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About rjbeery

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  • Birthday 09/23/1972

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  1. Agreed. I'll post to the forum if and when I find or produce a new analytic solution. Thanks so much for the patient and mature discussion.
  2. Have you actually read the OP? Or its references? Did you look at the numeric analysis I posted? I shared the spreadsheet so you can see that there are no fudge factors involved. The math works. That being said, I understand the tensor objection, which is why I'm asking for real-world examples where spacetime curvature and time dilation diverge. Maybe the full time dilation field requires more information than I'm presuming; maybe GR has redundancies in distinguishing mass/momentum and other forms of energy (IOW, two different systems could produce the same result); maybe there's more information in the EFEs than mere spacetime curvature; maybe this connection doesn't generalize and is only useful in limited analyses. I think about all of these things. But insisting that either this idea can either immediately and completely replace all of GR, or else it's worthless, seems premature.
  3. Feel free to throw out thoughts, I love hearing other perspectives. Dispersion and FLRW are things I had never considered, and I appreciated their mention.
  4. Markus, I understand your position and I appreciate your input. You're correct that I keep referring to the simpler Schwarzschild spacetime solution but that was to illustrate the theoretical connection to others who can't see it at all. I'm "facing many fronts" in this thread. I just spent 6 hours convincing another poster that the gravitational time dilation equation is mathematically valid. You might be right that the connection doesn't generalize, but I remain unconvinced. The FLRW spacetime example doesn't work, for example - the reason we know about cosmological expansion in the first place is due to time dilation (red-shifting of the distant stars). In fact, when people present me with apparent counter-examples that I can explain it does nothing but strengthen my resolve. If that's frustrating, I'm sorry. This is right but we've already covered it. It's the local time dilation gradient that determines gravitational movement. Remember discussing Newton's shell?
  5. I'm ignoring nothing. There are time units on the LHS (t0), and time units on the RHS (tf). The remaining units under the square root all cancel out. I literally did the math for you. Numerator units: GM = m^3/s^2 Denominator units: rc^2 = m^3/s^2 They are the same units. Meters cubed over seconds squared. What are you missing?
  6. Mordred...you're peer reviewing PhD astrophysics articles and you've never seen or dealt with the gravitational time dilation equation? Look at the numerator of the fraction under the square root: 2GM. This has units of m^3 * kg^-1 * s^-2 * kg. This simplifies to m^3 * s^-2 Look at the denominator of the fraction under the square root: rc^2. This has units of m * (m/s)^2. This simplifies to m^3 * s^-2 They cancel. It's a dimensionless scalar, as I've said multiple times. It's OK to miss a mass term in the numerator, or whatever you seem to be doing, but I don't understand how you aren't reading the words that I'm typing, explaining what the equation is, telling you exactly what you're looking at. If you don't like the equation, your problem is not with me but with the entire astrophysics community.
  7. No, you need to read the words I'm typing. The first equation is the equation for gravitational time dilation. I'm pretty sure the dimensions align without problem.
  8. The first equation is for gravitational time dilation. GM/c^2 is the Schwarzschild radius of a mass, and the additional radius term in the denominator makes the entire square root a dimensionless scalar.
  9. Both sides are L / t^2. I think it's great that you understand why, and I appreciate your patience while I try to get there myself.
  10. No I can't answer your question; I'd have to think about it but I'm currently thinking about perihelion precession. I don't aspire to replace GR, but it's pretty simple -- if all of GR can be described in terms of spacetime curvature, and we can equate spacetime curvature to time dilation, then we can describe all of GR with time dilation.
  11. Exactly. Folks seem to think that I'm trying to replace GR or, bizarrely, claim that Einstein was wrong about something. Please re-read the OP. I'm proposing a causal mechanism for gravity.
  12. I'm not arguing against Einstein in any way, I'm trying to understand where my model would have problems generalizing. I certainly am stubborn, but only to the extent that I will keep asking questions until I understand something. And your desire to close the thread is curious - the conversation is civil, people are learning, and this is the Alternative Theories channel. You give good explanations, but your answers don't bring clarity to me. Gravitational acceleration is determined by G, M, c, and r. Time dilation is determined by the same parameters. As written earlier, we can equate the variables to get: g = (c2/r)(1-(t0/tf)2) What's wrong with this equation? If time dilation and "gravitational acceleration" are independent variables perhaps you could describe an extreme scenario, in layman's terms, where "gravitational acceleration" exists but time dilation does not.
  13. If we take g = GM/r2 and t0 = tf * sqrt(1 - (2GM/rc2)) The equations rely on the same parameters -- we can equate them. Back of the napkin shows: g = (c2/r)(1-(t0/tf)2) where t0 is proper time between two events under the gravitational acceleration of g, and tf is the coordinate time of those same events for a distant observer. It's interesting to note that (t0/tf) is simply the analog of the refraction index of the material which would cause light to behave as if it were near such a gravitational influence.
  14. You're saying that there is a direct relationship between the variables, and also that they are not dependent. Please provide examples where their dependence breaks down (if you have any).
  15. Honestly, that's pretty surprising -- two massive bodies passing each other at great speeds seems to be a pretty fundamental physics problem. Let me ask you a question, Markus. Do you believe that time dilation and the so-called "gravitational attraction" (i.e. spacetime curvature) are independent variables in GR?
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