md65536

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.

I roughly calculated an order of magnitude somewhere between a Planck length and a quark. It depends on how big you say the universe is. There are many orders of magnitude between Planck length and quark though; it would be around some billionths the size of a quark, and some billions of Planck lengths.

Sure, everything has their own clocks. I'm giving an example the breaks the laws of physics. For example, say you have two observers A and B, a light year apart, and A sends a message to B. Then you stop time for A and B, but let the message keep going. Then start time so that A and B measure the message taking say only an hour, as if it instantly jumped across space while they and their clocks were stopped. But then suppose there's another observer C moving at high speed relative to A and B. Normally, if A and B, in their rest frame, are a light year apart and there's an event at A and another at B one hour later, then C can be moving such that the event at B happens before the one at A, which is normally fine because the events aren't causally related. But if A can send a message to B, that is causal relation, and if C can observe B receiving it before A sends it, causality is broken. By ignoring the laws of physics, I made an example that doesn't make sense, and is a paradox. For C, "time starts again" first, before B receives the message, then later "time stops" after A sends it. As long as you're ignoring the laws of physics, you could make up any number of ways to resolve this paradox, and if you're just making things up, then yes literally anything could be imagined.

And of course relativity of simultaneity, which is directional. A pair of clocks placed on a line perpendicular to their direction of motion remain synchronized with each other. Please work through an example of this on paper or numbers. Put it into geometry or use equations. You can reiterate the same philosophical questions for 10+ years and still not be any closer to a philosophical understanding of the answers. For example, suppose you have a stick 1 light second long, and you send light from one end (event A) to the other (B) and back (C). In the rest frame of the stick, the time between A and C is two seconds. In a frame where the stick is moving perpendicular to its length, A and B can be very far apart (many light seconds or even light years) because the stick moves, even without the stick's length changing. It can take much longer for the light to go from A to C, yet a clock on the stick only records 2 seconds during that time. There you have time dilation without length contraction. Then add a stick moving parallel to its length and see how length contraction is now needed. Draw this out on paper and if it still makes no sense, show the numbers that you're having trouble adding up.

The two frames are equivalent, the same reasons for length contraction apply equally to both of them. Motion is relative. If A is in motion relative to U, then U is in motion relative to A. Only moving things* are length contracted. If A measures "the world" as length contracted, then the world is moving relative to A. Any part of the world not moving relative to A, won't be length contracted according to A. * Or, trying to be more accurate: "the lengths of, and distances between, objects as measured in their rest frame, are contracted in frames in which they're moving".

I can't see how you could possibly break causality. Time is relative, and time is what clocks measure. Time, or a clock, will stop on a black hole event horizon according to an observer outside the horizon. That doesn't break causality, which is perfectly fine with that type of "time stopping". But you probably mean if all of time stops at once? That doesn't make physical sense in the universe as we know it (ie. described by General Relativity) so you'll have to specify what you mean by it. However, if you came up with an arbitrary definition of simultaneity that made physical sense for a particular abstract observer, and stopped all physical processes at the same time, then "later" (still letting time pass for the non-physical observer, whether that's even meaningful) they all continued as they were before and at the same time, then not only would causality not be broken, I don't think any physical thing would be able to measure any difference having happened at all... I think. So whether everything stopped and started all together, or didn't, doesn't even have any bearing on reality, which I think would make it basically a philosophical exercise rather than a scientific question. Even though things wouldn't all stop at the same time according to others, if everything stopped and started in the same way, I don't think they could possibly notice. However, you might be able to contrive some meaning of "stopping time" that breaks causality. For example if you temporarily stop time for some clocks but locally let a physical object keep moving as if time wasn't stopped, that object can move faster than light as measured by the stopped clocks, and that can break causality.

It sounds like you've moved on from the length-contraction aspects, but if a bubble is expanding at a rate of c in the bubble's frame, it should also expand at a rate of c in the ship frame. If it's a given size before you accelerate, I don't think it's possible to make it length-contract any smaller than that size by accelerating, if it's expanding at c. As a very rough look at this, suppose you have a particle moving away from you at c, and is "now" at location x, a billion light years away. Now say you accelerate so that the distance to x contracts to 1m. But due to relativity of simultaneity (think of the Andromeda paradox, or the twin paradox) the clock at x is now advanced a great time relative to your clock (almost a billion years), and the particle is not at x "now" but has long ago moved past it. Anyway there are a lot of interesting details related to this, a puzzle to figure out, if I say more I'll probably get it wrong.

It doesn't mean cloth, just like if someone talks about the makeup of spacetime, they don't mean it's made of cosmetics. In SR there's no single universal frame of reference that space is "in". The ship frame and the huge bubble frame are equal, there's no such thing as "one frame contains spacetime and the other doesn't". You might wrap your head around that by taking your example and having half your universe moving relative to the other half and vice-versa. Which is the universe? Or consider a universe made only of two identical ships moving relative to each other. Each, in its own frame, is at rest, not moving through space. SR has no problem with an object bigger than another in one frame, being completely inside it in another. Also, just like you can't contract a bubble to make the back of the ship stick out, you also can't use length-contraction alone to make it stick out the front. Either the end of the ship moves through the edge of the bubble (an event that happens in all frames, just with different timing), or the ship contracts along with the bubble. The seemingly paradoxical aspects of SR are resolved in SR, and what you're left with is a question that amounts to "What happens if the universe has an edge and something moves past that edge, where is it?" SR doesn't answer that. Thinking of it like the "fabric" has a rest frame and contracts to a finite size in another frame, is like supposing the universe is a finite bubble of Ether, with a rest frame, and then something leaves that bubble. SR doesn't imply that at all, but it also has no problem with that nor with an object leaving that bubble. In SR the frames of reference aren't finitely sized.

The "closing in" is a change of the length contraction factor, which only happens during acceleration. But combining this idea with this: As an example, suppose the ship has its back against a brick wall, and then the entire ship accelerates away from the wall in some coordinated way (it can't keep accelerating "simultaneously" according to the pilot because the ship never shares a single inertial frame while accelerating), it doesn't matter for this example how. If the pilot accelerates fast enough, SR says that the wall can contract toward the pilot faster than the pilot moves away from the wall. But the wall can never get closer than the back of the rocket is, to the pilot. (The wall won't length-contract through other stuff.) With that high acceleration, the back of the ship must also length-contract toward the pilot. This demonstrates that there must be an acceleration limit to Born rigidity. It also means the back of the rocket will never stick out the back of the contracting region it was in when it accelerated forward.

Sure, but it's best not to refer to it as "the universe" because 1) you're intentionally avoiding real properties of the universe that require GR, and 2) you're unintentionally treating your simple model as if it should be like the real universe. So let's call it a "bubble", say a spheroid region one billion light years in diameter, with a boundary and some stuff in it at relative rest, in an inertial frame. Then it has an inertial ship passing through it from one edge through the middle to the other edge. The ship has a proper length of 10m. The ship is traveling fast enough that the bubble is length-contracted to 1m in its own frame. Inside the bubble, the ship is length-contracted so it is flattened in the direction of its travel to less than the diameter of a quark. It takes just over a billion years for it to pass through the bubble, during which it ages only about 3.3 nanoseconds. In the rest frame of the ship, the bubble is a disk that is 1 m thick and has a diameter of one billion light years, which passes (thick-wise) through the ship at near the speed of light. It takes about the time it takes light to travel 1 m (about 3.3 nanoseconds) for any point on the ship to enter and then exit the bubble. That's one way to know that a point on the ship only ages 3.3 ns in the bubble's frame. [You probably don't want to know, but it's interesting that it take about 36.7 ns for the bubble to move 11 m and pass completely through the ship, and yet it only ages 3.3 ns according to an observer in the bubble. This is because of relativity of simultaneity. Clocks on the front and end of the ship that are in sync in the ship's frame, are out of sync by about 33.4 ns in the bubble's frame. In the bubble, if a clock at the front of the ship reads 0 on entry, a clock at the rear simultaneously reads 33.4 ns on entry, and then 36.7 ns on exit. The ladder paradox explains how the observer in the bubble can say the entire ship is inside the bubble, while an observer on the ship disagrees.] Okay so back to your "paradox". In the ship's frame, only the bubble is length-contracted. When you say "the entire universe" is length-contracted, you might be imagining all of space ie. all of the measurements of space around the ship, are contracted too, but the ship's inertial frame's measurements, or its space, doesn't get contracted. Where is the ship? It's in its own inertial frame, with all of its rest clocks and rulers behaving completely normally. If you suppose there's nothing else at rest in that frame except the ship, then all of the real clocks and rulers are on the ship, but the spacetime surrounding it would still be measured as normal, according to SR. Since it's only the bubble that's moving, that's all that gets length-contracted. Spacetime as measured in the ship's inertial frame, is not moving, and is not contracted. The spacetime isn't "stuff", I think it's nothing more than the measurements.

I got this wrong. There is a paradox if the ship starts in the middle of the simplified universe and accelerates, ending up sticking out both ends. It's resolved by Born rigidity https://en.wikipedia.org/wiki/Born_rigidity : If the ship started "inside" the universe and accelerated quickly enough that its 10m rest length would stick out both ends, that ship could not maintain a 10m length during that acceleration, and it would not stick out both ends. If the ship starts outside the simplified universe and is already inertial and 10m before the back of the ship enters the 1 m contracted universe, it could stick out both ends of the universe.

There's no paradox. You're talking about a finite spacetime that seems to be flat. Or basically an object with a proper length of over ten billion light years. You're calling that "the universe", which is fine as long as you avoid attaching meaning to that label, like that everything else you specify must be within that. Not everything in the (flat, toy) universe gets length contracted. Only the stuff that is moving relative to you does. The pilot isn't moving relative to the ship. If the ship is part of the universe, the universe won't be contracted to 1m, only the stuff moving relative to it. If the ship's not part of the universe, the universe can be like a 1m-thick wall traveling past the ship at near c. If you want to talk about the ship being at rest inside the flat universe, and then accelerating "instantly" to near c, then simultaneity is important if the universe is not static. It sounds like the ship is implicitly Born rigid, and clocks on parts of it would become out of sync with each other (by billions of years??). I think you would see the far edge of the approaching 'wall' appearing to age over twenty billion years in the nano seconds it takes to pass you, due to the relativity of simultaneity and relativistic Doppler shift. Actually, that idea's more complicated than I thought. Say the ship starts in the middle of a toy universe, and instantly accelerates to near c. Ignoring simultaneity, you might conclude that the universe contracts to a wall in the middle of the ship, with the ship sticking out both ends. But that's impossible because the back of the ship never travels backward. No part of the ship ever enters the "back" half of the universe. But with relativity of simultaneity, the different parts of the (Born rigid) ship travel through the front half of universe at different times... eek is that right? I think a pilot in the middle of the ship could consistently conclude, "I'm in the middle of the "universe" which is 1m wide and is smaller than my ship would be at rest (which it currently is not, it doesn't share a single inertial frame), but the back of my ship has already passed through the front edge of the universe has not yet reached the same speed as me and the universe is not yet contracted for them."??? That's confusing, I doubt I got it right. However, relativity of simultaneity does resolve this part of the paradox if you do it right. It sounds like you're referring to the spacetime as 'the universe' and others are referring to all the moving stuff in it as the universe? If all the stuff was moving, the pilot would measure it as length-contracted.

These two statements aren't consistent with each other. If the bike rider accelerates, ie. changes inertial frame, there is a shift in relative simultaneity with respect to the distant source clock. If the rider accelerates towards it, the coordinate time of the distant clock can change from 12:34 to 13:44 in a small local time, as in your example. But if the bike rider then accelerates away and returns to its former reference frame, the coordinate time can change from 13:44 to 12:34, or even earlier if it accelerates away more. If the first change in relative simultaneity is "the source clock runs very fast", how is the second not running backwards? It's because of confusion like this that I don't like the phrasing that a change in relative simultaneity means a clock is running fast, because it also implies a clock can run backwards. They're both just changes in relative simultaneity, but one is accepted as intuitively reasonable but the other isn't, meaning it isn't an intuitive way to describe it.

Are you okay with saying that the source clock runs backward if/while the very distant rider accelerates away from it? If that's not okay then what you wrote could be phrased differently to avoid it (eg. relative time instead of how the clock itself runs).

Yes, you're correct that it's about distance. The effect still occurs at low speed where time dilation is negligible. Google "Andromeda paradox", the effect can happen at walking speeds if the distance is large enough. The reason direction matters is that if the distant location is far enough, the travel time of light is long enough that you can move a significant distance even at slow speeds. If a source is millions of light years away, you can walk on the order of light days between "now" and when light arrives. Time dilation still applies but with vanishing speed it approaches zero. At walking speeds it might contribute seconds where light travel time contributes days. Assuming a time dilation factor rounded to 1, suppose two people separated by two light days walked toward each other, and meet after a million years, at which point they both receive a signal from a source that is "now" 1 million light years away. The one walking away from it says "the source is moving away from me and this light took one million years minus a day to reach me; the signal was sent after we started walking" and the other says "this same light took one million years plus a day; it was sent before we started walking" and they disagree on what is "now" at the source just like they did when they started walking. That is pretty much their "experience" of the phenomena. The virginia.edu link mentions a causal definition of past/future: When you're talking about "switching between past and future", you're talking about events that are in each other's elsewhere... it's switching from one part of the elsewhere to another. "Now" far away is neither in the causal past nor future of "now" here. The two observers moving in different directions only "experience" such a switch after a million years in this example, involving measurements made when they're far apart from each other. Edit: That last part's misleading, the observers don't have to be separated. Rather... direction matters because the distant object is moving in different directions relative to the two observers, so the observers disagree on how far the same light signal from it has travelled.

Actually, I think you can prove to yourself that a moving mirror must be able to change the angle of reflection. Try this: Have a box with a mirror on one interior surface, and two holes such that if you shone a beam of light through one, you could reflect it off the mirror and out the other hole. Consider that the stationary frame. Now in a moving frame (in a direction of the mirror's normal), the box is moving while the light makes its way from one hole, to the mirror, and out the other hole. If you draw this on paper using 3 positions for the box for when light enters, reflects, and exits, you'll see that the angle must be different than in the stationary frame. You can try this with or without length contraction (you'd have other contradictions), the angle of reflection is not going to be the same in all frames.

I did a bit of "common sense" analysis, just enough to resolve any apparent paradox in my mind. The path of a photon in the moving R2 frame would look something like this: ___ ___ ___ -> \_/ \_/ \_/ The angled legs are symmetric, and would have a length (or light time) of gamma times their length in the stationary frame. Due to aberration of light, the different mirrors would appear skewed in the R2 frame, in different ways depending on where the observer is. Do you happen to know, if there was a stationary mirror in the R2 frame, angled so that it matched the appearance of a moving skewed mirror, would light take the same path if it hit that stationary mirror as it would hitting the moving mirror? It seems it would but I'm not sure (a problem with using only common sense). That would mean that the light always appears to reflect at the "correct" angle with nothing visually paradoxical. Edit: It seems it wouldn't. Differently positioned observers sharing the R2 frame would see a moving mirror appearing skewed differently, but see the path of light being the same. The angle of reflection would change somewhat like a ping pong ball hit by a moving paddle. Is it now off-topic to discuss the relativity-related aspects of the topic? We should focus on the speculation? Should we start a new topic in Relativity if we don't want the thread killed when OP says the wrong thing, or is discussion of relativity just generally discouraged? (And would a new thread be killed if new OP says the wrong thing, eventually leading to the ideal condition where only people who already understand relativity can start a topic, but none start topics, and the Relativity forum is perfectly devoid of any active topics?)

You have two frames whose origins coincide at time 0. It looks like frame B is moving relative to A at velocity v. The equation x_A = v t_A describes a particle that is fixed to frame B's origin. Alice describes the moving particle to Bob... but it doesn't matter to Bob what gamma is because the particle is at Bob's origin. Eg. whether the length contraction factor is 2 or 3, if the proper length is zero, the relativistic length is still going to be zero. It could be that the equations are used here to find the equation describing B's origin relative to A. However that seems weird to me, because that form of the Lorentz transformation is based on the specification of how the origins relate, so it's like solving for something already known???