Non-relativistic derivation of Schwarzschild's equation


by allison johnson
Tags: derivation, equation, nonrelativistic, schwarzschild
allison johnson
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May13-07, 07:49 PM
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Since Masses in his book, "The Nature of Physical Fields and Forces", was able to derive Schwarzschild's equation using only non-relative physics, does any evidence supporting general relativity really exist? Is it important then that general relativity and quantum mechanics are in conflict??
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cristo
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May13-07, 07:51 PM
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What do you mean by "Schwarzschild's equation?"
pervect
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May13-07, 08:24 PM
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Quote Quote by allison johnson View Post
Since Masses in his book, "The Nature of Physical Fields and Forces", was able to derive Schwarzschild's equation using only non-relative physics, does any evidence supporting general relativity really exist? Is it important then that general relativity and quantum mechanics are in conflict??
As nearly as I can tell, this is a self-published book. (It's listed on amazon.com with the author as a publisher).

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 peer-reviewed 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 peer-reviewed Newtonian explanation for the perihelion shift. I find citing a vanity self-published 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 solar-system 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 Hafle-Keating experiments.

Garth
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May14-07, 01:15 AM
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Non-relativistic derivation of Schwarzschild's equation


Just as you can do a "hybrid Newtonian-SR" 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 Newtonian-SR" 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
shalayka
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May14-07, 04:41 PM
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Quote Quote by Garth View Post
Just as you can do a "hybrid Newtonian-SR" 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 Newtonian-SR" 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
The fact that you mention 1/6th is interesting to me. I once showed a precession method I had found to a trustworthy person, and they replied with a similar answer. Is this the same thing that you are referring to?


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 = 8.01124e-008

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 Misner-Thorne-Wheeler 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).
Chris Hillman
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May14-07, 04:55 PM
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Quote Quote by shalayka View Post
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:
Fer gosh sakes, shalayka (Shawn?), you're repeating the same weird mistake recently made by "Ian" in another thread, which I already corrected in that thread:
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 (weak-field) gtr.

Be this as it may, I agree with pervect that the book cited by Allison was self-published 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

In the book, "The Nature of Physical Fields and Forces" by Robert P. Masse,
a derterministic foundation for quantum mechanics is established. Has this
ever been done before?

Allison Johnston
http://physicsmathforums.com/showthread.php?t=2630
30 April 2007, 12:59 AM

In the book, "The Nature of Physical Fields and Forces" by Robert P. Masse,
Maxwell's electromagnetic equations for free space were derived from
classical elastisity theory alone. Has this ever been done before? Does it
argue for a physical medium for light to propogate in? Thoughts?

allison johnson
These are the only hits from Google!

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.
shalayka
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May14-07, 05:04 PM
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Quote Quote by Chris Hillman View Post
Fer gosh sakes, you're making the same weird mistake as Allison. As I already pointed out, circular orbits have no pericenter, so they can exhibit no precession.
Actually, I did mean circular orbit. It wasn't a mistake, it was a simplification.

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.
Chris Hillman
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May14-07, 05:28 PM
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Quote Quote by shalayka View Post
Actually, I did mean circular orbit. It wasn't a mistake
Too bad it's nonsense, then.

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.
ZapperZ
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May14-07, 05:46 PM
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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 off-topic.

Zz.


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