Relativistic Universal Law .......... [Archive]

wavelength

May15-04, 02:47 AM

Gordon D. Pusch

May17-04, 05:05 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n"wavelength" <wowsers@odsy.net> writes:\n\n> Following up on John Schoenfield\'s idea I have a new modification\n> which I propose is a relativistic correction to Newtons\'s Universal Law\n> of Gravitation -\n>\n> Fg = G m1 M2/ r^2\n>\n> where\n>\n> M2=m2/sqrt(1-(v^2/c^2) with v relative to the m2 IRF ( m1 considered to be\n> at rest v=0 )\n>\n> and m1 is understood to be in a IRF\n>\n>\n> so that the proposed law becomes\n>\n> Fg = G [ m1 { m2/sqrt(1-(v^2/c^2) } / r^2 ]\n>\n> Comments ?\n\nThe most obvious comment is that your force is not symmetric under\nthe interchange of suffix `1\' and suffix `2\'; hence, you have built in\nan explicit violation of Newton\'s 3rd Law of Motion, i.e., conservation\nof momentum, at second order in (v/c), i.e., at the same order at which\nrelativistic effects have already been observed in planetary and satellite\nmotion. Conservation of momentum is very well tested, and satisfied to a\nhigh degree of precision (for example, the recoil of the Sun in response\nto planetary gravitation must be taken into account in order to calculate\neven the "newtonian" portion of planetary motions), and your proposed force\nviolates it.\n\nThe second one is that both `r\' and `v\' are frame-dependent quantities,\nso your force is not well-defined until you have specified how `r\' and `v\'\nare to be determined, and have shown that the result yields a force that\ntransforms properly under change of frame of reference. You will find\nthat no such force can be constructed within the framework of Einstein\'s\nSpecial Theory of Relativity, which is one of the many reasons why\nflat-spacetime theories of relativistic gravity had to be abandoned\nin favor of curved-spacetime theories. (Some of the other reasons are that\nBonner\'s Theorem proved that the observation of gravitational time-dilation\nrequires that space _also_ be curved, or inconsistencies would result;\nalso, the observation of gravitational deflection of starlight at\n"double the naive newtonian value" also requires spatial curvature.)\n\nThere are many other reasons why such naive "force based" attempts at\nconstructing a relativistic generalization Newton\'s Law of gravitation\nare doomed to failure, because they are either self-inconsistent and/or\nfalsified by experiment, and they are discussed in some of the better\ntextbooks on General Relativity.\n\n\n-- Gordon D. Pusch\n\nperl -e \'\\$_ = "gdpusch\\@NO.xnet.SPAM.com\\n"; s/NO\\.//; s/SPAM\\.//; print;\'\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>"wavelength" <wowsers@odsy.net> writes:

> Following up on John Schoenfield's idea I have a new modification
> which I propose is a relativistic correction to Newtons's Universal Law
> of Gravitation -
>
> Fg = G m1 M2/ r^2
>
> where
>
> M2=m2/\sqrt(1-(v^2/c^2) with v relative to the m2 IRF ( m1 considered to be
> at rest v=0 )
>
> and m1 is understood to be in a IRF
>
>
> so that the proposed law becomes
>
> Fg = G [ m1 { m2/\sqrt(1-(v^2/c^2) } / r^2 ]
>
> Comments ?

The most obvious comment is that your force is not symmetric under
the interchange of suffix `1' and suffix `2'; hence, you have built in
an explicit violation of Newton's 3rd Law of Motion, i.e., conservation
of momentum, at second order in (v/c), i.e., at the same order at which
relativistic effects have already been observed in planetary and satellite
motion. Conservation of momentum is very well tested, and satisfied to a
high degree of precision (for example, the recoil of the Sun in response
to planetary gravitation must be taken into account in order to calculate
even the "newtonian" portion of planetary motions), and your proposed force
violates it.

The second one is that both `r' and `v' are frame-dependent quantities,
so your force is not well-defined until you have specified how `r' and `v'
are to be determined, and have shown that the result yields a force that
transforms properly under change of frame of reference. You will find
that no such force can be constructed within the framework of Einstein's
Special Theory of Relativity, which is one of the many reasons why
flat-spacetime theories of relativistic gravity had to be abandoned
in favor of curved-spacetime theories. (Some of the other reasons are that
Bonner's Theorem proved that the observation of gravitational time-dilation
requires that space _also_ be curved, or inconsistencies would result;
also, the observation of gravitational deflection of starlight at
"double the naive newtonian value" also requires spatial curvature.)

There are many other reasons why such naive "force based" attempts at
constructing a relativistic generalization Newton's Law of gravitation
are doomed to failure, because they are either self-inconsistent and/or
falsified by experiment, and they are discussed in some of the better
textbooks on General Relativity.

-- Gordon D. Pusch

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