[Spaceships] Real Life Non-Super Science Reactionless Engines

[Agemegos]

Originally Posted by malloyd

Can you? If you have a special frame (and hence can define an absolute clock, the one that runs in it) aren't space-like and time-like intervals cleanly separated?

Well, they can be if the other frames of reference use the special frame to synchronise their clocks, but then the Principle of Simultaneity won't hold in any frames except the privileged ones (ie. c won't be invariant, with odd implications for Maxwell's Equations). If the synchronisation of clocks within each frame is still done by the procedure that defines the frames of reference in Special Relativity then simultaneity is still variant between frames. If you take the latter approach dynamics will still be well-behaved; if you take the former I think the description of basic mechanics would become very involved: certainly electromagnetism would.

[scc]

Originally Posted by Agemegos

Agreed. I'm just saying that if you do (abandon the Postulate of Relativity) you can end up with a case in which travel occurs along a space-like interval (FTL in some inertial frames of reference, backward-in-time in others, instantaneous in boundary cases) but it is not possible for any signal from the arrival event to get back within the past-ward light-cone of the departure event.

Isn't there some law or rule in physics that says the amount of mass an energy in the universe is constant? Or has it been over turned?

And I'm pretty sure that if we never managed to detect tachyons the FTL debate will start back up again

[malloyd]

[QUOTE=Agemegos;1795379]Well, they can be if the other frames of reference use the special frame to synchronise their clocks, but then the Principle of Simultaneity won't hold in any frames except the privileged ones (ie. c won't be invariant, with odd implications for Maxwell's Equations).

But c is invariant (or more generally that the laws of physics, at least one of which involves c, and yeah Maxwell's Equations are that one, don't have to take into account the motion of your reference frame) *is* the principle of relativity. You don't get to keep it if you pick causality and FTL.

[Agemegos]

Originally Posted by scc

Isn't there some law or rule in physics that says the amount of mass an energy in the universe is constant? Or has it been over turned?

There is. It's one of the reasons that we are intensely skeptical of theories that allow closed timeline paths.

Note well that the Law of Conservation of Mass and Energy requires that the amount of mass and energy be constant in any inertial frame of reference. It does not require that all frames of reference agree what the constant is.

[Agemegos]

Originally Posted by malloyd

But c is invariant (or more generally that the laws of physics, at least one of which involves c, and yeah Maxwell's Equations are that one, don't have to take into account the motion of your reference frame) *is* the principle of relativity. You don't get to keep it if you pick causality and FTL.

Well, that's why I think that each frame synchronising its own clocks and getting the laws of dynamics and electromagnetism in an invariant form is more reasonable than them all adopting the clocks of the privileged frame and getting the laws of dynamics and electromagnetism in a form that depends on relative translation with respect to the privileged frame. The thing is that if they do that they disagree about simultaneity, and therefore they get the laws that describe the operation of the FTL mechanism in a form that is not frame-invariant. That seems horribly ugly, but I can't see anything that makes it inconsistent. You have FTL and causality but not relativity.

By the way, when I was taught Special Relativity the invariance of the speed of light was one postulate (my lecturer called it "the Principle of Simultaneity") and the Principle of Relativity was another. You can derive the invariance of the speed of light in vacuum from the Principle of Relativity, but only if you postulate Maxwell's Equations as invariant laws and derive the speed of an EM wave from them, or by accepting some other postulate that makes c a physical constant. The invariance of c is not derivable from the Principle of Relativity alone.

But that was a long time ago, and terminology does change. Why, in my day we still spoke of "rest mass" and "relativistic mass", which I'm told the youngsters now call "mass" and "energy".

[cosmicfish]

Juuuuust leaving this here:

http://www.xkcd.com/1404/