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Distorting spacetime: Links/references about fundamental limits

  1. Jul 11, 2013 #1
    I'm interested in reading about the fundamental limits imposed by known physics on distorting spacetime in ways that bring two masses closer together so that speed of light travel time between them is reduced.

    I'm familiar with the concept of inflation theory. I think of it as a rapid stretching of spacetime so that the space/distance separating all masses in the universe was rapidly increased. Masses initially in close contact and thermal equilibrium were separated by inflation such that after 13+ billion years of light travel, light from objects in opposite directions from us is just now arriving at the earth. One wonders if inflation is one way time directed or can it operate in reverse within the limits of known physics to bring objects closer together.

    I'm familiar with the curvature of spacetime in general relativity, which leaves me wondering how much spacetime can be stretched or compressed to change the amount of spacetime separating two objects.

    I'm passingly familiar with idea of the Alcubierre drive, but I'm not so much interested in space travel as in reading about the limits imposed by known physical laws that might allow inflation to run in reverse, or two objects to become closer, even where it's not even theoretically practical for use as a space drive.

    Thanks for any recommended links or books I might be able to review that would give me some insight.
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  3. Jul 11, 2013 #2

    Simon Bridge

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    Yoy are thinking about warp drives?
    You need the Einstein field equations.

    Basically, distorting space-time requires introducing a dense energy distribution... usually in the form of mass.
    So the limiting factors can be thought of as the minimum and maximum possible energy densities that can be held in the configuration you need for the particular distortion.
  4. Jul 15, 2013 #3
    Not really. Warp drive implies something that might usefully allow pseudo faster than light travel without locally exceeding the speed of light. I'm thinking about the more general concept of distorting spacetime to reduce the distance that light travels between two masses, in contrast to inflation's increase of the distance between two masses.

    What I really need is someone who understands EFE and has written on the subject I'm interested in. (plus some links) :)

    Does the introduction of mass (positive mass/positive energy) ever produce the effect of reducing the distance between two masses such that the travel time of light between those masses is reduced? Dark energy/cosmological constant seems to always increase the distance between two masses such that the travel time of light is increased. Inflation also seems to have that effect - increasing the distance. Are there known effects that reduce the distance? Physics/physicists seem to accept the effect of the above (inflation, etc.) to increase the distance that light travels by distorting spacetime to increase the spacetime between two masses, but are there any known effects that distort spacetime to decrease the distance?
  5. Jul 15, 2013 #4


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    Google for "Alcubierre Drive", you'll find plenty of links.
  6. Jul 15, 2013 #5

    Simon Bridge

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    Physically, a warp drive would be the informal term for any device that reduces travel-time by distorting space.

    There are lots - but there is no royal road to understanding on this - you need to do the background math at least.
    OTOH: you could just hire someone who already has the background?

    Nope - you need negative energy for that: lots of it by most calculations.

    Experiments are being done with the Casimir effect to see if this will count as negative energy for exactly this purpose. It's fringe stuff. Even if it does count (and that's a big if) you still need to get it into the right shape and that looks very unlikely. Still: smarter people than me are working on it.
  7. Jul 16, 2013 #6
    As I understand it, length contraction, as the reciprocal of time dilation can make "two objects to become closer..." as a high speed object with a slowed down clock travels between them... a well known thought experiment in special relativity. I too would very interested in an explanation as to how the distance between two objects contracts in such a case. (That "time has slowed down" for the high speed travelers and their clock is a given.)
  8. Jul 16, 2013 #7
    In my original post, I indicated I was familiar with the "Alcubierre Drive". I followed several links, but couldn't find anything that wasn't directly pointed at "Alcubierre Drive" and the problems with it - most relating to negative energy requirements and or crossing the bubbble/wave boundary problems. That's not quite what I'm looking for. In fact, I'm not 100% sure if it truly does decrease the distance between two points. I think of the A-drive as a method of continuously moving spacetime that's ahead of the warp bubble to a point behind the warp bubble. The spaceship inside that bubble need not have any velocity relative to the spacetime within the bubble.
    Last edited: Jul 16, 2013
  9. Jul 16, 2013 #8
    Yes, I should have mentioned Lorentzian length contraction in my first post. However, that's a reduction in distance only when comparing two different frames of reference. It seems unlike what happens in dark energy/cosmological constant, which seems to increase the amount of space between two points even when analyzed in a single reference frame. The same applies with inflation - inflation seems to increase the spacetime between two masses even when considered from a single RF.
  10. Jul 16, 2013 #9
    Yes, but I'm not trying to identify effects that "decrease travel time", per se. That implies an end run around lightspeed limits - and I'm not trying to do that, and I'm inclined to think it can't be done. Perhaps a boundary is involved that must be crossed that increases the total time. I'm just wondering if inflation is in any sense a reversible process, or if the cosmological constant can run in reverse (Big Crunch?) within the known limits of physics, without requiring something exotic like negative energy.

    I've taken and passed classes on tensor calculus and have audited classes on General Relativity - but that's all decades behind me. Besides. I'm not looking for math and detailed explanations, although I'm not afraid of them.

    So as far as you are aware, would it be fair to say that physics as we presently understand it does not allow spacetime to disappear or be "compressed" between two points (without assuming the existence of something never seen before, like negative energy), but does allow spacetime to be created or stretched between those two points (via cosmological constant process or inflation)?

    Yes, I've read of the work on Casimir effect/negative energy. I just wasn't sure if I was missing something fundamental. It does seem like there is an asymmetry here. In one sense, spacetime is like a rubber sheet that can be stretched (or perhaps created) to increase the distance between two points, but it can't unstretch or be uncreated to decrease that distance (at least not without running time backwards or coming up with an exotic new item such as negative energy).
  11. Jul 17, 2013 #10

    Simon Bridge

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    The last time I looked at it I had figured that contracting space time would also have entropy running the other way ... so anyone "inside the Universe" in question would percieve an expanding Universe regardless of whether they were in the contracting or expanding phase[1].

    I understand there are other models. The tldr response is that the Universe itself need not have lots of imaginary mass to go into a big crunch.

    ... you seem to have the background, you should probably review the GR stuff to get a better foundation to understand what people are talking about. Without that, you won't do better than an imaginative artsy pop-sci version ... and you know how we are allergic to that sort of thing around here. The alternative, like I said, is to ask a specific question and hire someone to do the math and tell you about it ... though you may get lucky and an enthusiast responds for free, this is the sort of stuff a lot of us got degrees to make money from. Beware of asking for professional help in a free forum: the idea behind this forum is to encourage you to learn and do it for yourself.

    No ... it's not. Not much...
    That is one of the pop-sci things that we try to avoid ;)
    I wonder if there's a sticky about that somewhere...
    Your "on the other hand" observation is an example of why we don't like it so much.

    In a way you can decrease the distance just by going fast - see "length contraction".
    The time it takes light to travel between point A and point B (in the same reference frame) separated by some proper distance D depends on the relative motion of the observer.


    [1] It is tricky to talk about this and I have adopted a kind of meta-time a la "Brief History of Time" in a desperate attempt to make some kind of sense.
  12. Jul 17, 2013 #11
    As I posted, I'm looking for links and information so I can understand this myself. I wasn't sure if there was some well known situation that resulted in spatial compression (around black holes or the like). Thanks for the reply. I'll take a look at the rubber sheet links. I'm already aware of many deficiencies in that analogy, but perhaps there will be some clues for more reading there.

    I'll look for more information on the big crunch or reversed entropy in a shrinking universe. At least it gives me some more keywords to search on. All I could find previously was discussions of the Alcubierre solution and negative energy, and although it was interesting, it didn't lead me towards anything helpful.
  13. Jul 17, 2013 #12

    Simon Bridge

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    It can be difficult if you don't know the useful questions to ask :)

    For understanding:
    The general stuff on how energy-densities warp space-time need EFE - and do the exercises in the online college-level classes on same. More lay-friendly stuff is available and will be very misleading if you try to draw conclusions and/or insights from it.

    The cosmology is speculative - of course.
    There are a lot of articles about the connection between space-time expansion/contraction, gravity, and entropy.

    The basic argument goes something like this: if we were to have a universal space-time change that caused entropy to run backwards ... how would we know? Our clocks work in the direction of increasing entropy and so do our memories. However, it is technically possible to have contractions that increase entropy... this end of cosmology is too speculative for me :) The "backwards time" thing is something that appeals to me and, therefore, I am suspicious of it.

    Per your original question - it is a well known condition that comes up a lot and is widely believed not to exist in nature (casimir effect notwithstanding) since it requires exotic matter.

    You still need to work out who you need the flight-time to be short for. AS with all relativty questions, the frame of reference is very important.

    It cannot be short for the light itself, since the time between events for light is a meaningless concept.
    Note: knowing the time for light to go from a to b for some observer is the same as knowing the distance between a and b for that observer - but may be easier to think about.
  14. Jul 19, 2013 #13
    I probably phrased the original question poorly, but I was in fact asking about distance changes due to spacetime curvature.

    Since you have phrased it well when you said: "the time for light to go from a to b for some observer is the same as knowing the distance," I can ask about LIGO the Light Interferometer Gravity_Wave Observatory and ask this: Isn't the point of LIGO that a propagating wave in spacetime causes the distance between two points (the mirrors at the ends of the arms) to vary in distance as the wave passes by?

    Is that a case where spacetime is briefly "compressed" between two points as the wave passes by? Or, does the entirety of the distance variation arise in a spacetime distance increase followed by a relaxation back to the original distance? "

    I tend to think of a gravitational wave as being similar to a compression wave in a slinky where two points get closer together and then farther apart (as compared to the distance between those two points when the slinky is at its default stretch). But perhaps that picture is too simple and gravitational waves never cause a distance decrease?

    Thanks for the other comments on entropy, which I will think about some more.
  15. Jul 19, 2013 #14


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    Yes, except that the waves on a slinky are longitudinal, meaning the distortion they cause is in the same direction as the propagation. Gravitational waves are transverse (perpendicular to the propagation). Furthermore they are quadrupole. Wikipedia has a nice animation of the effects caused by a passing gravitational wave.
  16. Jul 19, 2013 #15

    Simon Bridge

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    I believe I have already warned you about this kind of pop-science-level conceptualizing: it leads you in bad directions.
    Yeah - I suspect the "slinky" picture comes from the mapping chosen.
    All relativity stuff requires you to be careful about the observer... even the gravity bits.

    One could picture it like this though - flat spacetime is a horizontal line, the effect of positive energy on the line is to bend it. The distance along the curve is the distance under consideration.

    Can you come up with a way to curve the line so that the distance along the curve is shorter than that for a direct path?

    A gravity wave, on this picture, would just be a wiggle in line that travels.
    Is there any place in the wave where the distance between two points is less than if the wave wasn't there?

    ... and I repeat the previous warning: as compelling as these pictures are, they are not the whole picture.
    Careful letting you imagination run with them.
  17. Jul 22, 2013 #16
    To the latter question: No, not if I assume the line lies in flat space and not if it's a geodesic in curved space, but that does seem to avoid the question which asks if space is ever compressed. If I put the line on a flat rubber sheet then stretch that sheet, I have a decent analogy for the distances between points on that sheet in an infinite flat expanding universe. The line remains the geodesic for that model no matter the expansion. Similarly, it remains the geodesic if we look back in time to when the sheet was less expanded, or if we look forward in time and allow the sheet to shrink. I see nothing in the simple analogy that prohibits stretching or compressing regions of that sheet while remaining flat at all times. If stretching is permitted, why not compression?

    Please understand, I'm not asking anyone to apply this flat rubber sheet model and answer the question within the context of the model. I'm just trying to understand (find links to discussions on this) from those who've actually worked through the GR equations and published summaries of the results (accepted by the GR community) as to whether such compression of spacetime ever occurs in the absence of exotic mass/energy.

    What you are saying is that for the gravitational wave (and other ST curvature effects in the absence of exotic materials), there is never any compression of spacetime - only stretching.

    Which would imply for the LIGO experiment, it would be safe for me to conclude that the distance between the mirrors always increases as the wave passes through. Assume for this that the LIGO detection arms are initially in undistorted "flat" space - which is an unwarranted assumption if they are on the earth - but this allows us to ignore the possibility that in some limited and initially curved region the wave has the counteracting effect of "flattening" that initially curved space.

    I do realize the difficulty of trying to reason from the many analogies presented to describe spacetime curvature. I'm trying to avoid that, but it's difficult to even formulate some questions without a reference analogy to position the question in.

    Thanks for the replies.
  18. Jul 22, 2013 #17


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    No, I did not say that. If you read #14 above, I said yes, gravitational waves both stretch and compress.
  19. Jul 22, 2013 #18
    Seems like the 'extreme' of stretching is cosmological expansion on large [intergalactic or galactic cluster] scales, and on the other hand the formation of black holes in local spacetime as the 'extreme' of 'compressing' everything to perhaps Planck scales....called a 'singularity'...
  20. Jul 23, 2013 #19

    Simon Bridge

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    Actually it kinda allows you to answer it - which is the point. The idea, since you don't seem to want to believe what you are being told, is to get you to come to the conclusion yourself.

    - but you say "compressed", without saying with respect to what? To flat space-time? Or something else? Can you think of any way to "compress space-time" by adding curvature (i.e. real mass).

    You appear to be reluctant to give up the analogy with longitudinal compressions and expansions though...
    Can you express your question without referring to such a flawed analogy?
  21. Jul 24, 2013 #20
    Any appearance of reluctance on my part is entirely unintentional. As for not accepting what I'm being told - I'm just trying to understand what I'm being told, not disagreeing with it.

    With that clarification out of the way ...
    I'll do my best, but I suspect you could do it better. I'm trying to understand if spacetime is compressed during any known physical process (does not involve exotic energy, etc.) as compared to flat spacetime.

    Some answers here seem to say no. The reading I have done on the LIGO seems to say yes. Certainly, Wikipedia's entry on gravitational waves shows that the distance between particles in a ring of particles is reduced (the ring becomes oval) and that appears to be the type of spacetime "compression" I'm asking about.

    Now, perhaps I have to define "compression." I suppose in the LIGO experiment it's the number of wavelengths of the laser light that fits between the mirrors at the ends of the arms in the compressed arm versus the number of cycles in the arm that is in flatter space.

    Please understand, I'm not disagreeing with anyone. I'm just trying to understand and look for links. This isn't my field and I recognize that the questions are less well phrased than I'd like. I've read many descriptions of gravitational waves (although they weren't at the forefront of my mind when I asked the original question) and all seem to imply that flat spacetime is compressed and stretched during the transit of a gravitational wave.

    I came here as I understand that popular descriptions of such things are fraught with errors, and I had a decent chance at getting good information here. If it looks like disagreement, it's not. It's merely an attempt to resolve the disagreements between the models/analogies I've been exposed to and any statements here.

    If it turns out that gravitational waves only stretch spacetime, never compress it, and that the interference seen in a LIGO experiment due to gravitational wave passage results entirely from the lengthening of one arm - then so be it - and my knowledge of that phenomenon is slightly improved. If it turns out ... well you get the idea.

    The bottom line is that I came here to better understand physics.
  22. Jul 25, 2013 #21

    Simon Bridge

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    Apart from what you infer from the image, is there any part of the LIGO work where the word "compressed" (or related) is used to describe any part of the gravity wave?

    When you see a space contraction n the animation, remember that you also get a time dilation that is not shown.

    I suspect what you are trying to get to is something like this:

    You can also look at it in special relativity (the math is easier) by examining the various "simultaniety" exercises.
  23. Jul 25, 2013 #22


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    I can't believe this! :eek: Simon, are you actually maintaining that a gravitational wave causes no compression?! If so, you are really confusing the OP.

    All right, if you don't believe what the diagram plainly shows, the alternative is to be more mathematical, which we have been trying to avoid. Here's another reference. Skip all the way down to p 68, where the same picture is shown, and here's what they have to say about it:

    Is it clear what they're saying, or do we need do repeat it? At certain phases as the wave passes, distances between the test particles are decreased. That, in my book, is compression.
  24. Jul 25, 2013 #23

    Simon Bridge

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    I hope not, I'm trying to get OP to investigate better - but thanks for the link.
  25. Jul 26, 2013 #24
    Yes, I was/am confused :)

    You don't have to avoid mathematics for me. I'm willing to dig through it.

    Thanks for the link. It seems clear that proper distance decreases between the particles. The link is exactly the kind of thing I'm interested in, so again - thank you very much.

    It does make me wonder about the effect on an object traveling transversely to a suitably arranged array of parallel propagating GWs. I don't know enough about GWs to know if "beams" of GWs are permitted, comparable to light beams, to allow "a suitably arranged array of parallel propagating GWs." But assuming such beams are allowed, if the wavelengths and phases ofthe GWs were correctly selected, are there conditions under which an object traveling transversely to such beams could propagate at sublight speed, such that it passed through the "compressed space" at the right time to travel from point A to point B faster than light could travel from A to B in flat space?

    Just asking the question makes me fear that I'll get labeled as some crackpot FTL theorist, but that's not what I'm interested in. Instead, I want to know how light speed limits are imposed in a world in which spacetime compression can occur. Again, I'm not trying to get around light speed limits. I want to know how they work within the context of current physics. I'll spend some time digging through the link (which I noticed started pretty quickly on page 7 with the classic deformed rubber sheet analogy) :)
  26. Jul 26, 2013 #25
    I've worked through many simultaneity exercises in SR, and think I have a decent handle on them. I haven't looked at your link in detail yet, but it doesn't look like it's discussing what I'm interested in - changes in proper distance due to spacetime compression. The link starts off discussing the classic spinning disk problem where the circumference is Lorentz contracted, but the radius is not. Lorentz contraction when changing reference frames doesn't seem (to me) to be the same thing as proper distance compression transverse to a propagating GW.

    I suspect that whatever happens to an object or light ray that moves transversely through the path of a propagating GW, it involves proper time effects.

    Thank you for the comments and the link.
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