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 Apr 15 comment Distance in relativistic circular motion in invariant spacetime As a final teaser: what do you think would happen if one were to increase the energy of the proton (and hence also the speed), such that the circumference becomes less than the size of the proton? Apr 15 comment Distance in relativistic circular motion in invariant spacetime +1 for a good, clear answer. I would just like to add that in one of my 4th year particle physics lectures, the Professor calculated the circumference of the circle travelled by a proton circling the LHC in the frame of the proton (as if one were sitting on it.) At about 7TeV, he found that rather than the 27km circumference as measured in the lab frame (i.e. standing next to the LHC,) the proton was in fact circling a circumference of about 3m!! Unfortunately I don't has the calculation to hand but it shouldn't be too difficult to replicate. Apr 15 comment Why is the contribution of a path in Feynmans path integral formalism $\sim e^{(i/\hbar)S[x(t)]}$ +1 for taking the time to write this up. Whether a direct answer to the OP's question or not, it is certainly related and makes for some interesting reading. Mar 23 comment If the universe is expanding, what is it expanding into? In this answer you erroneously suggest that anti-particles have negative energy. This is incorrect. Any third/fourth year undergraduate course on introductory QFT will teach you about how Dirac derived his equation by seeking a relativistic form of the Schrodinger equation. His interpretation of the negative energy solutions is called 'the Dirac sea' but they are now understood as positive energy anti-particles, travelling backwards in time. See the Dirac equation wiki page for more information. (en.wikipedia.org/wiki/Dirac_equation) Feb 11 comment Does particle indistinguishability and quantised enery levels (in bound states) violate the Pauli Exclusion Principle? @gigacyan: So just to clarify, are you saying that all the electrons bound in Hydrogen atoms do indeed have slightly different energies, beit due to electromagnetic interaction or wavefunction overlap? Given the effect isn't measurable I'm not too concerned as to whether the prodominant factor is one of the other, just that A: the PEP still applies and B: the energies must therefore be different. Feb 11 comment Is there a fully quantum-field theoretic treatise of Planck's Law for black-body radiation? @Moshe I've not yet had much exposure to multi-particle QFT and would be very interested to see this calculation explicitely. I tried a search for a paper proposing to have derived the Planck distribution with QFT but couldn't find it. Does anyone know of a paper that tackles it? Feb 11 comment Does particle indistinguishability and quantised enery levels (in bound states) violate the Pauli Exclusion Principle? @gigacyan. Wrt your first paragraph, if indeed the wavefunctions of electrons bound in distinct Hydrogen atoms do indeed overlap - however negligable the effect, I believe it is to this that I was refering. In all honesty I'm now not so sure that the PEP even applies to electrons bound in distinct atoms?? Perhaps it is this part of the question that I remembered incorrectly.. Feb 11 comment Does particle indistinguishability and quantised enery levels (in bound states) violate the Pauli Exclusion Principle? @Lubosh - Thanks for the comment but this, to me, seems like the clearest attempt to actually answer the question; hence the +1. I agree with what you have said and therefore think I must have remembered the question incorrectly. Perhaps, instead, we could consider all the Universe's fermions in an instant just after the Big Bang. If the available space was sufficiently small (say less than the size of one Hydrogen atom) would this not require all the fermions to adopt minutely differing energies, so as not to violate the PEP? Feb 10 awarded Commentator Feb 10 comment Why does one experience a short pull in the wrong direction when a vehicle stops? +1 Nicely put, but I feel it prudent to point out that this argument (albeit less formal) has in fact been proposed in other answers. Feb 10 comment Why does one experience a short pull in the wrong direction when a vehicle stops? +1 Just read this after having made similar aguments in a comment above. This, IMHO, is the correct explanation. Feb 10 comment Why does one experience a short pull in the wrong direction when a vehicle stops? In addition to the tension built up, and released, by the passengers' limbs and torso, there will also be a similar release from the seat, carriage and brakes on the train. Clearly the seat fixings, the carriage-to-chassis fixings and the brakes-to-chassis fixings all have a small amount of 'give' in them (as does the actual plastic comprising the chair and the metal comprising the train). Thus, under braking, the torque due to the deceleration will build up a small, soon-to-be-felt, recoil once the deceleration reduces to zero. Feb 10 comment Why does one experience a short pull in the wrong direction when a vehicle stops? I beleive this is the correct answer but offer a slight extension to it: Feb 9 comment Interference of polarized light Agreed, +1 for content and style. (tiny typo in the first line though: "not to be unsubstantiated") Feb 9 awarded Scholar Feb 9 accepted How could spacetime become discretised at the Planck scale? Feb 8 asked Does particle indistinguishability and quantised enery levels (in bound states) violate the Pauli Exclusion Principle? Feb 8 asked Is there a fully quantum-field theoretic treatise of Planck's Law for black-body radiation? Feb 2 revised How could spacetime become discretised at the Planck scale? Added LQG to the list Feb 2 comment How could spacetime become discretised at the Planck scale? Thank you, I'm going to spend some time researching the other stack questions and the references from Penrose and Daniels answer. For now the issue of a Lorentz invariant quanta of spacetime seems to me like an interesting concept worthy of further research.