How many interpretations of QM do you speak?

[Matterwave]

Part 2. Grandfather Paradox
GR has vacuum solutions with closed timelike curves.

For example, some regions of the extended Kerr solution have CTCs. But note that they are hidden behind a horizon that, afaik, we wouldn't think we could pass through. The horizon at $r_-$ is unstable. Are there other known vacuum solutions with CTCs? Which ones were you thinking?

My claims here are based on Wald 12.3

Suppose I go into my past on such a curve and kill my grandfather before my father was born. How can I have been born to kill my grandfather when I could not have been born because I killed my grandfather? Do I believe that physics really predicts a contradiction in this case?

I think we should resolve first, the chronology protection conjecture:

https://en.wikipedia.org/wiki/Chronology_protection_conjecture

If the conjecture is true then no such paradox can arise and we can dissolve the problem.

My response: Show me the stress-energy tensor for this GR solution. Einstein's equations have a stress-energy tensor on the RHS and when you are having me "suppose" a person is being sent along the curve of a vacuum solution, even if that person doesn't change the metric to within experimental limits, you have introduced a non-zero stress-energy tensor.

Are you making a statement about stability of the solution you have in mind? If the CTCs in vacuum are stable I see no reason why we would need to introduce the added complexity of the stress energy tensor "of the person". If they are unstable you should mention it.

We make idealized arguments in physics all the time. There can certainly be cases where more detail resolves a paradox so I wouldn't dismiss your point off hand, but you still need to make an argument for why these particular details would resolve the paradox.

The Schwarzschild vacuum solution predicts clocks in orbit around Earth will run faster or slower than clocks on Earth based on their altitude. We can (and have) checked this by placing clocks in orbit on the geodesics of the Schwarzschild vacuum solution, i.e., it is possible to construct the stress-energy tensor for the clock in that otherwise vacuum solution that doesn't alter the metric so as to confirm the GR prediction.

I don't understand this "i.e."

As far as I know we've never needed to account for the stress energy tensor of the clock in order to make predictions of time dilation. If you are saying, e.g. Gravity Probe A predictions accounted for the mass of the onboard clock, I'd like to see a reference for it.

Sorry, call me stupid,

Certainly not :)

but I can't "suppose" someone being sent back in time on the curve of a vacuum solution leading to the grandfather paradox. In order to resolve the paradox (showing that physics doesn't predict a contradiction), I would need to see that stress-energy tensor.

I think you could get much more out of it by analyzing the solutions themselves, e.g. for the presence/nature of horizons that screen off CTCs.

Note that I haven't read the rest of your post or the long discussions in this thread. The GR piece piqued my interest. So I don't have context if you were using this rhetorically to make some other point.

 

[gentzen]

but I can't "suppose" someone being sent back in time on the curve of a vacuum solution leading to the grandfather paradox. In order to resolve the paradox (showing that physics doesn't predict a contradiction), I would need to see that stress-energy tensor.

https://scottaaronson.blog/?p=8861#comment-2009370

Do I know GR? I certainly know more GR today than I knew back then in 2012. However, my knowledge for that specific question has not really changed. I can not even tell you whether “many times its rest mass” is true for any CTC, or just for CTCs in Gödel’s universe.

@RUTA Do you have something along similar lines as those “many times its rest mass” in mind?

 

[PeterDonis]

https://scottaaronson.blog/?p=8861#comment-2009370

I don't understand your comment there. Proper acceleration is not the same as energy. Proper acceleration is invariant, but energy is frame dependent. So a large proper acceleration does not necessarily mean energy "many times the rest mass" of the object.

If you have a specific reference to a paper with a computation that makes the "many times the rest mass" claim, I would be interested in seeing it.

That's not to say that there are no issues with CTCs, of course there are. I'm just not sure that "requires energy many times its rest mass" is one of them.

 

[gentzen]

If you have a specific reference to a paper with a computation that makes the "many times the rest mass" claim, I would be interested in seeing it.

Wow, nobody on physics.se asked that question for the explicit reference back than. If any of them did, we would now just have the reference to the publications. Now I have to figure out how to get my hands on Palle Yourgrau's book again. This will probably take some time, but I guess in the end we will get the references.

 

[gentzen]

Now I have to figure out how to get my hands on Palle Yourgrau's book again. This will probably take some time, but I guess in the end we will get the references.

I could buy Palle Yourgrau's book for €6. I now asked Google-AI:

The calculation linking the closed timelike curves to an explicit restriction on a particle's rest mass and energy consumption comes from David B. Malament's papers: 'Minimal acceleration requirements for "time travel" in Gödel space-time' (J. Math. Phys, 1985) and 'A note about closed timelike curves in Gödel space-time' (J. Math. Phys, 1987). Malament expanded on a brief 1949 remark by Gödel and used the relativistic rocket equation to prove that the mandatory integrated acceleration dictates that a rocket's initial mass must be exponentially larger than its final rest mass to complete the closed loop.

Edit: Don‘t worry about the fact that the initial question talked about a particle, but the reference talks about a rocket. It was explicitly stated that there might be a misunderstanding / misinterpretation involved:

… that the energy for a particle with a finite rest mass required to run through such a curve is many times its rest mass. (I admit that I may have misunderstood / misinterpreted this last part.)

 

[renormalize]

If you have a specific reference to a paper with a computation that makes the "many times the rest mass" claim, I would be interested in seeing it.

Here is an easily accessible reference that summarizes the argument: OPTIMAL TIME TRAVEL IN THE GÖDEL UNIVERSE.

 

[PeterDonis]

I now asked Google-AI

Please be aware that AI is generally not an acceptable reference. In this case it appears to have pointed you at some, which is good, but it would have been better to just give them directly (the Malament papers, which are referenced in the paper @renormalize quoted from).

 

[Matterwave]

Note that the Gödel metric is not a vacuum solution. It includes a dust term and a negative, finely tuned, cosmological constant which is why I didn't think @RUTA was referring to the Gödel universe (at least, the post I read mentioned a vacuum solution with CTCs).

 

[PeterDonis]

Here is an easily accessible reference that summarizes the argument: OPTIMAL TIME TRAVEL IN THE GÖDEL UNIVERSE.

So to summarize the argument: it takes a certain amount of proper acceleration for a certain amount of proper time to complete one circuit around a closed timelike curve. The actual "optimal" curve in the paper appears to have free-fall segments interspersed with proper acceleration segments, but the final quantity in any case is what they call the "total integrated proper acceleration", which is basically "proper acceleration times proper time" integrated over the entire circuit.

By the rocket equation, that is then the logarithm of the mass ratio required for a rocket to provide the necessary thrust for the necessary amount of time. So I would say that "energy many times the rest mass" is not really a good description of the issue: it's the mass ratio--the ratio of the total rest mass of the fueled rocket at the start, to the rest mass of the payload--that gets very large.

The paper does say at the end that they have not proven that the minimum curve they found is a global minimum; it could be a local minimum or even a saddle point.

 

[zonde]

I'm even more extreme about this: telling me to suppose the cat or Charlie or Debbie are qubits is wrong. They're not. A system with $10^{30}$ or so atoms is not a qubit. Treating it as if it is, even in a supposedly highly idealized thought experiment, is not going to work out well.

Yes, asking to suppose that cat is qubit is wrong, but I don't think that number of atoms can be a factor in this distinction. The difference between qubit and cat is sharp like difference between conductor and superconductor but number of atoms above 1 won't make sharp difference.
It is interesting that author of cat thought experiment later tried to answer this question himself. Schrodingers answer was that living matter "feeds" on negative entropy and so it can exist only as an open system.
So I would say that the wrong part there is impossible requirement to suppose that open dissipative system is isolated.

 

[javisot]

Note that the Gödel metric is not a vacuum solution. It includes a dust term and a negative, finely tuned, cosmological constant which is why I didn't think @RUTA was referring to the Gödel universe (at least, the post I read mentioned a vacuum solution with CTCs).

Am I the only one who has asked AI about vacuum solutions to the field equations that contain CTCs?

(I was thinking about how interesting it would be to train a model specifically using EFEs, so that one could ask it questions of this kind, asking it to search for counterexamples, etc)

 

[Sambuco]

In order to resolve the paradox (showing that physics doesn't predict a contradiction), I would need to see, at minimum, the complementary measurement to 'open the box' and its outcome of Live + Dead.

Beyond my response in post #179, I recalled that, instead of measuring the friend + system composite in a complementary basis, it is equivalent to first reverse the time evolution of the friend + system composite and then measure only the system (see section II.E in this paper). Does this help resolve your objection?

Lucas.

 

[PeterDonis]

I don't think that number of atoms can be a factor in this distinction.

Sure it can. A qubit is the smallest possible non-trivial quantum system--it literally has just one degree of freedom. A system with $10^{30}$ atoms has something like that order of magnitude of degrees of freedom. That makes a huge difference in what kinds of states the system can have.

The difference between qubit and cat is sharp

What are you basing this on?

I would say that the wrong part there is impossible requirement to suppose that open dissipative system is isolated.

It's true that living systems can't be isolated from their environments. But even nonliving systems with large numbers of degrees of freedom can't be isolated from their environments for any appreciable length of time. If nothing else, they'll emit low energy photons, many of which will be unrecoverable. More generally, how difficult it is to keep a system isolated depends on how many degrees of freedom the system has, because that affects how many ways there are for it to, so to speak, un-isolate itself despite your best efforts.

 

[zonde]

Sure it can. A qubit is the smallest possible non-trivial quantum system--it literally has just one degree of freedom. A system with $10^{30}$ atoms has something like that order of magnitude of degrees of freedom. That makes a huge difference in what kinds of states the system can have.

Josephson junction can consist of $10^{10}$ atoms. I don't see principal difference between $10^{10}$ and $10^{30}$ atoms.

What are you basing this on?

Cats can replicate their state, qubits can't.

It's true that living systems can't be isolated from their environments. But even nonliving systems with large numbers of degrees of freedom can't be isolated from their environments for any appreciable length of time. If nothing else, they'll emit low energy photons, many of which will be unrecoverable. More generally, how difficult it is to keep a system isolated depends on how many degrees of freedom the system has, because that affects how many ways there are for it to, so to speak, un-isolate itself despite your best efforts.

A system in the ground state can't emit photons. And even large systems can be in the ground state.

 

[PeterDonis]

Cats can replicate their state, qubits can't.

I don't know what you mean by this.

A system in the ground state can't emit photons. And even large systems can be in the ground state.

Not unless they're at exactly absolute zero temperature. Which no real system ever can be. Even a very low temperature Bose-Einstein condensate like superfluid He is not at absolute zero temperature and will emit low energy photons.