De broglie

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In 1924, when de Broglie proposed the pilot wave, he seems to be saying that the velocity of the individual oscillations of the pilot waves, v', is always greater than the velocity of light c, and its relationship to the velocity of the particle v, is given by

v' = c^2 / v

Is this formula correct? and how could the individual oscillations be faster than c??
 

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  • #4
vanhees71
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The phase velocity of waves is never infinite. How do you come to the conclusion that might be so? Also there is no sensible physical interpretation of relativstic wave functions in terms of a single-particle theory. The first who realized this was Dirac who tried to make the Schrödinger way of description of quanta in terms of wave mechanics, working so well in non-relati istic physics, work for relativistic particles. He tried to get a wave function fulfilling an equation of motion which is of first order in the time derivative, and since Lorentz symmetry ties space and time so closely together he had also to assume that it's first order in the spatial derivatives.

However, when analyzing his famous equation (named after him as Dirac equation) for the case of electrons (indeed the wave function turned out to describe particles of spin 1/2, and the electron was known to have spin 1/2 at this time) that interact with an external electric potential he could not make sense of the equation without assuming that also the solutions with negative frequencies are physical. His idea was to let all these state be occupied in the ground state of the system, so that in the free case no electrons can go into such a state of "negative energy". Rather he interpreted probable holes in this Dirac sea as antiparticles (in the case of electrons dubbed positrons) with positive energy moving in the opposite direction. Then he could make sense also of the solutions for interacting particles, and it came out that in fact he dealt with a many-body problem, i.e., if the interaction is strong enough, an electron scattering at the potential might end up creating an electron-positron pair. Thus the electron number and the positron number are not conserved but only the net-charge number. Taking the electric-charge convention the electrons (particles) are negatively and the positrons (antiparticles) are positively charged.

This is a very complicated view on relativistic quantum theory, but it can be made working even for the more complicated case of interacting electrons, positrons and the electromagnetic field. It's in fact a valid way to describe quantum electrodynamics, but it's a quite cumbersome way and not very elegant to work with. That's the more true for the more complicated interactions (strong and weak interactions) of the standard model. That's why nowadays we start right away with the concept of quantum fields which from the very beginning incorporate the possibility that particle number needs not be a conserved quantum number but that it's possible to create and destroy particles in interactions.

At the same time the quantum-field theoretical method automatically takes care of causality and Poincare invariance, and the faster-than-light values of phasevelocities of massive realativistic wave equations is no more an interpretational problem in the modern formulation.
 
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  • #5
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Look at he wavefunction of electron . When the wavenumber k is zero (the momentum) then we have no spatial component.
The wave has infinite phase velocity.
 
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  • #6
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The positron is an electron is moving backward in time. You can not create particle, just can an electron to turn back in time .
 
  • #7
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When the wavenumber k is zero (the momentum) then we have no spatial component. The wave has infinite phase .
But its not physically realizable. Such are introduced purely for mathematical convenience.

Thanks
Bill
 
  • #8
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Whatever the equation tell this, Or you can tell whole of equation is wrong.
But I do not think soo. The solution of problem: there is no electron made of one planewave only. The electron must has lot of planewaves with different k value.
 
  • #9
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The positron is an electron is moving backward in time.
That's just a formal way of looking at it. It not really going backward in time.

A lot of stuff in QFT is like that - its just visual imagery for the math eg virtual particles.

Thanks
Bill
 
  • #10
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Whatever the equation tell this, Or you can tell whole of equation is wrong.
But I do not think soo. The solution of problem: there is no electron made of one planewave only. The electron must has lot of planewaves with different k value.
The reason things like plane wave solutions are introduced is purely for convenience - they do not physically exist because they are not zero at infinity as any sensible solution must be. Its why we have the rigged Hilbert space formalism:
https://cds.cern.ch/record/281746/files/9505004.pdf

Thanks
Bill
 
  • #11
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How do you know that? Can you show me?
What I see that the way of QED describe of reality. The QED use this picture of electron in equations.
another things
"Right-handed antiparticles have the opposite weak isospin."
https://en.wikipedia.org/wiki/Weak_interaction
The weak interaction affect only the left handed electron and the right handed positron
What do you think, why?
Because both are same thing. With differect time directions.
 
  • #13
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...and this is the only way to descibe the detectors of entangled photons separately.
If you ask me I will show you
 
  • #14
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How do you know that? Can you show me?
Well for one thing its symmetrical ie an electron can be viewed as a positron travelling back in time. But if you want to discuss that its way off topic for this thread - start a new one.

What do you think, why? Because both are same thing. With differect time directions.
Because one of the general features of QFT is the existence of antiparticles:
http://physics.stackexchange.com/questions/18705/the-causality-and-the-anti-particles

Thanks
Bill
 
  • #15
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"they do not physically exist" regarded to Copenhagen interpretation
Its got nothing to do with Copenhagen.

Its got to do with the Born Rule. You can only define a probability distribution if it falls off to zero fast enough.

Thanks
Bill
 
  • #16
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...and this is the only way to descibe the detectors of entangled photons separately.
If you ask me I will show you
Its obviously a model used simply for the purposes of analysis, it not 100% correct. Things like that with physically unrealizable boundary conditions are done all the time. Its so obvious no one even bothers to mention it.

Thanks
Bill
 
  • #17
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Well is not correct?
https://arxiv.org/pdf/quant-ph/0402001.pdf
P=0.5cos2(a-b) (3) The eqution of entanglement (TYPEI)
Well "unfortunately" this is same as equation of ONE photon goes through two polarizers.
"accidentally"
One photon of entangled photonpair is going backward in timedimension. Because it is antiphoton
 
  • #18
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Because it is antiphoton
The photon is its own antiparticle. And since photons travel at c the concept of time doesn't really make sense. That's another reason the concept is just for pictorial vividness.

It comes about because such must be included in Feynman diagrams - but what appears in such diagrams are simply terms in a Dyson series - not actual particles:
https://en.wikipedia.org/wiki/Dyson_series

Thanks
Bill
 
  • #19
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The another problem
" the speed of the quantum non-local connection (what Einstein called "spooky action at a distance") is at least 10,000 times the speed of light"
https://en.wikipedia.org/wiki/Faster-than-light
Okay looks like we have FTL...but
"As noted by Einstein, Tolman, and others, special relativity implies that faster-than-light particles, if they existed, could be used to communicate backwards in time."
https://en.wikipedia.org/wiki/Tachyon#Speed
"Faster-than-light communication is, by Einstein's theory of relativity, equivalent to time travel. "
https://en.wikipedia.org/wiki/Faster-than-light#Superluminal_communication
Soo if we have FTL we have retrocausality also
 
  • #20
ZapperZ
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We do not have FTL. It is a fallacy to use quantum entanglement for that, because nothing travels in that phenomenon! There are already numerous threads in here addressing that. You are very late to the party.

Zz.
 
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  • #21
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The another problem " the speed of the quantum non-local connection (what Einstein called "spooky action at a distance") is at least 10,000 times the speed of light"
Put a red bit of paper in an envelope, green in another. Open one and you automatically know the other with nothing passing between the slips. You have correlated the systems. That's all that is going on in EPR.

The only reason superluminal signalling may be required is - well its probably best if you nut it out for yourself:
http://www.drchinese.com/Bells_Theorem.htm

You are jumping all over the place and not sticking to the threads purpose. If you want to discuss others things start a new thread or this thread will, correctly, be shut down.

Thanks
Bill
 
  • #22
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The phase velocity of waves is never infinite. How do you come to the conclusion that might be so? Also there is no sensible physical interpretation of relativstic wave functions in terms of a single-particle theory. The first who realized this was Dirac who tried to make the Schrödinger way of description of quanta in terms of wave mechanics, working so well in non-relati istic physics, work for relativistic particles. He tried to get a wave function fulfilling an equation of motion which is of first order in the time derivative, and since Lorentz symmetry ties space and time so closely together he had also to assume that it's first order in the spatial derivatives.

However, when analyzing his famous equation (named after him as Dirac equation) for the case of electrons (indeed the wave function turned out to describe particles of spin 1/2, and the electron was known to have spin 1/2 at this time) that interact with an external electric potential he could not make sense of the equation without assuming that also the solutions with negative frequencies are physical. His idea was to let all these state be occupied in the ground state of the system, so that in the free case no electrons can go into such a state of "negative energy". Rather he interpreted probable holes in this Dirac sea as antiparticles (in the case of electrons dubbed positrons) with positive energy moving in the opposite direction. Then he could make sense also of the solutions for interacting particles, and it came out that in fact he dealt with a many-body problem, i.e., if the interaction is strong enough, an electron scattering at the potential might end up creating an electron-positron pair. Thus the electron number and the positron number are not conserved but only the net-charge number. Taking the electric-charge convention the electrons (particles) are negatively and the positrons (antiparticles) are positively charged.

This is a very complicated view on relativistic quantum theory, but it can be made working even for the more complicated case of interacting electrons, positrons and the electromagnetic field. It's in fact a valid way to describe quantum electrodynamics, but it's a quite cumbersome way and not very elegant to work with. That's the more true for the more complicated interactions (strong and weak interactions) of the standard model. That's why nowadays we start right away with the concept of quantum fields which from the very beginning incorporate the possibility that particle number needs not be a conserved quantum number but that it's possible to create and destroy particles in interactions.

At the same time the quantum-field theoretical method automatically takes care of causality and Poincare invariance, and the faster-than-light values of phasevelocities of massive realativistic wave equations is no more an interpretational problem in the modern formulation.
Uhm.. are you saying the old idea of Dirac sea of electrons are related to the phase velocity of the particle being real? Any papers about this? Also you are saying the Dirac sea can still be true although just more complicated? But complication is not criteria for physics truth. At least if the Dirac sea were true, the quantum vacuum can house structure.. any papers written about this Dirac sea still supporting all experimental criteria?
 
  • #24
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Thread closed as the OP does not stick to the original subject.
 

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