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Superluminal Recession

  1. Jun 18, 2008 #1
    Let's conduct a thought experiment involving a galaxy far, far away ("Galaxy FFA") from earth. Galaxy FFA is observed from earth to be receding at twice the speed of light.

    Let's hire very fast (.9c) alien spaceships to simultaneously release 999 test particles equally spaced across the distance between earth and Galaxy FFA. (We outsource this work to multiple alien space agencies because their home galaxies are located all along the route between earth and Galaxy FFA, so each spaceship has less distance to fly. This will help us achieve budget savings.) Clocks on the spaceships are pre-coordinated and adjusted for any differences caused by SR time dilation. Radar ranging is used to achieve evenly spaced drops. At the instant of release, all 999 test particles are released at proper rest with respect to earth and each other, i.e. no proper motion.

    At the instant after release, what is the proper speed of the test particle closest to Galaxy FFA, relative to Galaxy FFA?

  2. jcsd
  3. Jun 18, 2008 #2
    I really like the name of your galaxy! It seems you are giving more detail than is required for your thought experiment, however. Also, I am not sure what you mean by "proper speed." And are you asking what are the comparative speeds of particle 999 and galaxy FFA, relative to an earth observer?
  4. Jun 18, 2008 #3
    Hi poeteye,
    Thanks for asking. Actually my question can be phrased as, "What is the recession speed of particle #999 as seen by an observer on Galaxy FFA?" Particle 999 being the particle located closest to Galaxy FFA.

    I included details about the setup of the thought experiment because I want it to be very clear and not confused by peripheral SR quibbles, etc. Also, in case anyone is against free trade, I explained why the space work is outsourced to alien agencies.

    EDIT: "Proper speed" simply refers to the change in directly measured distance, per unit of time, as between two objects. This terminology is used to distinguish it from comoving coordinate systems.

    Last edited: Jun 18, 2008
  5. Jun 18, 2008 #4


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    Hi Jon,
    your thought experiment setup is a familiar one. IIRC Ned Wright uses it to clarify what he means by the distance at the present moment to a certain galaxy (e.g. your FFA).

    The idea is you do all this planning in advance so that a large number of collaborators are stretched out evenly in a line, between us and FFA, at the same moment, and they all measure the distance to their nearest neighbor at the same moment (universal CMB time, I guess) and we add up all the little increments.

    Ned Wright used that thought experiment setup to help describe comoving distance, because it concretizes the basic idea in it of the real distance at the present moment.

    I think to be quite operationally clear about it you would have to specify that all the collaborators are stationary with respect to the CMB. The CMB or hubbleflow gives us a universal idea of being at rest, and also a universal idea of simultaneity. That would help in the conceptual construction.

    To answer your question, I'd say the recession speed between any two neighbors is 0.002 c.

    That is, 2 c divided by 1000.

    Because the total distance to FFA is expanding at 2c, and the distance has been equally divided into 1000 increments.

    All your statements involving the term "proper speed" and "proper rest" are potentially confusing because you seem to be using those terms in your own special way. Or else I am missing something. "Proper velocity" as usually defined http://scienceworld.wolfram.com/physics/ProperVelocity.html
    as in Wolfram or in Wikipedia, is meaningful in the context of special relativity.
    But special rel does not apply because in special rel distances do not expand.
    There is no such thing as recession speed, in special rel.

    Maybe I am missing something. But I make sense of what you say by focusing on what I quoted, and forgetting about anything involving the words "proper".

    I hear you clearly when you put the question "what is the recession speed of particle #999 relative to galaxy FFA?" That makes sense, the terminology is not confusing, and the answer I think is 2/1000 of the speed of light.
  6. Jun 18, 2008 #5
    Hi Marcus,
    I think you are describing a scenario that is quite different from what I intend. Let's assume for the sake of discussion that the earth is stationary relative to the CMB frame. Of course it's not, as demonstrated by the measured dipole in the CMB.

    In this scenario then, only the earth is at rest in its local CMB rest frame. All 999 particles are at rest in the earth's local CMB rest frame, but not in the particle's own local CMB rest frame. By definition, no two significantly separated particles which are at proper rest relative each other can both at the same time be at rest with respect to their own local CMB frame.

    At the instant of release, the test particles are not in proper motion relative to each other and the earth. Instead, the proper distance between them is constant at the first instant. After the first instant, the test particles will begin to see the proper distances between each other decreasing, as per the Shell Theorem. But in this scenario we aren't studying what happens to the test particles at later times, we are observing only the proper speed of particle #999 relative to Galaxy FFA in the first brief instant.

    I don't think the concepts of "proper distance" and "proper speed" as I am using them are different from the normal meaning. Proper distance is directly measured radar distance (or physical rulers laid end-to-end). Proper speed is change in radar distance as a function of time.

    Last edited: Jun 18, 2008
  7. Jun 18, 2008 #6
    I don't want to bog down on the definition of proper distance (if we don't have to). Here is a simple GR description of the term from Taylor & Wheeler, Exploring Black Holes (p 1-4):

  8. Jun 18, 2008 #7
    Another description of measuring proper distance, from Barnes & Francis "Joining the Hubble Flow" (p2 and fn#1):

  9. Jun 19, 2008 #8
    There are so many different distance measures in cosmology that to call one of them 'proper' is asking for trouble. In my Cosmological Distances applet I use 6 different ones, and I think that there are a few more besides. The one you mean seems to be 'radar' distance (intuitively you would expect this to be what a rigid rod would measure, but I'm not sure whether there's any theoretical evidence to back this up)
  10. Jun 19, 2008 #9
    Hi chronon,
    Your applet is interesting. I'm a big fan of graphs!

    Surely we can adopt the premise that I didn't make up the name "proper distance". It is widely used in the technical literature, such as the textbook and article examples I cited. I can cite more examples if necessary. I hope I have not diverged at all from the customary usage of terminology.

    I definitely agree that "raw" radar distance may not be exactly the same as "ruler" distance; some adjustments may be required. Clock synchronization certainly. Also, redshift of the radar return signal needs to be checked to detect any dopler effect caused by a target and source which are not truly stationary relative to each other at the instant of transmission, reflection and/or reception.

    For the purposes of this thread, I hope we can get beyond the terminology. As I said in my posts, we can also use ruler distance instead of of radar distance if you find it clearer.

    Maybe it will help if I recast my original question in the simplest way: If we extend a very long rigid ruler from adjacent to earth (with that end kept stationary relative to earth) such that the far end of the ruler is adjacent to Galaxy FFA for an instant in time, at what proper speed (order of magnitude) will an observer on Galaxy FFA observe the end of the ruler (adjacent to Galaxy FFA) is moving away from her? Please don't worry about how realistic it is to deploy such a ruler.

    Last edited: Jun 19, 2008
  11. Jun 19, 2008 #10
    If FFA is receding from Earth at 2c and a rigid ruler is attached to Earth, I would think that FFA would view their end of the ruler as receding at 2c. Can it be otherwise, assuming that the ruler is truly rigid? It would seem that FFA would recede from the Earth and everything attached to it at the same rate, unless the length of the ruler changes.
  12. Jun 19, 2008 #11
    On the other hand, if the close end of the ruler moved away at 2c it would seem to violate relativity by exceeding light speed in local space. So therefor FFA must view the two ends of the ruler as moving away at different speeds? Hmm, I thought it was rigid!
  13. Jun 19, 2008 #12


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    Well, there is no such thing as a rigid ruler, even in theory. The ruler, made of matter, is pliable and will not violate any SR or GR laws.
  14. Jun 19, 2008 #13
    Hey, I appreciate all of the responses.
    I think that in cosmology thought experiments there is such a thing as a rigid ruler. I don't think we can short-cut the answer here just by assuming that the ruler stretches or shrinks. C'mon folks, let's lay it on the line here !

    Perhaps, even if the ruler is not pliable in the normal sense, it will be shorten as a result of a Lorentz transformation, or a series of Lorentz transformations along its length?

    Last edited: Jun 19, 2008
  15. Jun 19, 2008 #14


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    Hi Jon,
    poeteye in post #2 originally asked you what you meant by "proper speed" or "proper velocity". I dont think you said yet. The term "proper distance" we've all heard used a lot. But "proper velocity" is hard to find with google except in the context of special relativity, which doesnt cut it here. So maybe you could clarify.

    You talk about SIMULTANEOUSLY releasing a bunch of test particles. What reference frame what defines simultaneous? You talk about releasing test particles AT REST with respect to the earth, but some of the particles are out near the distant galaxy.

    Explain how this is physically possible, since to release a particle out at the galaxy so that it stays a constant distance from earth would require accelerating it to towards the earth at twice the speed of light.

    By the time the hired rocket ships have gotten out near the galaxy it is physically impossible for them to assume a station which is constant distance from earth. So the thought experiment is unthinkable. It simply breaks.

    But in any case it is not so welldefined mathematically since you seem to think you can have a minkowski reference frame (a la special rel) which extends out to a neighborhood of the distant galaxy. Bad fit. local reference frames dont fit the universe at large scale---they only fit a small patch. (Because they are not expanding, mainly.)

    Lot of vagueness here. You start all the spaceships out at their HOME GALAXIES. and yet you say they have coordinated clocks. How do you establish synchronized clocks?

    The main thing though is that the thought experiment seems very fragile because it is physically impossible for a hired rocket ship to establish itself at rest with respect to the earth, if it is very distant (like twice Hubble distance), no matter how much fuel it burns.

    A practical concept of "at rest" is to be at rest with respect to the hubble flow, or with respect to the Cosmic Microwave Background. That is easy to achieve anywhere in the universe. But that is evidently not what you want here.

    Let me know if you think I am missing something, or don't understand what you are driving at :smile:
  16. Jun 20, 2008 #15
    Yes, your quotes imply something like radar distance, but I think the term "proper distance" has also been used for comoving distance. I think it's best to avoid the term.
    It depends. If there is a cosmological constant then such a ruler would be impossible if it exceeded a certain length. Otherwise it's OK.
    I'm sorry but in the case of a non-accelerating universe it is possible to envisage a reference frame such as jonmtkisco suggests. This would either be in terms of rigid bodies, or in terms of radar measurements. In such a frame the FFA galaxy would be seen as moving at a subluminal velocity.

    In the case of an accelerating universe, it's more complicated, but it is still possible to envisage such a frame extending beyond the Hubble sphere. The Hubble sphere is not the Cosmological Event Horizon
  17. Jun 20, 2008 #16
    I think Chronon has an interesting point here. If a rocket passed the Earth heading towards FFA at 0.8c it would not see FFA as redshifted. The rocket moving at 0.8c relative to the Earth locally would effectively be at rest with FFA receding at 2.0c relative to the Earth. Wierd...

    Another interesting observation is that if a traveler headed towards FFA at a constant velocity of 0.1c relative to the local CMB, she would eventually get there in the model where FFA is at rest with the local expanding spacetime. If the spacetime was not expanding and FFA was really receding at 0.8c relative to the Earth then the rocket would never catch up with FFA unless it travelled at a minimum of 0.8c relative to the Earth.
  18. Jun 20, 2008 #17


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    Jon hasn't explicitly said what "proper speed" means, we only have some shared ideas of proper distance and we extrapolate from that. As I understand what it means to be at proper rest, it is physically impossible for something to be twice Hubble distance from earth, at this moment today, and also be at rest with respect to the earth.

    Jon wants one of his rocket ships (out there near the distant galaxy) to do that. Maybe you can show me how that could be done---real world rocket ship, real world local coordinates.

    Think about an active galactic nucleus (AGN) in a galaxy that is twice Hubble distance away from us (i.e. receding at 2c). Imagine that one of the two jets is pointed right at us and sending particles at us with speed 0.99 c.

    Do you think of those particles as not moving with respect to the earth?
  19. Jun 20, 2008 #18
    I am a bit confused. It was my understanding that the expansion of space does not affect bound bodies, from previous discussions. Now it seems that it does, if the ruler is long enough?

    What if you change the experiment just a bit and build the ruler first, so that the end of it is far far away (FFA). Now you release dust near the earth end and wait millions of years until the dust expands to the end of the ruler. Will the dust pass the end of the ruler at a relative speed greater than c?
  20. Jun 20, 2008 #19
    There seems to be an immediate problem, in that as soon as you build the ruler and attach one end to the Earth, the far end of the ruler will be moving at 2c relative to the CMB.
  21. Jun 20, 2008 #20


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    Yes. Any practical bound body operates on a local scale and it will have a molecular cohesion that overpowers expansion. A ruler as long as the one in your experiment is so long that it would not behave like a classically solid object.
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