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Everything posted by md65536

  1. Credit where due, you seem to be making progress. Using conventions like time on the y-axis and light signals shown at 45 degree angles really helps in communicating ideas. In cases where you start with bad assumptions and then show what happens, the conclusions aren't going to be useful. If you put "garbage in", you get "garbage out." Eg. the Doppler factor of 5 from assuming the clocks tick at the same rate, is not useful. You *can* assume the clocks tick at the same rate, but then you'll find that the speed of light isn't constant etc., which doesn't match reality. Where you lined
  2. Sure, they can measure different coordinate times. Those times can be a component of the invariant spacetime interval, without being invariant themselves. Different observers have different components that combine to the same interval. It's the proper time that is the invariant length of a spacetime interval. Everyone agrees on the time that a clock measures on its world line between two events. But to different observers, the clock's path with have different coordinate times, and different coordinate lengths. Consider an infinitesimal line element of such a world line. For some observers
  3. You're right, though it could but not really but actually it could, but not really. "All parts accelerating equally and simultaneously" in a single frame basically describes Bell's paradox, but kind of the inverse because you're slowing it instead of speeding it. Definitely you can't do it as a rigid object. If you stop a ruler all at once, you change its rest length. Its former length-contracted length becomes its new proper length, it must be compressed. To do this would require an opposite rule, that strain or stress doesn't affect the ruler's behavior, so it could be arbitrarily compressed
  4. True... if Earth alone stopped the ruler and the ruler approached the limit of perfect rigidity, it would take at least 2 years for Earth to see part of the ruler come to rest 1 LY away, twice as long as if the ruler stopped all at once. But that's why I specified that the entire ruler was "made to stop" simultaneously in a given frame, rather than that it just stopped. I avoid worrying about practical details because SR isn't limited to what's practical. But it would mean this is a poor example to use as a thought experiment to explain what can be expected in real experiments. Not that anyone
  5. So instead of saying the spacetime interval isn't invariant in curved spacetime, I should have said the interval defined for Minkowski spacetime, ie. the quantity (ct)^2 - r^2 isn't invariant in GR. I was going to ask if the spacetime interval in GR is a local thing only, that applies only to intervals between nearby events, but if it implies world line lengths are invariant, it might apply to any arbitrarily separated events? Oh but then, there can be multiple world lines between two events in GR, so the spacetime interval is local only??? and a world line's length depends on local variances
  6. The funny thing is, he's already accepted that a Doppler effect is acceptable in his definition of reality, and it's an easy modification of a twin paradox setup to make neither twin inertial and make it truly symmetric. Then just say "that's what they both see." It's also funny because for me, seeing the asymmetry in the Doppler analysis of the twin paradox is probably what fully sold me on the predictions of SR, and I never doubted the resolution of the paradox after that, even though I still would have struggled with "the Earth's clock jumps forward with the traveler's change in inerti
  7. The Pythagorean theorem seems to crop up a lot, and if you move one of the terms to the other side it looks like an equation for a hyperbola. Often you can see that in diagrams, where you have eg. a length in the x dimension, and one in ct, and the hypotenuse is meaningful in some way. Anyway I'm still figuring out things about that. The numbers I used were just an interval s^2=1, with (ct)^2=1,r^2=0 in one frame, and (ct)^2=4, r^2=3 in another. A common speed used in examples is approx 0.866 c ie. sqrt(3)/2, because the Lorentz factor in that case is a simple factor of 2. You might try s
  8. It's more about the coordinates (an inertial frame is 3 Euclidean space dimensions and a time that is the same everywhere within the frame), the clocks just represent a measure of the frame's time at different points. If you never had to consider different frames, you could use a single clock to represent time everywhere. I'll just keep talking because I hope more people talk about the meaning of the spacetime interval being invariant! But with respect to that, do you know the 3 types of interval: space-like, light-like, and time-like? The type is invariant, and depends on if s^2 is respe
  9. While waiting for a better answer... Having the events on the sun unnecessarily complicates things because of spacetime curvature. You're measuring distances from afar, in a different gravitational potential, so there's not one "correct" way to measure those distances. I don't think curved-spacetime intervals are invariant. However, if you're treating the sun as just a location in flat spacetime, that's fine. You wouldn't directly compare the arrival time of light signals from the events, you'd want the time those signals were sent. Basically you'd subtract the travel time of light t
  10. md65536


    The speed would change in different reference frames, exactly as the speed of an object would. To see this, imagine light through some medium, and an object traveling along with it at the same speed, so that they both pass through the same set of events. In another frame, if their speeds were no longer equal, they wouldn't pass through the same events, which would be a paradox. As swansont mentioned, because of the velocity addition (composition) formula, changing the observer's speed by non-relativistic v will change the speed of light in the medium by a LOT less than v.
  11. This is literally your thread now, I'm curious how this adds up in your examples, without relativity. You said that when traveling twin A stops, it doesn't immediately see Earth as stopped because of the delay of light. Relativity says Earth doesn't see A stop immediately, and you're saying A sees Earth appearing the same. For example, suppose Earth is at rest at the 0 mark on a ruler, and A travels to a 1 LY mark, and then stops. The whole time while traveling, A sees that Earth appearing to stay at the 0 mark, agreed? When A stops at the 1 LY mark, how far away does it see the
  12. Adding to that: A ruler doesn't measure "accumulated" distance, but an odometer does. While a twin makes a round-trip at constant speed, if its clock records half the time Earth's does, it will measure that it traveled half the distance Earth measured it traveling. Its odometer retains the accumulated effects of length contraction. (The trip's clock and odometer dicrepancy ratios would generally differ is the speed wasn't constant.)
  13. It is, see image (b). Image (c) is what the dice look like when you receive (at the same time) light that left the dice at different times and traveled different distances. Image (b) is what you see if you remove the differences due to delay of light. In fact, if you put points of light all over the dice and sync'd them to flash at a single moment in the observer's frame, what you see would look exactly like (b). This assumes persistence of vision or exposure time somewhat proportional to d2, since the light wouldn't all arrive at the same time. You could figure out so many mysteries
  14. Michel has established that he's spent 20 years denying relativity. There are many, many hijacked threads over the decades, any that have certain keywords (in this case, "time, direction"), turned into 6+ pages of failed attempts to get him personally to accept something about SR. He's stated in this thread that he's not interested in relativity, and of all the hundreds and hundreds of answers to his repeated questions, not a single one of them he acknowledges as an answer to his questions. The only time I've seen any calculation or attempt to work through a problem, is when he's twisting his
  15. Thanks for the interesting visuals, they're rarely shown. From what I understand, the only(?) differences between the length-contracted measured (b) and the seen (c) are abberation of light (where the orientation of a ray of light is different in different frames of reference, due to the time that it takes light to travel from source to destination while those points are moving) as well as different parts of the scene being seen in different positions due to delay of light from different distances. The rotation seen must be a rotation in 4 dimensions, nothing is rotated in 3? To demo
  16. Absolutely! You are absolutely correct! It was all worth it for the laugh. Sounds good. Your example has a traveler moving away for one hour, and then coming back in half an hour. What does Galilean relati ah forget it. Thanks for the laugh!
  17. No symmetry then? Abandoned the thought experiment the very second it didn't show what you wanted? Thus proving me a fool for even trying despite this obvious outcome. The trip that I described is realistic. If you travel outbound at one speed, and return at the same speed, it will take you the same time to make each leg of the trip. Galilean relativity even agrees with that. You've answered your own question! Denial of science is a lifelong pursuit, you don't just give it up. The same reason that we would keep trying to explain relativity to someone with an amazing commit
  18. I think you found something nobody considers; there is symmetry in the twin paradox! How can the maths possibly work out? You might convince me? Okay, let's say that a traveling twin travels outward for one hour while seeing Earth's clock appear to tick at half the rate. Then it returns with a symmetric trip and for one hour, it sees Earth's clock appear to tick at double the rate. Half the rate for one hour, and double the rate for one hour. What is the total time that it sees ticking on Earth's clock, during its own 2-hour round trip? Could it be that you were right? If you answer
  19. I think I misunderstood. "The spacetime interval is invariant" was used to explain several things, I think including (paraphrasing) "why are lengths and times different in different frames?" and "how is that consistent?" If you consider a single space-like or time-like interval, it being invariant seems to demonstrate on its own that the measurements between frames are consistent, but doesn't give a reason why the measurements are different. I think what I missed is: it's that *all* intervals are invariant that explains why the measurements must be different (which can be demonstrated just by
  20. re. "how can he have his own image so close and measure that the same image goes away from him at c? " So basically, say in an Earth frame, with a rocket approaching at near c, the image of the rocket when it began its journey can be very close to the rocket itself, for nearly the entire journey, but in the rocket frame the image reaches Earth less than half way through the journey (since the Earth is approaching at near c, Earth and the outbound image will meet near the halfway mark). The spacetime interval is invariant implies for example that... if you consider some pair of eve
  21. I don't think that's true. I don't see a single reply here from michel123456 that relates to trying to understand any of the answers and explanations given. No asking for further details. No working through a solution. Every reply is a justification of not making an effort to learn, an argument of why the explanations can be ignored. Literally 10 years ago he was asking about the same "problems" he had with relativity. 10 years from now, he'll have a similar list of "problems", after thousands of attempts by people to explain it to him, after 0 attempts to work through it. What he's
  22. That's not talking about relativity. Why not work through the explanations given, instead of ignoring them and always falling back to accepting some alternative, accepting that relativity is wrong? All of your problems have been explained to you before. They all have examples that you *could* work through. You *could* work through them and see how you arrive at the answers that SR predicts, or find where you're getting hung up. You *could*!... I gave you an example that *showed* the effect of time dilation without length-contraction perpendicular to the direction of travel. You expre
  23. Always I see the same pattern. Brush aside explanations and equations as if you didn't even read them, but always latch on to any idea that justifies a failure to understand relativity as if that's just another equally valid viewpoint. I think Asimov's "my ignorance is just as good as your knowledge" quote applies. You say your view is "simpler" but it's just a misunderstanding. It makes me think that people who put effort into trying to explain things to you over and over are just wasting their time. You ask questions as if you want to understand, and then reply to answers as if your question
  24. It's only important if you want to be consistent with what we actually measure of reality. It's a combination of the definition of speed being relative, and that measured speeds are consistent with that. If you have A moving at 0.8c relative to B, does it make sense that B is moving at a different speed relative to A? If you wanted that, you could define speed differently (eg. define speed to be absolute, and please call it something else), but you would end up with a system of measurements that is either inconsistent with measurement, or more cumbersome than what we have. I think
  25. I think so... but I'll nitpick. I wouldn't say the observer "needs" 2 separated detectors. For example Markus's method I think involves making only local measurements. Instead I would say, that if you *are* using 2 separated detectors, you have to coordinate them properly. Not all measurements that rely on a separation of detectors will be the same as a local measurement, just by making the separation smaller. But in this case, by making the two detectors closer, you're minimizing the time that the observer accelerates, so minimizing the effects of difference in speed, and yes getting clo
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