# How empty is the empty wave?

1. May 6, 2012

### San K

how empty (or filled) is the empty (matter) wave?

The de broglie-bohm interpretation posits that:

in a single particle double slit experiment,

the photon goes through one of the slits/paths and the matter waves go through both the slits.

the path without the photon and just the matter wave has, for convenience, been labelled as empty wave.

Also it is generally imagined that the empty wave has no energy or momentum. why is that so?

however does this not contradict with some of the below observations:

- the empty wave (travelling the other path) effects the behaviour/path of the photon. Is not some form of energy required to effect the path of the photon?

- the empty wave is blocked by opaque obstacles however it passes through transparent obstacles. if it was just a probability wave, why would it get effected by an opaque object but not a transparent object.

the matter wave passes through the same obstacles that a photon would pass through and gets blocked by the same obstacles that a photon would get blocked by. therefore its properties are similar to that of a photon

off track question (and I have asked this before but the response was weak):

Does the matter wave of a photon interact with the matter wave of an electron?

the above, i guess, must be easy to test experimentally.

2. May 7, 2012

### mattwoerd

First, the empty wave has no energy because it isn't mass. It is only the probability that the mass will exist.
Second, the energy that determines the path is generated by the observation. This is a mechanical aspect of quantum physics that is not known. I think it is created from the electromagnetic field generated by the neurons in our body.

3. May 7, 2012

### Demystifier

Because the empty wave is not directly observable. If you wished you could ascribe energy and momentum to the empty wave, but these would be unobservable energy and momentum.

Not necessarily. This would be required in classical mechanics, but Bohmian mechanics is not classical mechanics.

In Bohmian mechanics, the wave is certainly much more than a probability wave. It is a pilot wave.

Definitely, yes. This interaction is described by quantum electrodynamics.

4. May 7, 2012

### bohm2

Arguing against Bohm's "active information" hypothesis, Peter J. Riggs (a supporter of Bohmian mechanics) has suggested that there is energy transfer between field and particle that is really one system:
Reflections on the deBroglie–Bohm Quantum Potential
http://www.tcm.phy.cam.ac.uk/~mdt26/local_papers/riggs_2008.pdf

A criticism of Rigg's approach can be found here:

The Causal Theory revisited
http://itf.fys.kuleuven.be/~ward/documents/review-riggs.pdf

This an interesting but not very clear quote from Bohm's paper on what happens to the "empty" waves after interaction:
An Ontological basis for the quantum theory
http://www.tcm.phy.cam.ac.uk/~mdt26/local_papers/bohm_hiley_kaloyerou_1986.pdf

Last edited: May 7, 2012
5. May 7, 2012

### derek101

I have a question I am struggling to understand how a photon becomes polarized.In this model what changes when a photon is polarized?

6. May 8, 2012

### San K

thanks Demystifier and Bohm2

separate/aside question:
why/how does the need for non-locality arise in the DBB interpretation?

Last edited: May 8, 2012
7. May 8, 2012

### Demystifier

The photon wave function has two components corresponding to two orthogonal polarizations. Both components together determine how the photon will move, so the motion of the photon depends on polarization of the wave function.

8. May 8, 2012

### San K

on a separate note:
why/how does the need for non-locality arise in the DBB interpretation?

Last edited: May 8, 2012
9. May 9, 2012

### Demystifier

The velocity of any particle at a given time depends on the positions of all other particles (entangled with the first particle) at the same time.

10. May 9, 2012

### San K

is DBB assuming that the velocity of the photon/particle is not constant?

classical mechanics would say that speed of light remains constant (in all frames of reference and all mediums)

11. May 9, 2012

### Demystifier

True, but Bohmian mechanics is not classical mechanics.

12. May 9, 2012

### San K

why does Bohmian Mechanics assume that velocity of photon is varying when all the experimental data at any point in time and space throughout the experiment matches exactly with the fact that speed of light is constant.

what (assumption, explanation, bridging of logic) is Bohemian Mechanics trying to prove/achieve by assuming that speed of photon varies?

13. May 10, 2012

### Demystifier

What is constant is the propagation-velocity of the front of the photon WAVE. But inside the wave packet, the velocity of the photon POINT-PARTICLE may be different. Moreover, it must be different in order to explain interference fringes in terms of particle trajectories. In fact, a recent weak MEASUREMENT of photon particle trajectories confirmed that average photon particle velocities are not constant, but equal to those predicted by Bohmian mechanics:
https://www.physicsforums.com/blog.php?b=3077 [Broken]

Last edited by a moderator: May 6, 2017
14. May 10, 2012

### San K

Good point Demystifier...thanks for clarifying.

Is there a statistical distribution (for the velocities) per the equations under Bohmian framework?

Last edited by a moderator: May 6, 2017
15. May 10, 2012

### Demystifier

Of course. See e.g. Eq. (39) in
http://xxx.lanl.gov/abs/quant-ph/0208185 [Found.Phys.Lett. 17 (2004) 363-380]