md65536

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.

I agree this is irrelevant nonsense and you're incorrectly applying definitions that have no bearing on the issue.

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.

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.

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?

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.

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.

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.

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.

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.

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.

"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.

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.

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?

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?

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.

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.

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.

Yes, that seems valid. It doesn't matter whether they would measure it or find meaning in it, just that it's possible they could. It seems their meaning would basically be, "if there were other things not bound by gravity, the space between them is expanding." Just to add to what it all means: From https://en.wikipedia.org/wiki/Expansion_of_the_universe Expansion of our universe is stated in terms of comoving coordinates where general galaxies (or "comoving observers") that have not been accelerated by forces or gravity, have fixed spatial coordinates. Their distances would be considered at a common comoving time, where "The comoving time coordinate is the elapsed time since the Big Bang according to a clock of a comoving observer and is a measure of cosmological time." So for example if you had 2 galaxies not gravitationally bound to each other, on a line, one located at (0) in comoving coordinates and the other at (1), we say their locations are fixed and that the measure of distance between them is increasing. Say we call the distance between them "one intergalactic unit", which I just made up. Here, the meaning of "the measure of distance itself (in these coordinates) is increasing" is that an intergalactic unit is equal to an increasing number of lightyears, over time. The measure of a lightyear can remain fixed. It doesn't mean that every possible measure of distance is increasing, which would be meaningless (see several other threads) because a change in a measure of distance is relative to something else.

I agree, but then the topic's question could be reframed by that. Our universe and this toy universe are expanding due to vacuum energy or dark energy, but it would collapse if gravity was increased (put everything closer together, and/or add more mass). So if there was still this vacuum "expanding" influence on everything, but the universe collapsed, is there any way in which it could be said that the space itself is still expanding? Or is the metric still expanding? I no longer think this is a scientific question because the definition of expansion (as far as I know it) just doesn't apply. I think the question might be philosophical, and similar to asking "what is the true nature of the universe beyond what can be measured?" Conversely, for example say you have a toy universe with vacuum energy but where everything is gravitationally bound and collapses, except for one particle that is distant and not gravitationally bound, and separates at an ever-increasing rate. This fits the definition of expansion and I'd say that the space between the particle and the rest of the universe is expanding. This might be a stretch because the definitions are based on a universe that appears homogeneous.

Yes, but the effect of gravity would diminish as the energy was carried away. This is what I thought you were talking about when you first mentioned photons. In a Newtonian analysis, a symmetric "shell" of outbound photons (or an expanding shell with mass equivalent to the photons' energy) would stop attracting a mass to the center of the shell as soon as the mass was inside the shell (shell theorem, which also implies the gravitational effect would not diminish before that happened). Based on that, you could reason something like, the photons from the first mass that pass by the second mass stop attracting the second mass toward the first, and start attracting it away.

But what is space without matter? Isn't it just distance, and specifically distance between things? Isn't the vacuum itself observer-dependent? Space isn't made of some "stuff" that is measurable independent of other things, I think. Anyway I think scientific answers don't depend on those questions, because science deals with definitions and measurements. If expansion is defined as "expansion of the metric", and not of "space", then it doesn't matter what space is. If expansion is defined only for gravitationally unbound objects, and defined as their increasing separation, then I think there's no expansion without that separation, and no way to apply it to gravitationally bound masses. But yes, it doesn't make sense that matter would "stop" expansion. For example, consider 2 comoving distant galaxies that are separating due to expansion. Then say there are 2 gravitationally bound small masses somewhere between them. There is metric expansion between the 2 galaxies. It seems fine to say that space is expanding everywhere throughout the distance between them. What is happening between the 2 small masses? The definitions can answer that! In comoving coordinates, the galaxies have fixed coordinates, and the measure of distance itself is increasing. In these coordinates, for the 2 smaller masses to remain a fixed distance from each other in their local coordinates, one or both must be changing location in comoving coordinates. That gives the answer, that space is expanding between the gravitationally bound masses and they're moving through that space (at the very least mathematically!). But then, we can also consider the local coordinates of the gravitationally bound masses, where in this example they're stationary. You really can say that the masses aren't moving through space (which means nothing more than that they're not changing location in these coordinates). The metric is covariant but I'm still not sure if expansion would be something that is an absolute part of the metric, or dependent on the coordinates. I think it's reasonable to say "space is still expanding here" but with the implication that it's referring to space generally, or in other coordinates, not space in local coordinates. Interesting, I hadn't thought of the physics of the model beyond being an example. I think that even a bunch of photons scattered in all directions would start separation because of decreased mass density.

It doesn't violate GR. It is a prediction of GR given the values of several measured variables.

Well I changed my mind again. Geodesics aren't some set of lines that remain fixed relative to absolute space, because there is no such thing. Whether something's moving or not will always (I think) involve a choice of coordinates. Also, whether 2 masses are gravitationally bound depends not just on their locations, but their relative velocity. So for example, two comoving fairly distant galaxies can be unbound and separating due to expansion, while two similarly located galaxies can be gravitationally bound just by giving them enough velocity toward each other (basically an "unescape" velocity to overcome expansion). So I think the answer to whether some specific effect is expansion or not, can depend on a choice, and doesn't have a single answer. To get around that, the definition exists only where it is applicable, eg. per wikipedia "The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time." As well, to say whether something is moving or not, "comoving coordinates" are used, not because that represents absolute motion or anything, but because most of the observable universe approximately fits them pretty well. I think whether expansion is occurring on smaller scales between gravitationally bound masses is literally undefined, and a definitive answer would require some extra definitions and that would necessarily involve making some arbitrary choices of what's moving and what's not.

I think it's confusing because the expansion "breeze" would have to blow in all directions and not push on the ball bearing at all. But, the idea of expansion contributing and gravity contributing to the whole, makes sense. As for atoms expanding, what I've read is that that would only happen if the vacuum energy increased boundlessly, so that the scale at which expansion dominates gets smaller over time, approaching zero. But that would be speculative. I thought of 2 analogies that help me make sense of this. 1. Imagine the Earth is a perfect sphere and it's expanding uniformly. A rigid tectonic plate or island could represent a gravitationally bound region. This is analogous to universal expansion at all scales, since even though the island doesn't change in size, the underlying size of the Earth's surface does. Note that for the island to stay a fixed size, some other part of the crust would have to expand more than the average expansion, for the whole Earth to expand uniformly. 2. Imagine a patch of live skin cells that all slowly divide over time, so that any given area of skin doubles over some long time. A scab or patch of dead cells on it could represent a gravitationally bound region. In this case it's not needed for another area to expand faster to make up for the scab, because the whole isn't expanding with global uniformity and the distortion caused by the scab would be like curvature of spacetime. I think the second is a closer analogy to expansion in the universe, because it's attributed to local vacuum energy rather than some global expansion of the volume of space. I think the island analogy is wrong in that it confusingly represents space both as the crust (including the island) but also as some extra underlying thing that doesn't have a real analog in the universe. But beyond analogies as thought experiments, I think the technical answer needs to be based on the actual definition of expansion. Expansion refers to "metric expansion" which is a change in the measure of distance itself, rather than just a change in the distance between specific things. Well that's not helpful to think about, but what does it mean? The closest I've seen to a description of the technical meaning of expansion is that it involves a divergence of geodesics over time. I think in the case of a static gravitationally bound region, geodesics wouldn't diverge. It wouldn't matter how the rest of the universe was expanding, it would be like tattooed lines on a rigid scab. The geodesics would be like the fan and magnet contributing to a whole, or vacuum energy and gravity contributing to one metric. It would not be like the Earth analogy where one could imagine separate geodesics for an expanding Earth and a static island through the same place.