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Author | Topic: Is Faster Than Light travel the wrong question? | |||||||||||||||||||||||
cavediver Member (Idle past 3665 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 3665 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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kbertsche Member (Idle past 2153 days) Posts: 1427 From: San Jose, CA, USA Joined: |
quote:Yes, Newtonian mechanics is still an excellent approximation over the parameter space where it was experimentally verified. And I expect Einsteinian relativity will likewise remain an excellent approximation over the parameter space where it has been experimentally verified. Thus there is no realistic hope of physical travel to distant planets without a tremendous expenditure of energy.
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Son Goku Inactive Member |
Aaarrggghhh!!
What makes it even worse is that I checked the post with another physicist before I posted it. Which means we both didn't spot it! Thanks, I just got carried away with the analogy without thinking. Sorry for the mistake everyone, ignore the last paragraph of message #56. I'll try to reword things so that they are still understandable, but actually correct.
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cavediver Member (Idle past 3665 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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RickJB Member (Idle past 5012 days) Posts: 917 From: London, UK Joined: |
kbertsche writes: Yes, Newtonian mechanics is still an excellent approximation over the parameter space where it was experimentally verified. And I expect Einsteinian relativity will likewise remain an excellent approximation over the parameter space where it has been experimentally verified. I agree.
kbertsche writes: Thus there is no realistic hope of physical travel to distant planets without a tremendous expenditure of energy. Apparently not, but our current theories are less than 100 years old. Where will these theories be in 10,000 years if humanity is able to maintain scientific development? There may be a solution, we just don't know it at present. Edited by RickJB, : No reason given. Edited by RickJB, : No reason given.
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onifre Member (Idle past 2972 days) Posts: 4854 From: Dark Side of the Moon Joined: |
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. Thanks for that detailed explanation cavediver.
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. Can you explain in a little more depth how it is that one couldn't say who fire first? Does it have to do with not being able to exceed (c)?
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 QM...?
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. Can you explain this in a little more depth too? What maintains this consistency? Thanks again, - Oni
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cavediver Member (Idle past 3665 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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Perdition Member (Idle past 3259 days) Posts: 1593 From: Wisconsin Joined: |
And no, I didn't leave the apple on the desk for you...seriously...I wouldn't do that...no sir.
{AbE}But I think I saw that Onifre kid leave a tack on your chair. {/AbE} I'm looking forward to learning more here, as you saw, I'm probably way off the mark. Edited by Perdition, : No reason given.
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onifre Member (Idle past 2972 days) Posts: 4854 From: Dark Side of the Moon Joined: |
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! So then, it actually doesn't matter which event 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?
But try convincing the guy flying past at some large fraction of c... So which is first is observer dependent - however, it doesn't matter which is first because neither influences each other, and, both observers are right?
I think a lesson in hyperbolic geometry is in order to explain this well, but it may have to wait until later today... Please do as I have many questions, and I left no tac on your seat - so sit down, have some coffee and relax. Thanks again, - Oni
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onifre Member (Idle past 2972 days) Posts: 4854 From: Dark Side of the Moon Joined: |
But I think I saw that Onifre kid leave a tack on your chair. I wish I still was a kid! lol But thanks for the compliment old-timer. - Oni
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cavediver Member (Idle past 3665 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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Meldinoor Member (Idle past 4830 days) Posts: 400 From: Colorado, USA Joined: |
Just a minor quibble, but shouldn't the result of be and not ???
Respectfully, -Meldinoor
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bluescat48 Member (Idle past 4211 days) Posts: 2347 From: United States Joined: |
It should read = = 3
Edited by bluescat48, : Latex work Edited by bluescat48, : ditto Edited by bluescat48, : same Edited by bluescat48, : continuing latex attempts Edited by bluescat48, : trying again There is no better love between 2 people than mutual respect for each other WT Young, 2002 Who gave anyone the authority to call me an authority on anything. WT Young, 1969 Since Evolution is only ~90% correct it should be thrown out and replaced by Creation which has even a lower % of correctness. W T Young, 2008
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onifre Member (Idle past 2972 days) Posts: 4854 From: Dark Side of the Moon Joined: |
Neither occured first Sweeeet! I got it ... I got it, there is no such thing as first.
Oni writes: 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?
cavediver writes: Exactly! Sweeet again!
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. Like a photon, which experiences no time - It travels at c relative to us but relative to the photon it is not moving at any speed?
Notice that the 4d interval has not changed: The same for everyone And this is basically a length (Lorentz) contraction that finds "gamma"?
That's a start. Does that make any sense at all? It does, it really does ... please continue when you have more time. - Oni
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