Nonrelativistic derivation of Schwarzschild's equationby allison johnson Tags: derivation, equation, nonrelativistic, schwarzschild 

#1
May1307, 07:49 PM

P: 1

Since Masses in his book, "The Nature of Physical Fields and Forces", was able to derive Schwarzschild's equation using only nonrelative physics, does any evidence supporting general relativity really exist? Is it important then that general relativity and quantum mechanics are in conflict??




#3
May1307, 08:24 PM

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http://www.amazon.com/gp/product/B000O6CUVW Technically, it probably doesn't merit an extended discussion under PF guidelines (which insist that the theories we discuss be peerreviewed theories), but I'll give the thread a little bit of rope unless I get complaints about it. I don't believe that there is any peerreviewed Newtonian explanation for the perihelion shift. I find citing a vanity selfpublished book unconvincing as far as establishing that there is such a Newtonian explanation. Furthermore, and more to the point of the original question, there ARE other solarsystem tests of GR, most notably measurement of the Shapiro effect, an increased time delay in radar signals passing close to the sun. And of course there is the Harvard clock tower experiments and the Scout rocket experiments (both of which measure gravitational time dilation effects not predicted by Newtonian physics). Not to mention the HafleKeating experiments. 



#4
May1407, 01:15 AM

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Nonrelativistic derivation of Schwarzschild's equation
Just as you can do a "hybrid NewtonianSR" calculation of light deflection by treating a photon as having a mass equivalent to its energy and obtain the wrong answer, half the GR prediction, so you can do a "hybrid NewtonianSR" calculation of perihelion precession by treating Mercury as having a rest mass that increases with its kinetic energy, or alternately that subsumes its potential energy of the Sun's gravitational field. You also get the wrong answer  this time 1/6 the correct GR one.
Garth 



#5
May1407, 04:41 PM

P: 128

The conversation was as follows: Me: For a circular orbit, the body's average velocity is v = sqrt(G*M/r), where r is the average radius of orbit. The precession rate per orbit is: n = 2*pi*[1  cos(arcsin(v/c))]. For the planet Mercury: r = 57909176e3 v = 47873.5 n = 8.01124e008 Converted to arc seconds per Earth century: " = n*360*60*60*415 = 43.0876" Response: "Since v/c is small in this case, arcsin(v/c)=v/c and cos(arcsin(v/c)) = 1(1/2)(v/c)^2. Thus your formula reads n=pi*(v/c)^2 = pi*G*M/(r*c^2) which seems to differ by a factor of 6 from the standard result n=6*pi*G*M/(r*c^2); see MisnerThorneWheeler Exercise 25.16 or equation 40.18." Me: I believe that the discrepancy you noticed is because my method calculates in units of normalized orbit, where the standard method calculates in units of radians. How I resolved the discrepancy: r = 57909176e3; // Mercury's average orbit radius. Using the method in question: v = sqrt(G*M/r); n = 2*pi*(1  cos(asin(v/c))); // Orbits per orbit. n*(360*60*60)*415 = 43.0876; // Converted to angle * orbits per century. or, using the standard method: n = 6*pi*G*M/(r*c*c); // Radians per orbit. n*(180/pi*60*60)*415 = 41.1457; // Convert to angles * orbits per century. ... End conversation. So it really came down to how many terms one used when approximating cos and asin. Approximating pi to be 3.0 would also cause problems, but maybe that wrench was being saved for future use. I jest confidently because I've since used the method to approximate the precession of PSR 1913+16 (no where did I multiply anything by 6). 



#6
May1407, 04:55 PM

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P: 2,341

http://www.physicsforums.com/showthr...ession+Peacock It's rather disturbing that you would do that, particuarly since my point was so easy to understand, and the mistake so easy to correct. To repeat: circular orbits have no pericenter, so they can exhibit no precession. You meant "nearly circular orbit". See Peacock, Cosmological Physics for an elementary analysis of the pericenter precession for a nearly circular orbit, as given by (weakfield) gtr. Be this as it may, I agree with pervect that the book cited by Allison was selfpublished and from the description offered is extremely unlikely to provide anything of value to physics. I noticed something else which might be relevant in understanding what might be going on here: an "Allison Johnson" has made very similar posts to several other forums in recent months: http://www.advancedphysics.org/forum...ad.php?p=37405 26 April 2007, 16:35 30 April 2007, 12:59 AM I note that like Allison, you are a very new poster at PF, shalayka, and like her seem to be behaving oddly, as seen in your only other thread to date http://www.physicsforums.com/showthread.php?t=161810 I hope that's just a coincidence. 



#7
May1407, 05:04 PM

P: 128

That's like saying whomever came up with the equivalent approximation 3*G*M/(r*c^2) based on General Relativity was deluded into thinking Mercury's orbit is circular. I think you know better in both cases. For PSR 1913+16: n = 2*pi*[1  cos(asin(v/c))]/(1  e^2) = 4.4 degrees per year. I'm sure this is better suited to your tastes. My knowledge of physics does not directly correlate to my post count on this forum. I'd like you to think on that before you ever think about replying to my posts in the future. On second thought, don't reply at all. I'll find somewhere else to make intelligent conversation. Thank you for your time. 



#8
May1407, 05:28 PM

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P: 2,341

Shawn, this will be a short conversation on my side because I just took a quick look at your website [[deleted]] as mentioned in your other thread (where you describe yourself as a computer programmer in Regina, Sasketchewan, Canada), and I regret to say that I consider it yet another crankphysics site. Your computions are simply incorrect. You've badly misunderstood standard notation and terminology, the nature of physical theories in general and gtr in particular, the levels of structure in gtr relevant to the textbook analysis of precession which you claim to comment on, as well as the technique of perturbation analysis. Actually, your writings make very little sense. For other readers: I think this episode illustrates the dangers of stumbling over "simulations" on the web unless you have good reason to think some programmer knows their stuff, you should be wary. Contrast Shawn Halakaya's website with Greg Egan's wonderful website http://www.gregegan.net/index.html. Greg happens to be a talented Java programmer (but is best known to the reading public as a novelist), and like myself he is not actually a physicist by training. But anyone who knows the relevant physics/math will quickly see that he knows his stuff, so his simulations are as trustworthy as anything I've seen. Alas, I fear that those who do not know as much as I do might not find it so easy to tell the difference. 



#9
May1407, 05:46 PM

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P: 28,775

Please pay attention to the PF Guidelines, especially on speculative, personal theory. In addition, do NOT advertise websites that to not contain verified or unpublished physics.
This thread has gone horribly offtopic. Zz. 


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