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md65536

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Everything posted by md65536

  1. But that's not a paradox. I think that a one-way teleporting of information would not break causality (not sure though). To make the situation into a paradox you'd have to add something to it. You could assume generalization and 2-way travel, but I think you could also add restrictions to make a paradox impossible (use one-way wormholes or black holes). Yes, I think without more specifics, we can't conclude that there's for sure a paradox, or no possibility of a paradox. What does it mean for B to be five years in A's future? Can you explain in terms of events or coordinates? My reading of the description is that A and B can be assumed to be at rest, 10 ly apart. Say they have clocks sync'd to year 2020. The events are the ship leaves A when A's clock reads 2020, and arrives at B when B's clock reads 2020. 5 years in A's future is 2025? And B is in 2025? I'm obviously not getting that right but I don't see any meaning of an object being in another object's future. An event can be in another event's future, but I don't see any events here that can be described like that.
  2. After thinking about this, I think this is not a paradox. Instead of "space ship" you could have said "tachyon". You haven't described the ship doing anything that would break causality or do anything paradoxical. If by "you travel" you mean literally a person, then you can come up with something paradoxical, but it's not a paradox yet. (Edit: As for the rest of what you wrote after the above, I don't think it's right. Especially anything that adds a paradox, the paradox seems to come from an incorrect description.) Relativity doesn't specifically disallow nor predict the possibility of faster-than-light particles. Or wormholes for that matter. You can't accelerate something massive to the speed of light or faster, but if something's traveling faster than light already, it doesn't break anything. You can't use FTL to transmit information, because then you could break causality, but you haven't described any information transmitted, or anything else that would be a paradox. I think we'd all (anyone here talking about relativity) agree that if something doesn't agree with "common sense" or intuition, that doesn't make it a paradox. But then, when you describe something that "common sense" says disagrees with relativity, such as something traveling faster than light, we tend to jump to the conclusion that it does, along with any assumptions needed (eg. I might assume you're talking about accelerating a person from rest). There's a difference between a common sense paradox like this, and an actual paradox that's not theoretically possible.
  3. This doesn't sound like a scientific argument. Besides, you haven't described anything that you're seeing that is at all different than if you'd never stepped through the wormhole. You're seeing light from about a hundred years of Earth's worldline arrive at planet P. Why describe it as a story? Why not speak of events and light cones, etc? Why not use defined scientific terms? Your story doesn't help at all explain the meaning of "[you] are in effect travelling into the 'future' [...] of the person standing 2 m away from you". I doubt you could explain the meaning in that, because it seems meaningless. Can you point out a specific error in what J.C.MacSwell wrote? You dismissed it, but I don't see any error in it.
  4. I disagree. J.C.MacSwell has merely described the situation that others set up, in real terms like frames of reference, without any assumption about how that situation was arrived at. No false claims were made. Your idea of "traveling into the future of a person" doesn't make sense to me in any of the frames mentioned (which events are you comparing, and in which frame? If the events are in the same place (star B), it seems to describe only events in a mutual present). I don't see any paradoxes mentioned yet, but one could be built from the situation. In the frame of reference of an object moving slower than c in the direction from A to B, the ship arrives at B before it leaves A, which I don't think is itself a paradox, but can lead to one.
  5. Here's a bit of a meander through how I understand this topic. There are other ways to look at it that you might prefer. First, if you move a light clock across a timelike interval in a particular frame, you can derive the time dilation factor for the moving clock using Pythagoras theorem. It looks quite similar to the scene you described in the initial post. I'd take a look at this if you've never seen it, I could post a video. If you repeat this for a bunch of different frames, you'll find you're looking at a bunch of different triangles that all have one of their sides in common: the side representing the proper time measured by the clock. Or working in the opposite direction: If you look at the time dilation factor with these equations: t/tau = 1/sqrt(1-v^2/c^2), and r = vt, you get (c tau)^2 = (ct)^2 -r^2, the spacetime interval. You can also consider space-like intervals, and either add a ruler (a proper length) instead of a light clock, and/or replace the proper lengths with times measured by light passing over those lengths, effectively swapping time and distance to get the same situation as above. From this you have a simple geometric picture of the spacetime interval components, in a triangle that gets stretched for different frames of reference, but has one side remaining invariant, and you can see the equation of the spacetime interval in the Pythagoras theorem. I get the sense that you're trying to say something like, "The spacetime interval is some natural measure of separation, and the fact that it's invariant must say something fundamental about relativity." The way I see it, the definition of the interval was chosen because it's something that is invariant---proper time---and as seen above, simply relates time and distance in different frames. Rather than starting by defining it and then assuming it is invariant, I think we start by defining it as something that is already assumed to be invariant. Rather than deriving relativity from it, I'd say the opposite is true; since it represents the measurements (eg. of time) in a particular frame, it shows that Newtonian time in a "rest frame" can be derived from special relativity. Like Markus's video suggests, it shows that not everything becomes relative when going from a Newtonian model to SR. The fact that proper time is invariant is not saying anything more (to me at least) than that 1) there's a single measure of time between a pair of events in a single frame (same as with Newtonian time). Or, different clocks sharing a rest frame don't measure time differently, and 2) while different observers measure time differently than each other, they all agree on the (proper) measurements that each other is making.
  6. Thanks for that. Is the repeated use of the word "true" in the video not a standard scientific term (even misleading)? If someone said that if a measure of something being length contracted isn't a true measure of length, I'd argue that's wrong, whereas saying it's not its proper length is using a scientific term. About exact specification of intervals: If you have 2 events and you don't care about their locations, only their relative separation, then you're talking about their spacetime interval. Further if you don't care about how they're measured in one particular frame of reference, then all you need to completely specify the interval is the one value, s^2. So in OP's example, suppose that s^2 is about 39999.9999999999889111 light seconds squared. This describes two events that, in one frame, are separated by say 1000 meters and 200 seconds. But it also describes the same two events that, in another frame, are in the same place and separated by 199.99999999999997227774 seconds. The latter is a measure of the proper time between the two events. (Sorry for those numbers, but if I don't use that many digits, the 1000 meters gets completely lost to rounding.) But also... that same s^2 describes the same 2 events separated by billions of light years and billions of years, in yet another frame. It also describes 2 completely different events a long time ago in a galaxy far far away that had the same separation relative to each other. This seems to imply that all light-like intervals are "the same." They all have s^2 = 0. What this means physically, is that if you have a light signal from A to B, no matter how near or far they are in your frame of reference, you can find other frames of reference where that light signal is arbitrarily short, and others where it is arbitrarily long. Those all describe the same thing, and there is no one frame in which the distance or timing of the light signal is "proper". An exception is the interval between an event and itself??? That seems to produce a valid interval where s^2 = 0, yet there are no frames of reference that can separate the events in time or space. I've never seen any mention of this. Is "spacetime interval" only defined for two different points?
  7. I think you should! If you think it's a bad job and don't know how to make it better, then we haven't done a good job in explaining it. There are aspects of this topic that I'm going to keep getting wrong until I see it in the right way. I know for myself it'll take repetition, to keep looking at it. Besides, I don't think that you did a bad job. Originally you didn't specify the two events of the interval precisely, but 1) it was good enough to understand what you implied, and 2) the imprecision only changes the 200 seconds value by +/- 3.3 microseconds, so imprecision is not a problem there. I'm not concerned with the exactness of the example interval, but I'm concerned about the meaning of it especially with respect to multiple frames of reference.
  8. No, I think you're right. When OP wrote, you're basically saying that the 200 LS is imprecise or an assumption about where the reflection point is. I was treating it as though it was supplying the previously missing information, but that's not explicit.
  9. No, I didn't see that as a problem. The original spec is, "So we have 2 events ; the emission and the recapture of the signal," and "200 light.seconds taken by the signal to make the round trip." It's not specified where the reflection point is, but I don't think that matters because it's only used to establish the time between the two events, and that's given. For me the light reflection path is irrelevant. It's only used here as a clock, and any stationary clock would do. Yes, there are light-like intervals between the reflection point and each of the 2 events, but I wasn't thinking of those. I think I've completely confused the meaning of hyperbolic angle, which I tried to relate to the derivative dr/dt. With a given invariant spacetime interval, a change in the t and r parameters doesn't involve moving along a world line between the two events. It involves rotating the fixed interval through different frames of reference, to vary the t and r components that make up the same fixed interval. If you do consider a particle moving along such a world line, it's moving through different points along that line, ie. different events, each of which makes a different spacetime interval between it and the initial event. (Though, in the case of light-like paths, all of those intervals are 0! But they can still be rotated so that different observers measure light between the two events traveling a different distance during a different time. Lol I'm sure there's a simpler way to look at this.)
  10. You're in over my head! Hopefully someone else can help? That's the derivative of a hyperbola. I don't see it saying anything about switching places. When y (or r) is small, it changes quickly. As y gets bigger, it approaches x (or ct), and the rate of change approaches constant; a unit hyperbola asymptotically approaches the line y=x. If you take the spacetime interval and make r a function of t, I think what that means physically is... It describes how the spatial distance of the interval changes as a function of the time component of the interval, as you go through different frames of reference. The infinitesimal changes in t for example would mean, if you change inertial frames by just a little (ie. with infinitesimal change of speed), the time and spatial distance components of the interval change like a hyperbolic function does. Or, an infinitesimal change in speed corresponds with an infinitesimal hyperbolic rotation of the spacetime interval. Edit: I'll leave that there but it's wrong! When both x and y are very large, an infinitesimal rotation (I think) can still mean a huge change in x and y. So to correct that: A small change in inertial frame involves an infinitesimal change in t and an infinitesimal change in r. However, as speed approaches c, a small change in speed (but huge change in rapidity) can involve a huge change in t and r. That makes sense with respect to velocity composition, right? Maybe it's correct to say "an infinitesimal change in rapidity corresponds with an infinitesimal hyperbolic rotation of the spacetime interval", but I might change my mind again after learning more...
  11. "If it's not moving, it's not Lorentz contracted" seems like a good rule to me. "If it's moving, it's length-contracted" could be made into a rule of thumb, but it's problematic (point particles, c, distances between relatively moving points, I think don't easily fit). "If B is moving, then (something else) is length contracted" is not a rule as you seem to think. I don't remember stating a rule though, so you might not find it. I did ask you which of certain objects (not distances) were moving and which were length-contracted. Misinterpreting things like that, and misinterpreting what SR says, and assuming it says something that you've invented, is a recurring problem here. I wrote: Not that it'll matter for you, but it would have been helpful if I'd instead said something like that the "rest or proper distance between the dice is contracted in the frame where they're moving." If you're talking about a length being contracted, it's only relative to the length measured in another frame. Here the frames of reference are implied, but if you want to think about rules, it'd be better to be explicit about frames. If you want to think of a distance being contracted, think of a ruler that is measuring the distance. If that ruler is moving (in frame F) then distances being measured using that ruler are contracted (in frame F). If you're talking about measuring a distance to B, as measured by X, using X's ruler (that is not moving relative to X), then distances as measured using that (relatively) stationary ruler are not contracted according to X. I expect you to either ignore or twist this idea. Also, this is just my attempt to explain things as far as they make sense to me. It's not an "official rule of SR", and if it disagrees with SR or can be so easily misinterpreted, it's not a good rule. Certainly there are clearer and/or more precise ways to explain it.
  12. What are you trying to achieve here? I'd say the question of whether or not you will learn relativity is answered, your refusal to do so is just too strong. I think you've convinced others that you're interested in relativity, even though you've stated that you're not. I don't see what's in it for you, to waste time on this. Do you hope to have your mind changed? Do you hope to change anyone's mind? I'm fairly certain, no one's changing their minds here. This will go on to page 140+. Would you persist, knowing you'll never change the mind of someone who understands relativity? For others, how long is it worth persisting if the result is what we currently have? (For myself, it's only worth it to write about relativity in this thread if I'm doing it for myself, not to try to inform michel123456.) When you say "hyperbolic rotation", michel123456 reads "pirouette". You can't force-feed understanding to someone willing to put in the effort to avoid it.
  13. It's meters or lightseconds or any distance units, squared. The use of distance units is apparently a convention, see https://physics.stackexchange.com/questions/519707/is-the-unit-for-spacetime-intervals-time-or-space-distance Yes, for a time-like interval, the time component will be greater than the spatial. For time-like (or light-like for that matter) intervals, the ratio of r/t is the constant speed of a particle that moves between the two events. ct/r would be the ratio of the distance that light travels between the two events (along any path that gets it there, like your 200 lightsecond example) to the straight-line spatial distance between the two events, in the given frame. This ratio is frame-dependent, and undefined in frames where r=0. (ct)^2/r^2... I'm not sure of any meaning to that. As squares, the equation of the interval s^2 (a constant) =(ct)^2-r^2 is that of a hyperbola, and relates to the pythagorean theorem.
  14. Conventionally in SR "observer" refers to a frame of reference. If you used that convention (not that you have to, just that it can be helpful to think in these terms), then A and B are the same observer when they're not moving relative to each other. They measure times and distances the same. Local measurements differ, like the relative timing of perceived light from distant events, that each can see (ie. locally measure) in different orders, but that doesn't matter in your example. A and B measure the same as each other, the time between the two events, and the distance between the two events. They measure an interval with a length of negligibly less than two seconds. A moving observer (another reference frame) would measure a generally different time between the two events, and a different distance between the two events, but end up with the exact same interval length. The interval you're describing is a timelike interval (meaning a clock could travel between the events, and record its length as a proper time). The time component that A measures is simply c multiplied by the time on A's clock measured between the events. But of course that's the distance that A measures light traveling in that time, so you're right that it is 200 light seconds. The reflection point being 100 light seconds away doesn't really matter either, for the interval you're describing. Basically you're measuring the time between the events using a very big light clock that ticks just once between the events. A smaller light clock that reflects a light signal multiple times, can measure the same thing.
  15. I don't care whether you ever learn relativity. It's still interesting to find errors in what seems like paradoxes, but you're just adding complication on top of previous errors. Why not go simpler instead of more complicated? You don't have a solid foundation to build on, but you're building anyway. I think that's wrong. How do you get that X takes 45 minutes? If B starts at E, and the length to X is length-contracted to 0.6 LH (in B's frame), then X is already at that location (in B's frame) at B's time 0. A problem when introducing rods like this is that you can't just compare both ends of a rod at a single time that applies in multiple frames. You have to consider relativity of simultaneity (the real one, not "what I'm calling RoS" etc). You could always label the events that you're describing, in the frames you're describing (so it's not just an x-coordinate like Xb, but an x and a time coordinate, and they're different in different frames). But I still think you're wasting your time. I think you would do better trying to learn Galilean relativity.
  16. Yes, I agree. Even without the derivations, just much simpler examples, starting with the basics and without already deciding the answers before looking at the examples. One of the many problems here is that we're all looking at a relatively complicated example and trying to explain/understand step 10 of it, and Michel is effectively saying "I replaced step 3 with my own ideas, but can you keep explaining step 10 over and over? You're doing it wrong because I'm getting different results." Though, I still think giving up and not misusing the language of SR is a good option for him.
  17. Correct! Their numbers made sense and I could repeat the calculations of SR to get them, and when they referred to "relativity of simultaneity" they were using the established meaning of the term. Your numbers are based only on a denial of time dilation (your "?=30" is based only on having B's clock match X's, nothing else), and you use your own personal redefinition of RoS that seems to mean some combination of "light is delayed, and I've modified Galilean relativity so that it is not symmetric". Anyway, I'm not interested in discussing your alternative model, so... good day, sir.
  18. I see. That kind of makes sense... B measures a shorter trip but a delayed start and ends up with the same time that X has. That's not special relativity. There's no point in discussing what special relativity predicts any further, if we're talking SR while you're talking about your own ideas in the language of SR. I could demonstrate why "when B starts moving relative to X, X is delayed before moving relative to B" is inconsistent, but if you have no problem picking aspects of relativity that you like while rejecting others, you'll continue finding ways to make the numbers add up to whatever you want, with no regard for consistency. You won't understand relativity while ignoring what it predicts. I don't think that's a problem, and I don't think you do either. Not everyone needs to understand it. Sorry it didn't work out.
  19. Bold emphasis mine: That's your statement, it's about two clocks. I can't imagine how to explain why this is wrong if you don't understand that you're talking about different clocks. Are you purposefully making statements that you know are nonsense? (A strawman to defeat) Or do you think your statement makes sense and is true?
  20. But that's incorrect. Times on B's clock don't add up to times on X's clock. Do you at least understand that you're talking about 2 different clocks? I know it's only page 12 but do you understand that much so far? Agreed, there are so many ways to describe the concepts, and different people "get it" different ways, plus I often make mistakes. It's too bad this isn't in the relativity forum and might be read by others who'll get it. There's always something that makes more sense with someone else's explanation. I don't agree, as worded. Different observers do measure the ends of the stick simultaneously in their respective frames, and they get the correct relative length of the stick. But it's true those measurement times are different for different observers. The proper length is measured when the stick's at rest, it's not enough to measure at a single time, because any observer can do the latter. (Not mentioned here, but also it's no good to measure the length at times that are simultaneous in the stick's rest frame, because in other frames the stick moves between those two times.)
  21. The thread's question needs interpretation, and I might be interpreting it differently than others. I think that what you're asking is how much mass you would need to make everything in the universe gravitationally bound to it, despite the current rate of expansion. If I'm thinking about it right, any constant rate of expansion will result in a constant-size cosmic horizon, beyond which it is impossible for matter to be gravitationally bound across that distance. The reason is that the matter would have to be falling in faster than the speed of light, to overcome the expansion of space between it and the mass. The horizon is determined by expansion alone, so making a more massive BH won't help... except... If you had matter right on the cosmic horizon, you'd need to basically have it falling in at a speed of c to overcome expansion. That would imply a BH with an event horizon at the same radius as the cosmic horizon??? (assuming Schwarzschild BH) But then, if you had a BH even close to that size, matter on the cosmic horizon would be a lot closer to it than if it were a point mass, so wouldn't it fall in anyway? Or does it work out that the gravitational influence of a BH is still the same as if it were a point mass? This seems really weird, because even if we completely ignore expansion for a moment, wouldn't this mean that the gravitational influence of a BH is roughly proportional to 1/r^2, while the mass is proportional to 1/r, no matter how big it is? That seems to imply that if you could have a BH of unlimited mass, you could make it so that the Schwarzschild radius is so large that an object outside it is so extremely far away from the center of the BH that the gravitational acceleration is small, even if it is near the horizon. Am I thinking about this correctly? How would an infalling observer describe the BH? It seems that the event horizon (a lightlike surface) would still pass by it at the speed of light, despite minimal acceleration. Meanwhile it seems like another observer, hovering farther away, outside the horizon, could easily avoid falling in, and see that same event horizon as stationary. Where's the error in my thinking? Back to expansion, would it even make sense to talk about a constant rate of expansion of spacetime, in a volume that is entirely occupied by a massive BH? The BH curves the spacetime so extremely that the volume inside the horizon is not a part of the same spacetime outside??? Does curved spacetime expand the same as flat spacetime? Would a volume containing a large BH expand the same as a volume of empty space?
  22. Another answer based only on the sketch: 27+48=75 basically says "The amount of time that X's clock ticks while B travels, plus the time on X's clock when B begins, equals the arrival time on X's clock of 1:15" 27+48=75 expresses the sentence from B's frame. 75+0=75 expresses the exact same sentence, from the E+X frame of reference. Those are sensible statements because they're adding times measured by the same clock. 45+?=75 says "The amount of time that B's clock ticks while B travels, plus ??? equals the time on X's clock then B arrives." That doesn't make sense, because those times are measured by different clocks.
  23. The 3 "stages" sound good to me... Please don't go backward from this point, where the details are no longer fine! Answers: 1. RoS concerns the simultaneity of separated clocks or events, in this case the time at Earth relative to the time at X. It's not showing up yet because you're not comparing the times of things at E and X. However, your stages 2 and 3 are describing the same calculations. They're just "what is measured in B's inertial frame." RoS can be used in stage 2 to explain why, when B is arriving at X, B can find that X's clock is at 1:15 while E's clock is only at 0:27. Both have recorded 27 minutes passing (according to inertial B) during B's trip, but X started with a clock 48 minutes ahead (according to inertial B). Meanwhile, in the E+X frame, these same clocks are synchronized. That's relativity of simultaneity. 2. There's no reason, the "stages" are just calculations from different frames. You can calculate from any frame in any order that you want, and you don't have to do them all. Any one frame of reference can make all the measurements necessary, assuming all the clocks are accessible to them, to calculate the proper times mentioned here (B arrives at X at 1:15 on X's clock and 0:45 on B's clock, all frames of reference can show that on their own, using the initial conditions described above. 0:27 on E's clock is a coordinate time (measured by B from a distance) and is a frame dependent measure, differing in different frames again due to RoS). It doesn't make sense to line up all the stages as you did in the diagram. They're times measured by different clocks. By analogy, imagine if you made a map lining up all the countries in the world and attaching them vertically. It would show relative lengths of countries, but it wouldn't show how they're actually connected.
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