Inertial dependence upon local matter

[yogi]

I came across this quote recently:

"The general theory of relativity teaches that the inertial mass of a given body is greater as there are more ponderable masses in proximity to it; thus it seems very natural to reduce the total inertia of a body to interactions between it and the other bodies in the universe, as indeed, ever since Newton's time, gravity has been completely reduced to interaction between bodies. The results of calculation indicate that the universe would necessarily be spherical. (Einstein, 1954)"

Did Einstein really say this, and if so, is there a quantative connection between nearby matter and the inertial reactance of an accelerated mass predicted by GR?

Is there any experimental validation?

 

[JesseM]

I came across this quote recently:

"The general theory of relativity teaches that the inertial mass of a given body is greater as there are more ponderable masses in proximity to it; thus it seems very natural to reduce the total inertia of a body to interactions between it and the other bodies in the universe, as indeed, ever since Newton's time, gravity has been completely reduced to interaction between bodies. The results of calculation indicate that the universe would necessarily be spherical. (Einstein, 1954)"

Did Einstein really say this, and if so, is there a quantative connection between nearby matter and the inertial reactance of an accelerated mass predicted by GR?

Is there any experimental validation?

It looks like your source got it slightly wrong--this page has a somewhat different version of the quote (differences in bold) and says it's from 1921, not 1954. I'll include the previous paragraphs for some context:

It appears less problematical to extend the concepts of practical geometry to spaces of cosmic order of magnitude. It might, of course, be objected that a construction composed of solid rods departs the more from ideal rigidity the greater its spatial extent. But it will hardly be possible, I think, to assign fundamental significance to this objection. Therefore the question whether the universe is spatially finite or not seems to me an entirely meaningful question in the sense of practical geometry. I do not even consider it impossible that this question will be answered before long by astronomy. Let us call to mind what the general theory of relativity teaches in this respect. It offers two possibilities:

1. The universe is spatially infinite. This is possible only if in the universe the average spatial density of matter, concentrated in the stars, vanishes, i.e., if the ratio of the total mass of the stars to the volume of the space through which they are scattered indefinitely approaches zero as greater and greater volumes are considered.

2. The universe is spatially finite. This must be so, if there exists an average density of the ponderable matter in the universe that is different from zero. The smaller that average density, the greater is the volume of the universe.

I must not fail to mention that a theoretical argument can be adduced in favor of the hypothesis of a finite universe. The general theory of relativity teaches that the inertia of a given body is greater as there are more ponderable masses in proximity to it; thus it seems very natural to reduce the total inertia of a body to interaction between it and the other bodies in the universe, as indeed, ever since Newton's time, gravity has been completely reduced to interaction between bodies. From the equations of the general theory of relativity it can be deduced that this total reduction of inertia to interaction between masses—as demanded by E. Mach, for example—is possible only if the universe is spatially finite.

I'll leave others to comment on what he means when he says that stuff about inertia, but one result already seems outdated--he claims that the universe can only be spatially infinite if the average density of mass/energy is zero, meaning that most of the matter is concentrated in a small region of an asymptotically flat (empty) universe. I suppose this is because the quote was from before Hubble's 1929 measurements of redshifts which provided evidence for an expanding universe, so that Einstein was still only considering a static universe in the quote.

 

[yogi]

Thanks Jesse - the fact that the author of the post attributed it to 1954 was doubly troubling - it sounds totally Machian - which Einstein had substantially discounted even by 1917. It also seems that it is w/i experimental means to verify - for example an experiment could be conducted to measure inertia at the point between Earth and moon where the net gravity is zero.

Any other thoughts

Yogi

 

[gamburch]

Yogi: Let me give you some food for thought. One can calculate the average desnity of matter in the universe and a value has been given by Peebles. In addition the Hubble constant is known. The potential from a gravitationg body has the units of speed squared. One can thus compute the potential of all the universe that one can see at a nearby point. Guess what? It turns out to be very near the speed of light squared. Is this experimental confirmation or coincidence? I'll send you the references if you are interested.

 

[yogi]

Gamburch - yes - I am interested.

 

[gamburch]

Instead of attempting to compute the potential caused by each mass in the Universe, as seen by the particle, we shall assume the mass in the Universe can be smoothed out to a constant density d. Then, assuming the measured expansion rate of the universe and its estimated density, we find that kMo/Ro = xSq, where k ( = 6.670 x 10(-8) (cm.3/gm.sec2)) is the gravitational constant, (Handbook of Chemisrty and Physics (CRC Press, Boca Raton, FL, 1981) p F-97) , Mo is the mass of the universe, x is the gravitational potential, and Ro is the diameter of the universe. The gravitational potential has units of (cm/second)Sq. We used 13.5 billion light years for Ro (from the popular press, which yields the Hubble constant) ) and for d we used 1.88 x 10-29 gm/cm3, which value we have lifted from an article by P.J.E. Peebles. (P.J.E. Peebles in Temth Texas Symposium on Relativistic Astrophysics, Edited by Reuven Ramaty and Frnak C. Jones (New York Academy of Sciences, New York, NY,1981) p. 157). Performing the calculation we see the result is given by x = 3.585 x 10(+8) meters per second. This number is remarkably close to that of the speed of light.

Near a body the potential would be c Sq + 2km/r. To a distant (from the body) observer the time dt' between events dt (seconds per cycle) would thus be seen as dt' = dt(1+2km/rcSq), just like in the books.

 

[gamburch]

Pardon me xsquared is the gravitational potential.

 

[yogi]

Thanks Gamburch - I see what you have in mind - this relationship has always been a fundamental mystery of cosmology - Einstein commented upon the fact that there must be some deep significanc to the fact that GM/Rc^2 was approximately unity.

Some years ago I used this fact to derive an expression for the Gravitational parameter G based upon the expansion of the Hubble sphere

Regards

Yogi