[David Cooper]

I'm choosing an inertial frame in which part of your object is stationary while other parts are not.

That doesn't happen with my solution, but I don't think that solution is optimal.

Look at your ship before you start it moving. It's all stationary relative to the start line, and relative to the finish line. That's the initial frame, and it's the one I continue to use throughout. As soon as you start moving your ship, you have the back end moving through this frame while the front end begins to accelerate slowly from zero. You have different parts of the ship moving at different speeds relative to this frame. The spacing between the atoms at the back end is immediately wrong - it was right before you started moving the back, but as soon as you started moving it, you broke that. At the moment of the gun, the speed of the rear two atoms has gone from 0 to 452km/s even though they have travelled zero distance at that moment, while the distance between them is the same as it was when they were at rest. Do the same thing with the 1m-long ship and instant acceleration to nearly c and you should recognise the problem. By the time the rear atom has moved 1/1000th of the way towards where the atom ahead of it was itting before the gun, the correct spacing between it and that atom ahead of it can only be realised by moving the atom ahead backwards by almost 999/1000 of the original distance between atoms. You either have to teleport it back there or you have to teleport the rear atom forward the same distance instead (and further forward again to get correct spacing relative to the next atom beyond that, and the same again for the one beyond that, etc.). Your starting move is illegal.

The light is moving from two Spacetime locations (X and Z) to a single Spacetime location (Y) to the future of the original two. The light follows zero-length paths (XY and ZY) from the earlier locations to the later one.

Those paths are not zero length.  That's what I've been saying.  There is a separation (a frame independent one) between X and Y, and that separation is not zero.

For light, that separation is most certainly zero. I refer you to my previous post in this thread. If you're going to use a 4D model, you have a duty to accept its mathematical requirements, and these zero-length paths are unavoidable features of that kind of geometry. The reluctance of most physicists to admit that should not be allowed to mislead you. Recognising that 4D geometry works this way doesn't break the STR or GTR models - it merely forces you to see that any talk of the speed of light being c with such a model is actually the result of mixing incompatible models. Light only moves at c in 3D models. In 4D models light merely has an apparent speed of c while its actual speed is always zero. I don't know why people have so much difficulty accepting this when at the same time they have high-speed particles travelling through the same 4D geometry on near-zero length, near zero-time paths. If you want to ban that too, you're going to have to ditch the time dimension and bring in an absolute frame, at which point you're doing LET instead. You need to make up your mind which model you want to use and stick to its rules. You can't combine them in a single model - they're incompatible.

If the front accelerated as hard as the rear, the object would break.  That seems to be what you have sometimes proposed.

With one set of rules (where things are allowed to sit at uncomfortable separations if their functionality is practically halted), that is what I proposed. With another set of rules, I do not have the front accelerate as hard as the rear.

In the frame of your choice, what is the speed of the object at the point where the wave is?  We're talking the pure caterpillar method now.  That speed is undefined in any frame (since if it were defined in one, it would be defined in any frame).  It is delimited (somewhere between A and B), but not defined.

If I discuss a scenario in which a car drives around an oval track but I don't give you the speed that it's moving at, that speed is undefined. Does that mean it's breaking the laws of physics by going round the track at an undefined speed? No. If it accelerates by an undefined amount and now does each lap faster than the one before, does that mean it's breaking the laws of physics? No. My method has each atom move at legal speeds and accelerate between legal speeds and can have these accelerations apply over lengths of time slightly greater than zero. I don't know what those speeds or accelerations are, but none of them break the laws of physics.

But the atom has no defined speed at that point.

It will do once we've worked out what the ideal speed for it will be.

If all of those points are simultaneous, then the entire object has no defined speed at that moment.

The object is a composite with different parts moving at different speeds. If you want a defined speed for the object at any moment, it will have to be an average speed, and again we won't know what that speed is until we've worked out what it needs to be.

I never use infinite acceleration, and never let the proper distance between any parts of the object change for the duration of the motion.

What are you doing with the back end of the 1m-long ship if that isn't infinite acceleration? Whatever it is, I'm doing the same, except that I don't have to teleport atoms around to shift them to the right separations by magic when the gun goes off.

If your 1m-long ship can get its tail end up to nearly c in an instant without singularities, you should be able to do the same with the back end of your 100ly ship.

I did not do it in an instant.  I used an arbitrarily short time.[/quote]

I do everything in arbitrarily short times too.

What do you mean 'break my 55 day method'?  Break the object, or break the speed record?  It certainly seem to have the potential to do the latter.

If my method is breaking the rules, yours must be too. My method covers a case in which the front end accelerates identically to yours, so if it turns out that I'm not allowed to accelerate it that quickly, you won't be allowed to do so either.

I don't see how you can not have this rule and still retain the problem.  Without it, you're moving a line of sand, which can be moved one light hour in an hour, a trivial solution.  If the proper length of a Born-rigid object changes, then the object breaks, by definition.

I think you're already breaking that rule with the way you accelerate the back end. The same will apply when you halt the front end, because the second atom from the front will have to jump backwards to its destination.

You keep repeating this, but you're wrong.  If I didn't accelerate the tail that hard, it would lag behind the atom in front of it and the object would break as the proper distance between the two grew to a larger value.

I'm not wrong. Your second last atom has to teleport backwards in every single case - it's just a lot more obvious with the 1m-long ship than with the 100ly ship.

For two atoms, we can accelerate atom 2 to a fraction under c, then do the same to atom 1 as soon as the separation is right for comfortable separation at that high speed. This is the same as compressing the rear.

For small separations of the two atoms, this works great, but not so much for a large separation of the two atoms.

It needs to be done with the small separations that would exist between atoms of the real ship.

I predict that this method will yield the same total time as the two atom case where the middle of the 3 atoms is missing.  The atom in the middle adds nothing I think, which is why only 2 are needed.  The ones in the middle are interesting, helping you see what is going on, but adding atoms between the initial two doesn't change the end answer.  Adding them beyond the ends (as you describe below) does of course change the answer since that changes the total length, but then you could have done that total length with just 2 atoms again.

Case 1:-

With two atoms at normal separation, the rear one is almost instantly moving at almost c, so we just treat it as if it's doing c right from the starting gun. By the time it's reduced the distance between it and the lead atom to 0.5 the original length, the front atom should be doing 0.866c. Because the front atom starts moving before that point in time though, working out where both atoms are at the moment when the gap hits 0.5 hard. I'm sure it's dead easy if you know how to apply calculus to it, but I don't. (I could probably work out how to apply it through experimentation, but I don't know how long it would take me to find the right approach.)

Case 2a:-

With two atoms at double-normal separation, by the time the rear one has reduced the distance between it and the lead atom to 0.5 the original length, the front atom should be doing 0.866c, as before, but it must take exactly twice as long to reach that point as in the first case. In this case, the speed of the leading atom will be half that of the equivalent atom in case one at any point in time.

Case 2b:-

We can imagine a version of case 2 where the atom separations are normal rather than double and where the rear atom moves at 0.5c with the rear atom reaching 0.433c at the point when the separation becomes 0.5. This provides the same timings as case 2a. (You'll see how useful this is later.)

Case 3:-

With three atoms at normal separations, the first case applies to the rear two atoms too - it will be identical. The front atom has to accelerate more slowly though. Its relation to the behaviour of the middle atom is clearly different because the middle atom accelerates slowly rather than in a near instant, but its relation to the behaviour of the rear atom certainly looks similar to the original case, but can we prove that it's the same shape of relationship? In cases 1 and 2b, the acceleration of the lead atom is governed by an atom chasing it at a constant speed. In case 3, the acceleration of the lead atom is governed by an atom, the middle one, chasing it at very low speeds initially - much lower than the 0.5c in case 2b. I think that proves that it's a different curve, and if I'm right, then you can't just consider two atoms.

I never said anything about instant contraction.  It takes time to contract, and since the material immediately in front of the rear of the object accelerates so very much less than does the absolute rear, that contraction is exactly in sync with the speed of the object.

The contraction with the 1m-long ship will move some atoms backwards, and they'll then run into other atoms at high energies and break the ship.

[David Cooper]

In the same way, a ship of any length that's accelerated to a speed that practically stops functionality will not contract significantly

So if I plug .99999999999c into my Lorentz contraction calculation, I will get close to 1 (no significant contraction) because functionality is practically stopped.  Hmm, my calculator doesn't yield that result.  Or did I not use enough 9's?

You'll get a contraction figure to next to zero length, but you also get halted functionality which prevents the ship from achieving that contraction - it has insufficient time to contract any significant amount at all. The contraction doesn't suddenly apply in full by magic - it takes time to contract the ship, and we aren't giving it that time.

[Halc (OP)]

You'll get a contraction figure to next to zero length, but you also get halted functionality which prevents the ship from achieving that contraction - it has insufficient time to contract any significant amount at all.

Exactly.  Preventing its contraction is what breaks it, and why I will not consider such a solution.
The thing needs to be held at that unnatural length for an hour in the original frame, so the high speed does not in any way hide from us the incorrect length of the object.

Really, we're working on a viable solution that breaks no rules, and it isn't an obvious one.  Most importantly, it seems to have the potential to be 10x faster than my simple method that restricts itself to always being stationary in its own inertial frame.

[David Cooper]

You'll get a contraction figure to next to zero length, but you also get halted functionality which prevents the ship from achieving that contraction - it has insufficient time to contract any significant amount at all.

Exactly.  Preventing its contraction is what breaks it, and why I will not consider such a solution.

It doesn't break though because its functionality is slowed to a halt - the atoms don't have time to apply any significant contraction.

The thing needs to be held at that unnatural length for an hour in the original frame, so the high speed does not in any way hide from us the incorrect length of the object.

We don't need the incorrectness of the length to be hidden, and maintaining that for an hour is not a problem - we know that something moving that fast will have practically-halted functionality and we'd be shocked if we saw it breaking the laws of physics by contracting.

Really, we're working on a viable solution that breaks no rules, and it isn't an obvious one.

I did say that there are different sets of rules and different winning methods for some or each set. If the only rule is that you get the object there without breaking it and that no severity of acceleration of an atom will break that atom, then this is the fastest solution - the object is moved at a fraction under c and arrives undamaged. Moving to another set of rules does not dethrone this solution as the winner of its category.

Most importantly, it seems to have the potential to be 10x faster than my simple method that restricts itself to always being stationary in its own inertial frame.

The more restrictive sets of rules ban reliance on frozen functionality, requiring atoms to sit at correct separations, but how much of the time are we allowed to break that rule? With the fastest, multi-wave version of the caterpillar method, we try to keep each atom the right distance ahead of the one behind it at all times, but the one behind isn't at the right distance from it because it's going faster - it's impossible to satisfy both atoms at once, and with the leading atom accelerating throughout the entire trip, the one behind it will never feel at a comfortable distance from it. I don't think there are any viable sets of rules for doing what we're trying to do without having some kind of arbitrarily allowed exceptions. If the separations are always to be comfortable, we can't accelerate the ship at all.

With your method where you claim the separations are always comfortable, you're trying to hide the uncomfortable separations by imagining them away through the use of a composite frame that hides their existence. It may be possible to hide their existence if you do that: when you accelerate something, you create contraction forces in it and when you decelerate it you create decontraction forces instead, but viewed from another frame, those forces can be seen as acting the other way round. Pick another frame that accelerates an object from -v to v in an instant and you have no correction of the length being made at all. If you assume that this last way of looking it is the reality in all cases, then you can deny the existence of all such imbalances by changing real frame an infinite number of times in order to make each little change in speed look like a change from -v to v. In LET though, that's illegal - you have to stick to one real frame throughout instead of using a fake, composite frame.

[Halc (OP)]

I did say that there are different sets of rules and different winning methods for some or each set. If the only rule is that you get the object there without breaking it and that no severity of acceleration of an atom will break that atom, then this is the fastest solution

But that wasn't the rule.  The rule was to never change the proper length of the object.  The solution you suggest is a trivial one.  Any object can be moved a light hour in an hour that way.  What's the point in figuring that out?

Most importantly, it seems to have the potential to be 10x faster than my simple method that restricts itself to always being stationary in its own inertial frame.

The more restrictive sets of rules ban reliance on frozen functionality, requiring atoms to sit at correct separations, but how much of the time are we allowed to break that rule?

I don't ban the frozen fuctionality.  I ban the lack of correct separation.  There's no minimum time that can be violated.

With the fastest, multi-wave version of the caterpillar method, we try to keep each atom the right distance ahead of the one behind it at all times, but the one behind isn't at the right distance from it because it's going faster

Not if it is a continuous wave.  One atom is allowed to be faster or slower than the other if the proper separation never changes. You seem not to realize that.

 The discreet waves are illegal of course (since they involve small singularities), but making them smaller is a way of integrating the continuous wave solution that is not illegal.  The solution approaches a valid one.  Just making everything go as fast as you can does not do that.

I don't think there are any viable sets of rules for doing what we're trying to do without having some kind of arbitrarily allowed exceptions.

My 55 day solution had zero exceptions.  The proper length of the thing was fixed the whole time, and didn't even need integration to compute it since it wasn't a curve.  The optimal solution would seem to require integration to compute the proper length of the object en-route.

With your method where you claim the separations are always comfortable

They're not merely comfortable.  They're exactly correct.  There is not a small wiggle margin I'm allowing.

, you're trying to hide the uncomfortable separations by imagining them away through the use of a composite frame that hides their existence.

An inertial frame is not composite, but a curved object will need such a composite frame since in no frame will it be all moving at the same speed.  Anyway, with my 55 day solution, I invite you to point out where the proper separation of two points of the object are different that the original value.
The mathematics is pretty easy with that case.  Every point along its length accelerates at a proper rate of c²/D where D is the distance from a point arbitrarily close behind the tail of the object for acceleration, and a point similarly just beyond the nose of the object for deceleration.  Each point changes from acceleration to deceleration abruptly when 452 km/sec is achieved.  From that description, you can compute the exact location of any point on the object at any time, and notice that the proper separation between any two points is fixed the entire way.

It may be possible to hide their existence if you do that: when you accelerate something, you create contraction forces in it and when you decelerate it you create decontraction forces instead

Since I am accelerating at a modest pace for most of the time, these forces would indeed exist iff there was a change in proper separation, so it is a good thing we don't do that.

but viewed from another frame

Proper length of an object is frame invariant.  Looking at it from another frame won't change the answer.

In LET though, that's illegal - you have to stick to one real frame throughout instead of using a fake, composite frame.

Not sure what the one real frame is going to buy you when computing the proper length of something not stationary.  As I said, that computation is not different from one frame to the next, but for a non-rigid object, it might be different from one moment to the next, like changing the proper length of a rubber band by pulling it.

I suppose you could have a string that is half Born rigid where its proper length is not allowed to change, but it can bend effortlessly in any spaghetti curve you like. Could we move such a (straight) string faster than a similar rod of the same dimensions? I think not. The problem is equivalent to allowing a reduction in the original proper length of the rod, but not allowing an increase of it. More food for thought.

Proper length of an object is frame invariant.

This is debatable.  Proper length is of an object is, by definition the length in its own frame, but the figure can be computed in a different frame by integrating length/contraction over all simultaneous points in a given frame, which will give a different answer if the state (stretched or not say) of the object changes over time.  For the purpose of demanding that the proper length never changes, it is meaningful to compute said value in a frame of choice and it should not be different, but only because of this rigid property we're giving the object.  A non-rigid object could have a frame dependent proper length at a given time as defined by the chosen frame.
So if this computation yields a different proper length figure, we know we've violated the rules.

I did a quick one in my head (plus the numbers in post 55), using two waves instead of one.  The original wave was to 3135 km/sec which took 2 days for the wave and 4 days to move one light hour at that speed.  Total time is nearly 6 days.

So even if we allowed singularities, this solution is not optimal since we spend 4 days just coasting inertially, days which could be put to good use with some extra acceleration and deceleration, which would be perhaps another wave.  So of course more waves are better, especially since they also get smaller as you increase their number, and smaller waves have smaller singularities which gradually fade to nonexistence.

Lets bump the rear up to 2220 km/sec, at which speed the wave moves to the other end in only 1 day.  Then we immediately bump the rear again by a similar 2nd wave.  The time to move the light hour is now 2.8 days instead of 4, at least for the parts of the object moving at full speed, which none of them do for the whole distance.  The total time to move the object is now 4.8 days (each point is stopped for one day, half speed for 2 days, and full speed for 1.8 days).

Here I want to note that doing it in 2 waves reduces the full-speed coasting time to 1.8 days from 4.  Half the original 4 days were simultaneous in the original frame.  There are 2 full days where the entire object is moving at 3135 km/sec in the original frame, and 2 days that any particular point is dead stopped.  With the 2-wave method, there is 1 day of stopped and 1.8 days of full speed, and at no point in the original frame does the entire object move at that speed.  Some part of the object is always moving at half speed.  Both the stopped time and the 1.8 days of high speed is still a waste, time that could be used to milk a little more efficiency from the thing.  The optimal solution would reduce both stopped time and max-speed time to zero just like the 55 day solution.  For any given part of the object, acceleration will continue (at fixed or varying acceleration) until max speed is hit, at which point deceleration will immediately commence. 
I will try to write something to do this, and it will seemingly not need any parameters like the first function.  There will be no sweet spot for which I need to search.  It will just keep reducing the wave magnitude and use more and more of them until we cannot add more without overshooting our destination.  As wave magnitude decreases, the answer will converge to a valid solution.  When adding more waves makes no significant change to that final duration, we've got our answer.  At that point we can attack/defend the plan for being valid or not, and also search for further improvements to shave off even more time.

[Bored chemist]

I just wondered something; how does an object know if it is "long"?

[David Cooper]

I'm going to focus on a single point here which must not be lost in the noise.

With your method where you claim the separations are always comfortable

They're not merely comfortable.  They're exactly correct.  There is not a small wiggle margin I'm allowing.

They are not correct. Look at the atoms sitting at the back. Here's a diagram of them:-

O-------------------O-------------------O-------------------O-------------------O-------------------

That's them sitting at rest before the starting gun. They're going to move to the right when the gun fires. What do they look like the tiniest moment of time after the gun goes off? This:-

0-0--0---0----0-----

You have to teleport them to the left before they can start moving to the right.

[David Cooper]

Observers have no control over the effects of td and lc, which modifies their measurements. The effects result from a constant independent speed of light. I.e. it's built into the physical behavior of the universe.

If you are stationary or moving at constant speed and you assert that the speed of light relative to you from the north is c, if you then accelerate north to a different constant speed, the speed of light relative to you from the north is no longer c. If you want to claim it is now c relative to you, it can not have been c relative to you before. If you want it to be the same speed relative to you for both frames, you need to use a 4D Spacetime model in which the speed for light relative to you in both cases is zero. There is no valid alternative to these options in mathematics.

Length contraction occurs at high speeds.

Length contraction is not applied by magic. If you start with two ships sitting a mile apart in frame A with one directly ahead of the other and you accelerate them both identically to 0.866c (in the direction they're pointing), they will still be a mile apart in frame A after the acceleration. If you do the same thing with a single ship that's a mile long, that ship will have contracted to half a mile long (if the acceleration is gentle enough for the contraction to apply or if the acceleration was applied from the rear). In one case the contraction was applied, but in the other it was not. If I accelerate every atom of a metre long stick to a fraction under c in an instant, those atoms will still be sitting at the same separations after the acceleration - the contraction has not been applied, just as it wasn't with the two ships a mile apart. With the functionality of this stick effectively frozen, the contraction will be applied very slowly - so slowly that it will be impossible to measure it if the speed is close enough to c. For any finite length of time that you want to prevent the contraction from becoming visible, there is a valid speed less than c which will provide that.

A distance of zero is meaningless. SR is Euclidean geometry. GR is non- Euclidean geometry.

The same 4D model covers both. And the distance of zero is not meaningless - it means that there is a path available that has no separation between two points. Such paths exist between all Spacetime locations (although most of these require two zero-length steps to be combined).

Observer A's clock would record less time, as observed by E on the earth. A has a choice.
1. Assume an inertial frame and conclude the universe has contracted/, thus M32 arrived early.
2. Assume he left E in a ship, knows SR, so concludes he is experiencing time dilation.

If he chooses 2, he is using an absolute frame mechanism, so he's abandoned STR.

Which Relativity? With LET, yes - it's the propagation speed of light relative to space. With STR and GTR, it's just a constant which represents the apparent propagation speed of light relative to space, but with those models the real speed of light is zero. If you don't want it to be zero, don't use a 4D model.

SR or LET, there is no difference, especially since the coordinate transformations are equivalent! Both used Maxwell's equations as a basis for light propagation. The Lorentz version required a late correction (1905) by Poincare to maintain invariance.

There is a major difference. However, if you keep mixing models and imagine that you're doing SR while you're actually mixing LET and SR, then no wonder you're confused. In LET there is an absolute frame. In SR there is not, so you are banned from having time dilation - time cannot dilate for a stationary object, and all objects are stationary in SR.

Take the twins paradox. Twin A stays at home. Twin B goes away and back, recording less time passing than twin A. Did time dilate? Twin B is not moving according to SR during the first leg, so no - it could not dilate. Twin B is not moving according to SR during the second leg, so again no - it could not dilate. Twin A is also not moving according to SR, so again time did not dilate. You cannot have time dilation without an absolute frame mechanism, and you cannot have multiple absolute frames to switch between whenever it suits you because you are changing the speed of light relative to the content every time you change frame, breaking the rules of the universe where the speed of light is constant through space.

It is only by going to the 4D model that you can eliminate the contradictions, and you can only do that with a static block universe version of it, but even there the contradictions are still actually present - they are merely brushed under the carpet by refusing to address the generation phase of a block universe.

[Halc (OP)]

I'm going to focus on a single point here which must not be lost in the noise.

With your method where you claim the separations are always comfortable

They're not merely comfortable.  They're exactly correct.  There is not a small wiggle margin I'm allowing.

They are not correct. Look at the atoms sitting at the back. Here's a diagram of them:-

O-------------------O-------------------O-------------------O-------------------O-------------------

That's them sitting at rest before the starting gun. They're going to move to the right when the gun fires. What do they look like the tiniest moment of time after the gun goes off? This:-

0-0--0---0----0-----

You have to teleport them to the left before they can start moving to the right.

Not entirely clear picture.  If they move to the right, why does the picture show them having moved to the left?
Anyway, perhaps I see what you're trying to convey. The left-most one accelerates the most and closes the distance to the next atom the most.  So you'd expect them not to be the same distance apart since they're not moving at the same speed, and thus contracting differently along its length.  It seems you understand this since you've drawn it, but point it out like it is something wrong.

Oh....  You really are moving them to the left.  No, I'm not doing that. No acceleration takes place so fast that things have to move left to keep the thing the correct length. The left atom needs to move to the right to catch up with the ones to the right.  Nothing moves left.  You're contracting the thing before it begins to move.  Run the numbers into the acceleration formula I gave and you see that movement is always to the right, even if the picture looks like you 2nd one after the time it takes to move the leftmost atom a considerable distance to the right.

Here's a picture of the progression of the atoms you picture:

The seven lines at the bottom are the atoms, vertical at first (no speed), but each curving to the right (never left) as it picks up speed, getting closer to each other all the time at any horizontal line (simultaneous in the original frame) as the contraction takes effect.  Never mind the q= lines, which are irrelevant to what you're pointing out.  The q lines complete a coordinate system.

The picture assumes continuous acceleration, not reversing when some speed like 452km/sec is reached, so it is a fair depiction of the leftmost atoms of our meter-stick being moved a light-hour.

I just wondered something; how does an object know if it is "long"?

You get a small ruler (not moving relative to the segment being measured) and see how many of them fit from end to end.  That's its proper length. You can also just paint marks along the length of it, sort of like boats do to show draft (or draught), but painted marks become incorrect if the object experiences strain.  I'm not allowing any strain on my object, so that's not a problem for this topic.
Knowing the measurement doesn't tell you if it is "long" since nobody has provided a definition for that.  My example object is 100 light years in proper length, which seems "long" until you start talking about distances within and between galaxies.

[esquire]

lets make this simple. when gamma rays burst are detected via multiple radio waves signals and the radio signals appear as mutliple repeating signal burst, at the same time from the same location in space, it can be constued that they at one time constitued a single burst from a single source. if this in fact is the case, you have the answer as to
" What limits does relativity put on acceleration of long objects?". a simple time measurement of a single radio burst from a larger packet of radio bursts, can be back functioned in conjunction with a calculated algorithm, that determines the time/length spread function between qamma rays and radio wave over distance in space. once the spread of how long it takes for a gamma wave to elongate into a radio wave, you have the basis of determining the distance, speed and length variables for an accelerated light object. by interpolating the spread length betwen gamma and radio waves, multiplied by a time period of a single radio burst in a mulitple radio burst packet,  you have an approximation of velocity, distance and length. simple.



.

[David Cooper]

Anyway, perhaps I see what you're trying to convey. The left-most one accelerates the most and closes the distance to the next atom the most.  So you'd expect them not to be the same distance apart since they're not moving at the same speed, and thus contracting differently along its length.  It seems you understand this since you've drawn it, but point it out like it is something wrong.

But it does show something wrong. I had two options as to how to illustrate the problem, but I chose the one where the rear atom stays almost where it was before the starting gun while the rest move to their correct spacings from it for their newly acquired high speed. That requires them to be teleported to the left. The alternative way to illustrate the problem would have been to teleport the whole lot to the right, and that would be the better illustration because the object before the starting gun has every part of it stationary and no length contraction acting on it, whereas immediately after the gun there will be length contraction acting on it which means you have to jump the rear atoms forwards in an instant. How big a problem is this? Well, with your 100 lightyear long ship you're going to have significant length contraction acting on it even with the tail only moving at 452km/s. It's hard to work out the right contraction when different parts are moving at different speeds (and the front end doing 0), but if the whole thing was doing 452km/s the length contraction on the ship would be one light-hour. I'm going to make a guess that the contraction on the actual ship might be one light-minute rather than a light-hour, which would mean your rear atom is going to have to move that far before all the atoms are at comfortable separations, and given that it's moving at about 0.0015c, it's going to take 11 hours for it to settle to the right length, and throughout that time it is breaking your rules.

You'll have the same issue with the front end at the finish line if you want to halt that part of the ship at its destination: another 11 hours of breaking the rules.

[Halc (OP)]

But it does show something wrong. I had two options as to how to illustrate the problem, but I chose the one where the rear atom stays almost where it was before the starting gun while the rest move to their correct spacings from it for their newly acquired high speed.  That requires them to be teleported to the left.

If you look at the diagram, you see that nothing gets this 'newly acquired high speed' ahead of its allowed contraction.  The first atom accelerates far more than the next one, which is essentially still stationary at the first moment no matter how close we put the first atom to the dotted line.
Yes, if we accelerated the right any more than this maximum limit (such as you suggest in all your posts trying to hide the lack of contraction by reducing its duration to negligible time in one frame), the the atoms to the right would indeed need to teleport left to maintain correct spacing.  That's what keeps us from getting there any faster.

The alternative way to illustrate the problem would have been to teleport the whole lot to the right

No teleportation.  Each part of the object (be they atoms or light-year markers) follow the acceleration given by my specified formula c²/D, which is depicted by the dark lines in the picture.  Note that motion is contiguous (no teleportation) and always to the right, not the left.  Local contraction is always appropriate for the local speed.

How big a problem is this? Well, with your 100 lightyear long ship you're going to have significant length contraction acting on it even with the tail only moving at 452km/s.

Yes.  Exactly one light hour of contraction to be exact, which is the distance we wish to move.  It takes 55 days for the head (100 LY of D) to accelerate to that speed.  It takes more than 12 hours for the 1LY mark to get to that speed.  These hours are needed to prevent needing to move anything backwards to account for length contraction.

It's hard to work out the right contraction when different parts are moving at different speeds (and the front end doing 0),

The whole thing is doing 0 at first, but the tail has high acceleration so it doesn't stay that speed for long. All parts could just keep accelerating forever at that rate if we weren't worried about ever stopping the thing.

but if the whole thing was doing 452km/s the length contraction on the ship would be one light-hour.

In the original frame, the whole thing never goes full speed like that.  At mid-trip, the object has a total contraction of perhaps 3/4 light hour, but the speed varies along its length, going fastest in the middle.

I'm going to make a guess that the contraction on the actual ship might be one light-minute rather than a light-hour

In what frame?  I guessed 3/4 hour.  It isn't exact, but at such low speeds, it is really close to that.  At higher speeds, the 3/4 figure goes up, so it's hard to compute.  Calculus is your friend.
I notice you've not run any numbers demonstrating this fictional strain that you claim.  Show any segment of the object at some moment during the motion and the length of that segment will be correct for its speed.  If the two ends of the segment are moving at significantly different speeds, you will have to integrate the contraction over the length of the object, or just consider the contraction to be some figure that falls between the contraction for the two different speeds.

It seems I cannot describe a different way of moving the object when you cannot even see that the original slow way is a valid solution, if not optimal.  You claim the contraction will break it, but you've demonstrated no separation/length numbers that don't match.

lets make this simple. when gamma rays burst are detected via multiple radio waves signals and the radio signals appear as mutliple repeating signal burst, at the same time from the same location in space, it can be constued that they at one time constitued a single burst from a single source. if this in fact is the case, you have the answer as to
" What limits does relativity put on acceleration of long objects?"

A gamma ray burst is not a rigid object, nor does it accelerate from a stop nor come to a stop at its destination.

[David Cooper]

If you look at the diagram, you see that nothing gets this 'newly acquired high speed' ahead of its allowed contraction.  The first atom accelerates far more than the next one, which is essentially still stationary at the first moment no matter how close we put the first atom to the dotted line.

You are now using the caterpillar method for perhaps the first 11 hours of the trip before you get to a point where you have a regular speed distribution in place along the ship. You can reduce that time by moving the atoms faster during this phase, and indeed you'll have to if they're to catch up with the places they should be in, so you'll have to decelerate them to 452km/s once the length is right so as to avoid damage with the ship absorbing all the excess force. Your method isn't as pure as you made it out to be.

How big a problem is this? Well, with your 100 lightyear long ship you're going to have significant length contraction acting on it even with the tail only moving at 452km/s.

Yes.  Exactly one light hour of contraction to be exact, which is the distance we wish to move.[/quote]

One light hour would be the contraction acting on it if the whole ship was moving at 452km/s,  but you only have one end of the ship doing that at a time, so the total contraction will be a lot less.

I notice you've not run any numbers demonstrating this fictional strain that you claim.  Show any segment of the object at some moment during the motion and the length of that segment will be correct for its speed.

I've already shown you that it's wrong at the start. The rear atom has to travel at 904km/s for perhaps 11 hours to get to where it should be, and when it gets there, the excess energy that it's carrying has to be taken off it to get it to the correct speed to conform to your description of how the ship behaves.

It seems I cannot describe a different way of moving the object when you cannot even see that the original slow way is a valid solution, if not optimal.  You claim the contraction will break it, but you've demonstrated no separation/length numbers that don't match.

It may be a valid solution, but the atoms at the back have to follow more complex rules than the ones they follow subsequently - it already depends on the caterpillar method.

[Halc (OP)]

If you look at the diagram, you see that nothing gets this 'newly acquired high speed' ahead of its allowed contraction.  The first atom accelerates far more than the next one, which is essentially still stationary at the first moment no matter how close we put the first atom to the dotted line.

You are now using the caterpillar method for perhaps the first 11 hours of the trip before you get to a point where you have a regular speed distribution in place along the ship.

No idea what you're talking about.  There is no wave, except I suppose for the point at which the ship moves at max speed, which moves south to north in frames where the object is mostly northbound, moves north to south in frames where the object is mostly southbound.  But if we're just talking about acceleration and not turning around, there is no wave at all.  c²/D does not involve a wave.  The new method I'm working on does.

One light hour would be the contraction acting on it if the whole ship was moving at 452km/s,  but you only have one end of the ship doing that at a time, so the total contraction will be a lot less.

Not a lot less.  3/4 I figure since halfway, the ship is moving at 3/4 of the max speed on average.
452 was chosen because in the ship frame, the universe contracts a light hour over 100 LY, so in that frame the tail at the beginning and the head at the finish line are nearly (arbitrarily close) simultaneous events.  Go any faster than that, and the universe contracts more than a light hour and we'll have overshot the destination before we can stop.  So it took me by surprise to find a method that allowed us to go a lot faster, but it does it by having no inertial frame in which the object is at rest but the universe is unreasonably contracted.

I notice you've not run any numbers demonstrating this fictional strain that you claim.  Show any segment of the object at some moment during the motion and the length of that segment will be correct for its speed.

I've already shown you that it's wrong at the start.

No, you're just asserting it. You've not shown anything. The acceleration of everything is always to the right.  No correction is made for inappropriate contraction, so show me that the contraction doesn't match the speed it is going.  Use numbers...

The rear atom has to travel at 904km/s for perhaps 11 hours to get to where it should be,

904 km/s for 11 hours is 36 million km (ish) or a couple light minutes.  Why does it need to be there in 11 hours?
The contraction will be a lot more than 36M km.  I think that was perhaps a guess on your part, but we have 27.6 days of the rear moving faster than the front to allow it to reduce the separation of the two, so it does it in 27.6 days, not 11 hours.  No need for anything to move at 904. 

It may be a valid solution, but the atoms at the back have to follow more complex rules than the ones they follow subsequently - it already depends on the caterpillar method.

Another thing I don't understand.  All atoms everywhere accelerate at a finite c²/D, and decelerate at c²/D' (where D and D' are distances to points in space arbitrarily close to the start event at the rear and beyond the finish event at the nose, respectively).  Since all atoms have finite acceleration and deceleration, they're all treated identically.  No special rules for any point.

"If the rear acceleration takes 10 years (measured in local accelerating frame) to get up to say .866c, the front acceleration will take place for 10.866 years to get to that speed iff it ignites and ceases at the same time (object frame) as the rear acceleration."

.866c is essentially light, is it not?

Not sure what you mean.  Light is not a speed, even if it has a speed.
.866c is not essentially light speed since the acceleration can continue at the same g force for any amount of time past the 10 years and still not get to "essentially light speed", meaning anybody onboard might notice any difference without looking out of the window.

the object is a light year long, it must travel as a very intense frequency? does it not?

Objects like rocks don't travel at a frequency, intense or otherwise.  So no idea what you're talking about here.

[esquire]

"If the rear acceleration takes 10 years (measured in local accelerating frame) to get up to say .866c, the front acceleration will take place for 10.866 years to get to that speed iff it ignites and ceases at the same time (object frame) as the rear acceleration."

.866c is essentially light, is it not?

Not sure what you mean.  Light is not a speed, even if it has a speed.
.866c is not essentially light speed since the acceleration can continue at the same g force for any amount of time past the 10 years and still not get to "essentially light speed", meaning anybody onboard might notice any difference without looking out of the window.

the object is a light year long, it must travel as a very intense frequency? does it not?

Objects like rocks don't travel at a frequency, intense or otherwise.  So no idea what you're talking about here.

it seems obvious to me that anything traveling at or near the speed of light must adopt the parameters of light.
or else rock would be capable of traveling at the speed of light. nevermind!
 

[David Cooper]

[1. That's as observed by a second party. In my inertial frame, light speed in space is always c, regardless of my speed. Light speed is independent of its source, i.e. it does not acquire the speed of the source, which differs from material objects.

That's exactly the point - it doesn't acquire the speed of the source, which means that if the light is coming at you from the north at c relative to you in the first place, it cannot still be coming at you from the north at c relative to you after you've accelerated towards the north. To assert that it is still moving at c relative to you from that direction after the acceleration is to change retrospectively the speed of light relative to you from that direction before the acceleration. That is not legal in mathematics. That is one of the reasons why Minkowski changed STR into a 4D model - he could see that Einstein's original version was mathematically illegal.

2. "the speed for light relative to you in both cases is zero.", as observed by ?

As observed by any competent mathematician who looks at the 4D model.

If you start with two ships sitting a mile apart in frame A with one directly ahead of the other and you accelerate them both identically to 0.866c (in the direction they're pointing), they will still be a mile apart in frame A after the acceleration.

[Agree for frame A. In the ship frames, they will measure their separation as .5 miles.]

No they won't - they'll measure it to be 2 miles. The key point here though is that no contraction is applied in this kind of case.

A mass cannot be accelerated instantly.

Make it near instant and what I said still holds.

Length contraction happens at light speed over microscopic distances (electron cloud), which will be faster than a transfer of energy between particles. The incremental energy transfer will require increasing transit times as it progresses  This is also the reason why a material object cannot be accelerated to light speed. It's NOT due to increasing mass.]

Length contraction doesn't happen by magic - it takes time, and it's done by the particles adjusting to correct their relative positions. This certainly will not happen at the speed of light.

If he chooses 2 ["2. Assume he left E in a ship, knows SR, so concludes he is experiencing time dilation."], he is using an absolute frame mechanism, so he's abandoned STR.

His conclusion is based on 'he knows SR', and there is no absolute frame, which is the basis for the 'relativity principle'.

If there is no absolute frame, there can be no time dilation because there is no mechanism to support time dilation. All the clocks are stationary and cannot tick at different rates.

The following quotes from the 1905 paper by the author of SR:

"Examples of this sort, together with the unsuccessful attempts to discover any motion of the earth relatively to the ``light medium,'' suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest."

They don't suggest anything of the kind. They simply show that the maths of relativity makes it impossible to pin it down.

"The introduction of a ``luminiferous ether'' will prove to be superfluous inasmuch as the view here to be developed will not require an ``absolutely stationary space'' provided with special properties,"

If you're using a model in which light moves through space at c, that requirement demands an absolute stationary space for your light to travel through at c. Without it, you have no means of controlling its speed through space.

The moving twin's clock runs slow --> slowed by movement through an absolute frame. (If not slowed by this, cannot be slowed.)

The moving twin's clock takes a shortcut into the future --> shortcut only available when moving through an absolute frame. (If not moving, cannot take shortcut.)

[David Cooper]

There is no mixing. It's common knowledge that LET hypothesizes a fixed ether frame that serves as a medium for light  Human thinking desires to interpret new things in terms of older established things (supposedly) understood. Government laws may ban certain activities, theories do not.
Time dilation doesn't require an ether or a fixed frame. The effect results from motion, which alters the distance light must move in any EM process. There is no difference. In SR, events don’t move, which is equivalent to a fixed medium.
So who is confused? Have you read any publications on SR?

I have built models which show that STR doesn't work, and no one in the world has ever built any models in which STR does work - they all cheat by breaking the rules of the model to create the illusion of it working. They bring in an extra kind of time tied to an absolute frame to coordinate the action on different paths and then pretend they haven't done so, but in every single case they have. My models of STR are openly available and have been for a decade. Your side has completely failed to counter them by showing the simplest model that can handle the same action without cheating. A working model of STR is impossible if it works purely on STR's rules. It has to cheat because the model is broken.

The purpose of the 'twin scenario' is to demonstrate that relative motion causes clocks (EM processes) to run slower relative to a reference clock.

And the model doesn't work unless you put an absolute frame into it, so what do you do - you put an absolute frame in and use it to coordinate the action, then you deny that you depend on that absolute frame. Run a simulation of the model to test it properly and you'll see the problem right in front of your eyes - it has an absolute frame which causes the clocks on some paths to run slow. You can't run a simulation without selecting an absolute frame to coordinate the action.

[David Cooper]

In LET there is an absolute frame. In SR there is not, so you are banned from having time dilation - time cannot dilate for a stationary object, and all objects are stationary in SR

David is known for misquoting relativity when it serves his purposes.  This statement is indeed false, and the theory would easily be falsified if it said that.

I'm not misquoting it. I'm telling you what it logically requires when you apply the laws of mathematics to it correctly. You cannot have a clock run slow if it isn't moving, and all objects in STR can be treated as if they aren't moving, so they cannot be running slow. It isn't valid to play games where one of the clocks is still and the other's moving so that the moving one can run slow and then to reanalyse the same event and reverse the assertion about which one's moving in order to make the other clock run slow instead. The only way that mathematics lets you get away with playing that kind of game at all is in the 4D model, but even there you cannot do so in any version with running time (and running causality). Mixing incompatible models is not acceptable.

[David Cooper]

If you look at the diagram, you see that nothing gets this 'newly acquired high speed' ahead of its allowed contraction.  The first atom accelerates far more than the next one, which is essentially still stationary at the first moment no matter how close we put the first atom to the dotted line.

You are now using the caterpillar method for perhaps the first 11 hours of the trip before you get to a point where you have a regular speed distribution in place along the ship.

No idea what you're talking about.

You're moving the atoms at the rear in a manner where they are not at the correct separations for a long time, just like the caterpillar method with an infinite number of waves. You don't have them at the right separations from the ones they're chasing, although they may be at the right separations from the point of view of the member of each pair that's being chased. You only get out of this phase once the correct length contraction on the ship has been achieved.

I've already shown you that it's wrong at the start.

No, you're just asserting it. You've not shown anything. The acceleration of everything is always to the right.  No correction is made for inappropriate contraction, so show me that the contraction doesn't match the speed it is going.  Use numbers...

I gave you numbers, such as 904km/s for the tail applying for 11 hours to get to the right location to conform to the correct length contraction acting on the ship.

Why does it need to be there in 11 hours?

It doesn't. If you want to, it can take a lot longer than that before you get all your atoms in the right places to conform to the required length contraction on the ship, or alternatively you can move the rear atoms at much higher speed than 904km/s to reduce the 11 hour figure - whichever way you do it, this reveals that your atoms at the back are not in the right places for quite some time after the gun. If you want to reduce that time, then you have to use higher and higher speeds for the rear end to make the correction, and the extra energy they're carrying will then need to be scrubbed off to avoid your egg being smashed by a hammer.

The contraction will be a lot more than 36M km.  I think that was perhaps a guess on your part, but we have 27.6 days of the rear moving faster than the front to allow it to reduce the separation of the two, so it does it in 27.6 days, not 11 hours.  No need for anything to move at 904.

I think a simulation's going to be needed to make it clear what's going on and which rules are being bent when. It's just too inefficient trying to discuss it in the air.

Another thing I don't understand.  All atoms everywhere accelerate at a finite c²/D, and decelerate at c²/D' (where D and D' are distances to points in space arbitrarily close to the start event at the rear and beyond the finish event at the nose, respectively).  Since all atoms have finite acceleration and deceleration, they're all treated identically.  No special rules for any point.

The issue is with how you get the ship to conform to the correct amount of length contraction so that there are no stresses on it. As soon as it starts moving, it's too long to be comfortable, and it takes a long time to correct that.

[Halc (OP)]

You are now using the caterpillar method for perhaps the first 11 hours of the trip before you get to a point where you have a regular speed distribution in place along the ship.

No idea what you're talking about.

You're moving the atoms at the rear in a manner where they are not at the correct separations for a long time, just like the caterpillar method with an infinite number of waves.

This is getting old.  They're at correct separations at all times.  They're at the correct separation in the caterpillar method as well, except at the singularity, where separation is bounded but undefined.

You don't have them at the right separations from the ones they're chasing, although they may be at the right separations from the point of view of the member of each pair that's being chased.

If the two atoms are moving at different speeds, you need to integrate the motion between them (which is the same as adding more atoms).  If you will not do this, then the contraction between the two atoms moving at different speeds is bounded by the contractions for the two speeds in question.  If it falls between those two bounds, it is no strain, to the precision of one atom.  As you add atoms, those those bounds approach each other.

I gave you numbers, such as 904km/s for the tail applying for 11 hours to get to the right location to conform to the correct length contraction acting on the ship.

My object never moves that fast.  Show where the separation is wrong at any point along its length at time X.  You're seemingly claiming that it takes 11 hours for one atom to catch up with the nearly stationary one right in front of it.

At what point in time is the separation wrong?  What separation exists (between which two points) at that time, and what should it be if there is to be no strain?  It takes 27.6 days to achieve maximum contraction. That is far longer than 11 hours, so we have plenty of time to move both ends.

I think a simulation's going to be needed to make it clear what's going on and which rules are being bent when. It's just too inefficient trying to discuss it in the air.

Fine.  A simulation will do since it will show the numbers.

The issue is with how you get the ship to conform to the correct amount of length contraction so that there are no stresses on it. As soon as it starts moving, it's too long to be comfortable, and it takes a long time to correct that.

As soon as it starts moving, it is still essentially still stopped everywhere except possibly the tail (depending on how far back that arbitrarily close point is).  It has no contraction except at the hind-most bit.  So it hardly has changed in overall length, and doesn't need to because it is almost entirely still stopped.

We're talking in air as you say.  I see it always being the exact correct length.  It's not like I'm the first one to do the mathematics behind it.  Where do you think that picture came from?
The wave method is another thing.  I've found no sites that describe that sort of motion.  I'm seemingly on my own.