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    The Einstein Expansion Paradox
    By Sascha Vongehr | January 9th 2012 12:41 AM | 26 comments | Print | E-mail | Track Comments
    About Sascha

    Dr. Sascha Vongehr [风洒沙] studied phil/math/chem/phys in Germany, obtained a BSc in theoretical physics (electro-mag) & MSc (stringtheory)...

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    The universe expands. The galaxies, as they depart ever further from one another, are classically and even in Einstein’s special theory of relativity, described as dust particles: The universe as a cloud of dust expanding through space. However, in Einstein’s general theory of relativity, this same expansion is described as the universe itself expanding. There is no locally observable difference between these descriptions whatsoever – at least as far as we know. Classical expansion through space and Einstein’s general relativity describing expansion of space both fit together seamlessly.


    This conspiracy-like symmetry is paradoxical: in the Newtonian and special relativistic descriptions, the underlying space stays the same, uninvolved stage, while in the generally relativistic picture, space expands in the concrete sense that there is more of it than before (true even in infinite universes!). This is the “expansion-paradox” [1]:


    Space expands globally although it nowhere expands.


    The orthodox relativistic view likes to resolve this with help of space-time not being space in time: The four dimensional whole is one unchanging consistent arrangement, the “block universe”. The smaller space in the past is simply a different region of the whole. It did not grow into the larger space of today; it is still in the past.



    This seems to be a beautiful argument. The whole growth-of-space problematic seems to vanish. This is partially why the concept of abstract metric expansion is thought superior to the concept of expansion of space, which has been argued to be devilishly problematic [2][3].


    Such arguments aim to support an abstract view and orthodox relativity, refusing space substance like ethers. But such arguments fail especially where they favor expansion through space. Ironically, in arguing against ether theories, one perhaps should talk about expansion of space, because the growth of a hypothetical space-substance is their biggest difficulty; it violates the conservation of substance (continuity equation).


    For substance-models, the expansion-paradox is a strict contradiction: Substance cannot by some magic globally appear without being locally supplied somewhere (or everywhere, but still with a locally acting mechanism). Substance must flow in from the sides or locally expand or units must multiply, perhaps “rain down” from a higher dimension. Particularly considering fast cosmic inflation, many ether theories cannot come up with a mechanism that supplies space that rapidly.



    There is also the question about the costs of new material. Does not only mere emptiness come for free? Reconfirmed with the discovery of the Higgs ether recently, we know that space is not just emptiness. In fact, there has always been the big inconsistency of the orthodox view with particle physics.



    The modern standard model of physics is a Einstein local (Information cannot travel faster than light) micro physics (particle physics / local field theory), and if space does only globally know that it expands, it is inconsistent with a local micro physics point of view: That nothing locally expands anywhere is incompatible with there being overall more space – that is the expansion paradox, which is valid if space is not just mere emptiness, which space is not. On the other hand, given Einstein locality, if space expands everywhere, how does the local environment know about how much space it is supposed to produce in order to get the correct overall production of space that depends on the changing global average matter density? Local space cannot know the global density. How would it - not even the local curvature is close to the global average, which is moreover flat anyway!


    What is the solution to this paradox? It is actually straight forward: Just like the ever repeated “Einstein disproved the Ether!” or the falseFaster than light travels in time and kills your granny!” misconceptions, also the mantra of that “Space does not locally expand!” is simply wrong, nothing more than a misleading dogma brought on by an almost religious interpretation of general relativity as some sort of magical geometry rather than a mathematical description of physics that holds in a certain domain of applicability, as scientific theories always do. Space does locally expand! Yes it does, and this is not even my own discovery. (I wish it were, but others were faster – I can only claim to have provided a description of the local versus global consistency.[4])





    The expansion scalar of general relativity’s Raychaudhuri equation is formally a rate of local space reproduction [5]. This “local Hubble constant” does indeed, if averaged over the whole of the universe, which is highly nontrivial in curved space-time, add up to the overall observed expansion of the universe. Local physics does not need to magically know the global average density.


    The funny thing is: It is therefore consistent with orthodox general relativity that a space-substance procreates locally with a base rate (relative to cosmological time) that is time dilated according to the extrinsic curvature that the Raychaudhuri scalar depends on [4]. In lay terms: Even fast exponential inflation can be modeled with a slow dividing of fundamental units, namely only once every 108 Planck times. This is totally ridiculous from an orthodox point of view – yet also the same! Duality strikes again.


    The local expansion is very slow and it only adds up to a large global value because there is so much space in the observable universe. This ensures that we do not feel it locally in our living rooms or when watching the moon. That and the fact that we cannot feel un-accelerated expansion anyway inside systems that are bound by gravity, which is a very subtle point difficult to explain. And there is a third reason for that we do not locally see expansion: Around here, the local expansion is actually much much slower than in the mostly empty, vast stretches of vacuum out in the universe. Space expands the faster the emptier it is. This is ironically due to it wanting to pull itself together, making space the "Ultimate Sisyphus". Anyway, even the vacuum in galactic space (our living room) is rather full of particles compared to the large empty voids of the universe.

    ---------------------------------

    [1] Vongehr, S.: Supporting Abstract Relational Space-Time as fundamental without Doctrinism against Emergence. arXiv:0912.3069v2 (2009)

    [2] Peacock, J. A.: A diatribe on expanding space. arXiv:0809.4573 (2008)

    [3] Francis, M. J., et al.: Expanding Space: the Root of all Evil? Pupl. Astron. Soc. Austral. 24,95-102 (2007)

    [4] Vongehr, S: Metric Expansion from Microscopic Dynamics in an Inhomogeneous Universe. Communications in Theoretical Physics 54(3), 477-483 (2010), arxiv.org/abs/1008.2810

    [5] Buchert, T: On Average Properties of Inhomogeneous Fluids in General Relativity: Perfect Fluid Cosmologies. Gen. Rel. and Grav. 33(8), 1381-1405 (2001)

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    Comments

    Thank you for a well written and insightful piece. Einstien pointed out that space cannot exist devoid of field. Could you elaborate on that somewhat? Also, do you believe that the edge of the visible universe is not visible because the distant light has not reached us yet or because that horizon is receding away from us faster that light speed itself.

    vongehr
    Einstien pointed out that space cannot exist devoid of field. Could you elaborate on that somewhat?
    Sure there are spaces without EM field possible theoretically, and gravity is in a sense no field (field has values at every point of a space, but the metric itself kind of is the space - well at least there are no identifiable space-points on which it takes values). If he said it, it probably made a lot of sense in the context. His quantum philosophy was lousy, but I am pretty sure whatever he said there about pure general relativity was correct.
    Also, do you believe that the edge of the visible universe is not visible because the distant light has not reached us yet or because that horizon is receding away from us faster that light speed itself.
    You could define the "edge" relative to us as precisely the locations that travel at lightspeed away from us. Depending on how acceleration accelerates however, the light emitted at that location may become visible in the future. It is strongly recommended to only ask for what one can actually measure. Talking about things like "edges" (instead of say the future visibility of a photon now emitted at a certain metric distance) is a recipe for disaster in relativity.
    MikeCrow
    It seems to me (and I'm sure you'll let me know if I'm wrong :) ) that the edge of what we can see is the cmb, and that it is not (now) out of our light cone.
    Never is a long time.
    vongehr
    The cosmic microwave background (CMB) is everywhere and will always be visible everywhere. Now you are somewhat correct in that those photons are the oldest we can see, but that is just due to them originating from the surface of last scattering or first light (or close to that anyway, neglecting re-ionization I suppose, no idea how much of an issue that quantitatively would be and not interested since it is all kind of close to each other). If you wanted to make the furthest origin (source), i.e. the oldest (longest traveling time) stuff, that is seen today somehow the definition of your "edge", there are other phenomena that are older, say big bang gravity waves, neutrinos (not sure about their quantitative fraction today), and whatever may be detectable in the future. In principle, if you came across some unlucky particle that survived cosmic inflation, your thus defined "edge" could be FAPP infinitely far away.
    The CMBR as you say is from the last scattering at an age of 378k years (z=1089) whereas the first stars probably arose around z=25 (or maybe 65) and reionisation was around z=11, both much later.

    .. the distant light has not reached us yet or because that horizon is receding away from us faster that light speed itself.

    This is a common misconception, we can see galaxies out to a redshift of about 8 but objects at a redshift of more than about 1 are actually separating from us at the speed of light.

    That is also why it is not possible to model cosmology using SR and Doppler shift. The FLRW metric as mentioned models space itself expanding and does not suffer from these problems.

    There is no paradox here of course, the Minkowski Metric of SR is analogous just to a flat plane which is a tangent to a curved surface at a particular point.

    Interestingly, the earth is receding from the sun at a rate of 15cm per year. Scientists are not sure whether this is due to the sun losing mass through fusion and solar winds, tidal forces of the earth, or cosmic expansion.

    vongehr
    And the moon recedes from the earth. Such cannot possibly be due to the instantaneous cosmic expansion H(t) even if this Hubble constant would be much larger. There is no so called frame dragging in these situations. Moreover, although such receding can be due to extremely accelerated expansion (called "big rip"), the current acceleration is much much too small to lead to such a large effect even if it where everywhere the same (global instead of locally dependent on the energy density).
    The recession of the Moon is due to the tidal interaction with the Earth. The moon raises tides in our oceans but it orbits once a month while the Earth rotates once a day. The tides act like a very weak brake on our rotation but accelerates the Moon which moves away to conserve angular momentum.

    Thank you Sascha. I enjoy your articles and responses tremendously. Best wishes to you.

    vongehr
    I appreciate the flowers.
    Thor Russell
    Haha, I appreciate another reason not to sleep at night :)I never realized there was such a paradox, and had never thought about space-time dividing by itself like that. It reminds me of steady-state models where people desperately try to avoid a big bang by having matter spontaneously appear out of space by itself. If matter is just "pseudo-particles" in the ether, then is there some reason why this shouldn't also happen when space is created?
    Thor Russell
    "The universe as a cloud of dust expanding through space. However, in Einstein’s general theory of relativity, this same expansion is described as the universe itself expanding. There is no locally observable difference between these descriptions whatsoever – at least as far as we know."

    Just to make sure I understand what you are claiming, the two views are:
    1) flat space-time of special relativity, and according to some arbitrarily chosen inertial coordinate system, the particles are all moving away from each other
    2) a uniform universe in GR expanding -- the particles are all moving away from each other

    Is that what you are claiming? I think those are very much distinguishable.

    vongehr
    1) flat space-time of special relativity, and according to some arbitrarily chosen inertial coordinate system, the particles are all moving away from each other
    I mean the well known Newtonian dust cloud exploding from a point source so that after some time t the distances of the particles to the origin are proportional to the velocity with which they travel, which is the Hubble law. Also, in special relativity, there is the flat Milne model.
    I think those are very much distinguishable.
    Not sure what you mean. Globally of course (topology perhaps), more or less locally if you look for curvature too, but strictly locally not. It might help to consider that Newtonian mechanics is the non-relativistic limit of relativistic physics. In case of the Friedmann-Lemaetre-Robertson-Walker universes, some of the formulas happen to be precisely the same (extrinsic curvature looks like kinetic energy for example).

    "I mean the well known Newtonian dust cloud exploding from a point source so that after some time t the distances of the particles to the origin are proportional to the velocity with which they travel, which is the Hubble law."

    Okay, thank you for clarifying. This makes it clear the equivalence does not hold.

    For particles to move like v = H r in your Newtonian example, they need to be accelerating.
    So except for the very special/exceptional earth observer in your Newtonian example, any other observer could do a local measurement and see that they have a non-zero proper acceleration. They also would not see the same red-shifts / velocity distributions as the earth, and would immediately know there was a difference.

    Instead, in the uniform density universe in the GR example, every observer locally measures no proper-acceleration, and the same red-shifts / velocity distributions.

    So even local measurements distinguish these two cases, not to mention that GR explains it:
    1) without making earth an extraordinarily unique observer in the entire universe
    2) with a divergenceless stress energy tensor (the local energy conservation Einstein was looking for) unlike in the Newtonian example which requires this local energy conservation to be violated.

    So local measurements can very easily distinguish these two.

    vongehr
    For particles to move like v = H r in your Newtonian example, they need to be accelerating.
    ?!? They are Newtonian with Newtonian gravity. So they accelerate (negative acceleration in case of expansion).
    Do not confuse acceleration due to matter and the newly discovered accelerated expansion due to dark energy. Also, you write that local measurements can easily ..., but this "local" is somewhat dodgy. Local means "in a small space around the observer", but in discussions about relativity, it is space-time of course, i.e. including short time.
    It took a long time to see that there is any acceleration at all. You let it appear as if it is no problem to use measurements over small times to see the difference between Newtonian and relativistic acceleration.
    "?!? They are Newtonian with Newtonian gravity. So they accelerate (negative acceleration in case of expansion)."

    When you said the Newtonian dust cloud was moving according to Hubble's law, I thought you meant for all time. (In which case the acceleration was positive). No I was not conflating this with the cosmic acceleration of GR. The point was that an observer in a distant galaxy could measure this acceleration, since it would just be his local proper acceleration (also very unlike the cosmic acceleration in GR).

    Since you are now saying that they are just moving according to Newtonian gravity the whole time, there would not be proper acceleration to measure since they are free falling. However if v = H r, then dv/dt = H v = H^2 r. Whereas Newtonian freefall here should be dv/dt proportional to 1/r^2. So this would only match for a SINGLE lucky moment in time in which only from a SINGLE point in space, an observer could look out and see the proper red-shift distribution. Since this can only hold for an instant, there is no point in discussing the evolution of the particle motion and therefore you might as well just drop the Newtonian gravity all together, since you are then just saying equivalently: imagine at this specific time there are galaxy's distributed such that v=H r.

    Regardless, this doesn't change my point about local measurements in the Newtonian example easily distinguishing the two. Measure the red-shift distribution at one point and for a short time at some distant galaxy in the Newtonian example, and it would not match v = H r at any point in time. So they are only equivalent if you restrict to only local measurements at the one very specific spacetime point which you setup to be the same _by definition_ of how you artificially setup the situation.

    That is just as scientific as a young earth creationist saying: using nothing but the observation a fossil is in this sandstone, your theory that it came from million of years ago is equivalent to the creationist theory that it came from the flood only thousands of years ago.

    vongehr
    When you said the Newtonian dust cloud was moving according to Hubble's law, I thought you meant for all time. (In which case the acceleration was positive). No I was not conflating this with the cosmic acceleration of GR.
    What on earth are you going on about??? The exploding Newtonian dust cloud slows down just like the cosmic acceleration in the FLRW solution of GR. The equivalence of these descriptions is known since before I was even born. I have no time for this.
    "The equivalence of these descriptions is known since before I was even born."

    It is only equivalent if you restrict yourself to measurements at one special spacetime point. Local measurements anywhere else shows that they are not equivalent. I notice you keep ignoring that important point.

    Imagine an observer on a galaxy 1 billion light years away. In the newtonian case you describe, if he measures the distribution of redshifts from galaxies as a function of distance from his, he will NOT see Hubble's law. Do you disagree with that?

    It is a measurement he makes locally of starlight reaching him at a point in time. It is a local measurement. It distinquishes the too. They are not equivalent except for measurements from the one single spacetime point that you explicitly set them equal.

    vongehr
    Imagine an observer on a galaxy 1 billion light years away. In the newtonian case you describe, if he measures the distribution of redshifts from galaxies as a function of distance from his, he will NOT see Hubble's law. Do you disagree with that?
    I indeed disagree with that. Given a large enough Newtonian dust cloud that spends many billions of years or basically infinity like in the Milne model, there would be no difference between one dust particle or the next one a mere billion ly away. Anyway - the definition of local is a well known and useful one and that talking about local limits equals creationism is certainly news.
    blue-green

    “Space expands the faster the emptier it is.”

    Would it be crazy to trace this to something like the Casimir Effect?

    Theoretically, the effect can draw together parallel plates ….

    Experimentally, it is observed in nanodevices, however, a computation of the “forces” can be very difficult.

    It is not even clear in actual cases with complicated boundaries whether the net effect is attractive or repulsive.

    Is there a way to get a handle on Casimir-like effects to compute how much galactic clusters would respond to each other's presence due to Casimir-like effects alone? For computing the receding away of galactic clusters from the voids in between, one would be far from the model of idealized parallel plates … so maybe this is all stretching the Casimir analogy too far …. Maybe galaxies clump together, not just because of gravity, but because the most “empty” reaches between them have more long-wavelength vacuum energy states … yada yada … I know I can't do the math ... even if someone could, would it be an honest fit, or one with the books cooked to match the observed expansion?

    With all of the infinities roaming around in theoretical physics, people can cook up pretty much anything, and yet, there are precise and dark arts for making a tiny sliver of the approaches real. 

    Carry on Dark Lord.

    vongehr
    The remark of space expanding the faster the emptier it is seems to bug many. I call it the "The Ultimate Sisyphus".
    Just isn't a single definition of energy

    Indeed, this was already a classical problem, with potential energy defined either positively from zero, or negatively from infinity. There seems to be no way to reconcile these without introducing an effective infinity like the black hole horizon, hence the interest in Hawking's work. Or a gravitational uncertainty, via quantization. Either way, the potential energy implies relativistic mass, much where dark matter now appears. Erik Verlinde's 68% solution for dark energy reproduces the classical V - 2K = 0, but Lubos Motl disputes his definition of entropy. I agree, he's talking about Koolmogorov entropy of prediction, a metric invariant of automorphisms. So the duality won't go away just yet.

    Quentin Rowe
    Space expands [the] faster the emptier it is.
    Well, that is the essence of the article, after all.

    Space begets space, density begets density. It is the interplay between the two from which all structure seems to derive.

    That nothing locally expands anywhere is incompatible with there being overall more space – that is the expansion paradox...
    Ahh, so simply put. I've waited a long time to read this. It's what simpletons must intuitively think before their thoughts are hijacked by complexity and conformity.

    In wrestling with thoughts of energy currents in a dynamic and expanding universe, I've come across the problem of defining the boundaries of an arbitrarily sized region as a system. How do you do this when your physical references are constantly on the move? If I'm trying to use this region/system as a measure for greater scales, how can it apply? Is this approach what you refer in your article as the metric?


    vongehr
    Not sure whether I understand your question fully, but yes, the Friedmann-Lemaetre-Robertson-Walker metric is what one would use (I used it, plus inhomogeneities).
    muhammad
    Man! That is very deep. Keep going!
    Physics education.