Ernst Mach, a man to who influenced Albert Einstein significantly in his approach to relativity, did not quite seem to believe in space as a self-existing entity. I'm pretty sure it would be correct to say he thought it was created by matter.

So let's take that idea for a moment and run with it. Wouldn't the idea that matter creates space unavoidably create testable predictions about the nature of how forces work, especially over astronomical distances?

I say this because from my admittedly information-centric perspective, the only way matter can create something approximating what we call space is by creating relationships between particles. Space would then become nothing more than a particular set of rules for how those relationships interact and change over time, capturing for example the idea that they have locality and interact based on rules such as the $\frac{1}{n^2}$ fall off of some forces with distance. With large enough sets of particles, the resulting interactions would become sufficiently smooth and fine-grained to create the abstraction we call space. But Euclidean space as we know it would necessarily be an illusion. (Incidentally, I have no idea if this line of thinking might be related to holographic universe ideas.)

Now, the interesting thing about that argument is this: If one assumes as an experimental hypothesis that matter creates space, I don't easily see no way around the implication that the idea should be testable, at least in principle. That's because a simulation of smooth space created by the particle interactions will necessarily be incomplete and dependent on the distribution of those particles.

So for example, if you only had a universe of two particles, only one space-like relationship would exist. The resulting simulation of space could not possibly be as smooth or rich as the space we know while sitting at the Euclidean limit of a nearly number of particles and particle relationships. It would for example likely have some sort of predominantly one-dimensional field equations, e.g. a the universe with only one electron and one positron might maintain constant attraction between them regardless of their separation distance. (It's also interesting to note that constant 1D-like attraction is approximately how quarks behave when pushed far away from short-range asymptotic freedom envelopes.)

Detecting deviations from the Euclidean limit would be hugely more difficult in our particle-rich universe, but I cannot easily see how it would be flatly impossible. Asymmetries of matter at the scale of the entire universe would for example have to affect the nature of space by creating asymmetries in the number and richness of the underlying particle relationships. If a precise model could be made for how such relationship asymmetries affected our local space abstraction, testable predictions would be possible. The first approximation in any such model would simply be to map out the density and orientation of the relationships based on our best guesses at particle distributions, then see if those relationship sets correlate strongly to any known effects.

The unexpected and quirky distribution in dark matter could certainly be a candidate for such an effect. Again, as an information type I take high correlations pretty seriously, and some of curve fits between certain galactic phenomena and predictions made by the oddly simple MOND rule remain poorly explained at best. If such correlations somehow stemmed from asymmetries in space itself due to large-scale asymmetries in the galaxy-scale distribution of particles, a very different approach might be possible to explaining why the MOND rule sometimes produces such unexpectedly strong curve correlations.

So again, the question is just this: Has the possibility of testing the Machian hypothesis every been explored theoretically? And if not, why not? What am I missing?

(This question is a direct outgrowth of my earlier amusingly unproductive question about whether space exists independently of matter. For that one I received exactly one "yes" answer, exactly one "no" answer, and no up or down votes on either one. Flip a coin indeed!)

  • $\begingroup$ Ron's answer here contains some useful background (not a direct answer to your question though) $\endgroup$
    – twistor59
    Feb 22, 2013 at 7:53
  • $\begingroup$ I remember that answer! It got me looking into S-matrix theory a bit, which I had previously ignored as mostly an interim historical artifact. Ron, I'm sure you're out there. I'd be interested to hear your thoughts on this one, though I realize (and respect) that you are not actively participating in Physics SE these days. $\endgroup$ Feb 22, 2013 at 13:39
  • $\begingroup$ duplicate of physics.stackexchange.com/q/5483/4552 $\endgroup$
    – user4552
    Jun 3, 2013 at 2:03
  • $\begingroup$ Wow, that was some deep scouring! My original intent in that was more focused on fundamental limits of particle interactions for very small numbers of particles. I more-or-less assumed that to be Machian, so I described it that way. Your answer there is quite nice. The fact that Dicke co-wrote the B-D paper is intriguing; I was introduced to his work recently for his more flexible analytical framework for optical-scale Mossbauer, which I think only NIST currently has sufficiently precise equipment (Wineland et al) to detect experimentally. Can GR exist with very small particle counts, though? $\endgroup$ Jun 3, 2013 at 2:32
  • 2
    $\begingroup$ For once (or maybe the second time) in my life, I'm going to disagree with @Ben Crowell in terms of duplicates. The linked question is certainly related, but it asks for a yes/no result, while this asks for an explanation of how a measurement can be possible. Even though Ben Crowell's (excellent) answer addresses this, one can go broader here and say something like "there are other ways this test can be done" or "actually, here is a proof B-D theory is the only way to quantify Mach's principle." I at least am hoping for something deep like that. $\endgroup$
    – user10851
    Jun 6, 2013 at 4:28

2 Answers 2


Just my 2¢; the number of pairwise relationships between $N$ particles scales like $N^2$. Pairwise relationships (i.e., the distance from A to B) don't uniquely define spatial arrangement, so a somewhat larger set of relationships exist. For the universe, $N$, the number of relatable "objects" is large. Measuring the effect from one additional or one fewer particle on the whole would be an effect on the order of $1/N$, which is probably too small to measure, even if we had some idea of how.

  • $\begingroup$ No disagreement; in fact, the very smoothness of space would seem to require that sort of scaling. Yet if space works that way, I would suspect consequences of some sort. With the exception of some of the holographic ideas (anyone?), I'm not aware of that kind of analysis. I am mostly intrigued that the Machian hypothesis may not be just as matter of abstract philosophy, but might actually have testable implications, even if performable tests turn out to be only in principle. $\endgroup$ Feb 22, 2013 at 4:35

Although Ernst Mach was a big influence on Einstein, to get started and to shape the way Einstein expressed his initial researches on Relativity, the two men are quite different. For example, Einstein's equally important work on Statistical Mechanics was totally opposed to Mach's point of view. Einstein slowly drifted away from Mach's point of view in Relativity also. Mach's principle states that inertia is the product of the relation between a mass and the fixed stars...this has been abandoned, and is not at all part of General Relativity.

Space-time is certainly "physical" in that it has physical meaning.
But Einstein thought that space--time did not "exist" in the same sense that matter exists. So it is not created, either. Einstein concluded that space--time did not exist, rather, massive objects are "spatially related": the concepts of space--time are what we use to express physical relations between things that physically exist (including massless photons, of course). It has been said that the attitude change from Newtonian absolute space and absolute time to Einsteinian General Relativity is that in Newton's system, if all matter ceased to exist, space--time would still exist. But in Einstein's system, if all matter ceased to exist, space--time also would not exist. But this is just "talk": it is not Physics.

You have to define your terms.
What do you mean by "create" ? If we say that a gamma ray "created" an electron--positron pair, we know what we mean. But even there, it is not precise: in Feynman's world-line picture, this creation of a pair can equally well be seen as an electron travelling backwards in time gets scattered off the gamma ray and bends back to travel forwards in time.
Thus, no creation. This shows that the terms "creation" (and, I would claim, also "exists") have not been given a really logical definition. Until they are given clearcut definitions in terms of physical theory, and given definite unambiguous operationalisations in terms of experimental practice, your question is ill-defined and cannot be given a clear enough meaning to test experimentally.

I claim that they can never be given a clear meaning or tested experimentally. Part of my eidence for this claim is the Feynman re-interpretation of pair production, above. Other evidence, for me at least, is that in mathematical logic, the notion of "existence" cannot be clearly defined (there are non-standard interpretations of the existential quantifiers). I think this is why Wittenstein, educated as an engineer and interested in the reasons why Logic had applications to science, decided to banish the word "exists" from his treatment of logic. (Discussion omitted here.)


That said, one of the major difficulties in fundamental theoretical Physics, according to J.S. Bell, is that in Quantum Mechanics, the abstract axioms make perfect sense for a massive particle without using the concepts of space. (Only time.) And the phase space for a multi-particle system even if you build it on spatial coordinates, has lost touch with real three-dimensional space. But General Relativity is definitively tied to space-time coordinates. This difference in look-and-feel was, for him, a bad augur for unifying them. In Quantum Mechanics, you can talk about quantum systems without mentioning space and time....


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