Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Math Forum
»
Discussions
»
sci.math.*
»
sci.math
Notice: We are no longer accepting new posts, but the forums will continue to be readable.
Topic:
Mach's principle, today?
Replies:
3
Last Post:
Aug 23, 2013 3:34 PM



hanson
Posts:
1,651
Registered:
12/13/04


Re: Mach's principle, today?
Posted:
Aug 19, 2013 11:06 PM


"RichD" <r_delaney2001@yahoo.com> wrote: in message news:05496b8ed2e24811b95f91c0566790d4@googlegroups.com... > What is the modern interpretation, if any, of Mach's principle? > [....] > hanson wrote: Here's a repat of a post abiut that, from the "good old days" ca in s.p.: > There are volumes of quarrels over the meaning of Mach's principle, mostly of a qualitative to philosophical nature. I personally like a view which yields some quantitative insight and interpretation: Re: Mach: "hanson" <hanson@quick.net> wrote in message news:Hwiw7.11219$3i3.1241782@newsread1.prod.itd.earthlink.net... > "Paul Lutus" <nospam@nosite.zzz> wrote in message news:5Auv7.116007$hh.10028621@bin1.nnrp.aus1.giganews.com...in thread Re: One = Zero ? > [Paul] Ernst Mach once proposed that inertia (and therefore gravity) was an interaction between a particular mass and all the rest of the mass in the universe. This is an interesting idea, now called "Mach's Principle," unfortunately it is as remote from meaningful verification now as it was when it was first proposed. > [hanson] ....and said Mach: "when the subway jerks, it's the fixed stars which throw you down".  Difficult to verify experimentally, yes, but Mach's Principle can be demonstrated easily in a quantitative equation. Take the crudest, most trivial cosmological equation(s) which connect gravitation, Mass, Radius, Time (1/Hubble) and the speed of light with each other. This "cosmic 1234 power envelope" or whatever you wanna call it, says: c = (G*M*R^1)^(1/2) = (G*M*H)^( 1/3) = (G*M*b_R)^(1/4)
(c=lightspeed, G=Newton, R & M= observable radius & mass universe, H=Hubble, and b_R = a residual acceleration or tension of space in 3D due to the mass density rho_u = H^2/G), and use the last term and write > c = (GMb_R)^(1/4). > Then set b_R as F/m, the acceleration for this Force F caused by the cosmic mass totality M onto any test mass m and write
c^4 = GM F/m and reshuffle it as > F = m (c^4/GM)... (Mach's Principle Equation), > where this residual/basic cosmic acceleration, c^4/GM, may be seen as Mach's inertia principle, quantified, stating that the entire Mass of the universe maybe acting gravitationally onto any test mass, perhaps with a velocity of c^4, the Gravitational **feeler** speed at ~ 8E+41cm/sec. It really does show that "when the subway jerks, it's the fixed stars (M) which throw you (m) down", albeit not instantaneously but with the considerable speed of the forth power of the speed of light.
Numerically, the residual/basic cosmic acceleration b_R = c^4/GM yields ~8*E08 cm/s^2 with the currently accepted value of M. This minute acceleration value is ~ some 10 billion times smaller than the acceleration caused by the earth onto test masses with its g ~ 980 cm/s^2.
This 10 billion times weaker force is indeed difficult to measure experimentally. But with LIGO and VIRGO we may get into the realm where it could be nailed down. Another aspect of this Machian subject, F = m (c^4/GM), touches onto the nonKeplerian velocities observed in galactic rotations and a first effect of this may actually already have been measured in the Pioneer 10 anomaly:
[hanson, Friday, August 30, 2002 9:18 PM, sci.astro,sci.physics] "The Apparent Anomalous, Weak, LongRange Acceleration of Pioneer 10 and 11": > > [hanson] [I cite from the paper by John D. Anderson: http://arxiv.org/abs/grqc/0104064 " an apparent anomalous acceleration is acting on Pioneer 10 and 11, with a magnitude a_P ~ 8 x 10^{8} cm/s^2, directed towards the Sun (Anderson, Moriond). Much effort has been expended looking for possible systematic origins of the residuals, BUT NONE HAS BEEN FOUND.] > But, Mach's principle and the above b_R, maybe a simple reason and cause to explain this phenomena: For the Pioneer anomaly c = (G*M*br)^(1/4) is applicable as br = c^4/GM and this b_R, like John's Gx has the dimensions of L/T^2, an acceleration. Plugging in heuristic number estimates for M ~ 1.5e+56gr does yield b_R ~ 8.1e8 cm/s^2, which is within the range of Anderson's a_P = (8.74 +/ 1.33) x 10^{8} cm/s^2.
It is fascinating to speculate about that this b_R may eventually "stop" Pioneer 10/11 in intergalactic space and confine it to a position dictated by the gravitational constrains of the mass of the next "nearby" galaxies to then take up its "fixed" star place/position like all the other heavily bodies do, when viewed from sufficiently far away. > [2013 addon by hanson] Relate to, that Mach's principle depends on all other gravitational mass with the accessible universe, also touches and becomes manifest in Prokhov's 1970 suggestion that, the density (rho) of atoms in free (cosmological) space and the size of the Hubble constant H explain Gravity simply as being _ G = H^2 / rho  > This equation adds to the uncertainty of what is really going on in the cosmos. If G is not a fixedsized unalienable constant then the Hubble constant H & the large scale cosmic mass density rho can assume any value...... and all bets are off. > But if "G" IS numerically fixed, then the Hubble constant is a welcome measure of the cosmic mass density rho, and the scenarios that the universe expands are just brain farts. > As always, all these cosmological dreams are producing a living for a precious few folks in academia only. For the rest of the folks, they are beautiful fantasies, but they will not buy you a single crumb of bread and have the potential to get you fired for being a lunatic... ahahahaha...



