I’d recommend this book for anyone interested in meditating on these concepts…
textbooks.com/BooksDescripti … gQodK6EACQ
There are many fascinating concepts in it… one that strikes me the most is how 2D drawings can bring out motion and 3rd dimensions… it’s possible all the motion we see comes from a 2D universe that is “frozen”.
I was the first person to say that by the way, so I call dibs!!! Those dot matrixes can reveal 3d photos and optical illusions within those dot matrixes can reveal 3d motion… on an 2D surface!!! Wrap your head around that!!!
And it’s a great book… though doesn’t explain what I just explained.
Geometrical argument 3 for contraction:
If frame A moves perpendicular to frame B’s perspective on it at c, the coherence of the object in its appearance to us is zero. Space-time machinery can not account for different factors of c to exist on top of each other. The object simply does not compute; it is thus ‘flat’.
The contraction of the perceived object is in fact the inability of two frames to differ by more than c. It’s not entirely unlike frame dropping in real time animation that’s demanding too much of the processor.
Geometry in general:
A difference with Euclid is the asymptotic measure of the distortion of the scales vis a vis one another. But the geometry itself, as in how the angles are being forced to change, is straightforward and involves no weirdness. There is only one weirdness; the way c is tied to gravity, the “ring of power”.
Everyone,
I gave all your posts since Fixed Cross’s post a read, and my thoughts for the moment are that it’s too difficult to say who’s right and who’s wrong about this or that aspect of relativity–the reason being, like I said, that I’m no expert and I’m trying to peice it all together as I go along.
The options I find at my disposal at the moment are:
Einstein and the entire physics community are wrong, and have been wrong for more than a century, and that James (perhaps FC as well if he’s sticking his neck out) is smarter than all of them (this despite the fact that he hasn’t yet actually explained his alternative and shown how it works better in both theory and in terms of experimental results). ← This requires positing either that the whole of the physics community is too stupid to realize their errors or that there is a grand conspiracy going on where dissenters and falsifying evidence are being snuffed out, neither of which seem very plausible to me.
There is nothing wrong with Einstein’s theory nor the fact that the entire physics community supports it, and the counter-arguments seen here and elsewhere are simply the result of a misunderstanding of relativity (in James’s case, motivated by the desire to destroy a competing theory to his RM:AO). ← This one is actually very plausible in my eyes, for many-a-pseudo-paradox is quite easy to conjure up in the field of Einsteinian relativity–it happens by imagining scenarios in which not all the factors that relativity mandates be taken into account are actually taken into account, or are taken into account but wrongly (i.e. wrong values, wrong effects, etc.). When it comes to something complicated and counter-intuitive, in other words, it’s quite easy to get tripped up by misunderstandings and faulty moves of thinking, and if one doesn’t realize that this is what’s happening, one might be swayed by the illusion of an actual paradox.
My point is, not being in a position to say for sure which of these options is the correct one, I have to go with what seems plausible to me–and this is very much based on a gut reaction–for it seems way more plausible to me that we (myself included) are making mistakes and arriving at what appear to be paradoxes due simply to the fact that we don’t understand the theory well enough (in James’s case, I don’t think this is a result of not having studied the subject enough–I can see that he is very passionate about it and has most likely engaged in it with other thinkers for years–but is a result of, like I said, having the motive to compete with the theory coupled with his rash thinking style, which this thread has given ample examples of, by which he knowingly or not quickly jumps to the nearest, most convenient interpretation that makes his competition appear incoherent and fraught with paradoxes). My motives, on the other hand, have much less at stake, and so I feel comfortable simply saying that I don’t know all the answers, and that if something appears paradoxical to me, it most likely means that I don’t fully understand (or the one presenting me with the paradox doesn’t understand–either that or they’re deliberately trying to obscure the issue).
In any case, Fixed Cross:
Thank you!… I can handle disagreement, even harsh criticism, without getting upset when one expresses his willingness to be respectful such as you have shown here, and this encourages me to actually listen to what you have to say (no promises that I’ll agree, however). As for what you’ve been saying, it’s a little cryptic and hard for me to decypher, although I get the point that you think the electromagnetic bonding forces between particles is misguided. As I said, it was just an attempt, a current thought, that I figured might help (but maybe not). This is what James wanted, after all. Though I still think it must have something to do with it (the electromagnetic force is light particles, after all, and it seems to me that their transfer from one particle to another in the case of motion would probably shed some light (no pun intended) on the issue).
James:
Well, that’s true.
Now that I think about it, I think that in the case of the world moving back while you are propelled ahead (by electrical forces, by rocket boosters, by running, etc.) is a case in which the space between objects would contract–but still, the case in which it is two or more objects being propelled ahead by mechanical forces (electrical, rockets, running) such that it is those objects and only those objects being propelled (because it is those forces, and only those forces, acting as the causal factors) is a case in which the space between them would not contract.
The reason, once again, is GR.
Failure to take into account what GR says about these kinds of hypothetical scenarios is often a culprit in stumbling upon pseudo-paradoxes.
To say that the space between objects moving at the same velocity has been contracted implies that those objects have accelerated to that velocity (to suppose otherwise–that is, to suppose that those objects were always moving at that velocity since the beginning of time–would render the idea that the space between has contracted incoherent–what would be the difference, in other words, between such a contracted space and an un-contracted space that just so happened to be that wide?).
Now since are talking about acceleration, we are talking about GR (there’s no escaping it), which, as you all know, means that the Equivalency Principle applies: the uniform acceleration of everything in the universe in the same direction can be treated (mathematically and empirically) as though there were a uniform and universal gravitational field strewn throughout the whole of space. And IIRC (this is why I said “now that I think about it”), what a gravitational field amounts to, in the end, is just a warping of spacetime itself. In other words, the space between accelerating objects that are “falling” into a gravitational field will contract because that’s what gravity is. The space between objects accelerating due to mechanical forces (electrical, rocket boosters, running) are not subject to the warping effect of a gravitational field.
^^ So far I don’t see any logical inconsistencies in this account–doesn’t mean that I’m thinking of everything, nor even that I’ve got it right–but hey, you said you wanted to hear my thoughts, not Janus’s, so there you go. Anything that I may be missing or have wrong must be made known to me by someone else’s thought (I’m sure you’ll be more than pleased to supply those).
Hmm… sounds like you’re coming at this, not from an objectivist point of view, not even from a subjectivist point of view, but from the point of view of how the outer objective world affects our sensory perceptions of the world–it is the same objective world, same event for everyone, but affecting us differently in terms of our sensory experiences depending on our states of motion.
Gib, there is no such thing as a “uniform gravitational field”. If you think that there is, point one out.
And try to learn that it is the difference in velocity that dilates time. The acceleration might be involved in how much for each clock. But we are not talking about the difference in clocks right now. Any observer moving at extreme speeds measures the non-moving scene as contracted (by the theory). It doesn’t matter how he got to that speed. And at that same time, the non-moving observer measures the moving object(s) contracted as well. There is no “this one is the real moving object and that one is the real stationary object”. All reference frames have equal status (in SRT).
You’re problem Gib, is learning the theory that you are trying to defend. Granted there are multiple versions of it.
But since you are sticking with the theory that the space between comoving objects does not contract (despite Janus), do you agree that from the stations pov, because the trains did not change their relative positions to each other, their acceleration appeared the same which means that their time dilation ("td1&2) would also be the same?
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Gib, the fact that c is absolute does not rely on our sensory apparatus.
I think you misunderstand me entirely which leads me to think I misunderstand you, that I do not understand what your angle is here.
Length contraction is supported by very clear and unambiguous, one might even say simple logic. Far simpler than what you’re into with James, I suspect.
Length contraction is a geometrical necessity by virtue of the absoluteness of c. This goes for constant motion as well as accelerated motion.
This either/or setup by James is misleading.
Because Janus does not speak here of contraction with respect to S but with respect to another frame.
Gib, I am not following this particular investigation into the Stopped Clock paradox. I do not know and do not care to know how these reasonings fit into it, as I have already gone through the process and found there wasn’t anything there that contradicts relativity. But I came here to make a simple clarifying statement on length contraction, which apply both to SR and GR.
For the record, I found myself agreeing with your proposed solution, that given the proposed conditions of the situation, neither clock stops.
James, that’s a silly request. All I’d have to do is bring up a moment in your life in which you experienced being a driver or passenger in an accelerating car and felt the inertial forces against your back. The point is, this is indistinguishable from a universal and uniform gravitational field–ergo, by pointing the one situation out I’d also be pointing out the other. But by the same token, because they’re indistinguishable, you will very easily say “No, that’s just a car accelerating, not gravity.”
This is true once they’re coasting. But when they are accelerating, they have very different statuses (i.e. one is propelled by mechanical forces, the other by gravity).
But I thought you didn’t want me to learn the theory; I thought you wanted to hear “my own thoughts”.
I don’t know. Probably.
Yes, I know.
Probably. Like I said, you’re a little cryptic to read sometimes, but I was going on this:
You were talking about the “coherence of the object in its appearance” which lead me to believe that you were on about the interaction between the objective outer world (in which c is indeed a constant) and how we end up perceiving that world. The appearance of an object being flat when it travels at c is a sensory representation of the incoherency of that object (which is why objects never actually attain a velocity of c).
Yes, James does that a lot.
Any insight is very much appreciated.
Thank you.
You have no idea what supports it or doesn’t. Like Gib, you have to take other people’s word for things (Anti-“Nullius in Verba”) rather than working out the reasoning for yourself, very little courage unless given to you.
It doesn’t matter which frame he was referring to. By the current understanding, there isn’t any contraction BETWEEN the object of ANY frame.
So you claim that gravity is what pulls a person back in their seats?? You might have a hard time getting that one past high school physics.
You keep “confirming the consequent” in your arguments (“because it is true, it must be true”). Gravity specifically refers to mass attraction. Einstein mentioned that IF THE OBJECT IS SMALL ENOUGH and THE DURATION IS SHORT ENOUGH, then that object cannot distinguish gravitational attraction from acceleration. With today technology the object would have to be the size of an electron and the duration only nanoseconds, else any gravitational pull COULD BE distinguished from acceleration. Einstein and the Equivalence theory was talking about a SINGLE CLOCK situation. One single stand along clock cannot know the difference between being gravitationally pulled from being propelled.
We were talking about when they were merely coasting.
SRT states that any object with relatively high velocity will measure as shorter that that same object with no relative velocity. At any one time, no one can know the infinite history of each object so as to know which one accelerated more than the other. The theory is NOT proposing that only the one that accelerated is measured as shorter and time dilated. The theory say that each will measure the other as both contracted and time dilated. Now do you believe that of the theory or not?
And what that means is that if you had two space stations with a string between them and also two spaceships with a string between them no matter which one accelerated, BOTH STRINGS MUST BREAK (assuming the space between the objects did not contract).
Are you drunk??? 
If you are going to use your brain, you first have to learn what it is that you are trying to use it on.
Well in Gibbish, that means "Yes, but I don’t want to be held to it". The logic is simple enough. Anything associated with time dilation is identical for the clocks, so there is no choice but for any time dilation to be the same for both.
So since the time dilation is the same, in the Stopped Clock Paradox, the station would measure that both timers read the same and thus see both flashes go off at the same time and thus the station clock would stop. Isn’t that pretty obvious? Do you agree that in the paradox, the station clock must stop?
The more difficult thing to clarify is what is going on from the Train’s pov. But that is why I wanted to get one thing straight at a time.
So the agreement of high school kids is now our standard?
So if my answers to you come straight out of SR or GR, you say I’m “confirming the consequent,” but if they don’t, you say I don’t understand relativity enough.
(And by the way, I think you mean to say “begging the question”–affirming the consequence is a syllogistic fallacy: If X then Y. Y is the case. Therefore X.)
Then what does it mean to say the space between them has been “contracted”–for any length to contract, it must go from being wide to being less wide–the distance between objects that are travelling at uniform velocity is static. To say that it is “contracted” implies that the distance is “supposed” to be wider. But in a world where such objects underwent no acceleration, the distance between them isn’t “contracted,” it’s just the distance it always was since the beginning of time.
Sure, but I thought we were talking about the contraction of the space between objects, not the objects themselves.
Well, we’ve been over this (except with trains instead of rockets and space stations), so to get my response, you need but go back through the history of this thread. I’d remind you of the space contracting effect of the universal uniform gravitational field, but you’d just accuse me of echoing my “prophets” (despite that it would still be a logical answer to your question) or “affirming the consequence”.
But that requires consulting the experts, which according to you, is mutually exclusive with coming up with my own thoughts. These experts need not be members of an internet forum–they may be books, documentaries, websites–but any way you cut it, you’ll saying I’m blindly following my “prophets”.
Again, you are failing to specify the reference frame. The time dilation would be the same for both trains relative to an observer at the station.
I guess. Seems logical to me.
Ok, are we there?
The actual point to the Stopped Clock Paradox involves that exact response, a lack of confidence in one’s reasoning prowess.
[tab]The Stopped Clock Paradox was introduced here a few years ago as a special type of IQ test. The variable being tested involved a person’s inability to solve a logic problem due to emotional interference, especially any perceived authoritarian conflict (religiosity). When faced with the decision to be confident in one’s own reasoning prowess against a hostile adversary or to defend against ordained or authoritarian reasoning, which way does each person choose?
There have been extremely few with the self confidence to hold onto their own confidence to reason. The very largest mass of people are religious or conforming even against their own reasoning. Almost all are willing to say, “those smart guys over there know more than me, so if they say 2+2=3, then it must be true and all of those who disagree must be idiots. And I am certainly not an idiot.”.
Blindness and servitude are maintained by yielding one’s sight of truth to others.[/tab]
Gib, the lack of a privileged frame is a crucial point in all of Relativity. Any principle that applies to any one frame, must apply to all frames. The first principle is that any velocity between frames yields time dilation wherein each frame sees the other frame as time dilated. How the velocity got created, the acceleration period, is another issue and when SRT was first proposed, wasn’t of concern.
And along with time dilation comes length contraction. Both frames measure the other frame as contracted.
Thus the station will measure the space-trains as contracted (regardless of which accelerated) and the space-train observers will both measure the station as contracted. If there is a string between the space stations, that string will have to be contracted as well.
And that means that the string between the stations must be both broken and not broken at the same time.
But that is a separate (although related) issue from the Stopped Clock Paradox, SCP, issue.
So far, we have;
A) Station pov: There is no length contraction between the trains.
B) Station pov: The station stop-clock will stop.
Now still from the station’s pov, can you agree that the centered clock between the trains would move out from center between the flashes before the light from the flashes had a chance to get to it? And that would mean that the station would insist that the train stop-clock could not stop.
The TOP portion of this picture is all we are discussing right now (using a third train to carry a centered clock);
More like I just don’t care any more.
(You do recall that you brought up the Stop Clock Paradox before, don’t you? I never said “I guess” the first time.)
So let me get this straight. I respond with “I guess” and you conclude from that that I must be deeply religious?
Yep, and like I said, we’ve been over this.
Yep.
Yep.
Sure.
No, James. You are explicitly and emphatically forbidding acceleration or GR from entering the picture in this scenario. In other words, if the stations are X meters apart, then they were always X meters apart (regardless of how fast or in which direction they’re moving). There is nothing in this scenario that would cause the string to break. Either the string itself was always X meters long (or longer) in which case there would be no reason to suppose it breaks, or the string was always less than X meters long in which case it never tied the stations together in the first place, so why would it have broken?
Sure.
I mean the coherence of the appearance of one frame to another in terms of possible geometrical properties.
The subject is difficult to translate into words. I do not know how to say it better than I already have.
That’s fine, I think I get it. Sometimes clarity comes not from the words you use but from the answers you supply to questions.
By the station’s pov, if each station had been 20 meters and the string had been 20 meters. When the ships are passing, the ships might measure 19 meters for each station. Why didn’t the string measure as only 19 meters too? The string is a “length contraction object” too.
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Dammit! what does it even mean to say a clock stopped… but let’s assume they did for the purposes of this thought experiment. I already gave you the answer… you can have clocks moving at different speeds and be synchronized. This is the same thing James is trying to say in a rather IMO convoluted way. To say clocks don’t stop is meaningless as far as that banter between you and Fixed Cross… clocks are meant to go… what does that even mean???
If the clocks are supposed to stop when the train goes by… they will synchronize even though the clocks in the train are all moving at different speeds. sigh
I tried to explain this from Einsteins initial insight… what happens is the rock that curves covers more space than the rock dropped from the train, but they hit the ground at the same time, this is because there is a conservation of energy when the gravity is the same, even though the perspectives show different distances. One distance simply moves faster than another to conserve the energy.
And what would happen at C for the asteroid stations is nothing at first… in the vacuum of space, but then all of the asteroids would start to follow it’s gravitational field / magnetic field and accelerate until they hit the train and the train would be destroyed. I guess that’s synchronization =) To be more precise, the asteroids would hit each other and destroy each other, but residual energy from these collisions would hit the train and destroy it.
This is because the asteroids would bend the c of the train and slow it down, but they would maintain their momentum and catch up with the train… but as James tried to explain to me before, this isn’t about what would really happen, it’s about a thought experiment. Whatever that means.
It did. I’m not saying the string isn’t contracted, I’m saying it doesn’t break. Either the stations were never connected by the string, or they were always connected. In your scenario, there is absolutely no change (except in displacement which is just to say that things move with uniform velocity). For the string to break, there must be change–either the distance between the stations must increase beyond the span of the string, or the string must contract to less than the distance between the stations… but that occurs during the acceleration phase, which you don’t want to talk about.
Yes, and it won’t break in the middle timer’s pov either (the one on the middle train).
You seem not to want to switch to the middle timer’s pov just yet (I’m going to call this m-pov, and s-pov for the station, f-pov for the front timer, and r-pov for the rear timer). But if you want me to explain why I think the string will not break for the m-pov, I will have to now make the switch:
What’s happening in the lower half of your “Clock Synchronization Tie-string” diagram is that the string only appears to be stretched (and rotated), but what’s really going on is that you are seeing different parts of the string at different points in time.
You are right to illustrate the clocks as de-synchronized in the m-pov (as we had this discussion before with the blue-shifting front clock and the red-shift rear clock during acceleration, and how they remain de-synchronized once coasting begins, the scenario we are interested in here), but this means a little more than just that the rear clock has fallen behind the front clock–it means that the rear clock is literally further back in time and the front clock is literally ahead in time (both relative to the m-pov). That means that the part of the string which is attached to the rear clock is also further back in time and that the part of the string which is attached to the front clock is also further ahead in time (relative to m-pov).
The fact that the string looks rotated is just a consequence of where in space each part of the string was at the time that is being seen by m-pov. Same reasoning goes for its stretched appearance. It isn’t really being physically stretched, it’s just that different parts of it are being extended in different points in time. The string would only actually stretch, and thus break, if the rear end were at 11:00 (as in your diagram) and the front end were at 4:00 at the same time–but it isn’t at the same time.
(BTW, if you’re conceding to the de-synchronization of the clocks according to m-pov, then you have just concede the relativity of simultaneity.)
Let me try to help with my own illustration (it won’t be as suped-up as yours, but sticking with ASCII works for me):
Suppose you had two objects moving forward at the same velocity with a string linking them:
…()—()…
…()—()…
…()—()…
() represents an object and - represents a piece of string.
Now suppose that a man sat on the string in the exact middle and travelled along with the whole apparatus. Suppose that any time he looked at the rear (), he sees it as it was in the past, and any time he looked at the front (), he sees it as it will be in the future. Since, in the past, the rear () was actually further back in space, and since, in the future, the front () will actually be further ahead in space, that means that the distance between the rear () and the front (), as seen by the man in the middle, will be greater than in my ASCII diagram above. It will look more like this:
…()------()…
The string appears stretched.
But it doesn’t break because there is no actual tension in the string (nothing actually pulling on it); it’s just, that’s what it would look like if you saw different parts of it existing at different times.
(This actually works as an excellent explanation of length contraction too, if you think about it: a train that appears length contracted is actually a train of which you are seeing the rear in it’s future state–that is, as further along the track than you would expect it to be in a purely Newtonian context–and as further along the track, it will be closer to the front, thus appearing length contracted (you could also argue this in terms of the front being further behind in time–and all this from s-pov, of course)).
You have to understand the original Stop-Clock Paradox that James set up earlier in this thread–essentially, it’s a clock that stops when it received two light pulses at the same time (purely a mechanical device).
Huh? How does an object moving faster conserve energy?
You have said that the space between things does NOT contract due to relative velocities. There was 20 meters of space between the stations with a 20 meter string between them. If the stations and the string contract (relative to what they would have been in the station’s frame) but not the space between them, you end up with the ships seeing a 20 meter span being covered by a 19 meter string.
The space between the trains did NOT contract. But if we put a string between the centers of the trains, the string contracts and thus breaks. And that means that it is also true that the string between the stations would break.
You have it that the string contracts but the space it is spanning doesn’t contract = broken string.
Let’s get this worked out first.
No, actually, I said this:
I know, I know, I’m bringing in acceleration and GR, but even your scenario hints at a state of affairs that came about by way of acceleration (i.e. in the sense that everything in the universe is traveling backwards relative to the rocket ship coasting forwards). I’m saying in that kind of situation, you can assume the space between the stations will be contracted.
Even if you want to say that acceleration never happened–that the rocket and the stations were always on a course to pass each other–you can’t have it both ways at once. You can’t say that the distance between the stations is 20 meters from their own point of view, and at the same time the distance is 20 meters from the point of view of the rocket ship. The distance, for the rocket ship, will be 19 meters (always was and always will be in this scenario).
You tried to pull something similar in your original Stop-Clock Paradox. Let’s bring in the diagram for that one, shall we?
The only reason you’re able to pull off the pseudo-paradox you seem to think you’ve uncovered is because you have the front and rear clocks going off at the same time in both reference frames. You can’t do this. If the clocks go off at the same time in s-pov, they don’t go off at the same time in m-pov. And if they do go off at the same time in m-pov, then they don’t in s-pov.
Just the same, if the distance between the stations is 20 meters in s-pov, it can’t be 20 meters in m-pov.
The only reason this may seem like such an arbitrary assertion to you is because you refuse to take acceleration/GR into consideration (it’s almost like you’re in denial about it). But the whole point of that discussion we had about the blue-shifting future front clock and the red-shifting past rear clock was to show why de-synchronization must occur for m-pov if it is not to occur for s-pov. You can’t have your cake and eat it too.
You simply can’t have a situation in which a rocket is coasting by two space stations connected by a string unless one or the other (or both) accelerated up to the velocities that they pass each other at–this de-synchronizes both time and length between the two reference frames.
Even if you want to say that the rocket or the stations (or both) were always coasting since the dawn of time, you still have the fact that the distance between the stations will be 20 meters for s-pov and 19 meters for m-pov because that is the only consistent state of affairs capable of avoiding the broken string paradox you seem to think you’ve cornered me with. There is nothing saying that the distance must be the same for all observers–there is no logical inconsistency if the universe just so happen to be one in which the distance is 20 meters for s-pov and 19 meters for m-pov–this is what relativity says about the nature of variables like time, length, mass, energy, etc.–we simply don’t live in a world in which everyone must agree on their measurements.