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Everything posted by md65536

  1. Does GR tell you how much time is measured outside the warp "bubble" or at the other end of a wormhole? Or "when" it is on the other side? With the Alcubierre drive, is there a horizon between inside and outside, so you can't interact with the outside? Suppose there was a way to create the warp in one place, and something else to cancel it out in another place, so you could travel there. Then suppose there was a way to do that in the opposite direction, so you can come back. Does GR tell you when you'd come back? Eg. if you could spend a day traveling at 10c, then immediately spend a day returning at 10c, is the idea that you could return to Earth with 2 Earth days having passed? Or is it some other time or unknown or undefined? When it comes to the wormholes, "when" is it on the other side of the wormhole? Is that arbitrary? Can you have a wormhole or a series of them connecting you to beyond our visible universe? I can't make sense of the idea of "now" on the other end of a set of wormholes, yet no universal now. For example, if you had 3 extremely distant events A, B, and C, each connected to each other with a wormhole, either the relative timing of the events would be arbitrary, or it would establish a common 'now' between the 3 locations???
  2. Populated with what? Measurements of A? Or a prediction, based on the LT or the underlying definition of simultaneity? If simultaneity was not defined, could B say what the time at A "really" was? Is there for B, a physical "now" at the distant location A independent of that definition? Would you say that Einstein was wrong in writing that such a definition is needed? I didn't say "current". I said B can measure the total ageing of A without ever considering what the "current" or "real" time at A might be. It can measure what the time at A appears to be, using only the local current time at B. Why? He didn't, and got the right answer, never assuming anything at all about simultaneity. You say the speed of light must be considered, but don't you mean the one-way speed of light? B only needs to care about incoming light from A, to determine everything it needs to know about A, right? What is the one-way speed of incoming light? How do you know that light takes time to arrive? I'll just tell you the answer: You know it because the time it takes incoming light to cross a fixed distance is defined to be the same as the time it takes outgoing light to cross the same distance. You're wrong to say you "must" come to the same conclusion to be able to predict the ageing of A. I've just shown, B can predict the total ageing of A using only the relativistic Doppler effect, which is a real measurement that can be made without relying on any definition of simultaneity, and gives you the same answer regardless of how you define the "current time at a distant location." I'll just assume you're still using your own meaning of the word 'theory'. Both the LT and the relativistic Doppler effect can accurately let B predict the total ageing of A. Would you say there is no way to know which one matches reality? So, accepting that you can't know the answer to the question, you conclude that it must be the answer most reasonable to you? Can you conceive of the idea that the inability to measure the 1-way speed of light is the one "theory" that matches what is real??? It's not that a way to measure it hasn't been figured out yet, it's that there's no accepted theoretical way in which such a measure can meaningfully be made. It's like saying "Measurements of the Ether are all consistent with the fact that it doesn't exist," and someone arguing "I agree. Even though it exists, we may never have the ability to detect it." I agree! Einstein in fact did say something along those lines. He said, "in reality it assumes absolutely nothing about light" as I've quoted. In his 1905 paper he wrote, and then defined the equal timing of light signals in opposite directions. Thus he literally said that 1) we "might content ourselves" with an alternative, which I take to mean that it can provide workable solutions, and 2) a justification of the definition he used is that it is more practical. He knew what he was doing and didn't get mired in trying to base the theory on what he thought to be "real", only what agrees with experience.
  3. What's the definition of a clock's "existence" in another observer's frame? What if B doesn't know of relativity, and says "A's existence spans 2 of its years on my outbound journey, and 8 years on my inbound, and I've measured that to be true"? How can you prove to B that it's wrong and that your description of existence is the right one? Can you convince it that what it measures (2 + 8 years observed) is wrong and your numbers (unmeasured, but later verified to be consistent with a particular definition of simultaneity) are the ONLY ones that can be real? And can you do this without relying on Einstein's definition of simultaneity or an equivalent? Do you think that when Einstein defined simultaneity in such a way that real-world events could be tested against that definition to determine if they fit it or not, he actually did much more than that, and actually defined existence? Or could it be that his definition so perfectly aligns with your assumptions about reality, that you figure he is proving your assumptions correct simply by definition?
  4. That's wrong. B can SEE A ageing. B predicts that A's clock can be seen ticking at a rate of 0.5x its own, for 4 of B's years, and then ignores whatever happens at A while B turns around, then predicts A's clock can be seen ticking at a rate of 2x its own, for 4 of B's years. So it predicts A will be seen ageing 2+8 = 10 years, plus whatever it ignored. Why must it predict 6.4y, when it can predict the correct value? The rest of your post, you just keep repeating a similar false claim over and over. There's no such thing. Distant simultaneity isn't sensed. B doesn't "sense" a change in the time at A while it turns around (in negligible time). The coordinate time at A changes BY DEFINITION of simultaneity given by Einstein. Do you not accept that? You say his definition is a convention and then give pages and pages and pages of arguments that it's not. I've not convinced you of anything, and I'm repeating the same thing over and over, I give up. No thanks. I don't think that all of the unnecessary complications you're adding will help to understand the uncomplicated case. So start with something that makes sense. Don't just make random changes, choose the idea that you're trying to model. If you only change things that do not influence any real measuring device readings then the end result should agree with reality. Assume your "fused spacetime continuum" if you want. Just *don't* change something that doesn't affect real measurements, end up with something that agrees with reality, and then conclude that your changes must represent "true reality". (For example, choosing a random privileged frame will agree with reality, that doesn't make its privilege real.) Also don't take existing definitions that don't affect real measurements and conclude that they must represent "true reality".
  5. There's another simplification that can be made. How do you know what's a realistic acceleration? We could be talking about twin neutrinos. If we're talking about rockets, the physical properties of the rockets aren't given. That's fine because they don't matter. The mass of the object that accelerates doesn't factor into the SR equations. Therefore it can be simplified out. We can talk about abstract twin particles. Imagining they're something specific, just adds red herrings. Sure, but they're synchronized only (generally speaking) in the Earth/A/X inertial frame. Ie. B is momentarily at Planet X and at rest with it. B's now in A's inertial frame, and agrees with A's (X's) measurements: A is 3 LY away, and A's clock is Einstein-synchronized to X's, which reads 5 years (per OP's specs, halfway---according to any of A, B, C---through the experiment). Nah! How would you measure that sweep at A? You can definitely predict it, using SR, but if you didn't know SR but had any conceivable measuring device you can imagine, how would such a device measure (not predict) that sweep? If you can unambiguously measure it, I'll agree it's the only outcome consistent with reality. Just checking we're on the same page: What does X's clock read when B reaches it, comes to rest with it, and then leaves again (all in negligible B's proper time)? That's what makes it a philosophical argument, not a scientific one. Scientific theories do not pick a choice they think is "real" based on Occam's razor. You don't settle eg. Copenhagen interpretation or string theory based on Occam's razor. You also don't have to because the questions answered by science are about quantitative predictions, not "which model is the one true description of reality?". The conventions used in SR are not about picking a choice that one thinks is "real", it's about ... again, in Einstein's translated words: "that in every real case it must supply us with an empirical decision as to whether or not the conception that has to be defined is fulfilled." Ie. it is chosen because it is useful in making measurements. Any conventions that give you measurable predictions that equally agree with reality, are equally real. You need a different measurement given by different conventions, to be able to physically evaluate which is more "true-to-nature". Occam's razor tells you nothing about that, but it can tell you which are more practical than others.
  6. A possible way forward is to treat c as a constant local speed of light, as it is in GR. It might be possible not to worry about the speed of anything measured from a distance, in your equations? I don't recommend following any of my advice on anything, unless you agree with it! I'm 100% sure you understand the technical details better than I do. If you're interested in testing whether your results are in agreement with SR, you might try deriving the Doppler effect including any of your alterations. If it doesn't give the exact same values as SR, it's not going to agree with real measurements as SR does. But also, I'm not sure what you're working to accomplish, so I don't want to suggest more work. I think we'll never agree, because of philosophical differences. Of course, SR doesn't depend on philosophy, and I think anything "purely" philosophical is not part of the theory. The way I see it... SR is correct, independent of experimental validation. The theory is purely mathematical. You start with some assumptions and mathematical rules, and you end up with some consequences. It is an exact, error-free model. Experimental validation deals with how well that model corresponds with reality, not whether or not it is correct (or complete, or whatever). We find that when measuring the universe, it really does seem to adhere to the assumptions and rules that SR uses, and thus the predictions made by SR are accurate in the real world. Philosophically, the only things I treat as "real" are what are measurable. If there's some mathematical prediction or description, like "A sweeping contiguously through time relative to B in the instant B accelerates", but it is not measurable, for me it's just a part of the model, not something real. For me, it makes so much more sense when everything "optional" is left out (cut off by Occam's razor). That's why I like OP's experiment. Changing from "B and C pass by each other" to "B turns around" doesn't change the prediction, so there's nothing real in that left to figure out.
  7. Celeritas, I haven't followed the math very well. But back to an earlier subtopic, I think I'll no longer say that B turning around "doesn't cause" the difference in ageing seen at event AC (when A and C pass), because I don't know the meaning of that statement precisely enough. Here, C can refer to OP's C clock, or to B after an instant turnaround at event BC. Speaking in terms of causality, event BC *can* be causally related to event AC. AB is also causally related to AC (and to BC). Indeed, all events on all three clocks' worldlines between the events mentioned, can be causally related to AC. So you could say "A remaining inertial causes the difference in ageing seen at event AC", and "The entire time A and B/C are separated causes the difference at AC". You could also say something like "A and B passing causes BC" and get into interpretations, just like "B turning causes AC" is interpretive, but causal influence is possible. In terms of causality, the event BC is not causally related to any events on A's world line between proper times 2 years to 8 years. Therefore technically, B turning around doesn't cause (or is affected by) any events at A within that range. Back to what the LT says, if there is some physical change in the relative time at A when B accelerates (which I don't accept), that change is causally restricted to within event BC's light cone. For example, if B randomly decided only at event BC, whether to turn around or remain inertial, then A would not be able to detect any change due to that decision, until it had aged 8 years since leaving B, at which point it is able to see whether B turned or not. Yes, "who is ageing less" ie. "whose clock is running relatively slower" is relative and generally depends on reference frame. That's why in the twin paradox experiment, the relative ageing is only compared when the twins are together (ie. at individual events). When they're together, the difference in their ageing is not frame dependent, so all observers agree on it. In your experiments, different observers disagree, as per special relativity, but that's no argument against the the twin paradox, in which everyone agrees on the outcome.
  8. Ideally that would come from what you're trying to model. Or if you're seeing what happens with an arbitrary value, or if it's a value that can be chosen for convenience without modelling anything physical, then you can choose. It's beyond me at this point. I was surprised it worked for you, I'd assumed that with so many details and definitions that can be adjusted, it would be much likelier to come up with something that doesn't work. On the other hand, with all the measurements related, it might just need letting the related things conform to whatever changes you make. It's definitely messy that way, but maybe not a problem. For example, if you change the definition of speed, you might end up with a measure of momentum that is no longer constant for an inertial mass, and say "oh, this must be wrong," but if you're redefining everything, your alternative definition doesn't have to have the same properties as the standard definition. It might not be wrong, just less useful. I don't know what's happening with your x coordinates, but maybe something like that is expected? Proper time and proper lengths are measured differently. Proper times can be measured by a moving clock, but proper lengths are measured in a rest frame. The ruler distance along a world line is not invariant. In my example when I messed with the definitions, I ended up with an altered meaning of being at rest, and so distances didn't have the same intuitive properties as usual. It's a bit of a rabbit hole. If you're looking at something like the speed of light as "just a definition", and with distance defined by speed of light, it's also "just a definition." If that seems wrong, consider that the definition of a metre has changed several times in history, and each time the measured value of a given length changes slightly, but nothing physically changed with each new definition.
  9. Sure, I think I'm in agreement. Clocks passing or the intersection of world lines are events. Does it make it easier to deal with them as events? I think that 1-way speed of light differing from 2-way speed has turned out to be too complicated for me to handle. I don't even know if it can work, or how. In all the toy examples I've tried, if there's an easy-enough way to make some modification of simultaneity match the predictions of SR, I keep ending up with definitions where 1-way speed equals 2-way speed. Every time I've mentioned the definition of simultaneity I speak of the time it takes light to go in the 2 directions. It's easy to find alternative timing values that are still in agreement with SR; just borrow the measurements from another reference frame. Assuming standard SR agrees with reality in that frame, there's a set of definitions with which those same measurements agree with reality. But that trick doesn't work with the speed of light, because it's the same in the different reference frames. Even if you can get different speeds of light to work, there are other ways to get different working time/space coordinates that don't require a change in the speed of light.
  10. Those are proper times, though. You're talking about the time of an event that is measured by a clock that passes through the event. All observers agree that B's clock is at 4 years when it passes C. "The time at B" is a coordinate time for A for events at A. For example, if you have an event "half way through A's world line", which A's world line intersects at a proper time of 5 years, all observers will agree that A passes through that event at 5 years. What they don't agree on is the coordinate time at B or C relative to that event. For instance, A says that "half way through A's world line" is simultaneous with B and C's passing. Inertial B says that event happens before B and C's passing. C says it happens after. Sorry, I'm trying to look at this in too many ways. But alright, let's stick with 1-way <> 2-way speed. How are you defining that? You have the definition of simultaneity: "The time required for light to go from a to b is the same as the time required by light to go from b to a in a stationary system." Are you changing that, or leaving that alone? Are you leaving c as a constant, or will you replace it with a variable that depends on direction (and if so, how?). Finally are you leaving distance defined by c, or changing that? Will you have distance measured differently in different directions, or maybe change both c and the definition of distance so that distance is the same in different directions? In SR, the 1-way speed of light is the same as the 2-way by definition. If you want to consider an alternative, you're going to have to change at least one of the definitions. If you want it to be consistent, and to agree with reality, I think you'll have to change multiple definitions. Which definitions are you changing? I used the example of choosing a preferred inertial frame with which to define all the relative measurements. This is a bad alternative because it has no benefits for any other observers except the preferred frame. However, it is an easy way to make sure that all of the measurements are at least consistent, and can be physically verified (remembering that the one-way speed of light is a definition, not a measurement), and must give the same predictions (but with different coordinates) that SR does.
  11. Good idea. In that case the twins are symmetrical. There are observers that can measure A and B symmetrically, the simplest being one for which the speeds of A and B are both 1/3 c (so the composition is .6 c). Which twin ages more, is relative.
  12. Not theories. I've only talked about the theory of SR in this thread. I think they'd be called different coordinate systems. So much wrong with this. B passing C is an event. OP has set it up so that B's clock shows 4 years at that event, and C's clock shows 4 years at that event. Those are invariants. No change in coordinates can change what B's clock shows at an event that it passes through. It's the time at A, far away, not local!, when B and C pass, that depends on a coordinate system. You already know, that even using the standard coordinate systems of SR (I think we call them Minkowski coordinates?), A's time, when B and C pass, differs depending on which inertial frame you're describing it in. But it can also change if you use an alternative coordinate system. Not theories. B and C disagree on the coordinate time at A, when they pass, yet all observers agree on the time at A when A and C pass. Do you understand how that's possible in SR? I don't know where you're getting this from. It's the coordinate time at A that is relative, when B and C pass. A is not intersecting any of the other given world lines when B and C pass. It is only the time according to a clock that is some distance (not local) from the event, that is relative.
  13. No, I don't think so. How is the measure of speed defined? If other observers measure time AND distance the same as it is measured in the preferred frame, all observers measure the speed of light the same. That's the point I keep trying and failing to make. These values have definitions, you have to go by how they're defined. You can't just use a common-sense definition of speed, or mix-and-match definitions, altering one quantity but not another that is based on it. No. Multiple alternatives that give different values for RELATIVE quantities can be "right". There's no evidence of an ether frame, but lack of evidence isn't proof of non-existence. They haven't been proven false, just proven so-far useless. Everything still works if you decide a frame is preferred. This is a waste of time... ... but for another example, suppose you have an event, and observer A uses coordinates with the origin in one place, and B has the origin in another place, and they get different results for the coordinates of the event. Which observer is right? They both are. Suppose A uses Cartesian coords and B uses spherical, and they get different results. Which coordinate system is wrong? Neither. The LT gives you COORDINATES within a defined system, it doesn't claim that those coordinates are "real". Comparing different ageing at a meeting point is comparing values that are real. You can't come up with working alternative coordinates that make someone older or younger than they actually are at a given local event. You *can* come up with working alternative coordinates that make someone older or younger than the LT says they are relative to some distant event. Different simultaneity conventions that still corresponded with reality as SR and Einstein's simultaneity definition do, would simply give you different time coordinates of distant events. Which is right? Maybe all. Which is useful? I've never seen any better than Einstein's. Which is "real"? There's no theoretical answer and the question is likely meaningless. Analogous to "what are the real coordinates of the event, A's or B's?"
  14. Instead of describing a physical rocket and figuring out how the different points of it accelerate, you can specify how you want the different points to accelerate. If all you're comparing is two points, you can have the two points move independently and then not even care about the physical aspects of a rocket. For example, if you want to see what happens when they perform the same maneuvers, specify that the two points have identical acceleration measured from some inertial frame (eg. Earth frame). Or if you want the rocket to be rigid, use Born rigidity equations. It's especially pointless to describe the physical aspects of the rocket, then ignore the physics in some tiny details (like assuming it's completely rigid with one source of acceleration, which is impossible), and then try to figure out other tiny details of the physics. Sure. If the top and bottom accelerate at the same time and rate according to an observer on Earth, those clocks always read the same from Earth. While accelerating, the bottom clock ticks slower than the top (in their reference frames), this can be verified from the Earth frame just by considering the always increasing time it takes light signals to go from the bottom to the top (takes longer because the top is moving away during the time the light travels) vs top to bottom (takes less time). If the rocket then coasts, Earth says their clocks still read the same. On the rocket, the clocks now tick at the same rate but the rear clock is behind, in agreement with relativity of simultaneity. If the rocket reverses and returns to relative rest with the Earth, still with the same timing and rate of acceleration as measured by Earth, the clocks as always remain the same according to Earth, and now the rocket agrees with that. This would describe the situation in Bell's paradox, where eventually the rocket (fixed length in the Earth frame) rips apart. If you change that, so the clocks don't always have the same velocity as each other as measured by Earth, they can end up still out of sync after returning to Earth's inertial frame.
  15. The time it takes for light to go from points P1->P2 is the same as P2->P1 in a stationary system, by definition. The LT has a mathematical definition, it's not based on measured constants. It has c in it as a constant, which also is a defined (not measured) value. The metre is defined based on c. Which of those are you changing to get a 1-way speed not equal to 2-way speed? Depending on what you change, you'll change the LT. I don't know if it's possible to change multiple things to make a modified LT give the same results as the LT, while having different 1-way speeds of light in the x direction. The relative rates of a moving clock would typically change, the lengths of world lines between events would not. Here's an example. Suppose someone Q decided their own reference frame was privileged, and invented a system based on SR but where all relative measurements used their reference frame. Suppose they're moving relative to twins A and B (and clock C too), such that in their frame, the standard LT says that the time at A when B turns around (or passes C) is 6 years after A and B depart, as measured by A's clock. Then, on the outbound trip, B's clock measures 4 years while A's measures 6, so B's clock ticks at a rate of 2/3. On the inbound, B (and C) measure 4 years while A measures 4. As always, in this experiment A ages 10 years while B ages 8 in the end. These measurements are different than what the LT says for A and B (but it agrees with what the LT says for Q, so you know it isn't predicting something inconsistent with reality). Normally A and B measure things using their own reference frames, but if they adopted this alternative, they'd use a definition where the time between P1->P2 is the same as P2->P1 (because it is in Q's), which is weird for them, because P1 and P2 are not stationary in A's or B's frames, so using normal SR measurements they'd measure those two times to be different. So there's an alternative. It's bad, but it works. It doesn't match reality for A and B in the fact that their systems are not measurably distinguishable as less privileged than Q's, but they're defined to be, and things are measured differently in different frames to match what Q' measures. But they have still have consistent definitions for all the measurements they need wrt. things like the twin paradox, and can confirm them experimentally. I hope I'm not just making things more confusing. The only reason I'd mention alternatives is to figure out what exactly SR says and doesn't say. The twin's ages when they meet, are invariants. The values that are relative can be consistent with various different systems of measurement that give different values. I feel like I'm straying farther and farther off topic trying to clarify what I said earlier, but I'm failing in that because you keep thinking I'm saying something else. PS. If you really get what I'm saying, I think I accidentally described a screwed-up system where the 2-way speed of light is still the same as the 1-way, according to the definitions, even though if you have two points p1 and p2 that are stationary in A's reference frame, A measures the time from p1->p2 as different than p2->p1, because it's using Q's measurements and they're not stationary to Q. Sorry, it's excessively complicated now, but if you get that then you probably understand the way I see this. All these measurements aren't "common sense" descriptions of what we understand as time and distance and speed, they have precise definitions that don't care what common sense says.
  16. Right. Where the clocks intersect, its only events at the other clock (which are now local events) whose coordinate time is independent of how you define remote simultaneity. The solutions to the twin paradox remain the same. You can set all those other clocks everywhere else however you want to (eg. invent some alternative clock sync definition), but that won't affect the time measured by the two twins clocks.
  17. Yes, we all agree on that! Celeritas, you're right on that. However Markus, if you take clocks out of it you're no longer talking about the twin paradox, which concerns ageing. The geometric length of the world lines doesn't depend on the validity of the clock hypothesis (right?) but the twin paradox does. Back to OP's topic, the 3-clock variation also does not depend on the validity of the clock hypothesis. But in either case its fine because we assume the clock hypothesis is true in the twin paradox in any case, which means both OP's experiment and the geometric length measure the same ageing as does a clock that turns around (instantly, in this case corresponding to OP's setup). The situation in terms of geometry is the easiest and most straightforward, leaving no room for debate or confusion about physical aspects, and the lack of effects due to acceleration (that aren't fully accounted for in terms of velocity) is by definition of geometric length (I think). In the twin paradox the lack of effects due to acceleration (that aren't fully accounted for in terms of velocity) is by assumption and experimental confirmation "to very high accelerations".
  18. The point of the twin paradox setup is that it produces a result that's certain and independent of reference frame. You never *have* to compare distant clocks to resolve it. You don't need synchronized clocks, or a synchronization convention, or a definition of simultaneity. In that sense they don't matter. You don't need coordinate times or the LT to resolve the paradox. But if you try, using the LT, you always get consistent results. If you used any alternative that was consistent with reality, it would give you the same results at the events where the twins meet. Any other result isn't consistent with reality. If you use some other transformation or system of coordinates or definition of time where the one-way speed of light is different in different directions, if it was consistent with reality you'd get the same age difference that SR predicts when the twins reunite, but generally a different coordinate time of events at the other clock while they're separated. The coordinate times given by the LT would be different if they used a different definition of time other than Einstein's, where the time of a light signal between two locations is the same in either direction. You say "readouts" given by the LT, I guess you mean the calculated coordinate time in the distant clock's reference frame of the local event "now" ... the calculated coordinate time in the distant clock's reference frame, of an event at the distant clock's location, whose time in the local clock's reference frame is "now"???. At the intersections of two clocks' world lines, the "readouts" wouldn't depend on the one-way speed of light because the distance between the clocks would be 0, and the time of a light signal would be the same regardless. So I guess the answer, as best as I can understand your question, is "no", in general an alternative to the LT would give you different "readouts" everywhere except where the two clocks meet.
  19. Whether it's "true to nature" is neither testable nor even relevant! I'll repeat Einstein's argument: (emphasis mine) That one-way is the same as two-way is by definition. See Einstein's 1905 paper, eg. translated at http://www.fourmilab.ch/etexts/einstein/specrel/www/ where he writes: There's no test that can invalidate a self-consistent definition! IF on the other hand, some test found that SR does not adequately describe reality, then some other definition of time, or a modified definition, might be used instead. For example in curved spacetime, in cosmology etc, that definition isn't used and there is no such definition of a common time (or simultaneity) for different locations throughout the universe. If you think you're debating whether the LT or Einstein synchronization is "correct or incorrect", you're missing the point and wasting your time, because it's correct. But when you speak of what happens at a distant A when B does something locally, you are basing that off of definitions. What's happening at A is outside B's light cones, there is no causal effect, and arguments about what is "true to nature" are not supported by SR as written by Einstein. The difference in ageing when they meet is indisputable, testable, true to nature, geometrically measurable, etc. The time at A when B is far from it is NOT based on "nature", Occam's razor, experiment, etc., it is established by definition. Any true conclusions you make based off of that are true by definition, regardless of reality. As for Occam's razor, if something like the simultaneity of events at A and B can neither be physically proven real nor proven inconsistent, wouldn't it be simpler to neither assume that they're real nor wrong, and accept that it might be just a definition that can "supply us with an empirical decision as to whether or not the conception that has to be defined is fulfilled" and not necessarily physical? Also, I don't argue that acceleration plays no role in the twin paradox; B's path involves a turnaround that involves acceleration. I argue it plays no role in OP's experiment. But if you can agree that in the water boiling analogy (two twin cups of water A and B, B is poured into a kettle that's on the stove and it boils)... if you agree that "pouring the water causes it to boil" then I'll agree that "B accelerating causes the difference in ageing", because then I'll understand the intended interpretation of the statement. Please, can we just agree??? Otherwise, I think that the role of acceleration in the twin paradox is the same as the role of pouring the water; something that establishes the necessary conditions for the outcome of the particular experiment.
  20. Agreed. If twins are symmetric, they can't have aged differently at an event through which they both pass (or ever, in a reference frame in which they're always symmetric). Another example of asymmetry is OP's experiment, where the asymmetry is not due to acceleration. I agree, in the twin paradox class of experiments, twin B's acceleration is the cause of the asymmetry. In other experiments, acceleration doesn't cause asymmetry (eg. if two twins both accelerate), in others asymmetry doesn't cause a difference in path length (you can contrive two twins to have aged the same amount when they meet), in others asymmetry has a cause other than acceleration.
  21. Celeritas, I don't want to argue this. I can't prove simultaneity is merely a convention and you can't prove that it's physically real. Einstein's convention does work in the case of the accelerating twin, because there is always a momentary comoving inertial reference frame that it can use. Even in the case of instant acceleration, you can let the twin instantly sweep through all velocities from its outbound to its inbound velocities, and you can instantly sweep through all planes of simultaneity between outbound and inbound. Whether or not there's any physical meaning to that doesn't even matter, because whether you do it that way or not, you're not going to predict any different results. The LT uses Einstein's definition of simultaneity to establish the time at different locations within an inertial frame. I don't understand what you mean when you say the LT is real but Einstein's definition of simultaneity is a convention. When B and C meet (or when B turns around), the time at A is relative. There is no one "then" that you're asking about when you say "Does a clock truly read what it's hands then display?" The clock at A is correct at all times through its journey. Also you talk about what the clock at A "then displays". But you know that B and C when they meet see the same time appearing on A's clock, in accordance with the relativistic Doppler effect. That they disagree on when "then at A" is, can come down to the fact that they disagree on how long it has taken light from A to reach them at that moment (because in this situation, B and C each have A moving at the same relative speed in different directions, and they agree on the rate at which A's clock ticks in accordance with SR). They measure at that moment that the clock at A appears to display the same time, but they can say that the time at A is "really" a different time at that moment because of the "time" it has taken light to reach them. BUT the "time" it has taken light to reach them is based on the definitions that Einstein uses, which are the same that establish whether two distant events are simultaneous or not. So the relative time at A, according to some distant observer, is "really" what the LT says it is, exactly to the extent that Einstein's simultaneity definition is "real". Whether one believes it is or not, it is established by definition, not by physical measurement. That's why the results of the twin paradox and OP's experiment should be incontrovertible; they only require the comparison of proper times. I've been debating the meaning of coordinate time and that's not helpful. The outcome of the twin paradox is as certain as SR is, and doesn't depend on how distant clocks relate, about which I'm not going to agree with others.
  22. Oh right, gravitational potential energy is gravitational potential * mass, so a more massive clock would have higher potential energy, but wouldn't tick faster than a nearby lighter clock. If I worked out the maths I'd make fewer mistakes like this. Do you mean it depends on the position of the reference clock? Is it just the relative gravitational potential (determined eg. by height h and g(h)) of the two clocks that matters? If you have two clocks and all you know is their gravitational potentials relative to some arbitrary common reference point, can you determine their gravitational time dilation?
  23. It's not increased g but lower gravitational potential energy (depth in a gravitational well) that makes clocks relatively slower. It's easy to confuse because with common masses g is typically higher where the potential energy is lower. If you took a pendulum clock tuned for Earth's gravity and suspended it somewhere above the sun where g=9.81 m/s^2, you could confirm that the clock keeps time with a nearby light clock the same way one would on Earth. But it should be deeper in a gravitational well compared to the Earth's clock, so that if you compared the two pendulum clocks operating with an equal g, the one above the sun should be slower. That's the thing about "all other things being equal"; you can make all other things equal and you still get the relativistic effects, so you can rule out mechanical reasons for time dilation.
  24. No, that's false. The twin that turns at B-turnaround (aka BC event) measures the same contracted length between AB and BC that OP's inertial clock B measures between the same events. The distance between AB and BC is 3 light years according to A, and 2.4 light years according to twin B or clock B. If you have a marker at BC that is stationary in A's frame (so that the proper length between A and the marker is the length measured in A's frame), then the marker approaches B (twin or clock) at a speed of 0.6c for 4 of B's years, traveling 2.4 light years in outbound B's frame. Bringing this back to OP's post, I'll agree that your twin B's turn around causes it to follow the shorter world line made up of OP's B and C between the 3 events where clocks pass. Well let's consider that analogy. You have two twins A and B, and the only differences between them is that B turns around and ages less. In the absence of some other form of time dilation (GR), having B turn is necessary to have it age less. Therefore B's turnaround is the cause of it ageing less. Now say you have 2 glasses of water, A and B, and a kettle on the stove, and you pour B into the kettle and it boils. The only difference is that B was the one that was poured and it was the one that boiled. In absence of some other way to heat it, pouring B into the kettle was necessary to have it boil. Therefore, pouring B is the cause of it boiling. I suppose it's possible to interpret that as a true statement. But in isolation it is just misleading. Pouring water causes it to boil. Proper acceleration causes differential ageing. Then you do the equations and you find that the world line AB to BC to AC is shorter than AB to AC, and that the energy used by the kettle heated the water, and the pouring doesn't factor into the maths. Someone points out that if the water started out in the kettle, it would boil in the same time as if it was poured in. Then someone else says that involves hidden pouring. Edit: Maybe I'm dumbing down the argument too much. You're arguing that the change in coordinate time at A's clock when B turns around, is something real (because the LT says it is?) and I'd argue that's just a coordinate effect that disappears with a different system of coordinates or without a definition of simultaneity. Equivalently, you're arguing that Einstein's definition of simultaneity must be physically real? Or, back to OP's experiment, could we say the debate is about whether clock A is physically different to clock B vs. clock C besides how it appears differently to different observers? Would you argue that when twin B turns around (or if clock B were to turn into clock C), that causes a physical change in A? I say it doesn't, that the observed differences are only relative and depend only on the observer. If they're both inertial and their velocities are different, does that just mean that you're choosing a frame of reference where they have those velocites? Otherwise, regardless of the direction of their different velocities, if B's speed is v in A's frame, then A's speed is v in B's frame. The only way to have the twins age the same over a time t is to choose an inertial frame of reference where A's speed is the same as B's speed, right? (Of course there's no inertial frame where A is inertial and B turns to reunite with A, and they have the same speed relative to the observer the whole time.)
  25. "Makes it all happen" is too vague to be meaningful. What's "all"? B's acceleration doesn't determine A's ageing. One might as well say "B's proper acceleration is the magic that makes it work" and "magic" means the part that doesn't show up in the maths, or it's the answer to the "Why?" questions that aren't satisfied with knowing the "what". I don't know why people look for such explanations anyway. We agree everything that's "what" is there in the geometry, and it's there in the 3-clock variation when nothing physical accelerates. Does there need to be more than that? I think it's fair to say that twin B's velocity relative to A is affected by its proper acceleration. That's about all that's needed to explain acceleration's role in the twin paradox. If B undergoes the same proper acceleration but at A's location, there's no change in the coordinate time at A. So someone else might say "It's distance that makes it all happen!" Then someone else might suggest that if B instead orbits A at a very small distance but at 0.6c, you get the same ageing as in OP's experiment, but with B undergoing constant proper acceleration. So neither distance nor proper acceleration alone is making it all happen here. You can scratch a hole in your head trying to figure it out how one or the other is making it all happen. But if all you have is relative velocity and time, you can calculate it.
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