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High velocity travel.

  1. Oct 13, 2006 #1
    In a description of the discovery of the so-called 'Oh-My-God particle' (http://www.fourmilab.ch/documents/ohmygodpart.html), the following assertion is made:
    The idea seems to be, essentially, that it would take 21 years to go from Earth to the center of the galaxy at 1516c, while only taking 3 seconds to make the same trip at (very close to) c. How could that be? What sense does that make?
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  3. Oct 13, 2006 #2


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    Because under the Newtonian rules they're assuming in the 1516c calculation, there is no time dilation or length contraction; but with relativity, the clocks of a ship moving to the center of the galaxy at very close to c would be slowed down in the galaxy's frame, and by getting the ship arbitrarily close to c you can slow them down as much as you want, even to the extent that only 3 seconds would pass on the moving clock during the 30,000 years or so it would take in the galaxy's frame. In the ship's frame, its clocks are not slowed down, but the length of the galaxy is Lorentz-contracted, and again it can be contracted to an arbitrary degree, enough so that the distance from earth to the center in the ship's frame is less than 3 light-seconds.
  4. Oct 13, 2006 #3


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    In the frame of the OMG particle, the distance between the Earth and the center of the galaxy is length contracted, to a number much less than 1516 light years.

    If you consider the "round trip" case, this is just an example of the twin paradox.

    Twin A sets out at the velocity of the OMG particle, goes to the center of the galaxy in 3 seconds, turns around instantaneously, and proceeds back to the Earth in another 3 seconds, making the round trip in 6 seconds.

    Twin B, on Earth, experiences 60,000 years.
  5. Oct 13, 2006 #4
    Indeed. And why do they use "Newtonian rules" for the spacecraft? I assume it's because special relativity is invalid for speeds greater than c?
  6. Oct 13, 2006 #5


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    Partly that, and probably partly also because that's just how things seem to work on Star Trek, no one ever ages differently depending on what "warp" they've been moving at.
  7. Oct 13, 2006 #6


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    Mainly it's because to do otherwise would causes too many plot problems:

    Data: "Captain, we are receiving a distress call from Star Base 10. They are under attack by the Romulans.

    Picard: "How fast can we get there?"

    Data: " 15 minutes at warp 9, sir"

    Picard" Very well, plot a course and engage!"

    15 minutes later, by the ship's clock, the Enterprise arrives at Star Base 10, only to find that the battle has been over for some 2 weeks and the Star Base is now in the hands of the Romulans!

    IOW, for the sake of telling the story, Warp drive is assumed to side step Relativity issues.
  8. Oct 13, 2006 #7


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    Yes. It wasn't called Warp Drive just for fun...

    The technobabble explanation of the Warp Drive is that it shrinks the space in front of the craft and expands the space behind the craft. The "Warp factor" is not a "speed" at all, it is literally the factor by which it exaggerates this space "warping" effect. The craft does not actually exceed c in its local "Warp bubble" of space.
  9. Oct 13, 2006 #8


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    I don't think that explanation was ever used on the Star Trek show itself though, was it? There is actually a real proposal in general relativity that would work in a similar way, known as the Alcubierre warp drive, but I think it's not actually completely clear whether it could be used to travel to other stars or galaxies in less time than a light beam travelling through normal semiflat space would. As for Star Trek, the most logical explanation I've seen is the one here, which suggests that in the Star Trek universe "subspace" actually defines a preferred frame for FTL travel, thereby avoiding the problem of causality violations which would arise if it was supposed to be consistent with relativity (I would think if the Alcubierre bubble could get to distant destinations in otherwise flat space faster than a light beam travelling through the flat space would, then this would lead to causality violations as well, despite the fact that the ship inside the bubble does not locally travel faster than c...I know that GR predicts wormholes could lead to causality violations if quantum effects don't destroy them, even though no one locally travels faster than c when going through the wormhole either).
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