7 ms·

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

85 points by jorgenveisdal 4y ago

kkylin 4y ago
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.
thedudeabides5 4y ago
Does this mean that traveling faster-than-light can be considered a form of time travel?
- superposeur 4y ago
  Yes, which is why sci fi scenarios in which ships whiz between star systems will never, ever, ever happen.
  - n4r9 4y ago
    Also, any kind of instantaneous communication. Unless the theory of relativity is superseded by something quite radically different.
    - __Joker 4y ago
      High school educated talking here. Does Quantum Entanglement have any promise for instantaneous communication (theoretically) ?
      - karmakurtisaani 4y ago
        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 4y ago
        https://news.fnal.gov/2020/12/fermilab-and-partners-achieve-sustained-high-fidelity-quantum-teleportation/#:~:text=The%20quantum%20teleportation%20of%20a,the%20encoded%20information%20is%20teleported https://news.fnal.gov/2020/12/fermilab-and-partners-achieve-....
        OkayPhysicist 4y ago
        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".
      - explaininjs 4y ago
        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 4y ago
        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 4y ago
        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 https://en.wikipedia.org/wiki/Bell%27s_theorem
        BoiledCabbage 4y ago
        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.
        phkahler 4y ago
        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.
      - wiml 4y ago
        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.
  - pocketleaf 4y ago
    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 4y ago
      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.
      - chatmasta 4y ago
        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 https://youtube.com/watch?v=Ha4eG8gLSK4
        superposeur 4y ago
        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”.
  - jiggawatts 4y ago
    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.
    - shsbdncudx 4y ago
      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.
      - jiggawatts 4y ago
        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.
        shsbdncudx 4y ago
        That’s not what I meant, read the comment again
    - mr_mitm 4y ago
      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-time-travel 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 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.
  - 34611 4y ago
    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.
    - superposeur 4y ago
      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.
      - 34611 4y ago
        > 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.
daxfohl 4y ago
So to solve physics, you don't just have to be smarter and more creative than Einstein, but than Einstein and Godel combined.
- chatterhead 4y ago
  What is Tesla.
- renox 4y ago
  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 4y ago
    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 4y ago
      Given that you can't use quantum entanglement to send information, I fail to see where information is propagated faster than C.
- shsbdncudx 4y ago
  You don’t have to be smarter than them, no. Standing on the shoulders of giants etc.
  - User23 4y ago
    Indeed, in fact indirect evidence suggests that Sir Isaac, the source of that quote, probably had more intellectual horsepower than anyone until von Neumann.
- monktastic1 4y ago
  What would it mean to "solve physics"?
musgravepeter 4y ago
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 4y ago
  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 https://arxiv.org/archive/gr-qc
deleted 4y ago
[deleted]
volida 4y ago
test

85 points by jorgenveisdal 4y ago

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.

thedudeabides5 4y ago

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

superposeur 4y ago
Yes, which is why sci fi scenarios in which ships whiz between star systems will never, ever, ever happen.
- n4r9 4y ago
  Also, any kind of instantaneous communication. Unless the theory of relativity is superseded by something quite radically different.
  - __Joker 4y ago
    High school educated talking here. Does Quantum Entanglement have any promise for instantaneous communication (theoretically) ?
    - karmakurtisaani 4y ago
      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 4y ago
      https://news.fnal.gov/2020/12/fermilab-and-partners-achieve-sustained-high-fidelity-quantum-teleportation/#:~:text=The%20quantum%20teleportation%20of%20a,the%20encoded%20information%20is%20teleported https://news.fnal.gov/2020/12/fermilab-and-partners-achieve-....
      - OkayPhysicist 4y ago
        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".
    - explaininjs 4y ago
      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 4y ago
        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 4y ago
        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 https://en.wikipedia.org/wiki/Bell%27s_theorem
        BoiledCabbage 4y ago
        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.
        phkahler 4y ago
        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.
    - wiml 4y ago
      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.
- pocketleaf 4y ago
  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 4y ago
    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.
    - chatmasta 4y ago
      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 https://youtube.com/watch?v=Ha4eG8gLSK4
      - superposeur 4y ago
        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”.
- jiggawatts 4y ago
  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.
  - shsbdncudx 4y ago
    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.
    - jiggawatts 4y ago
      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.
      - shsbdncudx 4y ago
        That’s not what I meant, read the comment again
  - mr_mitm 4y ago
    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-time-travel 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 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.
- 34611 4y ago
  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.
  - superposeur 4y ago
    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.
    - 34611 4y ago
      > 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.

daxfohl 4y ago

So to solve physics, you don't just have to be smarter and more creative than Einstein, but than Einstein and Godel combined.

chatterhead 4y ago
What is Tesla.
renox 4y ago
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 4y ago
  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 4y ago
    Given that you can't use quantum entanglement to send information, I fail to see where information is propagated faster than C.
shsbdncudx 4y ago
You don’t have to be smarter than them, no. Standing on the shoulders of giants etc.
- User23 4y ago
  Indeed, in fact indirect evidence suggests that Sir Isaac, the source of that quote, probably had more intellectual horsepower than anyone until von Neumann.
monktastic1 4y ago
What would it mean to "solve physics"?

musgravepeter 4y ago

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 4y ago
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 https://arxiv.org/archive/gr-qc

deleted 4y ago

[deleted]

volida 4y ago

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