My understanding of Space, Time and spacetime

[Spacie]

Which object? The chain links are individual objects which must contract according to SR. The chain as a whole cannot contract in this scenario, because the rockets keep a constant distance in their initial rest frame.

I thought the chain represented the atoms that make up the string that connects the ships. Should not it contract under the length contraction? According to your picture, high speeds, instead of contracting the objects, should shatter them by breaking their molecular bonds.

Besides, what does it matter if there is just one string connecting the ships? Make it a gazillion of strings connecting the 2 ships (which effectively makes them one object). What happens to your paradox then? It's a moot paradox, and that's the second in this category that I count authored by Bell.

 

[A.T.]

I thought the chain represented the atoms that make up the string that connects the ships. Should not it contract under the length contraction?

It cannot contract as a whole because the ships keep a constant distance in their initial rest frame. How difficult is that to understand?

According to your picture, high speeds, instead of contracting the objects, should shatter them by breaking their molecular bonds.

If the objects are not allowed to contract by some boundary conditions, they will break. Usually they are not constrained in that way.

Besides, what does it matter if there is just one string connecting the ships? Make it a gazillion of strings connecting the 2 ships (which effectively makes them one object). What happens to your paradox then?

The same. The front end would just need stronger rockets to satisfy the condition given in the scenario: string part keeps constant length in its initial rest frame. If that is given, the strings break.

It's a moot paradox, and that's the second in this category that I count authored by Bell.

So what is the other one that you didn't understand?

 

[DrGreg]

Spacie, please read this post which explains a misunderstanding over what "Lorentz contraction" means.

 

[Passionflower]

A lot of people take the easy way out and determine time is completely imaginary after hearing about relativity, but it still is a noun which makes it a person place or thing. Funny, how velocity isn't seen as being half part imaginary when learning d/t makes up its only parts, but then again velocity is a more concrete concept that we can view.

I think it is easier to see how real it is by explaining relativity with velocity. Say you had a magic car that could only be seen to travel at one constant speed. Well, if you are traveling quickly in the opposite direction how could it perform this "magic". Velocity is only distance and time, so then it would have to alter the time and distance you measure it's velocity with to achieve this goal.

Time can become literally a dimension. If space was a page on a flip book, then time would be the direction the pages flip on top the previous pages. Then the amount of time you expereince could be interpreted as how quickly the pages flip or how fast you move in that direction.(although, "fast" implies higher dimensional time, please insert more dimensions, lol). Then spacetime dilation can be seen as only space contraction in hyperspace if traveling in the "time direction" didn't require time. Then again gravity wells in GR still require gravity for balls to fall in warps in rubber sheets...

Your views about time are valid for coordinate time only, which is always identical to proper time in Galilean spacetimes. A given coordinate time is only identical to proper time for certain observers in Minkowski spacetimes, in general however proper time is not identical to coordinate time in Minkowski spacetime. Proper time, which is the time measured by a local clock, is not a dimension at all but instead the distance of a path between two events in four dimensions.

 

[harrylin]

Ok then I'll also sketch my understanding of these concepts:
- "time" is a measure for the progress of physical processes - it started out with counting days etc.
- "space" is the combination of length, width and height, which are all linear measures that correspond to a number of aligned atoms in a material.
- "spacetime" is a tool for identifying and calculating physical events. It indicates the relationship between measurements of "space" and "time".

 

[Spacie]

Spacie, please read this post which explains a misunderstanding over what "Lorentz contraction" means.

Thank you very much DrGreg for excellent explanation and illustration. It makes sense to me and it underlies the point that contraction happens only for the moving observer. Just as I thought.

Which means, dear A.T., that for the frame of the ships, the string does not break. It breaks for the A ship in the original Bell's paper (with ships B & C connected). Which means that majority vote should win: for observers B&C the string did not break (and they were closer and at rest in respect to it!) "It seemed that it should have broken", said a confused ofserver from the A ship, "happened so fast, it was hard to see " In the mean time, the B & C ships crew proudly held the intact string.

With this I put this godawful paradox to rest. Seriously, I think this paradox is moot, because it stands on the false premise: it treats ships B & C as separate frames. But they are moving in unison, which makes them one and the same frame. Which means that it does not matter if objects are connected with a string or just empty space between them. How much there got to be of that empty space in between 2 objects --or atoms-- for them to qualify as one object or 2 distinct ones? There is no answer to this question. What matters is that all the objects are at rest in their frame. => ships B, C and the string in between them is one object and transformation applies to it as a whole.

Besides... With my question comparing light and on sound in another thread going, the other day I had an epiphany that SR is about appearances. The object does not really contract under the Lorentz transformation. It only appears to have contracted for the moving observer.

 

[DrGreg]

Spacie, please read this post which explains a misunderstanding over what "Lorentz contraction" means.

Thank you very much DrGreg for excellent explanation and illustration. It makes sense to me and it underlies the point that contraction happens only for the moving observer. Just as I thought.

Which means, dear A.T., that for the frame of the ships, the string does not break.

...which means you haven't understood what I wrote at all. The string certainly does break, as any reliable textbook that discusses this will confirm. Go back and carefully read what I wrote again, and read the the rest of the thread it was in.

 

[John232]

I would invest in new textbooks, sorry. But, there are millions of objects that could be traveling close to the speed of light relative to Earth, that are in observerable range, and all our strings are staying together just fine...

Any theory of relativity should never alter our physical measurements just because it is traveling at a high relative speed. If it could be done, it could prove every science experiment ever done wrong. As long as we are at a close speed relative to Earth every experiment should come out with the same results regradless of being observered by someone at relativistic speeds.

 

[A.T.]

that for the frame of the ships, the string does not break.

It breaks in every frame. SR says that objects are longer in their rest frame than in a frame in which they move. So if an object keeps a constant length in a frame in which it accelerates (as given in this scenario), then it must increase in length in its rest frame (proper length).

it treats ships B & C as separate frames. But they are moving in unison,

Only in their initial rest frame, they are moving in unison. In the accelerating frame they are moving apart.

How much there got to be of that empty space in between 2 objects --or atoms-- for them to qualify as one object or 2 distinct ones?

It is irrelevant how you define your "objects". You can break a single object, if you enforce a constant length in a frame where it accelerates.

What matters is that all the objects are at rest in their frame. => ships B, C and the string in between them is one object and transformation applies to it as a whole.

And that transformation says that an object must elongate in it's rest frame, if it keeps a constant length in the frame where it accelerates.

The object does not really contract under the Lorentz transformation. It only appears to have contracted for the moving observer.

Without defining what "really" and "appears" is, this is a meaningless statement.

 

[A.T.]

I would invest in new textbooks

No need for that. You should invest more time trying to understand what they say.

But, there are millions of objects that could be traveling close to the speed of light relative to Earth, that are in observerable range, and all our strings are staying together just fine...

Each of "our strings" has different lengths in the rest frames of all those millions of objects moving relative to us at different speeds (along the string direction). But in Bell's scenario the string is forced to keep a constant length in a frame where its speed changes.

every experiment should come out with the same results regradless of being observered by someone at relativistic speeds.

Every frame will agree that the string breaks. Just for different "reasons".

 

[Spacie]

...which means you haven't understood what I wrote at all. The string certainly does break, as any reliable textbook that discusses this will confirm. Go back and carefully read what I wrote again, and read the the rest of the thread it was in.

Ok, I read the first 3 pages of that thread and stand my grounds. Sorry. I find the whole topic distasteful. You think otherwise and that is fine. Let an actual experiment decide.

It breaks in every frame. SR says that objects are longer in their rest frame than in a frame in which they move. So if an object keeps a constant length in a frame in which it accelerates (as given in this scenario), then it must increase in length in its rest frame (proper length).

SR says that objects appear shorter in a frame in which they move. In comparison with the frame where they are at rest. Everything shortens in the moving frame, objects and space that houses them.

Only in their initial rest frame, they are moving in unison. In the accelerating frame they are moving apart.

-? In the first 3 pages of that thread everyone agreed and it was stressed several times that the distance between ships stays the same, including during acceleration.

It is irrelevant how you define your "objects". You can break a single object, if you enforce a constant length in a frame where it accelerates.

I disagree. In my book, all objects that are at rest in respect to each other constitute the same frame. Otherwise, all objects should break all the time. IN REAL LIFE.

And that transformation says that an object must elongate in it's rest frame, if it keeps a constant length in the frame where it accelerates.

No it does not. It says that objects appear shorter when they move fast in respect to observer (to that observer only!).

Without defining what "really" and "appears" is, this is a meaningless statement.

Yes, I had an epiphany last week that SR is all about appearances, about how things are not what they seem, how the same thing will look different for various observers. That's because the speed of light is a constant and Lorentz transform will make things look shorter at high speeds; and gravity bends light, making an object appear in a wrong place; and no object may be seen moving faster than c, because you see only what light delivers and its speed is fixed. Basically, what it says is that you should not trust what you see, especially if you're moving fast in respect to what you're seeing. That's what I understood last week, and for this I thank this forum.

 

[A.T.]

SR says that objects appear shorter in a frame in which they move. In comparison with the frame where they are at rest.

They don't "appear" shorter. They are shorter.

In the first 3 pages of that thread everyone agreed and it was stressed several times that the distance between ships stays the same, including during acceleration.

The distance stays the same in the initial rest frame of the rockets. It does not stay the same in all frames.

That's because the speed of light is a constant and Lorentz transform will make things look shorter at high speeds; and gravity bends light, making an object appear in a wrong place

Wrong. It is not about how objects "look". In fact a fast moving object would not look contracted:
http://www.spacetimetravel.org/fussball/fussball.html

Length contraction is not what you see. It is what is left after you account for finite light speed to calculate the actual size of the object

That's what I understood last week, and for this I thank this forum.

Well, your understanding is completely wrong. So no need to say thanks.