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)

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 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...

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 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 🙂

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. 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

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? But, what is the meaning of a own inertial frame if it is outisde of space? An own universe? 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 Actually, I want to know, but maybe deserves a different conversation 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 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 Still struggling, you see, but thank you 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

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 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 (?)

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)

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

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

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

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?

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 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

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 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

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

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?