joigus

It's perfectly understood. It's called proper time, and @Markus Hanke gave you the recipe to calculate it. The observer on the ground, who is aware of the theory of relativity, can use it to infer how much time has ellapsed in the frame associated to the muon. She, OTOH, can use her own coordinate time and observe the difference. You've been told: It's been measured. It's common knowledge. Misunderstood only by people who haven't studied physics. So maybe you're right about the 'widely misunderstood.' For the wrong reasons, of course.

I would say something like, virtual particles actually contribute to the mass, charge, and other quantum numbers of real particles. So, in a way, we do have indirect evidence of them playing a role. It's just that they never show up. They are modes of the quantum field. It's just they generally keep a low profile, so to speak. I would try to stay away from any metaphysical language here.

You don't, for all I can see. Euler forces* are transversal (centrifugal) or tangential (thrust experienced from inside the rocket, when measured in a non-inertial system), or a combination of the two. They're kinematical in nature. I agree it's not the same case. My comment was about maths and definitions, and what you decide to call 'the force on the system.' This requires to define what you mean by 'the system.' If 'the system' is both the rocket, the fuel and the exhaust, then all forces implied are internal and there is no net force. If it's just the rocket with the fuel that's left, well... You see? Thrusts are not kinematical, but sure enough passengers on the rocket will experience these forces as very much real. That's why astronauts must buckle themselves pretty tightly. * Sorry I may have used the term 'Euler forces' in a sense that's a bit more general. I meant ficticious forces in general, centrifugal and Coriolis included.

And I totally understand your dissatisfaction, believe me. It's part of the conceptual issues of QM. Is it there when I'm not measuring it? What does it mean that now it is? How does the formalism incorporate that fact? It's not that one virtual particle contributes to the mass of the measured particle, it is rather that all the wildest things you can imagine the particle as possibly doing within the strictures of HUP are somehow contributing to the measurable properties of the particle. And all of these ghostly presences interfere in every which way to produce the observed behaviour. That't what's difficult to swallow. But that's what the quantum formalism tells us. How to wrap your head around it in a pictorial way that helps you understand it better is another matter.

Can I interest you in, \[ f=ma \] \[ f=F-v\frac{dm}{dt} \] ? with \( f \) being the rocket-generalised force? That's similar to what you're doing when you go to a non-inertial frame with acceleration \( A \) and re-write, \[ F=ma+mA \] as, \[ F-mA=ma \] \( f=F-mA \) being the force and \( -mA \) the Euler force. To be honest, I'm not nearly as much concerned on how we call it as I am in preventing the possibility of rockets falling on my head because people don't apply the equation correctly.

Well, I don't know. A measurement is not just a particle hitting a screen. You can separate isotopes by their mass, for example. There's your nucleus. You certainly cannot centrifuge virtual particles. They do contribute to the particle's mass, but you can't separate them and analyse them as independent things. That's why people sometimes talk about a 'cloud of virtual particles' around the real, detectable particle. Again, a pictorial handle for the concept, not quite what it 'is' in the theory.

It's actually needed if what you mean is to argue that 'physics is in trouble.' You see, for some physical systems the concepts of force, or acceleration for that matter, or even position, are ambiguous or cannot be defined at all. It's also possible for them to have a surprising and totally non-intuitive definition that nevertheless makes mathematical sense. Take the case of a particle in a constant magnetic field. These systems are better treated in terms of a Lagrangian. And when you do that, lo and behold, the momentum of the system is not what you would expect, and includes the vector potential, turning out to be mv-qA, instead of just mv. In the case that you guys are discussing, it's because the definition of 'the system' is what's ambiguous. The rocket is losing fuel by the second, so part of 'the system' is going away. What do you do? You drop the definition that happens to be useless for this particular case --of F=ma--, and stick to the more secure, more general one of F=dp/dt, as knowledgeable members are telling you. Then you have two terms mdv/dt, and vdm/dt. The same equation that's been applied for decades to investigate how rockets move.

Actually, no. He's a well-known hackler of serious scientists in public talks. I know enough about him to know he's a crackpot magnet. He claims that all of physics since Planck is wrong --I was patient enough to watch one of his videos or two. That's some time down the drain I'm not getting back. He certainly doesn't understand the ideas behind renormalisation. I'm not saying quantum physics is problem-free, and there are no consistency issues. There are. But I see nothing of value in trying to substitute renormalisation strategies with WAG numerical games and numerical analysis. And all hand-waving. That's what he does. Very similar to what you did by copying and pasting some formulae from a 1968 paper and pulling some numbers from a part of your anatomy, and substituting a logarithmically divergent integral by your wild guess. Zero value from a scientific POV IMO.

Wrong! When you try to make an object get in a garage and it's longer than the door, you must rotate it to make it fit. That's forshortening. One would think forshortening is just a matter of perception. But if you don't rotate the object, you will end up damaging the door, or the object, or both. So it's real enough for me, and for anybody, and not just a matter of 'perception.' Now suppose you have a muon in the atmosphere, moving slowly towards the ground.* It doesn't reach the detector at ground level, simply because it doesn't live long enough. Move at close to the speed of light and it will reach the ground. Now, I don't know what you call real, but that's real enough for me. Time dilation is is the equivalent of forshortening due to rotation, but in this case it happens in space and time. Lorentz transformations are (hyperbolic) rotations within a certain (t,x) plane. Only when the observed object stops, or decays, this extra time due to time dilation can be 'cashed in,' so to speak. Clocks 'know' about it. Similarly, when we try to re-orient the object we got in the garage, we can tell it doesn't fit**. How did it get in then? The foreshortening we used to get it in was very real. The elongation of the muon's lifetime that allowed it to reach the ground was real too. Unless you're willing to take it one further step and start discussing what's real and what's not. I won't follow you down that road. Decades ago there was a famous problem about two tethered spaceships and whether space contraction was real. It went around the CERN cafeteria, and many --professional physicists, mind you-- thought the conclusion of the analysis was that it was just an illusion. John Bell managed to prove it must be real. * Not a typical situation, because cosmic rays typically reach the atmosphere close to the speed of light. ** Spatial equivalent of the twin brother in the twin paradox turning back to Earth, not being inertial anymore, and checking clocks.

I've skimmed through the article, and as far as I can see, this is more or less what I meant by, They don't appear in the measurements; they appear in the calculations. It's been claimed that when we hit a particle, and we produce jets of other particles, what we're doing is giving these amplitudes enough energy so that the virtual mode gets on-shell, so to speak, and can then be measured. That's, again, a way of speaking. But it's not too far off the mark, I would say.

Ok. Yes, I have no problem in accepting that actual photons hitting my eyes are not precisely sitting on a mathematical line that's an idealized mathematical object. All experiments have error bars. There are many ways that we can think of to try to come to terms with this --perhaps uncomfortable-- concept. I remember some words by Sidney Coleman to that effect, from his Harvard lectures on QFT. We know what the mathematics of the theory says. From the mathematics of QFT we know more or less qualitatively --or in some reasonable cases-- that classical trajectories are the most likely, because they are at saddle points of the action. We also know that any event with a continuous distribution of probabilities has a chance zero of happening. That doesn't mean it's impossible, but it does mean that --under reasonable assumptions of continuity and differentiability-- right next to it are infinitely many events that are almost 'as much zero chance of happening.'

Oh, I see. You mean the infamous narcissist heckler of Witten that says all of modern physics since Planck is nonsense: https://youtu.be/k7EnQd-VGqU?t=27 I know what you're up to now.

I'm not sure that's tenable, or necessarily true, or at least plausible. It could be. At present in QFT "virtual particles" is nothing but a fancy name for quantum mechanical amplitudes that cannot be made consistent with the on-shell condition, but must be included in the calculations. Nobody has seen a virtual particle, and I'm sure nobody will. In that sense, they might perhaps be comparable to the interior of a BH. Is it really there? I don't know, and I can't even think of a way to measure what's in there and report to the experimental physicists outside. You could say "I think ordinary space is made up of swarms of black holes that appear and disappear so rapidly that the deviation of their effect is immeasurably small." Similarly, I can't even conceive of a way to have a virtual particle do it's "virtual particle job" --participating in the amplitude off-shell-- and be possible to measure. You can perhaps always modulate a discontinuous pattern of behaviour by using an ad hoc sigmoid curve that does the trick. But remember virtual particles come in all kinds of flavours, masses, and other quantum numbers. So the concept is not to do with gauge bosons per se.

And I have absolutely no objection to any of your explanations, of course. It's just that, within the context of the OP question, @exchemist posed a very interesting --very much related-- meta-question about virtual particles perhaps being responsible for what we perceive as the force between charged particles and their currents. It's because of its interest, and there not being any direct derivation --that I know of-- from QED that gives you the law of force between macroscopic charges or currents, that I sketched that kind of argument. It's not completely general, of course. Also, charges in currents are already moving. But if they're moving at constant speed, there would be no reason --from a classical POV-- why they should radiate. Only accelerating particles should radiate. I'm sure the relativistic argument I presented here can be extended to particles moving at constant relative speed. You need some kind of mechanism that's equivalent to virtual particles at some point. The gist of it is: If you assume charged particles to start moving because of the exchange of a particle, it's impossible to assign an energy and momentum to this carrier of the interaction that's consistent with special relativity. Therefore, there must be so-called off-shell particles. That is, particles that violate Einstein's relation. Those are virtual particles.

That's a very interesting question I don't have a totally rigorous answer to. You are totally correct in making that distinction. So-called real photons are indeed those that can be detected with, eg, a photodetector. In some sense they're "somewhere there." Virtual photons, OTOH, are only those that appear in QED calculations as taking part in intermediate states that only are relevant to the effect of calculating the initial and final states of real particles, including other photons, or the vacuum. If you're familiar with Feynman diagrams, think of the external legs of the diagram as real particles. In between legs you have internal lines connecting vertices. These vertices represent local interactions via virtual particles that mediate the interaction, like in this image taken from Wikipedia representing electron-electron scattering: Now, this is all very interesting, but what happens when a big chunck of magnet attracts/repels another magnet? And when two charged pieces of matter do a similar thing? Can we extrapolate that picture somehow? I'm not aware that anybody has taken QED to do the detailed calculations on, say, a big piece of ferromagnetic material. But here's one reasoning that I think is very convincing to see why it has to be the case that it's virtual particles that are doing the job. One of the characteristics of virtual particles that we learn from QED is that they violate Einstein's energy-momentum constraint. They can do so because they're only allowed to exist for a very ephemeral time lapse consistent with HUP. The way to see that is that a particle at rest cannot emit a photon and start moving from the recoil. This is a very surprising consequence of special relativity. And here's the proof. A massive particle has 4-momentum that we can write as, \[ \left(E,c\boldsymbol{p}\right) \] satisfying Einstein's constraint, \[ \left(mc^{2},\boldsymbol{0}\right) \] Thin, of a charged massive piece of matter that's sitting somewhere, and consider the rest frame. We have a 4-momentum, \[ \left(mc^{2},\boldsymbol{0}\right) \] And now it emits a photon. We have --by virtue of energy-momentum conservation, \[ \left(mc^{2},\boldsymbol{0}\right)=\left(E,c\boldsymbol{p}\right)+\left(\hbar\omega,c\hbar\boldsymbol{k}\right) \] But the total 4-momentum is the very same 4-vector it was before, in particular it must satisfy the same Einstein relation, so that, \[ \left(E+\hbar\omega\right)^{2}-c^{2}\left(\boldsymbol{p}+\hbar\boldsymbol{k}\right)^{2}=m^{2}c^{4} \] The corresponding pieces must satisfy their respective Einstein relations, because someone seeing a piece of matter out there doesn't know it has just spat out a photon. Let's suppose the same goes for the photon. So, \[ \left(E+\hbar\omega\right)^{2}-c^{2}\left(\boldsymbol{p}+\hbar\boldsymbol{k}\right)^{2}=m^{2}c^{4} \] \[ \overset{m^{2}c^{4}}{\overbrace{E^{2}-c^{2}\boldsymbol{p}^{2}}}+\overset{0}{\overbrace{\hbar^{2}\omega^{2}-c^{2}\hbar^{2}\boldsymbol{k}^{2}}}+2\hbar E\omega-2c^{2}\hbar\boldsymbol{p}\cdot\boldsymbol{k}=m^{2}c^{4} \] so that, \[ 2\hbar E\omega-2c^{2}\hbar\boldsymbol{p}\cdot\boldsymbol{k}=0 \] and inevitably, \[ E\omega=-\hbar c^{2}\left|\boldsymbol{k}\right|^{2} \] which is impossible if both energies are positive. So photons emitted by a particle at rest seem to be an impossibility unless we admit the possibility that the electromagnetic field carries with it allowance for these ephemeral modes of propagation. As soon as the charged particle starts accelerating, then --I assume-- both real and virtual photons are being exchanged. The detailed picture being far more complicated than this. I forgot to say. The last step is on account that, \[ \boldsymbol{p}+\hbar\boldsymbol{k}=\boldsymbol{0} \] due to 3-momentum conservation.

\[ \overset{m^{2}c^{4}}{\overbrace{E^{2}-c^{2}\boldsymbol{p}^{2}}}+\overset{0}{\overbrace{\hbar^{2}\omega^{2}-c^{2}\hbar^{2}\boldsymbol{k}^{2}}}+2\hbar E\omega-2c^{2}\hbar\boldsymbol{p}\cdot\boldsymbol{k}=m^{2}c^{4} \] OK then.

Just been trying to remember something I'd read long ago about episodic memory that could be relevant to this discussion. https://www.psychologicalscience.org/uncategorized/myth-eyewitness-testimony-is-the-best-kind-of-evidence.html https://www.psychologicalscience.org/news/mandela-effect-what-is-it-and-why-does-it-happen.html https://www.researchgate.net/publication/256375079_Collective_representation_elicit_widespread_individual_false_memories https://en.wikipedia.org/wiki/False_memory#Mandela_effect (My emphasis.) While I have the greatest respect for the Law, and I always abide by it and recommend everybody to do the same, we should always keep in mind that in the end it is a product of human convention, while science ellucidates facts and correlations between those facts. If science makes it objectively, reproducibly, and unambiguously clear that we have reasons to believe witness accounts are not totally reliable, the Law --and the law people-- would be well advised to take science's salient facts into account as, in the words of a famous scientist, "Nature cannot be fooled."

Nay, it is thou who discombobulates me with thy maelstrom in a way.

Pardon? 😅

That's exactly what ChatGPT would say.

No, it's not. No, I'm not. This has taken me back to when I was aged seven, and having arguments with my classmates. Not very long after the paper you're trying to get credit for was published. Thanks for the memories.

Let me clarify further: It's not a new elastic action, is it? It seems to be good-old Sakharov's action in a bizarre notation. So what appears to be 'new' is how cavalierly you deal with divergent integrals by substituting them for a number and then using some numerical analysis by means of a handwaving 'technique.' It's actually your method for regularising the integrals that's to be subject to scrutiny. Experts are likely to ask you about that. Can you justify the only thing that's new, please?

Thank you. Feel free to add anything I may have missed.

Adding to what @studiot said, you can study the molecular structure of something by turning it into a crystal, and study the diffraction pattern. That's not exactly heating it. It's how Rosalind Franklin obtained the spatial patterns of DNA that helped Watson and Crick understand its structure. I hope we're converging to a satisfactory explanation here, but some feedback would be nice. I hope that helps.

Tipically you first make them gases. Solids have continuous spectrum. Gases have discrete lines of emission and absorption. These lines are kind of the ID of different elements and chemicals.