# elfmotat

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 Sep10 comment Dependence of sign on operators in wave equation? The form of an operator depends on what basis you're working in. For example, in position space the momentum operator $\propto \partial /\partial x$, while the position operator is just x. But in momentum space, position is $\propto \partial /\partial p$ while momentum is just p. In general you should be alright no matter what basis you're using as long as your operators satisfy the commutation relationships. Sep7 comment Gravity Concept Question The sun can't just suddenly disappear. What you're asking us to do is use the laws of physics to describe a situation that violates the laws of physics. May8 comment Chasing a photon @brightmagus This seems to have spurred an interesting discussion, but to reply to your original comment: I never claimed this was a proof. Velocity addition was originally derived from the assumption that c=const, so it had better work that way. Marco Prins asked whether or not a photons velocity would still be c if one were trying to chase it at high speeds, and what the equation to calculate such a scenario is. I provided him with what he asked for. Of course, you can't "prove" that c=const must be true simply via theory - this is something that must be confirmed by experiment. Jan17 comment Why don't positive charges move? They can move, but tend not to because they are held in place by other atoms. Aug26 comment How can we deduce the relation $m = \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}$ between relativistic mass and rest mass in special relativity? I remember Feynman did something involving analyzing collisions of masses in different reference frames, and concluding that, while $mv$ is not a conserved quantity, $\gamma mv$ is. It's therefore natural to modify either the definition of momentum or mass in order to maintain momentum conservation in relativity. Jun5 comment What's the basic premise of General Relativity? The Doppler factor (1+v^2/2c^2) that follows after "for our purposes" is an approximation that comes from a Taylor expansion of the exact factor. And Taylor expansion comes from calculus. May25 comment What force is responsible for anti-gravity? The triangle lifter you're referring to works by ionizing air and forcing it downward, producing lift. The Mythbusters crew tested it in a vacuum and it didn't work, so it's clearly not anti-gravity. It's just a highly inefficient way of obtaining lift. May5 comment QED photon propagator to one-loop order gets different answers Well that's not really what you asked for. How about this: 152.78.192.50/hepwww/staff/D.Ross/qft/aqft3.pdf ? Apr20 comment Transforming an equation to the co-vector version You're right. I've changed my answer to reflect this. Apr20 comment Transforming an equation to the co-vector version It's true as long as $\frac{d}{d \lambda} g_{\mu \nu} = 0$, which is true for most choices of $\lambda$ when considering a timelike geodesic (which is usually what one's interested in) when there's a timeline Killing vector. In physical scenarios where there's no t-symmetry, i.e. the FLRW metric, one's generally not interested in test particles anyway. Apr19 comment How do forces work Necessary classic: youtube.com/watch?v=wMFPe-DwULM Apr11 comment Einstein's theory tells us that gravity is a curve in space and time but how does that causes attraction in mass? youtube.com/watch?v=DdC0QN6f3G4 Apr4 comment Why does the index of refraction change the direction of light The easiest way to answer this is, of course, with Fermat's Principle. But that may not be what you're looking for. Mar23 comment Universe Expansion and two tennis balls Well, since we have no idea what "dark energy" actually is, that's a tough question to answer. Mar23 comment Universe Expansion and two tennis balls You're not reading it wrong, but you're missing Jerry's point. The reason the universe is expanding is because it is filled with dark energy, i.e. there is a nonzero cosmological constant. By "clear the universe of all matter" it was assumed that dark energy should also be removed. Remove the DE and space doesn't expand. Leave it in and it will, albeit at a different rate than we observe because the normal matter in the universe helps to "counteract" the effect of DE. Mar22 comment Future light cones inside black hole To add to this, you can't avoid falling toward the singularity any more than you can avoid growing older. Mar20 comment Einstein gravity versus Newton's gravity youtube.com/watch?v=DdC0QN6f3G4 Mar19 comment Generating artificial gravity by using rotation This is a rather subtle issue. In General Relativity, observables (like time, distance, etc.) are dependent on the metric tensor field. The value of metric is determined by the energy/momentum distribution in spacetime. It is assumed in your problem that the objects involved have little effect on the metric. The metric of a rotating coordinate system (i.e. the rotating clock) yields the above result. If the ring, etc., were sufficiently massive then they too would have an effect on the metric. Mar15 comment Trying to speak correctly of spacetime intervals and how to compare them Sure, why not? The signature of either (+,-,-,-) or (-,+,+,+) is completely arbitrary. As for your last question, you're free to invent any notation you like. Mar14 comment How can my water cool down more quickly? Uh, yes it is...