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md65536

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Posts posted by md65536

  1. 1 hour ago, vexspits said:

    I can’t say “at the same time” because that brings us right back to what you noted about the strikes both occurring at a shared tx point in only one frame. 

    I guess what I’m trying to point to when I say, “coexisting events” is something that cannot be confirmed to be the case for two events distanced from one another in Einstein’s thought experiment due to the limiting velocity of information.

    "The interval between the two events is space-like" describes everything you're talking about here, and it has a precise definition. "Event" has a precise definition as well. There no problem here.

    A lightning bolt could also be described not as a single event, but as something with spatial and temporal extent. Then it could be described with some other precise definitions that effectively describe sets of events, such as "world line".

    If "coexist" is given a precise definition, it would be fine, but there are already words that suffice, and it's a problem if you want it to mean something more or other than the definition you give it.

  2. If your brain was in a simulation, where every stimulus you received was somehow artificial, that could mean that everything you know (which you acquired through stimuli) might be made up. You probably wouldn't need to distinguish external stimuli (eg. the sense of touching things) vs. internal (eg. having a memory of having lived your life up to this point). That would mean the senses of remembering things could be made up... so maybe it is simulating a few minutes or just one moment in time, including any made-up memories of time before that. It could also mean that things like atoms could be made up too. Maybe the knowledge of atoms or even of there being 3 spatial dimensions is an artificial reality that is simulated in some other reality with no atoms and a different number of dimensions.

     

    As for whether it could be one "identity" being simulated, or everyone---or to put it another way, "what if I'm just a figment of someone else's mind?" etc.---I guess that's an open philosophical question related to whether there is some physical form to the feeling of having an identity, or if it's just emergent from the configuration of other physical things like brain cells. If you simulated an object's sense of being, like if you simulated the thought "I think, therefore I am" in something that otherwise wouldn't think that on its own, does that thought have any physical presence? I can think about these ideas and write them down, and I get the sense that I'm thinking them, but if other senses (eg. of touching something) could be simulated, why not the sense of having thought things? I feel like I'm here, but if that could be simulated, I don't think I'd need to exist at all.

    I don't see how I could prove to myself that I exist, IF the only way to test it is by sensing whether I exist, AND if what is sensed can be simulated. By a really coarse analogy, if I write a story about a character that realizes it exists, I can write convincing thoughts for it with dialog like, "I know I'm only a character in a story, but I exist!" By creating those "thoughts" on paper, I'm not making them real. You wouldn't read that dialog and claim that as evidence that the character has become real. If I myself could think up some thought test that proves to me that I exist, I could write a fictional character having those same thoughts, and yet that wouldn't really prove to anyone that the character really exists and can think. How can I as a person prove that I'm not just someone else's thought, if any action I could take to prove it could also be their thought? How could you know that the feeling of being real, is itself real?

     

  3. 2 hours ago, Capt. Paul Abraham said:

    1) The largest square that can be cut will have a side of 5√5 and will be an inclined cut along the line joining the mid point of a side to one of its opposite corners on one face to the corresponding  points on the opposite face, each having length:
    √(100+25) = √25x5 = 5√5

    Interesting shape! Am I understanding correctly that 2 opposite corners of the cut face are on the middles of edges (diagonal length 10√2) and the other two are on opposite corners of the cube (diagonal length 10√3)?

  4. 1.

    Spoiler

    10x10 is the only square possible? Or am I missing something?

    2.

    Spoiler

    With the cube edges aligned with x y z axes, cut with a normal of (1, 1, 1).

    Or in other words, align the cube with 2 opposite corners on a vertical axis, and make a horizontal cut. The cut should go through the midpoint of 2 adjacent edges on each of the cube's faces, separating each face into an area that is 7/8 of the original, and a corner cut off that is the other 1/8.

     

  5. 5 hours ago, studiot said:

    This issue, in Relativity, is complicated by the nature of the the subject.

    Here is a short extract from Professor Schrodinger's explanation of 'the metric' in his book on the subject.

    Maybe I missed the point, but the extract is basically explaining that in relativity, you deal with spacetime, not just space or just time. When you do, the things described in the text become simple. It's simple and mathematical, and the nature of the subject doesn't complicate it. If anything it seems to make issues irrelevant.

  6. ... continued from previous post.

    1 hour ago, md65536 said:

    if spacetime is multiply connected between A and B, where one connection is flat spacetime with a proper distance of 10 LY between A and B, and another connection is a stable wormhole between A and B, allowing instantaneous travel in either direction at any time t in one given inertial frame of reference

    But why stop there?! From here, I think you could add any number of wormholes from anywhere to anywhere, as long as they each linked two events using the same t parameter as all the other wormholes, ie. they each connected two events that were the same instant according to a single common frame of reference, and you wouldn't create any causality paradoxes. But then!, I think you could also add any number of wormholes, each with a different time parameter (so, some wormhole entrances link an event in your frame's present to an event in your frame's past and at a great distance, others to an event in your frame's future at a distance), without causality paradoxes, as long as you kept sufficient distance between the multiple wormholes' endpoints. For any worldline that goes through multiple wormholes, as long as you keep its events far apart enough to stay outside of earlier events' past light cones, there's no causality paradox. I think!)

  7. On 11/3/2020 at 7:50 AM, Moontanman said:

    Is the instantaneous of the movement causing a problem here? A warp drive could get you the same effect and not be impossible, it would depend on some improbable things like negative mass. if it took you one year to span that distance instead on no time at all would that make a difference? 

    If you could travel at all faster than light, multiple times in different directions, you could create paradoxes.

    I don't think the instantaneousness of it matters at all, unless you can apply it arbitrarily in different frames of reference. For a counter example without paradoxes (I think), if spacetime is multiply connected between A and B, where one connection is flat spacetime with a proper distance of 10 LY between A and B, and another connection is a stable wormhole between A and B, allowing instantaneous travel in either direction at any time t in one given inertial frame of reference---or in other words, you could instantly travel from A to B and back, and you could even have B earlier than A (or vice versa) in your frame of reference, but not so early that it's in A's past light cone, AND you can travel back from B to A, but never to an earlier time than you left A---then I think no causality paradoxes are possible without something more. Even though you can transmit information in 2 directions faster than light, and try to exploit the 2 different-length connections between A and B, there's no frame of reference in which information from an event at A can be sent to an earlier event at A. (Same with B and everywhere else.) The parameter t of the events never decreases.

    The difference here is, arbitrary travel at faster than light over great distances allows traveling to earlier times in both directions.

    HOWEVER, traveling through the wormhole I described is not traveling a great distance, and it can be done at low speed. So it's instantaneous travel, but not technically "moving faster than light". Just getting there faster via a shortcut. The difference is important because it's the changes in relative simultaneity across great distances that are exploited in (impossible) FTL time travel, and that doesn't apply to the wormhole here. I suspect it might not apply to the Alcubierre "warp" drive either.

     

     

    (Just a further thought on the example above. Say you tried to cause a paradox by switching between different frames of reference. You could start in one frame F such that a traveler leaves A in 2020, travels through the wormhole, and arrives at B "earlier" in your frame of reference. Then you could switch to another frame F' so that if the traveler leaves B just after it arrived, back through the wormhole, it can now arrive in a time at A that is "earlier" again than it left B, but in this other frame F'. However, you'll also find that in this new frame F', the first event where the traveler left A for B, is earlier (by the same amount) than the event of it arriving at B, and in this frame (like in any) you find that the traveler still arrives back at A after it left, without paradox.)

     

  8. 2 hours ago, jajrussel said:

    This is a great thread, but some of the post are more confusing than the OP, no offense intended Moontanman.🙂

    Yes, it's not a problem as long as everyone understands a statement consistently. Even "traveling to someone's future" could be discussed without confusion if someone defined what that meant and everyone agreed on it.

    2 hours ago, Janus said:

    Thus a message you sent 1.25 yrs after leaving Earth is received by you 0.8 yrs before you sent it!

    Combining this and OP's example: Say there are 2 events, A-2020 ("now" at A) and B-2020 ("now" at B). A ship (or message) travels FTL from A-2020 to B-2020. It travels from "the present" at A to "the present" at B (that is the present relative to the two events, in A & B's shared frame of reference).

    Then say B immediately accelerates away from A. In the new frame of reference, A's clock could "now" (according to B) read 2019. The event A-2020 is in the future of B-2020 in this frame. It's not in its future light cone, but in its elsewhere, and in the future relative to B's plane of simultaneity at B-2020.

    Then if B immediately sent a message instantly to A-2019 say, A in 2019 could receive information from A-2020, an event in A-2019's own future.

    In this example there's no mention of relative past or future until there's relative motion. Also, B receiving a message, accelerating, and sending a message, if done all at once, could be considered a single event.

    In both examples, the time travel requires two different inertial frames, with the corresponding two different ways that "now" or "instant" apply to the distant events. You send a message "instantly" using one frame's definition of an instant across space, and send another in a different definition of an instant.

     

    Also! in this example, B doesn't need to accelerate at all. If it were inertial and moving relative to A, the only change is that it doesn't agree with A about "now". In this case, the original ship or signal from A-2020 arriving at B-2020 (with B moving away from A and B saying that it is "now" 2019 at A), B can say that it originated from an event that has not yet happened in its frame of reference. However since that event's still outside of its future light cone, that alone doesn't violate causality yet.

  9. 3 hours ago, swansont said:

    C should not know this for 5 years.

    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).

    3 hours ago, swansont said:

    No specific information was listed, but that's because of the vague description of the scenario. It certainly exists.

    Yes, I think without more specifics, we can't conclude that there's for sure a paradox, or no possibility of a paradox.

     

    1 hour ago, jajrussel said:

    If at point C you are 5 years in star A's past and you are presumably between Point A and point B it is seemingly a paradox. But if you are seeing light five ly's in A's past and B is five years in A's future it seems more like an equal radius than 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.

     

  10. On 10/31/2020 at 9:19 AM, Moontanman said:

    I think I've come up with a small paradox. Well for me anyway. 

    Let's say we have two stars 10 light years apart, star A and B, you have a space ship with 'magical technology" that allows you travel 5 light years in an instant.

    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.

  11. 1 hour ago, MigL said:

    You guys are both aliens on a planet P, 100 LY away, looking at the Earth through a powerful telescope.You see the Earth of 1920 through that telescope.

    You step through a 'wormhole, where time is local at both ends, and instantly come to Earth.
    On Earth, you read a History book that outlines the rise of A Hitler, WW2, the rise of Communism, the Korean and Vietnam wars and the election of a game show host to the US Presidency; then you step back through the wormhole and instantaneously go back to planet P.
    You look through your telescope at the Earth again, and, for the next hundred years, you see the rise of A Hitler, WW2, the rise of Communism, the Korean and Vietnam wars and the election of a game show host to the US Presidency.
    What are you seeing ?

    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.

  12. 2 hours ago, MigL said:

    And a 'wormhole, or any other means of FTL motion ( however improbable, just for discussion sake ) allows you to break causality.
    IOW 'see' things before they 'happen'.

    You are trying to apply physical rules to an un-physical ( FTL travel ) situation.
    I'm only telling you what that un-physical situation seems to imply.

    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.

  13. 17 hours ago, geordief said:

    Can I also ask whether you think that adopting the invariance of the spacetime interval as a postulate leads to the requirement of  a  universal  and invariant speed limit ?

    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.

  14. 12 hours ago, Markus Hanke said:

    Could I perhaps suggest a very short (few minutes) video on the invariance of the spacetime interval:

    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?

     

  15. 1 hour ago, geordief said:

    I won't attempt to  patch it up as  I would probably make a bad job worse.

    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.

  16. 1 hour ago, joigus said:

    The problem is under-determined.

    Maybe I misunderstood something...

    No, I think you're right. When OP wrote,

    On 10/16/2020 at 7:33 PM, geordief said:

    Am I right to say that the spatial measurement component of the spacetime interval  between the 2 events is the 1000 metres and the time component ( ie the ct component) is the 200 light.seconds taken by the signal to make the round trip and return to the vicinity of its emission?

    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.

  17. 2 hours ago, joigus said:

    It is not specified well enough by Euclidean distances only. This may be at the root of the problem that @md65536 sees.

    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.)

  18. 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...

     

  19. 16 hours ago, michel123456 said:

    Is that your objection? (still searching the quote)

    "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:

    Quote

    The distance between the dice must contract the same as an object of the same length.

    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.

     

  20. 4 hours ago, michel123456 said:

    Show me.

    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.

  21. 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.

  22. 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.

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