[HN Gopher] Godel's solution to Einstein's field equations (2021)
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Godel's solution to Einstein's field equations (2021)
Author : jorgenveisdal
Score : 66 points
Date : 2023-01-31 13:16 UTC (9 hours ago)
(HTM) web link (www.privatdozent.co)
(TXT) w3m dump (www.privatdozent.co)
| [deleted]
| kkylin wrote:
| For anyone interested in this topic: there are commentaries on
| this paper as well as Godel's own lecture on this in Volume III
| of his Collected Works.
| daxfohl wrote:
| So to solve physics, you don't just have to be smarter and more
| creative than Einstein, but than Einstein and Godel combined.
| shsbdncudx wrote:
| You don't have to be smarter than them, no. Standing on the
| shoulders of giants etc.
| User23 wrote:
| Indeed, in fact indirect evidence suggests that Sir Isaac,
| the source of that quote, probably had more intellectual
| horsepower than anyone until von Neumann.
| chatterhead wrote:
| What is Tesla.
| renox wrote:
| 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..
| yarg wrote:
| 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.
| renox wrote:
| Given that you can't use quantum entanglement to send
| information, I fail to see where information is propagated
| faster than C.
| musgravepeter wrote:
| The 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
| immmmmm wrote:
| the gr_qc list on arXiv is quite vivid, it's pretty amazing
| what this system of equations yields as solutions.
|
| https://arxiv.org/archive/gr-qc
| thedudeabides5 wrote:
| Does this mean that traveling faster-than-light can be considered
| a form of time travel?
| superposeur wrote:
| Yes, which is why sci fi scenarios in which ships whiz between
| star systems will never, ever, ever happen.
| jiggawatts wrote:
| 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.
| avmich wrote:
| > 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.
| shsbdncudx wrote:
| 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.
| mr_mitm wrote:
| 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.
| gnad_sucks wrote:
| 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.
| Jaygles wrote:
| 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.
| n4r9 wrote:
| Also, any kind of instantaneous communication.
|
| Unless the theory of relativity is superseded by something
| quite radically different.
| __Joker wrote:
| High school educated talking here.
|
| Does Quantum Entanglement have any promise for
| instantaneous communication (theoretically) ?
| explaininjs wrote:
| Nope, entangled pairs are _basically_ the following in
| JS: class RawQuantum { value
| = () => this._hidden ??= Math.random() }
| class EntangledQuantum extends RawQuantum {
| valueA = () => this.value() valueB = () => 1 -
| this.value() } const {valueA,
| valueB} = new EntangledQuantum()
|
| 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.
| OkayPhysicist wrote:
| 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).
| moefh wrote:
| 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.
|
| [1] https://en.wikipedia.org/wiki/Bell%27s_theorem
| BoiledCabbage wrote:
| 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.
| moefh wrote:
| 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).
| phkahler wrote:
| 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.
| karmakurtisaani wrote:
| 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.
| chrismarlow9 wrote:
| https://news.fnal.gov/2020/12/fermilab-and-partners-
| achieve-....
| OkayPhysicist wrote:
| 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".
| pocketleaf wrote:
| 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?
| superposeur wrote:
| 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 Godel 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.
| chatmasta wrote:
| 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
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