# Interpretations of QM- help on points!

1. Jan 6, 2008

### muppet

I'm writing an essay on the description of nature QM affords us, and hence I want to discuss the different interpretations of it. (My questions are mainly conceptual rather than anything else, so I thought this would be better here than the homework help forum?)
First of all, a couple of points I'd like to check about the "standard" interpretation(s!)
-Does the fact that we observe interference in experiments mean that interpreting the wave function as describing our knowledge of the system fails, as the wave function clearly has some ontological significance prior to measurement?
-Is it true to say that although we have equations (Klein-Gordon, Dirac) that govern the time evolution of a system in a way that is compatible with special relativity, the fact remains even in QFT that the collapse of a wavefunction is not Lorentz covariant?

Secondly, one on Bohmian Mechanics. I'm reading the undivided universe at the moment, and in it Bohm states that the quantum field he postulates does not lend energy to the particle, but provides active information that merely guides the particle. He then states the equation of motion
$$m\frac{dv}{dt}=-\nabla(V)-\nabla(Q)$$
where Q is the quantum potential due to this field. He then states that this field satisfies Schroedinger's Eqn. So how does his Q term affect dp/dt without affecting the kinetic energy- which in non-relativistic QM is proportional to the square of the momentum? Is it to do with the way one inegrates the grad Q term wrt time? Or is it some funny complex vector with a zero modulus that essentially changes the direction of grad V?

2. Jan 6, 2008

### peter0302

I can answer this I think. We do not know if the collapse of the wave function is deterministic in the sense that we can point to a speicifc time when it occurs and cause. If it is deterministic, then it definitely is not Lorentz invariant, because measurement outcomes can apparently have an instantaneous correlation on measurements light years away.

But as to whether it even makes sense to say "the wave function collapsed THERE and THEN because of THAT", we don't know. If it is not deterministic then there is no problem with SR.

3. Jan 7, 2008

### Demystifier

The quantum potential DOES give energy to the particle. However:
1. The AVERAGE force from the quantum potential is zero.
2. The quantum potential contributes to the total energy in such a manner that the measured energy is equal to that in the standard interpretation of quantum mechanics.

One advice: When you read about the Bohmian interpretation, pay a particular attention to the theory of quantum measurements.

4. Jan 8, 2008

### muppet

Thanks for the responses guys- I was getting worried after 52 views without reply!

Last edited: Jan 8, 2008
5. Jan 8, 2008

### reilly

Bohm, in fact is just a curiosity -- his work has produced no new physics over the last 50 years, while regular QM has given us transistors, hence the Internet, what ever computer you use; lasers to do all manner of things, electron microscopes -- a very pure application of QM -- PET and MRI brain scans, and on and on -- ubiquitous you might say and pretty impressive.

Virtually by definition, measurements are not covariant; observers are not covariant.

Interference or not, the knowledge interpretation is alive and well, and, as I've stated in many threads, is, I think, the best game in town.It's an idea that's worked pretty well for several centuries.QM allows us to compute probabilities. So what's the problem? Standard QM has beaten off all challenges to it's current supremacy -- how long that will continue is anyone's guess.

Just for clarity: most work in QM is based on what
I call Bohr-Born, the BB approach. The absolute square of the wave function is a probability density, and the wave function itself is governed by the Schrodinger
eq, the form of which is often inspired by classical physics. Simple.
Regards,
Reilly Atkinson

Re knowledge-- look up Sir Rudolph Peierls, who championed the knowledge approach.

6. Jan 9, 2008

### Demystifier

But it is not, except in the nonrelativistic approximation. In the relativistic case, the wave function is not governed by the Schrodinger equation and its absolute square is not a probability density. In fact, the standard QM is somewhat ambiguous in that regime. Bohmian mechanics is not ambiguous and leads to new testable predictions:
http://xxx.lanl.gov/abs/quant-ph/0406173 [Found.Phys.Lett. 18 (2005) 549-561]
http://xxx.lanl.gov/abs/0705.3542

7. Jan 9, 2008

### reilly

Sorry, but the Schrodinger EQ. holds for relativistic and onoi-relativistic QM. Now that physicists are heavy into Lie groups and infinitesimal group generators, we say that the Schrodinger EQ. is defined as the infitesimal relation between time evolution, and the generator of that evolution, called the Hamiltonian -- true classically and quantumly. (Note that there is some very interesting work with what might be called non-covariant relativistic QM -- the free Hamiltonin for a single particle is H=SQRT(P^^2 + M^^2).

Further there are thousand of experiments and papers, that are based on the standard interpretation of QM -- my doctoral dissertation is one. I'll even send you a copy, if you promise to tell me what I did wrong by using standard QM -- like Feyman and
Schwinger. Or, how about parsing "The Experimental Foundations of Particle Physics -- R.N Cahn and G Goldhaber -- say Chapter 8, The Structure of the Nucleon.

If you are right, then we'll have to throw out at least 50 years of particle physics. Ouch -- I'll have to give up my degree.

Regards, Reilly Atkinson

PS -- Tell me what new physics has the Bohm approach given us? Perhaps I'm in error when I say, none. What do the experiments you cite tell us? -- not the theory, but the numbers from Nature.

8. Jan 9, 2008

### akhmeteli

My understanding is the predictions of the Bohmian mechanics coincide with those of quantum mechanics. So there can be no experiments to cite as favoring Bohm against Kopenhagen or vice versa. As for new physics, do the Bell's inequalities qualify as "new physics"? As far as I know, Bohm's interpretation was the inspiration for Bell.

9. Jan 10, 2008

### Demystifier

First, you should distinguish between relativistic quantum mechanics and relativistic quantum field theory. See, e.g., two books of Bjorken and Drell. Relativistic QM is not described by a Schrodinger equation. Relativistic QFT is.

Second, if you write down the functional Schrodinger equation for FERMIONIC fields, the corresponding wave functional $$\Psi$$ is Grassmann valued, so the quantity $$\Psi^*\Psi$$ is Grassmann valued as well, so it cannot represent a probability density.

Third, I am sure that you did nothing wrong in your thesis and that you does not need to throw away most of the last 50 years of particle physics. This is because most of the work in particle physics is done in the momentum representation, which is fine. What is missing in relativistic QM and relativistic QFT, is the position representation. This is not a practical problem because one is usually interested in the S-matrix only, for which the momentum representation is fine. Nevertheless, there is a problem as a matter of principle and experiments are conceivable (though not done yet!) for which the predictions of the standard theory are ambiguous. As an example, try to find the probability density of particle positions for a scalar particle in a superposition of two different 4-momenta, i.e., in the state
$$|k_1>+|k_2>$$

Finally, the experiments that could distinguish between relativistic Bohmian mechanics and standard theory are not yet performed. I hope they will in the future.

10. Jan 10, 2008

### Demystifier

It is true in nonrelativistic QM, but not necessarily in relativistic QM.

11. Jan 10, 2008

### MaverickMenzies

It is possible to provide a lorentz covariant description of quantum state description. For example, see chapter 11 of "The theory of open quantum systems" by H. P. Breuer and F. Petruccione (2006).

12. Jan 11, 2008

### akhmeteli

I remember discussing this issue with you (I guess that was in Croatia), so I guess you have in mind something along the lines of arXiv:quant-ph/0512065 . However, the reasoning there does not seem obvious to me. I see the travel-back-in-time parts of trajectories somewhat differently (as an anti-particle moving ahead in time), and am not quite sure Kopenhagen and Bohm give different predictions for that case. Maybe I am wrong. However, do you have other references illustrating your statement?

13. Jan 11, 2008

### Demystifier

We had a discussion in Sweden, Vaxjo. I have already answered these questions there. In particular, I have pointed out that the travel-back-in-time trajectories appear even for neutral particles, so they cannot be interpreted as antiparticles. Even if you say that they are a kind of "antiparticles", they are certainly not antiparticles in the sense of that in quantum field theory.

14. Jan 13, 2008

### akhmeteli

As far as I remember, we also discussed it shortly in Losinj, Croatia.
Whether neutral particles can be called their own anti-particles, is not important, IMO. It is important, though, that creation and annihilation of pairs of neutral particles is possible, as far as I understand. So for time-space trajectories with travel-back-in-time sections, it is possible that at some point in time they describe three particles, not one. Therefore, acting on one of those particles, you cannot change the past for the other two particles, only the future.
Actually, I was not trying to criticize your statement. It just does not seem obvious to me. You know that I respect and cite your research. What I was trying to understand was whether the statement on different experimental predictions of Kopenhagen and Bohm in the relativistic case reflects your personal opinion or it is generally accepted. That is why I asked you for references to other authors. Again, whether your statement is correct or not, is a different matter.

15. Jan 14, 2008

### Demystifier

No, it is not generally accepted. Actually, there is no any "standard" version of relativistic Bohmian mechanics, so no claim on relativistic Bohmian mechanics is generally accepted. In fact, many physicists that study this problem have more than one different theories that they study. I have also studied a few different theories, but now I favor only one of these.

Last edited: Jan 14, 2008