md65536

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.)

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 if you learned SR. Do you mean the lengths between the dice? Those lengths are contracted, see (b). Here's a thought experiment to show that the spaces between objects are contracted the same as objects themselves: Consider the dice in their rest frame. Put an enclosure around each die, and connect them with sticks. In the moving frame, everything contracts, and the dice never leave the enclosures. The distance between the dice must contract the same as an object of the same length. Edit: After catching up to the rest of the conversation I see my explanation isn't necessary. I think that if you showed the dice say 1s apart (big dice) in a Newtonian frame I guess??? in (a), and showed them "at the same events" 1/gamma s apart in (b), it would look the same as it does now. If (b) showed them 1s apart in the new frame, they'd be spaced farther.

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 beliefs and made-up definitions into a nonsensical answer that confirms that relativity is wrong. Trying to understand relativity is destructive to his goals, and completely avoided. So the answer is yes, anything that shows relativity working will be ignored. If you're enjoying explaining it, that's good. If you're hoping Michel will learn something, ... I wouldn't.

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 demonstrate, if you add rails that the dice slide on (say 4 rails that 4 edges of each die slide on), such that the rails are at rest relative to the observer, you'll see of course that the rails do not appear distorted, and that the dice edges never appear to leave the rails. For example, the tops of the 1-side of the dice still appear to follow an undistorted straight line, and the bottoms of the 1s follow another, and same with the 6-side at the back. When moving in the x direction, an objects's parts don't rotate off their yx coordinates, but instead appear stretched between them. That can also be seen in the black and white animation you posted earlier. Edit: I just noticed, the (d) image shows this... Instead of rails, have the dice slide along lines in the floor. It looks like the checkered floor is at rest relative to the observer, and each die has the same width and proper length as a floor tile. The sides of the dice appear remaining aligned with the straight floor tiles. The description also describes them as sheared, not rotated, but the shearing is how the 4D rotation appears in 3D? Edit2: No wait... I think there are 2 separate things. A hyperbolic rotation of lengths and times, between the x and t dimensions (y and z are not affected at all if there's no motion in those directions) and the superficial appearance of the objects appearing rotated. The observable effect of the actual rotation is length contraction. The distortion that appears similar to a rotation isn't a rotation at all, but shearing. The entire front (in direction of travel) of a die passes the parallel floor lines simultaneously, both in the die's frame and this observer's frame, but appears not to because the die face isn't all the same distance to the camera.

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!

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 commitment to avoid understanding it, keeps someone else trying to show that relativity is wrong, even if he thinks the people he's trying to convince are "insane to believe such a thing." Re. "at some point you need to realize you're wasting your time."... it's a battle of stubbornness, who will refuse for longer to give up? My bet's on Michel. You don't throw away 20 years invested in denying relativity, and risk it all by accepting something new now. You take it to the grave, regretting only that the insane people wouldn't listen.

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 this, it will prove that I'm a fool.

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 light-like intervals being invariant?). You have a knack for showing no interest in explanations, but continuing to get people to put effort into giving them.

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 events, one that the "image" passes through and one that the rockets passes through, that are spatially near each other (separated by x) in the Earth frame, they're also temporally near each other (separated by t) in the Earth frame, and you get a small interval (ct^2 - x^2). In the rocket frame, those events are far apart spatially, but also far apart in time, and you get the same small interval. Is that all there is to it? Does that sufficiently explain it? It seems to, but normally I'd have to figure out the separate time dilation, length contraction, and relativity of simultaneity to reconcile the different reference frames. Are those still needed, separately (or combined like in Lorentz transformation), to calculate the components of the interval? It seems like the interval being invariant isn't enough to know the x and t in another frame, without calculating one or the other separately?

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 good at, is asking questions that makes one think he's interested in learning about relativity. But look at the replies. The only interest is in what doesn't make sense to him. Anything making sense of it is ignored. That's the only answer he's interested in: that it doesn't make sense. All his questions are phrased as if the answer he expects is that it can't make sense, never a question about how the resolution to the problems work out correctly. So I think he's soapboxing, getting much better responses by stating "relativity is nonsense" as a question. Edit: To be fair, page 1 of this thread is full of counter examples to what I said, including asking about specific examples and numbers and their explanations. I don't know how we got from that on page 1 to page 2 with:

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 expressed incredulity and moved on. Go through the example. We can show you what you're missing. Don't look at any of the details, and the answer's simple: You're missing everything. However I think you're opposed to understanding relativity and are wasting people's time repeating the same questions about it while ignoring the answers. Go through the mathematical details of an example.

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 questions were only meant to demonstrate what you see as "problems with Relativity" and you had no interest in understanding how they're resolved. If you were interested in understanding it, you'd spend more time talking about what relativity says that doesn't make sense to you, and less about how much sense an alternative makes.

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 it's a 3rd option: I think you're determined not to accept relativity and so you're determined not to understand it. I think we could find out with a quiz! Do you think that a) you will accept relativity and understand it together, or b) you will eventually understand it, and then accept it after, or c) if you accept that it's correct first, that will make it easier to understand, or d) you will never accept it and it's more likely that you'll find a flaw in it before anyone convinces you that it's true. Or e) other: ______ ?

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 closer to what an inertial observer measures.

Oops, right! It's the relativistic Doppler factor, not the Lorentz factor. 🤕 brain damage

The frequency increases (blue shifts) the faster that you move toward the light source. At c/2 gamma is about 1.15, the frequency would be 1.15 times what was emitted, if moving toward the source (or redshifted to 1/1.15 times the emitted frequency if moving away). Everyone will measure the speed of light as c in their inertial frame. The two detectors I mentioned I was referring to A and B. Acceleration complicates things. The equivalence principle implies that you can set up a scenario where an accelerating O measures the same things as an O in a uniform gravitational field. So...... using 2 detectors depends on a lot of stuff (which direction O's accelerating, etc). One problem is that if O is changing speeds, and the 2 detectors must detect the light at different times (the events "A detects light signal" and "B detects same light signal" are separated by a light-like interval, so there is no reference frame where they are simultaneous) then effectively you're talking about 2 different measurements made in 2 different reference frames. O changes speed in the time that it takes light to travel the distance between A and B. You'd get a "speed of light other than c" if O treats the two measurements as if they were made in a single inertial reference frame, which they weren't.

Sure! It's "length contraction". In case I wasn't clear, I was talking about two different cases, depending on what the 10 LY refers to. Either the 10 LY is the distance from Earth to destination as measured by Earth, and John measures that as length-contracted to a shorter distance. Or 10 LY is the distance that John measures, and Earth measures a longer distance that John measures as length-contracted to 10 LY.

You said the trip was 10 light years, but didn't say what frame that's measured in. It sounds like you intended that to be in the Earth's reference frame, so Earth would measure the trip taking 11.11 years. In John's reference frame, the distance to the destination is length-contracted, so even though the destination approaches John at 0.9c, it arrives at John sooner than 11.11 years. Gamma is ~ 2.29, the contracted travel distance is 10 LY/gamma = 4.36 LY, taking 4.84 years at .9c, measured by John. This could be true (until the last sentence) if it was 10 LY as measured by John. If that were true, then it's true that he'd measure 11.11 years and that Earth would measure more (11.11 years * gamma = 25.49 years), but Earth would also measure the distance traveled as much greater too (10 LY * gamma = 22.94 LY), and the speed would still be .9 c. Earth would not experience time dilation in those measurements, it would measure 25.49 years as normal. The only time dilation it would experience is that a moving clock ticks slower, and it agrees that John's clock ticks only 11.11 years during Earth's 25.49 years.

That doesn't matter because you can use a short pulse of light, ie. simply use many many photons instead of one, and they'll all behave the same with respect to speed. Some of the photons can be detected at the first point, and others at the second. Yes and no. Assuming flat spacetime, yes: It is assumed that the speed of light is the same everywhere, and that agrees with experience. With GR, not really. Measuring the speed of light from a distance, at a different gravitational potential, isn't really meaningful. The local speed of light is invariantly c. Some might say "the coordinate speed of light in a gravitational well isn't necessarily c" but "coordinate speed" might not be an accepted scientific definition. There's not really any theoretically accepted way to directly measure the one-way speed of light without something like the definition below. If you're using measurements of timing made at two different locations, you need a way to relate those two measurements, for example using synchronized clocks. Einstein established the definition we use to say that sync'd clocks read the same time. The definition he used in his 1905 paper on SR is (translated): Using this you can measure the one-way speed of light between A and B because it's by definition the same as the two-way speed of light, which can be directly measured, and also because you can sync clocks at A and B, etc. Obviously, the one-way speed of light between A and B depends on the time it takes light to go from A to B, and the time at the different locations is defined. There's no way to independently measure the time at A and B without knowing that the one-way speed of light is the same as two-way, or to measure the one-way speed of light without knowing the time at A and B. So the time of a light signal is defined to be the same in either direction. (Of course... you could use alternative definitions as well. You could eg. put an observer C equidistant to A and B, and observe that one-way signals from A to B do take the same time as from B to A. But then you'd define (or assume) that the light from A to C takes the same as from B to C. Einstein did it right, defining instead of assuming that the time is the same, because if you used some alternative way to sync clocks in a consistent way, then you could make different assumptions on the timing of light that are true using your alternative definition of time.)

https://www.fallacyfiles.org/redefine.html https://www.logicallyfallacious.com/logicalfallacies/Definist-Fallacy 1. Define "heaven" to be something that's "scientifically supported." (Or maybe something simply vague enough that it can't be scientifically refuted?, ie. "not even wrong"?) 2. Therefore, heaven is scientifically supported. QED. 1. Define something as whatever I want to argue. 2. Therefore, whatever I want to argue.

Time t will vary along with v, but also with d (length of travel), which itself should vary, and depends on time and expansion. You're giving an example where the differences in v and t are small, and difference in d is negligible? (Due to being nearby and/or negligible rate of expansion? Or assuming a fixed distance of expanded space, instead of being sent from a common source that is receding over time?) However if we were talking about an object at the cosmological horizon, light from it would arrive after infinite time. For any speed less than c, there should be another nearer horizon, from which an object traveling at that speed would take an infinite time to arrive. For a speed like .999999c, if someone is in between that speed's horizon and the cosmological horizon, then light from them would arrive after finite time, but a rock at .999999c would never arrive. So you can have "nearby" cases where expansion adds less than a second to the time between arrival of light and arrival of neutrinos, and the extreme distant case where the neutrinos take infinitely longer to arrive. That would imply expansion does slow down an object, if the object is redshifted. If light from a distance source was redshifted to twice the wavelength by expansion, would a massive object launched from the source and traveling at near c (and arriving nearly at the same time as the light) also arrive with nearly twice the wavelength it was launched with?

There's this: https://www.forbes.com/sites/startswithabang/2018/07/28/ask-ethan-where-does-the-energy-for-dark-energy-come-from/ Including: Unfortunately I can't find anything about how expansion affects the energy of moving objects. I'd assumed it would be the same as with light.

I don't think that's right. I think the rock would have to lose energy to the expansion, which means it would arrive at a lower speed relative to its destination than its speed relative to the source when launched. Suppose a photon and a neutrino were sent, with the same energy. Say they arrived roughly at the same time, and the photon was red-shifted to half its energy. Wouldn't the neutrino need to have roughly half the energy it was sent with? In this example, the neutrino's speed is so close to c that it can lose half its energy to a decrease in speed and still be moving at a speed very close to c. In the case of a slower rock, I think it'd lose even more energy since it would take longer to travel. Since the expansion wouldn't affect the rest mass, I suspect it's a fraction of only the kinetic energy (of the rock or neutrino or photon) that is lost, not total energy.

My point is that "if time stopped" doesn't mean anything on its own, it needs more details, and those details can describe something that breaks the laws of physics including causality, or something that doesn't.

It's a fictional example. Everything has their own clock, and they can't all be stopped "at the same time". In fiction where "time stops" in some contrived way, some observers' clocks stop while other observers keep observing, because if there's nothing to observe that some clocks have stopped, the stop is meaningless and doesn't look good on tv etc. When they use "time is stopped" for things like time travel, it's some made up way with most likely no basis in reality.