[alancalverd]

No you cannot.  You need more information than that to measure radius.  There are 4 planets with gravity pretty much the same as Earth, so the guy measuring his weight change would not know the very different radius of the different planets.

No more information required, if you can solve simultaneous equations (most 12-year-olds can).

[Halc (OP)]

No more information required, if you can solve simultaneous equations (most 12-year-olds can).

I stand corrected on this one, from a non-relativistic standpoint.  A small radius produces a non-uniform gravitational field and the radius is determined by the Newtonian detection of that non-uniformity.

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.

[Halc (OP)]

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

They're your claims.

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.

See my comment above.  I was wrong on this one.  The rocket is equivalent to infinite radius gravitational field.

[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 8:

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 24:

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 29:

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 34:

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 9:

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 27:

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 30:

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 38:

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 39:

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 obvious 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 44:

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.

[Halc (OP)]

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.

My example did not do that.  All parts were accelerated at the same rate.  Did you even read it???  Your comments suggest that you have not.
Did you read the various articles I found on the web? None of them support your view. You are so sure that you are right that you will not read examples that show otherwise.

[Halc (OP)]

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.

The only way we can create a engine that pushes equally at all points is imaginary.

The sun accelerates Pluto in this way, so it is neither impossible nor imaginary.
You are posting about the engineering challenges of a thought experiment, which detracts from the points I'm trying to make.  I have no intention of actually needing to build this, so the engineering is of no concern.

[Toffo]

My example did not do that.  All parts were accelerated at the same rate.

Where is that example? I'm too lazy to search.

If all parts are accelerated at the same rate, then the accelerated thing breaks, right?

 We must 'manually' Lorentz contract our long and fragile object. Short and sturdy rods contract 'automatically'.

[Halc (OP)]

My example did not do that.  All parts were accelerated at the same rate.

Where is that example? I'm too lazy to search.

If all parts are accelerated at the same rate, then the accelerated thing breaks, right?

Bottom of post 45, after the = = =
Yes, I accelerate every part at the same rate, and bad things happen.

We must 'manually' Lorentz contract our long and fragile object. Short and sturdy rods contract 'automatically'.

Nothing sturdy involved.  The idea is to put no significant stress on the ship.  That means accelerating each piece differently.  If you accept this, then the main post on the table actually addresses the subject matter of the topic: A limit to how quickly a large thing can be moved.
See post 37 for that, where I show that a 100 LY object needs a minimum of 55 days to be moved (stopped, accelerate, and slow to a stop again) a distance of one light hour.  A short object can do it in about an hour of course.

[yor_on]

Not really Halc, a gravitational acceleration is still a geodesic as far as I know, that means that Pluto still is in a uniform motion. Then again, I missed the article you referred to in where the string breaks between the two ships so you already seen one definition. But, thinking of it this way it becomes slightly trickier.

Depending on acceleration rate, shouldn't there be a threshold for where that string breaks, meaning that if one just accelerate slow enough you might come up to a very high speed relative some distant suns blue shift without breaking that string. If that would be true then there would be two thresholds, one due to ones rate of acceleration, the other due to the impossibility for matter (proper mass) to get to 'c'?

After all, we all 'accelerate' as we move around in our daily life

[yor_on]

In which case I will agree on BC:s definition existing as a possibility too.

[Halc (OP)]

If that would be true then there would be two thresholds, one due to ones rate of acceleration, the other due to the impossibility for matter (proper mass) to get to 'c'?

Neither.

Perhaps I misunderstood what is being described here.
Completely on-topic, I don't see either of these two factors limiting how long it takes for an object to get from A to B, stopped at both ends.
I am assuming infinite acceleration, meaning any part of the ship can accelerate to the velocity of choice in zero time.  If it takes time to do it, then you can add that time to the total trip time I guess.
As for speed, moving at c will move us too far. We will overshoot our target (B).  A point-object like a photon can do that, but a ship with non-zero dimensions cannot without overshooting.  So none of the ships are requested to move at c, but if you're going a long way, you probably get pretty close to it.

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.

So if I have a ship that is a light-month in length and I want to get the nose of the ship to a planet that is a light-year away from the tail, L is one light year.  I need to compress L to a 12th its size in ship's frame, which happens at .9965c, so we accelerate the tail to that speed.  At that time (in the frame of the tail) we instantly stop the nose, and we're done.  The trip takes 364 days in inertial time, and about 97 days ship time.
That was a ship that was quite a bit shorter than the distance we wanted to move, so we were able to get it up to an impressive speed.  If the ship were much shorter, it would take almost the same inertial time, but almost no ship time.
I find it interesting that having a ship that is already a 12th of the way there (due to its length) to make almost no difference in the time required to get there.  Have to play with that more. 

[yor_on]

It's not possible Halc. No way you can accelerate at such a rate without the ship breaking into pieces due to LortentzFitzgerald contractions, as well as tensile material stress. That ship will need unobtanium to work I'm afraid.
=

you need to find a solution in where every point of that ship is in a same frame of reference relative the push of what engine you imagine, I don't see how that can be done myself.