Winterlong

(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)

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

@Winterlong

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...   

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 🙂

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

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 

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 (?) 

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) 

 

4 minutes ago, Strange said:

It sounds like yo are describing a rather extreme version of the ladder paradox: https://en.wikipedia.org/wiki/Ladder_paradox

(Note that, like all "paradoxes" there is no paradox here.)

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

20 minutes ago, Charles 3781 said:

If the ship underwent contraction as it approached light-speed, wouldn't the hydrogen atoms inside the ship get so squeezed together, that they underwent nuclear fusion, and blew the ship apart in a gigantic nuclear explosion?

 

Not for the pilot, the ship will be as ok as always for him... but he will see the rest of the universe doing so. If he has a certain sense of humor, he could call it the Big Bang 

It's a joke 🙂  I don't think that will happen, and if something, the Big Bang looks much more similar to what happens when the pilot decelerates and the 1 meter universe turns into a many billions light-year universe, expanding space-time and galaxies far faster than c, as the Lorentz-contraction losses effect 

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

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?

About the reference system:

In order to keep it simple, say that we consider an static universe. There could be movement of galaxies or starts or ships in this universe but not general expasion resulting in ligh-speed receding objects. The speed of the ship is, say, relative to Earth. It doesn't really matter in this scenario 

This universe is not the real one,  but neither is considered to be impossible in Relativity

The expansion makes things so much more interesting... but maybe deserves a different discussion

1 minute ago, swansont said:

Does it? Can you point to science that confirms this?

 

I cannot. The lengh defined as "the distance to be travelled to get back to the starting point" looks to me something not prohibited by relativity and somehow commonly accepted, but I don´t know it to be real or otherwise   

Still, this is beyond my point. The mental experiment I want to discuss applies equally to an universe without expansion, something seemingly not impossible within relativity principles 

8 hours ago, Markus Hanke said:

I think you need to be careful not to confuse the cosmological horizon (i.e. the limit to how far out we can observe) with the actual size of the universe. These are not the same things. The physical universe itself does not have any borders.

Right, but even so, the universe has a length;  the distance to be travelled to get back to the starting point. This length being small or big doesn't matter, that will be a matter of how close to c the ship has to travel to reduce such length to 1 m

8 hours ago, Markus Hanke said:

But this is not what physically happens - refer again to relativity of simultaneity. I would recommend a read of the link I gave earlier on the ladder paradox (if you haven’t already), it is conceptually quite similar to this scenario.

But whichever way you look at it, there will of course never be a physical paradox, since you can’t construct those within the axioms of special relativity. 

I see a paradox, and I don't see how the simultaneity can solve it. For the sake of simplicity, the pilot does studiot's calculations (assuming that he knows the true length of the universe) and concludes that the length of the ship is bigger than the length of the universe, without even opening the windows of the ship to look outside. How does the simultaneity fix it?

The expansion of the universe complicates the scenario (actually, solves the paradox) But to get to the point, imagine a static universe. How is the special relativity not applicable? The SR only requires absence of acceleration, and should be applicable to any amount of space, including the total length of the universe

Quote

15 hours ago, Markus Hanke said:

This is not as straightforward as you might think...

 

Right, but keep it simple. Even discussing curvatures, the resulting ship encroaching itself ten times is somehow awkward. As the speed remains constant, the restricted relativity should be enough for our discussion 

Quote

Have to factor in expansion as well.

For distant destinations, the distance is growing at a rate faster than the ratio c.

Indeed, that is true for any direction due to the fact that the border of the observable universe is receding at c in any direction. No matter how fast the ship travels, it won't catch it. Actually, the situation for the ship won't be special. The border still will recede at c for it, despite of its speed. The mental experiment is an impossible one 

This solves the paradox, but at the cost of making the recession of the border of the universe at c a necessity, rather than something that could be different

An universe in contraction, static or in a expansion slower than the current one, would still be sensitive to the paradox, hence, not possible. This explanation makes the recession of the border of the universe at c a requirement if the relativity to be true, something that could not be otherwise  

A ten meter ship travels as close to light speed as to have all the universe compressed to 1 m length, in the direction of the movement. As the ship remains stopped for the pilot, its length remains ten meters for him. If the universe is 1 m in length, where is the ship flying?