# Lorentz-contraction

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2 hours ago, studiot said:

So you have read my comments, even though you did not respond to them.

Apologies

2 hours ago, studiot said:

If (as i am inclined towards) the universe is infinite of course he never sees the reference point return and the maths has a division by zero error.

Right, but for this mental experiment we'll assume that the universe is finite in space. That could be right or wrong, but it is not prohibited in relativity

2 hours ago, studiot said:

The pilot sees the rest of the universe (the reference starting point) receeding away from him to the left at this incredible speed.

If the manifold is finite but closed he then sees the reference point approaching at incredible speed from the right a very short time later.

If (as i am inclined towards) the universe is infinite of course he never sees the reference point return and the maths has a division by zero error.

So as far as the pilot and his spaceship are concerned the rest of the universe is smaller than his ship and makes a circuit around it.

So what ? Where is the paradox ?

I don't understand this. We apply Lorentz-contraction and, for whatever length is considered, it is just a matter of to speed up close enough to c to contract it to 1 m. I imagine this contraction in the direction of the movement, like two walls closing on the ship from the front and rear. Why is it receding to the left?

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2 hours ago, Strange said:

The experiment you have described so far is non-physical (so you could pretty much make up any answer you like). You seem to think you have created a paradox. But if you invent an unrealistic thought experiment, then it isn't surprising that you can make it inconsistent.

Is it possible to frame your question in a way that applies in the real world? If not, that is because the paradox you are imagining does not exist in the real world.

I don't agree. As far as I understand it, the relativity does not prohibit an universe whitout a receding border travelling at c, and so I consider the question valid. The explanition of the aparent paradox, is what we are discusing

True, the experiment is unrealistic in the real universe, with its expansion, but the expansion is not usually considered to be an intrinsic need of the relativity.  A contracting or static universe is not in contradiction with the relativity

We can consider an universe as ours, with the receding border at c, as the only real possibility, a kind of intrinsic necessity of the relativity to work.  That would be consistent with our observations and solve the paradox, but that interpretation wouldn't go without challenges

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6 minutes ago, Winterlong said:

I imagine this contraction in the direction of the movement, like two walls closing on the ship from the front and rear.

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40 minutes ago, Winterlong said:

Apologies

Right, but for this mental experiment we'll assume that the universe is finite in space. That could be right or wrong, but it is not prohibited in relativity

I don't understand this. We apply Lorentz-contraction and, for whatever length is considered, it is just a matter of to speed up close enough to c to contract it to 1 m. I imagine this contraction in the direction of the movement, like two walls closing on the ship from the front and rear. Why is it receding to the left?

Ok finite universe.

Your problem is that you are not specific enough " it is just a matter of to speed up close enough to c to contract it to 1 m" spedd yes, but speed relative to what  ?????

So I picked a 'what' as the start point.

Why left ?

Well if you circumnavigate a finite universe you will arrive at your start point travelling from the opposite direction.

Again for specifity I picked left and right.

It could have been down and up or up and down or whatever.

So we have a spaceship travelling fast round the universe.

But this is relative which means it could just as well have been the universe travelling past the ship.

And it is that which the pilot observes.

He does not observe his own travel as he is stationary in his own frame.

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4 minutes ago, Strange said:

Indeed, only with the difference of considering the entire space available in the universe. The ladder paradox is explained by the simultaneity, and, if we were talking about  something local, like the distance between the ship and Andromeda's galaxy, this explanation would do. But when all the space is affected, the question is different, in my view

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13 hours ago, Winterlong said:

Indeed, only with the difference of considering the entire space available in the universe. The ladder paradox is explained by the simultaneity, and, if we were talking about  something local, like the distance between the ship and Andromeda's galaxy, this explanation would do. But when all the space is affected, the question is different, in my view

Actually, it's conceptually exactly the same (as I have pointed out twice before already). There would be a paradox only if the front of the ship is within the 1m interval, while the back end is simultaneously outside that same interval. But there is no such global notion of simultaneity (as described in the article), most especially not if background curvature cannot be neglected, as is the case here. So there's no paradox. As I've mentioned already, it is not possible to construct physical paradoxes from within the axioms of Special Relativity.

There's another issue here as well - if the observable universe is somehow contracted to 1m, while at the same time having the topology of a closed manifold, then the pilot will not measure his ship to be 10m long any longer. You need to consider GR effects for this, it is not a purely SR scenario.

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23 hours ago, md65536 said:
23 hours ago, md65536 said:

I got this wrong. There is a paradox if the ship starts in the middle of the simplified universe and accelerates, ending up sticking out both ends. It's resolved by Born rigidity https://en.wikipedia.org/wiki/Born_rigidity

Hi, I am taking into account the rest of your comments, even if I don't quote all of them:

I do my best to keep it within the Special Relativity, because it is this theory what I want to discuss. Including acceleration  changes that. It could be that there is no way to avoid it, but, in principle I believe the SR allows us to question "where is the ship flying" in an static, flat universe without considering the process of acceleration ( as far as the ship is not accelerating now) So speaking, I don't want to "run away" to the general theory because I cannot explain the special theory. I could have this wrong

The Born rigidity, which is new for me, could be an answer but I don't see it. It can limit the length of the ship during the acceleration, but then again, I don't want to consider the acceleration process. Also, if we consider the ship stopped and the universe moving, how does it work? It won't limit the lenght of the ship...

In summary, It could be, but I don't see why we cannot use the SR and the SR alone, as their premisses are fulfilled (hence, not considering acceleration)

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10 hours ago, Markus Hanke said:

You need to consider GR effects for this, it is not a purely SR scenario

As the ship is not accelerating, I don't see why it has to suffer the effects of acceleration, hence, require GR. I take it curvature of space-time = gravity = acceleration (correct me about this) Anyway,  the ship itself does not accelerate, so no curvature for it

And for the lack of simultaneity, it will happen, but I don't see its relevance. I see it in the ladder paradox, but not here

What will prevent the two "walls of contracting universe" to reach the extremes of the ship and to go on?  It won't happen simultaneously for both extremes, right, but in the end, beyond certain speed, a ship of ten meters will be flying in a universe of 9 m, then 8 meters, then... until 1 m, despite of where are the "walls"

I agree that the paradox is only apparent, one way or another, but I don't see why SR is not applicable

On 8/9/2020 at 3:35 PM, studiot said:

Ok finite universe.

Your problem is that you are not specific enough " it is just a matter of to speed up close enough to c to contract it to 1 m" spedd yes, but speed relative to what  ?????

...

And it is that which the pilot observes.

He does not observe his own travel as he is stationary in his own frame.

We can consider the speed relative to Earth, in a stationary universe with everything but our ship at the same speed than Earth

And I don't get the idea. The pilot can consider itself and his ship stationary and the universe moving,  right. But the question is where is the ship, if it if bigger than space? For the pilot there is only one frame, and, as far as he knows, he is partially outside the universe (?)

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19 minutes ago, Winterlong said:

We can consider the speed relative to Earth, in a stationary universe with everything but our ship at the same speed than Earth

Which is more complicated than what I said, but OK it will do.

19 minutes ago, Winterlong said:

And I don't get the idea.

I can see that

20 minutes ago, Winterlong said:

The pilot can consider itself and his ship stationary and the universe moving,  right. But the question is where is the ship, if it if bigger than space? For the pilot there is only one frame, and, as far as he knows, he is partially outside the universe (?)

The pilot does  (can't) measure 'the universe' he can only measure the distance to something that is moving relative to him

Remember all movement is relative. Movement without a reference point is meaningless.

His frame includes his ship and the whole rest of 'the universe'.

Here is an alternative look at the problem.

Let us suppose that when he is travelling at full speed, he passes by an object exactly 1 m long when it is at rest in his frame.

What will he see ?

He will see an incredibly foreshortened object, many many orders of magnitude smaller than 1m, which he can measure as he passes by first the back, then the front and knowing his speed relative to the object he can recover the 1m rest length, if his super computer onboard is better than wolfram alpha.

Now scale that up to the whole universe.

Does this help?

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7 hours ago, Winterlong said:

I don't see why we cannot use the SR and the SR alone, as their premisses are fulfilled (hence, not considering acceleration)

Sure, but it's best not to refer to it as "the universe" because 1) you're intentionally avoiding real properties of the universe that require GR, and 2) you're unintentionally treating your simple model as if it should be like the real universe.

So let's call it a "bubble", say a spheroid region one billion light years in diameter, with a boundary and some stuff in it at relative rest, in an inertial frame. Then it has an inertial ship passing through it from one edge through the middle to the other edge. The ship has a proper length of 10m. The ship is traveling fast enough that the bubble is length-contracted to 1m in its own frame.

Inside the bubble, the ship is length-contracted so it is flattened in the direction of its travel to less than the diameter of a quark. It takes just over a billion years for it to pass through the bubble, during which it ages only about 3.3 nanoseconds.

In the rest frame of the ship, the bubble is a disk that is 1 m thick and has a diameter of one billion light years, which passes (thick-wise) through the ship at near the speed of light. It takes about the time it takes light to travel 1 m (about 3.3 nanoseconds) for any point on the ship to enter and then exit the bubble. That's one way to know that a point on the ship only ages 3.3 ns in the bubble's frame.

[You probably don't want to know, but it's interesting that it take about 36.7 ns for the bubble to move 11 m and pass completely through the ship, and yet it only ages 3.3 ns according to an observer in the bubble. This is because of relativity of simultaneity. Clocks on the front and end of the ship that are in sync in the ship's frame, are out of sync by about 33.4 ns in the bubble's frame. In the bubble, if a clock at the front of the ship reads 0 on entry, a clock at the rear simultaneously reads 33.4 ns on entry, and then 36.7 ns on exit. The ladder paradox explains how the observer in the bubble can say the entire ship is inside the bubble, while an observer on the ship disagrees.]

Okay so back to your "paradox". In the ship's frame, only the bubble is length-contracted. When you say "the entire universe" is length-contracted, you might be imagining all of space ie. all of the measurements of space around the ship, are contracted too, but the ship's inertial frame's measurements, or its space, doesn't get contracted. Where is the ship? It's in its own inertial frame, with all of its rest clocks and rulers behaving completely normally. If you suppose there's nothing else at rest in that frame except the ship, then all of the real clocks and rulers are on the ship, but the spacetime surrounding it would still be measured as normal, according to SR. Since it's only the bubble that's moving, that's all that gets length-contracted. Spacetime as measured in the ship's inertial frame, is not moving, and is not contracted. The spacetime isn't "stuff", I think it's nothing more than the measurements.

Edited by md65536
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On 8/9/2020 at 12:47 PM, Winterlong said:

We apply Lorentz-contraction and, for whatever length is considered, it is just a matter of to speed up close enough to c to contract it to 1 m. I imagine this contraction in the direction of the movement, like two walls closing on the ship from the front and rear.

The "closing in" is a change of the length contraction factor, which only happens during acceleration. But combining this idea with this:

17 hours ago, Markus Hanke said:

There's another issue here as well - if the observable universe is somehow contracted to 1m, while at the same time having the topology of a closed manifold, then the pilot will not measure his ship to be 10m long any longer.

As an example, suppose the ship has its back against a brick wall, and then the entire ship accelerates away from the wall in some coordinated way (it can't keep accelerating "simultaneously" according to the pilot because the ship never shares a single inertial frame while accelerating), it doesn't matter for this example how. If the pilot accelerates fast enough, SR says that the wall can contract toward the pilot faster than the pilot moves away from the wall. But the wall can never get closer than the back of the rocket is, to the pilot. (The wall won't length-contract through other stuff.) With that high acceleration, the back of the ship must also length-contract toward the pilot. This demonstrates that there must be an acceleration limit to Born rigidity. It also means the back of the rocket will never stick out the back of the contracting region it was in when it accelerated forward.

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12 hours ago, md65536 said:

The ladder paradox explains how the observer in the bubble can say the entire ship is inside the bubble, while an observer on the ship disagrees

Ok, but disagreeing that the ship is within the space is a problem for me (is The Problem) The ladder people say that the ladder is "outside of the garaje" This is different from saying that the ladder is "outside of space"

Imagine that I tell you that there is a galaxy bigger than the universe. Somehow, only the observers inside it hold that opinion, for the rest of the universe it is quite normal galaxy. But the equations of the tenants of the galaxy are clear; the galaxy is bigger than all space. Wouldn't it be strange?

12 hours ago, md65536 said:

Where is the ship? It's in its own inertial frame, with all of its rest clocks and rulers behaving completely normally.

But, what is the meaning of a own inertial frame if it is outisde of space? An own universe?

12 hours ago, md65536 said:

The spacetime isn't "stuff", I think it's nothing more than the measurements.

This changes everything. Is spacetime itself is not "stuff" it maybe doesn't make a lot of sense talking about how it is "depleted"

I  don't disagree, but it is commonly accepted that space-time is kind of... fabric? For example, it is said to curve in the presence of matter

Also, is if is only measure, something not physical, why should it contract or expand?

Also, the distant galaxies that are carried out by the expansion of space would happen to be in fact receding faster than light on their own (?)

Again, not that I disagree, but neither I know

13 hours ago, md65536 said:

[You probably don't want to know, but it's interesting that it take about 36.7 ns for the bubble to move 11 m and pass completely through the ship, and yet it only ages 3.3 ns according to an observer in the bubble. This is because of relativity of simultaneity.

Actually, I want to know,  but maybe deserves a different conversation

17 hours ago, studiot said:

His frame includes his ship and the whole rest of 'the universe'.

Does this help?

How is that? Pilot's equations show a "rest of the universe" smaller than the ship. The ship itself is ok within its frame, but it is also bigger than the space/space time/universe/reality/hypersphere/bubble, you name it. That is strange

17 hours ago, studiot said:

Let us suppose that when he is travelling at full speed, he passes by an object exactly 1 m long when it is at rest in his frame.

...

Now scale that up to the whole universe.

I don't see a problem in objects being contracted as far as desired. I see a problem in the space itself being contracted as to be smaller than a material object that should be inside it

17 hours ago, studiot said:

Does this help?

Still struggling, you see, but thank you

12 hours ago, md65536 said:

The "closing in" is a change of the length contraction factor, which only happens during acceleration

Agree. My bad, I should keep it within SR, as far as possible

Something could simply exists at the required speed as to make the space smaller than itself, or anyway we should consider it when the acceleration process has finished

I could have this wrong, maybe the acceleration process must always be considered, but seemingly relativity does not require it

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18 hours ago, Winterlong said:

As the ship is not accelerating, I don't see why it has to suffer the effects of acceleration, hence, require GR. I take it curvature of space-time = gravity = acceleration (correct me about this) Anyway,  the ship itself does not accelerate, so no curvature for it

The distinction between SR and GR is not acceleration, but the geometry of spacetime. An accelerated frame in otherwise empty spacetime still falls under SR, because such a spacetime is still flat - accelerated motion does not equal spacetime curvature, it only implies a world line that is not a geodesic. You only get curvature if there are sources of energy-momentum present.

The problem is rather that the universe is not empty - in order for SR to apply, spacetime needs to have Minkowski geometry. But since the universe is not empty, it is not Minkowski, but has a different geometry described by the FLRW metric. If we are only doing a small local experiment, then this issue can be safely neglected; but your thought experiment is not local, so you cannot ignore GR in this. If you combine FLRW spacetime with an observer at relativistic speeds, you get something that is very much non-trivial.

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56 minutes ago, Winterlong said:

How is that? Pilot's equations show a "rest of the universe" smaller than the ship. The ship itself is ok within its frame, but it is also bigger than the space/space time/universe/reality/hypersphere/bubble, you name it. That is strange

Yes this is your basic problem, right at the beginning.

The basic fallacy is trying to combine two incompatible statements and preceeding from there.
That will always end in tears many famous paradoxes and other trick questions can be resolved by realising this.

Mathematically it is rather like a lazy teacher who wants to go off for a smoke so he sets the class the following problem and offers a prize for the solution when he returns.

Sove the following simultaneous equations for a and b.

a +  b  = 6

a + B = 7

You said

The ship is travelling in the universe

The ship is 10 m long.

So the universe cannot be '1m long'

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1 hour ago, Winterlong said:

[...] This is different from saying that the ladder is "outside of space"

[...] I  don't disagree, but it is commonly accepted that space-time is kind of... fabric?

It doesn't mean cloth, just like if someone talks about the makeup of spacetime, they don't mean it's made of cosmetics.

In SR there's no single universal frame of reference that space is "in". The ship frame and the huge bubble frame are equal, there's no such thing as "one frame contains spacetime and the other doesn't". You might wrap your head around that by taking your example and having half your universe moving relative to the other half and vice-versa. Which is the universe? Or consider a universe made only of two identical ships moving relative to each other. Each, in its own frame, is at rest, not moving through space.

SR has no problem with an object bigger than another in one frame, being completely inside it in another. Also, just like you can't contract a bubble to make the back of the ship stick out, you also can't use length-contraction alone to make it stick out the front. Either the end of the ship moves through the edge of the bubble (an event that happens in all frames, just with different timing), or the ship contracts along with the bubble. The seemingly paradoxical aspects of SR are resolved in SR, and what you're left with is a question that amounts to "What happens if the universe has an edge and something moves past that edge, where is it?" SR doesn't answer that.

Thinking of it like the "fabric" has a rest frame and contracts to a finite size in another frame, is like supposing the universe is a finite bubble of Ether, with a rest frame, and then something leaves that bubble. SR doesn't imply that at all, but it also has no problem with that nor with an object leaving that bubble. In SR the frames of reference aren't finitely sized.

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3 hours ago, studiot said:

a +  b  = 6

a + B = 7

There seems to have been a slip of the keyboard there

it should, of course be

a + b = 6

and

a + b = 7

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On 8/11/2020 at 11:38 AM, Markus Hanke said:

The distinction between SR and GR is not acceleration, but the geometry of spacetime. An accelerated frame in otherwise empty spacetime still falls under SR, because such a spacetime is still flat - accelerated motion does not equal spacetime curvature, it only implies a world line that is not a geodesic. You only get curvature if there are sources of energy-momentum present.

This is interesting. It's fair to say in advance that I don't understand properly all the terms below, but here we go:

• Sources of energy-momentum produce spacetime curvature
• Spacetime curvature is gravity (if not,  what is the difference?)
• Gravity and acceleration are the same thing (a principle in the GR)
• Conclusion:  spacetime curvature and acceleration are the same thing  (or at least, you never find one without the other)

A "world line that is not a geodesic" and "curvature of the spacetime" look impossible to separate to me. Can you provide an example?

Well, an "empty accelerating frame" could do, but  that looks like a "nothing" accelerating . A something material accelerating actually increases it mass (for external observers) which increases its gravity, and so, by its own acceleration, curves the spacetime

Not saying I am right, just interested in your opinion.

On 8/11/2020 at 3:16 PM, studiot said:

There seems to have been a slip of the keyboard there

it should, of course be

a + b = 6

and

a + b = 7

Well, the question I posted could be a silly or clever one, but so far I have received some answers pretty interesting

Even if in the end the question proves a silly one, some of the discussions, and the points of view about space behind them, have been worth of it by far

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24 minutes ago, Winterlong said:

Well, the question I posted could be a silly or clever one, but so far I have received some answers pretty interesting

Even if in the end the question proves a silly one, some of the discussions, and the points of view about space behind them, have been worth of it by far

I did not say it was silly (or clever) .

I don't know where you got it from, whether you dreamt it up or saw it somewhere.

The point is that your original statement is a compound statement of two mutually incompatible simple statements.

That is the reason you have reached a 'paradox'.

Such a technique is a recognised method of mathematical / logical proof /disproof of a proposition,

But you don't seem to want to write the last line

Which is "This results in a paradox, therefore cannot be."

I glad that the discussion has elucidated many other points for you however.

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On 8/11/2020 at 1:19 PM, md65536 said:

Thinking of it like the "fabric" has a rest frame and contracts to a finite size in another frame, is like supposing the universe is a finite bubble of Ether, with a rest frame, and then something leaves that bubble. SR doesn't imply that at all, but it also has no problem with that nor with an object leaving that bubble. In SR the frames of reference aren't finitely sized.

Fair enough, but it looks to me that this conception of the bubble-of-something is commonly accepted, consciously or otherwise

I don't disagree with your point of view, but the bubble -of-spacetime helped to understand certain facts. Without it...:

• Are the distant galaxies moving faster than light relative to us? Space expansion was a possible explanation for that
• And why are them receding, anyway, if not carried away by the expansion of space?
• What is the meaning of the inflationary universe, where there is no matter or energy involved?  What is expanding?

If we, on the other hand, want to keep the fabric-of-something idea. Well, then it should have a length for a particular observer, whatever it is, that can be contracted up to 1 m

Agree that without the fabric idea there is no problem with the contraction, but there are others

1 minute ago, studiot said:

Which is "This results in a paradox, therefore cannot be."

I glad that the discussion has elucidated many other points for you however.

My initial question is a paradox, therefore, it cannot be

The joy is, however, in the path to understand it, and the things I find along the path. From the early "yeah, but the universe expandes at c" to the last views of "spacetime, curvature? fabric?" or your calculations about the speed

So far, so good, for me 🙂

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32 minutes ago, Winterlong said:

Sources of energy-momentum produce spacetime curvature

Yes.

32 minutes ago, Winterlong said:

Spacetime curvature is gravity (if not,  what is the difference?)

Essentially yes.

33 minutes ago, Winterlong said:

Gravity and acceleration are the same thing (a principle in the GR)

No, that isn't really right. I think what you are referring to here is what is called the equivalence principle - it states that in a small enough local frame, uniform acceleration is equivalent to the presence of a uniform gravitational field. The emphasis here though is on the terms 'uniform' and 'local' - essentially, it means that if you are locked in a small windowless box, and you measure a constant acceleration in some direction, then there is no local experiment you can perform that will tell you whether this is due to the box being accelerated, or due to the presence of a uniform background gravitational field.

The problem though is that the gravitational field of a real-world source (such as a planet, a star, or whatever) is not uniform - it is tidal in nature. This is why the equivalence principle holds only on small local scales, where tidal gravity is negligible. But it doesn't hold globally, so gravity is not the same as acceleration, in a general sense. If the box you are locked in is large enough, you will eventually be able to detect tidal effects, which allow you to distinguish between the presence of a gravitational source, and mere acceleration. These two cases are not physically equivalent.

41 minutes ago, Winterlong said:

A "world line that is not a geodesic" and "curvature of the spacetime" look impossible to separate to me. Can you provide an example?

Geodesics are world lines that a test particle in free fall traces out; an accelerometer carried along with that test particle will read exactly zero everywhere along that world line. Anything that is not in free fall - i.e. anything where a co-moving accelerometer reads something other than zero - are not geodesics.

The world line of a meteorite freely falling towards earth (outside the atmosphere of course) traces out a geodesic.
A rocket that fires its thrusters somewhere far away from any planets etc will trace out a world line that is not a geodesic.

In both cases, if you project the world line onto a standard 'flat' coordinate system, you will get a curved trajectory.

48 minutes ago, Winterlong said:

A something material accelerating actually increases it mass (for external observers) which increases its gravity, and so, by its own acceleration, curves the spacetime

The source of gravity isn't just mass, it's a mathematical object called the stress-energy-momentum tensor. A tensor has the important property that it is covariant under coordinate transformations, which physically means that all observers agree on it, regardless of where they are and how they move. In other words, if a body exudes 'x amount of gravity' in one frame, it does so in all frames. The only thing that changes is the coordinate values the observer assigns to each event in spacetime.

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21 minutes ago, Markus Hanke said:

The source of gravity isn't just mass, it's a mathematical object called the stress-energy-momentum tensor. A tensor has the important property that it is covariant under coordinate transformations, which physically means that all observers agree on it, regardless of where they are and how they move. In other words, if a body exudes 'x amount of gravity' in one frame, it does so in all frames. The only thing that changes is the coordinate values the observer assigns to each event in spacetime.

Do you need moree explanation of this  ?

Markus loves tensors.

😉

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6 hours ago, Winterlong said:

If we, on the other hand, want to keep the fabric-of-something idea. Well, then it should have a length for a particular observer, whatever it is, that can be contracted up to 1 m
[...]

From the early "yeah, but the universe expandes at c" to the last views of "spacetime, curvature? fabric?" or your calculations about the speed

It sounds like you've moved on from the length-contraction aspects, but if a bubble is expanding at a rate of c in the bubble's frame, it should also expand at a rate of c in the ship frame. If it's a given size before you accelerate, I don't think it's possible to make it length-contract any smaller than that size by accelerating, if it's expanding at c.

As a very rough look at this, suppose you have a particle moving away from you at c, and is "now" at location x, a billion light years away. Now say you accelerate so that the distance to x contracts to 1m. But due to relativity of simultaneity (think of the Andromeda paradox, or the twin paradox) the clock at x is now advanced a great time relative to your clock (almost a billion years), and the particle is not at x "now" but has long ago moved past it.

Anyway there are a lot of interesting details related to this, a puzzle to figure out, if I say more I'll probably get it wrong.

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On 8/13/2020 at 12:45 PM, studiot said:

Do you need moree explanation of this  ?

Markus loves tensors.

😉

I can see that, but I am not in position to understand them properly

This said, thanks, Markus: Even without tensors, I get your point about the acceleration not being equal to curvature. I've got that wrong

20 hours ago, md65536 said:

It sounds like you've moved on from the length-contraction aspects, but if a bubble is expanding at a rate of c in the bubble's frame, it should also expand at a rate of c in the ship frame. If it's a given size before you accelerate, I don't think it's possible to make it length-contract any smaller than that size by accelerating, if it's expanding at c.

As a very rough look at this, suppose you have a particle moving away from you at c, and is "now" at location x, a billion light years away. Now say you accelerate so that the distance to x contracts to 1m. But due to relativity of simultaneity (think of the Andromeda paradox, or the twin paradox) the clock at x is now advanced a great time relative to your clock (almost a billion years), and the particle is not at x "now" but has long ago moved past it.

Anyway there are a lot of interesting details related to this, a puzzle to figure out, if I say more I'll probably get it wrong.

As I see it, if the particle, galaxy on the boder, or whatever object is in the direction of your movement, is running away from you at c, there is no problem

As you are not travelling at c, the object will keep travelling away from you at c (this speed being absolute)  No way to contract the space between you and it because your speed relative to it is cero...

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(I mean, your relative speed is not cero, but it is as if you were stopped, as it remains running away from you at c)

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On 8/14/2020 at 8:54 PM, Winterlong said:

I can see that, but I am not in position to understand them properly

This said, thanks, Markus: Even without tensors, I get your point about the acceleration not being equal to curvature. I've got that wrong

Understanding geodesics and curvature and how they interact is the key to this, not tensors. Tensors are just notation.

But beware there are many misleading descriptions out there.

Do you understand latitude and longitude?

Navigators have been using these geodesics and curvatures for 500 years. They can form a simple intelligible route into the subject.

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