Gödel's solution to Einstein's field equations (2021)
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Cambridge University Press has two good books: Exact Spacetimes in Einstein's General Relativity (Griffith & Podolsky) - good readable (if you speak GR) account of the more common solutions Exact Solutions of Einstein's Feild Equations (Stephani, Kramer, MacCallum, Hoenstelaers, Herlt) - encyclopedic, authoritative and mathematical. In my case an aspirational purchase
Unless the theory of relativity is superseded by something quite radically different.
Does Quantum Entanglement have any promise for instantaneous communication (theoretically) ?
class RawQuantum {
value = () => this._hidden ??= Math.random()
}
class EntangledQuantum extends RawQuantum {
valueA = () => this.value()
valueB = () => 1 - this.value()
}
const {valueA, valueB} = new EntangledQuantum()
Or make those "hiddens" in the code above globals. Problem solved.
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.
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.
You can't understand anything about quantum mechanics without knowing that in order to measure a qubit (or anything, really) you need an observable, which is completely missing from that JS code (for a qubit, the observable for a simple projective measurement could be represented by a direction in space).
To be able to move those sorts of distances and arrive at a time comparable to the origins absolute time would require the “time travel” aspect of ftl, right?
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 sufficient to surmount this obstacle in real life.
Incidentally the Gödel metric runs into causality violation in a different way: closed timelike curves. No need for ftl , it’s even less realistic as Einstein is quoted pointing out in the article.
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 super rich on the stock market.
You could only ever know information from your present or your past.
Imagine a hypothetical universe with a maximum speed ‘s’. The creatures in this universe could develop relativity and everything, the same as us. But what if ‘s’ is the maximum speed of sound in the gas that fills this toy universe? What if the creatures are all blind and use only sonar to get to know their world? Would travelling faster than ‘s’ be violating causality somehow? Or would it simply be the same as a supersonic plane, leaving a sonic boom behind it?
Having said all that, I very strongly suspect that FTL will never be possible. However, I don’t agree that it would result in time travel if it were possible.
Note that "instantly" is ill-defined in SR. Simultaneity of events is observer-dependent.
Edit: this is also known as the tachyonic antitelephone. It's described here: https://en.m.wikipedia.org/wiki/Tachyonic_antitelephone
Instead of warning about shrimp you could easily tell your past self to buy a certain stock.
There would be a frame of reference in which you appear to arrive before you left.
The analogy is with a sonic boom, where an observer using only sound for sensing the world would hear the plane arriving before it left.
This does not allow closed timelike loops, the type that would allow you to predict the stockmarket.
The observers can't create paradoxes through via a third observer with a high celerity in the same way that QM "action at a distance" doesn't allow causality violations either, or how moving a laser pointer across the surface of the moon doesn't allow FTL motion either.
It just looks like it does, that doesn't mean that it actually does.
PS: I'm fully aware that in the SR/GR model, appearance is reality, and hence the paradox within the framework of relativity. Clearly, if FTL were allowed, then relativity would be falsified by that, and a new framework would be required. I'm saying that that framework could be consistent, allowing FTL and relativity without allowing travel backwards in time.
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 ?
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.
For instance, it’s a common misconception that wormholes circumvent the relativistic prohibition against ftl travel. Actually, if a wormhole could facilitate travel between two events faster than a light ray moving between the same two events on the outside of the wormhole, then all the same causality troubles would ensue. This just highlights that that the particular mode of transport between events is not important to the argument. (Whether it be warp drive or secret tunnel.)
If the teleport is using a wormhole - a device which connect two points in space - we can consider this.
We have experimental confirmation of time dilation, if we have an accelerated motion. In other words, let's make the wormhole entry on Earth move for some time so that its time is behind, say, by 10 years from the Alpha Centauri.
Then, if you instantly teleport to Alpha Centauri by stepping from Earth into the wormhole, the time at Alpha Centauri is 10 years before. You may use, say, 7 years to fly back to Earth through "ordinary" space, with sub-light speed, and you'll arrive to Earth 3 years before you left.
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.
There was a time when the current model of physics couldn't allow for traveling to different planets.
Never say never.
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.
No. You are describing advancement, not revolution. Physics revolutions cause paradigm shifts. The difference between relativity ( refinement ) and quantum physics ( revolution ).
> So, for instance, gr gives similar predictions to to Newtonian gravity in an appropriate limit.
GR wasn't a revolution. It was adding onto and refining newtonian physics. As in newton gave us the laws of gravity, einstein showed us what gravity is.
> It is possible that relativity will be refined by further developments (quantum gravity?)
That's impossible because relativity cannot exist in a quantum world. Relativity/newtonian physics is deterministic, quantum physics is non-deterministic. Quantum physics gives us true randonmess whereas the relativistic world cannot.
> Hoping that exotic physics will allow ftl travel is like hoping that an exotic theory of gravity
No. I'm just pointing out that it's silly and naive to assume that physics will remain stagnant forever. Forever being the key word. Especially, as I pointed out, since modern physics cannot account for 95% of matter.
2000 years ago, someone could reasonably say man would never reach space because the current understanding of physics was so lacking. Today someone could also say man would never travel between the stars. But they would be assuming that no advancements in physics and knowledge would occur.
Retroactive causality implements the same functionality without requiring information to propagate faster than c.