md65536

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.

The difference isn't in the Lorentz factor (the actual tick rate) but in the apparent tick rate, which is different due to changing delay of light (corresponding to changing distance between the two). The rate at which a clock ticks is a frequency, and the rate that it appears to tick can be Doppler shifted. See again http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_vase.html#doppler -- The signals (ticks) leave the source at an even rate, but are received at a lower or higher rate when receding or approaching respectively.

Okay here's an alternative: - There is no concept of reality battling against observation. Or equivalently: Reality always wins. - What is measured is representative of reality. How about that? SR and GR then fit. It's simple, also consistent. Yours seems to be an interpretation of a misunderstanding of relativity. It's not the worst by far. It is probably fine if you intend to never use or understand relativity. It might even be especially useful for avoiding understanding relativity, because it puts up a wall where further understanding clashes with beliefs (eg. "length contraction's not real!"), and allows for inconsistency with a simple explanation that what it models and what is real are not the same (eg. "contradictions caused by length contraction's unreality are okay; this observer's measurements are simply wrong"). (If you meant specifically an alternative explanation of the meter stick through the posts, the basic explanation is something along the lines of: the stick makes it through the posts, and this happens in all frames. In the posts' frame, the stick passes through lengthwise, and is contracted enough to fit. In the stick's frame, it doesn't pass both posts simultaneously. The posts are contracted but also skewed allowing the stick to slip through not all at once, as though on an angle. I understand if this is not personally aesthetically appealing, but it is consistent and it works.)

The details of the turnaround are irrelevant. You still have to get the twins back to the same place to meaningfully compare clocks, you still have to have different spacetime paths to have a difference in aging. Here are a few more details of the Doppler shift analysis to show the asymmetry: I have gamma=2 and proper time tau=1 for each leg of the traveler's journey. Yes, both observers see the other's clock appearing to tick at a relative rate of .27 while receding, and 3.73 while approaching. The traveler sees Earth's clock tick slowly from 0 to 0.27 years (while itself ages 1 year), and fast from 0.27 to 4 years (while itself ages another year). Meanwhile Earth sees the traveler's clock appear to tick slow until it is seen turning around, ie. slow from 0 to 1 year (while itself happens to age 3.73 years), and then fast from 1 to 2 years (while itself ages another 0.27 years). So Earth sees the traveler's clock appear to tick slow for most of the experiment, while the traveler sees it for half of the experiment. Accounting for the delay of light, what they see matches what is calculated by the Lorentz transformation.

The only thing of interest that the turnaround causes is a switch in inertial frames. You're right that it doesn't matter how the turnaround happens. You're looking in the wrong place by focusing on the details of the turnaround, while ignoring the long stretches of relative velocity, where time dilation actually occurs. Before considering the details of the turnaround, consider this: Suppose a twin travels at high constant velocity away from Earth, for one year (by its clock). Then it enters a black box, somehow turns around in the box, and exits at the same speed in the opposite direction and returns to Earth in one year. Say gamma=2 and Earth ages 4 years while the traveling twin ages 2 (while out of the box). All of this will remain true no matter what happens in that box. Also, that twin will really SEE the Earth age 4 years. Using relativistic Doppler shift, the twin sees Earth age .27 years on the first leg, and 3.73 years on the second leg. This is true no matter what happens in the box. Now let's say the box is a billion light years long on all 3 sides, and contains a hyperdoughnut, several Kerr black holes, a Hawking Pretzel, a LaForge Ice Cream Cake, and a zero-point energy singularity. And some regular doughnuts too. Suppose that the twin has enough fuel to make the turnaround itself, or maybe the twin is a neutrino and can be turned around with little energy. Suppose also that the twin ages a million years while in that black box, and you have no idea what complicated manoeuvres took place while it was inside. Also suppose that to the twin, while it aged a million years between entering and exiting the box, it sees that Earth aged only a thousand, or perhaps a billion (it doesn't matter here) between the last image the twin saw while entering the box, and the first image it sees after exiting. Nothing that happens in the box changes the fact that the twin sees Earth age .27 years on the outward journey, and 3.73 years on the inbound journey, for a total of 4 years that Earth has aged while the twin spent 2 years leaving and returned. Whether the twin experienced any proper acceleration, and how much, doesn't change this. IF all those extra details are not so easy to ignore, you can just make the turnaround instantaneous and you get the same result. Once you understand how what happens on the long part of the journey matters, *then* you can look into the turnaround without setting yourself up for so much confusion. What does this mean, though? If you're doing Doppler shift analysis, very little interpretation is needed. The traveling twin actually sees the Earth age 4 years while itself ages 2. If you're trying to figure it out in terms of inertial frames, it might be something like: the difference in simultaneity between Earth and the twin is already inherent in the difference between the outbound and inbound frames of reference. The change in simultaneity does not need any special causal details; simply having the right velocity and distance from the other observer (Earth) is all that matters.

Suppose I do the experiment and measure what happens. Now how do I determine what really happened?

Just like the last time I remember this "rest frame is a preferred frame" topic was discussed, I must ask: How do you measure the distances between sets of moving objects? What is your "nice" FOR to measure distances that are changing?

Alright so we know what different observers measured. What really happened though, if not what was measured?

What is really happening then, if a length-contracted meter stick traveling at .99c slips lengthwise between two posts 0.8m apart? Is the meter stick really longer than the hole it fit through?

I'd recommend working through the details of a Doppler shift analysis example with a Minkowski diagram or with numbers. This analysis doesn't rely on anyone feeling acceleration, and it will work with the free fall gravitational turnaround idea. If you work through the details you'll see where the difference is. Earth and the traveling twin really do observe a different situation. Without seeing those details it will be difficult to understand them.

I disagree with your reasoning. If you think of it in terms of evolution, heights can be deadly. "Paralysis" can be a protective adaptation. If you're hanging around on a cliff, one who moves about freely and without fear may be more likely to fall and take themselves out of the gene pool. Then, we can automatically tend to freeze around heights without even needing to connect it with anticipation of pain, as an evolved association. I think it's why we tend to fear heights more than say speed. Evolutionarily, speed has pretty much always been an advantage. Nowadays, accidents involving speed can cause as much pain as those involving heights, but we haven't evolved aversion to speed. When considering evolved traits, one can't just take what one expects and extrapolate that into something that "should" be evolved. In the case of apes, it might simply be that skilled movement in trees combines better with increased mobility and low fear, and is selected preferably over fear and paralysis. I might be wrong, these are just ideas that make sense to me.

It's more like saying "If you draw a straight line between two points, and then draw a curved or bent line between the same two points, the straight line will be shorter." I could try to explain that analogy but it might not help. If you look at your example from any single inertial frame, it is not symmetric. "Your" frame of reference where you see the Earth leaving and then returning, isn't an inertial reference frame. The Doppler shift analysis of the situation http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_vase.html#doppler clearly shows how there is no symmetry here. If you turn around, you see the Earth change its relative velocity immediately. From Earth, your turn around isn't seen for some time due to delay of light. If you want to claim symmetry, you'll have to face it that the two observers aren't observing the situation symmetrically.

You can definitely calculate that. Not everything is symmetrical. Remember that these things are relative. The clock that flies by is inertial in this example. If you look at if from its perspective, it remains at rest while you fly by and then turn around and return. The usual calculations work out correctly. Who undergoes acceleration and when doesn't matter except in that it affects the spacetime path of the observer. You can have any number of observers, each taking different paths between the same two points, and each enduring their own particular proper time (aka. aging). Any of the observers' relative aging could be calculated in SR. If two twins accelerate symmetrically, their paths will be symmetrical, and they'll age the same. I've been told that the longer the path is spatially, the shorter it will be in time. An inertial path is the spatially shortest path between 2 points in flat spacetime, so if you include one inertial observer it simplifies the situation because that one will always age the most out of any possible paths taken. It matters that their spacetime paths are different lengths, not that one must not accelerate. As a quick example: Say you have a typical twin setup where an inertial observer ages 4 years, and a traveling twin ages 2, and add another faster traveling twin which ages 1. If you remove the inertial twin, then you still have 2 twins that both travel and return, at different speeds, and the first ages twice as much as the other.

In this situation all you're doing is eliminating "proper acceleration", so that the traveling twin doesn't feel any effects of acceleration. It's been used to argue that the effects of acceleration (other than the change of velocity) theoretically do not contribute to time dilation in SR. The traveling twin still changes direction. Its spacetime path between the two points where the twins are reunited is longer spatially and shorter temporally. Acceleration is required to get two twins to travel between two points along different paths. Once the velocity of the two along their paths is fully accounted for (whether using rockets or gravity wells or whatever), there is no further effect of acceleration that contributes to the time dilation in SR. This is theoretical (there's no theorized effect of acceleration) and agrees with experiments so far. However I think once you add in gravitational time dilation (GR) it gets more complicated. Edit: I think in either case (SR or GR) acceleration on its own does not contribute to time dilation, but of course it is related to velocity and gravity, so it can be easy to confuse oneself that "acceleration is doing something to time" when really it's velocity and gravitation that are doing it. I'm not sure if I'm saying this correctly.

The clocks don't *appear* to be ticking slow when the two are approaching, due to the diminishing delay of light. See http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_vase.html#doppler for explanation of what they see. They both see the other's clock appearing to tick very slow while receding, and relatively fast while approaching. The twin that turns around sees each for the same duration. The inertial twin sees the receding phase appear to take longer due to the delay of the image of the other's turnaround. The inertial twin measures the other's clock as slow the whole time. When the traveling twin turns around, there is a change in relative simultaneity for it that result in a "leap forward" of the inertial twin's clock. HOWEVER this leap is not seen, because of delay of light and a corresponding change in the time it takes for images of the other twin to arrive. The traveling twin *measures* the other clock as ticking slowly and getting behind, then leaping ahead of its own clock as it turns around, then ticking slow on the return trip. But it *sees* the other clock tick even slower on the trip out, sees nothing immediately happen during turnaround, and the other clock appears to tick faster on the way back. I didn't quite address the details of your question, but no one would see the other's clock suddenly leap forward in any case of slow or fast or instant acceleration. The leap is a change of relative simultaneity that corresponds with a change in inertial frame, but it is not immediately visible.

swansont also never said what you claimed, that length actually being relative implies there are "many realities". They are deformed (length contracted) because they're moving at a relative velocity. Of course, to move relative to something only makes sense if there IS that something, and that something can be called an observer, but the presence of the observer doesn't *cause* the length contraction. You're standing near 2 trees. Relative to your position, one is nearer. Moving so the other is nearer doesn't cause an effect on the trees. But one *really* is nearer. According to another observer, a different tree may be the nearer one, but that doesn't require multiple realities. Nearness is a relative property. So is length. I feel like this exact conversation has happened before with the exact same participants. Would you say that you reject relativity, or you don't understand it? (Or other, to prevent a false dichotomy, "it's presented wrong here" or something?)