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rjbeery

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About rjbeery

  • Birthday 09/23/1972

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    Philosophy of physics

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  1. You've written far more in the discussion of this paper than what exists in the paper itself. I removed the Newtonian reference that offended you. At this point it's pretty suspect that you can't otherwise be bothered, but you've spent weeks explaining that fact. Imagining a constant g is not the same thing as idealizing a frictionless surface. The former contradicts the theory, whereas the latter is ("merely") a practical impossibility. mgh is a first-order approximation, the same way 1/2 mv^2 is. We can use it for estimates, but we can't use it for making generalizations...particularly when the error in those generalizations is precisely tied to the terms we have excluded in our approximation.
  2. Then we both agree that the paper is congruous with the implicit assumptions (e.g. spherical body of mass M), and any further objections would have to provide a set of assumptions for which these calculations don't apply. In other words, we can both agree that the paper is self-consistent, and also that time dilation would occur under constant acceleration (but not vary under constant acceleration). So, really, the only thing we disagree about is whether constant gravitational acceleration is a physical phenomenon, and I'm fine leaving it at that.
  3. Time dilation would occur for any general form of acceleration, but constant gravitational acceleration is unphysical. The high school shortcut of PE = mgh was superseded with the actual formula. Time dilation (gamma) is literally defined by r I think it's odd that my Newtonian reference offended you enough to not even look at the paper, but you're holding on to what we both know is bad math because you've apparently attached your ego to it.
  4. I've rewritten the first section to derive the relevant equation (eq. 5) without any Newtonian references. I could rewrite the equations to put the potential in terms of g but, as I said, I suspect you'll be dismissive. Therefore I found a full derivation that I doubt you can object to: Relativistic Gravitational Potential and its Relation to Mass-Energy On page 404, equation 54, the author seeks to prove that Now that these objections are handled, do you have any other feedback? Because I'm going to be submitting this to a journal and I'm largely working in a vacuum.
  5. Well, apparently Relativity and gravitational potential don't play nicely; something about being impossible to localize potential energy. It's been a long-standing problem that I'm only just reading about. In any event, you shouldn't shut yourself off from what you may find to be very interesting: https://docs.google.com/document/d/1RCmoSXd5YbkMHuYT8OwV_gW8uY5nl8BrBTELQevVfNE/edit
  6. I'll come back to this. It should be as easy as putting potential in terms of g, although I'm not sure you'll concede the point, regardless. In an event, have you ever seen gravity's behavior completely described in terms of refraction? Have you actually read the paper? Because that's what it does.
  7. The reason it's difficult to discuss is because "constant g" is unnatural. It's mathematically impossible, so the premise is invalid. You're thinking in terms of "constant acceleration" as somehow adding to a value of velocity, which would increase the time dilation, but gravitational acceleration isn't true acceleration -- free falling objects are unaccelerated by definition. The bottom line is that there can't be stretches of space where velocity increases but gravitational acceleration remains constant. Potential is defined with r, g is defined with r, so potential cannot be independent of g.
  8. No problem. Please provide me with an exact equation showing me this.
  9. OK, so I've never looked at the derivation of the approximation before. This is a great synopsis: https://campus.mst.edu/physics/courses/409/Assignments/gravitational potential.pdf I think I understand. The approximation U = mgh has 'g' baked into it; we could rewrite this as g = U/mh, and if we take the derivative with respect to r (or h), the change in g is independent of a change in r (or h) in this form -- so you are right. However, the true math (sans approximation) is a full Taylor series expansion, with the height variable continuing on indefinitely to higher and higher powers. In other words, the full expression of g = U/mh is infinitely differentiable with respect to r and will always be dependent upon r. There is no scenario where the acceleration can exist in a form that is independent of r. So, yes, the approximation is exactly the cause of our disagreement.
  10. I think it's important that we agree on where we disagree. I don't deny anything about Einstein's elevator, except that it isn't a true equivalence if the acceleration is due to gravity, and that's because I don't believe "constant acceleration due to gravity" is possible, and the Newtonian approximation is obfuscating that fact. Light would obviously bend under acceleration, regardless of the source. You're asking me to prove that your approximation is an approximation. I may look at doing this, but at this point I don't see much benefit in convincing you as long as you haven't found any objective refutation in the mathematics of my paper.
  11. It doesn't give the same answer. Saying "the other [terms] are small and can be ignored" is like saying that pi is literally 333/106. If Einstein's elevator is your example of a physical scenario where potential increases over a substantial distance of constant gravitational acceleration, it isn't valid. It too is an approximation. We can imagine, in our minds, an elevator being accelerated uniformly from top-to-bottom, but the person standing in the elevator could use equipment (available today) to compare the gravitational acceleration at his head vs his feet. If they differ then he knows he is in a gravitational field. A gravitational field is defined as the negative of the gradient of the gravitational potential. If the gradient is zero, then the gravitational acceleration is zero -- how would you explain that?
  12. But it isn't. I agree with you that time dilation, and therefore refraction, are correlated with gravitational potential, but a change in gravitational potential requires a change in time dilation. I have given the full GR treatment of velocity and how it relates to a free fall in gravity in equations (1)-(6). I do the same in the second section with refraction. Yes, I did this, and we both agree that my math is an exact result, whereas the Newtonian approximation used by Pound-Rebka is just that. It is known to be inexact, and would quickly diverge from reality as the height of the tower increased. In other words, you're using a known approximation as a proxy for GR when we both know it is not. If you still disagree then I would like to examine a physical scenario where potential increases over a substantial distance of constant gravitational acceleration. The only one I can think of is in the center of a Newton's sphere (where potential remains unchanged).
  13. I understand now. You think that, because the approximation has varying time dilation with a constant g, then that's proof that GR claims the same thing. This is false, and equivalent to saying that Newton's approximations prove that the speed of light is infinite.
  14. What different result were you referring to here? To be honest, the things you're saying are just bizarre. This is from the Pound-Rebka wiki page: In other words, treating g as constant is a known approximation, and the proper calculation is literally listed. I solved that exact calculation to show you that it does not produce a "different result". If we used exact values for r_s and altitude then it would produce an exact result.
  15. I can't tell if you're being intentionally obtuse, but .009 is the approximate Schwarzschild radius of the Earth. I used that for r_s in the calculation. The above math was my response to you saying where the ratio of time dilation factors (using rough estimates) is a difference of 3*10^(-15), compared to the gh/c^2 = 2.5*10^(-15). The fact that they could not (at the time) measure the time dilation difference at a distance of 22.5 meters, forcing them to use the approximation you listed, does not mean that the GR answer is anything but correct.
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