My understanding of Space, Time and spacetime

[Spacie]

It sounded to me like you were stating that when a rod moves at a high rate of speed and contracts, that it causes a distortion in space (or the other way around). I disagreed and said there is no distortion of space and if there were, it would cause a measurable disturbance in the way light would travel through it.

But THERE IS a distortion of space (due to the motion of the observer). If there were none, the speed of light he would measure would vary in accordance with his speed. But the experiment shows that the speed of light propagating through empty space is a constant for all observers, regardless of their speed. This can happen only if 1. speed of light in empty space is a property of space itself, which makes it "a law of nature" and a constant. 2. space gets distorted by matter moving through it (it contracts in the direction of the movement with all objects contained in it contracting accordingly). To me it seems that it is you and not me or Halix who lacks true understanding and therefore is in danger of falling into heresy and sin against relativity.

 

[yoron]

Just a point. I find it meaningless to define 'time', even though I'm interested in it too. It's like a 'time dilation'. You have to fulfill a lot of prerequisites to prove it. I like to look at it as a 'clock' instead. And that 'clock' is, to my eyes, 'c'.

Anyway, you get a perfect harmony between what people experience locally, in any motion, relative what their neighbors expect them to experience as defined from their 'frame of reference'. And as 'gravity' dilates 'clocks', relative the observer, in much the same way as Einstein expected a uniform constant acceleration to do it?

And that helps me define what I call a 'frame of reference' too, I use the 'clocks', and where they will differ, for that. That we won't notice those differences doesn't mean that they aren't there. And from that definition I expect a Plank length to be the appropriate distance for any 'frame of reference' relative another. Although there are many other definitions of what 'frames of reference' should be seen as.

That makes 'c' as a constant slightly different to me, also a Plank time.
==

Eh, I do like to try to define time, but then I stumble away from relativity into Smolins world, strings and 'foams', and geometry.. Dar* In Einsteins definitions 'time' is a aspect of SpaceTime, and there it seems as pure geometry to me :)

 

[harrylin]

But THERE IS a distortion of space (due to the motion of the observer). If there were none, the speed of light he would measure would vary in accordance with his speed. But the experiment shows that the speed of light propagating through empty space is a constant for all observers, regardless of their speed. This can happen only if 1. speed of light in empty space is a property of space itself, which makes it "a law of nature" and a constant. 2. space gets distorted by matter moving through it (it contracts in the direction of the movement with all objects contained in it contracting accordingly). [..]

That's a misunderstanding, in fact the speed of light in SR situations can only be the same without distortion of space. The only model that works is one in which accelerating objects contract (or try to contract) in space - and measurements of distances in space with such objects and clocks are similarly affected. If you think that instead, "space" itself contracts with them, then you're in for Bell's Spaceship paradox (see the description in http://en.wikipedia.org/wiki/Bell's_spaceship_paradox).

 

[Spacie]

That's a misunderstanding, in fact the speed of light in SR situations can only be the same without distortion of space. The only model that works is one in which accelerating objects contract (or try to contract) in space - and measurements of distances in space with such objects and clocks are similarly affected. If you think that instead, "space" itself contracts with them, then you're in for Bell's Spaceship paradox (see the description in [PLAIN]http://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox[/URL]).

Thank you for your reference to Bell's Spaceship paradox. I see no paradox. The string should not break. That is because length contraction, first of all, affects the space and, by extension, everything it contains. In computer graphics it's called scaling and is considered elementary. Less graphically or geometrically-inclined people tend to focus on objects in space, which they tend to view as independent from space they are in, which may lead them to "get the wrong answer at first". The right answer is that the string will not break and that is because everything in that frame contracts, starting with space and ending with the string in it.

So, I'm afraid that the misunderstanding in this case is all yours. Please read on length contraction in http://en.wikipedia.org/wiki/Length_contraction

Length contraction was originally postulated to explain the negative outcome of the Michelson-Morley experiment, which in fact confirmed the invariance of the speed of light for all observers, regardless of their speed (yes, I am aware of the original interpretation of their experiment). This idea later on evolved to what is known today as Lorentz transformation that is at core of SR.

 

[harrylin]

Thank you for your reference to Bell's Spaceship paradox. I see no paradox. The string should not break. That is because length contraction, first of all, affects the space and, by extension, everything it contains. In computer graphics it's called scaling and is considered elementary. Less graphically or geometrically-inclined people tend to focus on objects in space, which they tend to view as independent from space they are in, which may lead them to "get the wrong answer at first". The right answer is that the string will not break and that is because everything in that frame contracts, starting with space and ending with the string in it. [..] Please read on length contraction [..]

Then you are aware that your idea does not fit with the consensus of how SR works.
Your assumption leads to a claim that is inconsistent, as different ways to solve the same problem lead to the contrary conclusion to what you state. However, that's a different topic on its own, to be discussed (and likely it already has) in a separate thread. And gwellsjr already sketched another, similar objection. In short, the way SR works doesn't match a space that is distorted by moving bodies. And I wrote a full paper in a mainstream physics journal on SR length contraction; you can read from me.

PS: You may also want to start the topic "Why is space not deformed by Lorentz contraction?".

Harald

 

[Spacie]

Then you are aware that your idea does not fit with the consensus of how SR works.
Your assumption leads to a claim that is inconsistent, as different ways to solve the same problem lead to the contrary conclusion to what you state. However, that's a different topic on its own, to be discussed (and likely it already has) in a separate thread. And gwellsjr already sketched another, similar objection. In short, the way SR works doesn't match a space that is distorted by moving bodies. And I wrote a full paper in a mainstream physics journal on SR length contraction; you can read from me.

PS: You may also want to start the topic "Why is space not deformed by Lorentz contraction?".

Harald

Why there should be the consensus on how SR works? The important thing is that my way of looking at things does not contradict the theory, helps me to understand it better, does not lead to false paradoxes or "a wrong answer at first".

What is the claim that is inconsistent, and inconsistent with what? And what is the contrary conclusion to what I state?

You seem more flexible on a neighboring thread:

The same thing can be "explained" in many ways, and it depends on your thinking which one you find most satisfying.

Some people like a more mathematical explanation (it's because of the invariance of c that lengths and times are measured differently at different speeds) or a more physical explanation (it's because speed affects the measurements of lengths and times in the right way that c is invariant). So what one person regards to be a consequence, another person will regard as cause - it's more of an interplay of phenomena that are consistent with each other.

Speed affects the measurements of lengths, you say. All the relevant lengths of all objects at once. It seems more logical and consistent to say that the space the objects are contained in is contracted, which affects all objects in it.

 

[A.T.]

It seems more logical and consistent to say that the space the objects are contained in is contracted, which affects all objects in it.

To me it seems more logical to say that space expands for moving objects, so the moving objects occupy less space, and therefore are measured contracted. This is more consistent with rotating reference frames, where space is non-Eculidean (more space around the circumference than 2*PI*R).

 

[Spacie]

To me it seems more logical to say that space expands for moving objects, so the moving objects occupy less space, and therefore are measured contracted. This is more consistent with rotating reference frames, where space is non-Eculidean (more space around the circumference than 2*PI*R).

Yeah but with your logic the string in Bell's Spaceship paradox will certainly break, no?

 

[Spacie]

I found this quote by HallsofIvy, who is PF Mentor with 31,611 posts:

One very fundamental distinction between Lorentz and Einstein was that Lorentz's theory only allowed for the contraction of physical objects in the direction of motion- which he saw as a "real" contraction caused by the increased magnetic pull of protons and electrons in that direction. Einstein's theory requires a contraction of the space between physical objects as well.

 

[harrylin]

[..]The important thing is that my way of looking at things does not contradict the theory, helps me to understand it better, does not lead to false paradoxes or "a wrong answer at first".
What is the claim that is inconsistent, and inconsistent with what? And what is the contrary conclusion to what I state? [..]

Your answer happens to be what Bell described as the "wrong answer at first" about his Spaceship example; and Wikipedia currently summarizes the consensus about it, which is that Bell was right on this, the string will be stressed and thus it can break.

I think that it's a very sensible rule of Physics Forums to not hijack a topic; as the topic of this thread is very general, I will respect that rule and not elaborate more on that inside this thread.
If you start a thread on the topic of space distortion, keep in mind the rule against "Overly Speculative Posts".

Harald

 

[harrylin]

I found this quote by HallsofIvy, who is PF Mentor with 31,611 posts:

I do not think that he meant it in the same way as you do (it's clearly again about another subject). On a side note of this side note, his argument still looks mistaken to me. It's a fact that even PF Mentors can make mistakes.

 

[A.T.]

To me it seems more logical to say that space expands for moving objects, so the moving objects occupy less space, and therefore are measured contracted. This is more consistent with rotating reference frames, where space is non-Eculidean (more space around the circumference than 2*PI*R).

Yeah but with your logic the string in Bell's Spaceship paradox will certainly break, no?

Yes, of course. Just like a rigid disc would break, if you spun it fast (Ehrenfest paradox).

 

[harrylin]

I do not think that he meant it in the same way as you do (it's clearly again about another subject). On a side note of this side note, his argument still looks mistaken to me. It's a fact that even PF Mentors can make mistakes.

PS. Spacie: you can ask HallsofIvy if he implied, as you do, that he disagrees with the standard solution of Bell's spaceship paradox. I bet that he does not; and I think that he's not even allowed, according to the rules.

 

[Spacie]

PS. Spacie: you can ask HallsofIvy if he implied, as you do, that he disagrees with the standard solution of Bell's spaceship paradox. I bet that he does not; and I think that he's not even allowed, according to the rules.

harrylin, frankly, I do not care for Bell's spaceship paradox, as I rarely care for these mental exercises. When someone makes an actual test of it, then I will be all ears. Until then, as far as Bell's spaceship paradox is concerned, I side with the consensus at CERN that Bell discovered in their informal discussions in canteen, and that was that the string should not break. Bell thought otherwise? Oh well... Let the actual experiment decide.

As far as SR, my understanding is the same as HallsofIvy, namely, that space does contract together with objects in it. That's the issue here. He expressed his opinion very clearly. Yours is different. Let us agree to disagree.

But what does empirical evidence say? Is there any?

 

[pervect]

Just a note: the published peer reviewed papers to date do NOT agree with the "informal coffee table consensus" reported by Bell. Bell's remarks about a consensus are also secondhand, i.e. hearsay.

Note however that not everyone who agrees with Bell's result agrees with his remarks about the implications of how to teach relativity.

So you're free to think what you want, but do realize that the mainstream position is that the string will break.

 

[A.T.]

I do not care for Bell's spaceship paradox, as I rarely care for these mental exercises. When someone makes an actual test of it, then I will be all ears.

You are confusing two different questions here:
- Will the string break in reality?
- Does SR predict that it will break?
The later can be answered without any tests, and the answer is yes.

Think of it this way: In the initial rest frame all the atoms in the string and the fields that hold them together are contracting, so they cannot fill the constant distance between the rockets anymore.

In more intuitive terms you can replace the string with a chain, and consider the individual chain links as elements, which are all contracting as the chain accelerates:

At some point they cannot contract further, without breaking.

 

[Spacie]

Thank you pervect for the info. I'll keep in mind that I my opinion on this paradox differs from both Bell and mainstream. As for alleged hearsay about CERN informal consensus, Bell tells it firsthand in his own words in his How to teach special relativity.Thank you for the picture, A.T. To me it does not look right. If anything, the length contraction should push the atoms closer together, rather than drive them apart by shrinking them in the same points in space. Besides, on the picture the overall length stays the same as before "contraction", only atoms shrink. Where is contraction of the object?

 

[John232]

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...

 

[A.T.]

Thank you for the picture, A.T. To me it does not look right. If anything, the length contraction should push the atoms closer together, rather than drive them apart by shrinking

"Contraction" itself doesn't mean "pushing" or "moving them closer". It means scaling them along one dimension, and that includes the fields that cause the bonding between them, and effectively determine the size of atoms. So if they were free to move closer together, the contracted field would move them closer together. But they cannot reduce their overall length in this scenario.

Besides, on the picture the overall length stays the same as before "contraction",

Yes. That's the scenario in Bells spaceship paradox. The distance between the rockets spanned by the chain is constant in the initial rest frame of the rockets.

Where is contraction of the object?

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.

That's the given scenario. If you think the chain won't break, then try to draw a picture of the chain moving at 0.99c in the initial rest frame, when the chain links are contracted even more than in the second picture. And keep in mind that the rockets still have the same distance in that frame.

 

[A.T.]

Then again gravity wells in GR still require gravity for balls to fall in warps in rubber sheets...

No they don't. That is just a very popular, but completely wrong analogy of how GR works. There are many threads here discussing this misleading visualization.

 

[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".