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  1. J

    Should photons be considered massless?

    Sorry, it was just meant as a joke. Honest, no offense intended. I agree with you. In a gravitational setting it seems difficult to distinguish the two. But I realize now that there are other fields where mass and energy really are separate in a meaningful way.For example this...
  2. J

    Should photons be considered massless?

    That is very interesting, I cant believe I never heard about this. Thanks for that good example.
  3. J

    Should photons be considered massless?

    First off F = -kx lol, sorry I had to. Second, I think there is a misunderstanding. Are you aware that all energy gravitates? At the beginning of this thread I specifically said this is a discussion in a general relativistic setting. What I am getting at, is what is the functional...
  4. J

    Should photons be considered massless?

    That seems problematic, imagine if I build a scale out of glass which has a lid and closed box. And I fill the scale with light, you would then claim that the light had mass using your definition. This is why it seems difficult to distinguish between mass and energy in any way. And hence why...
  5. J

    Should photons be considered massless?

    PAllen, thank you for your replies they have been very helpful.I have an additional question, would it be fair then to say that it is the total energy which resists motion? So for example the mass term m in newtons second law could be replaced with E/c^2 ? I realize that for many situations...
  6. J

    Should photons be considered massless?

    Ok thats fair enough, although it seems strange to define mass like that. Does anyone know how you would actually experimentally measure the rest mass as opposed to the total energy of something? What I mean is, say you put an object on a scale, you would actually be measuring its total energy...
  7. J

    Should photons be considered massless?

    See my reply to DaleSpam above. How can you say their rest mass is zero? How do you measure the rest mass of a particle opposed to just all the energy stored in it (including rest mass energy)? In a general relativistic setting what is the difference between stored energy and rest mass...
  8. J

    Should photons be considered massless?

    ahh ok thank you. I had never heard of a pp-wave spacetime before now. I have only taken one undergraduate course in gr (a senior level one). Edit: also to give more perspective that was at a quarter school, ie 10 week classes.
  9. J

    Should photons be considered massless?

    First time using the quote system, hopefully I dont screw this up. Ok thats fair (at least to the best of my knowledge) Well what I mean is how can you say the mass is zero? If I have a reflective box with an equal amount of anti matter and matter on a triple beam balance, and I let the...
  10. J

    Should photons be considered massless?

    Well Drakkith what I mean is, if photons curve spacetime, then what is the difference between massive and massless particles in a GR setting? How do they behave differently. Also WannabeNewton I dont understand your post. Are you saying photons don't curve spacetime? My question is, do...
  11. J

    Should photons be considered massless?

    Hello all, I am asking this question in the context of general relativity. In general relativity the stress-energy tensor is related to the spacetime metric through the Einstein field equations. The production of a curved spacetime is what creates what we call gravitation. For example a...
  12. J

    Weight difference between a charge and discharged battery

    Yes there would be a weight difference. The charged battery would weigh* more. All energy** gravitates. *here the working definition of weight, is what you measure on a scale **gravitational energy is a concept only useful in certain limits, and does not apply here.
  13. J

    Does negative potential energy reduce the effect of gravity?

    Thanks :) I am following it fairly closely up until the nuclear stuff. I also opt out of the curve fitting they do and instead generate a look up table by cycling through p(x) and epsilon(x). This was actually incredibly benefecial because despite their claims, there are actually 3 important...
  14. J

    Does negative potential energy reduce the effect of gravity?

    I should probably be more clear about that. This is calculating the local energy density. So my mentality is this. The Yukawa potential and model for the Pauli exclusion principle die off to be pretty much zero within 5 fm. And I am at nuclear densities, so my approximation could be phrased...
  15. J

    Does negative potential energy reduce the effect of gravity?

    pervect, I am getting pressure via the method outlined in this paper: http://arxiv.org/abs/nucl-th/0309041 in line 13 of page 9. I am using a numerical derivative. I am also using the TOV equation outlined in line 5 on page 6. I am doing my hexagonal close packing in flat space...
  16. J

    Does negative potential energy reduce the effect of gravity?

    I think I am lacking a fundamental understanding of what energy density is. Let me describe the exact problem I am running into with my research/modelling. I am taking my neutron star to be a degenerate fermi gas. This allows me to create an implicit pressure vs. energy density curve. I...
  17. J

    Does negative potential energy reduce the effect of gravity?

    Hello, my question is in the context of modeling static neutron stars via the TOV equation. This is for a 20 week research project for my undergraduate degree. I am creating different equations of state to relate energy density to pressure, I have already used ideal fermi gas models, and now...
  18. J

    Linearly independent eigen vectors

    ok I think I got it. http://en.wikipedia.org/wiki/Determinant#Block_matrices In the block matrices section. I can think of my matrix has the simple case where the block C is a (n-1)x1 matrix off all zeros. So I can get the eigen value from the top left corner element of the matrix...
  19. J

    Linearly independent eigen vectors

    I did take a look and try to find a classification of this matrix, but I did not see anything. If the first row was not present then I could easily do it, as the determinant of the nxn matrix can be represented through a recursive relation of the determinant of the (n-1)x(n-1) and the...
  20. J

    Linearly independent eigen vectors

    Hello everyone, this nxn matrix arises in my numerical scheme for solving a diffusion PDE. M = \left(\begin{array}{cccccccccc}1-\frac{Dk}{Vh} & \frac{Dk}{Vh} & 0 & 0 & & & \ldots & & & 0 \\[6pt] \frac{Dk}{h^2} & 1-2\frac{Dk}{h^2} & \frac{Dk}{h^2} & 0 & & & & & & \\[6pt]0 &...
  21. J

    Use of Laplace Transforms

    The Fourier series is a very important thing to study for a few reasons in physics. First, you can teach Fourier series in a almost mechanical way at first that is easy to understand. Usually your first go around with learning them is just proving that some integrals are equal to zero. Then as...
  22. J

    Exploiting a the inverse to determine eigen vectors?

    Hello, this is related to my research on RCW(FMM) analysis of light shone onto crossed gratings. main question: can you exploit having matrix A and its inverse A^{-1} to calculate the eigen vectors/values of A in a more effective way? backgroud: so my problem is this: I have an unusual...
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