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What expands if there's no rubber?

  1. Apr 22, 2007 #1


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    A famous Einstein quote:
    “Dadurch verlieren Zeit & Raum den letzter Rest von physikalischer Realität. ..."

    Thereby time and space lose the last vestige of physical reality”.

    for an online source see page 43 of

    This source includes two versions:

    117 In the introduction of the paper on the perihelion motion presented on 18 November 1915, Einstein wrote [color=blue]about the assumption of general covariance[/color] “[i]by which time and space are robbed of the last trace of objective reality[/i]” (“durch welche Zeit und Raum der letzten Spur objektiver Realität beraubt werden,” Einstein 1915b, 831).

    In a letter to Schlick, he again wrote about general covariance that
    “[i]thereby time and space lose the last vestige of physical reality[/i]” (“Dadurch verlieren Zeit & Raum den letzter Rest von physikalischer Realität.” Einstein to Moritz Schlick, 14 December 1915 [CPAE 8, Doc. 165]).

    To summarize, both quotes are from Nov-Dec 1915, one is from a paper on perihelion motion and the other is from a letter to Moritz Schlick a few weeks later.

    Some may wish to comment and tell us what they think it is Einstein meant to say. I include the quotes to highlight an ontological issue---the issue of What is really There:smile:---that comes up in connection with general covariance. (EDIT Just to be extra clear: [color=blue]general covariance is Einstein's term for what is nowadays often called [i]diffeomorphism invariance[/i], a consequences of which is my main concern in this thread.[/color])
    Last edited by a moderator: Apr 22, 2017
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  3. Apr 22, 2007 #2


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    Apparently in General Relativity spacetime does not have physical existence---is not an objective reality.

    I think the way students of GR often think of this is there is a CONTINUUM or 4D differentiable manifold which is not assumed to be physically real but rather to be a mathematical convention set up so that one can define the METRIC on it.

    People may sometimes equate the metric with the "gravitational field" but the latter involves going a step further---it is a class of equivalent metrics: two metrics are equivalent if either and its associated material can be morphed into the other.

    What is really there? Perhaps you could say that it is the gravitational field itself that is there.

    We can see language developing severe problems here. If what is really there is the gravitational field and if all one can say about it is that it is "an equivalence class of metrics under diffeomorphism", then how to communicate with a layperson?

    what is the gravitational field, in lay terms? could one say it is geometry? or a web of geometrical relationships?

    I think it makes us apt to come full circle in an attempt to communicate and to start calling the gravitational field "space" or "spacetime".

    If we come around full circle, in the use of words, then we start with Einstein telling us that points of spacetime have no physical meaning and the confinuum is not objectively there----what is there? the gravitational field---and what is that? the geometry of spacetime----ah!

    So we are back to spacetime, the only difference is that it is not thought of (if it ever was) as some material like rubber.

    It is instead a web or compendium of relationships.
    A web of geometric relations pertaining between the diverse crud of events.

    Not terribly satisfactory, perhaps. Does anyone feel inspired to tell us the right words to use?
    Last edited: Apr 22, 2007
  4. Apr 22, 2007 #3
    I think he said it extremely well. My thought would be "All of space-time is a dimensionless point, we can not measure it directly, and we only measure the movements of particles, relative to us, within it."
  5. Apr 22, 2007 #4


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    At PF Cosmo forum we are roughly at a lay/pro interface in language and I'm going to try to delineate a language problem that interferes with understanding at that interface.

    here is a chart relating the scalefactor ratio anow/athen, the redshift z, approximate temperature of CMB, and estimated time in Myr (millions of years) since Planck era.

    Code (Text):

    size ratio  redshift z   T[sub]CMB[/sub] in Kelvin       age in Myr
    1024          1023              2800                      0.42
    512            511              1400                      1.3
    256            255              700                       4.0
    128            127              350                       11.7
     64             63              175                       33.7
     32             31              87.5                      96.4
     16             15              ~44                       274
      8              7               ~22                      778
      4              3               ~11                      2190
    Just for continuity of perspective, the figure 2190 million years refers to when the universe's age was 2.19 billion, that is some 11.5 billion years ago. The point I'm making is that for the lay questioner I have in mind this parallel expansion of scalefactor and wavelength epitomizes much what we know about the universe.
    Since the time corresponding to z = 1023, it has expanded 1024-fold and in the course of this expansion the wavelengths of CMB light have expanded 1024-fold, making the CMB "cooler" by the same ratio.


    Wavelengths have gotten longer exactly in proportion as "space has gotten larger" or as the scalefactor a(t) has increased.

    I have warned (as have quite a few others here) against using the stretchy rubber analogy because it can give the misleading impression that
    1. space behaves like a physical substance, namely rubber, and
    2. the physical process by which wavelengths are extended as waves propagate thru space is analogous to "stretching" of squiggles painted on a sheet of rubber.
    I was warning against these misconceptions as recently as a few weeks ago, and noticed what seemed like a big emphatic condemnation of them from several posters even more recently than that!

    (Actually I don't recall hearing anyone employ the stretchy rubber analogy lately, I only recall hearing it condemned.:smile: Beating the absent horse. )

    The actual physical process by which waves are cooled as they propagate through typical regions of space is evidently quite different from the stretching of rubber. For this discussion we don't have to discuss how we imagine that process. People differ as to how they imagine it. Different mental pictures are apt to come down to the same mathematics. Pervect cited a nice textbook explanation from MTW---I recall one from a textbook by Frank Shu of UC Berkeley Astronomy that I read some years back and thought pretty intuitive.

    The first priority I think is to make the obvious observation that SOMETHING EXPANDS.

    People get very touchy about the word 'expands' because they want to stay miles away from suggesting that space is a material. Well, that's good. Then make it clear to the reader that it is not a material.

    The thing that expands can be completely insubstantial! It can be an immaterial web of geometric relations, and one can be highly explicit about this. But one obvious thing---a cardinal fact of modern cosmology---which one should be able to assure laypeople about, is that something embodying the scale factor expands. And in the vast bulk of space---where the geometry is not dominated by coagulated clustering---as electromagnetic waves propagate they are constantly being extended in step with the scale factor.
    Last edited: Apr 22, 2007
  6. Apr 22, 2007 #5


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    My $.02.

    Talking about the "reality" of space is basically philosophical. First you have to decide what "reality" is.

    If the question of the "reality" of space is not philosophical, there must be some experiment via which it can be tested, or some more precisely defined property that can also be tested by experiment.

    If there is no experiment that can test whether or not space is "real", it shouldn't be too surprising that one can argue about the matter indefinitely (as with most philosophical issues). This is IMO a direct consequence of non-testability.
  7. Apr 22, 2007 #6


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    I do too

    [tex]\mathfrak{Dadurch \ verlieren \ Zeit \ und \ Raum \ den \ letzter \ Rest \ von \ physikalischer \ Realitaet.}[/tex]
    Last edited: Apr 22, 2007
  8. Apr 22, 2007 #7


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    That is a good point. And in this case isn't the appropriate philosophical context what Einstein was talking about? That is the General Covariance feature of General Relativity and the consequent physical meaninglessness of spacetime points as sketched for instance in the Wikipedia article on The Hole Argument


    The Wikipedia discussion of General Covariance borrows a couple of the figures from
    Last edited: Apr 22, 2007
  9. Apr 22, 2007 #8


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    the story is fascinating and dramatic. From 1912 thru 1915 Einstein was in a RACE against David Hilbert (the top mathematician of that time) to find a geometrical theory of gravity.

    In 1912 Einstein had the essentials of GR but was stopped cold by the fact that its General Covariance (aka diffeomorphism invariance) feature deprived spacetime points of physical meaning.

    He agonized over this for 3 years, while frantically searching for a theory that would NOT have diffeo-invariance or General Covariance---knowing that Hilbert might get there first.

    Finally in 1915 he decided that it was ALL RIGHT for space and time to be objectively non-existent-----what mattered was events, places where worldlines cross, coincidences, material interactions. The geometrical relations between empty points dont have to be determined----only the geometrical relations between EVENTS are significant.

    So he published in 1915.

    Nowadays I believe we admire the diffeomorphism invariance of GR as something elegant. What worried Einstein so much is now seen as a positive feature.

    this is just a rough sketch of the story and may contain inaccuracies. I read it some years back in Rovelli's book Quantum Gravity, and it seems to correspond to what is in this Wikipedia article. but maybe someone else can correct details as needed.
  10. Apr 22, 2007 #9
    I fully agree. I would go one step further and say that the burden on proof is on those who claim the existence of space.

    In general relativity there is no need to postulate space, basically there are four arbitrary spacetime variables. Nowhere in the theory is defined what these four variables mean physically. Together however those four variables are related to how much proper time is measured. In a way one can think of general relativity as a chronometric rather than a geometric theory.

    With regards to the "expansion of space" in FRW familiy solutions, nothing in those solutions indicate what part space is either (actually it logically follows). Of course, many like to equate the hyperplane of constant proper time as space. If you want to call that "space", ok, but just because you define it as such does not make it physical.

    Classically, as opposed to quantum mechanically, there is really no need for calling something space, all we have is particle paths and intersecting light signals. All the stuff "in between" is simply not physically measurable. And clearly it is useless to claim that something exists if you cannot measure it. Since we are quoting Einstein, this is what he wrote about space in one of his letters to Mach:

    ''For me it is an absurdity to ascribe physical properties to “space.” The totality of masses generates a guv-field (gravitational field), which in turn governs the unfolding of all events, including the propagation of light rays and the behavior of measuring rods and clocks. Everything that happens is initially described in terms of four completely arbitrary spatio-temporal variables. If the conservation laws for momentum and energy are to be satisfied, these variables then need to be specialized in such a way that only (fully) linear substitutions connect one justified frame of reference to another. The frame of reference is, in a manner of speaking, tailored to the existing world with the help of the energy law and loses its nebulous a priori existence.''
    Last edited: Apr 22, 2007
  11. Apr 23, 2007 #10
    and elsewhere:

    This is where I'd like to add my R 0.02 worth from the lay side of the interface ... worth much less than Pervect's $ 0.02, I'm afraid.

    Perhaps when one feels philosophy looming, as in this thread, it's time to take a step back and appreciate what we are and what we're doing.

    Here comes the R 0.02 worth ..... it seems to me that we're simply the most loquacious critters on the planet. Like other critters, we're driven mostly by such hard-wiring as evolution has endowed us with: among our other faults we're hard-wired to chatter. We have a driven need to describe
    everything around us and everything we can possibly imagine. Hence forums.

    Cosmologists (try to) describe what's out there, using an abstract language (mathematics) filled with abstract concepts, such as the "geometry" of "space", that describe mysterious phenomena like gravity. Their descriptions don't always translate easily into, say, English or Zulu, and have other limitations.

    For instance, neither Newton nor Einstein's descriptions of gravity explain the means by which mass attracts at a distance or distorts "space".

    It's really better to abjure questions like "is (this or that) really (that or this)" . I recommend Percy Bridgman's operational approach. Describe as carefully as you can what gravity does here and elsewhere in the universe, and what you can do in "space". That should be sufficient for the day.
    Last edited: Apr 23, 2007
  12. Apr 23, 2007 #11


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    I really :smile: do agree with what you say. I like operational definitions---but not familiar with Bridgman's approach specifically.

    Einstein's HOLE ARGUMENT is a solid bit of logical/mathematical reasoning and I think it is very interesting. If you want, have a look at the wikipedia article
    (but Rovelli's book, which is online, is clearer)

    I think the Hole Argument has a solid operational meaning. It is not vague philosophizing.

    I think one way to say it is that in this thread we are not so interested in what you or I or Mrs. A and Mr. B mean by words like "objective reality" or "physical meaning". How random individuals use words or what they think are the correct way to use words is not what interests me in this thread.

    What interests me is what EINSTEIN was talking about. This is the issue of diffeomorphism invariance. The fact that solutions to the GR equation can be morphed and squooshed around and they are still solutions. Or that you can change from one system of coordinates to another in a free nonlinear squooshy way and you still have a solution no matter what funhouse mirror you choose to view it in.

    As I remember the story, from reading Rovelli's book, Einstein was stunned in 1912 when he realized that his theory had diffeo-invariance and when he discovered by means of the Hole Argument, that this deprives spacetime points of their fixed identity. There are points where stuff happens but where a particular event happens could be any generic mathematical point on the continuum indiscriminately. The continuum itself is just a mathematical convention---what matters are the EVENTS and the geometrical relations among them.

    It just occurs to me, oldman, that Bridgman should be happy about this. This is treating spacetime itself in a very OPERATIONAL way :smile:
    (or as some people call it, a relational way.)
    Last edited: Apr 23, 2007
  13. Apr 23, 2007 #12


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    I would suggest that it is pretty obvious that the principle of diffeomorphism invariance is empirically supported.

    Gen Rel has been tested against alternative theories of gravity, some of which are not general-covariant or diffeo-invariant. Over the course of many decades it has been shown to WORK BETTER.

    Thus there are operational grounds for expecting that a successful theory of spacetime geometry and gravity will turn out to be squooshy (diffeo-invariant.)

    Also notice that Einstein worked frantically from 1912 to 1915 to devise a theory of gravity which would NOT be diffeo-invariant. (he was bothered by the hole argument and the fact that covariance deprived spacetime of what he called "physical existence" apart from events.) The fact that he couldnt come up with an non-covariant alternative when he really wanted to is a suggestive hint that other folks won't either.

    So I regard diffeo-invariance as an empirically supported assumption about the world.
    (I don't like to argue, so i wouldn't argue about this, but I would be very interested to know if anyone on hand here disagrees with that. If you do, please let us know and thanks in advance.)
  14. Apr 24, 2007 #13
    Sure, I do. :smile:

    I am certainly not saying that it is not the case, but I think it is a bit far fetched to make such a claim based only on the fact that general relativity is a diffeomorphism invariant theory.

    Furthermore, while a mathematical theory can clearly be diffeomorphism invariant, I am not fully convinced, seemingly unlike Rovelli, that we even have a solid handle on what it means if we say that diffeomorphism invariance has a physical meaning.

    At any rate, I am not aware of any experiment that proofs or even suggests that reality is diffeomorphism invariant (whatever that might mean). And I think it is even doubtful if an experiment could ever determine that.
    Last edited: Apr 24, 2007
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