Concerns about ontological interpetations of Theory of Relativity

[JesseM]

Sure, there is no empirical reason to favor one definition over another, but my point should still hold; if you accept the second postulate as part of reality, you must accept the full impact it has on reality. It makes no difference what it looks like on various paper abstractions of reality, or that the observer can interpetate the reality from any given inertial coordination if he so wishes.

You are still completely misunderstanding the second postulate. It only says that if you construct coordinate systems in the way Einstein specified in part 1 of his 1905 paper--using a system of measuring-rods and clocks which are all moving inertially and at rest relative to each other, and with all the clocks synchronized using Einstein's clock synchronization convention--then you will find that the laws of physics obey the same equations in each of these coordinate systems (the first postulate), and that the speed of light is the same in all these coordinate systems (the second postulate). There is nothing in these postulates that says you must use such a coordinate system, and there is nothing in them that says light cannot move at a velocity other than c in whichever coordinate system you use. It's a simple if-then statement, saying that if you use the type of coordinate system he describes in part 1, then the two postulates should hold (the two postulates are described at the beginning of part 2 of that paper).

I mean Lorentz-contraction too is something that cannot be directly observed and is brought fourth by the exact same mechanic; relativity of simultaneity. Yet it is thought to be something that happens in real world, because the second postulate necessitates it.*

Nope, Lorentz contraction also depends on your coordinate system, and there is nothing that says you can't use a coordinate system where it works differently. Relativity only says that if you construct inertial coordinate systems in the way Einstein describes using his clock synchronization convention, then Lorentz contraction will obey the equation l = L \sqrt{1 - v^2/c^2}.

And the full effect of the simultaneity planes onto the experience of reality for an observer must be taken into account in the twin paradox too.

Nope, the twin paradox can be analyzed in any coordinate system you like, and provided you have the correct form for the equations of physics in that coordinate system, you will get the correct answer. And note that even if you use the inertial coordinate systems which are normally used in SR, there is no need to think about "tilting planes of simultaneity" or anything like that, because the usual approach is to pick a single coordinate system, and to say that if a given clock's velocity as a function of time in that coordinate system is v(t), then between the time t_0 when the clocks depart each other and the time t_1 when they reunite, that clock should have elapsed \int_{t_0}^{t_1} \sqrt{1 - v(t)^2/c^2} \, dt. No matter which inertial frame you pick, this will give the correct answer for how much time each clock has elapsed between the time they depart and reunite, and you will always find that the clock that moved non-inertially elapsed less time than the one that moved inertially. No need to switch between different frames, or consider different definitions of simultaneity, at all (see the spacetime diagram explanation from the twin paradox FAQ).

Yet when I describle how the second postulate leads into "events occurring backwards" the point of view of one observer, I find it quite odd that suddenly there is this denial about the reality of this; suddenly the relativity of simultaneity is just some sort of abstraction. Well, I say if one denies this, he must also deny all the other effects of relativity of simultaneity, like Lorentz-contraction.

No one is denying them, just pointing out that they are coordinate-dependent, and the first and second postulates only say that if you construct your coordinate systems in a certain way then you will see Lorentz-contraction and simultaneity work a certain way.

*Although I still don't understand how to solve the problems that arise from the asymmetric nature of Lorentz-contraction; the plane of simultaneity tilts only for the observer that actually changes direction from "rest". Since the observers has volume, the plane of simultaneity should tilt separately for every physical element of the observer, causing him to stretch by the same amount that the other observer contracts. The information in the bell-paradox page didn't really explain how to solve this, so I guess I'll start another thread about it soon...

There is no problem with Lorentz contraction if you pick a single inertial coordinate system and stick with it. Your confusion arises because you imagine Lorentz contraction would work the same way in some sort of non-inertial coordinate system which moved along with an accelerating observer, which is simply not true.

 

[pervect]

Assuming:
- Every event happens at some actual moment
- We can figure out the moment by knowing our distance to the event when it happened and the speed of light
- The notion of time is the same for every co-moving observer, regardless of the history if their world lines.
- Special Relativity holds true

I haven't had time to study this closely, but I have my doubts that all of the above can be true. For instance, in the Rindler metric of an accelerated observer, not every event in space-time has a coordinate, which is my interpretation of what you mean when you say "happens at some actual moment".

One can certainly come up with other coordinate systems in which every event does have a coordinate. But when one selects such a coordinate system, the notion that "the time coordinate is the same as that of a co-moving observer" is no longer true.

I was thinking about this some more, and I noticed that I was requiring every event to have unique coordinates, while you did not necessarily make that assumption (what I called coordinates you called by a different name, so your entities do not necessarily have all the properties that my coordinate-entities do).

If we relax the requirements that coordinates be unique, I think your approach could work, unless there is some other obstacle that I haven't noticed.

What I don't like about your approach is that it incoroporates obsever-dependent quantities into "reality".

Note also that your philosophical approach is not required - it's just one way of thinking about things. (That's a general category of any sort of philosophy - as long as it's self-consistent, it generally doesn't matter).

If you don't like some elements or conseqences of your philosphical assumptions, there are alternatives. I hope I have sketched out enough information to allow you to explore at least some of them. Basically, an alternate approach and the one I use is to get rid of the idea of "simultaneity" as being a part of "reality" and put it in the category of "observer dependent quantities".

 

[Longstreet]

This whole post is just opinion. It's not scientific at all. You can see that for yourself but this is just so you don't make ten posts about how unscientific I'm being; so save your fingers.

I actually argue that nothing is “real”. For instance, trees don't exist. A tree is simply a construct we have come up with to help us remember where to get oranges or apples or go to keep from getting eaten by a lion. The universe doesn't know what a tree is. Atoms will just go where they will and don't care about whether they are part of a tree. And of course I have to relate a tree with other things like apples and atoms and being able to climb them, but those are also simply constructs we have come up with to cope with reality. Ok, but enough of that, time to talk about these constructs.

I think one of the main things is the non-inertial reference frames you are trying to avoid, and this is true even without special relativity. Say you have an inertial reference frame and an object takes a curved path, say from some force. You can make a new coordinate system where the object is stationary the entire time, or in it's own "inertial" reference frame. However, this has some strange properties. The new coordinate system fixes everything by bending the paths of everything else by applying fictional forces. In classical physics this is not a problem because we can simply define "the" coordinate system where our lines are all nice and straight and apply forces that don't seemingly spring out of no-where. Unless of course we're just masochists and really like doing that.

First off I am really not familiar with GR at all. I pretty much know what assumptions you can and can't make. However, I think the main problem here is that since we can't have “the” universal coordinate system, we run into major problems when things start taking curved paths.

If I may, when you run away from the clocks the light signal looks like it's being bent. So not only do you worry about light going at the speed of light, but it seems to have to travel farther as it takes this weird path that you didn't expect. I think this is resulting in the whole light “line” getting shifted back at the source when you crunch your acceleration into a point, which makes it seem like something *really* funky is happening. I am having a hard time understanding your diagrams though so I'm only guessing.

On the another issue, however, I think Einstein held the belief that the universe had “a” state whether or not we were observing it. This is pretty evident as he trys to combat the “Copenhagen Interpretation”, such as with the EPR paradox. This thread is about relativity, I know, but that goes to the question of what reality is from Einstein's point of view.

Thanks,

 

[mitchellmckain]

On the another issue, however, I think Einstein held the belief that the universe had “a” state whether or not we were observing it. This is pretty evident as he trys to combat the “Copenhagen Interpretation”, such as with the EPR paradox. This thread is about relativity, I know, but that goes to the question of what reality is from Einstein's point of view.

This is off topic, but I already opened it above myself. Your understanding of the Copenhagen interpretation is coming from its detractors and is certainly not how it is expessed today. Accordingly, the universe has a state whether it is observed or not, but it is a quantum state (consisting of a wave function) not a classical state (consisting of positions and velocities of point particles). Bohr may have said at one time that reality was created by the act of observation but this was an unfortunate way of expressing only that the measuring process creates the result of the measurement. The measuring process alters the quantum state of what you are measuring to a state which is consistent with the result of the measurement. But that does not mean that reality has no definite state before the measuring process but only that this definite quantum state does not necessarily have a definite value for classical quantities such as position or velocity.

 

[AnssiH]

I think that I have to clarify that from my point of view "the plane of simultaneity for any given observer describes the map of the actual state of the real world around the observer at that moment".

I do not know if this just a difference of semantics for your point of you, but I think it is more than that.

Yeah, it is more than semantics. Although I have explored different approaches during this thread. One has been that the actual state of the world exists, and changes the way that is evident from the planes of simultaneity. And another has been that there is a kind of "physical" detachment between different inertial coordination systems, which falls close to planes of simultaneity merely describing a "map of reality"

We have to abandon our firm conviction that science is a methodology that provides the knowledge of the actual state of reality. Science is a methodology that provides information of the actual state of reality

Yeah, that's how it would seem regarding SR, although I am a bit uncomfortable with this. I feel a strong need to really find out the actual mechanic of things, and I am not happy with merely coming up with the right numbers. And I do believe that we, mere humans, are actually able to understand the real mechanics of the universe, all the way from the most fundamental interaction(s).

Even in classical physics the planes of simultaneity are different for two observers, and the results of physical measurements of events of real world are becoming equal only if the positions of the two observers are normalized according to a common reference system.

I'm not sure what you mean by this, but let it be said that it is the postulate, that the speed of light is "attached" to each perceiver, which is what causes the relativity of simultaneity. That is, if the speed of light was attached to something that is absolute for everyone, like the source of the light, then the notion of simultaneity would be absolute (albeit the natural perceptions of the observers would be just as non-simultaneous as in SR)

SR explains the paradox of subjective world around us in the sense that we are being informed, or not being informed, about the real events of the world by physical messengers who travel in a finite velocity. Therefore some messengers do arrive at our space-time position and others fail to arrive at our space-time position. The failure of arriving in our position is not a failure of reality; reality exists in the most objective way. The failure of the messenger to carry the information in our position is generated from our inability to stay in an absolute immobile position of space-time. The messenger always travels towards our position but we never stay still; we are the ones that move backwards and forward, not the events of reality of things.

This is very interesting, and this is just the kind of dialogue I would hope I see more. There's just this lack of desire to explain these things, perhaps due to most people having a purely technical point of view to SR.

That stuff you wrote immediately suggests something about the ontological nature of SR, which the time block view or timespace diagrams don't. Very good.

If we accept that view, it also tells us something about, say, Lorentz-contraction. In that view, Lorentz-contraction exists only in the imaginary "map of the actual state of reality", until the information of fast-moving objects actually reaches us so to "manifestate" the contraction as reality (although the visual image of Lorentz-contracted ship might not LOOK contracted, but that's another issue altogether)

And in that view it would be just as WRONG to say that "when a ship accelerates, it contracts", as it would be to say "when you accelerete away from things, their time slows down, possibly to the point of them moving backwards". Yet we hear about the contracting ships all the time.

Unfortunately, scientific methodology does not produce ontological data.

This made me wonder if theory of relativity and quantum mechanics are the only scientific theories that do NOT produce ontological data? Are there other such theories? Like the evolution theory, that tells us exactly what happens in the actuality of the world, and it immediately has a very clear ontological meaning.

 

[AnssiH]

It still bothers me that other effects of relativity of simultaneity, such as Lorentz-contraction, are still interpetated to be "real" for the worldline of an observer. I don't know what criteria for picking and choosing we could use here.

Well it just goes to show that the word "real" is pretty ambiguous and we really need to invent more precise word to describe these things.

You are so very right about that. I think it is one major part of the problem in the discussion of these things, that words like "reality" and someones "perspective" become very ambiguous in SR.

There's a three kinds of "reality" in this discussion.

One is the kind of block time view reality, objective data, not attached to an observer per se.

Another is the reality that an observer perceives with his senses.

And then there's the intermediate reality between these. The fuzzy "present" region for each observer. I would think this reality too must describe a single "state" for everything per each moment, even if it were permitted that some object could enter the same state multiple times.

It makes more sense to me, to change our understanding of past, present and future to fit the Minkowsky structure of space-time like this:

\.future./
.\.../
p.\.../.p
r..\.../..r
e...\../...e
s...\/...s
e.../\...e
n.../..\...n
t../...\..t
./...\
/..past..\

Where the simultaneous present extends to all regions of space-time which are not causally connected to our present moment. Then these divisions of past, present and future will remain completely unchanged by any change in velocity or inertial frame.

Yeah, that is all very well, and that's the way I think about it too, or more to the point, the way I think about the technical side of it.

But it does leave completely unexplained, what IS occurring in the "present" region. Of course it tells us how to treat it technically so to "come up with the right numbers", but it doesn't say what is its meaning to the world around us. And that is the topic of this thread. I.e. should we think that ALL the events in the "present" region exist at the same time, or that only some set of events exist, as a subject to the inertial coordination system of an observer, or something else?

As crazy as special relativity sounds to the non-scientist it makes perfect sense to the scientist

It makes perfect sense to me too, at least logically, and I had already accepted that SR means things move through my notion of time in my perspective just like I described, until the idea was shot down in this thread, without offering much of an alternative. I mean it is not an alternative to offer "this is what it looks like in block time view" or in Minkowski spacetime. Minkowski spacetime is what implied to me to my own conclusions in the first place. My conclusions are sitting on the technical descriptions, and they don't change by describing the same raw logics differently.

And I'm thinking part of the reluctance to talk about these things occur because we simply don't know what is going on ontologically. It gives us comfort to think that at least we have the numbers, but it is a grave injustice to science to just decide "we can never find out and there's no point to even ask the question". Call me old-fashioned, but I do think every phenomenon we can perceive has a solid explanation that tells us exactly what is going on around us, and a sheet of paper with a spacetime diagram on it apparently doesn't do this.

btw, about the "truly astronomical energies to accelerate that fast", you don't really need much energy at all since this same thing should occur every time you change direction at all

I do not understand what you are saying.

I'm saying that you need the astronomical energies ONLY if you wish to have the plane of simultaneity to cross its history at a very close distance to you, but if it suffices that it crosses 1000 lightyears from here, the needed acceleration is not that strong. And the effect should be technically the same regardless of if it happens three meters from you, or in another galaxy.

I mean if you imagine a virtual reality program that is showing how the Lorentz-contraction occurs from a clairvoyant point of view (well, you kind of have to have a clairvoyant view), this same VR progam would necessarily display events occurring in backwards manner.

This is no idle question for me since I am writing just such a program as you have seen. But it does not yet have the capability you are suggesting.

I urge, I urge you to please make a program that demonstrates Lorentz-contraction. :)

You will have to make a decision about the ontological nature of the "present" region.

Since you are demonstrating Lorentz-contraction, which is not a "visual illusion" but a description of the actual "unseen" state of the universe, you WILL have to make such an ontological decision that you will display the very state that the planes of simultaneity describe, through a clairvoyant view.

And having made that decision, it immediately leads into a system where you must potentially display the "actual" states of the world moving "backwards". (Especially if you amplify the effect by slowing down C)

Also, if you consider having a VR environment where more than one person can navigate around, you will notive such a system cannot be implemented at all. Because when these persons are trying to see how both of them Lorentz-contract when they are approaching each others, you must also display the actual FUTURE state of each person, which obviously you cannot know, since the doings of the real persons cannot be deterministic. (Although they can be in the real world)

The trouble is that it has objects which move freely under the influence of gravity and is constantly integrating their motion.

Yeah, I think to display Lorentz-contraction, you should probably stick with SR, and omit gravity from the equation altogether. Just have objects that can move around, and perhaps have little clocks attached to different parts of each object to display how Lorentz-contraction is, in fact, merely about time.

But physicists do not believe in clairavoyance

Obviously not, but it seems like it's a good word to communicate when one is talking about the actual state of the "present" region per observer, instead of the visual perceptions or of the whole present region in the spacetime diagram. So thanks :)

It is like being backed into a corner only to have to corner vanish from beneath their feet. From there they can either accept the downfall of determinism, reject either quantum physics or special relativity, or refuse to think about the nature of reality at all. I am in the first category and most physicists are in the last category.

Yeah, exactly so. And I think it is kind of wrong to refuse to think about the nature of reality for a physicist. Even if one has to say "I don't know", it's still better to at least try to find out. And if one doesn't care, he is always running the risk of getting a completely wrong idea about something and so eventually coming to a dead end in his theory.

Since you work on virtual worlds, you are probably painfully aware, how there always exists multiple technical mechanics to achieve the exact same end result. But still only one of these radically different mechanics is similar to what is occurring in the real world. So if you are just to stare at the numbers, you will never be able to tell what the actual mechanic is that spawns these numbers -> you could never make any meaningful progress.

As for me, I'm not sure if I belong to any of the three categories. When I'm backed to a corner in that way, it really pains me that I don't seem to have the true knowledge of the system (universe). And then when I start thinking, and I am willing to unlearn; back up on my path of learning as far as seems necessary to solve the issue. I am willing to backstep so far as to reject SR, if that's necessary. But I don't know if it is, and removing SR from the scientific worldview also pretty much means building the whole worldview again from scratch. Not for the weak at heart! :O

So let it be said I am not particularly glad about the concerns I am raising... I would be sleeping better at nights if I really grasped the ontological meaning of SR, but it is starting to seem this is impossible. If it was possible, someone would have done it, and I would know about it, I think.

 

[AnssiH]

Nope, Lorentz contraction also depends on your coordinate system, and there is nothing that says you can't use a coordinate system where it works differently.

I seem to have a lot of trouble interpetating your points correctly. That could be my failure.

I don't understand what you mean by "nothing says you can't use a coordinate system where it works differently". Are you saying, that everything I've ever heard of Lorentz-contraction is simply not true? That one could just decide it doesn't happen, or happens completely differently, by simply choosing a different coordinate system for himself? How can I interpetate the ontological meaning of such statement? How can we just "choose" what happens out there? I must be totally missing your point here.

Nope, the twin paradox can be analyzed in any coordinate system you like, and provided you have the correct form for the equations of physics in that coordinate system, you will get the correct answer.

Yes of course. But regardless of the technical method you solve it with, the reality is still that the other twin aged more. And it can be said, that the critical moment is the turnaround phase during which the plane of simultaneity, which is attached to the turning twin, does tilt.

This has an ontological meaning to the state of the "earth" from the point of view of the spacetwin (what is it?), and that meaning is the same for each different technical method to solve it. The ontological meaning doesn't change even if you change the math expression of the same thing.

Yet when I describle how the second postulate leads into "events occurring backwards" the point of view of one observer, I find it quite odd that suddenly there is this denial about the reality of this; suddenly the relativity of simultaneity is just some sort of abstraction. Well, I say if one denies this, he must also deny all the other effects of relativity of simultaneity, like Lorentz-contraction.

No one is denying them, just pointing out that they are coordinate-dependent, and the first and second postulates only say that if you construct your coordinate systems in a certain way then you will see Lorentz-contraction and simultaneity work a certain way. There is no problem with Lorentz contraction if you pick a single inertial coordinate system and stick with it. Your confusion arises because you imagine Lorentz contraction would work the same way in some sort of non-inertial coordinate system which moved along with an accelerating observer, which is simply not true.

I am not assuming an accelerating inertial coordination system at any point. This is very interesting though, I mean I know you are pointing out things are coordinate dependent in SR, to which I point out that an observer actually does exist in a coordination system so it cannot be said that the whole "present" region surrounds him at each moment, for example.

And everything you point out is something I agree completely, but I am kind of wishing there was a comment made about what do you think the world around you is like right now? You cannot just say that you are surrounded by a "block time", without adding some words about what is the actual meaning of such statement?

For example, do you believe, that right now, there is information approaching you steadily from your monitor? Do you think the monitor is in certain state right NOW (as oppose to all the possible states it could be in the "present" region), which you will perceive a short moment later? And if you do, then what do you reckon would have happened to that state, had you accelerated rapidly to another intertial coordination system, say, receding from the monitor?

 

[AnssiH]

I was thinking about this some more, and I noticed that I was requiring every event to have unique coordinates, while you did not necessarily make that assumption

Well yeah, I'm not sure. I think it kind of depends on the technical way to interpetate SR. I think we can attach unique 4D spacetime coordinate for each event, if we then just let different observers "read" the event from different locations. If we say that the plane of simultaneity of each observer is simply "reading" the data of the spacetime, then each event still has single unique coordinates, while a single observer could read the same coordinates multiple times. (Of course in this case, each state of a beam of light on its way towards the observer is also static information that can be read multiple times, and so multiple readings don't mean multiple signals sent to observer)

Anyhow, that's just another technical way to look at SR, it doesn't necessarily say anything about the ontological nature of it.

If we relax the requirements that coordinates be unique, I think your approach could work, unless there is some other obstacle that I haven't noticed.

Well it's the only approach I have been able to make work all the way. Could be I am missing something as well.

What I don't like about your approach is that it incoroporates obsever-dependent quantities into "reality".

Yeah, that's exactly the concern I am having, I'm glad you noticed it. It is kind of backwards logics, and that's not good at all. But then I would like to point out, that the technical, raw logic of Lorentz-transformation is backward in the same way, and that's what we are basically using to describe the effects of SR, like length-contraction.

If you don't like some elements or conseqences of your philosphical assumptions, there are alternatives. I hope I have sketched out enough information to allow you to explore at least some of them.

Yeah, I think you have. Thanks. I'd hope people were talking about these issues more in general. I think some interesting ideas might arise.

 

[AnssiH]

Say you have an inertial reference frame and an object takes a curved path, say from some force. You can make a new coordinate system where the object is stationary the entire time, or in it's own "inertial" reference frame. However, this has some strange properties.

Yeah, I don't think that's a good way to do things. Objects that move along curved path don't see the light rays moving straight, that should tell them they are absolutely curving or rotating. We cannot just attach a rotating frame on a spinning disk and expect everything else in the universe to behave physically correctly in this rotating frame.

First off I am really not familiar with GR at all. I pretty much know what assumptions you can and can't make. However, I think the main problem here is that since we can't have “the” universal coordinate system, we run into major problems when things start taking curved paths.

If I may, when you run away from the clocks the light signal looks like it's being bent.

Well, in the original pictures I had not included any acceleration at all, since it just tends to confuse people. The acceleration was instant. And in those examples, we can make that assumption, because I was not describing what happens while someone is accelerating, at all. I was just describing someone who is in one inertial coordination system, to move to another inertial coordination system.

In the last thought experiment, I added a little curve there, just to show that the object could accelerate from one direction to another, without interfering with how the planes of simultaneity are thought to behave in the inertial coordination system.

It's not like there's some kind of momentary "problem" during the change of direction, but this issue actually exists for quite a time while the object is moving uniformly. (The straight lines are uniform motion, not acceleration)

On the another issue, however, I think Einstein held the belief that the universe had “a” state whether or not we were observing it. This is pretty evident as he trys to combat the “Copenhagen Interpretation”, such as with the EPR paradox. This thread is about relativity, I know, but that goes to the question of what reality is from Einstein's point of view.

Yeah, I would agree, that's pretty much how I've understood Einstein's writings. And there are other examples. For example, he participated in the discussion about rotating disk paradox, when physicists started to consider Lorentz-contraction as some kind of optical illusion, so to get rid of the problem of the spokes not contracting. Einstein thought this was pretty serious misunderstanding (and so would I!) and made a comment on the problem.

http://freeweb.supereva.com/solciclos/gron_d.pdf
page 5:

In February 1911 V.Varićak claimed that according to Einstein’s theory the Lorentz contraction is a sort of observational illusion, and that in reality bodies are not contracted when moving. He thus concluded that there is no paradox. Einstein considered this misinterpretation of the theory of relativity to be rather serious and therefore gave an answer where he explained the relativistic meaning of the Lorentz contraction.

 

[JesseM]

Nope, Lorentz contraction also depends on your coordinate system, and there is nothing that says you can't use a coordinate system where it works differently.

I seem to have a lot of trouble interpetating your points correctly. That could be my failure.

I don't understand what you mean by "nothing says you can't use a coordinate system where it works differently". Are you saying, that everything I've ever heard of Lorentz-contraction is simply not true? That one could just decide it doesn't happen, or happens completely differently, by simply choosing a different coordinate system for himself? How can I interpetate the ontological meaning of such statement? How can we just "choose" what happens out there? I must be totally missing your point here.

It's not a question of whether it "happens" or "doesn't happen", it's a question of whether the laws of physics are such that it would happen if you chose to use the type of inertial coordinate system described by Einstein. No matter what coordinate system you use, it should be easy enough to figure out how your coordinate system maps to an inertial coordinate system of the type he describes (just figure out how a set of physical clocks and rulers moving inertially as Einstein described would behave in your chosen coordinate system), and to check and make sure that the laws of physics as you see them would obey the two postulates of SR when mapped into any such inertial coordinate system. As long as they would, then SR is correct in your universe, it doesn't depend on whether you actually choose to describe the universe and the laws of physics in terms of such an inertial coordinate system.

Nope, the twin paradox can be analyzed in any coordinate system you like, and provided you have the correct form for the equations of physics in that coordinate system, you will get the correct answer.

Yes of course. But regardless of the technical method you solve it with, the reality is still that the other twin aged more. And it can be said, that the critical moment is the turnaround phase during which the plane of simultaneity, which is attached to the turning twin, does tilt.

But I don't see why you think it's important to analyze it in terms of how simultaneity in the accelerating twin's own instantaneous inertial rest frame would shift. Like I said, the normal procedure would not be to try to figure out how things look from the accelerating twin's "point of view" in the first place, but just to figure out how everything looks in an inertial frame.

As an analogy, say you have two paths through 2D space which meet at two points, and one path is a straight line between the two points while the other has a curve in it, just like the spacetime diagram of the two twins in the twin paradox. You want to figure out the length of the two paths, and you can do so by drawing an x and a y axis, figuring out the equation for the slope of each path as a function of the x-coordinate, S(x), and then evaluating the integral \int_{x_0}^{x_1} \sqrt{1 + S(x)^2 } \, dx between the endpoints of the path x_0 and x_1, which unless I'm mistaken should give the total length of each path (note that for a small section of the path where the horizontal change is dx and the vertical change is dy, the slope will be S=dy/dx which means dy=Sdx, and the length of that small section will be \sqrt{dx^2 + dy^2} = \sqrt{dx^2 + S^2 dx^2} = dx \sqrt{1 + S^2}). Of course you will find that the straight-line path between the two points is always shorter than the non-straight path; that's just simple geometry. Now, if you liked you could associate each point on the non-straight path with a coordinate system where the x-axis was exactly parallel to the path at that point, and you could point out how along the section of the path that's curved, the y-axis of the coordinate system associated with each point is changing its angle. But would this really be the best or clearest way to understand why the non-straight path is always longer than straight path? Doesn't it make more sense to pick a single coordinate system to use to find the length of both paths, or just to point out that the geometry of 2D space is such that a straight line is always a geodesic and will thus be the shortest possible path between two points?

This has an ontological meaning to the state of the "earth" from the point of view of the spacetwin (what is it?)

No it doesn't. There is no ontological reason why you must consider the traveling twin's "point of view" to involve a series of inertial coordinate systems in which he is instantaneously at rest and which all use Einstein's clock synchronization convention. Even if you want to consider the traveling twin's "point of view" here as involving a series of inertial frames where he's instantaneously at rest, you could equally well consider a series of inertial coordinate systems which use a clock synchronization convention that insures they all agree about simultaneity, which would mean you'd use the transformation derived by Mansouri and Sexl to transform between these coordinate systems.

The ontological meaning doesn't change even if you change the math expression of the same thing.

In relativity the only facts that are considered truly "physical", which is perhaps close to what you mean by "ontological", are facts that don't change in different coordinate systems, such as the proper time along a particular path (the time as measured by a clock moving along that path). But the way the Earth clocks behave from the traveling twin's point of view is not such a physical fact, because it depends entirely on what non-inertial coordinate system the traveling twin chooses to use. There simply is no physical fact about this question, any more than there's a physical fact about my x-coordinate at a particular time. And unless you believe that some coordinate system is "metaphysically preferred" despite the fact that it's not physically preferred, then there should be no ontological fact about this either.

No one is denying them, just pointing out that they are coordinate-dependent, and the first and second postulates only say that if you construct your coordinate systems in a certain way then you will see Lorentz-contraction and simultaneity work a certain way. There is no problem with Lorentz contraction if you pick a single inertial coordinate system and stick with it. Your confusion arises because you imagine Lorentz contraction would work the same way in some sort of non-inertial coordinate system which moved along with an accelerating observer, which is simply not true.

I am not assuming an accelerating inertial coordination system at any point.

"accelerating inertial coordinate system" is an oxymoron. You are assuming a non-inertial coordinate system, because you are considering what things look like from the accelerating twin's "point of view". Even if you choose to just imagine what things look like in a series of inertial coordinate systems in which he is instantaneously at rest, if you stitch these observations from different inertial coordinate systems together and say, for example, that earth-clocks tick forward very fast as he accelerates, then you have created a de facto non-inertial coordinate system.

This is very interesting though, I mean I know you are pointing out things are coordinate dependent in SR, to which I point out that an observer actually does exist in a coordination system

I guarantee you that any physicist would say that the idea that "an observer actually does exist in a coordinate system" is completely meaningless, that there is no physical reason that a given observer should be uniquely associated with a particular choice of coordinate system, associating observers with coordinate systems is wholly a matter of convenience or aesthetics. Your belief that some coordinate systems represents the "truth" about that observer's "point of view" in an ontological sense is wholly idiosyncratic to you, it is not part of SR as any physicists understand it, and you have provided no physical argument as to why this belief makes any sense.

And everything you point out is something I agree completely, but I am kind of wishing there was a comment made about what do you think the world around you is like right now? You cannot just say that you are surrounded by a "block time", without adding some words about what is the actual meaning of such statement?

OK, it means there are events at various spacetime distances from me, and at different spacetime distances from each other, on the 4D manifold of spacetime.

For example, do you believe, that right now, there is information approaching you steadily from your monitor? Do you think the monitor is in certain state right NOW (as oppose to all the possible states it could be in the "present" region), which you will perceive a short moment later?

Not if "right NOW" is assumed to mean there is some unique ontological truth about a "present moment" associated with me, as opposed to just meaning something about the current time-coordinate in an arbitrary choice of coordinate system. If I draw two lines on a piece of paper and pick a point on one, do you think there is a unique ontological truth about how far the other line is from that point in the "horizontal" direction, one that does not depend on an arbitrary choice of how I orient my horizontal x-axis and vertical y-axis?

 

[Longstreet]

This is off topic, but I already opened it above myself. Your understanding of the Copenhagen interpretation is coming from its detractors and is certainly not how it is expessed today. Accordingly, the universe has a state whether it is observed or not, but it is a quantum state (consisting of a wave function) not a classical state (consisting of positions and velocities of point particles). Bohr may have said at one time that reality was created by the act of observation but this was an unfortunate way of expressing only that the measuring process creates the result of the measurement. The measuring process alters the quantum state of what you are measuring to a state which is consistent with the result of the measurement. But that does not mean that reality has no definite state before the measuring process but only that this definite quantum state does not necessarily have a definite value for classical quantities such as position or velocity.

Probably because I'm talking about Einstein's view, and Einstein very much detracted from the idea; I don't think a "quantum state" is quite what he had in mind for the universe. I'd say more but I don't want to get any further off topic.

 

[AnssiH]

But I don't see why you think it's important to analyze it in terms of how simultaneity in the accelerating twin's own instantaneous inertial rest frame would shift.

It isn't, and I'm actually omitting the acceleration from the equation altogether. I'm analyzing the situation by the terms of SR entirely. (Of course instantaneous acceleration is non-physical, but this approach does still keep the essential element of SR intact; the relativity of simultaneity)

As an analogy, say you have two paths through 2D space which meet at two points, and one path is a straight line between the two points while the other has a curve in it, just like the spacetime diagram of the two twins in the twin paradox. You want to figure out the length of the two paths...

...

...Of course you will find that the straight-line path between the two points is always shorter than the non-straight path; that's just simple geometry. Now, if you liked you could associate each point on the non-straight path with a coordinate system where the x-axis was exactly parallel to the path at that point, and you could point out how along the section of the path that's curved, the y-axis of the coordinate system associated with each point is changing its angle. But would this really be the best or clearest way to understand why the non-straight path is always longer than straight path? Doesn't it make more sense to pick a single coordinate system to use to find the length of both paths, or just to point out that the geometry of 2D space is such that a straight line is always a geodesic and will thus be the shortest possible path between two points?

No, it does not make more sense actually, since the other path being longer has nothing to do with why the other twin ages more and the other one less in SR. I can't see any reason why I would be interested of the length of the paths on the paper. In fact the twin who moves along the longer path, ages less.

Even if you want to consider the traveling twin's "point of view" here as involving a series of inertial frames where he's instantaneously at rest, you could equally well consider a series of inertial coordinate systems which use a clock synchronization convention that insures they all agree about simultaneity, which would mean you'd use the transformation derived by Mansouri and Sexl to transform between these coordinate systems.

If they preserve simultaneity, they cannot desrcibe a mechanic that is similar to SR. The SR mechanic of the twin ageing absolutely requires relativity of simultaneity. If I could just use a system where simultaneity is absolute, within the realm of SR, I would be glad to. What I am asking is found in this diagram:

http://www.saunalahti.fi/anshyy/PhysicsForums/Twins_Simultaneity.jpg

Red and blue lines are the twins. Black lines are planes of simultaneity for the red twin. Green lines are the last moment before of outbound leg, and first moment of inbound leg.

In SR, the moment just before the turn-around of the red twin, the so called "actual state of the world" can be "thought" to be, say, january 2006. Even if the turn-around period is thought to be instantaneous, when the twin is approaching earth, the "actual state of the world" is thought to be, say, june 2058.

It's not hard to grasp the mechanical side of this and then just accept it. But really, what happened? And how?

As for just measuring the lengths of the paths, or using some system which preservers simultaneity, nothing of this kind occurs.

If I draw two lines on a piece of paper and pick a point on one, do you think there is a unique ontological truth about how far the other line is from that point in the "horizontal" direction, one that does not depend on an arbitrary choice of how I orient my horizontal x-axis and vertical y-axis?

No, but I really think there ought to be in real world. I don't find it very useful to think that spacetime diagrams or block time could map directly to reality.

 

[JesseM]

It isn't, and I'm actually omitting the acceleration from the equation altogether. I'm analyzing the situation by the terms of SR entirely.

No you're not, because SR doesn't say anything specific about how you should define the "point of view" of an non-inertial observer. It doesn't, for example, say that you are obligated to say that at different points in his path, his definition of simultaneity must match that of the inertial frame in which he is instantaneously at rest. In fact, SR as a theory of physics does not even say you are obligated to define the "point of view" of an inertial observer using the type of coordinate system described by Einstein in his 1905 paper; this is only a matter of convention, not something that is dictated by the laws of physics.

As an analogy, say you have two paths through 2D space which meet at two points, and one path is a straight line between the two points while the other has a curve in it, just like the spacetime diagram of the two twins in the twin paradox. You want to figure out the length of the two paths...

...

...Of course you will find that the straight-line path between the two points is always shorter than the non-straight path; that's just simple geometry. Now, if you liked you could associate each point on the non-straight path with a coordinate system where the x-axis was exactly parallel to the path at that point, and you could point out how along the section of the path that's curved, the y-axis of the coordinate system associated with each point is changing its angle. But would this really be the best or clearest way to understand why the non-straight path is always longer than straight path? Doesn't it make more sense to pick a single coordinate system to use to find the length of both paths, or just to point out that the geometry of 2D space is such that a straight line is always a geodesic and will thus be the shortest possible path between two points?

No, it does not make more sense actually, since the other path being longer has nothing to do with why the other twin ages more and the other one less in SR. I can't see any reason why I would be interested of the length of the paths on the paper. In fact the twin who moves along the longer path, ages less.

This is simply a matter of the different geometry of space and spacetime; the measure of distance in space is \sqrt{dx^2 + dy^2 + dz^2} (the pythagorean theorem), while the measure of proper time (which is analogous to distance) in spacetime in \sqrt{dt^2 - dx^2 - dy^2 - dz^2}. Are you familiar with the idea of a "geodesic"? In flat space a geodesic path is the one with the shortest length, while in flat spacetime a geodesic path is the one with the greatest proper time.

If you are still bothered by this difference, then instead of an ordinary 2D piece of paper, suppose I was talking about the 2D complex plane, with real numbers on one axis and imaginary numbers on the other. In this case, if we still assume that the length of a small section straight of path whose horizontal change is dx and whose vertical length is dy would be \sqrt{dx^2 + dy^2}, and the total length of a curvy path can be found by summing a bunch of infinitesimal straight sections, then in this case a straight-line path will be the longest path between two points, while curvy ones will be shorter (assuming you only look at paths where every section of the path has an imaginary length, which is like assuming that every worldline should be timelike). In fact, it turns out that if you treat time as an imaginary spatial dimension, so that 1 year becomes i light-years, you can reproduce most of the structure of SR by applying ordinary geometric equations to this complex space--for example, if you use the pythagorean theorem to find the distance between two points in this complex space, it will be equal to i*(the proper time between those points)*c, and the Lorentz transform, when time is replaced by the imaginary distance i*c*time and c is replaced by -i and velocity is replaced by -i*(velocity/c), becomes identical to the equation for translating between ordinary spatial coordinate systems whose axes are rotated with respect to one another. Finally, if you use the same formula for the total length of a path in space that I gave earlier, \int \sqrt{1 + S^2} \, dx, but you assume the x-axis is the imaginary one that's equivalent to the time axis in relativity, so that dx = i*dt*c and S = dy/dx = (dy/dt)/(ic) = v/ic, then plugging into this equation gives \int ic \sqrt{1 + (v/ic)^2)} \, dt = ic * \int \sqrt{1 - v^2/c^2} \, dt, which of course is just ic times the formula for the proper time along a path in relativity.

So in terms of looking at paths in complex space, which really is mathematically equivalent to looking at worldlines in SR, would you say that the best way to understand why a straight path is longer than a non-straight path would be to consider a series of different coordinate systems whose imaginary axis is parallel to the non-straight curve at different points along it? Can't we just point out that the length of a path doesn't depend on how you orient your coordinate axes, so we can just orient the axes arbitrarily and evaluate \int \sqrt{1 + S^2} \, dx using the formula for S(x) in this coordinate system?

Even if you want to consider the traveling twin's "point of view" here as involving a series of inertial frames where he's instantaneously at rest, you could equally well consider a series of inertial coordinate systems which use a clock synchronization convention that insures they all agree about simultaneity, which would mean you'd use the transformation derived by Mansouri and Sexl to transform between these coordinate systems.

If they preserve simultaneity, they cannot desrcibe a mechanic that is similar to SR. The SR mechanic of the twin ageing absolutely requires relativity of simultaneity.

You are still confusing physics with coordinate systems. You can use any coordinate system you want without changing the laws of physics, provided you do a coordinate transformation on the equations of the laws of physics too.

With the Mansouri and Sexl transformation, it's assumed that you have one special coordinate system which is physically constructed according to Einstein's procedure, using a network of measuring-rods and clocks with the clocks synchronized using Einstein's clock synchronization convention, and then all other coordinate systems also use measuring-rods and clocks, but instead of using Einstein's clock synchronization convention they simply synchronize their own clocks so that they will agree with the special coordinate system on simultaneity. If the special coordinate system's coordinates are (X,T) and the coordinate system of someone moving at velocity v relative to it are (x,t), then the transformation equation would be:

x = (1/\sqrt{1 - v^2/c^2})(X - vT)
t = \sqrt{1 - v^2/c^2} T

so the reverse transformation should be:

X = \sqrt{1 - v^2/c^2}x + (1/\sqrt{1 - v^2/c^2})vt
T = (1/\sqrt{1 - v^2/c^2}) t

This is different than the Lorentz transform, which would be:

x = (1/\sqrt{1 - v^2/c^2})(X - vT)
t = (1/\sqrt{1 - v^2/c^2})(T - vX/c^2)

and

X = (1/\sqrt{1 - v^2/c^2})(x + vt)
T = (1/\sqrt{1 - v^2/c^2})(t + vx/c^2)

The key to keeping the laws of physics the same is that if you have some equation stated in the (X,T) system--the equation of one of the laws of physics, or the equation of a particular object's path--then you must use the same coordinate transform on the equation that you used on the coordinates. For example, if an object's path is given by equation X(T) = uT + r in the special coordinate system (X,T), then to find the equation for the path in the coordinate system (x,t) given by the Mansouri-Sexl transform, you just have to plug in X = \sqrt{1 - v^2/c^2}x + (1/\sqrt{1 - v^2/c^2})vt and T = (1/\sqrt{1 - v^2/c^2}) t
into that equation and solve for x as a function of t (which I won't bother doing). Likewise, you'd do the same with any equations of physics expressed in X,T coordinates, giving a new set of equations which correspond to the same laws of physics as seen in the x,t system. Since this is just a different coordinate description of the same thing, all your predictions about coordinate-independent physical quantities, such as the time that the clocks of the twins will read at the moment they reunite, will be exactly the same.

If you use the coordinate systems provided by the Lorentz transform, you don't have to worry about changing the laws of physics when you switch frames, because the theory of relativity predicts that all the laws of physics have the property that they will look the same when you transform from one coordinate system provided by the Lorentz transform to another, a property known as "Lorentz-invariance" (see this post for an explanation of this in terms of an analogy with Galilei-invariance in Newtonian physics). But with some other set of coordinate systems, the equations describing the laws of physics will vary from one coordinate system to another. This is not a variation in the laws of physics themselves, just in how they are described in different coordinate systems. So even though all the coordinate systems given by the Mansouri-Sexl transformation will agree with each other about simultaneity, they will still end up making the same prediction about which twin ages more slowly and by how much, once you transform both the equations of the twin's paths and the equation for time dilation as a function of velocity into each coordinate system.

We can try working through an example if you want, although I think it should be pretty clear on principle that transforming the same laws in differenct coordinate systems can't affect the predictions these laws make about coordinate-invariant facts.

If I could just use a system where simultaneity is absolute, within the realm of SR, I would be glad to.

You certainly can, although it makes things more difficult because equations that have the same form in every inertial coordinate system provided by the Lorentz transform, like the time dilation equation \tau = t \sqrt{1 - v^2/c^2}, will have to be translated into your new set of coordinate systems and will not be the same for different members of the set.

What I am asking is found in this diagram:

http://www.saunalahti.fi/anshyy/PhysicsForums/Twins_Simultaneity.jpg

Red and blue lines are the twins. Black lines are planes of simultaneity for the red twin.

But your use of "for the red twin" is problematic. What the black lines are is lines of simultaneity in the inertial coordinate system where the red twin is at rest at that moment, and where the coordinate system is constructed according to Einstein's procedure (including the use of his clock synchronization convention). If you instead chose to look at the lines of simultaneity in the inertial coordinate system where the red twin was instantaneously at rest with the coordinate system constructed according to the Mansouri-Sexl procedure, with the special (X,T) frame being the one where the blue twin is at rest, then all the black lines would be horizontal. And you're free to use even crazier coordinate systems, it doesn't matter as long as you remember to translate all the relevant equations into your new coordinate system.

If I draw two lines on a piece of paper and pick a point on one, do you think there is a unique ontological truth about how far the other line is from that point in the "horizontal" direction, one that does not depend on an arbitrary choice of how I orient my horizontal x-axis and vertical y-axis?

No, but I really think there ought to be in real world. I don't find it very useful to think that spacetime diagrams or block time could map directly to reality.

Well, that's a philosophical intuition of yours, it can't be justified in terms of physics. And I think most physicists who work with relativity would have intuitions more in line with the "block time" view where you just have a spacetime manifold containing various events, and questions of simultaneity are really just questions of what coordinate system you choose to use to describe this unvarying manifold.

 

[JesseM]

It isn't, and I'm actually omitting the acceleration from the equation altogether. I'm analyzing the situation by the terms of SR entirely.

No you're not, because SR doesn't say anything specific about how you should define the "point of view" of any observer whose path over the time period you're looking at is not entirely inertial. It doesn't, for example, say that you are obligated to say that at different points in his path, his definition of simultaneity must match that of the inertial frame in which he is instantaneously at rest. In fact, SR as a theory of physics does not even say you are obligated to define the "point of view" of an inertial observer using the type of coordinate system described by Einstein in his 1905 paper; this is only a matter of convention, not something that is dictated by the laws of physics.

As an analogy, say you have two paths through 2D space which meet at two points, and one path is a straight line between the two points while the other has a curve in it, just like the spacetime diagram of the two twins in the twin paradox. You want to figure out the length of the two paths...

...

...Of course you will find that the straight-line path between the two points is always shorter than the non-straight path; that's just simple geometry. Now, if you liked you could associate each point on the non-straight path with a coordinate system where the x-axis was exactly parallel to the path at that point, and you could point out how along the section of the path that's curved, the y-axis of the coordinate system associated with each point is changing its angle. But would this really be the best or clearest way to understand why the non-straight path is always longer than straight path? Doesn't it make more sense to pick a single coordinate system to use to find the length of both paths, or just to point out that the geometry of 2D space is such that a straight line is always a geodesic and will thus be the shortest possible path between two points?

No, it does not make more sense actually, since the other path being longer has nothing to do with why the other twin ages more and the other one less in SR. I can't see any reason why I would be interested of the length of the paths on the paper. In fact the twin who moves along the longer path, ages less.

This is simply a matter of the different geometry of space and spacetime; the measure of distance in space is \sqrt{dx^2 + dy^2 + dz^2} (the pythagorean theorem), while the measure of proper time (which is analogous to distance) in spacetime in \sqrt{dt^2 - dx^2 - dy^2 - dz^2}. Are you familiar with the idea of a "geodesic"? In flat space a geodesic path is the one with the shortest length, while in flat spacetime a geodesic path is the one with the greatest proper time.

If you are still bothered by this difference, then instead of an ordinary 2D piece of paper, suppose I was talking about the 2D complex plane, with real numbers on one axis and imaginary numbers on the other. In this case, if we still assume that the length of a small section straight of path whose horizontal change is dx and whose vertical length is dy would be \sqrt{dx^2 + dy^2}, and the total length of a curvy path can be found by summing a bunch of infinitesimal straight sections, then in this case a straight-line path will be the longest path between two points, while curvy ones will be shorter (assuming you only look at paths where every section of the path has an imaginary length, which is like assuming that every worldline should be timelike). In fact, it turns out that if you treat time as an imaginary spatial dimension, so that 1 year becomes i light-years, you can reproduce most of the structure of SR by applying ordinary geometric equations to this complex space--for example, if you use the pythagorean theorem to find the distance between two points in this complex space, it will be equal to i*(the proper time between those points)*c, and the Lorentz transform, when time is replaced by the imaginary distance i*c*time and c is replaced by -i and velocity is replaced by -i*(velocity/c), becomes identical to the equation for translating between ordinary spatial coordinate systems whose axes are rotated with respect to one another. Finally, if you use the same formula for the total length of a path in space that I gave earlier, \int \sqrt{1 + S^2} \, dx, but you assume the x-axis is the imaginary one that's equivalent to the time axis in relativity, so that dx = i*dt*c and S = dy/dx = (dy/dt)/(ic) = v/ic, then plugging into this equation gives \int ic \sqrt{1 + (v/ic)^2)} \, dt = ic * \int \sqrt{1 - v^2/c^2} \, dt, which of course is just ic times the formula for the proper time along a path in relativity.

So in terms of looking at paths in complex space, which really is mathematically equivalent to looking at worldlines in SR, would you say that the best way to understand why a straight path is longer than a non-straight path would be to consider a series of different coordinate systems whose imaginary axis is parallel to the non-straight curve at different points along it? Can't we just point out that the length of a path doesn't depend on how you orient your coordinate axes, so we can just orient the axes arbitrarily and evaluate \int \sqrt{1 + S^2} \, dx using the formula for S(x) in this coordinate system?

Even if you want to consider the traveling twin's "point of view" here as involving a series of inertial frames where he's instantaneously at rest, you could equally well consider a series of inertial coordinate systems which use a clock synchronization convention that insures they all agree about simultaneity, which would mean you'd use the transformation derived by Mansouri and Sexl to transform between these coordinate systems.

If they preserve simultaneity, they cannot desrcibe a mechanic that is similar to SR. The SR mechanic of the twin ageing absolutely requires relativity of simultaneity.

You are still confusing physics with coordinate systems. You can use any coordinate system you want without changing the laws of physics, provided you do a coordinate transformation on the equations of the laws of physics too.

With the Mansouri and Sexl transformation, it's assumed that you have one special coordinate system which is physically constructed according to Einstein's procedure, using a network of measuring-rods and clocks with the clocks synchronized using Einstein's clock synchronization convention, and then all other coordinate systems also use measuring-rods and clocks, but instead of using Einstein's clock synchronization convention they simply synchronize their own clocks so that they will agree with the special coordinate system on simultaneity. If the special coordinate system's coordinates are (X,T) and the coordinate system of someone moving at velocity v relative to it are (x,t), then the transformation equation would be:

x = (1/\sqrt{1 - v^2/c^2})(X - vT)
t = (\sqrt{1 - v^2/c^2}) T

so the reverse transformation should be:

X = \sqrt{1 - v^2/c^2}x + (1/\sqrt{1 - v^2/c^2})vt
T = (1/\sqrt{1 - v^2/c^2}) t

This is different than the Lorentz transform, which would be:

x = (1/\sqrt{1 - v^2/c^2})(X - vT)
t = (1/\sqrt{1 - v^2/c^2})(T - vX/c^2)

and

X = (1/\sqrt{1 - v^2/c^2})(x + vt)
T = (1/\sqrt{1 - v^2/c^2})(t + vx/c^2)

The key to keeping the laws of physics the same is that if you have some equation stated in the (X,T) system--the equation of one of the laws of physics, or the equation of a particular object's path--then you must use the same coordinate transform on the equation that you used on the coordinates. For example, if an object's path is given by equation X(T) = uT + r in the special coordinate system (X,T), then to find the equation for the path in the coordinate system (x,t) given by the Mansouri-Sexl transform, you just have to plug in X = \sqrt{1 - v^2/c^2}x + (1/\sqrt{1 - v^2/c^2})vt and T = (1/\sqrt{1 - v^2/c^2}) t
into that equation and solve for x as a function of t (which I won't bother doing). Likewise, you'd do the same with any equations of physics expressed in X,T coordinates, giving a new set of equations which correspond to the same laws of physics as seen in the x,t system. Since this is just a different coordinate description of the same thing, all your predictions about coordinate-independent physical quantities, such as the time that the clocks of the twins will read at the moment they reunite, will be exactly the same.

If you use the coordinate systems provided by the Lorentz transform, you don't have to worry about changing the laws of physics when you switch frames, because the theory of relativity predicts that all the laws of physics have the property that they will look the same when you transform from one coordinate system provided by the Lorentz transform to another, a property known as "Lorentz-invariance" (see this post for an explanation of this in terms of an analogy with Galilei-invariance in Newtonian physics). But with some other set of coordinate systems, the equations describing the laws of physics will vary from one coordinate system to another. This is not a variation in the laws of physics themselves, just in how they are described in different coordinate systems. So even though all the coordinate systems given by the Mansouri-Sexl transformation will agree with each other about simultaneity, they will still end up making the same prediction about which twin ages more slowly and by how much, once you transform both the equations of the twin's paths and the equation for time dilation as a function of velocity into each coordinate system.

We can try working through an example if you want, although I think it should be pretty clear on principle that transforming the same laws in differenct coordinate systems can't affect the predictions these laws make about coordinate-invariant facts.

If I could just use a system where simultaneity is absolute, within the realm of SR, I would be glad to.

You certainly can, although it makes things more difficult because equations that have the same form in every inertial coordinate system provided by the Lorentz transform, like the time dilation equation \tau = t \sqrt{1 - v^2/c^2}, will have to be translated into your new set of coordinate systems and will not be the same for different members of the set.

What I am asking is found in this diagram:

http://www.saunalahti.fi/anshyy/PhysicsForums/Twins_Simultaneity.jpg

Red and blue lines are the twins. Black lines are planes of simultaneity for the red twin.

But your use of "for the red twin" is problematic. What the black lines are is lines of simultaneity in the inertial coordinate system where the red twin is at rest at that moment, and where the coordinate system is constructed according to Einstein's procedure (including the use of his clock synchronization convention). If you instead chose to look at the lines of simultaneity in the inertial coordinate system where the red twin was instantaneously at rest with the coordinate system constructed according to the Mansouri-Sexl procedure, with the special (X,T) frame being the one where the blue twin is at rest, then all the black lines would be horizontal. And you're free to use even crazier coordinate systems, it doesn't matter as long as you remember to translate all the relevant equations into your new coordinate system.

If I draw two lines on a piece of paper and pick a point on one, do you think there is a unique ontological truth about how far the other line is from that point in the "horizontal" direction, one that does not depend on an arbitrary choice of how I orient my horizontal x-axis and vertical y-axis?

No, but I really think there ought to be in real world. I don't find it very useful to think that spacetime diagrams or block time could map directly to reality.

Well, that's a philosophical intuition of yours, it can't be justified in terms of physics. And I think most physicists who work with relativity would have intuitions more in line with the "block time" view where you just have a spacetime manifold containing various events, and questions of simultaneity are really just questions of what coordinate system you choose to use to describe this unvarying manifold.

 

[AnssiH]

No you're not, because SR doesn't say anything specific about how you should define the "point of view" of any observer whose path over the time period you're looking at is not entirely inertial. It doesn't, for example, say that you are obligated to say that at different points in his path, his definition of simultaneity must match that of the inertial frame in which he is instantaneously at rest.

Right. I guess it is a personal preference for me to look at the same situation from the point of view of different observers, because I'm trying to make out what the ontological meaning of the logics is. I.e. I ask the question "what the world is like around each natural observer?"

For example in the case of the twins, while on the outbound leg, since both twins think they are at rest (and I think this is likely to be physically correct also in any future theories even if they refute relativity of simultaneity), I can trivially work out from the SR logics that both of the twins should "exist" in such a place that the proper time of the other twin, is less. It is not enough for me to work out that only one twin thinks this way, even though I can do that.

So in SR it seems that I need to accept the relativity of simultaneity as a real world phenomenon. And that means I would need to accept something like, in the "place" where the red twin is on his outbound leg, the blue twin exists in one point of his worldline, and in the "place" where the red twin is on his inbound leg, even if this "place" could be (theoretically) the same spot in the spacetime, the blue twin exists in another point of his worldline.

So... ->

In flat space a geodesic path is the one with the shortest length, while in flat spacetime a geodesic path is the one with the greatest proper time...

...In this case, if we still assume that the length of a small section straight of path whose horizontal change is dx and whose vertical length is dy would be \sqrt{dx^2 + dy^2}, and the total length of a curvy path can be found by summing a bunch of infinitesimal straight sections, then in this case a straight-line path will be the longest path between two points, while curvy ones will be shorter

...while I think I see what you mean, don't I still need to account for what happens when the other twin is changing direction? Even if I assume he changes direction instantly.

I am probably misunderstanding something, but if I just work out the time dilation that occurs to the the proper time of each of the twins from the point of view of the other twin, or from the point of view of any arbitrary inertial coordination system, without taking into account the tilting of the simultaneity plane at turn-around, wouldn't the result be that upon returning to earth, the blue twin and the red twin are both paradoxically time dilated from each other?

And likewise, if instead of having the red observer performing a turn-around, we say the blue observer flies to where the red observer is. Then it will be the blue observer who has aged less. Or if they both turn around so that they will meet in the middle, neither has aged more than the other.

So can all these things be worked out without relativity of simultaneity?
What about Lorentz-contraction, can that too be worked out without relativity of simultaneity?

All the turn-arounds above are thought to be instantaneous.

With the Mansouri and Sexl transformation, it's assumed that you have one special coordinate system which is physically constructed according to Einstein's procedure...

...Since this is just a different coordinate description of the same thing, all your predictions about coordinate-independent physical quantities, such as the time that the clocks of the twins will read at the moment they reunite, will be exactly the same.

The only information I seem to be finding about Mansouri and Sexl transformation, is by someone who is making a case for ether theory, and who seems to be saying this transformation is completely different from Lorentz-transformation in that, indeed, it preservers simultaneity, but at the same time as I would expect, it doesn't produce the same results.

http://www.egtphysics.net/Ron1/Symmetry.htm

Hmmm, in fact he seems to be stating the same concern as I am "The Lorentz transformation occasioned by Stella’s turn-around has caused a magical jump in the position of the signal in transit."

So what's this all about?

And more to the point, if this transformation method is indeed equal to Lorentz-transformation, what does it suggest about the ontology of the world? For it to be a real-world phenomena, would one need to assume the existence of ether?

So even though all the coordinate systems given by the Mansouri-Sexl transformation will agree with each other about simultaneity, they will still end up making the same prediction about which twin ages more slowly and by how much, once you transform both the equations of the twin's paths and the equation for time dilation as a function of velocity into each coordinate system.

We can try working through an example if you want, although I think it should be pretty clear on principle that transforming the same laws in differenct coordinate systems can't affect the predictions these laws make about coordinate-invariant facts.

Yeah, that is pretty clear, I'm just so used to treat simultaneity as relative that I cannot see how these methods are in principle the same(?). It seems to me that the mechanic of just working out the time dilation as a function to velocity is a completely different thing to time dilation (or acceleration) that occurs to the objects around you when you do switch inertial coordinate systems.

The way I tend to think about SR is always in thinking how the world must be around an observer, if the speed of light is C for him. So I'm thinking, if the second postulate is reality, then this should be the method that is closest to what also occurs in reality;
http://en.wikipedia.org/wiki/Twin_paradox#The_resolution_of_the_Paradox_in_special_relativity

Well, that's a philosophical intuition of yours, it can't be justified in terms of physics.

Sure. I just hope there was more conversation about these issues, instead of just different technical methods :P

And I think most physicists who work with relativity would have intuitions more in line with the "block time" view where you just have a spacetime manifold containing various events, and questions of simultaneity are really just questions of what coordinate system you choose to use to describe this unvarying manifold.

I think so too. It just seems like it's bordering the rejection of reality to me.

 

[JesseM]

Right. I guess it is a personal preference for me to look at the same situation from the point of view of different observers, because I'm trying to make out what the ontological meaning of the logics is. I.e. I ask the question "what the world is like around each natural observer?"

Yes, but by "the world" you mean "all of space at a particular instant" as opposed to "all of spacetime". To me, the notion of dividing 4D spacetime into a series of 3D "instants" is just as arbitrary as the notion of dividing 3D space into a stack of 2D "xy planes", there isn't any reason the universe should care how you choose to slice things up.

For example in the case of the twins, while on the outbound leg, since both twins think they are at rest (and I think this is likely to be physically correct also in any future theories even if they refute relativity of simultaneity)

You're still confusing statements about physics with statements about coordinate systems. There's no meaningful sense in which it could be "correct" or "incorrect" for each observer to use a coordinate system where they are at rest, this is just a convention--if you disagree, then try to think up a possible future experimental discovery that would show this idea to be either correct or incorrect.

I can trivially work out from the SR logics that both of the twins should "exist" in such a place that the proper time of the other twin, is less.

Only if by "SR logics" you mean the convention of how each observer defines their own coordinate system. But this is just a convention, it has nothing to do with what "SR" means as a theory of physics.

So in SR it seems that I need to accept the relativity of simultaneity as a real world phenomenon.

See my previous comment--SR as a theory of physics doesn't say anything about what coordinate system you should use, it just says that whatever coordinate system you use, if you transform the laws of physics as stated in your coordinate system into how they would be stated in the different coordinate systems defined in the manner specified by Einstein in his paper, you will find that the equations of the laws of physics in all these coordinate systems will be the same.

In flat space a geodesic path is the one with the shortest length, while in flat spacetime a geodesic path is the one with the greatest proper time...

...In this case, if we still assume that the length of a small section straight of path whose horizontal change is dx and whose vertical length is dy would be \sqrt{dx^2 + dy^2}, and the total length of a curvy path can be found by summing a bunch of infinitesimal straight sections, then in this case a straight-line path will be the longest path between two points, while curvy ones will be shorter

...while I think I see what you mean, don't I still need to account for what happens when the other twin is changing direction? Even if I assume he changes direction instantly.

No, again, you don't have to figure out what things look like from each twin's "point of view" at all (since the whole notion of associating a 'point of view' with a particular observer is purely a matter of convention), you can just pick a single inertial coordinate system, find the equations for velocity as a function of time for each twin's path in this coordinate system, and then do the integral \int \sqrt{1 - v(t)^2/c^2} \, dt for each path in this coordinate system, between the time they depart and the time they reunite. This will give you the correct answer for how much time has elapsed on each twin's clock between these two times, no mucking about with multiple coordinate systems needed. And no matter which coordinate system you choose, you will get the same answer for the time elapsed on each twin's clock if you use this method.

Again, this is analogous to the fact that if you have two different paths between a pair of points on a 2D plane, the length of each path will be the same regardless of how you orient your x and y axes and integrate the slope of each curve as a function of x, \int \sqrt{1 + S(x)^2} \, dx to calculate the length in this coordinate system. Like I said, if you change the paths on a real 2D plane to paths on a complex plance, then finding the imaginary length of each path using the integral \int \sqrt{1 + S(x)^2} \, dx is mathematically exactly like finding the proper time along worldlines using the integral \int \sqrt{1 - v(t)^2/c^2} \, dt, as becomes clear when you treat time as an imaginary distance.

I am probably misunderstanding something, but if I just work out the time dilation that occurs to the the proper time of each of the twins from the point of view of the other twin, or from the point of view of any arbitrary inertial coordination system, without taking into account the tilting of the simultaneity plane at turn-around, wouldn't the result be that upon returning to earth, the blue twin and the red twin are both paradoxically time dilated from each other?

No, it is critical that you understand that every inertial frame will make the same predictions about all physical results, such as the time that two clocks read when they are right next to each other. Let's look at a simple example to see this. Say we have an earth-twin and a traveling twin, with the Earth twin moving inertially the whole time, and the traveling twin moving away from the earth-twin inertially at 0.6c for 5 years in the earth-twin's inertial rest frame (so she travels a distance of 3 light years), then turning around instantaneously and traveling back at 0.6c for another 5 years in the earth-twin's inertial rest frame. So in the earth-twin's frame, if she's moving at 0.6c her clock should be slowed down by \sqrt{1 - 0.6^2} = 0.8, so when 5 years have passed on the earth-twin's clock only 4 years should have passed on the traveling twin's clock in this frame, and then another 4 years will pass on the return voyage. So, in this frame we predict that when they reunite, the earth-twin's clock reads 5 + 5 = 10 years, while the traveling twin's clock reads 4 + 4 = 8 years. Also, in this frame we can identify the coordinates of the departure, the turnaround, and the reunion as:

departure: x=0 light years, t=0 years
turnaround: x=3 light year, t=5 years
reunion: x=0 light years, t=10 years

Now let's look at this whole situation in another inertial frame, a frame which is moving in the +x direction at 0.6c in the earth-twin's frame, which means that in this frame the traveling twin was at rest during the outbound phase of the trip. The Lorentz transform to transform coordinates in the Earth frame to coordinates in this frame is:

x' = 1.25 * (x - 0.6c*t)
t' = 1.25 * (t - 0.6*x/c)

So plugging in the (x,t) of the three events above into this, we get:
departure: x'=0 light years, t'=0 years
turnaround: x'=0 light years, t'=4 years
reunion: x'=-7.5 light years, t'=12.5 years

Since the traveling twin had moved a distance of 7.5 light years in the (12.5 - 4) = 8.5 years between the turnaround and the reunion in this coordinate system, the speed during the inbound leg must have been 7.5/8.5 = 0.882353c in this frame. We could also have deduced this if we used the formula for velocity addition in relativity, (u+v)/(1+uv/c^2), with u=0.6c and v=0.6c.

So in this frame, the earth-twin is moving at 0.6c throughout the entire process, so her clock should be slowed down by a factor of 0.8, and since 12.5 years elapse between the departure and the reunion in this frame, the earth-twin's clock should have elapsed 0.8*12.5 = 10 years. Meanwhile the traveling twin was at rest in this frame between the departure and the turnaround 4 years later, so her clock would elapse 4 years during the outbound leg according to this frame, while during the inbound leg she was traveling at 0.88235c so her clock would be slowed down by \sqrt{1 - 0.882353^2} = 0.470588. Since the inbound leg took 12.5-4=8.5 years in this frame, her clock would have elapsed 8.5*0.470588 = 4 years. So when they reunite, this frame predicts her clock will read 4+4=8 years.

In the end, what you see is that no matter which of these two frame you use to analyze the problem, you conclude that the Earth twin's clock will have elapsed 10 years between the departure and the reunion, while the traveling twin's will have elapsed 8 years. You'd get exactly the same answer if you picked any other inertial frame as well, in each case using the Lorentz transform to find the coordinates of the three events along with the speed of each clock at each point in the journey, and then multiplying the time each clock was moving a particular velocity in this frame by \sqrt{1 - v^2/c^2} for that velocity to find the time elapsed on that clock while it was moving at that velocity.

And likewise, if instead of having the red observer performing a turn-around, we say the blue observer flies to where the red observer is. Then it will be the blue observer who has aged less. Or if they both turn around so that they will meet in the middle, neither has aged more than the other.

So can all these things be worked out without relativity of simultaneity?

If by this question you mean "can we calculate the time elapsed on each clock using a single inertial reference frame", as I did with two different inertial reference frames in the problem above, the answer is yes. Don't take my word for it, try an example yourself!

The only information I seem to be finding about Mansouri and Sexl transformation, is by someone who is making a case for ether theory, and who seems to be saying this transformation is completely different from Lorentz-transformation in that, indeed, it preservers simultaneity, but at the same time as I would expect, it doesn't produce the same results.

No, it produces exactly the same results if you translate the usual relativistic laws of physics into the coordinate systems provided by the Mansouri-Sexl transform. Of course ether fans usually like to imagine that we will find some new laws of physics which work differently in a preferred "ether frame" that we can determine experimentally, but there is no need to believe this to make use of the Mansouri-Sexl transformation. Like I said, there may be aesthetic reasons for preferring to use one set of coordinate systems or another based on the laws of physics, but no matter what the laws of physics are you are free to use any set of coordinate systems you like, and provided you find the correct equations for the laws of physics in each coordinate system (just by doing a change-of-variables on the equations when written in some other coordinate system where you know what the laws of physics look like, as I described in my last post), you will not be led into making any new predictions.

For instance, we might take the situation I described above involving the two twins, and translate it into some coordinate systems related by the Mansouri-Sexl transform. In this case we could no longer assume that in each frame, a clock moving at velocity v will be ticking at \sqrt{1 - v^2/c^2}; we'd have to transform that law into the new coordinate systems. But if we did that correctly, then using the correct form for the time dilation law in these coordinate systems, we'd still end up predicting that the earth-clock would read 10 years and the traveling clock would read 8 years when they reunite. Would you like me to actually work out the math to show that it works out?

http://www.egtphysics.net/Ron1/Symmetry.htm

Hmmm, in fact he seems to be stating the same concern as I am "The Lorentz transformation occasioned by Stella’s turn-around has caused a magical jump in the position of the signal in transit."

So what's this all about?

He is also taking statements about coordinate systems and incorrectly imagining them to be statements about physical reality, as you have been doing. It shouldn't be too surprising that an ether advocate would show this sort of confusion!

And more to the point, if this transformation method is indeed equal to Lorentz-transformation, what does it suggest about the ontology of the world? For it to be a real-world phenomena, would one need to assume the existence of ether?

No, which coordinate system you use has nothing to do with the laws of physics. Any laws of physics can be translated into any coordinate system you want, just using a change-of-variables. Depending on how the laws of physics work, certain choices of coordinate systems may be more natural or aesthetically pleasing, like how Lorentz-invariant laws will have the same equations in every inertial coordinate system provided by the Lorentz transform, but this does not obligate you to use them.

The way I tend to think about SR is always in thinking how the world must be around an observer, if the speed of light is C for him. So I'm thinking, if the second postulate is reality, then this should be the method that is closest to what also occurs in reality;
http://en.wikipedia.org/wiki/Twin_paradox#The_resolution_of_the_Paradox_in_special_relativity

But the speed of light cannot always be c for an observer who does not move inertially. If you assume that at every moment t on his own clock, he should assign a position coordinate x to a distant light beam using the inertial frame where he is instantaneously at rest, then \Delta x / \Delta t will not always be c. For example, if he accelerates instantaneously, the position-coordinate x he assigns the light beam can jump instantaneously too. And if he's accelerating continously for an extended time, then the light beam can be moving faster or slower than c for an extended time, at least according to this method of assigning position coordinates to the beam at each time on his own clock.

Well, that's a philosophical intuition of yours, it can't be justified in terms of physics.

Sure. I just hope there was more conversation about these issues, instead of just different technical methods :P

Perhaps this sort of topic would fit better in the philosophy forum, then?

I think so too. It just seems like it's bordering the rejection of reality to me.

Well, only if it is part of your conception of reality that there must be a real "flow of time", an idea many philosophers reject as incoherent even apart from considerations of physics.

 

[AnssiH]

Yes, but by "the world" you mean "all of space at a particular instant" as opposed to "all of spacetime". To me, the notion of dividing 4D spacetime into a series of 3D "instants" is just as arbitrary as the notion of dividing 3D space into a stack of 2D "xy planes", there isn't any reason the universe should care how you choose to slice things up.

I think making a direct analogy between "jump from 2D-space to 3D-space" and "jump from 3D-space to 4D-spacetime" is not wholly justified, even if it is a popular one. Because apart from math, there's no reason to suppose that time and space are in reality the same thing.

And even when one makes such an analogy, then he must also see that the same way that the 2D-slices are real to the 2D life, the 3D-slices of the "state of the universe" are also very much real to us. I.e. Since we have chosen to see Lorentz-contraction like that, a slice of 3D space, shouldn't he then see everything like that? Is that wrong?

I don't think you need to worry about me not being able to see how it all unfolds in a 4D space, because I can see that, but I'm a bit surprised that the sliced 3D-reality that we are experiencing, is suddenly rejected altogether. In these slices, it should occur that events move forwards and backwards, because that's the only way to preserve causality in an SR world (assuming real symmetry of physical laws to different inertial coordination systems)?

You're still confusing statements about physics with statements about coordinate systems. There's no meaningful sense in which it could be "correct" or "incorrect" for each observer to use a coordinate system where they are at rest, this is just a convention--if you disagree, then try to think up a possible future experimental discovery that would show this idea to be either correct or incorrect.

I've understood this transformation stuff is basically about symmetry between different inertial coordination systems? So the experiment you ask about would be an experiment that would actually experimentally show how different inertial coordination systems would not be symmetrical? That there would exist a physical process that would work differently in different inertial coordination systems?

I personally cannot believe there could exist such an experiment. I don't think there exists asymmetry of anykind between different inertial coordination systems in the real physical world.

Isn't that the reason why special relativity with Lorentz-transformation is usually conceived to be "physically more correct" than transformations that assume different physical laws to different coordination systems, and need to top it with some sort of effect that prevents us from measuring the asymmetry? And that's why it could be said that even though we cannot measure any asymmetry, one can always assert that nature "has just blocked us from seeing it" or something like that?

This may be slightly off-topic, but the whole idea of ether seems completely unnecessary for the kind of system that the universe appears to be. It seems very odd to me, that people who find the idea of relativity of simultaneity (as it appears in SR) to be absurd, feel the need to use ether to anchor simultaneity into it.

I mean, what happened - historically - to the idea that preservers absolute symmetry AND absolute simultaneity in all frames; that information is propagated from all matter at speed C relative to the matter that IS propagating the information, instead of the one receiving it?

I think partially the reason to reject was due to argument that binary stars could not have been visually binary stars. An argument that we know today is likely to be invalid (vacuum of space is not perfect, especially around stars, and most binary systems (80-90%) are not visual binaries anyway; they are detected by doppler shift). Surely this cannot have been the only reason the idea was completely rejected right away?

By attaching the speed to the receiver, sure, you can preserve symmetry that way too, that's a completely logical road to take. But at the same time I don't think you can ever offer any experimentally verifiable explanation as to why/how the speed of light "adjusts" itself to your speed. Obviously no one thinks there is causality between your motion and that of the information still approaching you, but yet I think some explanation should be offered. Right now, it's just a necessity that occurs in the mathematical realm.

Only if by "SR logics" you mean the convention of how each observer defines their own coordinate system. But this is just a convention, it has nothing to do with what "SR" means as a theory of physics.

If by "convention" you mean that Einstein never assumed real symmetry between different inertial coordination systems, I think you are wrong about that. I think that was one of his main driving forces in coming up with the second postulate and sticking with it.

Somehow, Maxwell's equations gave people the idea that light needs to propagate in a transmitter medium, like sounds, or waves of water (which was pretty stupid, sound is motion of matter, hello? ), and I believe Lorentz-transformation was in its original form designed to offer an explanation as to how we cannot detect this ether.

Einstein made a choice - that was probably a huge step to the right direction - that there exists a fundamental symmetry, and no ether at all. (But I don't know why he readily felt the need to assert that any EXTERNAL speed of light is ALSO attached to the observer's inertial frame, since external influences have nothing to do with symmetry, and they are in fact not symmetrical in real world either).

I don't know of all the ways that SR has been treated since. I know it has been through a lot of misinterpetation. But I think the main thing that it claims is absolute, fundamental symmetry between different inertial coordination systems. And I believe this assertion is meant to be about the real physical world, as oppose to some sort of masquerade of the reality.

No, again, you don't have to figure out what things look like from each twin's "point of view" at all (since the whole notion of associating a 'point of view' with a particular observer is purely a matter of convention)

It is not a matter of convention for the natural observer. Such as me. And I am interested about what that slice of the 4D-spacetime is like around me.

In the end, what you see is that no matter which of these two frame you use to analyze the problem, you conclude that the Earth twin's clock will have elapsed 10 years between the departure and the reunion, while the traveling twin's will have elapsed 8 years. You'd get exactly the same answer if you picked any other inertial frame as well, in each case using the Lorentz transform to find the coordinates of the three events along

Lorentz-transformation is well understood here. But you were talking about Sexl & Mansouri. So I take it that the result is the same, but one cannot assume fundamental symmetry of different inertial coordination systems?

And likewise, if instead of having the red observer performing a turn-around, we say the blue observer flies to where the red observer is. Then it will be the blue observer who has aged less. Or if they both turn around so that they will meet in the middle, neither has aged more than the other.
So can all these things be worked out without relativity of simultaneity?

If by this question you mean "can we calculate the time elapsed on each clock using a single inertial reference frame", as I did with two different inertial reference frames in the problem above, the answer is yes. Don't take my word for it, try an example yourself!

No no, you are probably right. If to try out an example by myself, I'd need to transform the laws of physics for different inertial frames, no thanks :)

I suppose that's the reason everybody are using Lorentz-transformation the way Einstein uses it?

I'd think it's safe to extend the idea of absolute symmetry to the real world, if it really hasn't been done yet... That's not to say the method Einstein uses would be correct, of course, but still.

Have you worked out anything about length-contraction? I suppose that is an effect produced only by the "Einstein-convention" of using Lorentz-transformation? If one doesn't think that convention says anything about the reality per se, then Lorentz-contraction is also a matter of convention?

And since you have thought about Sexl & Mansouri transformation, what would you say it suggests about the ontology of the world? My interpetation of their idea seems to be that they think there is no fundamental symmetry between different inertial coordination systems, but there just "appears" to be?

But the speed of light cannot always be c for an observer who does not move inertially. If you assume that at every moment t on his own clock, he should assign a position coordinate x to a distant light beam using the inertial frame where he is instantaneously at rest, then \Delta x / \Delta t will not always be c.

Yeah, the semantical "beam of light" is not approaching the non-inertial observer at speed C, and by the same logic this semantical "beam of light" might even be "stationary", or moving backwards. It's a direct effect of relativity of simultaneity. And it is also the same thing as all this talk about slices of 3D world. In this "imaginary slice" the beam of light does all kinds of odd things. If you appreciate it as a "real world" effect that the speed of light is not C for non-inertial observer, then you should appreciate everything that the same logic says the beam of light does.

Only in the 4D-spacetime the beam of light is found to have approached the observer at speed C. Only after observation in the 3D world, the "moment" something actually occurred is decided by the way the information has been assumed to approach the observer.

It's just that the 3D slices ARE the ontological truth for us, much more than the 4D-spacetime.

SR seems to be a lot more radical idea than it superficially seems... Either one cannot place any real meaning to his "now"-moment, or one needs to accept that in his "now"-moment so called "beams of light" can move forwards and backwards. One should probably forget any ideas such as "beams of light" that fly around, when you're looking at things according to SR.

Perhaps this sort of topic would fit better in the philosophy forum, then?

There's no physicists there... I don't think most philosophers really even understand what it means when someone asserts that speed of information is attached to each observer. Usually people go "ok" without thinking at that point because they've heard this assertion so many times. It takes a moment for this idea to sink in until they go "What? How's that possible?" and then you need to talk about Lorentz-transformation and blaa blaa blaa. :)

I think so too. It just seems like it's bordering the rejection of reality to me.

Well, only if it is part of your conception of reality that there must be a real "flow of time", an idea many philosophers reject as incoherent even apart from considerations of physics.

I don't find it impossible to reject an "absolute" flow of time, but I should clarify, that by "rejection of reality" I mean ignoring the idea that we do in fact experience the world as slices of the spacetime, not any actual spacetime. And by "ignoring" I mean not finding it necessary to explain what these slices are really like around each of us. Are there beams of light moving faster and slower than C, or even backwards, or are the inertial coordination systems like different realms altogether, or what?

 

[robphy]

The OP might enjoy this:

"International Conference on the Ontology of Spacetime" (2004)
http://alcor.concordia.ca/~scol/seminars/conference/

http://www.elsevier.com/wps/find/bookdescription.cws_home/707989/description#description

"Second International Conference on the Ontology of Spacetime" (June 2006)
http://www.spacetimesociety.org/conferences/2006/

http://plato.stanford.edu/entries/spacetime-holearg/ (and other discussions on "space and time" and "spacetime")

 

[Ich]

sorry for disrupting, but this is an important point:

I don't find it impossible to reject an "absolute" flow of time, but I should clarify, that by "rejection of reality" I mean ignoring the idea that we do in fact experience the world as slices of the spacetime, not any actual spacetime.

This may be the misconcetion that leads to all your trouble with SR. You NEVER experience those slices of reality. What you experience the information that reaches you at a given moment, and what you have experienced is the information that reached you in a succession of moments. These are invariants, and you should restrict your ontology those things.
There´s no point in assigning "reality" eg to the order in time of events that in principle cannot influence each other. It simply makes no difference to anything anyone could ever experience.

 

[AnssiH]

sorry for disrupting, but this is an important point:

This may be the misconcetion that leads to all your trouble with SR. You NEVER experience those slices of reality. What you experience the information that reaches you at a given moment, and what you have experienced is the information that reached you in a succession of moments. These are invariants, and you should restrict your ontology those things.
There´s no point in assigning "reality" eg to the order in time of events that in principle cannot influence each other. It simply makes no difference to anything anyone could ever experience.

This is very well understood. It has been under discussion in this thread a few times, even though I tried to make it clear in the first post that what is being discussed is the world behind our perceptions. The "now"-moment, if you will.

I.e. even though perceiving the world is one thing, we should not reject that there are events occurring out there even at moments when we haven't yet observed them.

And more to the point, according to SR, it should be wrong to even think there is any information approaching you right now from a distant galaxy 100 light years from here. While you may think there's going to be a hundred years old piece of information reaching you any moment, if you suddenly accelerate into near the speed of light towards another direction, you may receive this information, but now it is only few seconds old (and the galaxy is just few light seconds away from you, flying away at near the speed of light). It would be completely wrong to say the event had happened 100 years ago.

Thank you robphy for the links.

 

[robphy]

This is very well understood. It has been under discussion in this thread a few times, even though I tried to make it clear in the first post that what is being discussed is the world behind our perceptions. The "now"-moment, if you will.

I.e. even though perceiving the world is one thing, we should not reject that there are events occurring out there even at moments when we haven't yet observed them.

There's a difference between
accepting the existence of such yet unobserved events and
assigning a grouping (e.g, what one calls "now") to some of those events.