Why can’t you build an electromagnetic version of a Tipler cylinder? Are electromagnetism and gravity fundamentally different?
Well yes, to the best of our knowledge they are: Electromagnetic charge doesn’t bend space-time in the same way that gravitational charge (ie mass) does. However, finding a description that unifies electromagnetism (and the weak and strong forces) with gravity is one of the major goals of modern physics; it could be the case that, when we have that theory, we’ll be able to describe an electromagnetic version of a Tipler cylinder, or more generally to say how spacetime bends in the presence of electric charge, if it does.
How does quantum configuration space work when dealing with systems that don’t conserve particles (such as particle-antiparticle annihilation)? It’s not like you could just apply Schrödinger’s equation to the sum of configuration spaces of different dimensions, and expect amplitude to flow between those configuration spaces.
You have reached the point where quantum mechanics becomes quantum field theory. I don’t know if you are familiar with the Hamiltonian formulation of classical mechanics? It’s basically a way of encapsulating constraints on a system by making the variables reflect the actual degrees of freedom. So to drop the constraint of conservation of particle number you just write a Hamiltonian that has number of particles as a degree of freedom; in fact, the number of particles at every point in position-momentum space is a degree of freedom. Then you set up the allowed interactions and integrate over the possible paths. Feynman diagrams are graphical shorthands for such integrals.
A while ago I had a timelss physics question that I don’t feel I got a satisfactory answer to. Short version: does time asymmetry mean that you can’t make the timeless wave-function only have a real part?
I’m afraid I can’t help you there; I don’t even understand why reversing the time cancels the imaginary parts. Is there a particular reason the T operator should multiply by a constant phase? That said, to the best of the current knowledge the wave function is indeed symmetric under CPT, so if your approach works at all, it should work if you apply CPT instead of T reversal.
Why can’t you build an electromagnetic version of a Tipler cylinder? Are electromagnetism and gravity fundamentally different?
Well yes, to the best of our knowledge they are: Electromagnetic charge doesn’t bend space-time in the same way that gravitational charge (ie mass) does. However, finding a description that unifies electromagnetism (and the weak and strong forces) with gravity is one of the major goals of modern physics; it could be the case that, when we have that theory, we’ll be able to describe an electromagnetic version of a Tipler cylinder, or more generally to say how spacetime bends in the presence of electric charge, if it does.
There’s something very confusing to me about this (the emphasized sentence). When you say “in the same way”, do you mean “mass bends spacetime, and electromagnetic charge doesn’t”, or is it “EM change also bends spacetime, just differently”?
Both interpretations seem to be sort-of valid for English (I’m not a native speaker). AFAIK it’s valid English to say “a catapult doesn’t accelerate projectiles the way a cannon does”, i.e., it still accelerates projectiles but does it differently, but it’s also valid English to say “neutron stars do not have fusion in their cores the way normal stars do”, i.e., they don’t have fusion in their cores at all. (Saying “X in the same way as Y” rather than the shorter “X the way Y” seems to lean towards the former meaning, but it still seems ambiguous to me.)
So, basically, which one do you mean? From the last part of that paragraph (“if it does”), it seems that we don’t really know. But if we don’t, than why are Reissner-Nordström or Kerr-Newman black holes treated separately from Schwarzschild and Kerr black holes? Wikipedia claims that putting too much charge in one would cause a naked singularity, doesn’t the charge have to bend spacetime to make the horizon go away?
I encountered similar ambiguity problems with basically all explanations I could find, and also for other physics questions. One such question that you might have an answer to is: Do superconductors actually have really, trully, honest-to-Omega zero resistance, or is it just low enough that we can ignore it over really long time frames? (I know superconductors per se are a bit outside of your research, but I assume you know a lot more than I do due to the ones used in accelerators, and perhaps a similar question applies to color-superconducting phases of matter you might have had to learn about for your actual day job.)
Superconductor resistance is zero to the limit of accuracy of any measurement anyone has made. In a similar vein, the radius of an electron is ‘zero’: That is to say, if it has a nonzero radius, nobody has been able to measure it. In the case of electrons I happen to know the upper bound, namely 10^-18 meters; if the radius was larger than that, we would have seen it. For superconductors I don’t know the experimental upper limit on the resistance, but at any rate it’s tiny. Additionally, I think there are some theoretical reasons, ie from the QM description of what’s going on, to believe it is genuinely zero; but I won’t swear to that without looking it up first.
About electromagnetic Tipler cylinders, I should have said “the way that”. As far as I know, electromagnetism does not bend space.
Thank you for the limits explanation, that cleared things up.
About electromagnetic Tipler cylinders, I should have said “the way that”. As far as I know, electromagnetism does not bend space.
OK, but if so then do you know the explanation for why:
1) charged black holes are studied separately, and those solutions seem to look different than non-charged black holes?
2) what does it mean that a photon has zero rest mass but non-zero mass “while moving”? I’ve seen calculations that show light beams attracting each other in some cases (IIRC parallel light beams remain parallel, but “anti-parallel” beams always converge), and I also saw calculations of black holes formed by infalling shells of radiation rather than matter.
3) doesn’t energy-matter equivalence imply that fields that store energy should bend space like matter does?
2) what does it mean that a photon has zero rest mass but non-zero mass “while moving”? I’ve seen calculations that show light beams attracting each other in some cases (IIRC parallel light beams remain parallel, but “anti-parallel” beams always converge), and I also saw calculations of black holes formed by infalling shells of radiation rather than matter.
A moving photon does not have nonzero mass, it has nonzero momentum. In the Newtonian approximation we calculate momentum as p=mv, but this does not work for photons, where we instead use the full relativistic equation E^2 = m^2c^4 + p^2c^2 (observe that when p is small compared to m, this simplifies to a rather more well-known equation), which, taking m=0, gives p = E/c.
As for light beam attracting each other, that’s an electromagnetic effect described by high-order Feynmann diagrams, like the one shown here. (At least, that’s true if I’m thinking of the same calculations you are.)
1) charged black holes are studied separately, and those solutions seem to look different than non-charged black holes?
3) doesn’t energy-matter equivalence imply that fields that store energy should bend space like matter does?
Both good points. I’m afraid we’re a bit beyond my expertise; I’m now unsure even about the electromagnetic Tipler cylinder.
Do superconductors actually have really, trully, honest-to-Omega zero resistance, or is it just low enough that we can ignore it over really long time frames?
It’s for-real zero. (Source: conference La supraconductivité dans tous ses états, Palaiseau, 2011) Take a superconductive loop with a current in it and measure its resistance with a precise ohmeter. You’ll find zero, which tells you that the resistance must be less than the absolute error on the ohmeter. This tells you that an electron encounters a resistive obstacle at most every few ten kilometers or so. But the loop is much smaller than that, so there can’t be any obstacles in it.
It’s for-real zero. (Source: conference La supraconductivité dans tous ses états, Palaiseau, 2011)
Man, that is so weird. I live in Palaiseau—assuming you’re talking about the one near Paris—and I lived there in 2011, and I had no idea about that conference. I don’t even know where in Palaiseau it could have taken place...
Re Tipler cylinder (incidentally, discovered by van Stockum). It’s one of those eternal solutions you cannot construct in a “normal” spacetime, because any such construction attempt would hit the Cauchy horizon, where the “first” closed timelike curve (CTC) is supposed to appear. I put “first” in quotation marks because the order of events loses meaning in spacetimes with CTCs. Thus, if you attempt to build a large enough cylinder and spin it up, something else will happen before the frame-dragging effect gets large enough to close the time loop. This has been discussed in the published literature, just look up references to the Tipler’s papers. Amos Ori spent a fair amount of time trying to construct (theoretically) something like a time-machine out of black holes, with marginal success.
Well yes, to the best of our knowledge they are: Electromagnetic charge doesn’t bend space-time in the same way that gravitational charge (ie mass) does. However, finding a description that unifies electromagnetism (and the weak and strong forces) with gravity is one of the major goals of modern physics; it could be the case that, when we have that theory, we’ll be able to describe an electromagnetic version of a Tipler cylinder, or more generally to say how spacetime bends in the presence of electric charge, if it does.
You have reached the point where quantum mechanics becomes quantum field theory. I don’t know if you are familiar with the Hamiltonian formulation of classical mechanics? It’s basically a way of encapsulating constraints on a system by making the variables reflect the actual degrees of freedom. So to drop the constraint of conservation of particle number you just write a Hamiltonian that has number of particles as a degree of freedom; in fact, the number of particles at every point in position-momentum space is a degree of freedom. Then you set up the allowed interactions and integrate over the possible paths. Feynman diagrams are graphical shorthands for such integrals.
I’m afraid I can’t help you there; I don’t even understand why reversing the time cancels the imaginary parts. Is there a particular reason the T operator should multiply by a constant phase? That said, to the best of the current knowledge the wave function is indeed symmetric under CPT, so if your approach works at all, it should work if you apply CPT instead of T reversal.
There’s something very confusing to me about this (the emphasized sentence). When you say “in the same way”, do you mean “mass bends spacetime, and electromagnetic charge doesn’t”, or is it “EM change also bends spacetime, just differently”?
Both interpretations seem to be sort-of valid for English (I’m not a native speaker). AFAIK it’s valid English to say “a catapult doesn’t accelerate projectiles the way a cannon does”, i.e., it still accelerates projectiles but does it differently, but it’s also valid English to say “neutron stars do not have fusion in their cores the way normal stars do”, i.e., they don’t have fusion in their cores at all. (Saying “X in the same way as Y” rather than the shorter “X the way Y” seems to lean towards the former meaning, but it still seems ambiguous to me.)
So, basically, which one do you mean? From the last part of that paragraph (“if it does”), it seems that we don’t really know. But if we don’t, than why are Reissner-Nordström or Kerr-Newman black holes treated separately from Schwarzschild and Kerr black holes? Wikipedia claims that putting too much charge in one would cause a naked singularity, doesn’t the charge have to bend spacetime to make the horizon go away?
I encountered similar ambiguity problems with basically all explanations I could find, and also for other physics questions. One such question that you might have an answer to is: Do superconductors actually have really, trully, honest-to-Omega zero resistance, or is it just low enough that we can ignore it over really long time frames? (I know superconductors per se are a bit outside of your research, but I assume you know a lot more than I do due to the ones used in accelerators, and perhaps a similar question applies to color-superconducting phases of matter you might have had to learn about for your actual day job.)
Superconductor resistance is zero to the limit of accuracy of any measurement anyone has made. In a similar vein, the radius of an electron is ‘zero’: That is to say, if it has a nonzero radius, nobody has been able to measure it. In the case of electrons I happen to know the upper bound, namely 10^-18 meters; if the radius was larger than that, we would have seen it. For superconductors I don’t know the experimental upper limit on the resistance, but at any rate it’s tiny. Additionally, I think there are some theoretical reasons, ie from the QM description of what’s going on, to believe it is genuinely zero; but I won’t swear to that without looking it up first.
About electromagnetic Tipler cylinders, I should have said “the way that”. As far as I know, electromagnetism does not bend space.
Thank you for the limits explanation, that cleared things up.
OK, but if so then do you know the explanation for why:
1) charged black holes are studied separately, and those solutions seem to look different than non-charged black holes?
2) what does it mean that a photon has zero rest mass but non-zero mass “while moving”? I’ve seen calculations that show light beams attracting each other in some cases (IIRC parallel light beams remain parallel, but “anti-parallel” beams always converge), and I also saw calculations of black holes formed by infalling shells of radiation rather than matter.
3) doesn’t energy-matter equivalence imply that fields that store energy should bend space like matter does?
What am I missing here?
A moving photon does not have nonzero mass, it has nonzero momentum. In the Newtonian approximation we calculate momentum as p=mv, but this does not work for photons, where we instead use the full relativistic equation E^2 = m^2c^4 + p^2c^2 (observe that when p is small compared to m, this simplifies to a rather more well-known equation), which, taking m=0, gives p = E/c.
As for light beam attracting each other, that’s an electromagnetic effect described by high-order Feynmann diagrams, like the one shown here. (At least, that’s true if I’m thinking of the same calculations you are.)
Both good points. I’m afraid we’re a bit beyond my expertise; I’m now unsure even about the electromagnetic Tipler cylinder.
It’s for-real zero. (Source: conference La supraconductivité dans tous ses états, Palaiseau, 2011) Take a superconductive loop with a current in it and measure its resistance with a precise ohmeter. You’ll find zero, which tells you that the resistance must be less than the absolute error on the ohmeter. This tells you that an electron encounters a resistive obstacle at most every few ten kilometers or so. But the loop is much smaller than that, so there can’t be any obstacles in it.
Man, that is so weird. I live in Palaiseau—assuming you’re talking about the one near Paris—and I lived there in 2011, and I had no idea about that conference. I don’t even know where in Palaiseau it could have taken place...
That one talk was at Supoptique. There were things at Polytechnique too, and I think some down in Orsay.
Re Tipler cylinder (incidentally, discovered by van Stockum). It’s one of those eternal solutions you cannot construct in a “normal” spacetime, because any such construction attempt would hit the Cauchy horizon, where the “first” closed timelike curve (CTC) is supposed to appear. I put “first” in quotation marks because the order of events loses meaning in spacetimes with CTCs. Thus, if you attempt to build a large enough cylinder and spin it up, something else will happen before the frame-dragging effect gets large enough to close the time loop. This has been discussed in the published literature, just look up references to the Tipler’s papers. Amos Ori spent a fair amount of time trying to construct (theoretically) something like a time-machine out of black holes, with marginal success.