*Jgabase, I generally concur with your view of empty space in our gravitational world (our Universe) (I could add some detail and refinements to your concept of the elasticity and structure of empty space, but I will not get into that here), and I agree with you that the intrinsic energy density of empty space is a component of “dark matter” (although not the only one)—although some do not consider it as dark matter). Incidentally Jgabase, I know nothing about your background, but I sense your wonder about the Universe and about physics, and I sense that you have a inherent “feel” for physics--I know not whether such a “feel” for physics is genetic or acquired or what, but not everyone has it.
*Now for your new question: How could you prove or demonstrate the gravitational properties of a “infinite and uniform distribution of mass”?
*I took a look at the YouTube video you referenced. I concur with the reasoning presented there, but differ with its assumption that the Universe is infinite--but I am sure the reason he extended the mass distribution to infinity was to get around the boundary effects of the mass distribution, for at the boundary the distribution does have effects. In any case, we have reason to believe that the Universe is finite but unbounded (It is closed upon itself in its spatial dimensions but effectively open in the temporal dimension, if you will). If the video’s reasoning is applied to a finite but unbounded universe, it would show that any element of static mass in a universe in which the mass of the Universe is distributed uniformly throughout the Universe would suffer no gravitational forces from the rest of the Universe, until it is displaced. But this is what would be expected from the symmetry of the model.
*In any case, after watching the YouTube video you referenced, I think I have a little better understanding of what you are asking. Since the video is produced with the mass distribution of the Universe in mind, and with the idea that many of the gravitation forces of the Universe tend to cancel out because of symmetry, I propose that you take the word “infinite” out of your new question and add a reference to the Universe to make it read:
*If the mass of the Universe were uniformly distributed throughout the Universe, how would you detect or measure the gravitational properties of the Universe?
*With your indulgence, I will reply to your question as modified above. Incidentally, although there are lumps of mass scattered throughout the Universe, the average mass in the Universe is more or less uniformly distributed. Furthermore, as is generally conceded in the literature today, the amount of visible mass in the Universe is very small compared to the amount of unseen mass in the Universe, dark matter as it is usually referred to. The amount of rest mass in the Universe, seen or unseen, is also quite small compared to the amount of effective mass in it. And, as noted earlier, there is reason to believe that even if the Universe had no rest mass in it at all, that it would still have an effective mass due to the intrinsic energy density of empty space.
*The possibility of the intrinsic energy density of empty space comprising a major component of dark matter has been addressed in the literature. In fact, the YouTube video you referenced has another YouTube video entitled “The Mystery of Empty Space” on the same page in which Kim Griest, a physicist of the division of natural sciences at UCSD, is telling us that the energy density of empty space is a component of “dark matter”. (See the video entitled, “The Mystery of Empty Space” at:
http://www.youtube.com/watch?v=Y-vKh_jKX7Q&feature=channel). He is also telling us that if it exists, the expansion of the Universe will be increasing with time rather than slowing, and that experiments have recently been made in which it was unexpectedly observed that the expansion of the Universe actually is increasing with time, experiments that also measured the rate of acceleration of expansion. (The rest mass in the Universe would slow it. The reason that the energy density of empty space increases it is that the volume of space is increasing with the expansion.) These measurements enabled the researchers to go a step further and calculate the equivalent mass density of empty space, which turned out to be, according to Griest, about 10 to the -26 kilograms per cubic meter (which is about 1 proton mass per cubic foot). (There are questions in my mind about whether other sources of “dark matter” (and I know that there are other sources), which are technically not part of the energy density of empty space, are large enough to skew this result, but evidentially they are not). In any case, this is one experiment that has arguably “demonstrated the gravitational properties of the Universe”.
Note: I think the name of this research project, a coordinated effort made by astronomers from various telescopes about the world, was named “The Supernova Cosmology Project”, and that it was based at Lawrence Berkeley National Laboratory in California. It used data from the redshift of type IA supernovae in wide ranging galaxies to determine the expansion rate and acceleration of the expansion of the Universe.
*Einstein, by the way, included the mass density of empty space in the equations of his general relativity theory (which is actually a theory of gravity), a constant that he referred to as the now famous “Cosmological Constant”. Although he later regretted it, calling it his greatest blunder, because of the problems and complications it presented to his theory (it opened a can of worms so to speak)--but he was kind of stuck with it, it was something of a necessary evil, so to speak, for the theory is less complete without it--it has to be there. Physicists, however, have disagreed in the literature over what the value of the Cosmological Constant might be.
*Now let me show you something interesting (and I am telling you this in order to put some meat on the concepts we have been discussing). Empty space, as already noted, has certain physical properties, including springiness and inertia, and it momentarily compresses or stretches when an oscillating gravitational wave passes through it. The speed of transverse waves moving through media that possesses springiness and inertia (such as the speed of gravitational waves moving through empty space) is equal to the square root of the ratio of the springiness of the media (of space in its spatial dimensions) to its inertia (See, for example, chapter 3, pg 32 of the teacher’s edition of the fascinating little book entitled: Similarities in Wave Behavior, by Dr. John N Shive, director of education and training Bell Telephone Laboratories, Waverly Press, Inc., third printing 1964. (Springiness is designated by a spring constant, which gives the ratio of the force to the stretch). These physical properties of space (springiness and inertia) are directly related to Newton’s universal gravitational constant, and to a gravitational constant that is the gravitational analogue of the magnetic force constant in electromagnetism, and they can be written in terms of these constants). The speed of gravitational waves through empty space in terms of these gravitational constants is equal to the square root of the ratio of Newton’s gravitational constant to the gravitational analogue of the magnetic constant. Now although we have not physically detected or measured the speed of gravitational waves, there is reason to believe, on purely theoretical grounds, that the speed of gravitational waves is the speed of light.
*We can summarize all this as: S/I = G/M = c, where c is the speed of light, G is Newton’s gravitational constant, M is what I will call the “massnetic field” constant (the massnetic field is the gravitational analog of the magnetic field, and the “massnetic” field constant is the analog of the magnetic field constant), S is the spring constant that characterizes the springiness of empty space, and I is the inertia (or equivalent mass) of empty space. Now since both the ratios in this equality pertain to the gravitational properties of empty space, there is reason to believe that S corresponds to G, and I corresponds to M, in which case the constant M would be the inertia of empty space. So if the constant M were integrated over the volume of our entire Universe (remembering that this volume is finite), it would yield the total mass of our Universe (not including the rest mass in it, but which is believed to be negligible by comparison). In any case, M, which is the mass in a unit volume (a cubic meter of space) is the inertia of a cubic meter of space. Plugging in the known quantities, M is (7.421 X 10 to the -28) kilograms/cubic meter. If this reasoning is correct, then this is the effective mass per unity volume of empty space in our gravitational universe.
*Comparing this result to the equivalent mass density of empty space obtained by the researchers in their “expansion of the Universe” measurements cited above, we see that this is within approximately an order of magnitude of their value. Surprisingly close, when you consider that the value that Kim Griest gave in his video was an order of magnitude approximation of what the researchers calculated, and when you consider that he said that the equivalent mass of the empty space of the Universe was about twice that of the dark matter in it, which could cause it to be off by as much as half—I do not have copies of the original paper to see if more accurate numbers are available).
*Now let me show you something else that is very interesting. Realizations of Mach’s theory that enable us to derive interactions between local mass and the mass of the Universe yields a fascinating relationship between the total mass of the Universe and the radius of the Universe (remembering that the Universe is finite in both its volume and in its mass). See, for example, the paper “On Possible Realizations of Mach’s Program”, by F.A. Kaempffer, “Canadian Journal of Physics”, Vol 36 (February 1958). This is one of best papers I have seen on Mach’s theory, it is straight forward and easy to understand, and it covers the progress in the field to the date of publication. And I highly recommend it. In it, Kaempffer derives Newton’s second law for linear acceleration and also for rotational motion from Mach’s program. The derivation exactly yields Newton’s law if and only if the ratio of the total mass of the Universe to the radius of the Universe is equal to a constant, namely to c squared divided by G, where c is the speed of light and G is Newton’s universal gravitation constant.
This only gives the ratio of mass to radius, and not the actual mass or radius, but the equation from which this came is [4(pi)G(ro)(R squared)/3(c squared)] = 1, where ro is the mass density of the Universe, G is the universal gravitational constant, and R is its radius, which relates the mass density of the Universe to its radius. And we already determined the mass density of the Universe to be (7.4210 X 10 to the -28 kilograms per cubic meter), and plugging it into this equation we get R = 6.584051073526e+026 meters (or 6.959495e+10 light years).
Note: the radius of the Universe has also been calculated from Einstein’s general theory of relativity, also using a spherical model of the Universe. And the expression used to derive this Einstein radius (the radius of curvature of space in Einstein’s universe), an expression that came out of Einstein’s general theory, is identical to the Machian expression given above except that the 3 is missing from the denominator. As a result, the “Einstein radius” would differ from that derived above by a factor of three, all else being equal. Both derivations give a radius for the Universe on the order of 10 to the 10 light years.
Note: there is one caveat to the Mach theory paper: since the authors of this paper had to assign a geometry and mass distribution to the Universe for the purpose of making their calculations, they arbitrarily assumed that the mass of the Universe was essentially uniformly distributed over a sphere (just as was done for the Einstein radius calculations from the theory of general relativity). We know that the mass of the Universe is indeed essentially uniformly distributed, but that it is not a sphere, so their expression for the ratio of the mass of the Universe to its radius may be off by a numerical factor. But this is no big problem, for the geometry does not negate the argument, and we can always come back later, plug in the correct geometry, and recalculate to get the exact results.
In conclusion, the numbers discussed here are subject to change as the model of the Universe used in the calculations changes and so on, but the relationships discussed here are what is important. What I am trying to point out here is that our gravitational Universe is finite but unbounded, that the empty space in it (and therefore the Universe itself) has properties like springiness and inertia that can be measured and used to determine the total mass and radius of our universe, that our Universe would possesses an intrinsic energy and effective mass even if there were no rest mass in it, and that the ratio of the mass of our Universe to its radius is a constant. And in the process, I hope to have demonstrated how you can detect or measure the gravitational properties of the Universe.
