Gravitational Waves on Heisenberg's Uncertainty Principle

[..]

Just a quick thought -

The only reason the Uncertainty Principle is effective is because we need to bounce a photon off the quantum particle to measure its position. But since measuring gravitational waves does not result in the interaction with the source of the wave, and since the singularity of a black hole is at the very center of said black hole, if you can measure the gravitational waves of a black hole, you can essentially determine the exact position of the singularity without directly interacting with it. This would mean that if the black hole were moving relative to another observer, you can also determine the momentum of the singularity as well, violating the Uncertainty Principle.

I assume I have probably made an assumption in my logic, such as, the fluctuations of the singularity being measurable in gravitational waves, but as I said, just a thought.

Any ideas/thoughts?

 

[Marbles]

Are you sure the uncertainty principle arises due to interference during measurement? I have heard conflicting statements about that, and I do not know enough physics myself to determine what is true. There is also a distinction between the uncertainty principle and the observer effect. Are you thinking of the latter?

Regardless, it's a fascinating idea to determine the location of a singularity through detection of gravitational waves. It begs the question whether a singularity has a fixed position at all, or if it excibits the "fuzziness" of elementary particles. I suspect the latter is the case. Are you saying you asume the gravitational waves would pick up on fuzziness, in your last paragraph?

Imagine the immensity of a solar system condensed to a singularity and popping in and out of existence, existing nowhere and everywhere at once. This is far beyond my understanding of physics. If our gravitational measurements were presise enough for the uncertainty principle to be relevant, would the singularity's wavefunction collapse?

I don't really have anything to contribute, this is far above my head, but it's a really interesting idea. I might ask a friend who studies physics if he has any thoughts.

 

[Ex-User (14663)]

as far as I know, uncertainty principle has nothing to do with interaction or the observer effect. It's an inherent property of quantum particles irrespective of the method of measurement.

I have a vague understanding of it in terms of fourier transforms; particles can be described by wave functions where the frequency is the momentum of the particle and the amplitude is the probability density of its position. So if you have only one momentum (i.e. you know the momenum exactly) you have a single sine wave so the position can be anywhere. In order to localize the amplitude at a single point (i.e. having its peak amplitude at a single point) you have to add up infinitely many momenta i.e. losing knowledge of the particle's momentum.

 

[Marbles]

Neat, succinct explanation. I think I understand the model, but I have no idea how you turn observations into that wave function. Speed is frequency, alright, but how does position translate to amplitude? Do we imagine the particle travels in a 1D trajectory, and the amplitude above a 1D "coordinate" is the probability of the particle being located there?

Someone asked what free degree we would like... Definitely one in quantum physics.

 

[..]

as far as I know, uncertainty principle has nothing to do with interaction or the observer effect. It's an inherent property of quantum particles irrespective of the method of measurement.

Oh ok, thank you. I didn't know that the Uncertainty principle was independent of the observer effect.

 

[Ex-User (14663)]

Neat, succinct explanation. I think I understand the model, but I have no idea how you turn observations into that wave function. Speed is frequency, alright, but how does position translate to amplitude? Do we imagine the particle travels in a 1D trajectory, and the amplitude above a 1D "coordinate" is the probability of the particle being located there?

That's my understanding, yes. The particle does not have any particular position but rather a probability distribution of positions, and the probability of any particular position is the squared absolute value of the wave function (according to Borne Rule).

Here is how the position distribution looks if you only have one momentum (it's completely flat and all positions are equally likely):

plot (|e^(ix)|)^2 from -20 to 20 - Wolfram|Alpha

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.

www.wolframalpha.com

Here I have added 4 waves with momenta 1, 1.2, 1.4, 1.6, which makes the position probability more localized at 0:

plot (|e^(ix) + e^(1.2ix) + e^(1.4ix) + e^(1.6ix)|)^2 from -20 to 20 - Wolfram|Alpha

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.

www.wolframalpha.com

I'm sure someone with real knowledge of quantum physics would laugh at my feeble attempt at interpreting the theory, but hey, it's fun to be an amateur quantum physicist

 

[Marbles]

Very cool, thanks! My math is really rusty. Isn't the absolute value of the function zero when the sine wave crosses the x axis? Why isn't the probability of that position zero, then?

 

[Ex-User (14663)]

@Marbles you would be correct if the wave function were only in the real plane, but the wave function is a complex number so it actually consists of 2 waves; the real part and imaginary part. This can be seen e.g. from Euler's formula

The absolute value of a complex number is the euclidean norm of the number in the complex plane, i.e. in this case the square root of cos(x)^2 + sin(x)^2 which is always equal to 1.

 

[Marbles]

Awesome. It is really cool how accessible you manage to make this. Thanks

 

[Inexorable Username]

@Marbles you would be correct if the wave function were only in the real plane, but the wave function is a complex number so it actually consists of 2 waves; the real part and imaginary part. This can be seen e.g. from Euler's formula

The absolute value of a complex number is the euclidean norm of the number in the complex plane, i.e. in this case the square root of cos(x)^2 + sin(x)^2 which is always equal to 1.

Woah, this is cool! I mean, I should have probably have known that from taking calculus...but. I didn’t! (so sad)

Are you a big math kind of person? Can I ask a question?
Do you think there is anything inherently remarkable about the Fibonacci sequence? Or is it it just a mathematical observation of the world that we made, and proceeded to get throughly overexcited about?

I’m interested in how math expresses the reality we live in. I wish I knew more of it - ie: life math. I’m horrendous at learning concepts in isolation, but generally much better at it when I can explain why/how they work, or I’m able to relate the concept to something I already understand. This is why I suck at remembering dates in history...

This is an inspiring conversation. I feel really intrigued. Makes me wonder if there’s a math professor out there that I could hire to explain calculus concepts to me in the context of real world knowledge...

 

[Ex-User (14663)]

Are you a big math kind of person? Can I ask a question?
Do you think there is anything inherently remarkable about the Fibonacci sequence? Or is it it just a mathematical observation of the world that we made, and proceeded to get throughly overexcited about?

I think it has some occurrences in nature, but that's not really surprising considering that it's a trivially simple series (just always adding up the previous 2 numbers). Personally I'm a big fan of Fourier series, it's one of the most beautiful concepts in math. The fact that one can represent any function by adding up sine waves of different frequencies is pretty magical.

 

[Inexorable Username]

Are you a big math kind of person? Can I ask a question?
Do you think there is anything inherently remarkable about the Fibonacci sequence? Or is it it just a mathematical observation of the world that we made, and proceeded to get throughly overexcited about?

I think it has some occurrences in nature, but that's not really surprising considering that it's a trivially simple series (just always adding up the previous 2 numbers). Personally I'm a big fan of Fourier series, it's one of the most beautiful concepts in math. The fact that one can represent any function by adding up sine waves of different frequencies is pretty magical.

WHAT?! I've NEVER heard of this!!!! That is SO cool! Thanks for sharing. That will be tonights brain food! I can't wait!

 

[Ex-User (14663)]

Are you a big math kind of person? Can I ask a question?
Do you think there is anything inherently remarkable about the Fibonacci sequence? Or is it it just a mathematical observation of the world that we made, and proceeded to get throughly overexcited about?

I think it has some occurrences in nature, but that's not really surprising considering that it's a trivially simple series (just always adding up the previous 2 numbers). Personally I'm a big fan of Fourier series, it's one of the most beautiful concepts in math. The fact that one can represent any function by adding up sine waves of different frequencies is pretty magical.

WHAT?! I've NEVER heard of this!!!! That is SO cool! Thanks for sharing. That will be tonights brain food! I can't wait!

here ya go

 

[Grayman]

as far as I know, uncertainty principle has nothing to do with interaction or the observer effect. It's an inherent property of quantum particles irrespective of the method of measurement.

Oh ok, thank you. I didn't know that the Uncertainty principle was independent of the observer effect.

Yes, but if you could find a way to measure position and momentum, you would prove the uncertainty principle wrong. This would be a huge push towards bohmian mechanics and away from the Copenhagen interpretation.

 

[Rebis]

Yes, but if you could find a way to measure position and momentum, you would prove the uncertainty principle wrong. This would be a huge push towards bohmian mechanics and away from the Copenhagen interpretation.

Of course, but quantum particles do not have a concrete trajectory only a confidence interval of where the particle could predictably be. If you only have the initial state and not the trajectory, you can't calculate the subsequent momentum and the position of the particle.

 

[Inexorable Username]

Are you a big math kind of person? Can I ask a question?
Do you think there is anything inherently remarkable about the Fibonacci sequence? Or is it it just a mathematical observation of the world that we made, and proceeded to get throughly overexcited about?

I think it has some occurrences in nature, but that's not really surprising considering that it's a trivially simple series (just always adding up the previous 2 numbers). Personally I'm a big fan of Fourier series, it's one of the most beautiful concepts in math. The fact that one can represent any function by adding up sine waves of different frequencies is pretty magical.

WHAT?! I've NEVER heard of this!!!! That is SO cool! Thanks for sharing. That will be tonights brain food! I can't wait!

here ya go

This concept is so frustrating @_@ ...oh my gosh. What have you done to me. My brain is cluttered with circles...like someone dumped a bag of popcorn in through the top of my head, and each little popcorn piece is attached to a slightly larger popcorn piece and they’re all spinning and...well things are a mess up there.

This is what I’ve always hated about math. The numbers are cool. The functions, I get. I can understand the whole stacking the sin waves concept...

But I can’t understand why this works. What is driving me NUTS about it is that visually, I feel like the answer is right there. I can see that it absolutely should work that way, and it makes perfect sense that it does, and it seems obvious to me that just by looking at it and thinking about it some...I should be able to summarize why it does...

But. I can’t @_@
Now I will dream about this. And neurotically, sporadically watch YouTube videos and read articles about it...which is even more frustrating, because nobody in math ever likes to talk about it the real world. They just want to swoon over their little number language on sheets of paper.

I think I need to start with better understanding sin waves. I only ever learned them through the context of equations. Never from a context of real life where I could have a visual fantasy in my brain that shows me a model from which I can understand why the various little laws of sin waves make practical sense.
This awesome video gives me a semi-realistic model...but in such an abstract, high-level fashion, that I feel like I missed a class in visual model analysis.

My mind is shaken. This is probably the last time, for at least two months, that I meet someone who is all about math and ask them to indulge me with their knowledge of mathematical phenomenons. What have you done Serac. ._.

Look. You see this: &&(!:8-264829&:@!(!/?!?WTF???11:;(!!!!!!

That is my brain on the Fourier sequence.

 

[Rebis]

Beautiful, beautiful maths and I can only observe from the sidelines for now. I'll definitely be burying myself in math textbooks after my exams.

 

[Grayman]

Yes, but if you could find a way to measure position and momentum, you would prove the uncertainty principle wrong. This would be a huge push towards bohmian mechanics and away from the Copenhagen interpretation.

Of course, but quantum particles do not have a concrete trajectory only a confidence interval of where the particle could predictably be. If you only have the initial state and not the trajectory, you can't calculate the subsequent momentum and the position of the particle.

But that's an assumption and a very big one. If Bohmian Mechanics is a correct interpretation then the variables that dictate its trajectory are simply hidden. In bohmian mechanics the particles wave interferes with itself causing it to have what looks like a random unpredictable direction but this direction is actually expressible in math and can theoretically be predicted if we could find the hidden variables.
It's kind of like you can predict the direction of a ball going in a straight line. If that ball suddenly deviates from its path, it is technically not random, we simply haven't accounted for another force that contributed to its deviation like wind ora magnetic field or something.

 

[Rebis]

It would certainly be interesting if we were to discover other hidden variables in the quantum world. I would need to read more about it. By the sounds of it it would make the quantum world a lot more understandable, even illuminating on superposition and entanglement occur and how this can be better manipulated in a quantum computer.

What would be the equivalent function for determining the spin of an electron, in the sense that qubits operate on inherent parallelism through spin and superposition?

 

[Ex-User (14663)]

But I can’t understand why this works. What is driving me NUTS about it is that visually, I feel like the answer is right there. I can see that it absolutely should work that way, and it makes perfect sense that it does, and it seems obvious to me that just by looking at it and thinking about it some...I should be able to summarize why it does...

a lot of math is best understood visually (perhaps all math). Newton for example believed geometry was the only "real" math and that algebra was for plebs who couldn't to math. Also, when people examined the brains of mathematicians they saw that the parts associated with visualization were the biggest in size.

and I myself, when I have trouble understanding a math concept I usually draw it, and then boom – it becomes clear.

Anways, I hope your torment had some enjoyable elements in it lol

 

[Inexorable Username]

But I can’t understand why this works. What is driving me NUTS about it is that visually, I feel like the answer is right there. I can see that it absolutely should work that way, and it makes perfect sense that it does, and it seems obvious to me that just by looking at it and thinking about it some...I should be able to summarize why it does...

a lot of math is best understood visually (perhaps all math). Newton for example believed geometry was the only "real" math and that algebra was for plebs who couldn't to math. Also, when people examined the brains of mathematicians they saw that the parts associated with visualization were the biggest in size.

and I myself, when I have trouble understanding a math concept I usually draw it, and then boom – it becomes clear.

Anways, I hope your torment had some enjoyable elements in it lol

I mean...if you can call madness enjoyable (which it sort of is!)

That’s interesting about visualization. I always shied away from my tendency to “fantasize” because it seemed childish. (By that I mean - to have mental visuals)
I used to do it sheerly for entertainment purposes but I got a lot of flack as a kid for getting that “out of focus” look on my face and being out in la la land. Frustrated adults were annoyed that I wasn’t being attentive and observant.

I only recently started realizing though that this mental realism I can create actually has massive problem solving potential. I’ve found that if I sleep for short bursts, I can actually have dreams that can handle some issues that have been on my mind. Have you ever slept for a short enough period where you wake up confused as to whether or not you had been sleeping? That is how it happens. I take power naps and I remember visualisations (which I suppose are actually dreams at that point) that end up giving me these intuitive leaps of understanding that I wasn’t able to reach consciously with problem solving.
Its only happened twice, but it’s confusing and exciting when it has.

Most of what I see is wasteful though. I see goals, or stories, or unrealistically dramatic challenges I could face and how I would handle them. Emotional things that I try not to indulge. It was only when I started to appreciate that society’s opinions about what I needed to “fix” weren’t helpful for me, that I started seeing the mental imagery as something that could be used for better problem solving.

That’s what frustrates me about the Fourier sequence the most...I think. I’m not as good now with my visualisations as I was when I was a kid. Either I can’t hold them in my head for very long, or there’s weird vague, out of focus bits in them. So I can visualize myself with the Fourier sequence, but only for a blip at a time. I tried to fall asleep thinking about it :/
But I had a weird dream about something totally useless and irrelevant that I don’t even remember. I think a cat was involved.

Now I really sound like a lunatic! Lol! I would never admit to this anywhere but here. It makes me feel a little bit better hearing what you said about mathematicians. It sounds really unhinged, but sometimes I legitimately worry that I might be slightly mad...because I can’t find people to relate to. Finding this forum has really been helpful.

 

[Grayman]

It would certainly be interesting if we were to discover other hidden variables in the quantum world. I would need to read more about it. By the sounds of it it would make the quantum world a lot more understandable, even illuminating on superposition and entanglement occur and how this can be better manipulated in a quantum computer.

What would be the equivalent function for determining the spin of an electron, in the sense that qubits operate on inherent parallelism through spin and superposition?

I think the math for spin is the same. The only difference is the physical interpretation of what spin really is. I am not sure that 'superposition' is the right term for how it operates in Bohmian Mechanics but basically the particles wave is what is being measured when measuring spin.
By measuring the spin, you interfere with the wave. I have not yet learned how exactly it interferes with the wave.
Since this a pilot-wave theory, any change to the wave will alter the path of the particle hence you see the results in the below experiment.

Stern–Gerlach experiment - Wikipedia

en.m.wikipedia.org

 

[PeopleDoSuck]

Just a quick thought -

The only reason the Uncertainty Principle is effective is because we need to bounce a photon off the quantum particle to measure its position. But since measuring gravitational waves does not result in the interaction with the source of the wave, and since the singularity of a black hole is at the very center of said black hole, if you can measure the gravitational waves of a black hole, you can essentially determine the exact position of the singularity without directly interacting with it. This would mean that if the black hole were moving relative to another observer, you can also determine the momentum of the singularity as well, violating the Uncertainty Principle.

I assume I have probably made an assumption in my logic, such as, the fluctuations of the singularity being measurable in gravitational waves, but as I said, just a thought.

Any ideas/thoughts?

Actually, I don't think this is wrong. We are quite negligible compared to a black hole, so it works for studying the black hole. It's just that the gravitational waves of particles are thought to be miniscule and immeasurable compared to the bosons they interact with. But if that wasn't the case, our measurement equipment's gravitational forces would not be negligible and would interfere with the results of measurement. But your thought is definitely sound.

The thing about Heisenberg's Uncertainty Principle is that we know that electrons interact with and change energy levels based on the photons they receive or emit. So theoretically you could create a Gamma Ray Microscope that uses photons to let you see what's going on inside an atom. So Heisenberg thought about this microscope and realized a problem, Gamma Ray Photons, although smaller and more precise, would hit particles with more energy [because E^2 = (mc^2)^2 + (pc)^2 and E=hf and with higher frequency/energy, p must increase], resulting in a drastic change in their momentum p. So the more precise you measure something, the more energy/momentum you introduce into the particle, and the less you can predict the effect of your measurement. And since particles seem to have a wave-particle duality, the same applies for an electron microscope, where the size/accuracy of the electron depends on how much energy it has, which is really interesting because particles do not have a definite 'size'.

But, and this is a big but, in reflection of this understanding, the conclusion that particles exist as a wavefunction that breaks down when we observe them, is simply a poetic assumption based on our inability to accurately measure the quantum world, without also influencing it. We do not know if this is the reality, but it might be OUR reality, if you know what I mean.

 

[dr froyd]

Heisenberg thought about this microscope and realized a problem, Gamma Ray Photons, although smaller and more precise, would hit particles with more energy [because E^2 = (mc^2)^2 + (pc)^2 and E=hf and with higher frequency/energy, p must increase], resulting in a drastic change in their momentum p.

it sounds more like something you made up?

observer interaction has nothing to do with the uncertainty principle. The latter is a result of the wave function - that's a function that describes particle dynamics regardless of whether someone observes them

 

[ZenRaiden]

What if quantum world is actually symptom of things that are literally beyond time and space.
Like we talk about these things in spiritual sense, but what if physically photons or electrons are just expressions of things from another dimension, where the particle wave, is just energy signature of something from the great beyond.

For instance we know of other dimensions mathematically.

So it is clear that some lets call it electron is some dot of potential manifesting it self in space in our dimension.
However part of the real"""" electron energy its real potential is in the other dimension.

Time is a weird dimension, because the more we slow down things there seems to be more time.

So for instance what happens when we slow down time for the electron so much it stops.
Are we freezing the electron? Not really? It just stops moving in respect to everything else.

But lets imagine you are the electron a conscious thing running in zig zag wavy ways, then you move through time and space.

If I am very tiny human particle, and you crash anything into me you are going to kill me, and my dead ass trajectory will be of mark.

So any interaction where quantum has to be observed has to be by inference only.

If then know that particles behave certain way it means that the energy they have has to be enough to influence other particles.
It is thus possible there are entire fields of quantum particles that do not interact with matter in this universe, but can at some point.
I believe here the real question is gravity influences space, which means that gravity is type of field configuration that makes waves interact in more stronger forces that pull energy from the other dimension, hence gravity intensifies.

So I think wave interactions are pretty much set on how the energies configure in relation to the other masses in the great beyond.

 

[dr froyd]

i obviously have no clue as to the reality behind the wave function and its probabilistic nature, but it's an interesting experience to learn about these things coming from a background of mostly probability/stochastic theory, because there everything is a random variable - nothing is realized or observed, everything exists purely as probability distributions, expected values, etc etc. So when physicists say "quantum mechanics is impossible to understand!" i feel the only problem is that people think of reality as composed of realized, actualized, deterministic objects, and if something is described as a stochastic entity there must be something incomplete with the theory, or that there's some deeper reality that creates randomness. Well.. why shouldn't reality be stochastic at its core, why shouldn't objects be random variables? To me, the aversion to that is just the human brain trying to impose its own perceptions on reality. I'm perfectly fine with a cat being both dead and alive.

 

[PeopleDoSuck]

Heisenberg thought about this microscope and realized a problem, Gamma Ray Photons, although smaller and more precise, would hit particles with more energy [because E^2 = (mc^2)^2 + (pc)^2 and E=hf and with higher frequency/energy, p must increase], resulting in a drastic change in their momentum p.

it sounds more like something you made up?

observer interaction has nothing to do with the uncertainty principle. The latter is a result of the wave function - that's a function that describes particle dynamics regardless of whether someone observes them

What did I make up? Explain. It's on wikipedia - Heisenberg Microscope. Why so hostile btw? If you disagree, please explain, otherwise you are obnoxious and make people not want to even express their thoughts. What's your deal?

 

[PeopleDoSuck]

Bro, the wavefunction isn't proven. We can't see what's happening, but at the moment find probability clouds. How exactly is that proof? It's still an assumption.

Are you even INTP? 0.o Some of the things you all say here is so odd for a site that's supposedly geared towards "INTP".

 

[dr froyd]

@PeopleDoSuck geez im sorry i didn't sugarcoat my disagreement into a palatable form for babies like you

but im gonna admit, I hadn't heard about this thought experiment before, it appears he actually did put forward that argument. It sounded a bit silly to me based on the current understanding of quantum mechanics. It does appear that most people agree the argument was wrong, although the conclusion (the uncertainty formula itself) was in a way correct.

modern physicists warn that it only hides an imaginary classical mechanical interaction one step deeper, in the collision between the photon and the electron. In fact Heisenberg's microscope, although it was a big help in developing and teaching the quantum theory, is not itself part of current understanding. The true quantum interaction, and the true uncertainty associated with it, cannot be demonstrated with any kind of picture that looks like everyday colliding objects. To get the actual result you must work through the formal mathematics that calculates probabilities for abstract quantum states.

Heisenberg / Uncertainty

This web exhibit from the American Institute of Physics dives into the life of the founder of quantum mechanics and the uncertainty principle.

history.aip.org

 

[PeopleDoSuck]

Wow, dude, okay. I don't want to talk to people like you. This isn't a fucking court room and I'm not on trial. Just fuck you. Just fuck you. 0_0

 

[dr froyd]

lmao