[Halc (OP)]

This thread is meant to investigate relativistic limits on the acceleration of large objects.  To drive the points home, my objects will be large and fast, but never with impossible properties like being massless, infinite rigidity, or with instantaneous acceleration, all of which can be shown to violate fixed speed of light.

Consider a long object, say a light year in length, which is fairly fragile in that it will allow only negligible physical compression or stretching before it breaks.  Hence the force of propulsion is spread as needed over the entire length of the object. Our engines/rail-guns are as powerful as they need to be.

For slow accelerations, the clock at the front of the object will get ahead of the ones further back, so the acceleration further forward run is lower, but for a longer time.  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.  The points in between can accelerate proportionally.  In this way, the entire object might be under acceleration at once, but only in the object's own frame.

That seems viable for only slow accelerations, and even then, in any other frame, part of the object is accelerating and the part of it not, so right there it seems on first glance to be putting strain on our object, but I cannot prove that since the two parts are always separated in a space-like manner, and so cannot directly effect each other.

Scaling up the acceleration demonstrates the limits if not the deficiencies of my proposed methods.  Clearly at some point there is strain the way I am doing it.  Is there a strain-free way of accelerating a long object?  More exactly, is there a way to do it that never changes the object's proper length?

There is proof of sorts that there is a correct solution, since if there is compression or tension somewhere in the object, we could compensate for that with a thrust function that applies more or less force at points further forward.  There must be a solution that involves zero strain, but even then the length of the object puts an absolute limit on the magnitude of the acceleration.

Edit:  There seems to be nothing impossible about near instantaneous acceleration.  Many of my examples assume as a limit an acceleration to a desired speed in negligible time.  If this is found to violate finite light speed or some other law, kindly post details since it will effect my answers for minimum time to get a big thing somewhere.

Update, Feb 2019:  I think I found that very violation.  See post 97.  Infinite acceleration makes the speed undefined, and without a defined speed, the proper length is undefined.  Acceleration can be arbitrarily high, but not infinite.

[yor_on]

As always, I don't know :)

But depending on definitions, you take something that compress under acceleration and put it as close as you can to lightspeed. Presuming that  bonds microscopically holds relative time dilation's and length contractions there should be no problem. Otherwise you need a infinitely rigid structure to make it work, which would make that 'rocket' into a singularity of its own.

A interesting question here would be to presume that there can be objects coasting, aka uniformly relatively moving, close to light speed. That way you can avoid the acceleration and just question where the difference lies.
=

the real point of 'c' is that it is observer dependent.
either one ignore it or acknowledge it.

if you accept that as something that defines your universe, as well as every one else's 'universe' then 'c' is a constant.
Yes, it's local, but so are all experiments proving it to be a constant.
And so is 'repeatable experiments'.

That's where 'physics' comes from

[yor_on]

A very funny thing is considering a 'black hole' spinning at the speed of light, or let's put it just under that limit. If you want to argue that it is 'space' doing it, what about the black hole?

does it even need to spin?

[Halc (OP)]

But depending on definitions, you take something that compress under acceleration and put it as close as you can to lightspeed.

I'm not attempting to get close to lightspeed.  I'm trying to accelerate a long thing, something that cannot take stress.

Presuming that  bonds microscopically holds relative time dilation's and length contractions there should be no problem. Otherwise you need a infinitely rigid structure to make it work, which would make that 'rocket' into a singularity of its own.

No rigidity at all.  That was the point of the thread.  I said up front that infinite or massless things destroy the point being made.

A interesting question here would be to presume that there can be objects coasting, aka uniformly relatively moving, close to light speed. That way you can avoid the acceleration and just question where the difference lies.

I will get to that.  How long of a coasting object can exist?  It doesn't even have to move, which it doesn't anyway since it has to have a frame in which it is stationary.  Think about it.  Go for really long lengths.

A very funny thing is considering a 'black hole' spinning at the speed of light,

Speed of light isn't a rate of spin.  Black holes don't spin at a 'speed' nor at a particular angular velocity.  They have a particular angular momentum.

does it even need to spin?

Yes it does.  Conservation laws demand it.  It means that Hawking radiation needs to preserve it, as do gravity waves given off by objects spinning in.

[Bored chemist]

For slow accelerations, the clock at the front of the ship will get ahead of the ones further back,

How?

[Halc (OP)]

For slow accelerations, the clock at the front of the ship will get ahead of the ones further back,

How?

Gravity and acceleration are locally indistinguishable, so the front clock is functionally identical to one higher up in a building in a uniform gravitational field, and the clocks up there go faster since they're less dilated by gravity.

Similarly for any accelerating observer, clocks in the direction of acceleration advance, and those behind fall further behind (even into negative territory).  The Andromeda 'paradox' illustrates this quite well.  Small acceleration, but multiplied by large distance.

[yor_on]

Hmm, would you mind expanding a little on this one Halc?

"     A very funny thing is considering a 'black hole' spinning at the speed of light, "

Speed of light isn't a rate of spin.  Black holes don't spin at a 'speed' nor at a particular angular velocity.  They have a particular angular momentum. ""

Never said that the speed of light is a angular momentum? But if something as a wheel, moves around with a point marked at its circumference, where we find that point to move at a same or slightly less speed as measured for light. Then you can make a comparison I think?  https://www.universetoday.com/109308/how-fast-do-black-holes-spin/

[yor_on]

Also I would slightly alter that statement of yours that conservation laws demand the black hole to spin :)
In this case, as I questioned what spins I would put it as conservation laws demands 'something' to spin, suggesting it then to be the space around it. Now, if we find a black hole spinning faster than its allowed " The speed limit is set by the event horizon, eventually, at a high enough spin, reaches the singularity. You can’t have what’s called a naked singularity. You can’t have a singularity exposed to the rest of the Universe. That would mean that the singularity itself could emit energy or light and somebody outside could actually see it. And that can’t happen. " :)

Wouldn't that be interesting?

[alancalverd]

If the ship cannot tolerate longitudinal stress, it cannot be accelerated by a finite number of engines since the thrust of each engine must be transmitted to the intervening material by stress.

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.

This is quite different from a rigid rod, propelled from one end. The propulsive force is transmitted at the speed of sound in the rod which leads to mechanical compression and loss of synchronism way in excess of any relativistic effect, and is the reason that pushrods were abandoned in favour of overhead camshafts in high-revving engines.

[Bored chemist]

Gravity and acceleration are locally indistinguishable, so the front clock is functionally identical to one higher up in a building in a uniform gravitational field, and the clocks up there go faster since they're less dilated by gravity.

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.

There is a tiny gravitational effect due to the mass of the ship which means that the middle of the ship (where the fore and aft masses cancel out) are subject to a smaller field than the ends but that's hardly going to matter.

[Halc (OP)]

Never said that the speed of light is a angular momentum? But if something as a wheel, moves around with a point marked at its circumference, where we find that point to move at a same or slightly less speed as measured for light. Then you can make a comparison I think?

Wheels have different properties.  Earth is a wheel, and in the rotating frame of Earth, yes, there is a circumference where stuff moves at light speed, and there is stuff beyond that circumference.  It means that all stars but our own move at greater than light speed in that rotating frame, which isn't a contradiction since laws are different in such frames.

The link you provide is interesting, but it says that physicists use units for angular momentum that are cast in terms of mass, not in terms of speed.  So it is unclear how the author suddenly assigns a speed to a spin rate.

I find the concept of the naked singularity interesting, but very off topic for this thread.  My long fragile ship would break up if its engines did not everywhere compensate for stresses put on it by gravity sources.

Now, if we find a black hole spinning faster than its allowed " The speed limit is set by the event horizon, eventually, at a high enough spin, reaches the singularity. You can’t have what’s called a naked singularity.

There is no limit to the angular momentum of it, but if it spins that fast, it does become naked, and is no longer a black hole, just a collection of mass being flung away because it collectively has too much angular momentum to ever form a black hole.  It seems an interesting way to un-black an existing hole.  Just spin it faster, beyond its limits.

You can’t have a singularity exposed to the rest of the Universe. That would mean that the singularity itself could emit energy or light and somebody outside could actually see it. And that can’t happen. "

It can happen.  It just wouldn't be a singularity anymore. Actually, it probably cannot happen, because as the black hole shrinks, it becomes more and more difficult to apply more angular momentum to it.  At the limit, none can be added.  So yes, that cannot happen.

Wouldn't that be interesting?

Intersting yes, but there is a spinning black hole thread active right now.  Why not post this stuff in there?  My topic has nothing to do with them.

[Halc (OP)]

If the ship cannot tolerate longitudinal stress, it cannot be accelerated by a finite number of engines since the thrust of each engine must be transmitted to the intervening material by stress.

Maybe it applies force the way a uniform gravitational field accelerates Earth without putting additional stress on it. OK, the sun's field is not totally uniform, so we get tidal stresses.
For the sake of this example, the ship can locally take the stresses from its engines.

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.

Pretty much, yes.

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.

We need to pinpoint those rules.
There can be no change in proper length.  But there is very much going to be changes in relativistic length.
For it to have a proper length, it needs to be stationary in its own frame.  I fretted a lot about that one since it seems to be difficult to avoid, but decided it was a mandatory requirement, and that the solution to the problem lies exactly in that requirement.
Your last one is unreasonable.  There will be a perceived change of clock rates just as there would be in a building on a planet.  We’re accelerating after all and barring a window to look out of, the occupants cannot tell the difference between the two situations.  Clocks forward of a given observer will appear to run faster, and clock behind a given observer will appear to run slower.  The amount they get off depends on the separation, the acceleration rate, and how long we keep it up.

This is quite different from a rigid rod, propelled from one end.

I started out with that as my example, but it cannot be immune to strain, else it would transmit the thrust immediately to the other end, violating the light speed limit on information travel.  So I do it as a fragile ship where all the local ‘engines’ know the flight plan.  There can be no quick decisions by the pilot, since the new plan must be transmitted to all engines before any of the engines can react.

The propulsive force is transmitted at the speed of sound in the rod which leads to mechanical compression and loss of synchronism way in excess of any relativistic effect, and is the reason that pushrods were abandoned in favour of overhead camshafts in high-revving engines.

My original post talked about speed of sound like that.  I abandoned it for the time since I didn’t need the complication.  Speed of sound has an upper limit of c.  No material can be physically more rigid than that.

[Halc (OP)]

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.

Not so.  See the thread-breaking topic in the new-theories forum.  It was that topic that got me thinking about this topic.

There is a tiny gravitational effect due to the mass of the ship which means that the middle of the ship (where the fore and aft masses cancel out) are subject to a smaller field than the ends but that's hardly going to matter.

It would seem to only matter near the ends, and even then, our ship is narrow and not likely to generate a significant local gravitational field.  I cannot say it is massless, violating my stipulation about that, but for the purpose of the thought experiment, we can either ignore that or have the engines make that micro-compensation for it.

[yor_on]

I'm afraid those threads tend to go of in divergent angles Halc, and I admit to being guilty here :). What you were discussing was whether something can hold together being accelerated to the speed of light, or as close as possible at least, if I got that right? That made me think of rotating black holes, and also about the way we see our universe accelerating expanding. A rotating black hole has a 'speed' of sorts, although it also can be seen as forever accelerating although that dot we put upon it never increase its 'speed per distance done'  if you get ny drift. And looked at that way they are the 'fastest' objects I know of, 87% of the speed of light if I remember right? They do hold together, and seem to have no problem doing so under their whole evolution. If you think of spinning up a disk to that speed there are two possibilities, either it should crack as the rim will be at a different speed relative its interior, aka Lorentz Fitzgerald contraction, or it doesn't. I find the idea of black holes rotating very interesting. If we now instead look at 'space' then there is no limit to its 'speed' meaning that in a accelerating expanding universe we can use two buoys and define the space between them to expand FTL without us needing any new theory of Relativity. You made me think of a lot of things there Halc :)

[Halc (OP)]

My first cut at this was incorrect I think, but I'll describe it here.
I reached an inconsistency if I accelerated the ship hard:

I have a ship that is a light year long.  In frame P (parked) it extends from 0 (tail) to 366 (nose) light days.
Now I accelerate it (or at least the tail) to .866c (dilation 50%) in one month as measured by a P clock.
The tail of the ship is now at perhaps location 15 light days, and the ship, if moving at .866c, is dilated to half its length, so only 183 light day long.  So the nose is 15+183=198 light days away, much closer than it was when parked.  In fact, it would need to move faster than light to get to that spot.
This all seemed quite contradictory, and so I supposed there might be an acceleration limit based on the length of the object.

Where I seemed to go wrong is to consider the state of the ship in frame P as it is accelerating.  In no other frame is the entire ship moving at one uniform velocity, but this doesn't mean there is stress or strain on it.  In the ship's own accelerating frame, the thing is always stationary, and thus stress free.  In that frame, the nose never moves backwards since there is no length contraction.  You can accelerate as hard as you like.  There seems to be no limit.

[yor_on]

I'm not sure about that one Halc, as soon as your ship start to move its structure will contract at the speed of sound, as its 'accelerating motion' carries/pushes its structure. Made out of unobtanium  the speed of sound should be regulated by 'c' in which case it will accelerate to that limit. Were it made of steel? Also, and here's one really tricky part, the speed of light is observer dependent. Although we agree on getting the same limit 'c', it doesn't matter from what uniformly moving frame you measure that speed. And uniformly moving 'laboratories' can indeed be found to have different 'speeds' relative each other. So when you define it as shrinking you also will need to define what frame of reference you're using for observing that shrinking. I'm guessing we could use earth for it.
=

What I mean by it contracting is that its acceleration won't touch the whole ship simultaneously, unless it's made out of unobtanium. It's the same principle as you moving a very long rod to touch the moon. Your acceleration of the rod travels at the speed of sound, and speed depends on the rigidity of the rods material.

[Halc (OP)]

What you were discussing was whether something can hold together being accelerated to the speed of light,

Just accelerated at all.  Not to the speed of light, or necessarily particularly close to it.  I just use higher accelerations and speed to illustrate where the problems appear.

And looked at that way they are the 'fastest' objects I know of, 87% of the speed of light if I remember right?

There are constructs that fire Jupiter-size bullets at well over .99c, so maybe that qualifies more as a faster object.  The amount of violence represented in a thing that can do that is fairly unimaginable.

[Halc (OP)]

I'm not sure about that one Halc, as soon as your ship start to move its structure will contract at the speed of sound, as its 'accelerating motion' carries/pushes its structure.

My ship has engines the whole length to prevent exactly that speed of sound problem.  Read the OP.  The ship is fragile (brittle), not made of unobtanium.

Also, and here's one really tricky part, the speed of light is observer dependent.

No it isn't.  It is the same for all observers.

[yor_on]

Yes, its the same :)
It's 'c'. But you can still define different speeds to different laboratories, with one requirement, no acceleration involved for them. they will all give you the same limit 'c', no matter what 'speed' you define them too.

[yor_on]

Also it doesn't help making the whole ship into a engine, as the push effect from it will start at some point instead of being simultaneously pushing at the whole ship. It would be very difficult to create engines that pushes equally/simultaneously at all parts.
=

But you made a really good point there. Would that be a principle for how a (rotating) black hole holds together under its evolution? It can't be, can it?