[Halc (OP)]

OK, so we have an acceleration limit on our long object.
So let's give an example, and see if we can generalize afterwards.

I have a ship that cannot take stress as I've described.  It is 100 light years in length, stopped in Frame F.  I want to move it forward by one light hour (about 1.08 billion km) in frame F.  How quickly (as measured in F) can I do that?  Obviously a tiny object can do it in about an hour at maximum speed.

We can't go at maximum speed.  If the tail T accelerates to c in negligible time, the nose N requires 100 years to get up to that speed and by that time it has moved far further than a lousy light hour.  So it seems we want to accelerate T just enough to get the nose of the ship to our destination (100 LY + 1 light hour) in the frame of T, and then accelerate N by the opposite amount to drag the tail up the same distance.  Boom.  We've moved the desired distance.

So let's see, there are 876000 hours in a century, so we want to dilate the distance between the target of N and the current position of T by that factor (876000/875999) which happens at about 452 km/sec.  So I accelerate T to 452 km/sec, and then slow down at a steady pace until I stop.  That's an average of 226 km/sec, so it takes over 55.3 days to move my ship that far.  It cannot be done faster.  Passengers near either end will die of the G forces if the engines don't accelerate them with the rest of the fragile ship, but the ones in the middle will experience a snail-like acceleration of about 0.68 m/sec every hour.
I will get disagreements of course, but I'm going to defend that answer.

Your ship is no different from a building sitting on a planet with a gravitational field identical to the acceleration of the ship.  The upper floors accelerate less (you can tell because you weigh less up there),

It is very plainly different.

Einstein says they're identical, except that the building would need to be in a uniform gravitational field, and Earth's field is uniform only over limited heights.  The exact analogy would be a building in a perfect uniform field.

I can measure the gravitational field as I go up + down  building, and I can work out from those reading how big the planet is.

That is a non-local test. The equivalence principle is a local principle.

But on a ship, in space there's no planet nearby.
So there's nothing to calculate the change of acceleration with distance.

You can walk up and down the ship with a scale, just like you did with the building in a uniform gravitational field.

Fundamentally, you are saying that my ship falls apart as I watch , but no matter how hard I look on my ship, I can find no source of the force that causes it to break up.

The force is the front of the ship pulling too hard, trying to get further ahead of the rear, the same force that breaks the string in Bell's spaceship 'paradox'.

A uniform field is equivalent to infinite radius, and that is what would be experienced in an accelerating ship.  You weigh less on the ship due to relativistic reasons: A rock dropped at the bottom of the ship/building might accelerate at 9.8 m/sec, but one higher up (a lot higher up) will fall at 9.7 m/sec, partly because the clock up there runs faster and the rock is measured for a shorter duration, but also because you weigh less up there.

Please comment on the contradiction I pointed out in my prior reply to you.

[Bored chemist]

The force is the front of the ship pulling too hard, trying to get further ahead of the rear.

No.
I carefully set the engines to produce the same acceleration.
Each section of the ship has the same mass.
So, they all are subject to the same forces.
All that force (for each section) goes into moving that bit of the ship
So there's none left over to pull my ship apart.

Please comment on the contradiction I pointed out in my prior reply to you.

OK.
Your contradiction is based on claims that you can not justify.

No you cannot.

Yes I can- because the change in apparent mass is not linear.
Essentially, if the change with height is slow then the radius is big.

Einstein says they're identical, except that the building would need to be in a uniform gravitational field

So, it's only identical if you have an infinitely large planet.
Since infinite planets don't exist there is a difference.
Thanks for confirming that I'm right.

[alancalverd]

For one, the different parts of the ship are not accelerating at the same rate, else the ship would break apart.

That is obviously incorrect.

[Bored chemist]

They're your claims.

Don't be silly. The title of the thread is your claim not mine.

[alancalverd]

You (Halc, not BC) seem to forget  that relativity is just that. There is no relativistic effect within a body subject to uniform acceleration because there is no external comparator for it to be "relative to".

[Halc (OP)]

They're your claims.

Don't be silly. The title of the thread is your claim not mine.

The thread title is a question.  It implies a potential claim that there are limits that prevent long things from moving as fast as smaller things.

The claims being put out by you and alancalverd seem to fall into two categories of clock synchronization and the fact that all parts of a ship accelerate uniformly.

As for the former:

From post 3:

Therefore the ship must be modelled as an array of infintesimal elements, each with its own engine and some means of ensuring that they work together in complete synchronism. Thus the entire ship must accelerate as a single entity. There being no change in length, there can be no relative velocity or acceleration between the front and the back of the ship and thus no change in perceived clock rates between observers on the ship.

From post 11:

So I know that the acceleration of the two ends are the same (and the clocks , which are stationary from my PoV, run at the same rate).

OK, those quotes had claims about both categories.

From post 15:

Clocks forward of a given observer will appear to run faster, and clock behind a given observer will appear to run slower.

No, because you have stipulated that they are all accelerating at the same rate. You can't have your cake and eat it!

I have stipulated no such thing.  If they all accelerate at the same rate, the ship breaks apart.  That is the essence of your red claim vs mine.  We're dealing with the time thing here.

Post 19:

Fundamentally, you are saying that my ship falls apart as I watch , but no matter how hard I look on my ship, I can find no source of the force that causes it to break up.

Since time moves faster for the front of the ship, if it accelerated at the same rate as the rear, it would do so for a longer time, and pull away from the rear.  That is a way of viewing the force that tears apart the ship.
---
My simple example is this:  I have two small ships N and T that accelerate identically to some significant speed.  Their clocks are synced as they start, simultaneously in the frame F where they were at rest.  They're 1 light year apart initially, with N in the lead.  Let's say they accelerate to .5c and then coast at that speed.
Their clocks will still be synced in frame F because both ships have done identical things.  Do either of you disagree with that?
In the inertial frame of either ship after both have stopped accelerating, their clocks are not in sync.  Different frames order events differently, so when the T clock reads Jan 1, the N clock will read I think Apr 14 or so.

If the two ships were in fact one long ship accelerating like that, the clocks, in the frame of the ship, would get very out of sync.
If their clocks are still in sync as you both seem to claim, then the synchronization of clocks moving at identical velocity can be done in any frame.  This is what I'm getting from both of you.  Tell me if I am misrepresenting your position.

- - -

On to your claims that all parts of a ship must accelerate identically.
See the red portions above, but I have plenty more:

Post 4:

If the front and back of the ship are not accelerating at (at least very nearly) the same rate, you are tearing your ship apart.

Post 13:

As the string all speed up all the rulers shorten. All the ships shorten and all the gaps between the ships shorten And they all shrink to exactly the same extent.
So the rulers all still fit exactly into the gaps.

Post 16:

The gaps do shorten from someone else's perspective. But those people don't see anything fall apart, they just see the ship shrink slightly along its length

If a ship moves uniformly at .866c, the people left behind should see it shorten by half, not just 'slightly'.  I don't claim that it moves uniformly in frame F since the parts are not accelerating identically.  So I don't get this contradiction.

Post 21:

I carefully set the engines to produce the same acceleration.
Each section of the ship has the same mass.
So, they all are subject to the same forces.
All that force (for each section) goes into moving that bit of the ship
So there's none left over to pull my ship apart.

What is left over is the ships pulling apart from each other in their own frames.  They remain equally spaced only in the original frame.

Post 22:

For one, the different parts of the ship are not accelerating at the same rate, else the ship would break apart.

That is obviously incorrect.

What is probably obvious to you is Newton's rules, and he was wrong (or at least very incomplete) about it.  Please comment on my example below that illustrates what follows from what you find obvious.

Post 24:

There is no relativistic effect within a body subject to uniform acceleration because there is no external comparator for it to be "relative to".

I can locally feel acceleration, without consulting any external comparator.  Speed is definitely relative, but acceleration and rotation are not, and both have relativistic effects.

OK, that seems to be my list of quotes where one or the other of you seems to claim that the front of a ship accelerates identically (same g force) as the rear.  So I put together my little counterexample assuming that claim.  Neither of you commented on it except for BC claiming that it was based on my claims, not his.  I'll do it again.

= = = =

There is a long ship (20 light years) made up of a lot of small ships bolted together nose to tail.  The small ships are all blue except every light year there is a yellow one with a big number on it.  Each numbered ship (Y0 through Y20) is parked next to a space dock labeled D0 through D25 spaced every light year, and everything is stationary in frame F.  The ship ends at D20, but there are 5 more just so we have a grid extended a little further.  All clocks are synchronized in frame F, at least before movement starts.

In addition, just for jollies, we can have 21 independent pacer (P0-P20) ships that sit alongside the yellow D ships.  They’re identical, just not bolted to the entire mass.  Their intent is to keep pace with the big ship.

Flight plan: Each ship is going to accelerate at 1.95g in the 20 direction, for 1.31 years (ship clock) and then coast.  All parts of the big ship plus all the little pacing ships do the same thing.
As a passenger with no window to see the space docks go by, there would be no way to tell which of the ships you are on since they all pull the same g for the same amount of time.

After 1.73 years pass in frame F, each ship is moving at .866c, enough for 50% dilation of everything.  The acceleration is paced exactly so that this velocity is achieved just when each ship passes the next space Dock:
Y0 and P0 are at D1,
Y1 and P1 are at D2,
 ….
Y20 and P20 (the nose of the big ship and its pacer) are at D21.

Each space Dock sees these things happen at the same time on their clocks, which is 1.73 years from time 0.  The ships also see their first dock go by, but their clocks each show 1.31 years because they’re running slower at that speed.  Point is, they all log the same time on their local clocks as they see the first space dock go by.  Do you agree with that?  All 21 yellow ships and 21 pacer ships have executed the identical flight plan at the same time.

So at time 1.73 years. (as defined by frame F) the entire big ship is going at .866c, it is only 10 light years in length, but its tail is at space dock 1 and the nose is at space dock 21.  That’s still 20 light years separation.

I see that as a blatant contradiction.  Either the ship hasn’t contracted as relativity says it should, isn’t actually moving at .866c, or it has shattered into a bunch of separated little ships.  My vote of course is with the last one.


Please tell me where I went wrong with all that.  Don’t assert something else like you’ve been doing.  Tell me where the story above is wrong.  The whole thing is pretty much as seen in frame F, the only frame in which the ship is expected to contract.

From the ship frame, the space docks are contracted and only half a light year apart, and the ship is the original 20 light years in length.  So why is each yellow ship logging a space dock going by?  They should be seeing only the even numbered space docks since the odd ones are each halfway between two numbered yellow ships.  So another contradiction.


None of this matches my story, where the rear accelerates harder than the front.  The passengers very much know which end of the ship they’re in.  Clocks do not stay synchronized from front to back.  My story is not self contradictory.

[Bored chemist]

What is left over is the ships pulling apart from each other in their own frames.  They remain equally spaced only in the original frame.

Because they all move identically, they all experience the same "frame".The clock on my mantelpiece is in the same frame as my head so they agree on time. Both are effectively accelerating (at about 9.8 m/s/s) but that affects both equally.
The clock upstairs reads slightly differently but "upstairs" is only relevant because there's a well defined "up" here- because of the variation of the gravity of Earth.

You only get a gradient of time dilation if you have a gradient of acceleration. And I built my ship so that it all accelerates at the same rate.
Sure- none of the clocks says the same thing as those on the launchpad but, from the PoV of the ship's crew, "ship time" is well defined.

[alancalverd]

OK, that seems to be my list of quotes where one or the other of you seems to claim that the front of a ship accelerates identically (same g force) as the rear.

Your initial condition,  that the ship is fragile,  demands it. There is nothing to discuss, otherwise.

[Halc (OP)]

Your initial condition,  that the ship is fragile,  demands it. There is nothing to discuss, otherwise.

So discuss it.  I took exactly that premise and drove it to inconsistency in the example in the end.  I asked that you find the flaw in the example, else your assertion is worthless.

I asked explicitly for you to take apart my example, showing me where it went wrong.
All I get is more assertions.

Maybe argument from google search will help.
I found a similar situation at https://www.av8n.com/physics/hyperbolic-motion.htm
Section 2.1 shows a cluster of 5 unconnected ships spaced every 0.2 LY, (very much like my pacer ships) accelerating at 1g for half a year.

1) the ships spacing in the original frame (which they call the terrestrial lab frame) remain the same: No length contraction of the space between them, just like I said.
2) The red dashed lines are lines of constant time in the inertial frame comoving with the cluster.  The black dots are constant time as measured on the ships.  The red dashed lines are not parallel with the dots, so the clocks are not in sync, in contradiction with your assertions.

A few quotes from the bullets below the diagram:

Relative to the clock in the middle, the clock at the back of the cluster racks up less elapsed proper time.
By the same token, relative to the clock in the middle, the clock at the front of the cluster racks up more elapsed proper time.

This is just as I had worked out earlier in the thread.  The engine at the front runs longer, but at lower power (less g).  In the end, all ships are going the same speed after they shut down.

Another quote, directly to the point:

What’s far more serious is that at the end of the maneuver, the cluster is not the same shape as when it started out! The length between sub-rockets has increased.

This is of course what tears the ship apart if it is one big ship instead of a cluster of little ones.

Hey, the problem has a name!

This was pointed out by Dewan and Beran (reference 6) and eventually became known as Bell’s Spaceship Paradox.

The references are not links, so I just googled that.
Wiki has a page on it:
https://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox
The original problem seems to be a pair of ships connected by a string as they accelerate identically.

Both spaceships start accelerating simultaneously and equally as measured in the inertial frame S, thus having the same velocity at all times in S. Therefore, they are all subject to the same Lorentz contraction, so the entire assembly seems to be equally contracted in the S frame with respect to the length at the start. Therefore, at first sight, it might appear that the thread will not break during acceleration.

This argument, however, is incorrect as shown by Dewan and Beran and Bell.[1][2] The distance between the spaceships does not undergo Lorentz contraction with respect to the distance at the start, because in S, it is effectively defined to remain the same, due to the equal and simultaneous acceleration of both spaceships in S. It also turns out that the rest length between the two has increased in the frames in which they are momentarily at rest (S′), because the accelerations of the spaceships are not simultaneous here due to relativity of simultaneity. The thread, on the other hand, being a physical object held together by electrostatic forces, maintains the same rest length. Thus, in frame S, it must be Lorentz contracted, which result can also be derived when the electromagnetic fields of bodies in motion are considered. So, calculations made in both frames show that the thread will break; in S′ due to the non-simultaneous acceleration and the increasing distance between the spaceships, and in S due to length contraction of the thread.

Proof by wiki, Q.E.D.

[yor_on]

BC

It's seldom I don't agree with you
But this, ahem, I don't agree to :)

" As the string all speed up all the rulers shorten. All the ships shorten and all the gaps between the ships shorten And they all shrink to exactly the same extent. So the rulers all still fit exactly into the gaps. "

I don't see how that is possible. We're talking a acceleration here, and in any acceleration there has to be a point of 'force' initiating it, and keep on doing so each time something needs to pushed to a higher speed. To spread it out you will need uniform motion as I think.
=

spelling sux

[yor_on]

The only way we can create a engine that pushes equally at all points is imaginary. It would have to be 'dragged' in all points to do it. Which then means you need to create a 'extrinsic force' acting on each point of that engine equally. Now that would be a cool idea if someone knew how to create such a force acting on our spaceship

[alancalverd]

So discuss it.  I took exactly that premise and drove it to inconsistency in the example in the end.  I asked that you find the flaw in the example, else your assertion is worthless.

The flaw is in the notion that you can accelerate different parts of an object at different rates without distorting the object. That is too obvious to merit further discussion.

[Bored chemist]

Can someone help me out here please?
I'm meant to be leading this "ship"- it's actually a flotilla of little ships.
All the pilots know that they can accelerate their craft at well defined rates and they all move at the same speed WRT the launch pad (which they left long enough ago that its local gravity isn't a factor)
 I know that I can hold the fleet together simply by making sure all the little bits of my ship accelerate at the same rate.
But someone is now saying that , in spite of being deliberately held together, it will fall apart.

He refuses to give a mechanism, but my crew are still starting to get jumpy.

What should I tell them?
Do I tell them to rely on common sense, or do I tell them that magic gremlins are pulling the ship apart?

(These are experienced spaceship pilots. they consider relativity to be common sense)

[David Cooper]

My method of moving the ship is quite simple.  You have a length L that is the distance between the starting point of the tail of the ship and the destination point of the nose of the ship.  Accelerate the tail as quickly as possible (instantly?) to whatever speed is required to contract L down to the length of the ship.  That brings the nose to its destination (or actually brings the destination to the nose).  Now we instantly stop the nose, which springs L back to its original length, bringing the tail to its final destination.  We're done.  The time it takes to do that is the same as the amount the clocks get out of sync between the nose and the tail.

What stops you accelerating it faster than that? If you can individually accelerate each atom to a tiny fraction below c and get the timing right, all of them can then move at that speed with a delay until the front of the ship is moving too, and then when you stop, the rear ones stop first, being decelerated to a speed that makes them fully happy to sit next to the atoms stopped around them - the length of the trip shouldn't limit you to slower speeds than that on shorter trips. With the right kind of launch and catch system, this could be done in such a way that nothing breaks despite the astronomical acceleration force because the arrangement of atoms isn't broken in any way - they are just momentarily the wrong distance apart, but that's put right again at a rate that propagates along the ship at a fraction below the speed of light.

[Toffo]

Can someone help me out here please?
I'm meant to be leading this "ship"- it's actually a flotilla of little ships.
All the pilots know that they can accelerate their craft at well defined rates and they all move at the same speed WRT the launch pad (which they left long enough ago that its local gravity isn't a factor)
 I know that I can hold the fleet together simply by making sure all the little bits of my ship accelerate at the same rate.
But someone is now saying that , in spite of being deliberately held together, it will fall apart.

He refuses to give a mechanism, but my crew are still starting to get jumpy.

What should I tell them?
Do I tell them to rely on common sense, or do I tell them that magic gremlins are pulling the ship apart?

(These are experienced spaceship pilots. they consider relativity to be common sense)

This is launchpad personnel's view:

If the readings of the accelerometers of the ships are the same, then the increasing time delay of light signals traveling towards the front causes a pilot to see a ship at the rear becoming increasingly retarded. Said pilot should see an elastic band connecting the ships stretching, otherwise there is a inconsistency: Pilot sees other ship falling behind, but does not see the connecting elastic band getting longer.


If on the other hand the observed accelerations observed by the pilots are the same, then the readings of the accelerometers are not the same.




Oh yes, it was the pilots' view that was requested. Well it's that everything happens slower on ships closer to the rear. Whatever happens inside a rocket motor happens slower, whatever happens inside an accelerometer happens slower. Slowed down accelerometer measures slowed down motor to accelerate the ship 'normally'. 

[Halc (OP)]

What stops you accelerating it faster than that?

I need to stop when I get there.  I accelerate the tail just enough to contract the distance I need to travel to be exactly even with the nose of the ship.  If it goes any faster, the nose overshoots the place where it needs to stop.
Keep in mind that during the acceleration phase, the tail of the ship never moves.  If I accelerate over finite time, then yes, the tail moves.

If you can individually accelerate each atom to a tiny fraction below c and get the timing right, all of them can then move at that speed with a delay until the front of the ship is moving too,

That makes parts of the ship not stationary, and other parts stationary.  It can't take that (right ?!).  Perhaps it is a mathematical stipulation that the ship always be stationary in its own frame.

I think I see what you're envisioning, sort of compressing the ship at light speed like a slinky.  Any two parts of the ship going a different velocity are always separated in a space-like manner, never a time-like manner, so the discrepancy cannot cause breakage.  It violates my mathematical stipulation, but can a brittle ship take that?  I cannot identify what would break.  What the tail is doing at event X is of no concern to parts of the ship outside X's light cone.

With the right kind of launch and catch system, this could be done in such a way that nothing breaks despite the astronomical acceleration force because the arrangement of atoms isn't broken in any way - they are just momentarily the wrong distance apart, but that's put right again at a rate that propagates along the ship at a fraction below the speed of light.

This is actually a cool idea.  The example of my 100 LY ship moving only one light hour would have the tail start and stop long before the nose ever moves.  The wave of movement would propagate up to the front (at what rate?).
The thing would move exactly like a caterpillar.
Would that be faster?  My ship took 55 days (see post 20), but a 100 LY ship would seem to need more time than that for the 'wave' to reach the front.

It seems not to violate the brittle-ship thing.  There is a point in the ship where all the matter to the rear is moving nearly at c, but the stuff in the other direction is stopped.  If that persisted for even a moment, it would shatter, but it doesn't.  The wave passes before any stress/strain can build up. If we accelerate the tail to light speed, the wave propagates at light speed, but the wave seems to move faster with slower ship speeds, so for instance if we accelerate the tail to .866c, the wave moves at about 1.732c (sqrt(3)), if I did that correctly.  The caterpillar gets there faster if it moves slower.  Whodathunkit?

For slower speeds (well under c), the wave propagates faster than 2c.  We need to find a sweet spot that balances wave speed with physical speed.  It would depend on the ratio of ship length to trip length it seems.  My method I suspect is independent of trip length, at least for short trips.  I think it takes 55 days to go any short distance.  The figure is not specific to  travel of one light hour.

If on the other hand the observed accelerations observed by the pilots are the same, then the readings of the accelerometers are not the same.

What are the pilots reading if not the accelerometers?  How do they otherwise decide that they're the same?

Second note is, same as what? Identical to the value measured on other ships, or just identical from moment to moment?  Nobody seems to be proposing that a particular ship vary its acceleration during the process (except David just now), but it isn't off the table either.

An accelerometer on a ship will measure proper acceleration.  Not sure what meter the lauchpad guy is reading, but that one will read acceleration in his frame, not the ship's proper acceleration.  The former falls off as speed grows, while proper acceleration should be constant for the duration.

[Toffo]

What are the pilots reading if not the accelerometers?  How do they otherwise decide that they're the same?

Second note is, same as what? Identical to the value measured on other ships, or just identical from moment to moment?  Nobody seems to be proposing that a particular ship vary its acceleration during the process (except David just now), but it isn't off the table either.

An accelerometer on a ship will measure proper acceleration.  Not sure what meter the lauchpad guy is reading, but that one will read acceleration in his frame, not the ship's proper acceleration.  The former falls off as speed grows, while proper acceleration should be constant for the duration.

Bell's spaceships are seen to accelerate at the same rate by the launchpad ... and clocks in the ships are seen to tick at the same rate. And accelerometers screwed on the ships and observed by a telescope from the launchpad are seen to read the same value.


A pilot of a normal spaceship sees all parts of his ship to accelerate at the same rate.

[Bored chemist]

I think I might be able to see what you are on about.
Imagine I assemble my crew of pilots + ships in space then set them off at 1 second intervals.
As they leave the launch point they are quite close together.
At their destination, they also arrive at 1 second intervals. And now they are doing 100,000 miles a second
But they are now travelling at high speed so 1 second is long enough to travel 100,000 miles
So the flotilla has "stretched" in transit.

But the problem there is that you can't say at what time I launched the flotilla. Was it when I set off the first ship, the last one, tee one in the middle or what?
If there wasn't a flotilla at the start, how can you say it stretched?

(Obviously, this isn't a relativistic effect)

[alancalverd]

If an array of particles all launch at the same time, with the same acceleration vector, their mutual relative velocities will remain zero so they will  remain at the same separation relative to one another. No relative motion = no relativistic effects.

If the initial array was a straight line, then an observer at the launch point will see the line contract in the radial direction, but not in the tangential direction, as they approach c relative to the launch point. Relative motion = relativistic effects.

[Toffo]

Agree to all but the last one.  Our pilot would need an accelerometer bolted to either end of his ship, and if he looked at them, they'd read a different value.  If the ship is short as most are, they'd not read very different, but it gets quite apparent with longer ships.  They're getting shorter in launchpad frame, so the front isn't getting up to the same velocity in that frame.  In ship frame, the front clock is running faster, so it takes more time to do the same acceleration.  In both frames that spells different reading on the accelerometers at either end of the ship.

Yes, the accelerometers show different readings, and from that we know that I did not say or mean that the accelerometers show the same readings.

I meant the eyes of the pilot tell him that the accelerations are the same, the same way as the eyes of drag racers tell the guys in the cars what the difference of accelerations is.