md65536

Do you know what calculations you might use? Such a black hole is about 11.5 times the mass of the Earth. The rod wouldn't fall to Earth. I'm not sure how you'd keep those separated. There isn't sharp separation between an area where time is measured as "normal" and one where time is very dilated. If you dangled a very long rod into a black hole, preventing your end from falling in, the rod would necessarily break. Along the length of the rod the farther parts would look increasingly dimmer, redder, and slowed. I guess that if the break happened when you could see it, you'd see the broken part fall in and seem to shrink or "pile up" near the event horizon without ever crossing it from your distant viewpoint.

Alright I see what you're saying now, but I don't agree with how you're saying it. With that type of explanation, if someone asks "Can an observer change reference frames by accelerating?" you could explain that if an observer accelerates, an object still remains in its own frame, so no the object's frame doesn't change. That too is true (you don't change an object's reference frame by accelerating another observer) but like length and time and density, it depends on whose frame of reference you're speaking of, and this explanation puts too much emphasis on one frame (the object's) without capturing the essence of relativity, which is that any other frame is equally valid. The solution to the main problem here isn't that density is invariant (which it isn't), nor that "the object's own frame is the one that's important", but that the relation between density and black hole formation also isn't invariant, so you can't use calculations that apply to one frame (like the object's rest frame) to calculate if an object will collapse using measurements from another frame. I think this is the main point that SamBridge is missing.

What relativistic effects are you excluding? Does it depend only on density, independent of relativistic effects? If it were independent of relativistic effects why do you need to exclude them? Or is it possible that density alone doesn't tell you whether gravitational collapse will occur, allowing density to be different in different frames of reference without implying a collapse in one frame but not another? Edit: Also, is it the Schwarzschild metric that lets you calculate if a mass will collapse based on its density? And it's the same regardless of charge? Regardless of rotation? Density is really all that matters?

Close enough I guess. Yes, I'm adding nothing new to the resolution of the train tunnel paradox. The resolution is straightforward special relativity. It's just that the description of it can be reasonable and straightforward in relativistic terms, or weird and confusing with classical ideas treated as what should be expected.

Why? Does density alone determine whether something becomes a black hole or not? Are you basing this on the Schwarzschild solution, and does that solution work for moving bodies? DaleSpam and snoopies622 explain this better than I can, here: http://www.physicsforums.com/showthread.php?t=247484

From a thread in the astronomy forum: I just want to disagree with the statement that "the reason why they agree that the train doesn't get smashed is different," which I've seen stated before in these forums. The reason the train doesn't get smashed is the same in all frames: The front guillotine comes down before the front of the train reaches it, and the the back guillotine comes down after the back of the train passes by. Each of these two things describes an event that happens at a single respective location (the location of the respective guillotine), and all observers agree on those statements. The fact that the two events are simultaneous in the tunnel observer's frame is beside the point, and is NOT a necessary part of the reason that the train isn't smashed. It is merely circumstantial. The only way that observers would disagree on what is happening, is if they describe it in a frame-dependent way (such as relying on the two causally unconnected events occurring "at the same time"). But describing the reason something happens is describing causality, which isn't frame-dependent. The cause of the train's survival is not frame-dependent. That type of statement, that the reason is different depending on frame, fits with the interviewer's incredulity, and with other statements like "If you get a stupid answer you've probably done it right because the results of special relativity are so bizarre." It's only bizarre if you're holding on to the concepts of absolute time and length, and thinking along the lines of "measuring things differently means the reasons that things happen are different". I feel that such statements are detrimental to understanding relativity because they suggest that it is incomprehensible, and that incorrect outdated notions still "make sense" even if they're wrong, and so there is less incentive to let go of those wrong notions while learning. The description of what happens is different, but the reason why it happens is the same. Just 2 cents.

I don't think this is stated correctly (though I agree SamBridge is mistaken, but not Delta1212. I also agree that different frames "agree" only as in "are mutually consistent" but not as in "have the same measurements"). If an object's density is relative, then its measured density depends on the frame of reference in which it is measured. An object's density can be different in different frames, and that doesn't require that it changes in its own frame. Of course the object's density (or length etc) doesn't change due to relativistic effects in its rest frame. So for example this statement is perfectly sensible: 'Heavy ions that are spherical when at rest should assume the form of "pancakes" or flat disks when traveling nearly at the speed of light. And in fact, the results obtained from particle collisions can only be explained, when the increased nucleon density due to length contraction is considered.' http://en.wikipedia.org/wiki/Length_contraction Doesn't that mean that density is frame DEPENDENT? Its "rest density" would be frame independent (vacuously I guess, because it specifies the frame in which to measure).

There's always the Speculations forum, which would be more appropriate. http://www.scienceforums.net/forum/29-speculations/ I think your ideas and questions would fit in well there. If you're going to reject relativity theory, you'll probably never get satisfactory answers in the Relativity forum.

I agree with the idea. My own ideas and science news blurbs I've read seem to fit well, though not all of my own ideas make sense. Yes, black holes were once called "frozen stars" because time at the Schwarzschild radius is infinitely dilated, and light that is directed outward doesn't move in our coordinates. However, locally, to an inertial observer that light is traveling outward at the usual speed of light. If I understand that correctly it means that a black hole that is roughly fixed-size in our coordinates, can be expanding at the speed of light to an observer who enters, and maybe even faster to observers closer to the center. This is similar to how we measure the size of our universe. That alone suggests that from the inside, the observable size of the black hole is the same as that of their observable universe.

'No' was to your first question. 'Yes' was to your other question. To repeat, the twins do NOT agree on how long half of the experiment is. You can't describe "half the experiment" as a universal duration and make sense of that from everyone's perspective. To repeat, yes THAT situation is symmetric. I don't know of any way to understand relativity without learning about relativity. If you want shortcuts, to somehow get understandable answers to situations you can't make sense of, then ignore my posts. I don't think they're helping. I think it would be more productive to research the basics of special relativity first.

No. Put it in numbers. Write down the times of these events in your example, so that calculations can actually be done to determine the answers. Is there any example with actual numbers where what you wrote makes sense? A caveat, everyone will agree on how much time has passed for B at the time of B's turnaround. Different observers will not agree on the time at A that is simultaneous with B's turnaround. Yes, with no turnaround the situation is symmetric. They'll both observe the other symmetrically. The relativistic effects will be symmetrical. Careful with the word "yet" because it is different for different observers. If you add an event at B's location, it has a definite time on B's clock, but does not have a definite time on A's clock.

Well, no, I think what SamBridge said is consistent with what I said. Say twin A ages 4 years over the experiment and B ages 2, with the usual setup. Twin A's clock measures a proper time of 4 years between separation and reuniting, and B's clock a proper time of 2 years. The situation is symmetrical up to 1 year by either clock. But the turnaround doesn't happen until year 2 on A's clock, as observed by A. So it is not fully symmetrical right up until the turnaround. Another way to put it is that each twin observes the turnaround happening halfway through the experiment, but the duration of half the experiment isn't symmetrical.

No. Try again using some actual maths that correspond with SR. If you get stuck, post what you've got so far. Otherwise I'll just be repeating.

Essentially yes, you can set it up that way. In your set up it is that way. On the other hand, if for example you had specified a long period of acceleration for one of the twins, then that involves a different velocity profile for the twins. That will make the situation more complicated but it won't change who ages more in the end. Here's how to prove that the one who accelerates away doesn't matter: First, take Earth out of the picture, and call the twins A and B. Suppose one will turn around half-way through the experiment, and the other will remain inertial (other than any initial separation acceleration). Calculate the results you get if A accelerates away but B turns around, or if B accelerates away and B turns around, or if they both accelerate away symmetrically and B turns around. Once they have that initial departing velocity, twin A now remains inertial for the rest of the experiment and will age more over that time, regardless of who accelerates in the beginning. If you assume a negligible acceleration time, then "who accelerates away" makes a negligible difference, and you can see that in the Lorentz transformation. You can ignore this part or really any answer until you understand the basics, but if the twins start symmetrically with a relative velocity, and one turns around after a proper time of tau, then the situation is symmetrical up to a proper time of tau for either of the twins. For example with gamma=2, and twin B turning around at tau=1 unit of time, up till then B calculates A aging 0.5. Symmetrically, up till A ages a proper time of 1, it has that B ages 0.5. But for A the situation isn't symmetrical "up until the time of the turn around", because for A that happens at local time 2, when B has aged 1. Twin A experiences aging from 1 to 2 without a turnaround, and B never experiences that in this setup, so it is not symmetrical beyond local time of 1. As an example, if the setup is "the twins depart symmetrically with relative velocity v=0.866c. At local time of 1, exactly one of the twins will receive a signal to turn around. Who will turn around is unknown at the start." Up until time 1, there is no distinguishing features between the twins; the situation must be symmetrical. However if a twin passes a time of 1 and hasn't got the signal, it knows that it isn't the twin that turns around, EVEN THOUGH the other twin has only aged 0.5 units of time and it is only halfway to the time that it will receive the turn-around signal. There is nothing odd about any of this unless you reject relativity of simultaneity. Also this is not "flip-flopping", it is "relativity". The various different points of view are mutually consistent.

No. For one thing, they calculate the timing differently regardless of the travel time of light (due to relativity of simultaneity). For another thing, (only) the twin who turns around sees the change in relative velocity immediately. The situation is asymmetric, as explained in many ways. It is measured differently, seen differently, felt differently, timed differently. The symmetrical slowing of clocks and the resulting "paradox" is only a partial application of SR. You know the situation is asymmetrical, but you think that applying a part of SR keeps it symmetrical. However, a full application of SR (considering time dilation, length contraction, and relativity of simultaneity) resolves the paradox and shows you where the differences are. You are fighting every explanation that involves SR, yet you keep demanding an explanation of SR. I don't think you'll get much further without understanding the theory a bit more. Keep in mind that you're so sure that the other twin's clock ticks slower, but why? Just because it is predicted by SR? Do you see the physical mechanism for it? If so, what is it? And if not, then why do you require a physical mechanism for the other predictions of SR while rejecting the other theoretical predictions and explanations? Eg. the traveling twin does not remain in an inertial frame, so the "slowing of other clocks" doesn't apply without relativity of simultaneity. If you work through some examples with numbers, it might give you a concrete understanding of the important concepts and make it impossible to brush them aside.

And when does each first observe this happening in your example, according to SR (according to the math)? Use any simplifications you want. Are the moments just before the rocket's relative velocity changes according to an Earth observer, and just before the Earth's relative velocity changes according to a rocket observer, simultaneous in any frame? If so, which? Is that symmetrical?

"Time slows down near the speed of light" doesn't explain it just like "it'll affect your insurance premiums" doesn't explain what happens if you set fire to a fireworks factory---it is just one part of it, it is not ALL of it. The situation is physically asymmetric. You've set it up that way. You've set it up so that one twin turns around. THAT is the cause of the asymmetry. Yes, there are some symmetries (such as the relative time dilation factor as they are receding, or any other aspect up to the point of the turnaround). Just because the results of SR correlate with the asymmetry in the situation, doesn't mean that is CAUSES the asymmetry. Consider this: Two twins leave Earth in different directions at the same speed. Each travels a proper time of one year and turns around and they reunite back at Earth. Suppose gamma relative to Earth is 2, each way. Then the twins each aged 2 years (while Earth aged 4). Now these twins are in a symmetrical situation, and their relative aging is the same. This is a symmetrical situation! Now take this situation, and change it so that SR predicts a difference in aging in the twins. THERE IS THE CAUSE OF YOUR ASYMMETRY. Whatever you did to make the situation asymmetrical, that is the cause. In the original situation, you have one twin turn around while the other doesn't. THAT is the cause of the asymmetry. The relativistic effects that occur due to the asymmetry are NOT the cause of it! Can you use the words "relativity of simultaneity" in your attempts at explaining what's happening, so that at least we know that you're trying to fit this essential concept into your understanding of the situation? If you don't yet see that it's important, you'll get a lot further ahead a lot quicker by looking up what it is and what it means, instead of trying to figure it out without it. I feel like you're trying to understand SR while insistently avoiding SR.

I don't understand the continuing confusion. It's been explained several times in this thread that the whole situation in SR involves all three of time dilation, length contraction, and relativity of simultaneity. The two twins measure the local time until a turnaround event as different. The two measure the length that the other has traveled away as different. Only one of the twins measures a change in relative simultaneity. None of these things is symmetric. Neither is the overall Doppler effect, velocity profiles, and proper acceleration, consistent with the 3 main things. It makes no sense to look at just one of the three and say "There must be more". ALL THREE together form a consistent picture. What makes you think the situation is symmetrical at all in the first place? It is because some one detail of SR is symmetrical (their relative closing velocity, or the time dilation factor, or the color of their hair or any other of many single details that you might focus exclusively on). So SR says that one detail is symmetric, but SR also says the situation is not symmetric, if you look at the whole thing and consider all three of time dilation, length contraction, and relativity of simultaneity together. It makes no sense to have one without the others. You're only thinking the situation is symmetrical because of what SR tells you, yet you refuse to consider all of what SR is saying. It's mind boggling. It's as if the words "relativity of simultaneity" mean nothing, and so they can be safely ignored, and instead just repeat "There must be something more to this!"

Maybe take another look at the graph. Look at the arrow marking 2004, above the dotted line. Look at the sharp rise in the "recent proxies" box. The sharp rise in temperatures is so recent that it doesn't yet show up on a smoothed long-term chart. You spent a few minutes talking about what you don't see, and saved a few seconds by not even looking.

Well now we're well beyond anything I can usefully comment on. The reason we see the asymmetry is that the situation is inherently asymmetrical. I can't say what would happen if there was no delay of light. You'd probably have to make up a whole new set of rules, and it wouldn't match anything real. I don't see how anything piles up. In the standard interpretation you can have many photons en route to an observer, interspersed across the distance to the source, and the photons at different locations carrying info from the source as it looked at different times. Rather than "piled up" I'd say that since information doesn't travel instantly, any changes take time to propagate. That is certainly related to the asymmetry here. A change in velocity can have an immediate effect on the accelerating observer, but not on the remote observer. How the relativistic Doppler effect relates is simply that it describes the Lorentz transformation while accounting for delay of light.

Not really. You don't need photons at all, just the velocities. If the twins separate and exchange no information until they reunite, their clocks will show the same difference in aging that you'd get if they were constantly observing each other. Their paths through spacetime really are asymmetrical, whether watched or not. Edit: Or, to interpret what you said a different way: If the delay of light wasn't what it is, relativity wouldn't work the way it does. So I don't know if you could meaningfully describe the scenario without a delay of light. I guess that looking for the resolution only in the long durations of relative velocity is like considering only time dilation, and looking only at the turnaround is like looking only at relativity of simultaneity. The resolution of the paradox is in all of these things considered together. What occurs, how it's seen, who feels it, what the clocks say, these are all related and tell the whole story in a consistent way, but no one of these aspect makes sense isolated from the others.

Sorry for the confusion. There is a difference between what "is" a clocks tick rate and the rate at which one "sees it appear" to tick. I incorrectly assumed that this was well understood and clearly stated. The relativistic Doppler effect and Lorentz transformation agree with each other. If you want to understand why, maybe look to the math. The most important factors are time dilation, length contraction (and thus relative velocity), and relativity of simultaneity (and thus asymmetrical paths). The difference in appearance and any difference in proper acceleration will be there because of the asymmetry, and they *should* by now make it clear that the observers aren't symmetric, but they do not directly show how the paradox is resolved. Time dilation, length contraction, and relativity of simultaneity resolve the paradox. The "paradox" only arises in the predictions of SR, and you really have to look at those details to resolve it, instead of looking for some answer that is not relativity of time, length, and simultaneity.

I fear you may be mixing up the relativistic Doppler effect and the Lorentz transformation. Others are right, time dilation and length contraction are the same whether you're receding or approaching. The Doppler effect is different because of the way things change during the travel time of light. The Doppler effect simply shows how it looks, and how the two observers cannot see the described situation symmetrically. You may be satisfied with that --- the outbound and return trip look different --- but that's not describing things according to the Lorentz transformation, independently of how things look from a particular viewpoint within an inertial frame. Once you accept that the situation is not symmetrical, the details still come down to time dilation, length contraction, and relativity of simultaneity. The relativistic Doppler effect includes those, but also includes delay of light, but it doesn't make sense without those first 3 things.

Oops, I blame myself for an earlier suggestion along those lines. I should have realized something was wrong. If you take a regular tetrahedron, you can successively divide each triangle into 4 equilateral triangles, recursively. Then you have a bunch of equal-sized triangles. If however the tetrahedron is inscribed in a sphere, and you extend all the interior triangle vertices out to the surface of the sphere, the points will not all be translated the same distance. So the triangles on the sphere would not all be equal. I should have realized that equal size on a such a polyhedron wouldn't mean equal size on a sphere, but I didn't until told.

I hope so too, because for most people going from classical understanding of reality to a relativistic one is very difficult, and if we see others arguing that it doesn't make sense, that can be an "easy way out" of struggling through the understanding. One might say "Other people think it doesn't make sense, so it's okay if I accept that it doesn't make sense." Look at this thread. It started off as a question of the understanding of relativity, and ended up an argument over whether it is even real. There may be only one reality (SR is compatible with that). However, absolute length and time are not an aspect of reality. It's not terribly more complicated than that. I don't think it's terrible that nobody's mind was changed. I think belief and understanding happen in lock-step. It's hard to understand something when you refuse to accept it could be true. If you believe that it could be true it's easier to understand. The more you understand the more believable it is. Eventually everything just clicks. To change beliefs might be a personal choice, not something one person convinces the other of on a forum. http://en.wikipedia.org/wiki/Ladder_paradox#Bar_and_ring_paradox is probably a close enough picture. The posts would be the tips of the ring. I said the posts were "skewed", but their description "rotated" would be more accurate.