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Mr. Cooper stumbled upon an interesting feature of relativity theory.
One day, if he learns to do SR, he may actually be able to incorporate this into his JavaScript program. I wish him the best of luck and health on this.
https://en.wikipedia.org/wiki/Wigner_rotation
Now, what's all this about? Are you trying to suggest that if I start at rest in Frame A and then race off northwards to be at rest in Frame B instead, when I then send my squares along my east-west-aligned rails which I have taken with me they will behave differently from a rocket launched from rest in Frame A to end up co-moving with my squares which are now racing along between Rails B and B2 such that they have rotated out of alignment with the rails rather than simply taking up the same rhombus shape?
Well, if they do that, they're still demonstrating different physics from what we would see when running squares along between Rails A and A2 which (the rails) are at rest in Frame A - no such rotations or distortions which change the angles of square/rectangle edges occur there. However, in reality they have no choice other than to be length contracted in the NW-SW direction, no matter what kind of rotation you might be adding to them (whether rightly or more likely wrongly).
I see PhysBang hasn't shared his calculations for the arangement of things in Frame A when the rails are moving north instead of co-moving with the rhombus. I wonder if he's bothered to do them at all.
No. What happens is that the rail is no longer oriented in such a way as to produce the kind of motion that you imagine. The composition of velocities and directions is not a simple linear combination.
SR is different than Galilean relativity.
I haven't bothered, since I haven't had the time to work through the Wigner rotation required.
But if you want to make an argument about SR, then I suggest that you use SR rather than just DCR. Because if you just use DCR, then you are a crank.
if you have the rails at rest in Frame B, they'll be aligned perfectly east-west in Frame A,
SR and LET deal with these frames identically when it comes to how things appear in their Euclidean metrics, and I'm doing LET (which SR is forced to conform to, and that means I'm also doing all the relevant parts of SR).
QuoteI haven't bothered, since I haven't had the time to work through the Wigner rotation required.All you need to do is work out how those rails are aligned in the Frame A diagram, and that's no harder than any of the other things you've already worked out. Tip: there's no double boost involved, so you're barking up the wrong tree.
If you can't see that SR has to conform to everything I'm doing here, you're the crank.
Quote from: David Cooper on 15/08/2016 23:26:30if you have the rails at rest in Frame B, they'll be aligned perfectly east-west in Frame A,Well, no. Because of the correction for time, at any moment simultaneous in Frame A the tracks will be at an angle. This is an aspect of the relativity of simultaneity that you just aren't taking into account.
I'm not sure what "LET" is supposed to be, but you are using DCR.
Says the person who can't work out where the rails will be because he can't work out when the rails will be. If you are speaking of trying to sync up moving W-E in a frame moving S-N in order to get a motion that is SW-NE, then you are speaking of a double boost.
Yes, I agree that I am being a crank by refusing to include the time parameter and refusing to do actual transformations and instead just using a series of shortcuts.Oh, wait, I'm not the one refusing to use SR. So who is the crank again?
The angle's perpendicular to the direction of travel when the rails are moving north. You are determined to try to have them co-moving with the rhombus because it's the only thing you can do to keep them aligned with the edges of the rhombus, but even if I allow you to do that, what are you going to do when I send another square NW so that it becomes a rhombus aligned the other way and doesn't fit between your tilted rails? Are you going to have the rails co-moving with that at the same time as they're co-moving with the first rhombus?
LET is Lorentz Ether Theory, as you ought to have learned as part of your training.
The rules of how things behave in the Euclidean metric of a frame and how they appear in other frames is described both by LET and by SR. If the LET approach is used to create diagrams, SR must produce matching diagrams if it isn't to have objects violating the rules. For example, if you want a square at rest in Frame B to be given an eastward shove such that it's co-moving with the rhombus on the rocket, it has to obey the same rules of time dilation and length contraction so as to avoid having a different speed of light operate for it, and that means it must take up the same shape (unless it has somehow rotated, but even then it must have the same amount of length contraction and time dilation applied to it).
You know full well that the rails are not moving east or west at all, but purely north, so there is no double boost. You're turning into a troll - all you're doing now is polluting a thread by dumping your garbage in it.
Yet again you claim I'm not including the time parameter, and yet it's inherent to the diagrams that time is identical for every point shown on them, so you're just repeating a well-worn lie, and that's trolling.
You aren't going to do anything, because you aren't going to work out the time coordinates. Because you are a crank.
No, I have no training in being a crank; I do not know what crazy acronyms a crank is going to use.
And LET has to use time dilation and relative simultaneity between frames of reference just like SR does. You don't get to ignore the rules of LET.
The second boost is to the square, which has to get one boost to match the frame of the tracks and then to follow the tracks. Do you not realize that the square is moving relative to both frames you are imagining?
Cranks love to claim that people asking them for the proper scientific rigor are trolling. I agree that time is inherent in the diagrams, which is why you produce bad diagrams.
You do not have two boosts to pin down what Rails B and B2 are doing as they're moving north through Frame A and only take an acceleration in one direction to get them from rest to relativistic speed in that direction. Likewise, you do not have two boosts to pin down what the square does when you accelerate it from rest to relativistic speed in the direction NE. You can therefore calculate with absolute ease how these items will appear in Frame A diagrams, and to claim that you need two boosts to find the arrangement of either of those rails or the rocket (with the square on it which now appears as a rhombus) is plain wrong. For a square being sent along the rails subsequently, it's another issue, but any rotation that you imagine is magically going to appear on it is going to put it out of alignment with the rails, so again that shows different physics for different frames.
The problem with this reasoning is that it assumes that the square sent off at an angle is equivalent to the square set off along the rails of the second frame. This is not necessarily the case, since no work has been done to show that they are the same; the composition of velocities in SR is not the same as the composition of velocities in Galilean Relativity, no matter how much someone invokes "Euclidean metric" over and over again.
Quote(3) If these rockets are extremely small and they're crewed by tiny robots, we can have them fly over the corners of one of our standard 1m x 1m squares (made of some kind of rigid material, so let's just say it's metal - the atoms of this material are in constant communication through forces which determine their separation). C, D, E and F are now holding station over the corners of one of our squares between Rails B and B2, and it's co-moving with them as they travel directly north. Maybe. You have to establish that this does, in fact, line up this way. The composition of velocities in Galilean relativity suggests that they do, but it is not clear that this happens in SR.
(3) If these rockets are extremely small and they're crewed by tiny robots, we can have them fly over the corners of one of our standard 1m x 1m squares (made of some kind of rigid material, so let's just say it's metal - the atoms of this material are in constant communication through forces which determine their separation). C, D, E and F are now holding station over the corners of one of our squares between Rails B and B2, and it's co-moving with them as they travel directly north.
I've found something I didn't think would ever be possible, but it looks as if there may be a way to pin down an absolute frame of reference.Imagine a disc lying flat with four points marked on the circumference, N, E, S and W (for the four compass directions). We will move the disc northwards in a moment while rotating it clockwise, but let's first spin it up to speed without moving it along through space. I want to spin it until the edge is moving at 0.866c relative to the centre, a speed at which length contraction should act on the edge in such a way as to halve its length. If we also sandwich our rotating disc between two non-rotating discs of equal size we can eliminate all the non-Euclidean SR distractions by imposing a tight Euclidean metric upon our rotating disc in the middle of the sandwich and use that to lay down the law about how the rotating disc must behave in that space.We can see that there is no longer enough material in our rotating disc to fill the whole space between the non-rotating discs, so it must stretch or break. Let's assume it splits and leaves us with gap in it, the gap being much wider the further out you go from the centre as the length contraction becomes more severe. It turns out then that we're going to need to mend our disc once it's been spun up to the target speed so as to fill in the gap, and it's only after that that will we have a complete disc rotating at our target speed. This appears to go against some of the teachings of SR in relation to the behaviour of rotating discs, but it doesn't go against the rules as to how SR works for things moving in straight lines, and we can show that the two things are actually equivalent, which means that many of the existing ideas about how rotating discs behave are wrong.Any rocket following a tangent to our rotating disc at 0.866c must display length contraction to half its rest length, and this must be matched by the material in the edge of the disc as they move side by side for a moment. That means that the edge of the disc must appear length contracted and cannot possibly fill the space all the way round the space demarcated for it by the two non-rotating discs. We can also eliminate most of the change in direction of the material in the disc's edge by using a disc of a diameter measured in billions of lightyears across, which means that the material in the disc's edge will be moving at the same speed and in the same direction as the material in the rocket flying past at a tangent to the disc not merely for an instant, but for many hours with the material in the disc edge and the rocket potentially being side by side and only a micron apart throughout that time - this is more than long enough to rule out any role for accelerations in breaking the normal rules of length contraction and time dilation. So, we can show that a rotating disc cannot behave the way that most SR experts claim it does: it turns out that they have been breaking some of the most fundamental rules of SR.Our next step is to move the whole disc, and we want it to move at 0.866c northwards. By the way, our non rotating discs are transparent, so we can see the rotating disc through them, and our N, E, S, W markers are printed on the non-rotating discs, so N is always the leading point of the discs as they move through space, while S is the point most aft. Once we are moving our disc sandwich along at 0.866c, the material in our rotating disc starts to behave in unexpected ways, bunching up as it moves slowly past point W and whipping back past point E with all length contraction removed there. At point E the material is not moving in the frame of reference we're using as the base for all our measurements, but at point W it is moving northwards at 0.99c and the local length contraction is to 1/7. (To calculate this speed and length contraction at point W, I imagined a rocket moving north at 0.866c and firing a missile ahead at 0.866c from its point of view, and so in our reference frame that works out at 0.99c - that rocket must behave the same way as the material at the edge of the disc where the rocket may travel alongside it for a while as it follows a tangent to the disc at that point.) Our non-rotating discs have length-contraction applying across them exclusively in the NS direction, reducing all measurements running that way to 1/2 of their rest lengths, so the discs' shapes are now elliptical with the NS diameter half the length of the EW diameter. The rotating disc should match that shape if the idea of relativity is correct, but the length contractions on the material of the rotating disc and directions in which it contracts will be different in places, and it's in exploring this that I've found something that I thought couldn't happen.The key thing is what happens at points N and S. The material there is moving at 0.968c (which can be broken down into two vectors: it's moving north at 0.866c, and it's moving sideways at 0.433c) which means that the length contraction will make the material sit four times as close together in its direction of travel as it would do at rest, and this contraction acts at an angle of 63.4 degrees forwards of the EW line. (I worked out the 0.433c figure by thinking about how a light clock aligned EW would work here: the light in it would actually move at 60 degrees ahead of sideways, and that reduces its progress between points E and W to half, so the same halving will apply to anything else moving from E to W and back.) The component of this contraction to 1/4 is greater in the NS direction than the length contraction in the non-rotating discs at points N and S (which is to 1/2), and that's the crucial thing here - this means it must pull the rotating disc in more at N and S than the non-rotating discs, so their shapes will no longer match up in the way they do when the apparatus is not moving along through space - the sandwich filling can no longer fill the whole space between the outer discs. On the non-rotating discs we have length contraction to 1/2 of the rest length all the way from N to S. On the rotating disc we only have that amount of length contraction at the very centre of the line NS: at all other points on the line NS we have more length contraction than that (running in the NS direction). That means that SR must have a theoretically identifiable preferred/absolute frame of referrence.Again we can send a rocket at 0.968c over point N or S at the same angle as the material of the disc there is moving to illustrate that it must contract in exactly the same way in the disc as it does in the rocket, and by giving our disc a huge diameter measured in the billions of lightyears, we can reduce all the pesky accelerations caused by the rotation to such a low level that they can be ignored (while reducing the centrifugal forces to the point of irrelevance at the same time) - the material in the disc can now be thought of as moving in almost perfectly straight lines while we're comparing its behaviour with that of the material in the rockets which are temporarily co-moving with it.
(6) We haven't looked at what our rockets C, D, E and F do when they're given the same movement eastwards as Square B (again without losing the component of their speed taking them northwards). If C, D, E and F have not resynchronised their clocks for Frame B and still have them set for Frame A, they will all accelerate simultaniously from the point of view of Frame A observers and will remain in a rectangle formation,...
...but since these rockets have adjusted their positions to try to make their formation look like a square to themselves, they really ought to have resynchronised their clocks for Frame B. If they've done this, rockets F and E will move off first (from the point of view of Frame A observers), while C and D will move off a moment later, and the result of this will be that Frame A observers will see their formation turn into a parallelogram with its sides parallel to Rails B and B2.
Ah David - I see that you have come across a hurdle.
Under the remit of reference to a Newtonian time, you say that relativity is safe. However... SR is rather contradictory to the underlying philosophy of Newtonian time...
Since all these length contraction maths are still fresh in your mind, try this on for size if you fancy.Dispensing with Newtonian time, create 2 scenarios where both are experiencing different SR time dilations, and state the observation each will make of the other reference frame as time frame dependent and proportional to the difference in rate of time.With time frames missing from the observation of the other reference frame, will it appear as though a length contraction has occurred?
SR and LET are both relativity theories, and any other theory wanting to compete with them will also have to be a relativity theory in order to fit in with how the universe behaves (and how we measure things in it). So long as we can't pin down a preferred frame, relativity survives (even if there is a preferred frame and some other being outside of the universe is able to tell which frame it is). SR attempts to get rid of Newtonian time, but in reality it can't function properly without it as it either generates an infinite number of contradictions or it describes universes in which the future can't be generated out of the past (depending on which version of it you want to use). There are two other models which fix these problems, but in each case they can only do so by adding Newtonian time.