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Author Topic:   Is Faster Than Light travel the wrong question?
cavediver
Member (Idle past 3634 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 76 of 81 (534194)
11-05-2009 4:37 PM
Reply to: Message 75 by onifre
11-04-2009 11:17 PM


Re: Spacetime
And this is basically a length (Lorentz) contraction that finds "gamma"?
Well, it is both length contraction and time dilation in one - it is a Lorentz Transformation (LT). What we call 'speed' is simply an LT with very small . The LT is a 'rotation' - we see this in what I say here (really want you to get this point if you haven't already):
quote:
But our traveller at 0.8c sees something different - he sees the distance as 0 lyrs and his journey time as 3 yrs (why 0 distance? If he does nothing, he will simply arrive at P2 simply by letting time pass - his velocity has rotated his coordinates so that Alpha C (P2) now lies directly in his future.)
The LT is a 4d rotation and, as we know from 3d, rotations preserve the length of vectors. So our LT preserves the length of the space-time interval. However, unlike 3d where vectors always have a positive squared norm, in 3+1 space-time we have three possibilities...
Consider a space-like interval: now on Earth and 3 yrs time on Alpha C. What is the interval?
Hmmm, if we perform LTs, the 4lyrs and 3 yrs will be transformed to other values but the (imaginary) length will be preserved. So LTs cannot take a time-like interval (+ve squared norm) into a space-like interval (-ve squared norm). Have we just shown that there is a speed limit???
Finally, what about a null or light-like interval? Now on Earth, and 4yrs time on Alpha C. Interval is
Edited by cavediver, : No reason given.
Edited by cavediver, : No reason given.

This message is a reply to:
 Message 75 by onifre, posted 11-04-2009 11:17 PM onifre has replied

Replies to this message:
 Message 77 by RickJB, posted 11-06-2009 5:30 AM cavediver has replied
 Message 80 by onifre, posted 11-09-2009 4:24 PM cavediver has not replied

  
RickJB
Member (Idle past 4981 days)
Posts: 917
From: London, UK
Joined: 04-14-2006


Message 77 of 81 (534235)
11-06-2009 5:30 AM
Reply to: Message 76 by cavediver
11-05-2009 4:37 PM


Re: Spacetime
Interesting stuff, but I have a question:-
cd writes:
Consider a space-like interval: now on Earth and 2 yrs time on Alpha C.
Where you write "(3^2)-(4^2)=-7", what does the "3" refer to?
Edited by RickJB, : No reason given.
Edited by RickJB, : No reason given.
Edited by RickJB, : No reason given.

This message is a reply to:
 Message 76 by cavediver, posted 11-05-2009 4:37 PM cavediver has replied

Replies to this message:
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cavediver
Member (Idle past 3634 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 78 of 81 (534241)
11-06-2009 6:20 AM
Reply to: Message 77 by RickJB
11-06-2009 5:30 AM


Re: Spacetime
Sorry, should have been 3yrs time on Alpha C. Changed it and hope that makes sense now. Thanks for the heads up.

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Iblis
Member (Idle past 3886 days)
Posts: 663
Joined: 11-17-2005


Message 79 of 81 (534422)
11-08-2009 3:41 AM


not backwards in time, time backwards
Hi peoples, love these threads, cavediver and son goku as usual and now also apparently onifre and others, have the math covered better than I could hope to. I just want to throw in something for the sake of the thought experiment, for the people who are wanting to believe that "somehow" traveling faster than light would equal "somehow" traveling backward in time.
Let's just allow for the argument that we "could" travel faster than c (yes, postulate magic.) I don't mean any kind of cheating either, like wormholes or space warps or teleportation, traveling from point a to point b without passing through intervening points. (That's a whole different causality breakdown!) I just mean the thing we want to imagine, traveling say 299,999 kps and then speeding up 2 kps and thereby being ("somehow") at a speed of 300,001 kps.
We would like to believe, that if we could do this, we would then be traveling backward through time, yes? That is, we would continue experiencing time moving forward for us, in our spaceship, but observe the universe outside our ship as experiencing time moving backward, like a movie running in reverse, so that when we arrived at our destination, it would be at a date earlier than we left, or at least earlier than when we jumped the "time barrier". Yes?
But this is just a delusion encouraged by science fiction. It isn't the logical result of what backwards duration would really mean in relation to what the physics are telling us about our own duration at near-light speeds. Let's look at what is actually happening and do the "magic" extrapolation for ourselves instead of trusting Buck Rogers.
As we get near the speed of light, time slows down for us. That is, an objective observer outside our frame of reference would see our clocks (and hearts, and thoughts, and actions) moving slower and slower. Yes? Then as we actually arrive at the speed of light, if we could, they would see our clocks stop. Yes? So then if we "could" go even faster, our clocks would appear to be moving backwards. It would look like a movie running in reverse, not outside the spaceship, but inside it!
This may sound like six of one and half a dozen of the other, but it isn't. The spacetime event, our spaceship, is still moving forward in time, in that when it gets another second along, it would have gone 300,001 kilometers. But it would be some time period earlier inside the ship than the time when the speed had increased. Herein lies the paradox, if time were running backwards in our ship, and when it was running forwards, we were accelerating, then now what we would be doing, from an objective viewpoint, would be what? anti-accelerating? decelerating?
Sticking with the movie analogy, as we get to the frame where we are breaking the c barrier, the movie would stop. If we "somehow" got to the frame where we were going faster than light, the movie would move one frame backward -- to the point where we were only going as fast as light -- and again, stop.
This is functionally equivalent to, never going faster than light, at all. Any such speed would rewind itself right out of ever having happened, at all, at all.
* note intentional inexactness with c to ease analogy, it's actually 299,792,458 meters per second plus or minus maybe 4 billionths in change, subject to further whacking
Edited by Iblis, : corrective note

  
onifre
Member (Idle past 2941 days)
Posts: 4854
From: Dark Side of the Moon
Joined: 02-20-2008


Message 80 of 81 (534589)
11-09-2009 4:24 PM
Reply to: Message 76 by cavediver
11-05-2009 4:37 PM


Re: Spacetime
Well, it is both length contraction and time dilation in one
Right...
quote:
But our traveller at 0.8c sees something different - he sees the distance as 0 lyrs and his journey time as 3 yrs (why 0 distance? If he does nothing, he will simply arrive at P2 simply by letting time pass - his velocity has rotated his coordinates so that Alpha C (P2) now lies directly in his future.)
I understand why he sees 0 distance (because he's just experiencing time), and how the spacetime interval is preserved.
Finally, what about a null or light-like interval? Now on Earth, and 4yrs time on Alpha C. Interval is
And thus the two do not influence each other...
However, do you mind breaking this down again:
Hmmm, if we perform LTs, the 4lyrs and 3 yrs will be transformed to other values but the (imaginary) length will be preserved. So LTs cannot take a time-like interval (+ve squared norm) into a space-like interval (-ve squared norm). Have we just shown that there is a speed limit???
I don't know exactly what you man by "LTs cannot take a time-like interval into a space-like interval" ... I think I do but I don't want to mislead myself.
Thanks again cavediver,
- Oni

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Taz
Member (Idle past 3282 days)
Posts: 5069
From: Zerus
Joined: 07-18-2006


Message 81 of 81 (534901)
11-11-2009 4:46 PM
Reply to: Message 55 by Aware Wolf
11-03-2009 8:23 AM


AW writes:
I suppose you would need the object to be of variable mass such that the delta in forces remains in the 1 - 5 G range or whatever's safe. Otherwise prior to acceleration you'd be experiencing the heavy Gs just from the gravity of what your standing on.
You're not using your imagination. I'm not talking about normal matter being the mass. Suppose we have a mass plate of something really really dense, like neutron matter. A ship sufficiently large enough (or rather long enough) could have the the mass plate at the far end of the ship. Any personnel could be placed in a movable compartment. The more the ship accelerates, the closer the movable compartment will move toward the mass plate.

This message is a reply to:
 Message 55 by Aware Wolf, posted 11-03-2009 8:23 AM Aware Wolf has not replied

  
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