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Topic: Mach's principle, today?
Replies: 3   Last Post: Aug 23, 2013 3:34 PM

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Registered: 12/13/04
Re: Mach's principle, today?
Posted: Aug 19, 2013 11:06 PM
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"RichD" <> wrote:
in message
> 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" <> wrote in message
> "Paul Lutus" <nospam@nosite.zzz> wrote in message
news:5Auv7.116007$ thread
Re: One = Zero ?
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.
....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
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
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

Numerically, the residual/basic cosmic acceleration b_R = c^4/GM
yields ~8*E-08 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

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 non-Keplerian 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, Long-Range Acceleration
of Pioneer 10 and 11":
> > [hanson]
[I cite from the paper by John D. Anderson: " 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
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 ~ 8.1e-8 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 fixed-sized 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...

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