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481192
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location New York City
age 40
visits member for 3 years, 1 month
seen 6 hours ago

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
24
comment Are gravitomagnetic monopoles hypothesized?
@BenCrowell: I gave a quick informal physicist's proof of positive mass in a question: it requires only the weak energy condition--- the positive mass is a requirement that distant black hole's area increase upon absorbing the configuration. A pure monopole is forbidden by positive mass, because it must have a mass, and therefore a regular mass. Birkhoff's theorem is not sufficient, nor are no-hair theorems, because a monopole field is not necessarily spherically symmetric, and it must not come with a horizon.
Aug
23
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?
@DImension10AbhimanyuPS: No, a continued fraction is when the infinite nesting is in the denominator--- yours is in the numerator. Expand out your formula, you will see.
Aug
23
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?
@DImension10AbhimanyuPS: Yes, that formula is correct, but it is not the sum of your infinite series--- you deluded yourself in the manipulations into thinking you got the right answer. The actual power series for ${1\over\sqrt{1-v^2}}$ is 1+v^2/2 + 3v^4/8 + 15v^6/48 and so on, the general term is (product of first k odd numbers)/(2^k k!). Your thing gives coefficients of 1/2^k, it is not the same power series (check it carefully). When you know what you're supposed to get in advance, and you are sure the argument is correct, it is easy to delude yourself, you don't check carefully enough.
Aug
23
comment Why is there a deep mysterious relation between string theory and number theory, elliptic curves, $E_8$ and the Monster group?
@DImension10AbhimanyuPS: With someone as young as you, people will just assume you don't know anything, so just make sure.
Aug
23
comment How would a Lagrangian be used to recover the Schrodinger equation?
Oh, then it should be a comment, not an answer. Once you know what the question is asking, then you give an answer.
Aug
23
comment Why does tachyon arise in bosonic string theory?
Oh, but then you shouldn't say "it's a misconception that ..." because then people think you are under the impression that RNS strings exist as theories. Ok, no worries, it's just miscommunication.
Aug
23
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?
@DImension10AbhimanyuPS: Ok, you know E= m + .5mv^2 to order v^2, why should the v^2 term suddenly change it's coefficient? If you went to order v^4, E = m + .5mv^2 - 1.5 mv^4, you could substitude the fouth-order expression for the mass in front of v^2, or in front of v^4 (maybe both). The issue is that the actual v^2 dependence is only a lowest order thing in v, it is intrinsically modified, not just the coefficient. It is hard to say why something isn't true. It just isn't. You should think about why you think it should be true, and figure out the mistake, because it gives the wrong answer.
Aug
23
comment Why is there a deep mysterious relation between string theory and number theory, elliptic curves, $E_8$ and the Monster group?
@DImension10AbhimanyuPS: ok, but you shouldn't write what I said, which is technically wrong--- E8 is not E6xSU(3), it's a simple group, but it has an embedded E6xSU(3) and fills in the off-diagonal parts with extra crud that's broken when you have SU(3) gauge fluxes which follow the holonomy of the manifold. The precise decomposition is described in detail in Green Schwarz and Witten, which has a nice description of E8.
Aug
23
comment Intuitive understanding of the irreps like Wigner-D matrix?
I explained it in my answer here: physics.stackexchange.com/questions/10403/… . The irreps are symmetric tensors of SU(2), and the D-matrices are just a particular basis for writing the symmetric tensor in terms of the number of "1" indices. When you're doing anything, it's always easier with the tensor representation, there is nothing to memorize then.
Aug
23
comment How does Boscovich's argument show that force must act at a distance?
@julianfernandez: The forces are not primarily electrical, but due to the increase in energy when the electron wavefunction clouds begin to overlap, due to the Pauli exclusion. This is obvious if you consider any sort of simple model of the situation, or even a complicated model, yet still everyone gets it wrong.
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.