Any resolutions to FTL paradoxes?

[meberbs]

Constant or not, the gravitational potential sets the baseline for the rate at which the clock ticks. That gravitational potential has a source, assumed to be at the center of mass of whatever field(s) created that potential. Kinetic energy must be measured relative to that, regardless of where in the universe the clock is located.

Your assumption is bad. There can be multiple sources, distributed sources, and sources moving with varying velocities relative to each other.

And effectively constant potential does matter, because the apparent rate of clocks ticking depends on the velocity as well. If you ignore this, then you can't explain constancy of speed of light regardless of the velocity of a frame.

In regards to your question, here is the procedure:
The observer who comes onto the scene where there are 2 clocks in motion relative to each other, and relative to him.

1. He must first determine where is the center of gravity for region of space, and then adjust his position and speed to match that frame.

This step makes no sense, how do you define this frame, what if the field comes from 2 equal masses equally far away in different directions, moving at different speeds? Note that the fact that they are moving at different speeds, means that you can pick frames where you are closer to one or the other. To give you a start on this, the fields are determined by the retarded position of the masses rather than the current position, because gravity propagates at the speed of light (although you have to take into account the velocity dependent effects. In Electromagnetism this results in the E-field pointing towards the current location of a moving charge rather than the retarded position.)

2. Then measure the rate of each clock by comparing their rates and kinetic energy, in this frame.

So in the end of the day you are just picking a preferred frame despite the fact that the Michelson Morley experiment and related tests says that there is no preferred frame.

Some thought experiments for you to work through, in all cases start with the clocks some distance apart and moving directly away from each other, assume they were synchronized when they were next to each other. Have one be initially at rest in your preferred frame.

1. Give the moving clock a delta-v equal to 2*v (where v is its initial velocity) to bring them back together.
2. Give the stationary clock a delta-v of 2*v/(1+v^2/c^2) to bring them back together. (slightly less velocity change in your "special" frame due to the same change in momentum having less change in velocity as the object speed approaches c.

If for both cases 1 and 2 it is the clock that you gave the delta-v to that is slowed, (and by the same amount in both cases) then it is clear that this is a reciprocal situation, and your special frame has nothing special about it. If you get a different answer than this, then if you explain what you did I will be able to find a contradiction either within your procedure or between your procedure and experiment.

It doesn't have to be a universal rest frame. It only has to be a gravitational field from which to derive a baseline. The spectral energy density of the vacuum is free to be different from place to place in space-time, and any matter will conform (scale) itself to establish equilibrium with that local density. That kinda makes it difficult to measure!

If it is not a universal frame, then observers in the different frames will still disagree on which clock is slowed, and you do not have the universal time that you keep claiming.

It is not just difficult to measure, but you have failed to actually define how to measure it. Your method here was to "determine the center of gravity" which is both an undefined concept and an undefined method. You don't actually use the clocks for the main determination. This undercuts your point, because if one is absolutely right and not the other, their must be a way to measure that. If there isn't, you are just back to relativity where both are "right" because their is no special frame.

[dustinthewind]

This seems connected to the discussion. 

Dark energy: the absolute electric potential of the universe

In this essay we will discuss one of the most striking consequences of
electromagnetism in the cosmological context, which is the possibility that
the universe at large scales not only sets a privileged reference frame, but
could also determine an absolute electric potential. Indeed, it is well known
that the presence of matter and radiation in the universe implies that, on
large scales, the universe as a whole has associated a privileged reference
frame. That frame is nothing but the cosmic center of mass frame [2] of the
different components (baryonic and dark matter, radiation and dark energy).
In the case in which all such components are at rest with respect to each
other, the frame can be identified with that of the observers who see an
isotropic cosmic microwave background.
...
Does it make sense
to talk about a privileged electromagnetic gauge? We will argue that dark
energy, responsible for the accelerated expansion of the universe, could be
nothing but the energy density associated to such absolute electric potential

[WarpTech]

Given two clocks at rest wrt each other, in empty space.

Scenario 1)
1. Give clock 1 a kick to provide kinetic energy. It's energy has been increased, therefore this clock is now running slower than clock 2. The two clocks now have a relative velocity of v.
2. Give clock 1 a reverse kick to stop it's motion, v=0. Now, both clocks tick at the same rate.
3. Give clock 1 another reverse kick to bring it back to clock 1. The two clocks now have a relative velocity -v. Clock 1 is ticking slower than clock 2 again.
4. Give clock 1 another kick to stop its motion when it arrives at clock 2. v=0. You will find that clock 1 ticked off less time than clock 2, because it spent most of the time in a higher energy state.

Scenario 2)
1. Give clock 1 a kick to provide kinetic energy. It's energy has been increased, therefore this clock is now running slower than clock 2. The two clocks now have a relative velocity of v.
2. Give clock 2 the same kick towards clock 1. Their relative motion ceases, v=0. Both clocks tick at the same rate, but slower than their original rate.
3. Give clock 2 another kick towards clock 1. The two clocks now have a relative velocity -v. Clock 2 is now ticking slower than clock 1.
4. Give clock 2 a reverse kick to stop its motion relative to clock 1, when it arrives at clock 1. v=0. You will find that clock 1 has ticked off more time than clock 2, because clock 2 spent more time in a higher energy state.
5. At the end of this scenario, both clocks are ticking slower than they were at the end of the first scenario above.

Energy in SR may appear to be frame dependent, or observer dependent. But in fact the kinetic energy is a real quantity that had to be given to, or taken away from one clock or the other.

[meberbs]

Given two clocks at rest wrt each other, in empty space.
...

Those are correct and accurate descriptions of what you see from the initial rest frame. If you start just after step 1, and use the clock 1's frame while it is moving at v relative to clock 2 the exact same descriptions work, just flipping which is scenario 1 or 2. There is therefore nothing special about the first frame, and things are perfectly reciprocal, unless you are claiming that the numeric value of the observed time delta when the clocks meet back up is not the same in the 2 situations, in which case you need to repeat this description using numbers and math.

Energy in SR may appear to be frame dependent, or observer dependent. But in fact the kinetic energy is a real quantity that had to be given to, or taken away from one clock or the other.

Except for the fact that it is frame dependent and your descriptions illustrate this. The 2 situations are exact mirrors of each other. Scenario 2 is the exact description of scenario 1 if you come in just after the first step, and pick the clock that gets the kicks in the middle as your frame of reference, because as far as you know it was the other clock that got the initial kick.

[WarpTech]

Given two clocks at rest wrt each other, in empty space.
...

Those are correct and accurate descriptions of what you see from the initial rest frame. If you start just after step 1, and use the clock 1's frame while it is moving at v relative to clock 2 the exact same descriptions work, just flipping which is scenario 1 or 2. There is therefore nothing special about the first frame, and things are perfectly reciprocal, unless you are claiming that the numeric value of the observed time delta when the clocks meet back up is not the same in the 2 situations, in which case you need to repeat this description using numbers and math.

Energy in SR may appear to be frame dependent, or observer dependent. But in fact the kinetic energy is a real quantity that had to be given to, or taken away from one clock or the other.

Except for the fact that it is frame dependent and your descriptions illustrate this. The 2 situations are exact mirrors of each other. Scenario 2 is the exact description of scenario 1 if you come in just after the first step, and pick the clock that gets the kicks in the middle as your frame of reference, because as far as you know it was the other clock that got the initial kick.

They are not exact mirrors because, in Scenario 1 the two clocks end with the same rate they started with. In Scenario 2 the two clocks end while running at a slower rate then they were at when they started. The end of the experiment is NOT the same.

IMO, such a scenario that skips step 1 is not a well defined problem, therefore the answers will be ambiguous. That is where you make an assumption that it doesn't matter. The rate of the clocks at the end of each scenario are different, therefore the two scenarios are not the same and step 1 does matter.

[meberbs]

They are not exact mirrors because, in Scenario 1 the two clocks end with the same rate they started with. In Scenario 2 the two clocks end while running at a slower rate then they were at when they started. The end of the experiment is NOT the same.

Except there is NO way to tell that they are different. If you execute scenario 2, but use the frame of clock 1(after the unnecessary step 1) then clock 1 will be ticking at a constant rate the entire time, and both clocks end up ticking at that same rate at the end, with clock 2 being slow during all the times that it is moving. This is EXACTLY scenario 1.

IMO, such a scenario that skips step 1 is not a well defined problem, therefore the answers will be ambiguous.

That is not an opinion, that is a factually incorrect statement. The answers aren't ambiguous, because you get the same result either way. The only thing that is not well defined is how you determine this special rest frame you claim everything has to start from.

That is where you make an assumption that it doesn't matter. The rate of the clocks at the end of each scenario are different, therefore the two scenarios are not the same and step 1 does matter.

I am not making an assumption that it doesn't matter, but demonstrating that you get the exact same conclusion from either frame. It is the conclusion, and was not assumed, just tested to see if it was true.
You are the one that is making the assumption that they both have to start at the same velocity and there is something special about that initial velocity. You have not demonstrated anything special about that velocity though.

[WarpTech]

They are not exact mirrors because, in Scenario 1 the two clocks end with the same rate they started with. In Scenario 2 the two clocks end while running at a slower rate then they were at when they started. The end of the experiment is NOT the same.

Except there is NO way to tell that they are different.
....

Add a 3rd clock to step 1 whose energy is never changed by any kicks and it remains in the initial rest frame. Then at the end of Scenario 2, the two clocks that are in motion will be running slower than the 3rd clock. Whereas, at the end of Scenario 1, they are all three running at the same rate, but have elapsed different times during the experiment. See the difference?

They all agree at the end of both experiments, that the 3rd clock that didn't move elapsed the most time.

[meberbs]

Add a 3rd clock to step 1 whose energy is never changed by any kicks and it remains in the initial rest frame. Then at the end of Scenario 2, the two clocks that are in motion will be running slower than the 3rd clock. Whereas, at the end of Scenario 1, they are all three running at the same rate, but have elapsed different times during the experiment. See the difference?

No, because, you can just have the third clock already moving with speed v instead. Your choice of relative speed for the third clock is arbitrary, and has no effect on anything. It is equivalent to picking the frame you are working in, having the clock moving at speed v to start with is what I did when I said "use the frame of clock 1(after the unnecessary step 1)" Everything therefore still remains unchanged.

They all agree at the end of both experiments, that the 3rd clock that didn't move elapsed the most time.

No, when clocks are spatially separated, there can be no agreement on the relative reading of the clocks, you would have to extend the scenario to bring the clocks together to make this statement, and the answer would depend on which clocks you accelerate in the process.

Did you actually read the rest of my post? Because you are still using the unjustified assumption that the clocks start in a special rest frame.

[Jim Davis]

Did you actually read the rest of my post? Because you are still using the unjustified assumption that the clocks start in a special rest frame.

This exchange reminds me of another special relativity doubter:

http://www.mathpages.com/home/kmath024/kmath024.htm

[Phil Stooke]

For the benefit of readers just joining this thread, who don't have time to read through the previous 20 pages, a brief summary follows:

Blah blah blah.
You're wrong.
No, you're wrong.
You're wrong.
No, you're wrong.
You're wrong.
No, you're wrong.
You're wrong.
No, you're wrong.
...
...
...
You're wrong.
No, you're wrong.

[meberbs]

For the benefit of readers just joining this thread, who don't have time to read through the previous 20 pages, a brief summary follows:

Hey, quite a ways back there were a couple of actually productive conversations that resulted in some relevant conclusions for the thread title.

Some have been summarized in the first post indicting how if you pick one frame (probably the CMB rest frame) and your FTL drives are constrained to be forward in time in that frame, then you get no paradoxes.

There was also a paper that was put forth as a denial of the time travel conclusion, that while the paper seemed to draw incorrect conclusions, some of the work did indicate that there could be a preferred direction rather than a preferred frame, basically meaning you can FTL to the left but not to the right basically making FTL a one way trip.

We don't know of anything that actually behaves like this, but at least we can describe some potential constraints for a new discovery that would allow some sort of FTL without completely contradicting known physics.

[Dave G]

All of the math I've seen indicates:
1) You can't travel back in time.
2) You can't travel faster than light.

But even with these limitations, you can still travel to another galaxy in just 30 years. Another 30 years to come back, and you can make the round trip within a single lifetime.

But you may not want to come back, since 5 million years would have passed on Earth.

In other words, we may want to stop thinking in terms of round trip missions.  Instead, they may be like colonies that go out and explore until they find a place to settle.  Once they leave, we never see them again.

[KelvinZero]

Some have been summarized in the first post indicting how if you pick one frame (probably the CMB rest frame) and your FTL drives are constrained to be forward in time in that frame, then you get no paradoxes.

Thanks meberbs.

Yeah guys. Have a look at the first post for a summary/index of what I think were the most relevant conclusions. I think we found a nice "good enough for SF" solution using either CMB rest frame or CMB temperature. I don't think there has been any other proposal that really describes the behaviour of its version of FTL in a clear way. (parallel universes were brought up but imply a very fuzzy and undefined relationship between what enters and exits FTL)

Also, as an aside, I think maintaining an index of key quotes to later messages in the OP is quite a nice technique. There are a bunch of threads eg on radiation mitigation and on atmospheric pressure and Oxygen partial pressure for a mars base that had a lot of good material, but it tended to get lost as the threads  just grew and grew, and people restarted the conversations without consuming everything on the dozens of pages beforehand.

[ppnl]

Did you actually read the rest of my post? Because you are still using the unjustified assumption that the clocks start in a special rest frame.

This exchange reminds me of another special relativity doubter:

http://www.mathpages.com/home/kmath024/kmath024.htm

Wow. That is a long and sad journey for Dingle. It seems to me that he was not so much incapable of understanding relativity as that he stubbornly refused to do so. The more people tried to explain it to him the more defenses he erected. He went from an honest if misguided attempt to explain relativity to being convinced of a massive world wide conspiracy to cover up the flaws of relativity. His correspondents went from an honest attempt to explain it to him to total frustration and finally to silence.   



I see the same trajectory in many others with ties to fringe science. The cold fusion mess is the best example in recent history. Who can forget Jed Rothwell's "cold fusion (sorry, need to stop here for a second and just say that I have to use stupid words to get my point across. I know that means I must have a weak argument, but that's why I use bad words)."? 

[Torbjorn Larsson, OM]

Some have been summarized in the first post indicting how if you pick one frame (probably the CMB rest frame) and your FTL drives are constrained to be forward in time in that frame, then you get no paradoxes.

Thanks meberbs.

Yeah guys. Have a look at the first post for a summary/index of what I think were the most relevant conclusions. I think we found a nice "good enough for SF" solution using either CMB rest frame or CMB temperature. I don't think there has been any other proposal that really describes the behaviour of its version of FTL in a clear way. (parallel universes were brought up but imply a very fuzzy and undefined relationship between what enters and exits FTL)

Also, as an aside, I think maintaining an index of key quotes to later messages in the OP is quite a nice technique. There are a bunch of threads eg on radiation mitigation and on atmospheric pressure and Oxygen partial pressure for a mars base that had a lot of good material, but it tended to get lost as the threads  just grew and grew, and people restarted the conversations without consuming everything on the dozens of pages beforehand.

Assuming I am not restarting the conversation then, I am a bit baffled by the philosophical slant on speculations of new physics as summarized. The physical paradox, if you will, with a solution in general relativity - which can still be physically non-realizable since there is no principled way to eliminate unphysical solutions - that has a reference frame that admits matter-energy traveling  above the universal speed limit is that there is no way (that I know of) to place said matter-energy at that speed within the frame. Because, you know, the universal speed limit (USL).

A principled method to pick physically realizable solutions in general relativity seems to include rejecting spacetimes that breaks special relativity, in the same way that principled methods to pick physically realizable solutions in quantum field physics includes rejecting fields that do so [ https://en.wikipedia.org/wiki/Quantum_field_theory ].

[KelvinZero]

Sorry Torbjorn.. I honestly couldn't parse most of what you just said.

Leave your principles at the door for this topic. This is not a discussion of whether FTL is realisable or how. It is just about resolving things like the grandfather paradox.

[birchoff]

For the benefit of readers just joining this thread, who don't have time to read through the previous 20 pages, a brief summary follows:

Hey, quite a ways back there were a couple of actually productive conversations that resulted in some relevant conclusions for the thread title.

Some have been summarized in the first post indicting how if you pick one frame (probably the CMB rest frame) and your FTL drives are constrained to be forward in time in that frame, then you get no paradoxes.

There was also a paper that was put forth as a denial of the time travel conclusion, that while the paper seemed to draw incorrect conclusions, some of the work did indicate that there could be a preferred direction rather than a preferred frame, basically meaning you can FTL to the left but not to the right basically making FTL a one way trip.

We don't know of anything that actually behaves like this, but at least we can describe some potential constraints for a new discovery that would allow some sort of FTL without completely contradicting known physics.

Asside from it being interesting side discussion. Does it matter? I ask becasue in the end you only know if the proposed constraints are actual constraints after validating and carrying out additional tests on a real FTL device. Could turn out we have subtle holes in our understanding. Also could turn out that it is physically impossible to build a FTL device.

[meberbs]

For the benefit of readers just joining this thread, who don't have time to read through the previous 20 pages, a brief summary follows:

Hey, quite a ways back there were a couple of actually productive conversations that resulted in some relevant conclusions for the thread title.

Some have been summarized in the first post indicting how if you pick one frame (probably the CMB rest frame) and your FTL drives are constrained to be forward in time in that frame, then you get no paradoxes.

There was also a paper that was put forth as a denial of the time travel conclusion, that while the paper seemed to draw incorrect conclusions, some of the work did indicate that there could be a preferred direction rather than a preferred frame, basically meaning you can FTL to the left but not to the right basically making FTL a one way trip.

We don't know of anything that actually behaves like this, but at least we can describe some potential constraints for a new discovery that would allow some sort of FTL without completely contradicting known physics.

Asside from it being interesting side discussion. Does it matter? I ask becasue in the end you only know if the proposed constraints are actual constraints after validating and carrying out additional tests on a real FTL device. Could turn out we have subtle holes in our understanding. Also could turn out that it is physically impossible to build a FTL device.

It matters for 2 things:
-writing hard sci-fi (which is what KelvinZero was after when starting this thread.) The preferred direction thing applies less to this since it is somewhat unintuitive, and I haven't figured out how to interpret the 3d generalization yet.
-The exercise is attempting to find holes in our understanding. Without some radical new discovery we are fairly certain we can't build an FTL device. This is figuring out what (unlikely) new discoveries would have to look like to allow FTL without contradicting causality or known experiments. It helps for keeping an open mind and improving our understanding.

[WarpTech]

Add a 3rd clock to step 1 whose energy is never changed by any kicks and it remains in the initial rest frame. Then at the end of Scenario 2, the two clocks that are in motion will be running slower than the 3rd clock. Whereas, at the end of Scenario 1, they are all three running at the same rate, but have elapsed different times during the experiment. See the difference?

No, because, you can just have the third clock already moving with speed v instead. Your choice of relative speed for the third clock is arbitrary, and has no effect on anything. It is equivalent to picking the frame you are working in, having the clock moving at speed v to start with is what I did when I said "use the frame of clock 1(after the unnecessary step 1)" Everything therefore still remains unchanged.

They all agree at the end of both experiments, that the 3rd clock that didn't move elapsed the most time.

No, when clocks are spatially separated, there can be no agreement on the relative reading of the clocks, you would have to extend the scenario to bring the clocks together to make this statement, and the answer would depend on which clocks you accelerate in the process.

Did you actually read the rest of my post? Because you are still using the unjustified assumption that the clocks start in a special rest frame.

Given 2 clocks with a relative velocity that are spatially separated, we have an ambiguous situation. If we "assume" the 2 clocks were synchronized when they passed each other, this alone says nothing about the rate of either clock because it is only 1 event. Work must be done to one of the clocks to bring them back together. It is the clock that had no work done to it, that will have the longest elapsed time. Okay?

[ppnl]

It is the clock that had no work done to it, that will have the longest elapsed time. Okay?

That is true of a completed journey where the clocks end up in the same place. But that isn't exactly new. Of course you have to accelerate in order to travel a different path through space/time. It is simple geometry.

But the situation is still symmetric.

Say you have two spaceships with twin one in ship one and twin two in ship two. Now say both twins crawl into a hibernation unit after which one of the ships accelerate to some velocity away. The twins awaken to see relative velocity between them but don't know which of them accelerated.

So what can they do to determine who has the real velocity and slow clock? After all they see each others clock as slow. If twin one travels back to twin two he will find that the twin one clock is slow. But if twin two travels back to twin one he will find that the twin two clock is slow. Exactly reciprocal.

Under special relativity neither clock can be said to be slower or faster than the other until they end up at the same place. Yes it is the acceleration of one or the other that causes one clock to be slower. But it isn't some physical effect of acceleration on the clock mechanism that causes a clock to slow. Ultimately the speed of the clock depends on the path it takes through space/time and acceleration changes that path. It is simple geometry.

Now I understand that you want to have the speed of the clock depend on the motion through a local region of space relative to a center of mass. Well maybe you could make such a thing work but you have a very very VERY long way to go to get there. For example it isn't clear what you could possibly mean by "region of space". You talk about objects traveling through the earths gravitational field with velocities relative to the center of mass of the earth but in fact we are much deeper into the sun's gravity field than we are the earth's. Shouldn't we use the sun as the center of gravity of of our "region of space"? I think your whole idea of such a "region of space" is incoherent.

The whole point of a transform like the Galilean transform or the Lorentz transform is that it allows you to calculate how things look from any frame of reference at all. Until you define a mathematical WarpTech transform that defines your "region of space" and allows us to transform between between any region at all you have nothing. I think it will be more difficult than you think to come up with such a transform. But good luck.