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md65536

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Everything posted by md65536

  1. Did you mention you already figured this was wrong? I figure that the correct velocity should be greater than c for all v<c, otherwise the accelerations won't be simultaneous in any frame. As well, when v approaches 0, this velocity should approach infinity, because for vanishing v, the frame in which the accelerations are simultaneous approaches the track's frame.
  2. You're not still using "rapidity" as a synonym of acceleration, are you?
  3. Just to expand the realm of possibility, the rail gun wouldn't have to be in the ground/tracks frame. Both what I described and what OP did, here, describe a set of events that are simultaneous in some frame, when gamma is high like 2 in the example. It's as easy to coordinate the events as it is to synchronize a (maybe large) set of clocks in that frame. Then, the rail gun would only need to be as long as the length-contracted train in that frame (by a factor of less than 2 in this example, because the train's speed is less than v in that frame). When figuring out the rate at which the acceleration events happen along the length of the train, I saw that the proper length of the train gets simplified out of the equation. That means that the rate is the same whether the train is short or long. Whether "long" means 1 m or a billion light years, the same answer applies (with the railgun length proportional to train length, as is the timing in the ground frame). (Then yes, it would be impossible to accelerate a full-size train fast enough, so just make the train out of electrons or something lighter, etc.)
  4. Nothing physical is moving faster than c, it's just the timing of the local accelerations across the length of the train moving faster than c. It's only the phase velocity of this wave that's traveling faster than c. That's fine because the propagation of the wave isn't causal; the parts of the train are accelerating independently of each other. I can avoid calling it a wave to be less confusing. Yes, I've assumed "local engines" all along, that was implied by OP. I'm just saying the engines don't have to be part of the train itself. I'm trying to talk about the effects of SR without getting hung up on the difficulties of building a physical version of a thought experiment. I don't want to debate whether it's possible for 2 events to be simultaneous ie. not causally connected.
  5. As mentioned, this isn't a rigid body and that's fine because it's not being accelerated as a rigid body, rather all the parts of the train are accelerated independently, as if it is modelled as a soup of particles. I also think it's not describing a practical impossibility, where every smallest part of the train needs to be a train engine, because the cause of the acceleration can be external. For example the train could be a metal object accelerated by a rail gun. I think it's possible that the train might not feel any stress from being stretched or compressed, it might only feel the local proper acceleration, temporal distortion, etc. This is because the acceleration "wave" crosses the train at a rate faster than c. For any particle on the train, even though the one "behind" it has started moving first, the particle has accelerated before the one behind has caught up and before any causal effect of the particle behind it has reached it. And even though the particle is moving before the one in front moves, by the time the particle gets to the location of the one in front, the one in front has already accelerated. This is true no matter how small you make the separation of the particles. (I guess this assumes that any field effects that can be felt, like EM field, are also accelerated along with the particles. Is this impossible?) On second thought... after a particle has accelerated it is now in the new inertial frame, in which the particle in front has already accelerated first! It has accelerated to rest. This gives an observer in the middle of the train (and who accelerates along with it) a bizarre account of what happens! According to her, the rear of the train begins to compress forward (not fast enough to see or feel it) while the front of the train remains stationary. Then she feels proper acceleration, then the rear of the train begins to stretch backward (but not faster than can be felt??? It seems this compression would have to be visible) while the front of the train again remains stationary! That seems surprising enough that I wonder what details I'm missing or getting wrong. Edit: Due to delay of light I think she'd see the front of the train appear to be approaching and stretched out (due to aberration of light). These are images of the front of the train before those parts accelerated, seen in the post-acceleration frame. But if it can be seen it can be felt?
  6. https://en.wikipedia.org/wiki/Born_rigidity The "Class A" section contains an entire class of applicable motions. Instantaneous (not generally simultaneous) acceleration using the solution I proposed (different from OP's I think), does not satisfy Born rigidity, because it requires different parts of the train to accelerate at different times, in the 2 rest frames (before and after acceleration) of the train. Therefore the train's length changes in those frames, and its proper length doesn't even seem defined while accelerating. However, it should be the only solution that involves a single instantaneous acceleration at each point of the train, with which the train has the same proper length before and after the acceleration. It would seem not even Born rigidity can be satisfied with an instantaneous acceleration. However, OP's proposal never mentioned anything about a requirement of rigidity. For that matter, they neither required that the proper length of the train is the same before and after, I assumed that. The way I figure it, if you have the back of the train accelerate at time 0, the rest of the train accelerates over time until the front of the train finally accelerates when the length of the train has become L/gamma in the initial frame, where L is its original proper length. By that time, the back of the train has traveled a distance of (L - L/gamma) at velocity v. Therefore the time when the front of the train accelerates would be t=d/v = (L - L/gamma)/v. Then the velocity of the "wave" would have to be d/t = Lv/(L - L/gamma) = v/(1 - 1/gamma) For gamma=2, it seems intuitive that the wave would have to travel at 2v, to reach the front of the train at the same time that the back of the train traveling at v gets halfway there. With v = 3^0.5 c/2, I get a velocity of the wave equal to 3^0.5 c. Like you said this is faster than c, so it's non-causal and needs local forces to accelerate the parts of the train.
  7. This doesn't refute the validity of Born rigidity especially in terms of kinematics. If you understood Born rigidity you'd know this thread is concerned with the "irrotational motions" class of Born rigidity, which is broken if the train turns. So bringing it up is a strawman argument. It sounds like you're trying to argue that Born rigidity can't be satisfied, by bringing up irrelevant counter-examples where it is not satisfied.
  8. I've thought about it more and I still think my first reply is correct. The issue is, if there's an instant change in velocity, does length contraction apply to all of the velocities in between as if it accelerates through them all in an instant, and I say it doesn't. SR doesn't predict the effects of acceleration, rather it is an assumption that acceleration doesn't have an effect, only velocity itself does (the "clock postulate"). SR neither says that the train would survive the acceleration, nor that it wouldn't. It says the train would be contracted at the beginning velocity, and also at the end, but not what strains would happen to the train in the zero length of time in between. So, whether the train can accelerate instantly or not is an assumption we have to make, not one we can derive from SR itself. If the train parts can instantly accelerate from 0 to v, then I think my answer works, and if not then it doesn't, and SR doesn't change that. But yes, if there's any frame in which a train is moving and then all parts of it simultaneously stop, SR says its new proper length is smaller than it was, so it physically must get squished. Going from -u to +u instantaneously doesn't have a moment when it is at rest, so SR does not by itself say it will behave as if at rest in that case.
  9. I agree this is irrelevant nonsense and you're incorrectly applying definitions that have no bearing on the issue.
  10. It's not a problem if we consider only the the kinematics of the system, and treat the train as a set of particles, and consider only as many particles as needed. Usually one at the front of the train and one at the back is enough for most things. The solution to Bell's spaceship paradox is the same if you consider one large metal ship, or 2 small ships with an imaginary string between them. Einstein used trains in thought experiments without problems. Considering only kinematics, the forces on the train and communication between the parts is irrelevant. Things like lengths and speeds are what's important. I think this is wrong but I'm not certain. If it squishes (like, physically crumples) in that one frame, that must happen in all frames. I don't see how that's possible in the moving train's frame, where the train is simply stretching out from length-contracted to rest length. Are you saying that what I described will crush the train with high v, or that I made some other mistake? Also, if the train "loses contraction" only for an instant, the effects of the "squishing" would be causal, and there's no time for the effects to propagate. Also, the "squishing" seems to imply that you can't accelerate an object without either stretching or compression strain on the object (you can only minimize it with gradual acceleration), do you agree? However, Born rigid acceleration is possible without spacial strain. I'll have to think more about this.
  11. Right, the parts of the train aren't accelerated simultaneously in the ground frame, only the in-between frame. The parts are each accelerated instantly but not simultaneously, in other frames. In the ground frame, the train starts at its proper length and ends up length-contracted; the rear of the train must accelerate first. In the post-acceleration train's frame, the train starts length-contracted and ends at rest at its proper length; the front of the train must accelerate first. This isn't a question of practicality, it's mathematical. If an object can be made to accelerate all at once from -u to +u, it doesn't get pulled apart (in any frame) or physically squished, just length-contracted. If you want to debate whether a real train can do this, you should probably find out what v is before deciding if it can handle it, because in practical cases v is small enough that length-contraction is negligible.
  12. You can do it if all the parts of the train can change speed instantly. Say you have a train of proper length L, at rest on some tracks, and instantly accelerate each part of it to velocity v so that it has a proper length of L in its new frame. There's a frame of reference in between those two, where the tracks + rest train are moving in one direction at some velocity -u, and after the train accelerates, it's moving in the opposite direction but same speed +u, so that the length contraction factor before and after are the same. This is the frame in which all parts of the train would accelerate simultaneously. You can find u using the composition of velocity formula, so that v is the composition of u and u. Is that what you're talking about, and does this match your result? I suppose that if you did this repeatedly using small accelerations, in limit form you'd get Born rigid motion?
  13. I'm trying to make sense of this and can't. I think you have it backwards. s^2 is the spacetime interval between 2 events. I don't think that equation can directly represent length-contraction of an object, because the length of an object in a reference frame is the spatial distance between 2 simultaneous (in that frame) events. The spacetime interval is the measure between the same 2 events in different frames, while length contraction compares 2 different sets of events in different frames. I don't think you can put 2 lengths of an object (ie. proper and contracted) into the equation and get the same s^2, or in other words I don't see how you can express "longer t and shorter x" with that equation. The interval being invariant implies that the space and time coordinates actually change in the same way, not opposite. That means that in one frame, if 2 events are a certain time apart and distance apart, in another frame where they're a longer time apart, they're also a greater distance apart. I always confused that idea with the way that length contraction seems to say the opposite of that, so I'll just go through an example to show how relativity of simultaneity clears up the confusion. Say you have a train passing through a tunnel so that in the train's frame, the train is exactly the length of the contracted tunnel. The events are the front of the train passing the exit of the tunnel, and the rear of the train passing the entrance of the tunnel, simultaneously. The spacetime interval has (delta)t=0 and x=the proper length of the train = contracted length of tunnel, so s^2 is negative, a spacelike interval. In the tunnel frame, the tunnel is longer than it is in the train frame, while the train is length-contracted and fits entirely inside the tunnel. s^2 is the same since it's invariant, with x'=proper length of tunnel > x, but now t' is also larger than t because the train's rear enters the tunnel before the front of the train leaves. If I were to confuse things, I might say "let x' be the contracted length of the train, and it is smaller while t' is larger", but those statements are talking about 2 different spacetime intervals.
  14. There are additional replies better than I can give here: https://astronomy.stackexchange.com/questions/32445/head-on-collision-of-two-black-holes If energy is lost from a system (in its CoM frame), the system loses mass. The binary system is losing mass equivalent to the gravitational wave energy radiated away, before the collision. If an individual component of the system doesn't radiate energy itself, that component don't lose rest mass. Radiating gravitational waves can reduce angular momentum, so the remnant BH should be decreasing its angular momentum during merger and ringdown. After they're merged, the system only has the one object in it. Your question is basically asking about the components of the system before the merger, and the system as a whole after, that's the main difference. Also, I think the energy radiated while merging is vastly greater than that radiated during the inspiral phase.
  15. These are inspiral orbiting black holes. Yes, I see the numbers in the wiki add up to zero kinetic energy included. However if you look at the references eg. [4], the numbers don't add up exactly, and the uncertainties in the estimates of the black hole masses are so huge that it's not possible to give an exact figure for other energy in the system from the masses. The equation describing this would be more like, remnant BH mass Mf = m1+m2+everything_else_ignored - radiated_energy/c^2. It's likely that whatever is ignored is small on a scale of solar masses. These aren't two masses falling directly toward each other, they come together because their orbits decay due to energy lost to gravitational waves. The kinetic energy is being radiated away as they approach. When they merge they'd generally have net angular momentum, resulting in a spinning black hole. The rotational energy of a black hole contributes to its mass (https://en.wikipedia.org/wiki/Kerr_metric#Mass_of_rotational_energy). Certainly then, some kinetic energy of the orbiting black holes contributed to the mass of the resulting black hole. In this case, at about 8 solar masses of energy radiated, much much more than any energy not accounted for is lost to gravitational waves.
  16. What are you basing this on? You're saying it should be one thing but is "really" another, where do you get the latter from? If you apply your equations to quarks forming a proton, it really does include the KE. From https://en.wikipedia.org/wiki/Proton "The mass of a proton is about 80–100 times greater than the sum of the rest masses of its three valence quarks, while the gluons have zero rest mass. [...] The rest mass of a proton is, thus, the invariant mass of the system of moving quarks and gluons that make up the particle, and, in such systems, even the energy of massless particles is still measured as part of the rest mass of the system." In the case of a black hole you can't measure or assert any internal motion, but the externally measurable rest mass is still there and the energy is still conserved.
  17. It's easy to explain the hyperbolic rotation relation in terms of other things. If you assume that the speed of light is constant, and consider a path of light c*tau long in one frame, then consider it in another frame (as commonly done with a light-clock at rest and moving, in thought-experiments used to explain time dilation), chosen to form a right triangle with a sides x and c*tau and hypotenuse c*t (right? am I messing up the details?). Then by the Pythagorean Theorem, the value of x^2 - (ct)^2 is constant for a given tau. That equation happens to describe a hyperbola. You don't need to explain why it's described by a hyperbolic rotation, if you instead explain why the speed of light is constant and why Pythagoras' theorem holds. "Hyperbolic rotation" is just an equivalent mathematical description of the relationship. But likewise, a constant speed of light and Pythagorean theorem could also be just descriptions of what's happening, equivalent to some other things. Maybe there's some simplest explanation of what's "really" happening, or maybe they're all just equivalent descriptions of what we observe. I think we have the same point, that you don't need to explain a given description of a phenomenon to explain the phenomenon itself. Likewise, you don't need things to "really" be rotating for a mathematical equation for rotation to be a valid description.
  18. As far as I know (which is not much and hopefully someone else can explain or correct me), whether an experiment is measuring the distribution of many particles or a single entangled pair doesn't matter much because the results are consistent. However, even with a single observation, I think there is always an inherent randomness to them (at least where probability wave functions are involved), which makes drawing a conclusion from it probabilistic. A single photon doesn't show a diffraction pattern in a double-slit experiment, it just follows the probability distribution of the pattern. For example say you have an experiment to see if some action maintains the entanglement of a pair of particles, or breaks it. Suppose a measured event is expected to happen 70% of the time for entangled particles, and 50% of the time for random particles. If you observe a single pair and the event happens, were they entangled, or was it random chance? If the event doesn't happen, were they not entangled, or a random entangled outlier? My under-educated impression is, anything you do to make a result 100% certain ("collapsed wave function") removes the interesting effects you only see with the interaction of probability wave functions.
  19. "Magic" wasn't the right word for me to use, especially since we're taking it to mean opposite things. Yes, entanglement gives some the idea of FTL communication, but when you look at the details of what's actually being measured, there's nothing there to actually do it. Like a trick illusion, where you get the impression of something extra happening, but if you look closely you see it didn't. The idea can still remain, because it's based on nothing real and can continue as such regardless of real measurements. Real measurements of entanglement show correlation (or at least statistical correlation), but not necessarily communication. The geometric explanation of the twin paradox can be measured using real measurements, so I disagree that it's magical. There are no quantum effects that have suggested any future experiment in which we would expect to see FTL communications. Speculatively, it's possible that some future experiment does show that it's possible. That speculation is effectively that there's something new that we haven't yet discovered that in some way goes against the observations and understanding we have so far.
  20. Entanglement doesn't imply or even suggest the possibility of ever sending a signal faster than light. It is consistent with relativity in that sending such a signal seems theoretically impossible. You can interpret entanglement in such a way that some signal is sent faster than light, but you're basically adding your own "magic," something made up that hasn't been or maybe can't be experimentally observed. Magic could be something reasonable, or not, it's made up. Then if you ask, "Is magic forbidden by relativity?", the answer is probably no. Relativity has nothing to say about magic. A faster-than-light signal could break causality, which along with relativity can lead to paradoxes, so I suppose faster-than-light communication is forbidden by consistent causality plus relativity. Besides, special relativity doesn't forbid faster-than-light particles, it forbids accelerating particles from slower than light to faster than light. We haven't seen faster particles and probably shouldn't expect them to exist. It's other parts of reality as we know it that forbid them or using them for communication. Suppose you have a pair of sealed boxes each with a coin in it, and they have the property that the first time a coin is looked at, whether it's heads or tails, it's 100% certain that the first time the other coin is looked at, it will be the opposite. An equivalent device should be possible with entanglement. Say you have as many of them as you want. How would you use it to send a message from one coin holder to the far distant other, say a short message like 0 or 1 decided independently by someone else? Both coin holders can agree to a strategy beforehand. Anything anyone does to examine whether a coin is currently heads or tails counts as an observation. If you can find a way to send a message, it's certain that this is a bad analogy for entanglement, and not that entanglement allows sending messages. This is just an analogy, but there should be no way to force a coin to be either heads or tails without first observing what it currently is, and no way to know what's happened to the other coin, including whether it's been looked at. The weirdness here, if such a device existed, would be that you could shake both boxes, then open them to see that they're opposite, or you could shake both boxes, assume that they'd be opposite if you looked at them, and then purposefully flip one of them over, then look at them and see that they're only now opposite. This is an analogy only, and the analogy is that if you have 2 entangled particles, and you do different things to them but maintain their entanglement, they'll still maintain their entangled properties. In reality, excess manipulation will probably break the entanglement. It's mysterious and unintuitive, but not magic.
  21. Yes, I mixed up KE and momentum. The kinetic energy of its parts contribute to the system's rest mass. In its center-of-momentum frame, the system has net zero momentum, and the total energy of the system is equivalent to its rest mass. This is galaxy PG1211+143 they're observing, about a billion light years away. Wouldn't they compensate for cosmological redshift? Wouldn't they describe the speed of stuff falling into a black hole relative to the black hole, and not the Earth?
  22. If they fall directly toward each other, it goes into the resulting combined black hole. Consider a simpler example of light "falling" into a black hole. Photons have no rest mass, yet adding light to a black hole increases its mass. Your system of 2 black holes has a rest mass in the frame of the center of momentum of the system, where the total energy (including mass and kinetic energy of the 2 black holes) is the mass of the system, and the system as a whole has net zero kinetic energy. Assuming no energy is radiated away as gravitational waves etc., the mass of the system is the same before and after they collide. The coordinate system. Is it clear to you what coordinates or frame of reference they're talking about?
  23. Maybe OP can clarify? But in the meantime, a search shows headlines like, "Matter clocked speeding toward a black hole at 30 percent the speed of light". https://astronomy.com/news/2018/09/matter-clocked-speeding-toward-a-black-hole-at-30-percent-the-speed-of-light Is the meaning of that speed understood, or does it need more details? It seems ambiguous. I'd assume they mean different things depending on how far from the black hole the matter is.
  24. You could do Lorentz transformations for two local inertial frames at a location the event horizon passes. (However the horizon itself is lightlike so you can't use it as an inertial frame or even describe the speed of the object relative to the horizon except in some other given frame of reference.) Relativistic effects due to high speeds still occur in curved spacetime. I'm not sure how the effects combine but it seems easy to set up an example with A and B "nearby" and related by a Lorentz transformation, and a distant C related to B by gravitational time dilation say, and if light from A passes through B and reaches C then the total redshift between A and C will be the Doppler shift between A and B multiplied by the gravitational redshift between B and C (you can see this by letting B be a signal repeater and consider what it observes of A and sends to C). In this way you could separate the relativistic effects due to SR and GR in some specific example, and have "gamma factor" be meaningful, but not only would you have to define frames of reference and/or what the free-falling object's velocity is relative to, but depending on what one means, such as in my example, one might also have to define gamma if it's not standard. Regardless of whether there's any sense in what I wrote above, you'd at least have to say what frame of reference you're using, and depending on that, different objects could have different velocities as they cross the horizon, so that would also need to be defined.
  25. I feel like you're running around in circles. Altogether the response has been something like 1) There's no reason to either accept or 2) refute your claims because you're not making any testable predictions at all, and 3) you'd need some equations or quantification of effects that make a useful prediction and 4) it would need observational evidence that fits it for it to be treated seriously or accepted, and maybe 5) other stuff I'm forgetting. You're jumping back and forth attacking individual points without considering them all together. It's like it's a puzzle with many missing pieces and you're asking "why can't we ignore this one piece and work on the rest of the puzzle?" and others are asking to see one piece, any piece, show something, and each time they do, that's the piece you want to ignore next. This idea is probably perfectly acceptable except that it's missing all the pieces. Missing pieces doesn't mean it's wrong, just that there's nothing there that can be evaluated to see if it's right.
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