Gödel's solution to Einstein's field equations (2021)
privatdozent.coThe article mentions "few known exact solutions". There are actually quite a number. Most are from after 1950.
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
the gr_qc list on arXiv is quite vivid, it's pretty amazing what this system of equations yields as solutions.
For anyone interested in this topic: there are commentaries on this paper as well as Gödel's own lecture on this in Volume III of his Collected Works.
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.
Also, any kind of instantaneous communication.
Unless the theory of relativity is superseded by something quite radically different.
High school educated talking here.
Does Quantum Entanglement have any promise for instantaneous communication (theoretically) ?
Nope, you can't pass information through entangled particles. All you know when you measure you particle is that the other one will turn out the same (or is likely to, I forgot the exact details). This does not lend itself to any communication protocol.
Nope, entangled pairs are basically the following in JS:
You can give valueA to one procedure and valueB to another and know that whenever the _hidden field is observed, the two will have complementary views of the data. But this doesn't give the two procedures any way to communicate, and there's no measurable difference between resolving the _hidden filed now or later.class RawQuantum { value = () => this._hidden ??= Math.random() } class EntangledQuantum extends RawQuantum { valueA = () => this.value() valueB = () => 1 - this.value() } const {valueA, valueB} = new EntangledQuantum()That only works if you replace "basically" with "not really". With this code you can't violate Bell's inequalities[1], which is a really important feature of Quantum Mechanics.
For someone who is trying to learn the basics of quantum entanglement, the distinction between local and non-local hidden variables isn't take that essential.
Or make those "hiddens" in the code above globals. Problem solved.
The problem is not the distinction between local and non-local hidden variables, but the that the "value" in that code doesn't depend on the measurement being performed.
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).
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.
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.
I'm also struggling to make sense of what you're saying. Non-local measurement outcomes have very little to do with causality. Are you arguing against specific interpretations such as Bohmian mechanics, which require privileged space–time foliations?
To elaborate somewhat on the basically, the key difference between this example (and the more common "put a left shoe in one shoebox, a right shoe in another, shuffle, and send each to different people" example) and actual quantum entanglement involves being able to choose from a multi-axis spectrum of different measurements, and the resulting level of correlation precluding the possibility of there being a local hidden variable (the leftness or rightness of the shoe in the box before opening).
That's about transmitting qubit-encoded information. It has absolutely nothing, at all, to do with FTL communication. It's a somewhat more elegant solution than USPS for solving the problem of "I have a qubit here, I want to move it over there".
It probably doesn't, but if it does, it could be used to send messages back in time. Relativity doesn't care how something goes FTL, it's just really clear there's no room for "FTL but not time travel" unless you introduce some odd and unphysical-seeming extra restrictions on the universe.
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.
> Most physics revolutions refine rather than replace their predecessors.
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.
In reality it’s debatable, but within the logic of the fiction universe it holds, yeah?
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?
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 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.
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.
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”.
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 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.
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 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 arrive before you left
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.
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.
And allowing non-flat space time refines but doesn’t alter the picture.
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.)
Studying a spacetime diagram is hard work. It's a lot easier to just say "I never understood why it's so certain" and leave it at that.
> If I instantly teleported to Alpha Centauri, that wouldn’t put me in the future.
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.
True teleportation would not hit the same limits. The idea is, in conventional travel, your velocity has a time and space component that are hard linked, the faster you are traveling through space, the slower you are traveling through time. The speed of light is the maximum speed you can travel through space, because you've run out of the time component you must take away from to get a larger spatial component. An object that has a spatial speed greater than the speed of light must have a negative time component, aka traveling into the past, which under current understanding isn't possible.
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.
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
So to solve physics, you don't just have to be smarter and more creative than Einstein, but than Einstein and Godel combined.
But you know that the Bells equations for the 'spooky action at distance' are violated by QM, which they didn't. Among many other new experiments results..
Spooky action at a distance doesn't need to be a thing.
Retroactive causality implements the same functionality without requiring information to propagate faster than c.
Given that you can't use quantum entanglement to send information, I fail to see where information is propagated faster than C.
You don’t have to be smarter than them, no. Standing on the shoulders of giants etc.
Indeed, in fact indirect evidence suggests that Sir Isaac, the source of that quote, probably had more intellectual horsepower than anyone until von Neumann.
What would it mean to "solve physics"?
What is Tesla.
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