alternative to quantum mechanics?

[fullerene]

http://www.iop.org/EJ/article/1751-8121/41/35/352003/a8_35_352003.pdf

I don't understand every word of what they're saying in there, but the parts that I do understand are fascinating. The authors were also pretty clear that they did not intend for this theory to be a complete reformulation of quantum mechanics, but it sounded like it was only because they couldn't explain all QM phenomena by it yet, and didn't want to overstate their findings. I'd personally love it if someone picked up where they started and framed what are commonly thought to be QM results with a deterministic theory like this, though. It'd be a nice slap in the face to all the humanities folks who use it to justify their worldviews, at least .

 

[Nicholas A. A. E.]

This is really cool and I'm going to try to read more later.

It would be nice if I could figure out Hamiltonians totally. And I guess to do that it would help if I'd taken a differential equations course. Oh well.

 

[morricone]

http://www.iop.org/EJ/article/1751-8121/41/35/352003/a8_35_352003.pdfI'd personally love it if someone picked up where they started and framed what are commonly thought to be QM results with a deterministic theory like this, though. It'd be a nice slap in the face to all the humanities folks who use it to justify their worldviews, at least .

If the complex variable thoery describes exactly the same phenomena as the QM, what difference would there be? It'd just be another mathematical model, which may be easier to understand. But the world wouldn't change.

 

[Nicholas A. A. E.]

The point is that the model is deterministic instead of probabilistic. As I understand it.

 

[fullerene]

*nods*, that was the idea.

I think that there's also some fundamental mathematical contradictions between General Relativity and Quantum Field Theory. I googled for it an found a Caltech paper at http://www.theory.caltech.edu/people/jhs/strings/str115.html that describes them a bit. It looks like a conclusion to a paper on string theory, but it does detail a bit of the dilemma between QM and GR. Neither one works when applied to the other--they're inconsistent.

As I understand it, adding complex energy would eliminate the need for treating particles like waves, since it describes how some (at the moment) of the wave-like phenomena could be observed given certain values of complex energy. "Normalization" (which I suspect is similar to the renormalization mentioned in that article, though I'm not positive) is a QM thing dealing with treating the wavefunction for a particle as the square root of a probability density for finding the location of that particle. If things were deterministic, and particles were merely particles, I don't think you would ever need to normalize things, and this wouldn't be a problem.


I don't think there would ever really be a nail in the coffin until scientists discovered some way to measure the complex energy, though... which seems unlikely, since complex quantities are never (to my knowledge) observable. The closest I can think of is when the complex part of the gain (in an electrical circuit) determines the phase shift on the output signal... but mostly that's just because the math works. Although I guess you could make the argument that all of physics is like that.

The world wouldn't change, but you're kidding yourself if you think our current models are perfectly complete and unified.

 

[Nicholas A. A. E.]

Mmm, I've never learned the ideas behind complex numbers arising in electromagnetism. I'm taking an introductory class in physics involving EM, but you can bet they're not going to even mention complex numbers. Bastards.

 

[del]

Granted I don't understand 90% of that, but I'm not understanding how this doesn't violate Bell's Theorem. Anyone?

 

[morricone]

The objective of this conjectural paper is to demystify some well-known quantum effects
by showing that their qualitative features can be reproduced very simply by the deterministic
equations of classical mechanics (Newton’s law) when these equations are extended to and solved in the complex plane. Specifically, we take the uncertainty principle mean that there is intrinsic uncertainty in the energy of a particle, and in this paper we consider
the possibility that this uncertainty may have an imaginary as well as a real part. We find that
a deterministic classical particle whose energy has a small imaginary component can exhibit
phenomena that are associated exclusively with quantum mechanics. We do not necessarily
claim that quantum mechanics is a deterministic hidden-complex-variable theory. Indeed,
there are important quantum phenomena, such as interference effects, that we cannot as yet
reproduce by using complex classical mechanics. However, the results that we obtain from
complex classical mechanics bear a striking qualitative and quantitative resemblance to many
well-known quantum phenomena such as tunneling and wave-like effects.

So, still non deterministic.

 

[fullerene]

I saw that, but I think they mean "there's some unmeasured(/unmeasurable, at the moment) complex quantity of energy that accounts for the heisenberg uncertainty principle," for several reasons.

1. The Heisenberg Uncertainty comes from non-commuting operators acting on wavefunctions (http://en.wikipedia.org/wiki/Uncertainty_principle#Wave_mechanics). No wavefunction, no "hard" claim of uncertainty... only the "soft" claim that we can't measure it.

2. Throughout the rest of the paper, they never once brought up the uncertainty principle again, in any of their specific examples. They took a particle, gave it a determined complex energy, and said "look at the trajectory." They never appealed to it again.

and 3. In your own quote, they said "We do not necessarily claim that quantum mechanics is a deterministic hidden-complex-variable theory. Indeed, there are important quantum phenomena, such as interference effects, that we cannot as yet reproduce by using complex classical mechanics." This seems to imply that if they could explain things like interference effects in this way, then quantum mechanics could be considered a deterministic hidden-complex-variable theory. In this paper, however, they wanted to be sure they didn't overstate their claim, because it doesn't completely explain all the evidence that current QM does.


So I'm not really sure what you're talking about. It's the difference between saying "there's inherent uncertainty in the world," and "there's uncertainty because our techniques for measurement aren't sophisticated enough yet." QM says the first, but I think their paper says the second.

I could be misunderstanding them, of course, though. Please explain to me how I'm wrong if I am.


I've never heard of Bell's Theorem, del. I wikipedia'd it, but don't have the time to read it thoroughly right now. Will try to understand it better sometime soon, though, hopefully.

 

[Latro]

Mmm, I've never learned the ideas behind complex numbers arising in electromagnetism. I'm taking an introductory class in physics involving EM, but you can bet they're not going to even mention complex numbers. Bastards.

About all I know about is the relationship between complex numbers and eigenvalues of matrices, and how those can be used to look at differential equations or systems thereof. So yeah

 

[morricone]

So I'm not really sure what you're talking about. It's the difference between saying "there's inherent uncertainty in the world," and "there's uncertainty because our techniques for measurement aren't sophisticated enough yet." QM says the first, but I think their paper says the second.

I could be misunderstanding them, of course, though. Please explain to me how I'm wrong if I am.

Did you ever hear of the double-slit experiment? If you know it, it should IMHO be obvious why there will always be uncertainty. And this experiment is easily done, without (too) sophisticated equipment. Alas I did not read the paper entirely and I didn't quite get into the hidden variable theorie.

The delayed choice quantum eraser experiment is interesting, too.

 

[GarmGarf]

A few days ago I stated on another forums that I don't believe in the uncertainty principle.

Nice find cryptonia!

 

[Nicholas A. A. E.]

1. The Heisenberg Uncertainty comes from non-commuting operators acting on wavefunctions (http://en.wikipedia.org/wiki/Uncertainty_principle#Wave_mechanics). No wavefunction, no "hard" claim of uncertainty... only the "soft" claim that we can't measure it.

....

So I'm not really sure what you're talking about. It's the difference between saying "there's inherent uncertainty in the world," and "there's uncertainty because our techniques for measurement aren't sophisticated enough yet." QM says the first, but I think their paper says the second.

The meaning of the uncertainty principle is a matter of QM interpretation. Some interpretations say there is a "hard"claim of uncertainty (this is the mainstream view nowadays), some say only the "soft" claim (historically more common, incl. Heisenberg I think).

 

[Darby]

what I don't understand is why it's "uncertain" I understand why we can't calculate it, that's not what I'm saying, I just don't see why that means the universe isn't certain, just because we can't calculate it doesn't mean it's not certain

maybe I just totally don't understand any of this, but that's how I feel about the whole thing with the information I have

 

[Latro]

what I don't understand is why it's "uncertain" I understand why we can't calculate it, that's not what I'm saying, I just don't see why that means the universe isn't certain, just because we can't calculate it doesn't mean it's not certain

maybe I just totally don't understand any of this, but that's how I feel about the whole thing with the information I have

You can look over the derivation on wikipedia, but it's pretty confusing. But it isn't about our inability to calculate it, according to the uncertainty principle momentum and position do not exist at full precision in the quantum world, as I understand it. Our instruments probably won't ever get anywhere near the precision that the uncertainty principle restricts us to, though.

 

[fullerene]

Ahh latro... I forgot about you. Can you tell, from the wikipedia derivation, what assumptions their derivation is based on? It's over my head, but you're far better at math. I always thought that the uncertainty principle came straight out of the math, when non-commuting operators act on a wavefunction... which seems to me to force the strong claim. I don't really know, though, and couldn't follow that at all.

Do you have anything readable on the soft claim of it, nick?

Did you ever hear of the double-slit experiment? If you know it, it should IMHO be obvious why there will always be uncertainty.

I do know of the double-slit experiment (it's pretty famous), but do not see why this makes it obvious why there will always be uncertainty. Could you explain?

 

[Nicholas A. A. E.]

The logic for the strong uncertainty principle runs something like this: (stoled from wiki)

The only kind of wave with a definite position is concentrated at one point, and such a wave has an indefinite wavelength. Conversely, the only kind of wave with a definite wavelength is an infinite regular periodic oscillation over all space, which has no definite position. So in quantum mechanics, there are no states that describe a particle with both a definite position and a definite momentum. The more precise the position, the less precise the momentum.

Leaving aside the question of wavefunctions, at least a little.

cryptonia: this is almost all i know about it. I think.
http://en.wikipedia.org/wiki/Uncertainty_principle#Uncertainty_principle_and_observer_effect

 

[Agent Intellect]

I find this all interesting, but I'm not sure what comments to make, as I don't really understand complex energy or anything like that. I have always thought that the uncertainty principle was because of the wave nature of particles itself (as described here).

 

[typondis]

what I don't understand is why it's "uncertain" I understand why we can't calculate it, that's not what I'm saying, I just don't see why that means the universe isn't certain, just because we can't calculate it doesn't mean it's not certain....

Exactly. This suggests the following:

- that the universe does know, at least at the Plank length/time

- that any one's perception of the world is limited such that uncertainty can't be perceived - essentially, the 'human senses are restricted to four dimensions' schtick.


I think, in general, both are true.

 

[Latro]

Ahh latro... I forgot about you. Can you tell, from the wikipedia derivation, what assumptions their derivation is based on? It's over my head, but you're far better at math. I always thought that the uncertainty principle came straight out of the math, when non-commuting operators act on a wavefunction... which seems to me to force the strong claim. I don't really know, though, and couldn't follow that at all.

I haven't worked with Hamiltonians and so forth, so no, sorry.