Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Kryptid on 30/09/2013 07:30:25
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Yes, we all know that you can't travel faster than the speed of light in a vacuum. At least not in a normal sense. However, some think that we can "cheat" by using a "warp drive" of sorts to move a bubble of space-time faster than the speed of light. Space can expand and contract faster than light in principle, and this seems to be the grounds for the concept of a faster-than-light warp drive. However, I came to a realization when I thought about the Rietdijk-Putnam Argument/Andromeda Paradox: http://en.wikipedia.org/wiki/Andromeda_paradox (http://en.wikipedia.org/wiki/Andromeda_paradox)
If I read this article correctly, the implications are that faster-than-light travel, even by "cheating" with space warps, should violate causality. Let me try to set up my own thought experiment using a similar argument to the article.
Let's say that a person named Alice is aboard an aircraft that is flying away from the Andromeda Galaxy. In her reference frame, a discussion is being held by aliens in that galaxy as to whether they should invade Earth or not. She calls a space agency, which has invented an extremely fast spacecraft which can use warp drive to get to Andromeda and back in a matter of minutes. She asks for the agency to investigate Andromeda to see what is happening there at the time. In her reference frame, the spaceship goes out and returns in a few minutes. Once it returns, they alert her to what the aliens are discussing.
Meanwhile, another person named Bob is aboard a similar aircraft which is flying towards the Andromeda Galaxy. In his reference frame, the discussion being held by the aliens has been over for days now and they are on their way to invade Earth. Like Alice, he calls a similar space agency to send a craft to investigate Andromeda. Once it returns, they alert him to the invasion.
Now, Alice and Bob contact one another and discuss their discoveries. It would seem that, because of warp drive, Bob has access to information about Alice's future (despite the fact that both of them seem to share a common "present"). If he tells her that the aliens are already coming in his own reference frame, then couldn't it be possible for Alice to send out a warp-powered ship to attack and destroy the aliens before they even begin their invasion? If she does, then that would contradict the information present in Bob's reference frame.
If it is impossible to exceed the speed of light, even in principle, then the causality is preserved because there is no way that the information required to create a time paradox could be obtained (as the Andromeda is much too far away to be observed in real time).
Does this make sense to anyone?
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If there is a way to travel faster then light at a speed (say) c'=10,000*c then why not define a new plane of simultaneity corresponding to the new maximum speed possible c'?
In this new plane of simultaneity I believe there will be no paradox unless someone goes even faster then c' (in which case a newer plane of simultaneity can be defined according to the fastest possible speed).
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Perhaps I need to learn how to draw this as a Minkowski diagram.
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Perhaps the Andromeda Paradox disproves General Relativity.
If you consider the Hafele–Keating experiment (http://en.wikipedia.org/wiki/Hafele-Keating_experiment), with 3 atomic clocks.
The eastbound clock lost 59 nanoseconds.
The westbound clock gained 273 nanoseconds.
If every clock discrepancy spawned new multiverses, we would be in a big mess. And, in fact, it should be impossible to rejoin the three clocks once again.
My belief is that time did not change, but merely the measured speed of the clock changed. The atomic clocks are based on the frequency of a signal to affect the energy state of an atomic transition. This complex process of control of the clocks is energy based and necessarily dependent on the background energy state.
I suppose the question then is what truly is time?
Perhaps we should think of time as some sort of energy unit. Somewhat like the opposite of Absolute zero.
Absolute zero would be a base state with zero energy.
The speed of light would be a point where the kinetic energy is infinite.
This, of course, only affects whatever is within the reference frame. In a larger reference frame, the time/energy just chugs on without respect to the energy state within certain reference frames.
If we considered the entire universe to be our reference frame, then it would be October 1st in both the Milky Way, as well as Andromeda irrespective of the speed the clocks are moving due to kinetic, orbital, and gravitational energy state of any particular planet or star.
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If there is a way to travel faster then light at a speed (say) c'=10,000*c then why not define a new plane of simultaneity corresponding to the new maximum speed possible c'?
In this new plane of simultaneity I believe there will be no paradox unless someone goes even faster then c' (in which case a newer plane of simultaneity can be defined according to the fastest possible speed).
There can be only one preferred reference frame in which it might be possible to communicate instantaneously (or any speed faster than light) across vast distances without implying a paradox.
Let P be the preferred reference frame; M is a reference frame moving in the +x direction relative to P. Communicators A and B are stationary in M. B is in the +x direction from A.
A sends a signal to B. To an observer in P, the message arrives at B at the same instant that is leaves A. To A and B, the message appears to arrive t seconds before it was sent.
Then B instantly acknowledges receipt of the message. To the observer in P, both the message and acknowledgment occur at the same instant at both A and B. To A and B, the acknowledgment appears to be delayed by t seconds. Therefor, two-way communications would be instantaneous in M. There is no paradox as long as there is only one preferred reference frame.
If there is such a preferred reference frame, there's a good chance that it is the commoving cosmic reference frame. Based on dipole Doppler shift of the CMB, our solar system is moving about 371 km/s (0.001238 c) towards the constellation Leo, relative to the commoving cosmic reference frame. (Get a different velocity every time I Google it.) That gives a relativistic gamma of 1.000000766.
The time equation is (https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fupload.wikimedia.org%2Fmath%2F0%2F0%2Fe%2F00e678d679807b1ea435df665487c95f.png&hash=e629bea5a246c42db8b08a093133c875).
From that, I calculate that the time shift along a line toward Leo is about 4.13 ns/km. (Last time I did the calculation, a year ago, I got about 9 ns/km. At least I'm not off by orders of magnitude.) A "quantum teleportation" experiment sends a signal 16 km toward Leo. (The sending and receiving clocks are synchronized in the manner described by Einstein. Light pulses from the mid point will arrive at both clocks simultaneously in Earth's reference frame.) If the signal is instantaneous in the preferred reference frame, the receiving clock should indicate that the signal arrived 66 ns before it was sent. A signal sent in the opposite direction should arrive 66 ns after it was sent.