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- Thread starter Helena Wells
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- #26

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- #27

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Energy / momentum is not conserverd in QFT for small time intervals.

- #28

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The Feynman diagrams have energy-momentum conservation built in (even for virtual particles). The virtual particles do not, however, stay on their mass shell.Energy / momentum is not conserverd in QFT for small time intervals.

- #29

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According to the Heisenberg Uncertainty energy can appear as long as it dissapears quickly.That means if we have defined the momentum with great precision and have a great uncertainty of the position of the particle , momentum can come from nowhere as long as it dissapears quickly.Quantum field theory is based on Quantum Mechanics and in Unrelativistic Quantum Mechanics those things can happen , why not in QFT?The Feynman diagrams have energy-momentum conservation built in (even for virtual particles). The virtual particles do not, however, stay on their mass shell.

- #30

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That is essentialy just a popular science sound-bite, which has no meaningful relation to the real physics - and very much out of place in an A-level thread.According to the Heisenberg Uncertainty energy can appear as long as it dissapears quickly.

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And if you want to clear up some others misconceptions about quantum mechanics, this article (by our @Demystifier as I recall properly?) https://arxiv.org/abs/quant-ph/0609163 is very good for that purpose. Section 3 is devoted to energy-time uncertainty, that's why this paper came to my mindThat is essentialy just a popular science sound-bite

- #32

mfb

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The uncertainty relations make no such statement. There is no process that violates energy or momentum conservation - not even for a short time. This is true for all types of quantum mechanics - nonrelativistic, relativistic and QFT.According to the Heisenberg Uncertainty energy can appear as long as it dissapears quickly.

- #33

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3:25 and watch it for 10 seconds.The uncertainty relations make no such statement. There is no process that violates energy or momentum conservation - not even for a short time. This is true for all types of quantum mechanics - nonrelativistic, relativistic and QFT.

- #34

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This is what's called "popular" science, where science is presented in a simplified form for those not willing or able to tackle university level text books, or academic papers on the subject.3:25 and watch it for 10 seconds.

This video is aimed at a audience that is interested in science but not actively studying it at university level.

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@Helena Wells can you show us a proper textbook or a peer reviewed paper that claims the same thing?

- #36

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Here's something on what the Time-Energy uncertainty principle really says:

https://physicspages.com/pdf/Griffiths QM/Uncertainty principle - energy_time.pdf

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- #38

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It's not so much wrong, as a simplified version designed to try to explain a more complicated subject to a

- #39

George Jones

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Read carefully the except below from the text "Intoduction to Elementary Particles" by David Griffiths, who is also the author of the quantum mechanics text referenced by @PeroK in post #36.

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- #42

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And where are you getting this from?

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From the same video. 3:10-3:50 watchAnd where are you getting this from?

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- #45

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Well ok you can google it right now 'Mass of photons in QED'.

- #46

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That's too broad and will bring up tons of pages not related to what you speciffically wrote. And what you wrote is not something that one would find in most textbooks, that is why I ask you if you have other sources of this claim. This video is not an acceptable source, and you've already been said why. If you want to learn something you should study textbooks, not fun videos on YouTube, even if they were recorded by someone from FemiLab. Even figures like Hawking wrote some very questionable things in their pop-sci books. That's why PF has this policy regarding sources. Argument from authority does not count.

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- #47

mfb

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- #48

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"One should present physics as simple as possible, but not simpler." (free quote by Einstein). Sometimes there are legends built by popular-science writers that violate this rule, anc unfortunately the wrong legends are used again and again in the lack of a better idea. Taking "virtual particles" as real or reading Feynman diagrams as something different than an utmost efficient notation of formulas to calculate S-matrix elements is among them. I don't blame the scientists in there attempt to explain physics to the general public though. I've also no idea how to explain things without the only language we know, which is math. But still one should explain the science to the general public.

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As previously pointed out by others QFT doesn't admit such "small time" breakings of energy-momentum conservation. I particularly find the pop-science to handle this quite silly and complicating the actual situation. While it is true that the actual reason the exact conservation is kept requires certain amount of mathematical sophistication I think it can be explained before entering more complicated perturbative situations in the free complex scalar field case given that anything concerning this conservation is sorted out in QFT even before interaction and the perturbative methods enter(and this indeed makes the math much more complicated).Energy / momentum is not conserverd in QFT for small time intervals.

So for the propagation of these quantized free fields that are going to serve later to build the classical limit(what particle physicists sometimes refer to as the tree level) in the full theory, there is what the author of a well knows QFT textbook calls a "beautiful Lorentz-invariant object", the Feynman propagator and this object involves a certain integral and this integral(written in one of the ways it can be represented) converges only in the limit in which a certain parameter #\epsilon#, that we can think of for this didactic purpose as the "small time intervals" you found in popular divulgative media, goes to zero.

So this keeps exact energy-momentum conservation already even if by itself it appears to be a "non-local" expression because it involves certain quantum tunneling properties, but in this limit this is exactly canceled out by oppositely charged fields in the relevant quantum commutation relations so the final result is fine. Of course all this gets more complicated with interaction and radiative corrections but the basic block are still the free fields and the radiative corrections at higher order are built from the tree level so this picture of exact conservation should hold.

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https://arxiv.org/pdf/0706.1216.pdf

There it's said that that the electron, muon and tau are the exact charged lepton mass eigenstates. But how do you justify this claim? Is there a possibility of even a little bit of mixing of those species in the mass eigenstates, or does something crazy result from the electroweak theory if you assume that?

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