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Gödel's solution to Einstein's field equations (2021)

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Re: Gödel's solution to Einstein's field equations (2021)

#41

Post by superposeur »

chatmasta wrote: post #21
superposeur wrote: post #18

Earlier quoted context omitted.

Most sci fi just pretends relativity doesn’t exist. Yes, the point is that any way to send a signal between space like separated events A and B (in sr or gr) would also allow a return signal to be sent back from B to event C in the past of A. So any means of ftl signaling (wormhole, warp drive or whatever) is tantamount to building a time m achine. No amount of techno optimism or can-do cleverness will ever be suffic…

I enjoyed this lecture [0] from Scott Aaronson about closed timelike curves and the impact they would have on computational complexity theory. Basically, they would give you the ability to spend an eternity computing some subcalculation, and then return to where you started with the result in hand. [0] https://youtube.com/watch?v=Ha4eG8gLSK4

Yes it’s really interesting how the quantum information folks have managed to recast known features of classical physics (second law of thermodynamics, no closed timelike curves) as “implausible computational tasks”.

Re: Gödel's solution to Einstein's field equations (2021)

#42

Post by andrewflnr »

jiggawatts wrote: post #26
superposeur wrote: post #4

Earlier quoted context omitted.

Yes, which is why sci fi scenarios in which ships whiz between star systems will never, ever, ever happen.

I’ve never quite understood why this is so certain. If I instantly teleported to Alpha Centauri, that wouldn’t put me in the future. Sure, if I turned a telescope back towards our system and watched Earth, I would see myself wandering around as I was four years ago and then… after four years… I could watch myself step into a teleporter. This is entirely consistent and in no shape, way, or form would this let me get s…

It doesn't really make sense until you grok how relativity thinks of events and "observing" them, and then stare at the relevant spacetime diagram for a while.

Note that the time when the light arrives from (in your scenario) Earth is not the same as "observing" it; observing is a much stronger sort of hypothetical measurement, more like assembling all the evidence in retrospect and deducing a consistent physical story. That's the story where, if stuff is moving FTL, you start seeing cause and effect reversed.

Ed: the key difference between c and your hypothetical speed of sound is that light is the same speed no matter how fast the observer is moving. Two observers both have to see a laser moving at c, even if A also sees B moving in the same direction at c/2. With your example, B can actually see the relative speed of an object moving at s as s/2.

Re: Gödel's solution to Einstein's field equations (2021)

#43

Post by consilient »

NoThisIsMe wrote: post #40
consilient wrote: post #39

Earlier quoted context omitted.

> I think they like exotic and unintuitive sounding stuff. Exactly the opposite, nonlocality is by far the most exotic resolution here. It means losing existence and uniqueness of solutions to differential equations - i.e., causation.

Could you expand on this, or provide a source? I don't see how physics could yield a pure math result like that.

Other way around. Of course physics has nothing to do with whether a theorem is true or false - but it has everything to do with whether our universe satisfies that theorem's hypotheses.

Re: Gödel's solution to Einstein's field equations (2021)

#44

Post by shsbdncudx »

jiggawatts wrote: post #36
shsbdncudx wrote: post #27

Earlier quoted context omitted.

You could do something on Alpha Centauri, instantly teleport back, and then make a bet on what’s going to be observed in 4 years time.

You'd be seeing Earth's past at Alpha Centauri. You have only the information you take with you through the wormhole (the present), and information that has been travelling through space for 4 years (the past). You have no information from the future, and I've never seen a convincing argument as to how it would be possible to cheat this via instant travel.

That’s not what I meant, read the comment again

Re: Gödel's solution to Einstein's field equations (2021)

#45

Post by gtech1 »

mr_mitm wrote: post #30
jiggawatts wrote: post #26

Earlier quoted context omitted.

I’ve never quite understood why this is so certain. If I instantly teleported to Alpha Centauri, that wouldn’t put me in the future. Sure, if I turned a telescope back towards our system and watched Earth, I would see myself wandering around as I was four years ago and then… after four years… I could watch myself step into a teleporter. This is entirely consistent and in no shape, way, or form would this let me get s…

If you "instantly" teleported to alpha centauri, then there would be a frame of reference in which you arrive before you left. To another observer, you would travel back in time. It's not something you can disagree on. Instead, convince yourself by studying the spacetime diagram: http://www.physicsmatt.com/blog/2016/8/25/why-ftl-implies-ti... Note that "instantly" is ill-defined in SR. Simultaneity of events is obser…

Does this assume a single universe ?

In other words, can causality be broken if we assume we live in a multi-verse and achieving FTL from Time-PointA in Universe 1 to Time-PointB in Universe 2 ?

Re: Gödel's solution to Einstein's field equations (2021)

#46

Post by 34611 »

superposeur wrote: post #4
thedudeabides5 wrote: post #3

Does this mean that traveling faster-than-light can be considered a form of time travel?

Yes, which is why sci fi scenarios in which ships whiz between star systems will never, ever, ever happen.

That's assuming the current model of physics is true for all time. The current model of physics which cannot account for 95% of matter in the universe.

There was a time when the current model of physics couldn't allow for traveling to different planets.

Never say never.

Re: Gödel's solution to Einstein's field equations (2021)

#47

Post by mr_mitm »

gtech1 wrote: post #45
mr_mitm wrote: post #30

Earlier quoted context omitted.

If you "instantly" teleported to alpha centauri, then there would be a frame of reference in which you arrive before you left. To another observer, you would travel back in time. It's not something you can disagree on. Instead, convince yourself by studying the spacetime diagram: http://www.physicsmatt.com/blog/2016/8/25/why-ftl-implies-ti... Note that "instantly" is ill-defined in SR. Simultaneity of events is obser…

Does this assume a single universe ? In other words, can causality be broken if we assume we live in a multi-verse and achieving FTL from Time-PointA in Universe 1 to Time-PointB in Universe 2 ?

Yes it assumes a single universe. I'm not aware of any multiverse solution to this. There is, however, the Novikov self-consistency problem which could solve this. It's entirely speculative, of course.

Edit: IIRC Novikov only covers wormhole-type time travel, i.e. configurations of curved spacetime, while we were only talking about flat spacetime until now.

Re: Gödel's solution to Einstein's field equations (2021)

#48

Post by phkahler »

consilient wrote: post #39
phkahler wrote: post #24

Earlier quoted context omitted.

Non-locality seems to be the least favorable way to resolve the Bell inequalities as far as most physicists are concerned. I'm not sure why though. I think they like exotic and unintuitive sounding stuff.

> I think they like exotic and unintuitive sounding stuff. Exactly the opposite, nonlocality is by far the most exotic resolution here. It means losing existence and uniqueness of solutions to differential equations - i.e., causation.

>> Exactly the opposite, nonlocality is by far the most exotic resolution here.

I think a multiverse, or anything "spooky at a distance" or the other stuff is exotic. Non-locality does take away our ability to do experiments in isolation I suppose, which is kind of a big problem, but it is limited to certain kinds of experiments and not (seemingly) relevant at larger scales.

Re: Gödel's solution to Einstein's field equations (2021)

#49

Post by superposeur »

34611 wrote: post #46
superposeur wrote: post #4

Earlier quoted context omitted.

Yes, which is why sci fi scenarios in which ships whiz between star systems will never, ever, ever happen.

That's assuming the current model of physics is true for all time. The current model of physics which cannot account for 95% of matter in the universe. There was a time when the current model of physics couldn't allow for traveling to different planets. Never say never.

Most physics revolutions refine rather than replace their predecessors. So, for instance, gr gives similar predictions to to Newtonian gravity in an appropriate limit.

It is possible that relativity will be refined by further developments (quantum gravity?), but it is reasonable to expect that the refined understanding will reduce to relativity in an appropriate limit, one core feature of which is the causal structure of events in space time.

Hoping that exotic physics will allow ftl travel is like hoping that an exotic theory of gravity will give a radically different prediction for the time it takes an apple to drop from tree to ground. True that “never” is a strong word but this is just about as never as any fact we know.

I use this strong word as a corrective to the impression you get reading discussion threads, where you may suppose ftl is next up on musk’s bucket list, or just limited by sluggish tech development.

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