The velocity of Pilot-wave and the Double slit experiment

[sha1000]

Hello,

Its been a while since I'm trying to understand the concept of the pilot wave theory and it's relation with the deBroglie wave. What is the fundamental difference between the two?

My confusion comes from the double slit experiment. The velocity of the deBroglie wave is c^2/v so I assume that it must be the same for pilot wave (maybe it is this assumption which is wrong). In this case, the speed of the pilot wave of the photon is equal to c . But if the speed of the photon and its pilot wave is the same how can we get an interference pattern? As far as my logic goes the interference of the wave must build up in front of the photon (wave going faster than c). Am I wrong?

How one can explain this? Is the speed of the pilot wave greater than c? In this case the pilot wave is not the aame thing as the deBroglie wave since it doesn't obey the c^2/v relation.

I would be very grateful if someone can help me with this question.

Thank you.

 

[Demystifier]

As far as my logic goes the interference of the wave must build up in front of the photon (wave going faster than c). Am I wrong?

Yes, you are wrong about that.

 

[sha1000]

Yes, you are wrong about that.

Thank you for the response.

It's difficult for me to find the answer in the paper that you attached in your response.

So it is right to say that the photon and its pilot wave have the same velocity c (following the c^2/v relation)?

If that is the case, let us suppose that the photon is traveling at the wavefront of its pilot wave (since same speed). The pilot wave goes through two slits simultaneously, giving two "new" waves which originate from each slit. The photon passes through one of the slits and then continues to move at the wavefront.
The destructive (or constructive) interference is always achieved "behind" the photon and never in front of it. So how can the photon feel the pilot-wave interference?

 

[DrChinese]

Thank you for the response.

It's difficult for me to find the answer in the paper that you attached in your response.

So it is right to say that the photon and its pilot wave have the same velocity c (following the c^2/v relation)?

If that is the case, let us suppose that the photon is traveling at the wavefront of its pilot wave (since same speed). The pilot wave goes through two slits simultaneously, giving two "new" waves which originate from each slit. The photon passes through one of the slits and then continues to move at the wavefront.
The destructive (or constructive) interference is always achieved "behind" the photon and never in front of it. So how can the photon feel the pilot-wave interference?

FYI that paper is part of Demystifier's signature, and I don't believe it was intended for this thread specifically.

Also: I assume you are aware that the pilot wave is an element of certain interpretations of quantum mechanics. It is by no means generally accepted. Demystifier is one of our resident experts on Bohmian Mechanics (which includes the pilot wave element). To make any sense whatsoever of how to apply pilot wave to the double slit experiment, you will need to understand BM to some degree.

 

[sha1000]

FYI that paper is part of Demystifier's signature, and I don't believe it was intended for this thread specifically.

Also: I assume you are aware that the pilot wave is an element of certain interpretations of quantum mechanics. It is by no means generally accepted. Demystifier is one of our resident experts on Bohmian Mechanics (which includes the pilot wave element). To make any sense whatsoever of how to apply pilot wave to the double slit experiment, you will need to understand BM to some degree.

Oh I thought that his signature was related to the answer :), my fault.

Yes, ofc I understand that the pilot-wave scenario is only an interpretation. It seems to me that it can't describe the double slit experiment in case of the photons. But I also understand that it probably comes from my poor understanding of physics in general. Thats why I asked the question :).

 

[Demystifier]

It's difficult for me to find the answer in the paper that you attached in your response.

As @DrChinese told you, it's only my signature.

So it is right to say that the photon and its pilot wave have the same velocity c (following the c^2/v relation)?
If that is the case, let us suppose that the photon is traveling at the wavefront of its pilot wave (since same speed). The pilot wave goes through two slits simultaneously, giving two "new" waves which originate from each slit. The photon passes through one of the slits and then continues to move at the wavefront.
The destructive (or constructive) interference is always achieved "behind" the photon and never in front of it. So how can the photon feel the pilot-wave interference?

Ah, now I think I better understand what confuses you. The initial position of the photon is usually not at the wave front. It usually starts somewhere behind. So even if the photon and the wave front have the same speed, the photon typically will not catch the wave front. I believe it answers your question.

For an analogy, you can imagine that the wave is like a train and the particle is like a man walking through the train. The man inside the train can walk, so he can be slightly faster or slightly slower than the train. But he can never walk outside of the train. So if the man arrives at the front of the train (which he almost never does), at that moment he cannot move forward faster than the train.

 

[sha1000]

As @DrChinese told you, it's only my signature.Ah, now I think I better understand what confuses you. The initial position of the photon is usually not at the wave front. It usually starts somewhere behind. So even if the photon and the wave front have the same speed, the photon typically will not catch the wave front. I believe it answers your question.

For an analogy, you can imagine that the wave is like a train and the particle is like a man walking through the train. The man inside the train can walk, so he can be slightly faster or slightly slower than the train. But he can never walk outside of the train. So if the man arrives at the front of the train (which he almost never does), at that moment he cannot move forward faster than the train.

Thank you again for the response.

The assumption that "photon starts somewhere behind the wave" is it something that can be demonstrated? Or we need to assume this in order to explain the observations?

 

[Demystifier]

The assumption that "photon starts somewhere behind the wave" is it something that can be demonstrated? Or we need to assume this in order to explain the observations?

Both. We need to assume it to explain the observations, but under certain conditions it can be explained by certain statistical arguments.

 

[sha1000]

Both. We need to assume it to explain the observations, but under certain conditions it can be explained by certain statistical arguments.

I think I got my answer. I need some time to think about the answers you gave me.

Just an off topic question. I read some papers about the non-zero photon mass and its implications in phyisics. I think that it could be a good alternative assumption which could explain why the photon is not in the wavefront of the pilotwave but is slightly behind (since in this case photons velocity is a little bit smaller than c).