[Space] Ditching Relativity, with minimal collateral damage

[Anthony]

Originally Posted by malloyd

Your preferred frame won't preserve causality (and isn't actually "preferred") if there are other frames in which elapsed time between events can be different.

It will as long as it's the only frame in which FTL is possible. It's not necessary to have a preferred frame for any other purpose.

[teviet]

Originally Posted by vicky_molokh

[...]Wholly Newtonian treatment of physics, including photons being 'just' particles. Neat and convenient, but probably incompatible with anything past 1900.

Actually more like 1800, because the wave nature of light was pretty well established around that time.

Originally Posted by vicky_molokh

What about if we allow photons to be slowed down, but only by gravity?

Fine if you allow photons to be particles and nothing else (i.e. pre-1800 corpuscular theory of light). In fact you get exactly the same formula for the size of a black hole as you do with relativity (I would call this a mathematical "coincidence"; the various factors of 2 just happen to cancel out). But if you treat light as a wave, then you need either time dilation or ether drag to produce a black hole.

Originally Posted by vicky_molokh

What other nastiness does a Preferred Reference Frame cause?

Not much if you're careful. The only main consideration is what is the preferred frame? It can't just be the "fixed" frame of the stars, because of course the stars aren't fixed. And if you allow the frame/medium to be dragged along with, say, the Galactic rotation, then you have the possibility of traveling back in time if you circle the Galaxy backwards with your FTL. The obvious choice for a preferred frame is the CMB rest frame, which is moving a few hundred km/s relative to the Sun and other local stars.

Originally Posted by vicky_molokh

One of the interesting consequences that I see is that with a PRF, photons do not necessarily move at c relative to any given observer. Wonder how that ties to my first paragraph in this post.

No you can still have photons, and every phenomenon we've observed to date, obey the usual rules of relativity: they are not aware of the preferred frame. It's only the particular exotic physics allowing FTL that somehow interacts with the preferred frame or medium. So the speed of a photon is still the same for all observers, but the speed of an FTL probe depends on the observer.

TeV

[Anthony]

Originally Posted by teviet

So the speed of a photon is still the same for all observers, but the speed of an FTL probe depends on the observer.

And in at least some reference frames and some directions, will appear to be infinite or negative.

[Ulzgoroth]

Originally Posted by Anthony

It will as long as it's the only frame in which FTL is possible. It's not necessary to have a preferred frame for any other purpose.

It seems impossible for FTL to be possible in one reference frame and no other, since traveling FTL in any given reference frame will still be FTL in many other reference frames.

What's the actual connection needed between the PRF and FTL?

[teviet]

Originally Posted by Anthony

And in at least some reference frames and some directions, will appear to be infinite or negative.

Exactly. So the FTL probe can go "backwards in time" in some directions, but on the return trip it will go forwards in time at least enough to cancel out.

Originally Posted by Ulzgoroth

It seems impossible for FTL to be possible in one reference frame and no other, since traveling FTL in any given reference frame will still be FTL in many other reference frames.

What's the actual connection needed between the PRF and FTL?

FTL is possible in every reference frame, but the speed of the FTL effect depends on the reference frame and on the direction of FTL motion.

For example, suppose you have an FTL drive that can go a parsec per day, or 1000c, in the preferred reference frame ("FTL medium"). But the Sun is moving at 300km/s, or 0.001c, with respect to this frame. Then if you start from the Solar system and jump backward in the opposite direction of the Sun's motion, then your apparent FTL speed is only 500c, while if you jump forward along the Sun's motion then your apparent FTL speed is infinite (you get to your destination instantly according to a set of clocks synchronized with Sol).

If your FTL drive is rated at 2 parsecs per day or 2000c in the preferred frame, then your apparent FTL speed is 667c if you go backward or -2000c if you go forward. The negative sign means that you are going forward in space but backwards in time: you arrive at your destination before you set out, according to a set of synchronized clocks. But this isn't really time travel, because if you tried to send a message back to Sol telling yourself not to set out, it would always arrive after you left (due to the fact that the backward-propagating effects always go slower than their rated speed in the preferred frame).

All nice and clear? I can give the formula if you'd like... :)

TeV

EDIT: Fixed an error defining "forward" vs. "backward" motion

[Ulzgoroth]

Originally Posted by teviet

FTL is possible in every reference frame, but the speed of the FTL effect depends on the reference frame and on the direction of FTL motion.

For example, suppose you have an FTL drive that can go a parsec per day, or 1000c, in the preferred reference frame ("FTL medium"). But the Sun is moving at 300km/s, or 0.001c, with respect to this frame. Then if you start from the Solar system and jump forward in the same direction as the Sun's motion, then your apparent FTL speed is only 500c, while if you jump backwards against the Sun's motion then your apparent FTL speed is infinite (you get to your destination instantly according to a set of clocks synchronized with Sol).

If your FTL drive is rated at 2 parsecs per day or 2000c in the preferred frame, then your apparent FTL speed is 667c if you go forwards or -2000c if you go backwards. The negative sign means that you are going "backwards in time" as well: you arrive at your destination before you set out, according to a set of synchronized clocks. But this isn't really time travel, because if you tried to send a message up to Sol telling yourself not to set out, it would always arrive after you left (due to the fact that the forward-propagating effects always go slower than their rated speed in the preferred frame).

All nice and clear? I can give the formula if you'd like... :)

TeV

I believe I've gotten it, but I have to say I didn't find your explanation helpful past the first paragraph (which shook loose the clue I needed) and am completely boggled by your examples, which look unbelievable given the relatively tiny velocity of Sol, though assuming they're correct I ought to be able to figure them out if I take the time to lay out the math.

I had forgotten that the key to the whole FTL/time machine business was moving FTL with respect to reference frames with different time axes, so to speak. Which locking the FTL to one reference frame prevents directly, regardless of whether it still looks like FTL in some other reference frames.

Given how flaky my relativistic thinking seems to be, I'd like to check...does this manage to preserve apparent causality in every reference frame? It seems like it should work that way, but my reasoning for why is clumsy.

[Anthony]

Originally Posted by Ulzgoroth

What's the actual connection needed between the PRF and FTL?

What's required is at least one reference frame in which all FTL trips take non-negative time. Typically a PRF is a reference frame in which FTL speed does not vary with direction of travel, but it's not required that such a reference frame actually exist.

Originally Posted by Ulzgoroth

Given how flaky my relativistic thinking seems to be, I'd like to check...does this manage to preserve apparent causality in every reference frame? It seems like it should work that way, but my reasoning for why is clumsy.

Depends how you define 'apparent' causality. Under relativity, any form of FTL is a causality violation, but a strong causality violation is one in which round trip time can be negative.

[teviet]

Originally Posted by Ulzgoroth

I believe I've gotten it, but I have to say I didn't find your explanation helpful past the first paragraph (which shook loose the clue I needed) and am completely boggled by your examples, which look unbelievable given the relatively tiny velocity of Sol, though assuming they're correct I ought to be able to figure them out if I take the time to lay out the math.

Sorry. It's easier to explain with a spacetime diagram, but it's going to be counterintuitive in either case. In fact I got confused myself: I mixed up my relative directions (Sol relative to PRF and vice versa). You get faster (or even infinite) speeds in Sol's frame if you jump forwards along the direction of Sol's motion! I've edited to fix this. (Even people who do this for a living can get their directions mixed if they're not careful.)

But the formula is simple (it's the relativistic velocity addition formula) if you consider only jumping "forward" or "backward" along Sol's motion relative to the preferred frame. If u is your rated FTL speed (in the preferred RF), and v is Sol's speed (relative to the preferred RF), all measured in units of c, then your measured FTL speed w relative to Sol is:

w = ( u - v )/( 1 - u*v )

if you jump forward along the direction of Sol's motion, or:

w = ( u + v )/( 1 + u*v )

if you jump backward against the direction of Sol's motion.

It's the term in the denominator that gives you infinite speeds, or even negative "backwards in time" speeds. Even if v is very small, as long as u is correspondingly large you can get these odd effects.

Originally Posted by Ulzgoroth

Given how flaky my relativistic thinking seems to be, I'd like to check...does this manage to preserve apparent causality in every reference frame? It seems like it should work that way, but my reasoning for why is clumsy.

It guarantees causality in the sense that you cannot come back (or send a message) to your own past. You can arrive at a distant destination at an earlier "calendar date" than when you set out, but if you try to go back to Earth the additional delays guarantee that you'll return at a later date than when you set out.

TeV

[Ulzgoroth]

Originally Posted by teviet

It's the term in the denominator that gives you infinite speeds, or even negative "backwards in time" speeds. Even if v is very small, as long as u is correspondingly large you can get these odd effects.

It's actually the enormous reductions in positive FTL speed that looked (still look) bizarre to me, though obviously they follow from the equations you present. I'll need to brush up on special relativity on my own time to make the whole thing look sensible though.


On topic, this definitely seems like the best scheme for building a coherent FTL-capable setting that functions like your average semi-hard SF.

[malloyd]

Originally Posted by Anthony

It will as long as it's the only frame in which FTL is possible. It's not necessary to have a preferred frame for any other purpose.

I don't think this even makes sense. What exactly do you think a reference frame is?

But suppose it did. If there is only one reference frame in which FTL is possible, then it's pretty much useless, since the *point* is to travel between places in our universe faster than light. An observer on each of those places defines a reference frame. If you can't make an FTL trip in those frames, then when you leave Earth for Alpha C with your "FTL" drive you must arrive at least 4 years later by the clocks of both Earth and Alpha C. Make the round trip and you cannot come home to a family less than 8 years older than when you left. What exactly have you gained?