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.
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.