compare on a macro level, but not a micro level..

The thing is that for me the mathematics makes it far more easily to communicate than explaining it purely in English. To me it doesn't make much sense to approach Heisenberg's uncertainty theorem until you understand the physics which it applies to. Likewise, Schrödinger's equation looks kind of arbitrary until you understand the
eigenvalue problem. Interestingly, AI stated the formula in such form.

How much mathematics do you know? Linear algebra? Integral calculus? Vector calculus?
Are you familiar with the usual statistical concepts - standard deviation, expected value, variance, probability density?

I guess I will attempt a sort of plug and play explanation.



We will let our wavefunction = ψ(position,time)

Note that Fourier showed us that any periodic function can be reduced to a sum of sines and cosines (or equivalently a complex exponential via Euler)

Now as stated, we don't actually have a particle, but rather a probability amplitude, where we would expect an interaction could occur.

Now analogous to a probability density, this is given by |ψ(x)|^2

Or equivalently,

in 3d (also analogous to probability density)

To get the probability at a given point, you would solve for specific limits, and substitute that given point in.

Also not that if you definitely expect a particle to exist, then

(in 1d and the equivalent in 3d)
This is the normalisation condition and allows you to solve for a normalisation constant.

(also remember, if ψ is complex, then ψ^2 implies multiplying it by its conjugate)

To determine the value of an observable (eg momentum, or position) which are analogous to expected values in statistics, we need to introduce an operator for that particular observable and solve.

The position operator Q is given by:

For momentum, the operator P is given by:

For position in a 1D case, the expected value is given by:

(the p(x) is obviously the probability density, and if you are wondering what the other part is, its stated in Dirac Bra-ket notation)

Likewise for momentum:

In AIs example, the delta X, delta p can also have a statistical interpretation - sigma x, sigma p.

Also note that in AI's example, the wave function is arbitrary - it doesn't necessarily represent a real particle. To determine a real wave function, you must do some real physics - either measure one, or create a physical model.
The theoretical approach is to solve the eigenvalue problem for a real case.

This is the Schrödinger equation, where E represents the energy operator and H represents the Hamiltonian operator.

We then have the following expanded equation.

The ∇^2 is just the Laplace operator which is analogous to the second derivative, only for vectors.
The V(r) is the potential energy.

Which leads us to everyone's favourite illustration, which still isn't real but happens to be a nice example.

The particle in a box:

http://en.wikipedia.org/wiki/Particle_in_a_box (note the diagrams!)

On an interesting note, if you use this approach where there happens to be an infinite (eg an infinitely high barrier due to a delta function), something peculiar happens - the probability distribution still occurs on the other side of the barrier. Which is to say Quantum tunnelling can occur.

Unfortunately, you will have to be a bit more familiar with the formalisation/notation of QM to understand the proof of the Uncertainty principle, the derivation in my textbook isn't really any clearer than the one on Wikipedia. It is quite neat if you go through it though.

(equations from Wikipedia links previously mentioned)

 

[BigApplePi]

Reading this over again:

I must correct the misunderstanding:

Least action principle = classical (non-quantum) physics (including general relativity). More precisely the expression "least action" is abusive, in fact it is stationary action (= the first derivative of the action with respect to any modification of the scenario cancels).

In quantum physics, the same concept of action is used, but managed another way. The action is no more required to be stationary, but scenarii of any action S contribute with a factor exp(iS/hbar) . Those near stationary action interfere constructively with their neighbours (variations of S < hbar), and those far from stationary action (variations of S > hbar) interfere destructively with their neigbours.
What is meant by "constructive-near" and "destructive-far"?

So, mixing the expression "least action" with concepts of quantum theory in the same sentence, makes no sense.

The expression "the least action of a virtual photon" especially makes no sense either. A photon could be approximated into a classical particle if we forget its wavy behaviour. As a classical particle it can be described using the least action principle. But the behaviour of virtual photons is no way close to the one of a classical particle obeying the least action principle. Instead, what can be described by the least action principle for interactions, is the classical field of interaction (not expressed as particles).
So we want to know about waves.

If we want to stay simple, what is charge: it is the ability for a particle to interact with a field.
Let's take an intuitive example: the scalar field in 2-dimensional space defined by the altitude function on a surface of water. An insect can stay on the water. The weight of the insect is a charge that bends the surface of the water, thus modifying the field of surface's altitude around itself.
This field would be massless (long range) if we were in a zero-gravity environment. But the effect of the gravity on the field, is the precise definition of a massive field, that makes a short-range interaction (= that decreases exponentially with distance). Indeed, 2 insects close to each other walking on water, have a short-range attraction to each other through their weight that bends the water surface.
Is this like two balls on a curved surface rolling toward each other? That fails to say why the balls cause the surface to curve. Their mass= radiation= wave= energy must be doing something to the space-field.

Don't try to imagine this interaction as an exchange of virtual bosons that would look like particles. The expression of interactions in terms of virtual particles, is so abstract that it can only be misleading for the imagination of anyone who does not master quantum physics.
In other words it can't be translated into English.

In order to explain what short-range has to do with mass of interactive boson:

A spatial short-range is described by an exponential decrease of the field with distance. But from space lengths to time lengths the ratio is imaginary (square root of a negative number). The exponential of an imaginary variable, is an oscillation (exp(ix)=cos x + i sin x).
And this oscillation in time is the wavy expression of the mass of a particle in relativistic quantum physics.

As in quantum theory there is no difference between a field and a type of particle, so the same concept of charge, as an interaction between a particle and a field, can as well be described in terms of ability for 2 particles to collide: this is the cross-section of collision (uh, I did not check how this may depend on relative speed). Or in terms of interaction between 2 fields...
I feel like I'm being pressured to give in to the Heisenberg Uncertainty principle by the other two guys and here I'm inclined to wish I'd never heard the word, "particle." So what do we have left? Some kind of wave-energy affecting a field-space?

If you want to understand motion as physicists understand it, you are still very far.
Forget about time. Space-time is not space and time. Rather, it is a 4-dimensional space with a pseudo-euclidean geometry. A classical particle appears as a stretched elastic there. The definition of "motion" between 2 particles, is that these stretched elastics are not parallel.
Sounds good, but very tautological.

 

[BigApplePi]

I started a thread entitled: Re: How To Understand Anything. Here is a progress report on the present thread:

1. There are three perspectives.
1.1 The real physical world "out there."
1.2 The world of mathematics.
1.3 The human view.

6. There are four levels of reality.
6.1 The human view. (ours)
6.2 The relativistic one. (large & small(?))
6.3 The quantum level. (small & large(?))
6.4 String Theory. (very small)

2. Translation is where a difficulty comes in.
1.1 <-> 1.2 is being worked on.
6.2<->6.3<->6.4 are being worked on.
Translating 6.3 into 6.1 may require new words for the English language. Just as words used in classical physics are different from the words of chemistry are different from the words of biology, the ordinary human is too immersed in 6.1 words to pick up 6.3.

 

[spoirier]

I'm not sure to have used the standard English phrasing, as my native language is French.

I meant that contributions of different scenarii interfere; in this interference, the paths close to obeying the least action principle add up their contribution with their neighbours, and are therefore preferred scenarii; those far from obeying the least action principle cancel away with their neighbours and have therefore a low probability to come to reality (approaching zero when the approximation of classical physics applies).
You can understand this by considering classical optics as an approximation of the theory of electromagnetic waves.

As for

Meanwhile I think what I want is an admission that probability is a cop out or is another word for "we don't know and can't tell."

Don't you know that this question has of course been extensively addressed, by the work on hypothetic hidden variables theories and some impossibility theorems about them ?
Who do you think physicists are ?
How do you think they could have so officially declared that the result of a measurement does not display a preexisting reality but is randomly produced by the act of measurement itself, if not because they had very solid reasons to say so ?

This reason is found in the EPR paradox. Well, I'm sorry that usual presentations of this paradox don't explain it well. So I'm going to write here a simple description of this paradox in English. I consider it very important to understand it well, as the strangeness of wavefunctions and their status with respect to "reality" (what is the problem in trying to interpret wavefunctions), relies on it.

Imagine a pair of 2 crosses, first attached together, oriented like x and +, so that they form a star with 8 vertices. On each of these 8 vertices is a bulb.
One experimenter keeps the + on Earth; another one takes the x with him to Mars.
Each experimenter is free to wait any amount of time, then, at any time, decide to select one of both axis of his cross (disregarding whether both experimenters do their selection of axis in either order or simultaneously; no communication is possible between them, especially if they are simultaneous, as no information can go faster than light)
As soon as each experimenter selects one axis, one and only one of both bulbs at the ends of this axis lights on.

Then, provided that the crosses had been properly prepared together before separation, the theory predicts that, no matter whether the experimenters have any strategy or not regarding the time and choice of the axis they will select, there are 85% chances that the two vertices that light on (one on the Earth, the other on Mars) had been neighbours before separation.

Now, if you want an "explanation", assuming that observations are mere discoveries of a previously unknown but existing reality, then you cannot do better than a 75% probability of having neighbour vertices light on. This (maximum allowed by Bell's inequality) is obtained by preparing the crosses so that the vertices that would light on if their axis is selected, were 4 consecutive ones - but we don't know which ones yet.

Now, quantum mechanics, which has always been confirmed, says it is possible to ensure a 85% chance. You can think it however you want, you'll never find an "explanation" of this by saying observation discovers a local hidden reality that was just unknown.

Now we can come back to the Heisenberg inequalities.
Take one cross. One axis represents "measurement of position"; the other represents "measurement of momentum".
You cannot measure both. Indeed, in the previous example, an experimenter could not select both axis of the same cross to see 2 bulbs light on, one on each axis, and still have for each the same chances of result as was described no matter what the other experimenter would choose (that he may have not chosen yet).

 

[Agent Intellect]

No dice.

Need more quote breaks.

While the electron is very fast, I am very sloooo.

I do NOT accept probabilities. Probability = ignorance. That's my point.
God does not shoot crap and I don't take crap unless very stressed.

I find the conservation of mass disconcerting, too. Just because we've never seen the wholesale creation or destruction of mass doesn't mean that's how reality works, does it? As far as quantum mechanics, it walks like probability, it quacks like probability, it smells like probability, so it's probably probability. It doesn't matter whether you like it or agree with it, it's the way it is.

Is the electron "spread out" or "collapsed"? Which is it or is it BOTH? You cannot be a gorilla AND a tree -- or is the quantum physicist saying BOTH? I think Herr Heisenberg got lost in the jungle one day and is now praying to the Planck god to save him because he didn't know where he was.

It's collapsed from Wave function collapse or Quantum decoherence:

Spoiler

n quantum mechanics, quantum decoherence is the mechanism by which quantum systems interact with their environments to exhibit probabilistically additive behavior. Quantum decoherence gives the appearance of wave function collapse and justifies the framework and intuition of classical physics as an acceptable approximation: decoherence is the mechanism by which the classical limit emerges out of a quantum starting point and it determines the location of the quantum-classical boundary. Decoherence occurs when a system interacts with its environment in a thermodynamically irreversible way. This prevents different elements in the quantum superposition of the system+environment's wavefunction from interfering with each other. Decoherence has been a subject of active research since the 1980s

Basically, interactions with an electron causes it to lose it's superposition (it's ambiguous position).

Let's try something in between a gorilla and a tree. A bee. A bee always stays near the hive. So one knows the bee's motion and it's position at the same time.

Unlike the bee, I think I'm being told we can't tell what kind of wave an electron is. Just because we can't tell by observation doesn't mean the wave doesn't exist. Saying we can't measure position and velocity because we don't know what something is, is a tautology.

The wave is the probability for the particle to be somewhere. Higher amplitude = higher probability for the particle to be there. The wave is observed as the pattern that it creates in a double slit experiment, or the 0%-16% chance of reflecting off glass due to it's thickness. The wave is the ambiguous, probabilistic nature of the quanta.

EDIT: I suggest (to anyone interested in this) watching Richard Feynman's lectures on quantum electrodynamics.

 

[spoirier]

That fails to say why the balls cause the surface to curve.

Well this should be clear: here I take as an axiom the fact that the balls have weight. Then the equilibrium of the surface (where equilibrium = minimum energy = least action) can be computed, and the result is that it has to curve.

Their mass= radiation= wave= energy

Uh ? some property of the wave depends on mass, and indeed frequency=energy but...

In other words it can't be translated into English

Well I can still try: the interactive particle's worldline (which is 1-dimensional in the 4-dimensional space-time) has an amplitude (rather than probability: the probability is the square of the sum of all amplitudes) of being there, given by the decreasing exponential of its length (because the action is proportional to the length), just like happens (but with probabilities instead of amplitudes) in thermodynamics with Botzmann's law if you imagine an elastic whose energy would be proportional to its length.

Indeed, we have a dictionary between 2 theories with the same basic mathematical structure, though they don't relate to reality in the same way:

Statistical description of thermodynamic equilibrium / relativistic mechanics
Euclidean space / 4-dimensional space-time
Probability / Amplitude
Potential Energy / Action
Bolzmann's law / exp (iS/hbar)

Now this elastic subject to thermic agitation, is not straight. Its shape is very chaotic. Still somehow its average length is proportional to distance between ends, and thus its amplitude of being there decreases exponentially with long distances.
But this all does not explain how this description is equivalent with the one in terms of field. Well...

I'm inclined to wish I'd never heard the word, "particle."

The wavefunction describes the movement of 1 particle. Indeed it is about particles, as the particles number can be counted: there is only 1 particle described by the wavefunction. If you want 2 particles you have to use a wavefunction in a 6-dimensional space, and so on.
If you want a classical wave, then the particles number will be undetermined.
If you want the particles number in a wave to be determined, the phase will be undetermined.
This is why when you take 1 electron, its particles number is determined, therefore its phase is relative.

I find the conservation of mass disconcerting, too. Just because we've never seen the wholesale creation or destruction of mass doesn't mean that's how reality works, does it? As far as quantum mechanics, it walks like probability, it quacks like probability, it smells like probability, so it's probably probability.

You mean the conservation of energy I guess ? Well sorry to contradict you but this conservation is a theorem of the known laws of physics, it cannot be violated by any means without mathematical self-contradiction. More precisely it is a theorem of general relativity, though its formulation there is more subtle than just a quantity to be preserved.
What is true in quantum physics, though, is that the value of this energy for a given system, can be undetermined. When it is undetermined, its measurement gives a random result that is produced by the measurement. (while the undetermination remains somehow in terms of Everett's parallel universes).
But this does not mean that the conservation of energy can be violated by any means.
If you have a system with a determined energy and you measure there a quantity which is incompatible with a determined energy, then this measurement process requires you to exchange with that system the undetermined quantity of energy that explains the system's undetermined value of the energy at the end.
Consequently, if you measure again the energy after this, then the possibly different values you can obtain do come from somewhere.

 

[Architectonic]

It may take me a couple weeks to settle down with this. Unfortunately I'm trying to do too many things at once: Taxes, address leaks in my apartment ceiling, plant the garden, edit Adymus's Cognitive Functions, watch the stock market, meet with a new group, and more.

No problem. You have a lifetime left. Just realise that there are no easy answers - you must invest the time if you wish to understand.

Your link here looks promising: Wikipedia when I get the chance to look at it.

Well right now it probably doesn't make much sense as you don't yet understand bra-ket notation.

Meanwhile I think what I want is an admission that probability is a cop out or is another word for "we don't know and can't tell." From what we do know we can measure and do mathematics and experiment and play with it and get results. This doesn't say what lies underneath for me.

As we keep telling you, maybe the failure lies in your commitment to classical thinking.
The fact is that Quantum Mechanics is the most well tested physical theory ever. Now it is true that it doesn't describe everything (it does not claim to). But more complete theories still describe the small scale interactions in the same way as QM. Which is to say, there are no local hidden variables, reality is probabilistic. (see Bell's Theorem)



Here are the links that follow up Spoirier's post:

http://en.wikipedia.org/wiki/Copenhagen_interpretation
http://en.wikipedia.org/wiki/Epr_paradox
http://en.wikipedia.org/wiki/Bell's_theorem

Note that there are other interpretations, involving things like "many-worlds" and "superdeterminism". But the funny thing is, these in reality are exactly the same as the Copenhagen interpretation. They are equivalent (and please don't do anything silly like bringing non scientific principles like Occam's Razor into this).

I don't know what those operators Hamilton and LaPlace are but they don't sound much like new mathematics to me.

It is indeed nothing new - 19th century mathematics.

I recommend learning/brushing up on partial differential equations and vector calculus, as well as some of the linear algebra if you want to follow this stuff.

The rest of the formalism - bra-ket notation, some of the linear algebra used is usually explained in Quantum Mechanics textbooks. The one we used was Introduction To Quantum Mechanics by Griffiths. (which can be "found" on the web by the way)


PS, try not to quote whole slabs when replying. Also, the blue text clashes horribly against the standard dark background on this forum. You can just type in [/quote] tags, it doesn't take long.

 

[BigApplePi]

I'm not sure to have used the standard English phrasing, as my native language is French.
Well I would say your use of English is superior to the average English speaking native. I tend to lapse into dialect depending on whom I am speaking to. You should see some of the trash I write on the internet, lol.

I meant that contributions of different scenarii interfere; in this interference, the paths close to obeying the least action principle add up their contribution with their neighbours, and are therefore preferred scenarii; those far from obeying the least action principle cancel away with their neighbours and have therefore a low probability to come to reality (approaching zero when the approximation of classical physics applies).
You can understand this by considering classical optics as an approximation of the theory of electromagnetic waves.

As for *** you left this out deliberately??? ***
Don't you know that this question has of course been extensively addressed, by the work on hypothetic hidden variables theories and some impossibility theorems about them ?
Who do you think physicists are ?
I don't think of them as any group.

How do you think they could have so officially declared that the result of a measurement does not display a preexisting reality but is randomly produced by the act of measurement itself, if not because they had very solid reasons to say so ?
I don't question their belief in themselves. I question their beliefs. Also I distinguish between the ability to measure and what is being measured.

This reason is found in the EPR paradox. Well, I'm sorry that usual presentations of this paradox don't explain it well. So I'm going to write here a simple description of this paradox in English. I consider it very important to understand it well, as the strangeness of wavefunctions and their status with respect to "reality" (what is the problem in trying to interpret wavefunctions), relies on it.
Okay but you may be sorry. I will look for assumptions that are assumed.

Imagine a pair of 2 crosses, first attached together, oriented like x and +, so that they form a star with 8 vertices. On each of these 8 vertices is a bulb. Where did you say these bulbs are located? Did you mean end point or vertex? http://www.mathopenref.com/vertex.html
One experimenter keeps the + on Earth; another one takes the x with him to Mars.
Each experimenter is free to wait any amount of time, then, at any time, decide to select one of both axis of his cross (disregarding whether both experimenters do their selection of axis in either order or simultaneously; no communication is possible between them, especially if they are simultaneous, as no information can go faster than light)
As soon as each experimenter selects one axis, one and only one of both bulbs at the ends of this axis lights on.
Addition: How could I have left this out? -- Which end lights up? Random or biased? To identify which, let's color the north side of the star black & the south side, red.

Then, provided that the crosses had been properly prepared together before separation, the theory predicts that, no matter whether the experimenters have any strategy or not regarding the time and choice of the axis they will select, there are 85% chances that the two vertices that light on (one on the Earth, the other on Mars) had been neighbours before separation. (by neighbors you mean 2 of the 4 vertices?)
1. What are the chances if there was "no preparation"? Isn't the chance 50% (not 75%). Can't we simply the experiment and only one experimenter picks?
2. What is this "preparation"? -- never mind you said later.
3. This is not a real experiment (no one has done this) so you must have a real one in mind.

Now, if you want an "explanation", assuming that observations are mere discoveries of a previously unknown but existing reality, then you cannot do better than a 75% probability of having neighbour vertices light on. This (maximum allowed by Bell's inequality) is obtained by preparing the crosses so that the vertices that would light on if their axis is selected, were 4 consecutive ones -
I don't know what this means. You said one and only one bulb lights.
but we don't know which ones yet.

Now, quantum mechanics, which has always been confirmed, says it is possible to ensure a 85% chance. You can think it however you want, you'll never find an "explanation" of this by saying observation discovers a local hidden reality that was just unknown. (Why not? I thought of something right away, but I may not be understanding this experiment.)

Now we can come back to the Heisenberg inequalities.
Take one cross. One axis represents "measurement of position"; the other represents "measurement of momentum".
You cannot measure both. Indeed, in the previous example, an experimenter could not select both axis of the same cross to see 2 bulbs light on, one on each axis, and still have for each the same chances of result as was described no matter what the other experimenter would choose (that he may have not chosen yet).

.

 

[BigApplePi]

There are certain things one should not touch:

1. A hot stove - it changes the touching agent
2. Fine china with clumsy hands - not if you wish to preserve the china
3. Private parts - you are being naughty
4. I forgot this one.

Add to these four, the electron.
5. If one wants to know what its wave nature is, stay the hell away from it first -- and don't look at it.

 

[BigApplePi]

You have a lifetime left.
That is the funniest line on this thread. YOU may have a lifetime, but I'm running out.

As we keep telling you, maybe the failure lies in your commitment to classical thinking.
Let's see.

The fact is that Quantum Mechanics is the most well tested physical theory ever. Now it is true that it doesn't describe everything (it does not claim to). But more complete theories still describe the small scale interactions in the same way as QM. Which is to say, there are no local hidden variables, reality is probabilistic. (see Bell's Theorem)
I'm going to call "probabilistic" classical thinking.


Here are the links that follow up Spoirier's post:

http://en.wikipedia.org/wiki/Copenhagen_interpretation
http://en.wikipedia.org/wiki/Epr_paradox
http://en.wikipedia.org/wiki/Bell's_theorem

Note that there are other interpretations, involving things like "many-worlds" and "superdeterminism". But the funny thing is, these in reality are exactly the same as the Copenhagen interpretation. They are equivalent (and please don't do anything silly like bringing non scientific principles like Occam's Razor into this).
I'll have to get to those links sometime. Re:Occam's Razor. Metaphor is not the same as analysis.



It is indeed nothing new - 19th century mathematics.

I recommend learning/brushing up on partial differential equations and vector calculus, as well as some of the linear algebra if you want to follow this stuff.

The rest of the formalism - bra-ket notation, some of the linear algebra used is usually explained in Quantum Mechanics textbooks. The one we used was Introduction To Quantum Mechanics by Griffiths. (which can be "found" on the web by the way)


PS, try not to quote whole slabs when replying. Also, the blue text clashes horribly against the standard dark background on this forum. You can just type in

tags, it doesn't take long.[/QUOTE]

I have a beautiful easy-to-read white background with light-blue "slabs" and black type or dark blue type. Go to the Home Page, scroll to the bottom. There are many styles to select from. I chose "default" but am not sure my default will be your default. Let me know if that fixes the readability for you so I don't have to change my style.

 

[Architectonic]

I'm going to call "probabilistic" classical thinking.

Good point. Maybe I should give up the dualistic language.

The "Default style" is the ugly VBulletin default style, which is not the same as "Use forum default" which defaults to "Dark_Castle_Fixed" which happens to also be my favourite style anyway.

5. If one wants to know what its wave nature is, stay the hell away from it first -- and don't look at it.

I don't understand your cynicism.

*** you left this out deliberately??? ***

No, that is where he put your quote - look at his post again. The forum software automatically removes the double quotes. (for better or worse..)

 

[spoirier]

Uh, of course I meant bulbs are located at the ends.
By neighbors, I meant: neighbors in the list of 8 ends with their circular order.
They were neighbors only at first, but then they are one on Earth and the other on Mars. So we had to mark them with figures 1-8 to notice if they were neighbors... like this (uh, I had to add dots as many spaces are not preserved):

On Earth:
...|
-----O
...|

On Mars:
\ ./
.\/
./\
/. O

Of course you can do the measures with 1 experimenter but then I think you have no more paradox...

Yes of course it has not been done yet in this way but the theory says it's possible, and Aspect's experiments tested essentially the same problem though of course by other means. So I wrote the description in a way that is easily understandable. What was actually done did not look like this but the depth of the question is the same.

(Why not? I thought of something right away, but I may not be understanding this experiment.)

Well just try to write it down and you'll problably see it does not work, otherwise post it and we'll see.
I could write down the reason why you can't, but it's simple enough that it will be a good exercise for you to understand it by yourself.

 

[BigApplePi]

When setting up an experiment or looking into cause and effect, the precision in the set up should be in proportion to the precision of the looked for effect. Here are some examples.

1. If I want to please my loved one by buying her flowers, I don't have to take great care in the purchase as any ol' bunch of flowers will please her.

2. If I wish to teach my child to swim, there are many ways to go about it, but I do have to take care that the process doesn't risk drowning. Otherwise anything goes.

3. If I wish to set up an ESP (Extra Sensory Perception) experiment, the very existence of ESP would be a great find, so I have to take ultra extreme great care in setting up the experiment lest any flaws contribute to a false conclusion.

4. Same with this "star" experiment. Suppose when the star experiment is set up, there is a slight bias that northern end lights will light up. Then that bias will remain when you break up the star. Maybe that is enough to explain the 85% versus the 75%.

Imagine a pair of 2 crosses, first attached together, oriented like x and +, so that they form a star with 8 vertices. On each of these 8 vertices is a bulb.
One experimenter keeps the + on Earth; another one takes the x with him to Mars.
Each experimenter is free to wait any amount of time, then, at any time, decide to select one of both axis of his cross (disregarding whether both experimenters do their selection of axis in either order or simultaneously; no communication is possible between them, especially if they are simultaneous, as no information can go faster than light)
As soon as each experimenter selects one axis, one and only one of both bulbs at the ends of this axis lights on.

Then, provided that the crosses had been properly prepared together before separation, the theory predicts that, no matter whether the experimenters have any strategy or not regarding the time and choice of the axis they will select, there are 85% chances that the two vertices that light on (one on the Earth, the other on Mars) had been neighbours before separation.

Now, if you want an "explanation", assuming that observations are mere discoveries of a previously unknown but existing reality, then you cannot do better than a 75% probability of having neighbour vertices light on. This (maximum allowed by Bell's inequality) is obtained by preparing the crosses so that the vertices that would light on if their axis is selected, were 4 consecutive ones - but we don't know which ones yet.

Now, quantum mechanics, which has always been confirmed, says it is possible to ensure a 85% chance. You can think it however you want, you'll never find an "explanation" of this by saying observation discovers a local hidden reality that was just unknown.

I'm not sure to have used the standard English phrasing, as my native language is French.

When I made the comment about vertices we were talking about the use of the English language. Vertex in English relates to two intersecting lines, not the end of a line. Sorry there was a misunderstanding in language.

When I reviewed the experiment I think I commented a lot on the steps. Every step is important and any one step could go wrong. I don't call this a simple experiment. Sometimes I misunderstand though.

 

[spoirier]

Suppose when the star experiment is set up, there is a slight bias that northern end lights will light up. Then that bias will remain when you break up the star. Maybe that is enough to explain the 85% versus the 75%.

No it's not enough and will never be. Remember, the claim is that this 85% chance will remain no matter what axis every experimenter chooses.
You did not define any example how you can explain this 85% whatever the choices. You only cast a suspicion with an incomplete idea. To make sense of your "example" you need to specify everything.

OK about vertex vs ends. I had done a phd of maths written in English about abstract graphs with vertices and edges. I just did not hear that when the number of edges connecting a vertex is reduced to 1, it is not a vertex anymore... in French the word would have remained the same.

 

[Architectonic]

Strictly speaking the vertex refers to the crossing point (or collision point). But what you were trying to say was pretty obvious, so I personally didn't notice a problem when I read your example.

But surely there is a neat way of explaining the Cauchy–Schwarz inequality in English?

 

[BigApplePi]

Strictly speaking the vertex refers to the crossing point (or collision point). But what you were trying to say was pretty obvious, so I personally didn't notice a problem when I read your example.

But surely there is a neat way of explaining the Cauchy–Schwarz inequality in English?

Architectonic. Are you okay yet with coloration?

I see you like to use words like, "obvious." One man's obvious is another's months of work...

Whose example? spoirier or BAP?
spoirier's experiment (That example has yet to be explained. My questions about it have yet to be answered.)

BAP's questions, half way down starting with the word, "Addition."

Or maybe AI. You presented no link? Don't forget Architectonic I am an INTP. My mind is all over the place. Unless people put things in linear order to prop up my memory I have a bad time recalling.

One of the reasons why mathematicians require rigorous mathematical proofs nowadays is people in earlier centuries got away with error in their logic or tried to explain things vaguely without desirable precision. I apply such a frame-of-mind to you nuclear physics guys even though nuclear physics is not mathematics.

Here is the Cauchy–Schwarz inequality in English

If you have trouble with any of the terms, think of them as hyperlinks. They will lead to more English. Thank God you didn't ask for a whale in English. I would have to spend months typing out Moby Dick. I'm too lazy for that.

 

[spoirier]

Yes of course:
No preparation (completely random and uncorrelated result) = 50% chance to have neighbor results.
"Which end lights up? Random or biased?"
Well, that's the whole question. If just random it would be 50% chance to have neighbors, so it is something else... The problem is, how can it be biased so as to produce a 85% chance no matter the choices of axis ? this is the magic of quantum physics.
(more precisely, the result that QM predicts is that if you consider one cross and forget the other, the chances will still be 50% for each end whatever the axis; if you consider the whole system for a given pair of choices of axis you have 85/2 = 42.5 % for each of both pairs of neighbor ends and 15/2 = 7.5% for each of both other results, but this does not resolve nor deepen the mystery by any means)

"let's color the north side of the star black & the south side, red."
well of course all sides must be identified to find out whether the 2 ends that light on were neighbors or not...
The 85% comes from (1 + (0.5^0.5)) / 2 = 0.85355... (not sure how to use latex here, what I tried did not display in preview)

"What is this "preparation"?"

In theory this could be formed by a pair of electrons (as in a helium atom) that were separated, one electron in each cross: then the axis is the one along which the spin of the electron is measured. Except that you have to reverse the result in one cross, because electrons from a pair have opposite spin rather than equal ones.
But I cannot really see how this can be made in practice because how is it possible to preserve the spin of an electron for a long time ? if the electron is free then its spin is lost by interaction with thermic radiation. It would have to be put in an environment at 0 Kelvin. Or I don't know if there are other means.
In practice experiences were made with photons because they preserve their polarization well...

 

[BigApplePi]

I owe you guys an apology for giving up here. I gave up because I went down paths I was led and got lost. I failed to realize I had questions that I needed answered that either you guys presupposed were true or I failed to understand their truths. I guess I hoped something would come to me and when it didn't I gave up. Here is what I have now --

1. The Heisenberg Uncertainty Principle. I haven't accepted it. What are its foundations?
2. Spoirier's puzzle -- why must one accept such events occur? Where is the experimental evidence?

 

[Melllvar]

So apparently gravitational mass and inertial mass are non-equivalent. Discuss.

http://www.technologyreview.com/blog/arxiv/25331/
http://arxiv.org/abs/1006.1988

 

[BigApplePi]

What kind of masses are we talking here? Can we skip the jargon and ask, are they talking:

1. substance within the object itself?
2. how the substance at "rest" distorts space?
3. when it's moving?
4. waves are different?

Which of those are the same?

 

[Melllvar]

Sorry to post and not respond, I don't follow this forum everyday like I did when I first found it. Anyway...

They're basically saying that the effective mass as acted upon by gravitation is different from the effective mass as determined by it's tendency to accelerate in a potential gradient (I think... I've never studied GR beyond wikipedia level stuff)... which is basically the equivalence principle (gravitational mass and inertial mass are the same). This is saying they aren't. Apparently this has been proposed before, but I'd never heard of it, so it's pretty fascinating to me.

The question would naturally arise "how can an object have two masses?" I'm going to speculate that it doesn't (which seems reasonable), but our layman's idea of mass as an intrinsic property must be a little off. Classically mass is (on a mathematical level) just a proportionality constant in the various equations [F = G*M*m2/R^2 and F=M*(d^2/dt^2)r], so I'm interpreting this (classically) as simply saying that the proportionality constants M are in fact different in those equations, which allows me to mentally get around the idea of mass as being a tangible thing the object can only have one of. This doesn't really give any useful insight but it at least avoids wondering things like "what's the total mass if the thing has two different masses" and such.

I have to say though that I don't really know what I'm talking about, and in fact flunked out of physics (twice), and I don't like that I'm trying to put a theory based in quantum mechanics and general relativity into classical terms. It's just that I can't help but think in those terms at this point, so if any of that seems horribly wrong to anyone I'd love to hear why.

Also, I'm wondering what the technological implications of this could be. They say the difference could be made arbitrarily large, and if it can happen on a macroscopic scale I'm imagining things like inertially massive objects that would experience, in my own words, less gravity than they should (like a large solar collector in orbit that didn't need massive thrusters to overcome the free fall), or on the other hand a spaceship that has both low resistance to non-gravitational accelerations but can still utilize gravity assists from planets unusually well. I probably just watch too much sci-fi, but since some macroscopic systems exhibit quantum mechanical properties it doesn't seem totally impossible to me.

I probably should have posted all this on physics forums instead, but I remembered this forum and thread and thought people here might get a kick out of this.

Oh and to try and answer your listed questions:

1. substance within the object itself? - like I said above I don't think there is a single such thing we can call the "mass." you could rather think of it as the different proportionality constants involved in different equations describing an object's motion
2. how the substance at "rest" distorts space? - this would be the gravitational mass
3. when it's moving? - this would be the inertial mass, barring gravitational/warped space-time accelerations
4. waves are different? - no answer cause i don't really have any idea how to relate this to wave-particle duality. they seemed to be treating the "objects" as waves in what I read and linked to though, IIRC.

Of course, I may be wrong or completely confused about any or all of this.

 

[BigApplePi]

Sorry to post and not respond, I don't follow this forum everyday like I did when I first found it. Anyway...

They're basically saying that the effective mass as acted upon by gravitation is different from the effective mass as determined by it's tendency to accelerate in a potential gradient (I think... I've never studied GR beyond wikipedia level stuff)... which is basically the equivalence principle (gravitational mass and inertial mass are the same). This is saying they aren't. Apparently this has been proposed before, but I'd never heard of it, so it's pretty fascinating to me.

The question would naturally arise "how can an object have two masses?" I'm going to speculate that it doesn't (which seems reasonable), but our layman's idea of mass as an intrinsic property must be a little off. Classically mass is (on a mathematical level) just a proportionality constant in the various equations [F = G*M*m2/R^2 and F=M*(d^2/dt^2)r], so I'm interpreting this (classically) as simply saying that the proportionality constants M are in fact different in those equations, which allows me to mentally get around the idea of mass as being a tangible thing the object can only have one of. This doesn't really give any useful insight but it at least avoids wondering things like "what's the total mass if the thing has two different masses" and such.

I have to say though that I don't really know what I'm talking about, and in fact flunked out of physics (twice), and I don't like that I'm trying to put a theory based in quantum mechanics and general relativity into classical terms. It's just that I can't help but think in those terms at this point, so if any of that seems horribly wrong to anyone I'd love to hear why.

Also, I'm wondering what the technological implications of this could be. They say the difference could be made arbitrarily large, and if it can happen on a macroscopic scale I'm imagining things like inertially massive objects that would experience, in my own words, less gravity than they should (like a large solar collector in orbit that didn't need massive thrusters to overcome the free fall), or on the other hand a spaceship that has both low resistance to non-gravitational accelerations but can still utilize gravity assists from planets unusually well. I probably just watch too much sci-fi, but since some macroscopic systems exhibit quantum mechanical properties it doesn't seem totally impossible to me.

I probably should have posted all this on physics forums instead, but I remembered this forum and thread and thought people here might get a kick out of this.

Oh and to try and answer your listed questions:

1. substance within the object itself? - like I said above I don't think there is a single such thing we can call the "mass." you could rather think of it as the different proportionality constants involved in different equations describing an object's motion
2. how the substance at "rest" distorts space? - this would be the gravitational mass
3. when it's moving? - this would be the inertial mass, barring gravitational/warped space-time accelerations
4. waves are different? - no answer cause i don't really have any idea how to relate this to wave-particle duality. they seemed to be treating the "objects" as waves in what I read and linked to though, IIRC.

Of course, I may be wrong or completely confused about any or all of this.

Melllvar don't worry about timely responses. It was I who deserted the ship when there was a chance to ask more questions. Both Agent Intellect and Architectonic seems to be well read and Spoirier is actually a French professor of nuclear physics.

That leaves amateurs who only tool is they can think, lol.
My guess is that "mass" consists has characteristics that can be subdivided where some parts are gravitationally involved and others are motion involved. Waves could be part of that. The task would be to separate and identify.

As to equations? I think they are symbols for measurement and behavior. They are not the masses themselves. Equations are like rulers. We can measure but we don't know what we are measuring.

Spoirier are you there?

 

[spoirier]

Coming back now as I see more questions:

"1. The Heisenberg Uncertainty Principle. I haven't accepted it. What are its foundations?"

What sort of answer to this question can you reasonably expect for your satisfaction ?
The problem is that this "principle" is an expression in the language of classical physics, of some consequences of a theory that cannot be expressed in terms of the basic concepts of classical physics. For this reason, it is and will always remain "unacceptable" to those who focus on it while keeping it expressed as such, that is, without entering the full expression of quantum physics.

But, instead of an "explanation" in classical terms, I think that the deep reason to accept it is to just observe that, well, the predictions of quantum physics have already been verified by experience zillions of times in many ways, and therefore this theory must be accepted as a rather accurate description of reality, no matter whether we like it or not. And therefore its basic consequences should be accepted too.

- "my" puzzle, well, indeed it has not been experienced exactly this way, but I wrote it as a simplified presentation of what :
1) precisely comes as something doable in theory according to quantum theory.
2) is in principe equivalent (same paradox or nearly) as experiments really made by Alain Aspect and others.

In reply to the last message: I'm indeed French but sorry I'm not a professor of nuclear physics. I'm rather an independent thinker, former victim of the teaching institutions as I could better learn and search on my own than under their guidance, with officially "only" a PhD of mathematics (on a subject with a connection to quantum field theory but...) after some courses attended in quantum physics, and 1 year experience teaching mathematics at university a few years ago.

 

[BigApplePi]

Hello spoirier. Glad to see you dropped by. I will also check in every once in a while. I probably won't be able to be as careful as I'd like to be in my questioning and some issues may have already been covered as I have a lot on my agenda during the summer.

I'm facing a problem in that I don't know how to phrase the proper question that says where I am coming from and where I want to go. Phrasing a question in the right way sometimes gives a clue as to what the answer should be. Sometimes a link you or someone else provides seems to answer if only I would study it enough, but then I'm not sure. I wind up looking too broadly at things. The results are interesting but scattered. I think I would like to try focusing and see exactly why what I'm focusing on can or can't be answered.

 

[BigApplePi]

Coming back now as I see more questions:

"1. The Heisenberg Uncertainty Principle. I haven't accepted it. What are its foundations?"

What sort of answer to this question can you reasonably expect for your satisfaction ?
The problem is that this "principle" is an expression in the language of classical physics, of some consequences of a theory that cannot be expressed in terms of the basic concepts of classical physics. For this reason, it is and will always remain "unacceptable" to those who focus on it while keeping it expressed as such, that is, without entering the full expression of quantum physics.

I will address just The Heisenberg Uncertainty Principle. If I can do that perhaps I can clarify what is bothering me. Here is Agent Intellect posting about the Principle here. Suppose I accept what is being said about an electron or photon, then we have a formula referring to Planck's Constant.

Does Planck's Constant come from experiment? They seem to have it down rather accurately. I take it it has to do with quanta which has to do with energy and time -- whatever those are. Anyway that seems to be the foundation for the Uncertainty Principle. This brings me to this question:

Why can't some other experience break this "energy-time"? We don't have to accept what we observe at such a "high" level! Why couldn't some other tool (theoretically) analyze why the quantum jump occurs in the first place? Does String Theory break into Planck's Constant or the treatment of it or are we still stuck with it?