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I do not participate on this site any longer, except to respond to comments regarding my own text, if that text is unavailable in another form. I do not accept the political moderation atmosphere here, it is not compatible with open science. I participate at physicsoverflow.org.


Aug
22
comment Combining metric tensors/curvature tensors
You can do this addition at weak field, so long as your coordinates make the metric nonsingular (rectangular coordinates as the unperturbed metric), and add the usually negligible corrections perturbatively.
Aug
22
comment Relative to the speed of light
To be precise, the light is travelling forward from A to B, but it is also going "up" in time in the moving frame, due to the "tilt" of the simultaneity lines in the moving frame. I can't explain without a picture, but you can see it in my answers to relativity questions--- you need to tilt the constant time line to explain why this happens. To see why, answer this: why is light moving backwards in the moving frame also moving at the speed of light as measured in the frame, same as light moving forward?
Aug
22
comment Conservation of quantum Noether current
@EdwardHughes: We are not misunderstanding anything, you are just wrong. The Heisenberg equation are the classical equations, and I derived them in some generality from the path integral here (it's standard): physics.stackexchange.com/questions/26888/… . There is a proper notion of product (product of operators) and a right notion of derivative (take the derivative).
Aug
22
comment Relative to the speed of light
Yes--- the time taken and the distance travelled are not just rescaled, you also have to add the distance travelled (or subtract) times the velocity, it's the failure of simultaneity that is the major effect, and the speed of light is constant no matter who measures it.
Aug
22
comment Equivalence of canonical quantization and path integral quantization
@EdwardHughes: I know the path integral, I did not make a mistake. The things in the path integral are number-functions (or Grassman variables), but they are also operators, in that they act on path-integration states, and their algebra is exactly the same as the Heisenberg algebra, including the correct non-commutativity when you move the time-order of the insertions past each other. You should read the answer properly before downvoting, it may be stating things differently from other places, but this is not because it is incorrect, it just sounds wrong because it is original presentation.
Aug
22
comment How do Einstein's field equations come out of string theory?
If you wish to derive the beta-function, use Riemann normal coordinates, this is the best way. It's described on Wikipedia, then the beta-function calculation is a piece of cake (relatively, once you figure out what you're doing exactly).
Aug
22
comment Does relativistic mass have weight?
The actual level 2 approximation does not change r in a straightforward way, it has an attraction given by the product of the energies (relativistic masses) but with a peculiar radial dependence given by the gravitomagnetic contribution, which is best to work out by boosting to the rest frame of one of the objects, where the gravitational field is known.
Aug
22
comment Does relativistic mass have weight?
The answer is just yes.
Aug
22
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?
No, this is not right--- you don't get a square root. The result of this infinite series is (m-.5mv^2/(1-v^2)), it isn't right because the rational coefficients of the expansion of the square root is 1/2, -1/4, 3/8,15/16, and so on, involving successive products of odd numbers on top, while your thing has 1/2,1/4,1/8,1/16 and so on. It's not right, but it was very clever. There is no reason to assume that the mass shift can be used recursively like this--- the correct formula is found geometrically, from requiring relativity.
Aug
22
comment Connection between $\Delta x \Delta p \geq \frac{\hbar}{2}$ and $\Delta E \Delta t \geq \frac{\hbar}{2}$
This is what Bohr and Einstein knew, but the quantum formalism makes it hard to make precise. It's correct for waves, of course, just you need to translate to a formalism.
Aug
22
comment Why does tachyon arise in bosonic string theory?
But the theory is inconsistent without GSO projection. The easiest argument is Witten's--- the theory has a gravitino, so it must be space-time supersymmetric, and therefore have no tachyon and come in equal number of bosonic and fermionic particles at each level. The GSO projection is really necessary, it is interpreted as summing over spin structures on the worldsheet, which means certain of the naive modes don't contribute.
Aug
22
comment How would a Lagrangian be used to recover the Schrodinger equation?
The reason your answer was downvoted is, I suppose, that the two different equations are completely separate ideas--- one derives the Schordinger equation as a field equation, the second as an equation for particle amplitudes, so you shouldn't write both together, or at least describe the different ideas of the two formalisms.
Aug
22
comment Best EM/Photon rocket using avalable tech?
You are assuming the energy source isn't carried with the ship, the OP assumed the ship would carry the source. You can definitely push a ship from outside using a mounted energy source, that's not the issue, the issue is to do it when you don't have a momentum-sink, you need to conserve momentum, so you need to eject stuff, and since OP doesn't want to eject stuff, he need to eject photons.
Aug
22
comment Is 3+1 spacetime as privileged as is claimed?
You should clarify "too quick"--- it is difficult to know how quick is too quick. The orbits wouldn't work. But perhaps you could have 4+1d life, with another thing, not planets. Who knows.
Aug
22
comment Quantum mechanics and everyday nature
Friction is not particularly quantum, and "electricity" is too vague, if you mean "electrical conduction", yes, true. But the rest are good.
Aug
22
comment Relative to the speed of light
The intution is not about the formalism, but about how it works. This probably requires a picture to explain, to see the failure of simultaneity, which is the thing people generally fail to get when learning relativity from popular sources (but it's the first thing Einstein discusses).
Aug
22
comment Relative to the speed of light
This answer is wrong, the main effect is the failure of simultaneity at a distance, this makes the speed of light the same in the backward and forward direction in the moving frame.
Aug
22
comment Is normalization consistent with Schrodinger's Equation?
This answer is kind of pointless, it isn't helpful, you can just say "The SE is linear".
Aug
22
comment Is there a maximum number of types of elementary particles?
This is true, but the "particles" we see in accelerators are just the massless particles, and there are a finite number of these. This is probably the best interpretation of the question.
Aug
22
comment Do the laws of physics evolve?
You should know that the large-numbers coincidence is now called the "Hierarchy problem", together with the fact that there are three scales--- the neutrino/cosmological-constant scale at .1 eV, the Higgs scale at 1TeV, and the Planck scale at 10^19 GeV. These are equally spaced in log, hence the large-numbers, and the cc-scale is comparable to the age of the universe, probably as Weinberg suggested, because it's anthropic.