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v' = c^2 / v

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

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- #1

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v' = c^2 / v

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

- #2

bhobba

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Its the phase velocity which isn't really physical:Is this formula correct? and how could the individual oscillations be faster than c??

https://www.quora.com/Why-is-the-phase-velocity-of-de-Broglie-waves-greater-than-the-speed-of-light

Forget De Broglie - its simply of historical interest and has long been superseded.

Thanks

Bill

- #3

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Well why we have infinite phase velocity? Because this is the spatial coordinate axis of reference frame due to special relativity.

The De Broglie wavelength just a spatial components of matterwave from external reference frame.

https://en.wikibooks.org/wiki/Speci...ation_and_length_contraction#De_Broglie_waves

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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.

- #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.

The wave has infinite phase velocity.

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- #7

bhobba

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But its not physically realizable. Such are introduced purely for mathematical convenience.When the wavenumber k is zero (the momentum) then we have no spatial component. The wave has infinite phase .

Thanks

Bill

- #8

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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

bhobba

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That's just a formal way of looking at it. It not really going backward in time.The positron is an electron is moving 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

bhobba

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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:

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.

https://cds.cern.ch/record/281746/files/9505004.pdf

Thanks

Bill

- #11

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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.

- #12

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But there are lot of interpretations.

Like retrocausality.

https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics#Time-symmetric_theories

- #13

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If you ask me I will show you

- #14

bhobba

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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.How do you know that? Can you show me?

Because one of the general features of QFT is the existence of antiparticles:What do you think, why? Because both are same thing. With differect time directions.

http://physics.stackexchange.com/questions/18705/the-causality-and-the-anti-particles

Thanks

Bill

- #15

bhobba

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Its got nothing to do with Copenhagen."they do not physically exist" regarded to Copenhagen interpretation

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

bhobba

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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.

If you ask me I will show you

Thanks

Bill

- #17

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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

bhobba

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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.Because it is antiphoton

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 speed of the

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

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Zz.

- #21

bhobba

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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 another problem " the speed of thequantum non-local connection(what Einstein called "spooky action at a distance") is at least 10,000 times the speed of light"

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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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?

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.

- #23

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""Within a naïve classical word view, quantum mechanics can even mimic an influence of future actions on past events," says Anton Zeilinger."

https://www.sciencedaily.com/releases/2012/04/120423131902.htm

- #24

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Thread closed as the OP does not stick to the original subject.

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