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Author | Topic: Is Faster Than Light travel the wrong question? | |||||||||||||||||||||||
cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
that I wish Cavediver were here to discuss. Oh, I'm here Just VAT return time as ever...
what is really keeping us from going from here to Alpha Centauri in one year, or sooner? Nothing - if you can accelerate hard enough and safely enough, you can reach Alpha C as fast as you like - couple of days maybe. Of course, your round trip as measured by someone on Earth will take 8.6 years, but you can do it so to age as little as you choose.
Does time slow as we experience it? I'm not sure what this means. Do you mean, can we see our own watch tick slowly? No, definitely not. You only see those watches that are travelling at speeds relative to your own as ticking slowly (or more quickly in some circumstances)
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
For somebody moving past you at high speeds because they'll label events differently they'll see your "now" and your "ten seconds ago" as occuring at the same time, but at different points in space. Hmmm, you been drinking? You can't transform a time-like interval into a space-like interval unless really drunk
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
No matter where the observer is (you at the events, me on a plane watching the event from above, or SonGoku on Venus) while we'll disagree on the time it took to get from position (A) to position (B), none of us will see them backwards (B happening before A). This is essentially the heart of the "causality" you have been hooked on. Any pair of events can be placed into one of three categories: space-like separated, time-like separated, and null separated. Time-like means that a path through space-time can be taken between the two events, such that c is never exceeded. All observers, no matter their motion, will agree on which event is in the past and which is in the future (SG made a slight slip here.) Space-like means that no sub-light path can be taken between the two events. In this case, which event occurs first is observer-dependent. There is no such thing as one event occuring later than the other. A good example would be me firing a pistol on Earth at 23:00 GMT, and you firing a pistol on Mars at 23:05 GMT. We can have the most perfectly synchronised watches ever built, but in NO ABSOLUTE WAY can it be said that I fire first!! Null-separated is the in-between state where a light-ray can connect the two events. Just to add some spice, not all space-times admit such a causal structure. It is possible to have non-time-orientable space-times where even time-like separated events can have their time-ordering reversed! But we're getting into messy territory here ABE: just to stress - if two events are space-like separated, they will appear space-like separated to ALL observers, no matter their motion. Likewise, null-separated events will always be seen as null separated. Edited by cavediver, : A little clarification
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
Thanks, I just got carried away with the analogy without thinking. No problem - I hate to think of some of the things I have said in the heat of a great analogy
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
Can you explain in a little more depth how it is that one couldn't say who fire first? Ok, I have to be a bit careful here because, annoyingly, the Universe does have a preferred rest frame which means that much of Special Relativity doesn't carry the weight it should... In SR, there is no state of rest. All states of motion are equally valid. There is no preferred frame of reference. One observer may see one gun fire first and then the second, but another observer will see the second gun fire first. And this is after taking into account the finite travel speed of light... there is no actual order of two space-like separated events! In our Universe, the expansion of the Universe creates a frame of rest, essentially that where the CMBR is seen to be non-red/blue-shifted in any direction. We are near as damnit sitting in that rest frame while we are travelling slowly wrt the Earth/Sun/Galaxy/Local Group. So wrt this frame, we can say with some credibility that the 17:00 GMT gun fires before the 17:05 GMT gun. But try convincing the guy flying past at some large fraction of c...
QM...? No, not at all. This is 'simple' General Relativity in 'interesting' space-times Actually, QM sort of comes undone in such situations and needs rescuing if it is to make any sense. QM is usually rather dependent on a well behaved sense of time.
What maintains this consistency? Why, the very structure of space and time Seriously, that is what Minkoswki space gives you. And it is directly connected to the finite speed of light. I think a lesson in hyperbolic geometry is in order to explain this well, but it may have to wait until later today...
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
So then, it actually doesn't matter which event occured first Neither occured first
since the distance between them is so great that they are causally disconnected (one can't influence the other) due to the cosmic speed limit? Exactly! But be careful not to trivialise this point about the 'speed limit' - c is not a speed limit in any real sense. At c you arrive at your destination in zero time. That's not a limit. It's a breakdown of this concept you think of as speed. Remember that reality is a 4d space-time, but our conciousness and perspective deals only with 3d. A 3d observation of a 4d quantity is typically observer dependent. Any two events in space-time are separated by a 4d-vector. The space-time distance or 'interval' between the two events is a universal quantity, a scalar value upon which all 4d beings will agree. But as 3d beings, we cannot see the 4d vector nor its length, we can only see 3d projections of the vector, and the length of thse projections. Consider only being able to see the shadow of a 1m ruler. The ruler is always 1m long, but the length of the shadow is not... So, take the two events of leaving Earth today, P1, and arriving at Alpha C in 5 years time, P2 (Alpha C is 4 lyrs away for this example.) The space-time interval is (taking a ---+ signature; bear with this) is , but we don't see this. On earth we just see 4 light years distance, and 5 years time. 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.) Notice that the 4d interval has not changed: (ABE: thanks guys for the correction!) That's a start. Does that make any sense at all? Edited by cavediver, : No reason given. Edited by cavediver, : No reason given.
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
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: 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.
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cavediver Member (Idle past 3674 days) Posts: 4129 From: UK Joined: |
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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