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A clever cosmologist refutes relativity

  1. Apr 9, 2010 #1


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    Okay, so the title is overly dramatic, but I couldn't think of anything else to call this. Not trying to actually refute relativity, those of you who know me should know this by now. This is just an interesting problem I thought up not long ago.

    So support we send our (very skinny) clever cosmologist away from the earth at ultra-relativistic speeds. I mean something like gamma=10^15. Our cosmologist notes that relative to his rest frame, the galaxy Andromeda is approaching with gamma=10^15. So he calculates the energy needed for this motion, gamma*mc^2, and finds it is orders of magnitude larger than the rest mass energy of the observable universe! Absurd, he concludes! In some sense, then, he thinks that he must be the one who is really in motion, for it would be impossible to impart the requisite energy to Andromeda to produce the motion he observes.

    Where has our poor friend gone awry?
  2. jcsd
  3. Apr 9, 2010 #2


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    There is no 'really in motion'. He will see the galaxy approaching at a certain speed and they will see your poor friend approaching at the same speed.

    Your friend has assumed absolute motion in order to deduce it exists.

    He might say, 'I have a relative velocity v towards Andromeda so I most probably fired my engines at some time unless I have always existed in this state'. And that doesn't require absolute motion.
    Last edited: Apr 9, 2010
  4. Apr 9, 2010 #3


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    Yes yes. But this probably becomes an absolutely in the case where Eobserved>Euniverse, does it not? So without ever experiencing the acceleration he deduced he must have. Is this not an issue? Okay, I may have phrased too strongly in the initial post, but is there some issue with this statement?
    Last edited: Apr 9, 2010
  5. Apr 9, 2010 #4


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    What would be implausible would be for the Andromeda galaxy to gain or lose that much energy. It's not implausible that it simply *has* that much energy.

    Similarly, my desk has as much kinetic energy as a fighter jet -- when viewed in a frame of reference in which we see the earth spinning.
  6. Apr 9, 2010 #5


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    Can you explain exactly why the conclusion that Andromeda contains more energy than the universe can provide is not problematic? I realize energy is in no way invariant... But perhaps I have just thought of the solution my self. When we calculate the total energy of the observable universe, it's in the earth's inertial frame, say. But to then apply this energy in the new frame of the man moving with gamma=10^15 is incorrect, since energy is not invariant. If our cosmologist re-did his studies in this frame, he would likely find that in this new frame andromeda has decidedly less energy than the rest of the universe, correct? Okay, so that takes care of that one, cool.

    So let's imagine our cosmologist has a light stomach and doesn't like accelerations. So we snatch him from his house in the middle of the night, drug him, put him in the rocket, and blast him off. He wakes up and the last thing he remembers is being on Earth. By the argument from my first post (He doesn't pay attention to his surroundings -- he's a cosmologist), he can deduce that it was he who accelerated, not the galaxy. Nothing strange about this statement, really? =\
  7. Apr 9, 2010 #6
    Total energy of the universe? Total energy of any system always depends on the frame of reference, so where do you purport this speeding cosmologist get his value exactly?

    But if you're set on "refuting relativity", all you had to do was simply to note that the cosmic microwave background (and thus the universe) is empirically well-known to have a preferred frame of reference.
  8. Apr 9, 2010 #7


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    Realized this in the above post ^^

    Indeed, but this is a separate point from what I was going for with my thought experiment.

    My current question, then, is whether there is anything funny about inferring with absolute certainty they a certain reference frame accelerated and not another without actually experiencing the acceleration. Although, perhaps not. Consider the twin paradox. If we just knock the twin in the spaceship out for the period of acceleration, he won't know it was he who accelerated until he meets up with his twin back on earth. At which point he realizes that since he is younger, he must have accelerated while he was blacked out (or I guess he could ask his twin if he remembered any acceleration, but he was comatose the whole time as well). Any salient differences between these two examples, I wonder?

    Not going for anything in particular here, just throwing ideas around.
  9. Apr 9, 2010 #8
    What do you mean. Can you elaborate?
  10. Apr 9, 2010 #9

    D H

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    Our clever cosmologist is using more than relativity; he knows the prior relative state of the Andromeda galaxy. So let's wipe that prior information out. Don't just knock the cosmologist out, put him in a spaceship, and accelerate that spaceship toward Andromeda (no paradox there; we know what we did). Knock him out, put him in a spaceship, and send it through a wormhole that opens up near a galaxy far, far away. When he wakes and finds himself speeding at gamma=15 toward who-knows-what galaxy, well, who knows what is speeding toward what?
  11. Apr 9, 2010 #10

    The Earth is moving ~600km/s relative to the CMBR frame based on parallax and temperature dipole anisotropy. In galactic coordinates the direction of motion is l=276, b=30.

    Thus we are able to calculate a local velocity relative to something resembling a global frame. This also appears to be near our velocity relative to our local super cluster in the De Sitter space.

    Anyone have any thoughts on this being tied to being in a gravitational well, with the CMBR being Lorentzian invariant only where the Hubble Flow dominates?
  12. Apr 9, 2010 #11
    Not exactly, there is no such thing as "CMBR frame". The 600km/s is calculated wrt the frame in which CMBR appears to be isotropic.

    There is no such thing as a "global frame".

    What gives you this idea?
  13. Apr 10, 2010 #12


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    Forgive me for being obtuse, but I'm not sure I grasp where you're going with this. Simply trying to remove the knowledge of Andromeda from the picture? Or are you trying to erase the knowledge of the global properties of the universe altogether? In your wormhole case, could our cosmologist not perform some measurements of the galaxy, deduce its mass, and similarly conclude that its energy is far too high to have come from the universe he knows (assuming, that is, he has data from before we started this horrid experiment) and deduce that he accelerated into this frame?

    Could you please explain a little more if I'm too far off base?
  14. Apr 10, 2010 #13


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    ( my bold)

    What does he think the bold terms mean ? Does he believe in an absolute frame in which he has the greater velocity ? Does he not remember being sent away from the earth ?

    I don't see any challenge here to the principle that the only 'real' velocity is relative velocity.
  15. Apr 10, 2010 #14
    The velocity that is necessary for physical matter to have a gamma of 10^15 would be [1 - 10^(-30)*c] (I can't even bring it up on my calculator.)

    You are saying that there isn't enough matter in the observable universe to generate the kind of energy (through "rest energy") that would be required to "push" him up to that velocity. Well, we don't know how much matter is in the universe so we cannot say that your statement is correct. It is conceivable that what is posited here is impossible to achieve, as the necessary velocity is so close to light speed that there isn't enough energy in the universe to produce it, but this is unknowable. Even if this last sentence is true, we have no way of determining what the upper limit of achievable energy is in the universe, so the question is rhetorical - no answer. The cosmologist in his own frame of reference does not have near infinite mass, only near infinite mass relative to whatever frame of reference is booking at 0.9999999999999999999999999999....*c the other way.

    Surely, the total amount of energy in the universe would be the sum of all the "rest energy" plus whatever "free energy" (such as photons - which are energy particles with no mass) or other energy exists. Clearly an unanswerable question, but this does not state that it is impossible for a space traveler or particle to travel so fast. Clearly, we have not as yet observed anything so close to this.
  16. Apr 10, 2010 #15
    gamma*mc^2 is TOTAL energy, where "m" is the mass of the Andromeda galaxy

    Why would the cosmologist compare the TOTAL energy of Andromeda with the REST energy Mc^2 of the universe, where "M" is the mass of the universe? To make the problem even more irrelevant, TOTAL energy is FRAME DEPENDENT, it depends on "gamma" through the relative speed "v" between the cosmologist frame and Andromeda.

    The problem statement appears absurd, indeed.

    He's comparing apples and oranges.
  17. Apr 10, 2010 #16
    How is this anything other than another way of struggling with the concept of relative motion? I don't see how this "thought experiment" is materially different from Einstein's elevator, except that now we're complicating instead of simlifying the issue.
  18. Apr 10, 2010 #17


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    Ok everyone who has responded since my post #12 seems to be ignoring the previous posts in this thread. I dropped any absolute motion claim a while ago. I realized total energy is frame independent, so he cannot compare the two so haphazardly. It doesn't look to me like anyone has even mentioned the question I brought up in post #7. Is there anything wrong with him deducing that he must have accelerated, not the other way around, on the basis of knowing the energy content of the observable universe? Perhaps I should just reformulate the experiment altogether:
    a) Cosmologist on earth measures the energy content of the observable universe.
    b) Cosmologist is knocked out, sent away on spaceship, wakes up in deep space.
    c) Cosmologist measures relative velocity to andromeda, gets an answer like gamma=10^15. Calculates energy needed to ACCELERATE andromeda from its previously known state, relative velocity to earth a pitiful hundred km/s, to gamma=10^15. Concludes this amount of energy does not exist in the observable universe.
    d) Cosmologist concludes that it was he who must have accelerated at some point, not the andromeda galaxy, on the basis of this alone.

    1) Yes 10^15 is ridiculously large. That's why I specified he's a very skinny cosmologist. My point is: for a sufficiently small mass, it would not be absurd to accelerate him this fast, but it would be to accelerate a galaxy to the same velocity.
    2) Yes it's difficult to determine the total energy content of the observable universe, but why, in principle, can it not be done from the Earth's frame? This is a thought experiment. Unless there is any fundamental reason why this number cannot be known through detailed observations, this is a moot point.
    3) If you really want, fine, don't compare total energy. Use the kinetic energy, mc^2(gamma-1). I'm sure 10^15-1 is going to give us much better accuracy.

    Ok. I hope this clarifies where things are at right now in the discussion. Now, are there any problems with the cosmologist's conclusion? The answer could very well be "No, not at all!" In which case, that's fine. Case closed. It just smells a little fishy to me is all, which is why I'm asking about it here.
  19. Apr 10, 2010 #18

    D H

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    Nothing fishy. The issue isn't who is moving; it is which object (the cosmologist or the Andromeda galaxy) was accelerated. The cosmologist knows that one of the two underwent acceleration because of his prior knowledge of the relative velocity between him and the Andromeda galaxy. Unlike velocity, acceleration is not relative. That acceleration is not relative is why accelerometers can work.

    If the cosmologist is instead whisked away to somewhere far, far away that prior knowledge is gone. We know, due to the expansion of space, that distant galaxies are receding from us at incredibly high gamma (some superluminally!) The cosmologist merely sees a galaxy retreating at a high gamma. He does not know which galaxy, or where he is. Whether the wormhole conserves energy/momentum, who knows? The cosmologist can't tell. He might have been whisked away to some not-so-remote region via a wormhole and accelerated by the passage, or or might have been whisked far, far, far away and not accelerated.
  20. Apr 10, 2010 #19
    It is materially different in that no measurements are taken during the period of acceleration in this case, while the acceleration is locally constant in Einstein's elevator.

    By comparing measurements of space before and after acceleration it is possible to determine the amount of change in velocity that has been introduced in the interim, even if the nature of the acceleration is unknown.

    Lets also observe that the cosmologist would see the Milky Way and other components of the Local Cluster and even the local super cluster accelerated by a similar amount, adding to his evidence that he has been accelerated based on information from nearly every direction.

    Actually it would be better to estimate that the total acceleration was split among parts inversely proportional to the rest energies involved. Since his mass is much less than that of the Local Cluster, he would have been the one accelerated.

    This suggests that local dominant energy distributions define a reference frame that an observer in the local area can measure a difference relative to.
  21. Apr 10, 2010 #20
    ...Which again assumes prior knowledge. D H just answered this perfectly.
  22. Apr 10, 2010 #21


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    The point is that "the total energy of the observable universe" is a frame dependent quantity. If the cosmologist measures it in his rest frame at two points in time and gets two different answers then he can indeed conclude that his rest frame is non-inertial. None of that refutes relativity in any way.
  23. Apr 10, 2010 #22
    Consider a second observer (O2). He is moving with gamma=10E15 wrt the CMB. O2 considers himself to be stationary and as far as he is aware he has never accelerated in his life. From the point of view of O2, the available energy of the universe is (and always has been) 10^15 greater than the available energy of the universe from the point of view of an observer that is at rest rest with the CMBR. The available energy of the universe from any given observer's point of view, is not just the rest mass energy of the universe, but also includes the total momentum energy. Let us say the skinny cosmologist (O1) was initially at rest wrt the CMB and then accelerates into O2's rest frame. From O2's point view, O1 has just used a tiny fraction of the universe's available energy to decelerated and come to rest. So although O1 can claim he has used x amount of energy to change his velocity, he has no grounds to claim what his absolute final velocity is. It is perfectly consistent from O2's point of view that O1 had an initial velocity and decelerated to a state of rest. No paradox. No refutation.

    This is similar to standing outside at night and looking at the stars while completing one revolution on the spot. Have you just used your muscle power to rotate your body, or have you just rotated the entire universe and effectively accelerated distant stars to superluminal velocities? Most people would agree you just rotated your body. In this sense, acceleration is absolute. You can determine that you have in fact rotationally accelerated by using accelerometers, gyroscopes, Sagnac devices etc. What you have not determined, is your absolute initial and final velocities.
    Last edited: Apr 11, 2010
  24. Apr 10, 2010 #23


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    Thanks for the responses, people, especially kev and DH. Makes sense now.

  25. Apr 10, 2010 #24
    I'm confused...
    @kev: I always thought my muscles DID move the universe... are you trying to tell me that I'm wrong?! No wonder all those women laughed and walked away when I said that... :smile:
  26. Apr 10, 2010 #25
    I think the problem here is the cart before the horse, so to speak.

    If one comes up with a velocity so great that it is so close to lightspeed that the amount of energy required to obtain it is beyond anything conceivable, considering all the available mass and energy there is in the universe, then the original question cannot happen, i.e. , the "cosmologist" cannot be travelling at such a speed that his gamma is 10^15.

    Since we do not know how much energy is potentially available in the universe to "push" our friend along, then we cannot categorically state that we have refuted relativity. Maybe the cosmologist or particle did have access to a source of energy that gave him the speed he needed to calculate to the postulated gamma (10^15.)

    At this point, I believe I am entirely missing the what the original question is driving at.

    Capasci? Verstehst du? Entiendes?
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