Concerns about ontological interpetations of Theory of Relativity

[AnssiH]

First of all, browsing this forum, I feel that the level of competence regarding theory of relativity is higher than on average science forums. It may not be much to say, but the only reason I want to post here is because I believe criticism and comments might actually come from people who KNOW what they are talking about. In other words, People who usually do most of the arguing regarding theory of relativity, seem to be the ones who have very vague idea about what the theory actually means and describes. This includes both pro and anti-relativists, and I don't wish to be associated with either group :)
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I find that ontological interpetations of Einstein's theory of relativity are incredibly sparse, while the mathemathical expressions are abound. As always, the ontological nature of the theory does not readily reveal itself from mathematical expressions. Incidentally, I find that the collective understanding of such key concepts as the relativity of simultaneity is very poor.

This could be suprising, being that Einstein himself made it very clear how important the relativity of simultaneity is in making the theory actually work. But then, surely Einstein's incredibly poor choice of words in his famous thought experiment involving railway embankment and a moving train have contributed to this misconception:

About Relativity Of Simultaneity by Einstein - See section 9

Einstein makes it sound as if he is simply talking about how the lighting flashes are not SEEN simultaneously due to their limited propagation speed. Had the text not been written by Einstein, I'd claim writer didn't understand the relativity of simultaneity.

I mean;
"...he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A"

Sound rather much like someone is describing an emitter theory. While the above IS what happens from the point of view of the embankment, it is very easy to get the wrong impression.

Incidentally, this idea about how different things are SEEN at different times I find to be to most common misconception about the relativity of simultaneity. I have even seen TV-documentaries that convey this same erroneous idea about how "special relativity talks about how things visually appear".

It should not be such a difficult idea to communicate, that the "very own speed of light" of every moving observer necessitates that a single beam of light could not begin its journey at the same moment for every observer. This would have been easier for everyone to see in a version of the train thought experiment, where the beams of light, the standing observer and the moving observer all meet in the midpoint simultaneously. Once you puzzle it out, the fact that in Einstein's version the moving observer moves away from the midpoint while the rays of light are propagating has NOTHING to do with the relativity of simultaneity, contrary to what most people would pick from Einstein's most confusing choice of words.

Anyhow, since it has been established that the isotropy of speed of light requires that the actual moments when beams of light begin their journey undergo a transformation, which must occur in an actual time dimension which holds in itself all the events of the world, this seems to imply some things I never hear people discuss about anywhere. Yet they are perhaps the most important things to grasp about Special Relativity. At least in an ontological sense. (Of course ontology doesn't mean anything to mathemathicians, but it should to the physicists, and it definitely does to all the rest of us :)

And since I don't really hear anyone talk about these things, I must wonder if there exists better interpetations (if so, haven't heard of those either). In other words, these are the ontological implications I've simply come to realize myself.

Determinism in Special Relativity:
Since the relativity of simultaneity is a key element in SR, then accepting SR also means we are accepting that the events that lie in our future, have already happened from the point of view of other objects. Namely, objects that are moving towards us fast enough and/or are distant enough. And thus every event in our future must be pre-determined. Rather problematic, but not an impossible idea. (Actually I expect determinism even without SR, but that's another issue and is not due to future already having happened from some perspective)

Things moving back in time routinely:
People usually have some sort of grasp about time slowing down in theory of relativity, but when you mention things moving routinely forwards and backwards in time, you often get an outcry; "Theory of relativity claims no such thing!". But of course it does, since simultaneity is relative.

Let there be two observers "at rest", RED and BLUE.

Blue shoots a beam of light towards Red.

While the light is on its way, Red will change direction away from Blue.

http://www.saunalahti.fi/anshyy/PhysicsForums/Simultaneity01.jpg
(Vertical axis is time, horizontal is location. The planes of simultaneity are black/grey, light is faint yellow -> speed of light is in 45 degree angle)

The POV of RED:
Even though the beam of light was well on its way BEFORE Red changed its direction, AFTER changing direction the light suddenly had not even began its journey.

http://www.saunalahti.fi/anshyy/PhysicsForums/Simultaneity02.jpg

While this is a bit problematic philosophically (especially since there is no actual mechanic to explain it in the theory, rather it is derived as a necessity to the 2nd postulate), I guess there's no reason to think it is impossible. After all, there is nothing with which we could have ever directly see/experience this effect. But this does lead me to a worrying observation about SR, which doesn't really reveal itself in the math expressions.

In the above example the Red did, in a sense, "hasten away from the beam of light". Even if the beam of light was just 2 seconds away from hitting the Red at the moment of acceleration, after the acceleration it can take a lot longer than 2 seconds for the beam of light to arrive. In this particular example, the two seconds would become about 5 seconds as measured by the Red itself (and about 7 from the POV of blue). But even then we can say that the SPEED of the beam stayed constant, since we assert that the moment when the light began its journey changed. This is basically what Lorentz-transformation does in SR, it adjusts moments of events in such manner that we can always interpetate the speed of light as C relative to ourself.

So superficially, the Red could either decide he was indeed hasting away from the light, or he could decide to use the constant C to derive the actual moment of shooting and thus conclude the shooting took place much later than what the Blue is claiming. (Of course we should expect differences in details between different theories, yet the above should be understood about the nature of Lorentz-transformation)

On top of the above, there are still issues I haven't been able to interpetate ontologically at all, nor have I found anyone even mentioning such scenarios. I wish to present these problems here, in case someone knows some solutions outright:

Two rotating wheels on shared axis.
I believe it has been established that the circumference of a rotating wheel, and thus the whole wheel, does in fact Lorentz contract in SR, when observed from the center:
http://freeweb.supereva.com/solciclos/gron_d.pdf

This is problematic in the case when there are two wheels that are rotating in separate directions on a shared axis. According to SR, both the POV of either wheel, the other should be smaller. In other words, both wheels could push sticks from their circumference so that the sticks completely encircle the other. This does not seem logically possible in any kind of interpetation of SR that I can conceive.

Obviously this is NOT the same case as two trains passing each others, in which case it is quite trivial to demonstrate how "both of the trains are shorter than the other", due to the relativity of simultaneity. As oppose to the passing trains, in the case of two wheels there is nothing passing anything in the direction of radius; there in fact exists no point in time when any outermost element of the circumference of either wheel actually exists within or outside the radius of the other wheel. In other words, we cannot really choose any moment in time when one wheel could be smaller than the other. So I'm at total loss here.

Co-accelerating spaceships
In my opinion, this displays particularly well my struggling with the second postulate of SR:

Two identical spaceships which are at rest, perform identical acceleration events to identical direction, beginning simultaneously, as seen below:

http://www.saunalahti.fi/anshyy/PhysicsForums/Simultaneity03.jpg
(Red ones are the space ships. Right one will be called the ship in front (since ships will be moving in line to the right). Blue one is an observer who stays at rest. The acceleration event is instantaneous here, but we will add real-world acceleration into the pile soon)

From the POV of FRONT SHIP:
As the front ship changes its direction, so does the rear ship. However immediately after changing direction, the ship on the rear MUST have gone back in time and not begin its acceleration in a while. (As is seen from the plane of simultaneity, in black)

From the POV of the REAR SHIP:
Vice versa happens. Immediately after the acceleration, the front ship MUST jump forward in time, and now "has been moving" for a while already.

Due to this, while the distance between the ships stays constant from the POV of the blue observer (as he would expect since the ships go through identical acceleration procedure), from the POV of the ships the distance should increase:

http://www.saunalahti.fi/anshyy/PhysicsForums/Simultaneity04.jpg

Even though they did go through the same acceleration procedure, after the fact these procedures exist in different moments in time.

But we should arrive at the same conclusion even if there is a steel rod between the ships. Thus making it appear that we should expect any fast-moving object to be Lorentz-contracted ONLY if it is the observer itself has changed direction from "rest". If an external object accelerates, then we should expect it to experience stretching by the same mechanic that usually causes contraction, and thus remain at constant length from the POV of the observer.

Very confusing, but that's not even the real bastard problem yet.

The acceleration occurs instantly in the diagram, but if you will, please imagine little curves there in the place of the sharp corners, as would actually be the case. This doesn't actually remove the above problem, as you can surely imagine, but rather it reveals the whole magnitude of the problem;

When the front ship begins it's acceleration, the rear ship begins identical acceleration. Since the acceleration event is identical, the ships should basically preserve their mutual conception of simultaneity at all times (since they would be co-moving at all times). In other words the ships & the rod should keep their length from their own perspective, and contract from the perspective of the blue observer.

But the second postulate also very concretely requires that, for example, the rear ship must move backwards in time from the POV of the front ship during acceleration. If we assert it doesn't go back in time, then it becomes very trivial to demonstrate that light didn't move at the speed C relative to the observer by sending light signals from one ship to the other just before launch.

So from the POV of the front ship, the rear ship would need to meet two mutually contradicting requirements; stay in the same inertial coordination system with the front ship (co-accelerate), and stay at "launch pad" longer than the front ship.

And vice versa for the ship on the rear.

I hope someone is able to point out a solution because this is driving me stark raving mad

 

[JesseM]

In a lot of these cases you are talking about how things look from the point of view of a non-inertial observer. But as you point out early in the post, asking how things "look from a given observer's point of view" is not really a question about how they see things using light-signals, its a question about when and where things happen in the coordinate system where they are at rest. But when you talk about an accelerating observer, there is no "standard" way to construct a coordinate system where that observer is at rest, unlike with inertial observers. Thus it isn't really right to say things move back in time from the point of view of an observer who changes velocity, for example; it's true that if you look at series of inertial reference frames where the accelerating observer is instantaneously at rest, then events which had already happened in an earlier frame in the series may have yet to happen in a later frame in the series, but this just shows that you have problems constructing a single well-behaved non-inertial coordinate system for the accelerating observer such that his definition of simultaneity at any given moment will agree with that of his instantaneous inertial rest frame at that moment.

I talked a little more about the problems I saw with defining a coordinate system for a non-inertial observer in post #18 on this thread. I think it is possible to adapt SR to non-inertial coordinate systems using tensor mathematics, although you'd have to ask someone else to elaborate on this; but again, unlike with inertial observers there isn't a single "standard" agreed-upon way to define the coordinate system of an accelerating observer, you'd have a choice of different coordinate systems which would give different answers to questions involving simultaneity and so forth. And certainly you couldn't assume that the usual rules of SR (stated without tensor mathematics) would apply in such coordinate systems, like the rule that light must always have a coordinate velocity of c or the rule that time dilation and lorentz-contraction are based solely on coordinate velocity. So unlike with inertial observers, there will be no standard answer to what a non-inertial observer "observes" in a given situation, where "observes" is taken to mean what is true in the observer's rest frame as opposed to what he actually sees using light signals.

 

[robphy]

[I fear that with such a long first post (with many issues and questions) this thread will be quickly convoluted... unfortunately. It may have been better to ask a single succinct and well-posed question... then proceed from there... possibly to related questions in other threads.]

Just a comment concerning "Blue shoots a beam of light towards Red"... Red, of course, did not react to Blue's shooting... In other words, events "Blue Fires" and "Red Turns" are spacelike-related (i.e. causally-disconnected).

On that website, you have some interesting graphics and animations of spacetime diagrams. Unfortunately, I need a translation and more explanatory text. The spacetime diagrams will help to discuss and hopefully resolve the issues you raise. Loosely or poorly defined words won't help. I suggest adopting operational definitions of various concepts.

My $0.01

 

[pervect]

I have to agree, it's difficult to tell where to start with such a long post.

The first point that I want to make is that one needs to disentangle the notions of causality with the issues of assigning coordinates.

Coordinates are a purely human invention, like a map of a territory. The specific assignment of coordinate values to events in space-time has no physical significance whatsoever (the map is not the territory).

Causality is something that's physically significant. When a light signal is emitted at event A, and is received at event B, A and B are causally related. A is in B's past (I think this is sometimes called past domain of dependency).

If two events are space-like separated, so that light cannot reach from A to B, then there is no causal relationship between them. Sticking different coordinate lables on them does not change this physical fact.

The OP in this thread seems to be attaching too much physical and philosophical significance to human choices - the choice of a particular coordinate system. The fact that A has a lower time coordinate than B is not enough to establish a causual relationship (as can be seen by the definition using light cones).

For instance, the two space-ships that accelerate "at the same time" in the two spaceship diagram are spacelike separted. This general paradox is called "Bell's spaceship paradox", and it's discussed somewhat in the sci.physics.faq, though not all the questions that the OP asks are answered there.

http://math.ucr.edu/home/baez/physics/Relativity/SR/spaceship_puzzle.html

There is no "unique" coordinate system associated with an accelerated obsesrver, since all coordinate systems are arbitrary. The choice of Fermi-Walker transport to define a local coordinate system is a very popular choice though, and is discussed at length in some textbooks such as MTW's "Gravitation".

The mathematical defintion of this might help. The graph on pg 173 of MTW's gravitation would be even better (FIgure 6.4) - this graph can be construced by plotting the following equations which are easier to communicate than the graph itself is:

If we let \tau, \chi be the coordinates of the accelerated observer with a constant acceleration g, we can map them into inertial coordinates with the following equations:

<br /> t = (1/g + \chi) \mathrm{sinh}(g \tau)<br />
<br /> x = (1/g + \chi) \mathrm{cosh}(g \tau)<br />

Plotting lines of simultaneity (constant \tau) will reveal that they are all straight lines, with different slopes.

Plotting the lines of constant \chi will reveal that they are hyperbolas.

The "grid" of lines of constant \tau and constant \chi form the "grid" of a local coordinate system (the Fermi-Walker coordinate system of the accelerated observer) - just as the grid of lines of constant t and lines of constant x form the "grid" of the cartesian inertial coordinate system.

They define a coordinate system because a unique point is given by the intersection of a line of a specific \tau and a line of specific\chi, just as a unique point is given by a specific line of constant t and a specific line of constant x.

Actually, there is a "gotcha" here.

The lines of simultaneity cross at the origin of the graph. This indicates that the coordinate system described does not cover all of space-time, because the coordinate lines are not allowed to cross in such a manner. A single point is not allowed to have more than one set of coordinates.

For more on this, see my previous post
https://www.physicsforums.com/showpost.php?p=887032&postcount=91

The graph of \chi=0 will be the graph of the worldline of the accelerated obsever.

 

[leandros_p]

Dear AnssiH,

Einstein also explained in his book "Relativity: The Special and General Theory" Chapter 16 :

"According to this theory there is no such thing as a “specially favoured” (unique) co-ordinate system to occasion the introduction of the æther-idea, and hence there can be no æther-drift, nor any experiment with which to demonstrate it. Here the contraction of moving bodies follows from the two fundamental principles of the theory without the introduction of particular hypotheses; and as the prime factor involved in this contraction we find, not the motion in itself, to which we cannot attach any meaning, but the motion with respect to the body of reference chosen in the particular case in point. Thus for a co-ordinate system moving with the Earth the mirror system of Michelson and Morley is not shortened, but it is shortened for a co-ordinate system which is at rest relatively to the sun."

Einstein was genius enough to understand that Physics is about physical information. It is not about ontology.

Physics does not provide a knowledge of physical reality. Physics provides information about physical reality. Therefore, for the science of Physics a singular physical term, like a specific co-ordinate system in an experiment, "is shortened" and "is not shortened" at the same time. This is not a statement conflicting with itself, because the "is" and the "is not" refer to the physical information that the physical reality provides to different observers. The science of Physics does not provide the absolute knowledge of physical reality. It only provides relational information about physical objects of physical reality.

In this context, Einstein made clear in the above passage that: "we find, not the motion in itself, to which we cannot attach any meaning, but the motion with respect to the body of reference chosen in the particular case in point".

By the moment that we realize that "we can not find the meaning of the motion in itself, but we can find the meaning of motion with respect to the body of reference chosen in the particular case in point", we can realize Einstein's scientific perspective of finding physical information "with respect to...chosen reference".

So, Einstein did not produced an ontology, but he invented/defined new mathematical/physical relations by which he was able to express in a scientific way the physical information of ratio between "space" and "time".


"Simultaneity" is a term that, before Einstein, was used as a physical term that was defined by "time". Einstein made clear, in his work, that (Chapter 17) : "The four-dimensional mode of consideration of the “world” is natural on the theory of relativity, since according to this theory time is robbed of its independence". In this context, the term "simultaneity" according to Einstein's work is also “robbed of its independence”, defined after his work by four dimension of "time-space" - not just by the dimension of time.

Having said that, we should also read carefully the following words of Einstein (Chapter 17): "It must be clear even to the non-mathematician that, as a consequence of this purely formal addition to our knowledge, the theory perforce gained clearness in no mean measure."

Einstein does provide a mathematical analysis of the four dimensional world at the Appendix 2, where he writes: "From a “happening” in three-dimensional space, physics becomes, as it were, an “existence” in the four-dimensional “world.” "

You can find a very nice VIDEO, about "Simultaneity" provided by "National Science Foundation" . In this video you can visualize the example of train, that Einstein used. Check also another video on "Time Dilation"

Leandros

 

[Hurkyl]

Bleh, I hate the word "ontology" -- I can never figure out what it means. But I'll take a shot at responding.


A crucial feature of Special Relativity is that it asserts that space-time is a (3+1)-dimensional Minowski space.

(Similarly, a crucial feature of classical mechanics is that it asserts space is a 3-dimensional Euclidean space)

I would suppose that this completely characterizes the ontology of SR -- everything about which one might wish to speak can be expressed geometrically, and thus has its meaning reduced to the above statement.

 

[AnssiH]

In a lot of these cases you are talking about how things look from the point of view of a non-inertial observer.

I was intending to describe what is happening from the point of view of an observer. If something gave the impression that I was describing what something looks like to an observer, it probably needs some clarification, so please point such cases out :)

I talked a little more about the problems I saw with defining a coordinate system for a non-inertial observer in post #18 on this thread.

Ok, I see. I remember hearing the same thing, that there are difficulties in SR with non-inertial frames. You said in the other thread:
At each moment along the object's worldline, should its definition of simultaneity match that of the inertial frame where it's at rest at that moment? If you try to do it this way, you can have problems with planes of simultaneity at different points along the wordline intersecting each other, so that the same event is sometimes assigned multiple time coordinates, and distant clocks can run backwards as coordinate time runs forwards.

Don't the planes of simultaneity criss cross anyway after the acceleration, when the object is back at rest? Because of this, and because relativity of simultaneity is a key requirement, it seems to me that we cannot discard anything as false just because clocks need to run forwards and backwards routinely. It seems to me that they necessarily must do this in SR.

So, regardless of how we treat the notion of simultaneity while changing direction, AFTER changing direction there necessarily exists events in your future that had already happened before you changed direction.

 

[AnssiH]

[I fear that with such a long first post (with many issues and questions) this thread will be quickly convoluted...

True... Well, the point of the first part of the post was mostly to make sure I have grasped the correct idea of SR. It seems to me that just about all the paradoxes I've heard revolve around not grasping the relativity of simultaneity concretely. But then I'm at total loss with probelms that seem to arise BECAUSE of relativity of simultaneity.

But if the first part seems about right, then I wish to concentrate only on the two actual problems; the spinning wheels, and two spaceships & a rod.

Just a comment concerning "Blue shoots a beam of light towards Red"... Red, of course, did not react to Blue's shooting... In other words, events "Blue Fires" and "Red Turns" are spacelike-related (i.e. causally-disconnected).

Yes, this is very well understood. The point is just to discuss how the world actually operates according to SR. So in the above case the red could just be pre-timed to change direction, and the point of interest is the fact that the light actually cannot be on its way after the change of direction has happened.

 

[AnssiH]

The OP in this thread seems to be attaching too much physical and philosophical significance to human choices

Yes, sounds like me :) Although I would like to argue about the "too much", because the philosophical aspect is the part which sparks my interest; how do things actually work. It's not the math, it's the actual interpetation of the math.

But let it be said that I attach SO much philosophical significance to SR, for instance, that I am ready to accept that clocks can just do swoosh forwards and backwards. I just see no other choice. Basically I stand where Hurkyl appears to stand in his comment. Everything reduces to the statement about spacetime, or even further; to the postulates. That is, if you accept that the speed of information is in reality isotropic, then you also accept the full impact this has on the reality, as described by SR. There's no pick and choose here, you HAVE to accept it all.

Of course that is not to say there couldn't ever come a better description of reality than the theory of relativity, but then such a description also necessarily has different postulates, and also comes as a full package that must be accepted as a whole.

Thank you very much for the link about the two spaceships, I'll take a look at a better time...

The lines of simultaneity cross at the origin of the graph. This indicates that the coordinate system described does not cover all of space-time, because the coordinate lines are not allowed to cross in such a manner. A single point is not allowed to have more than one set of coordinates.

Is not? Why so? And if not, how do we maintain the idea of isotropic speed of information propagation, since the simultaneity lines of two inertial coordinates can cross too (like they do in the spacetime diagrams in the opening post) This is interesting since this is something that should have a direct impact on our notion of reality.

 

[AnssiH]

Einstein was genius enough to understand that Physics is about physical information. It is not about ontology.

Well, I would argue that the mechanic with which the physical information propagates IS part of reality. So the SR description of this does come with all its features attached.

What Einstein meant with the relativity of simultaneity is well understood at this end, and surely Einstein also did understand perfectly well what a profound impact SR has on the actual reality of the universe. It is not just a mathematical construct, if its postulates are real.

 

[chronon]

The trouble is that we use a lot of time-based words like before, after, is. In SR people tend to use these based on the time coordinate of a given inertial frame. I think that it's better to use them to reflect the structure of SR, so that before means 'in the past light cone of' and after means in the 'future light cone of', and the spacelike hypersurface called now has no significance whatsoever.

 

[leandros_p]

Well, I would argue that the mechanic with which the physical information propagates IS part of reality. So the SR description of this does come with all its features attached.

What Einstein meant with the relativity of simultaneity is well understood at this end, and surely Einstein also did understand perfectly well what a profound impact SR has on the actual reality of the universe. It is not just a mathematical construct, if its postulates are real.

Einstein said, in one of his lectures:

“At this point an enigma presents itself which in all ages has agitated inquiring minds. How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality ? Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things ?

In my opinion the answer to this question is, briefly, this: as far as the proposition of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality. It seems to me that complete clarity as to this state of things became common property only through that trend in mathematics which is known by the name of “axiomatics”. The progress achieved by axiomatics consists in its having neatly separated the logical-formal from its objective or intuitive content; according to axiomatics the logical-formal alone forms the subject matter of the mathematics, which is not concerned with the intuitive or other content associated with the logical-formal.”

“Geometry and experience”, lecture by Albert Einstein before the Prussian Academy of Science, January 27, 1921.

 

[JesseM]

Ok, I see. I remember hearing the same thing, that there are difficulties in SR with non-inertial frames. You said in the other thread:

At each moment along the object's worldline, should its definition of simultaneity match that of the inertial frame where it's at rest at that moment? If you try to do it this way, you can have problems with planes of simultaneity at different points along the wordline intersecting each other, so that the same event is sometimes assigned multiple time coordinates, and distant clocks can run backwards as coordinate time runs forwards.

Don't the planes of simultaneity criss cross anyway after the acceleration, when the object is back at rest? Because of this, and because relativity of simultaneity is a key requirement, it seems to me that we cannot discard anything as false just because clocks need to run forwards and backwards routinely. It seems to me that they necessarily must do this in SR.

Even if an observer starts out moving inertially and later returns to moving inertially, you can't just take the two different inertial frames and say that this is how things happen from that observer's point of view, because having a "point of view" that covers two different parts of a path demands having a single coordinate system which covers both parts. If this observer was traveling alongside an inertial observer A before accelerating, then after accelerating was traveling alongside another inertial observer B, he could say that an event that was in A's past before acceleration was in B's future after accelerating, but that wouldn't mean he could say an event that was in his own past before accelerating was in his own future after accelerating. If we are using "past" and "future" to refer to coordinate time, a statement like this can only make sense if the observer has his own coordinate system which covers both the time before he accelerated and the time after he accelerated.

As chronon said, though, another way to talk about a given observer's past and future is using light cones instead of coordinate time, and in this case you can talk in an absolute way about which events are in the past and which are in the future and which are "elsewhere" for any observer, even an accelerating one, at any point on his path.

 

[pervect]

Yes, sounds like me :) Although I would like to argue about the "too much", because the philosophical aspect is the part which sparks my interest; how do things actually work. It's not the math, it's the actual interpetation of the math.

But let it be said that I attach SO much philosophical significance to SR, for instance, that I am ready to accept that clocks can just do swoosh forwards and backwards. I just see no other choice.

My position is that it's not clocks that swoosh forwards and backwards. It's coordinates (things without any real physical significance) that can jump around.

An actual clock will always tick in one direction - forwards.

Basically I stand where Hurkyl appears to stand in his comment. Everything reduces to the statement about spacetime, or even further; to the postulates. That is, if you accept that the speed of information is in reality isotropic, then you also accept the full impact this has on the reality, as described by SR. There's no pick and choose here, you HAVE to accept it all.

I would say that causality in alive and well in SR, and that it is handled mathematically by the idea of globally hyperbolic space-times (Minkowski space-times are always globally hyperbolic).

This is additional structure "on top of" Minkowski space-time. I suspect that Hurkyl can define the extra structure more clearly using less words than I can :-).

Things do get more complex in GR - it is possible to construct space-times that are not globally hyperbolic. These space-times are generally not regarded as being physically significant, however.

Is not? Why so? And if not, how do we maintain the idea of isotropic speed of information propagation, since the simultaneity lines of two inertial coordinates can cross too (like they do in the spacetime diagrams in the opening post) This is interesting since this is something that should have a direct impact on our notion of reality.

The simultaneity lines of a single inertial observer never cross in the flat space-time of SR. They are parallel lines.

It is only when an observer accelerates that the lines of simultaneity can cross. The crossing of these lines results in ill-behaved coordinate systems (where a single point has more than one coordinate), which results in a llimitation on the size of the coordinate system of an accelerated observer.

The "Fermi-Walker" approach to defining the coordinate system of an accelerated observer basically means that the accelerating observer uses as his defintion of simultaneity the same defintion that an instantaneously co-moving observer uses.

This is a very useful and practical coordinate system, but it does inherently have a limitation on its size, so it only works "nearby" the accelerating observer, because of the "line crossing" problem.

 

[AnssiH]

The simultaneity lines of a single inertial observer never cross in the flat space-time of SR. They are parallel lines.

I seem to be missing something here... Aren't the lines of two different inertial coordinates always crossing at far enough distance? I mean, you can replace the instantaneous acceleration with a curve here:
http://www.saunalahti.fi/anshyy/PhysicsForums/Simultaneity01.jpg
...and you still get the lines crossing each others. How should that be solved?

As for the rest of the responses;
Is it your message to me that the notion of relativity planes is not an attempt to describe what happens in reality, but instead is a description of some sort of meta-reality, from which reality manifestates? In which case, aren't we completely missing a description of what happens in reality?

I mean, I believe there is such a thing as reality which operates by certain simple laws. As a system builder, I am perfectly capable of thinking about how certain mechanics manifestate certain things, and as for the SR, I find it easier to just purge everything I THINK I know about reality, such as that time always flows forwards and everything can only happen once all that, and then lay down the mechanics of SR on a clean table.

It becomes much much easier to see how information propagates in SR and how it all really operates, if I dream up a kind of "virtual" environment from scratch, where the speed of light is, say, 10 m/s.

Suddenly stuff like you see in:
http://www.saunalahti.fi/anshyy/PhysicsForums/Simultaneity01.jpg
becomes up-close and intimate, and the reality of it all slaps you in the face (well, slaps ME in the face anyway :)

So now if I actually implement the mechanic of SR, it will mean that a beam of light which is approaching an observer, CAN move backwards in time and back "into" the lightsource if the observer moves away. And while the learn operates in such a "backward" manner", observer will still learn of reality just like we do, and should find it quite impossible that time could flow backwards.

So, it would seem the reality of the second postulate demands this, OR then we should treat the second postulate as a description of some sort of meta-reality, from which the "actual reality" arises, whatever that means.

In any case, the ontological significance of SR cannot be stripped just if it sounds crazy, as long as its mechanic would produce a world just like we experience this one.

Oh, and btw, the explanation of the twin paradox problem also relies on the factual nature of the relativity of simultaneity. If we accept that the clocks on Earth could just jump years and years forward during a turning phase which could take just few moments, it should not be too hard to also accept that the clocks could factually move backwards?

I mean, I am kind of sensing a collective reluctance to really think of these issues, perhaps they are not too interesting to anyone but me? :) But hey!

Anyway, thanks for all the responses so far. Anyone has any clue as for how to solve the two wheel spinning problem? I would feel much more confident in my understanding of SR if I knew how that is solved...

 

[JesseM]

As for the rest of the responses;
Is it your message to me that the notion of relativity planes is not an attempt to describe what happens in reality, but instead is a description of some sort of meta-reality, from which reality manifestates? In which case, aren't we completely missing a description of what happens in reality?

It's just a description of different coordinate systems for describing the same spacetime. The question of whether any coordinate system's definition of simultaneity is more "correct" than any other is akin to the question of whether any placement of the origin of your coordinate axes is any more correct than any other.

So now if I actually implement the mechanic of SR, it will mean that a beam of light which is approaching an observer, CAN move backwards in time and back "into" the lightsource if the observer moves away.

Not if you stick to a single inertial coordinate system it won't. This sort of thing only happens if you attempt to construct a coordinate system in which an observer who accelerates is always at rest, and you try to construct it in such a way that this coordinate system's definition of simultaneity always matches that of the inertial reference frame in which he is instantaneously at rest. But the theory of relativity does not demand that you define a non-inertial coordinate system in this way, that's just an arbitrary choice that you are making.

So, it would seem the reality of the second postulate demands this

You are still failing to understand that the second postulate is only meant to apply to inertial coordinate systems. The second postulate will be false in many (all?) non-inertial coordinate systems, because light beams will not in fact have a coordinate velocity of c at all times in these systems. The second postulate was never meant to say anything about what things should look like from the point of view of an observer who accelerates at any point on his worldline, simply because there is no standard agreed-upon way to construct a coordinate system for such an observer. And keep in mind the the "standard" definition of the coordinate system of an inertial observer is also just a matter of convention--but it so happens that the laws of physics have the property that they will obey the same equations when written in these different inertial coordinate systems, a property known as "lorentz-invariance", so it makes things more simple and elegant if you define the coordinate systems of inertial observers in this way.

In any case, the ontological significance of SR cannot be stripped just if it sounds crazy, as long as its mechanic would produce a world just like we experience this one.

You're correct insofar as you're free to use just about any crazy coordinate system you want to describe the same spacetime and the same laws of nature. Which coordinate system you prefer to use is a matter of aesthetics, not physics. However, a coordinate system which assigns the same event multiple coordinates would probably not be considered "well-behaved", and I'm not sure it would be possible to write equations for the laws of physics in this coordinate system which would make all the same predictions as the laws of physics stated in well-behaved coordinate systems--you might get multiple possible solutions to the equations, or mathematical singularities, issues like that.

Oh, and btw, the explanation of the twin paradox problem also relies on the factual nature of the relativity of simultaneity. If we accept that the clocks on Earth could just jump years and years forward during a turning phase which could take just few moments, it should not be too hard to also accept that the clocks could factually move backwards?

The usual explanation of the twin paradox doesn't say anything about clocks jumping forward, it just points out that when you analyze the problem from the point of view of anyone inertial frame, you conclude the accelerated twin will have elapsed less time. You can also point out that in the inertial frame where the traveling twin is at rest during the return voyage, the clocks immediately after the acceleration are far ahead of what they read immediately before acceleration in the inertial frame where the traveling twin was at rest during the outward voyage, but this is not equivalent to saying that the clocks "jumped forward from the traveling twin's point of view" or anything like that, it's just a comparison of two separate inertial frames. If you want to define a coordinate system where the traveling twin is at rest at all times, you have to define a non-inertial coordinate system, and again, the choice of how simultaneity will be defined in this coordinate system (and thus what the Earth clock will be doing during the accelerating phase) is basically a purely aesthetic one. Presumably you could come up with a wide range of non-inertial coordinate systems which would all give different answers about how the earth-clock behaves throughout the voyage, including weird ones where, say, the Earth clocks run slow until the traveling twin is 3/4 of the way home and then begin running fast. There is no physical reason to say that any non-inertial coordinate system's opinion on simultaneity is any more valid in an "ontological" sense than any other's.

Anyway, thanks for all the responses so far. Anyone has any clue as for how to solve the two wheel spinning problem? I would feel much more confident in my understanding of SR if I knew how that is solved...

The usual way to analyze any problem in SR is to pick an inertial frame and apply the standard equations of SR in that frame. But you ask us in your description of the problem to take the POV of one of the wheels, and there is no single standard definition of what the POV of a non-inertial object should be in SR. You'd have to specify what coordinate system you want the wheel to use in order for your problem to have any well-defined answer.

 

[robphy]

Just a comment concerning "Blue shoots a beam of light towards Red"... Red, of course, did not react to Blue's shooting... In other words, events "Blue Fires" and "Red Turns" are spacelike-related (i.e. causally-disconnected).

Yes, this is very well understood. The point is just to discuss how the world actually operates according to SR. So in the above case the red could just be pre-timed to change direction, and the point of interest is the fact that the light actually cannot be on its way after the change of direction has happened.

Yes, but this would also happen in non-relativistic Galilean spacetime. Your diagram could be interpreted as an ordinary distance vs time graph. One would simply say that "Blue missed". Of course, in the Galilean case, "Blue Fires" and "Red Turns" are causally-related...specifically, "Red Turns" is in the Galilean-causal-future of "Blue Fires".

 

[pervect]

I seem to be missing something here... Aren't the lines of two different inertial coordinates always crossing at far enough distance? I mean, you can replace the instantaneous acceleration with a curve here:
http://www.saunalahti.fi/anshyy/PhysicsForums/Simultaneity01.jpg
...and you still get the lines crossing each others. How should that be solved?

If you change inertial frames of reference, you always have the problem at some distance. But there is no problem for an inertial observer who does not accelerate (change frames of reference).

Infinite accelerations (as in your diagram) are very unphysical, and cause problems anwhere were x < 0 (for acceleration in the x direction).

Finite accelrations have the overlap occur at x < -c^2/g (again for accelerations in the x dirction).

As for the rest of the responses;
Is it your message to me that the notion of relativity planes is not an attempt to describe what happens in reality, but instead is a description of some sort of meta-reality, from which reality manifestates? In which case, aren't we completely missing a description of what happens in reality?

All I am saying is that coordinates are not reality - they are just labels that we stick on events. We can change a coordinate in a blink of an eye - this has no impact on reality, which is limited to lightspeed.

I can go a bit further, putting on my philosphical hat, and say that the notion of "now", because it is observer dependent, is not a part of "reality" when "reality" is defined to contain only events that are observer independent.

Philosophical notions vary so widely that perhaps other people view things differently, perhaps including observer dependent events as part of "reality".

Explaining my point further, our brains, for instance, synthesizes the notion of things that are happening "now" by sorting various signals that travel at velocities a lot lower than that of light. It can get confused and put events in the wrong order.

If two events are 1 foot apart, there is no ultimate resolution of what "now" means that is sharper than a nanosecond. Causality is caused by light speed signals, and if two events are 1 foot apart, it will take light 1 ns to travel between them. When events are space-like separated - i.e. so far apart that light cannot travel between them - there is no notion of causality, no unique "now", no preferred coordinate system.

Two events happen, and we cannot unambiguously say which came "first", and which came second.

Oh, and btw, the explanation of the twin paradox problem also relies on the factual nature of the relativity of simultaneity. If we accept that the clocks on Earth could just jump years and years forward during a turning phase which could take just few moments, it should not be too hard to also accept that the clocks could factually move backwards?

It is not necessary to believe that clocks can jump years forwards and backwards during a turning phase - it is only needed to believe that coordinates can change that quickly.

For the accelerated observer, a careful analysis shows that clocks only run forward in the region in which the coordinate system of the accelerated observer is valid. The region below the Rindler horizion (at -c^2/g) is not a region in which the coordinate system of the accelerated observer is valid.

Anyway, thanks for all the responses so far. Anyone has any clue as for how to solve the two wheel spinning problem? I would feel much more confident in my understanding of SR if I knew how that is solved...

I'd suggest starting another thread for that question, this one is long enough already. I will mention that my favorite reference on the spinning disk is by Tartaglia, and can be downloaded from arxiv. If you start another thread I'll give you the exact reference.

 

[AnssiH]

All I am saying is that coordinates are not reality - they are just labels that we stick on events. We can change a coordinate in a blink of an eye - this has no impact on reality, which is limited to lightspeed.

I can go a bit further, putting on my philosphical hat, and say that the notion of "now", because it is observer dependent, is not a part of "reality" when "reality" is defined to contain only events that are observer independent.

Philosophical notions vary so widely that perhaps other people view things differently, perhaps including observer dependent events as part of "reality".

If two events are 1 foot apart, there is no ultimate resolution of what "now" means that is sharper than a nanosecond. Causality is caused by light speed signals, and if two events are 1 foot apart, it will take light 1 ns to travel between them. When events are space-like separated - i.e. so far apart that light cannot travel between them - there is no notion of causality, no unique "now", no preferred coordinate system.

Two events happen, and we cannot unambiguously say which came "first", and which came second.

Yes, this is very good stuff. This is just the kind of things I wanted to discuss about. But it's not as simple as stating that the moments of times are different for two different observers and that while an observer is accelerating we don't really know how we should handle the math of planes of simultaneity.

This is a response for JesseM as well; here's about the simplest way I can present my concern;
----
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

Thought experiment:
- Speed of light is 1 meter per second for every observer (it is slow just to make it easier to comprehend the situation. It makes no difference to SR; 1 m/s becomes the speed limit)
- There is a stationary red clock.
- There is a blue observer who is initially at rest with the red clock, 5 meters away from it.

Blue observer knows the clock sends a light signal every day at a precise moment of 0s; he knows to expect to see it at 5s if he doesn't move from his location.

Let there be also a purple clock standing right next to the observer, which has been synchronized to show the actual time of the red clock. So despite the information delay from the red clock, the blue observer knows what the red clock is ACTUALLY showing. The BLUE clock has also been synchronized to show the same time initially.

http://www.saunalahti.fi/~anshyy/PhysicsForums/BackwardsEvents1.jpg

Timeline:

(BLUE) 0s - The blue observer knows the signal has been sent.
(BLUE) 2s - The blue observer knows the signal is is only 3 meters = 3 seconds away from him. He decides to start running away from the clock. He will have no actual proof of the signal really having been sent at 0s, but there can be other observers who will tell him later that the light signal was indeed sent at 0s, as usual.

We completely ignore what exactly happens to planes of simultaneity while he is accelerating. The acceleration period is marked in transparent since it makes no difference to us. Let's say the blue accelerates for 1 second. When the acceleration ends, and the blue observer is back in an inertial coordinate system; the second postulate of SR should hold true exactly again.

http://www.saunalahti.fi/~anshyy/PhysicsForums/BackwardsEvents2.jpg

(BLUE) 8s - The signal reaches the blue observer. (=At about 10s in the inertial coordinate system of the red clock)

Now the blue observer has to make a CHOICE concerning reality. He knows the light signal was sent when the purple clock showed 0s. And he knows the light signal was only 3 seconds away from him before he started running, yet while he was receding from the clock in uniform motion, it still took about 5 seconds for the light to reach him.

He must either:
1. Conclude that because of receding from the clock, the light was approaching him with speeds less than C.
Or
2. Conclude that the light was approaching him at the speed C even while he was receding from the clock. It immediately follows, that the light must have begun its journey at the moment that is marked in the diagram with "Signal sent again?"; when blue clock was at about 4s, not 0s (This is the moment the light started its journey for ALL the observer that are now co-moving with the blue observer)

The first option obviously violates the second postulate of SR.

The second option means accepting SR, and accepting that there exist two REAL moments in the world line of the blue observer, in which he simply KNOWS the signal must have been actually sent, so to obey the rules of SR. 0s, and 4s. He can also verify this later from the other observers, who will tell him that yes, the light signal was indeed sent at BOTH moments he suspects must have been the case in his world line.

http://www.saunalahti.fi/~anshyy/PhysicsForums/BackwardsEvents3.jpg

Any other options? All the other options I can think of include ideas of meta reality and strange things about events not actually occurring unless there is someone to see and every observer living their own reality in which everyone else claims non-true things about the propagation of light. So there is a concern here in understanding what happens in reality when we are not there to see. The only logically sound assertion is that time does flow backwards when you are not there to see (albeit this is totally unintuitive).

Does that sound strange?

I'd suggest starting another thread for that question, this one is long enough already. I will mention that my favorite reference on the spinning disk is by Tartaglia, and can be downloaded from arxiv. If you start another thread I'll give you the exact reference.

Ok, I'll do that in few days. (JesseM, to answer your question, I would like to know how the situation looks from the point of view of either wheel, as if there was an eye in the CENTER of the wheel. Which is co-rotating with the wheel. I am not sure if it makes no difference in SR whether both wheels are actually rotating in separate directions, or whether one is stationary and other one is spinning. In any case, the premise of SR should imply, that both wheels could push sticks from their circumference, that would completely encircle the other wheel)

 

[leandros_p]

This is a response for JesseM as well; here's about the simplest way I can present my concern;
----
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

Thought experiment:
- Speed of light is 1 meter per second for every observer (it is slow just to make it easier to comprehend the situation. It makes no difference to SR; 1 m/s becomes the speed limit)
- There is a stationary red clock.
- There is a blue observer who is initially at rest with the red clock, 5 meters away from it.

Blue observer knows the clock sends a light signal every day at a precise moment of 0s; he knows to expect to see it at 5s if he doesn't move from his location.

Let there be also a purple clock standing right next to the observer, which has been synchronized to show the actual time of the red clock. So despite the information delay from the red clock, the blue observer knows what the red clock is ACTUALLY showing. The BLUE clock has also been synchronized to show the same time initially.

http://www.saunalahti.fi/~anshyy/PhysicsForums/BackwardsEvents1.jpg

Timeline:

(BLUE) 0s - The blue observer knows the signal has been sent.
(BLUE) 2s - The blue observer knows the signal is is only 3 meters = 3 seconds away from him. He decides to start running away from the clock. He will have no actual proof of the signal really having been sent at 0s, but there can be other observers who will tell him later that the light signal was indeed sent at 0s, as usual.

We completely ignore what exactly happens to planes of simultaneity while he is accelerating. The acceleration period is marked in transparent since it makes no difference to us. Let's say the blue accelerates for 1 second. When the acceleration ends, and the blue observer is back in an inertial coordinate system; the second postulate of SR should hold true exactly again.

http://www.saunalahti.fi/~anshyy/PhysicsForums/BackwardsEvents2.jpg

(BLUE) 8s - The signal reaches the blue observer. (=At about 10s in the inertial coordinate system of the red clock)

Now the blue observer has to make a CHOICE concerning reality. He knows the light signal was sent when the purple clock showed 0s. And he knows the light signal was only 3 seconds away from him before he started running, yet while he was receding from the clock in uniform motion, it still took about 5 seconds for the light to reach him.

He must either:
1. Conclude that because of receding from the clock, the light was approaching him with speeds less than C.
Or
2. Conclude that the light was approaching him at the speed C even while he was receding from the clock. It immediately follows, that the light must have begun its journey at the moment that is marked in the diagram with "Signal sent again?"; when blue clock was at about 4s, not 0s (This is the moment the light started its journey for ALL the observer that are now co-moving with the blue observer)

The first option obviously violates the second postulate of SR.

The second option means accepting SR, and accepting that there exist two REAL moments in the world line of the blue observer, in which he simply KNOWS the signal must have been actually sent, so to obey the rules of SR. 0s, and 4s. He can also verify this later from the other observers, who will tell him that yes, the light signal was indeed sent at BOTH moments he suspects must have been the case in his world line.

http://www.saunalahti.fi/~anshyy/PhysicsForums/BackwardsEvents3.jpg

Any other options?

Do you understand that you can not use the same space/time frame for both clocks ? You have to use two different sheets for your diagrams, one for every clock. You can not use just one sheet of paper with the same orthogonal scale for both clocks. If you want to use a single "sheet" of paper for both clocks you have to use a curviformed sheet of paper; you must use a 3D surface, not a 2D surface.

Leandros

 

[JesseM]

Assuming:
- Every event happens at some actual moment

But this assumption has no basis in relativity. Every event happens at some actual location in spacetime, but the question of whether separated events happen at the "same moment" or not depends on an arbitrary choice of how to lay a coordinate system on spacetime.

- We can figure out the moment by knowing our distance to the event when it happened and the speed of light

Asking where you were "at the same time" the event happened is a question of simultaneity, so again this depends on your coordinate system. And if you are using a non-inertial coordinate system, there is no reason to assume that a light signal will have a coordinate velocity of c.

- The notion of time is the same for every co-moving observer, regardless of the history if their world lines.

"co-moving" is usually taken to mean two observers are moving alongside each other, with no spatial separation--is this what you mean? If so, then in anyone coordinate system this would be true, but unless the two observers are moving inertially in flat spacetime there won't be any "standard" choice of coordinate system for them to use, you can pick any you like.

Thought experiment:
- Speed of light is 1 meter per second for every observer (it is slow just to make it easier to comprehend the situation. It makes no difference to SR; 1 m/s becomes the speed limit)

Usually people just define distance and time units so that the speed of light is 1--you could measure time in seconds and distance in light-seconds, for example--but OK, we can also change the speed of light so that a light-second equals a meter.

- There is a stationary red clock.
- There is a blue observer who is initially at rest with the red clock, 5 meters away from it.

Blue observer knows the clock sends a light signal every day at a precise moment of 0s; he knows to expect to see it at 5s if he doesn't move from his location.

I take it we are working in the inertial coordinate system where both are at rest--in a different choice of coordinate system the two clocks might not be synchronized, so even though the red clock would still read 0s when the signal is emitted and the blue observer's clock still reads 5s when it is received, the coordinate time for the signal to cross between them needn't be 5s.

Let there be also a purple clock standing right next to the observer, which has been synchronized to show the actual time of the red clock.

There is no "actual time" of a distant event in relativity, only the time in a particular choice of coordinate system. There is a "standard" way to define the coordinate systems of inertial observers, but there is nothing physical that says they must use such a coordinate system, it's just a human convention.

Timeline:

(BLUE) 0s - The blue observer knows the signal has been sent.
(BLUE) 2s - The blue observer knows the signal is is only 3 meters = 3 seconds away from him. He decides to start running away from the clock. He will have no actual proof of the signal really having been sent at 0s, but there can be other observers who will tell him later that the light signal was indeed sent at 0s, as usual.

We completely ignore what exactly happens to planes of simultaneity while he is accelerating. The acceleration period is marked in transparent since it makes no difference to us. Let's say the blue accelerates for 1 second. When the acceleration ends, and the blue observer is back in an inertial coordinate system; the second postulate of SR should hold true exactly again.

The second postulate should only hold true in an inertial coordinate system where he is currently at rest, but you must assume that the origin of this inertial coordinate system was moving at constant velocity for all eternity, so he wasn't at rest in this coordinate system before he accelerated. If you want a coordinate system where he was at rest before accelerating and after, this cannot be an inertial coordinate system.

http://www.saunalahti.fi/~anshyy/PhysicsForums/BackwardsEvents2.jpg

(BLUE) 8s - The signal reaches the blue observer. (=At about 10s in the inertial coordinate system of the red clock)

Now the blue observer has to make a CHOICE concerning reality. He knows the light signal was sent when the purple clock showed 0s.

Only if he chooses to use the inertial coordinate system where he was originally at rest but is now moving at constant velocity. If he uses the inertial coordinate system where he is currently at rest, then it is not true that the light signal was sent when his clock reads 0s. If he wants to use a coordinate system where he was at rest before accelerating and is at rest afterwards, this is a non-inertial coordinate system.

And he knows the light signal was only 3 seconds away from him before he started running, yet while he was receding from the clock in uniform motion, it still took about 5 seconds for the light to reach him.

He must either:
1. Conclude that because of receding from the clock, the light was approaching him with speeds less than C.

If he uses a non-inertial coordinate system, this is certainly possible.

Or
2. Conclude that the light was approaching him at the speed C even while he was receding from the clock. It immediately follows, that the light must have begun its journey at the moment that is marked in the diagram with "Signal sent again?"; when blue clock was at about 4s, not 0s (This is the moment the light started its journey for ALL the observer that are now co-moving with the blue observer)

No, if he uses an inertial coordinate system, he will conclude either that he was not at rest in this system and therefore the relative velocity between him and the light beam was not c (remember, the second postulate only says that light moves at c relative to an observer at rest in a given coordinate system, it is certainly possible for the distance between an observer and a light beam to change at a rate greater or smaller than c if that observer is in motion in the inertial frame you're using), or that the light beam was not emitted when his clock read 0s, depending on whether he uses the frame where he is at rest before accelerating or the frame where he is at rest after accelerating.

The first option obviously violates the second postulate of SR.

Not if you are using a non-inertial coordinate system, because the second postulate was only intended to apply to inertial coordinate systems.

The second option means accepting SR, and accepting that there exist two REAL moments in the world line of the blue observer, in which he simply KNOWS the signal must have been actually sent, so to obey the rules of SR. 0s, and 4s. He can also verify this later from the other observers, who will tell him that yes, the light signal was indeed sent at BOTH moments he suspects must have been the case in his world line.

http://www.saunalahti.fi/~anshyy/PhysicsForums/BackwardsEvents3.jpg

Any other options?

Again, if you pick a single inertial coordinate system to analyze this problem there is no need for any clocks to run backwards. You can either accept that the signal being sent was not simultaneous with his clock reading 0s, or you can accept that although the velocity of light is c in your coordinate system as demanded by the second postulate, the "closing velocity" between him and the light (ie the speed that the distance between him and the light is decreasing) need not be c in any inertial coordinate system where he is not at rest.

(JesseM, to answer your question, I would like to know how the situation looks from the point of view of either wheel, as if there was an eye in the CENTER of the wheel. Which is co-rotating with the wheel.

A rotating coordinate system would still be a non-inertial one. Again, I don't think there'd be any "standard" coordinate system for a rotating observer, and even if there is this is just a matter of human convention, not of ultimate physical truth, you'd be free to define the observer's coordinate system in a nonstandard way.

 

[mitchellmckain]

I find the combination of comments by AnnsiH a little peculiar in complaining both about a lack of understanding about the relativity of simultaneity and the excess of mathematics. Any true understanding of the relativity of simultaneity must use the mathematics since it is primarily a mathematical concept not a philosophical one. I think than anyone with a good understanding of the relativity of simultaneity will naturally use the mathematics more, for it is only way to achieve clarity on the topic. The relativity of simultaneity is critical in resolving apparent paradoxes and apparent contractions between how observers in different inertial frames interpret events. I will demonstrate this in a moment. First I would like to praise AnnsiH for pointing out the importance for making a clear distinction between the main results of specital relativity and what is SEEN. The latter must take into account the phenomena known as the aberation of light. I would also like to express that I keenly share with AnnsiH an interest in ontology and metaphysics and the implications of modern physics in these topics.

Consider the phenomena of lorentz contraction. An observer (let us say that it is you) watching an object traveling at a speed relative to him (you) which is an appreciable fraction of the speed of light, will after accounting for the different times that the light from the object takes to arrive at his position, will conclude that the object is shorter in its direction of motion compared to the observations of a second observer who is traveling with (and in this case shall we say residing on) this speeding object. The puzzling thing is that the second observer will likewise determine that the first mentioned observer (you) and whatever home in which he (you) is residing is traveling at an appreciable fraction of the speed of light in the opposite direction and that it is you and your home which is shorter in the direction of your motion. The point is that motion is relative and so each concludes that it is other which is moving and therefore that it is the other which is shortened in the direction of their motion.

This seems like a contradiction but it is not. The fact is that you and this observer on the moving object interpret the entire universe very differently. One of the key differences is that you and he do not interpret the events in the universe as occurring in the same order. For example, suppose you see a star 10 light years in front of you (that is 10 light years in the direction that the object and the observer residing on it is moving) going nova at the same time as you see a star 10 light years behind you (10 light years in the direction opposite the way the object is moving) also going nova. Since you know that it takes 10 years for light to travel 10 light years distance you know that the two novas occurred at the same time 10 years ago, right? Well the observer on the moving object would not agree. You see from his point of view the two stars are moving. One is moving towards him and the other is moving away from him. So even though he sees the novas at the same time just like you (since he was passing through your vicinity of space at the time), he knows that the light from the nova of the star coming toward him must have traveled farther than the light from the nova of the star going away from him. This is because even though at present time both stars are equally distant, the star coming toward him was farther away just a short time ago and the star going away from him was closer. Therefore, he concludes that the nova of the star coming toward him happed first before the nova of the star going away from him.

For me it always help keep things straight to put numbers to these things so suppose the object is moving 86.6% of the speed of light. Then according to his calculations the light from the nova of the star coming toward him left that star 37.32 years ago when that star was 37.32 light years away. The light from the nova of the star going away from him left that star 2.68 years ago when that star was only 2.68 light years away. So while you think the two novas occurred at the same time, he thinks that they happened 34.64 years apart. During the 2.68 years that the light from the receding star is traveling towards him the star moves .866 times 2.68 = 2.32 light years farther away so that it is now 2.32 + 2.68 = 5 light years away. During the 37.32 years while the light from the approaching star is traveling towards him, the star moves .866 times 37.32 = 32.32 light years towards him so that it is now 37.32 - 32.32 = 5 light years away.

But wait a minute. For you the two stars were 20 light years apart, while for him the two stars are only 10 light years apart. The fact is that for him, you and the two stars are moving at 86.6% of the speed of light and so you, the two stars and all the spaces in between are all shorter (according to lorentz contraction) by a factor of two. For you it is the object (on which the other observer resides) which is moving and which is shorter by a half. In order to see the full symmetry between you and this second observer suppose there are two more stars which are not moving from his point of view, 20 light years apart, 10 light years away in each direction, then you would see these stars as moving and only 10 light years apart. It seems crazy and contradictory but contradictions are resolved by this fact that you and he do not see events occurring in the same order.

To see this more clearly let's label the first two stars Af and Ar, and label the second two stars Bf and Br. Then you see this,

Ar...(5 ly)...Br->...(5 ly)...you...(5 ly)...Bf->...(5 ly)...Af

while he sees this,

Br...(5 ly)...<-Ar...(5 ly)...him...(5 ly)...<-Af...(5 ly)...Bf

This is possible because, while for you Br has already passed Ar, for him this has not happened yet, and while for him Af has already passed Bf, for you this has not happened yet. All the events which have already happened to your rear (Br passing Ar and Ar going nova), for him have happened more recently (Ar going nova) or haven't even happened yet (Br passing Ar). All the events to your front, one of which has not happened yet, have for the other observer, already happened (Af passing Bf) or happened long ago (Af going nova). So in sense you could say that the observer on the "moving" object sees to the rear what you would call your past and he sees to the front what you would call your future. In fact as he looks at you, your front side is slightly in the future compared to your rear side, and during that time difference your front side has traveled closer to your rear side, and so he calculates you to be shorter from front to rear.

This is not what he actually sees, because that is subject to a further distortion due to the fact the light which he sees you by takes time to travel to his eye. The light from your farther side has to travel a little farther than the light from your closer side and at 86.6% of the speed of light, you move a significant amount during that time. The result is that when you are in front of him moving toward him you actually appear elongated and it is only when you are behind him traveling away from him that you appear shorter (even shorter than half).


Ontology: (major topic switch to philosophy rather than physics)

Now as for the topic of ontology, I would like to point out the highly geometric nature of the observation of Hurkyl. That is to say that the ontological implication of special relativity concerns the geometry of space-time. It is my opinion that this conforms very well to a modernized version of Aristotle's ontology of matter and form, where what he destribes as matter more nearly fits the modern concept of energy and his idea of form has been given much greater clarity in the geometrical concepts of modern physics. The implications of modern physics is that being consist of energy and geometrical form, and that everything is some form of energy.


--------------------------------------------------------------------------
See my relativity simulator at my website http://www.relspace.astahost.com

 

[AnssiH]

The second postulate should only hold true in an inertial coordinate system where he is currently at rest, but you must assume that the origin of this inertial coordinate system was moving at constant velocity for all eternity, so he wasn't at rest in this coordinate system before he accelerated. If you want a coordinate system where he was at rest before accelerating and after, this cannot be an inertial coordinate system. Only if he chooses to use the inertial coordinate system where he was originally at rest but is now moving at constant velocity. If he uses the inertial coordinate system where he is currently at rest, then it is not true that the light signal was sent when his clock reads 0s.

Oh ok, that kind of makes sense... It's not very neat ontologically, but there is a logic to it.

The reason it is not very neat is that basically the history of the path of the light beam is decided only once it actually hits the observer. Surely this is a kind of a backwards way to see it, but then there is a sort of backwards logic in how SR was built too (in the sense that the mechanism for relativity of simultaneity is not explained, rather it is a necessity to make world work, whatever the actual mechanic underneath it may be)

So, in the example I gave, we cannot then really say that the light from the POV of blue observer had ever begun its journey at 0s, rather it must have left ONLY when his clock reached 4s.

This has to do with determinism too. In a sense, the future of the world line of the blue observer must be "known by the universe" at 0s. In this interpetation the universe must kind of know that the world line will turn, and thus every beam of light that will hit the world line after the acceleration is, in a sense, kept in hold (or sent on its way sooner at the other direction)

Obviously the above statement is backwards to the highest degree, but still I think your view is propably better backbone to build a real-world interpetation of SR on, than that of mine. I.e. all this should just imply that a better ontological interpetation to information propagation is needed than "beams of light" or anything of that sort. That in an SR worldview, we should purge all ideas in which any EMS information is propagated in any manner that we currently know of at all. There could be a link between quantum physics and SR to be found somewhere in here... Very cool.

 

[JesseM]

The reason it is not very neat is that basically the history of the path of the light beam is decided only once it actually hits the observer.

I don't understand, why do you say that? If the observer is determined to use the inertial frame in which he was at rest at the moment the light hit him, then of course he can't decide which frame that actually is until the light actually hits him, and only once he has picked the frame can he assign a time-coordinate to the event of the light being emitted. But there's nothing that obligates him to use this frame at all, that's just an arbitrary personal preference. Any problem in SR can be analyzed from any choice of reference frame you wish. He could equally well have decided to use the frame in which he was at rest before accelerating (or even a frame moving at 0.97c relative to his original rest frame), in which case he doesn't have to wait until the light hits him to assign a time-coordinate to the event of the light being emitted.

 

[AnssiH]

For me it always help keep things straight to put numbers to these things

There's a neat trick which I came up with regarding Lorentz-transformation. I don't know if people have used it before.

Basically if you just draw a spacetime diagram like the ones I've posted (one axis for location and one for time), and then set the light cones in 45 degree angle, you can basically just use any 3D-modeling software to simply SCALE the worldlines in a 45 degree angle so that when one axis shrinks, another one stretches uniformly. And when you tilt the worldlines in upright position by scaling them like this, it equals to switching frames.

http://www.saunalahti.fi/anshyy/PhysicsForums/Scale-transformation1.jpg
http://www.saunalahti.fi/anshyy/PhysicsForums/Scale-transformation2.jpg

You can include the planes of simultaneity and everything, and it just works. After all, that's basically what Lorentz-transformation does, it simply scales the distances between the events and the moments of observations in the spacetime. Once you know the moment when an event has been observed, Lorentz-transformation "decides" when it actually occured.

Now as for the topic of ontology, I would like to point out the highly geometric nature of the observation of Hurkyl. That is to say that the ontological implication of special relativity concerns the geometry of space-time. It is my opinion that this conforms very well to a modernized version of Aristotle's ontology of matter and form, where what he destribes as matter more nearly fits the modern concept of energy and his idea of form has been given much greater clarity in the geometrical concepts of modern physics. The implications of modern physics is that being consist of energy and geometrical form, and that everything is some form of energy.

Well yeah... This will get wildly off-topic, but since the topic is pretty much covered already, I'll just be mumbling my mind.

Let it be said that I for one won't be very surprised if it turns out that simultaneity is not actually relative after all -> that the second postulate doesn't hold true. I don't know if it's a popular view among people (I'm guessing not), but that has to do with the very idea of 4D spacetime where objects are transformed back and forth inside the time axis.

Using the spacetime to come up with the correct numbers is one thing, but in real world, obviously time itself can never actually be measured. We can only compare the speed with which one physical system operates and compare it to the operation speed of another physical system. Or compare the speeds with which two identical systems operate in different environments.

Say, consider a virtual system where information propagates like bullets (kind of like in emitter theory). And consider an object consisting of atoms that are attached together on the basis of this limited speed information (like in our world, but without implications of SR).

When such an object accelerates in such a world, obviously the net delays in information propagation between atoms rise along with the strength of acceleration. That means that an object suffering from acceleration necessarily slows all its physical processes down, while time itself is absolute (in the sense that simultaneity is absolute).

As a neat side effect of such information propagation, such object also experiences inertia without having been assigned any mass. The object basically gains mass out of mere energy, and the fundamental particles of the object need not have any mass at all. And if this information that bonds the atoms has any tendency to propagate towards, say, other objects nearby, the objects will start moving towards each others W/O experiencing inertia (or time dilation), and will do so with exactly the "speed" that the information itself tends to change direction REGARDLESS of the mass or size of the object, since ALL the mass is caused by the very bonding that now has a tendency to move somewhere...

Hehe, I am not sure if you can so readily imagine these effects if you don't happen to have an alignment to think about dynamic systems & processes, but if you were to make a visual simulation of such information propagation between atoms, these effects would become pretty obvious... So you see, I'm a system builder, I think about dynamic systems ;)

But while such a system has some pretty neat features, like it readily explains the mysteries of gravity and inertia and missing mass between a proton and the three quarks that it consists of and what have you, let it be said that SR is a different beast altogether in its mechanic with how time dilation occurs, and it is about the ONLY conceivable system that predicts time dilation between two observers in an uniform motion.

Although I don't know about that many experiments that measure time dilation of something in uniform motion, or that measure speed of light independent of source. Of the former there are fast-moving myons having extra-ordinarily long half-lifes at least, and of the latter there is a test of T. Alväger at the sixties regarding pions moving near the speed of light and breaking into gamma rays (I think) whose speed is measured.

Of course, in a theory where information propagates like bullets from matter, one must include an idea that information being refracted by an atom of, say, an air molecule basically causes the refracting atom to regulate the speed of information that it relays. To which has been stated the following:

...Note that the gamma rays observed in this experiment pass trhought some beryllium, a thin mylar window and about 60 m of air before their velocity is measured. As this material is refractive, the extinction theorem implies that the original gamma-rays from the moving source will be slovely absorbed and replaced by similar radiation re-emitted by the stationary medium, thus invalidating this experiment [7]. This effect becomes important if the phase delay due to the medium exceeds say lambda/2pi, where lambda is the wavelength of the gamma rays. Deriving the refractive index for gamma rays from the forward scattering amblitude per electron A = e^2/mc^2, the maximum allowable distance becomes dmax = (lambda n A)^-1 ~ 5 km of air for the gamma rays of 6 GeV, where n is the number of electrons per cm^3 of the medium"

Well anyway, I think one day it would be interesting to actually build a simulation of the microscopic scale interaction between atoms inside an object, and see if what I stated about inertia and stuff, occurs with the mechanics of SR. I'm guessing yes, but it is just SO much harder to imagine it all in your head.

 

[AnssiH]

I don't understand, why do you say that? If the observer is determined to use the inertial frame in which he was at rest at the moment the light hit him, then of course he can't decide which frame that actually is until the light actually hits him, and only once he has picked the frame can he assign a time-coordinate to the event of the light being emitted.

I'm saying it part because it is not the observer who gets to decide how the information reached him, and part because of assuming that reality has an objective nature to it underneath it all. So it follows what I said afterwards in that post; this all seems to be begging an interpretation that we simply don't have, we just have the math.

 

[robphy]

There's a neat trick which I came up with regarding Lorentz-transformation. I don't know if people have used it before.

Basically if you just draw a spacetime diagram like the ones I've posted (one axis for location and one for time), and then set the light cones in 45 degree angle, you can basically just use any 3D-modeling software to simply SCALE the worldlines in a 45 degree angle so that when one axis shrinks, another one stretches uniformly. And when you tilt the worldlines in upright position by scaling them like this, it equals to switching frames.

http://www.saunalahti.fi/anshyy/PhysicsForums/Scale-transformation1.jpg
http://www.saunalahti.fi/anshyy/PhysicsForums/Scale-transformation2.jpg

You can include the planes of simultaneity and everything, and it just works. After all, that's basically what Lorentz-transformation does, it simply scales the distances between the events and the moments of observations in the spacetime. Once you know the moment when an event has been observed, Lorentz-transformation "decides" when it actually occured.

Congratulations... you have discovered for yourself the so-called Dirac light-cone coodinates... which point along the eigenvectors of the Lorentz Transformation... The eigenvalues are the Bondi-Doppler k-factors. Moreover, the area of that parallelogram (which is an invariant of this transformation) is proportional to the square interval relating timelike-related events at the two opposite corners.

See
http://people.ccmr.cornell.edu/~mermin/homepage/ndm.html
(Look at (2.).
See also http://www.lassp.cornell.edu/~cew2/P209/P209_home.html , in particular, http://www.lassp.cornell.edu/~cew2/P209/part10.pdf
and papers by Mermin in
http://scitation.aip.org/dbt/dbt.jsp?KEY=AJPIAS&Volume=66&Issue=12
http://scitation.aip.org/dbt/dbt.jsp?KEY=AJPIAS&Volume=65&Issue=6
)

as well as...
http://arxiv.org/abs/gr-qc/0407022
http://arxiv.org/abs/physics/0505134
You might enjoy
http://www.phy.syr.edu/courses/modules/LIGHTCONE/LightClock/

 

[JesseM]

I'm saying it part because it is not the observer who gets to decide how the information reached him

how, no, but when the information was sent, yes (since when it was sent depends on your choice of coordinate system).

and part because of assuming that reality has an objective nature to it underneath it all.

But you seem to be assuming not just an objective reality, but an objective flow of time. Philosophically, the findings of relativity seem more compatible with the idea that all events in spacetime have equal ontological status, that there's no particular set picked out by reality as happening 'in the present'. This is sometimes called the "block time" view, or the "B series" description of time by philosopher James McTaggart. See this article by Paul Davies:

http://urgrue.org/lib/mysterious-flow.html

 

[AnssiH]

See my relativity simulator at my website http://www.relspace.astahost.com

Very cool! Nice work.

 

[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.

 

[leandros_p]

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

AnssiH, how can you "know your distance to the event when it happened" ?

Both space as well as time are unknown physical variables. Both distance and time are calculated in reference to observer, counted by the unit of speed of light. The only physical knowledge that we have is that the ratio of space divided by time is constant, for all frames. This ratio is expressed by the speed of light.

I think you do accept the relativity of space. Am I wrong ?

Leandros

 

[AnssiH]

how, no, but when the information was sent, yes (since when it was sent depends on your choice of coordinate system).

Well yeah, but while it is very trivial to choose the moment "when" in raw logics, it's not that simple ontologically.

I mean, if you have this idea that there is FACTUALLY information approaching you steadily when you are in one inertial coordination system, even though you haven't observed it yet, the experience of the blue observer becomes very puzzling (in the previous thought experiment with the red clock).

I mean think about it, let's say you are the blue observer, talking with the purple observer;

BLUE: It's 2 seconds past, want to bet if the signal is on its way towards us?
PURPLE: Yes of course it is, it's always sent at 0s
BLUE: Ha! We'll see about that! Will you stay here and wait for the signal, while I'll switch to inertial system where the signal hasn't been sent yet.

Blue starts moving away... ...observes the signal at 8s...
...and comes back to talk to the purple observer.

BLUE: I catched the signal at 8s, so it cannot have been on its way when we last talked, the signal cannot just jump back into the clock.
PURPLE: You are wrong, I catched the signal at 5s, as usual
BLUE: Of course I saw you catching the signal when you showed 5 seconds, but you are not to decide when the signal begun its journey any more than I am.

PURPLE: Sure, but do you assert that while you were making your bet, the world around you was not the same as the world around me? Do you not think, that if there actually was information approaching me, it was approaching you too?

Who wins the bet in your opinion? If neither, why?

I expect that people who want SR to describe actual, philosophically coherent reality, would go bonkers here. People who are happy with the raw logic see no need to even think of such problems.

There are many other similar ontological problems. Like, it is quite puzzling to think about observers out there who are approaching you rapidly. From your perspective, they must be RIGHT NOW in such an inertial coordination system in which there must information about YOUR future approaching them already. Of course this information is not approaching them from your perspective, I realize that, but even from your perspective THEY exist in such a "place" where it must be so. (And vice versa)

So there is this kind of odd detachment of different inertial systems from each others, that is not very easy to explain. Apart from raw logic, and I do see the clarity of that.


You know I've been thinking that it would be interesting to build like this simulation of a virtual SR-world where time passes at very slow speeds (like 10 m/s), and in which you could run around and observe very concretely the phenomenons of SR.

And if I want to REALLY show the phenomenons, I would add an option to see how things relate to each others if you were able to see them without the information delay (i.e. what actually happens). To see what the effect of the second postulate itself is on the world. And also visualize the information itself propagating through space.

Now, the only way to actually implement such a world, is to allow the events & light to move backwards in time when the observer switches directions. Otherwise SR is not in the realm of Turing machines at all, since I cannot actually predict how the observer is going to move in the world.

I remember hearing that physics students that are more sensitive with the notion of reality, usually have more difficulties in really grasping the idea of SR, as opposed to students who are more aligned towards math. And I'm not surprised at all. I mean, the raw logic of SR is not that difficult to grasp at all, but the problems arise only once you try to apply the ideas to real world situations.

What mitchellmckain said is indicative to this "Any true understanding of the relativity of simultaneity must use the mathematics since it is primarily a mathematical concept not a philosophical one. I think than anyone with a good understanding of the relativity of simultaneity will naturally use the mathematics more, for it is only way to achieve clarity on the topic."

If clarity can be achieved ONLY though mathematics, it means there is something missing.

But you seem to be assuming not just an objective reality, but an objective flow of time. Philosophically, the findings of relativity seem more compatible with the idea that all events in spacetime have equal ontological status, that there's no particular set picked out by reality as happening 'in the present'.

Of course, this is well understood. The problem is more in detecting how/when does the information actually move towards you, since any information that is propagating towards you right now, is subject to the inertial coordination system you WILL be in once the information hits you.

See this article by Paul Davies:
http://urgrue.org/lib/mysterious-flow.html

Thanks

 

[AnssiH]

AnssiH, how can you "know your distance to the event when it happened" ?

Both space as well as time are unknown physical variables. Both distance and time are calculated in reference to observer, counted by the unit of speed of light. The only physical knowledge that we have is that the ratio of space divided by time is constant, for all frames. This ratio is expressed by the speed of light.

I think you do accept the relativity of space. Am I wrong ?

Yes I accept the relativity of space, but it is just something I've come to figure out myself from observing Lorentz-transformation, so my interpetation of this could be horribly horribly wrong. In any case, length contraction seems to be basically the same thing as relativity of simultaneity, and what I've picked up is that while the speed of light is the absolute speed limit, one could still travel hundreds of light years in a fraction of a second because near the speed of light, hundreds of light years could turn into few hundred meters. (of course hundreds of years of time has passed in the destination)

As for the thought experiment, it should suffice that you know what the distance to the event was from your perspective. This is enough to reveal you the moment the event actually happened in your perspective.

So now what is puzzling is simply the immediate history of your worldline, right before the moment you finally observe the event. Since the moment the observed event "actually happened" is in the raw logics decided by the inertial coordination system you are in WHEN you observe it, this leaves it unexplained what was happening to the information while it was propagating and you were NOT yet in the inertial coordination system in which you made the observation.

It seems that in the raw logics there is this sort of causal connection between "the moment of something being observed" and "the moment of the information being dispatched from the source". Only that the direction of this causality is running from the observation (future) to the dispatching (past).

I.e. you cannot decide when some information begins to propagate, UNTIL you know for certain which way you are moving at the moment of observation. Obviously you don't know "which way you are moving" for certain until you actually observe the information, and thus you also know the moment of dispatching ONLY once you have observed the information.

I.e. even if someone messages you 10 light seconds away, "I will send a test signal towards you 5 seconds after sending this", you may think then that this test signal must be following the message 5 seconds afterwards -> it must be halfway on its way towards you already. Only this is not true in the case you decide to change your direction rapidly into inertial coordination system that is receding from the source.

 

[JesseM]

Well yeah, but while it is very trivial to choose the moment "when" in raw logics, it's not that simple ontologically.

I mean, if you have this idea that there is FACTUALLY information approaching you steadily when you are in one inertial coordination system,

But if you simply believe in the "block time" view, and don't believe there is any objective flow of time and thus no objective coordinate-independent truth about whether the signal is "already on its way" or whether it "hasn't been sent yet", then there is no problem here.

I mean think about it, let's say you are the blue observer, talking with the purple observer;

BLUE: It's 2 seconds past, want to bet if the signal is on its way towards us?
PURPLE: Yes of course it is, it's always sent at 0s
BLUE: Ha! We'll see about that! Will you stay here and wait for the signal, while I'll switch to inertial system where the signal hasn't been sent yet.

First, of all, why does Blue have to start moving to "switch to an inertial signal where the signal hasn't been sent yet"? He doesn't have to move relative to Purple at all, he can do this just by declaring "I'm going to analyze this problem in inertial coordinate system A which is different from our own rest frame." Part of the problem here is that you are arguing as though each observer has an intrinsic frame that they are physically obligated to use, when in fact each observer has no obligation to use the inertial frame in which they are currently at rest, that is just a matter of convenience.

Blue starts moving away... ...observes the signal at 8s...
...and comes back to talk to the purple observer.

BLUE: I catched the signal at 8s, so it cannot have been on its way when we last talked, the signal cannot just jump back into the clock.
PURPLE: You are wrong, I catched the signal at 5s, as usual
BLUE: Of course I saw you catching the signal when you showed 5 seconds, but you are not to decide when the signal begun its journey any more than I am.

PURPLE: Sure, but do you assert that while you were making your bet, the world around you was not the same as the world around me? Do you not think, that if there actually was information approaching me, it was approaching you too?

Who wins the bet in your opinion? If neither, why?

Neither, as long as they both understand that asking whether the signal "had already been sent" at the time they talked is not a physical question at all, its just a question of coordinate systems. Analogously, suppose you have two people standing on a piece of paper, and each one wants to know if a certain dot at a different point on the paper is above their x-axis or not (assume each observer is at the origin of their own coordinate system). If they use different coordinate systems with the x-axes oriented at different angles, it is perfectly possible for the same dot to be below one guy's x-axis but above the other's. Similarly, if you picture spacetime as a 2D sheet with events as dots at different locations on it, then two observers at one point in spacetime who use coordinate systems with their t=0 axes oriented at different angles (again, assume they are both at the origin of their systems) can disagree if a distant event happened before or after t=0.

I expect that people who want SR to describe actual, philosophically coherent reality, would go bonkers here.

Not at all. The reality is the spacetime, the coordinate systems are just things you lay on top of it. Again, picture a 2D sheet with dots representing events at different locations on it, and then different people laying different coordinate systems drawn on tracing paper on top of it--the location of the dots relative to one another on the sheet never changes (all the spacetime intervals between the dots remain the same, for example), even if different coordinate systems disagree on issues like whether two events happened at the same time or not.

There are many other similar ontological problems. Like, it is quite puzzling to think about observers out there who are approaching you rapidly. From your perspective, they must be RIGHT NOW in such an inertial coordination system in which there must information about YOUR future approaching them already. Of course this information is not approaching them from your perspective, I realize that, but even from your perspective THEY exist in such a "place" where it must be so. (And vice versa)

Again, you're talking as though each observer is physically obligated to use the inertial frame in which they are currently at rest, but this is purely an aesthetic choice made for convenience.

But you seem to be assuming not just an objective reality, but an objective flow of time. Philosophically, the findings of relativity seem more compatible with the idea that all events in spacetime have equal ontological status, that there's no particular set picked out by reality as happening 'in the present'.

Of course, this is well understood. The problem is more in detecting how/when does the information actually move towards you, since any information that is propagating towards you right now, is subject to the inertial coordination system you WILL be in once the information hits you.

I don't think you understood my point at all, since the question of what is happening "right now" has no physical meaning in the block universe view. You simply have the same frozen spacetime, and different coordinate systems with their surfaces of simultaneity drawn at different angles, just like a piece of paper on which you can put different coordinate systems with their x-axes drawn at different angles, so in one coordinate system dot A and B may both lie on the x-axis while in another dot A lies on it but dot B lies below it. This is exactly analogous to the idea that in one coordinate system the event of my clock ticking 0 and the event of a distant signal being emitted both lie on the t=0 plane (ie they both happen at the same time) while in another coordinate system the event of my clock ticking 0 lies on the t=0 plane while the distant signal event lies above it (the event 'hasn't happened yet' in this coordinate system). If you can accept that the 'ontological reality' of the dots at different locations on the sheet of paper is independent of the choice of coordinate systems we lay on top of the paper, then you should also be able to accept that the ontological reality of spacetime with a bunch of events in it with intrinsic spacetime distances between them is independent of the choice of coordinate systems we lay on top of this spacetime.

 

[AnssiH]

Hmmm... I don't understand. Does the idea of block time tell us something about the ontological nature of what we usually think of as "beams of light approaching us"?

I mean, I don't really have problems in grasping the raw logic of this idea, and I don't even have problems in accepting the "ontological reality" of spacetime; that the world could basically operate this way.

But I don't understand how can one accept the idea of SR and still think that it is not necessary for events to basically run backwards from your point of view. What difference does it make that it is only your point of view? Obviously I understand there is no objective time flow which needs to reverse itself just because of you, and that passage of time is expressed by laying down the events on spacetime diagrams and using lines / planes in different angles to represent the "present" for different observer.

But when you do that, does not the change in the orientation of this plane of "present" actually mean that there are events which pass through it "backwards", and for this observer they will also occur in reverse order? (And don't worry, I understand this is not a problem for causality since it is exactly what preserves causality)

Block time view just reinforces that idea, doesn't it? Shouldn't we think of this as factual too? I mean, I really don't understand how could we have SR without this. The notion of present does change, doesn't that tell it all?

And even if you think of switching frames as switching from one "place" to another, it makes absolutely no difference to the reality around the observer. The reality around the observer in SR is that things around him slide in time in a non-absolute way, and possibly even backwards, yes?

 

[JesseM]

Hmmm... I don't understand. Does the idea of block time tell us something about the ontological nature of what we usually think of as "beams of light approaching us"?

I don't understand what you mean by this question. Since there is no flow of time in the block time view, a light beam only "approaches" us in the same sense that two lines drawn on a piece of paper can approach each other, there's no real change happening at the level of the block universe.

But I don't understand how can one accept the idea of SR and still think that it is not necessary for events to basically run backwards from your point of view.

What does "point of view" mean? Each observer only directly perceives things which happen at his immediate location, like light hitting his retinas. When observers talk about when distant events happen "from their point of view", what they really mean is laying a coordinate system on spacetime which they choose to use to analyze events, usually a coordinate system in which they are at rest. But again, this is just an aesthetic choice, each observer could use any coordinate system they wanted, there is no "ontological" truth about which coordinate system represents a given observer's "point of view" and which does not. In terms of the paper analogy, if you have lines at different angles drawn on the piece of paper, you could adopt the convention that each line's "point of view" would be described in terms of a spatial coordinate system where the y-axis is parallel to that line, but this would be purely a convention, you have no obligation to define the phrase "point of view" in that way.

Obviously I understand there is no objective time flow which needs to reverse itself just because of you, and that passage of time is expressed by laying down the events on spacetime diagrams and using lines / planes in different angles to represent the "present" for different observer.

No, the different coordinate systems do not "represent the present for different observers" at all, they are simply a set of different coordinate systems which can be used by any observers. Again, you can adopt the convention that each observer at a given moment uses the inertial coordinate system in which they are at rest, but this is purely a convention, you could equally well adopt the convention that each observer uses the inertial coordinate system in which they are currently moving at 0.7c along the x-axis, and that would define simultaneity "for them". In the block time view these are purely conventions, there is no physical or ontological reason for a given observer to say that one coordinate system represents his "point of view" while another doesn't.

 

[AnssiH]

I don't understand what you mean by this question. Since there is no flow of time in the block time view, a light beam only "approaches" us in the same sense that two lines drawn on a piece of paper can approach each other

Yes, and such is the case of all motion in block time view, it doesn't mean we could not think about information "being in motion" just like we think of anything else being in motion.

I understand this, and somehow I'm starting to get the feeling we are probably talking about the same thing with different terminology.

I mean I'm not at total loss here with these things. Obviously I understand that an observer cannot observe any information which is still on its way moving towards him (if I may call it movement).

I don't have any formal training on these things, I'm just self-taught, so that will probably show in my terminology, but I hope you could see through semantical issues without assuming in every turn that I don't understand anything about the nature of spacetime in SR.

(I think another thing that will show in my lack of formal training is that I probably view the same technical mechanics in totally different way than you might. But if the technical aspects are correct, there shouldn't be telling which semantical view is more correct than the other. Perhaps different takes on things could be seen as advantageous too?)

What does "point of view" mean?

When referring to POV, I mean the state of the universe around the observer whose POV I'm talking about. I am assuming there actually is a universe around me in certain state. I understand it is not in the same state for everyone else. Yet it is in one state from my point of view, even if I cannot see, hear or smell it.

In spacetime diagrams, my plane of simultaneity is expressing this state that I am talking about.

Each observer only directly perceives things which happen at his immediate location, like light hitting his retinas. When observers talk about when distant events happen "from their point of view", what they really mean is laying a coordinate system on spacetime which they choose to use to analyze events, usually a coordinate system in which they are at rest. But again, this is just an aesthetic choice, each observer could use any coordinate system they wanted, there is no "ontological" truth about which coordinate system represents a given observer's "point of view" and which does not.

Yes, exactly, it is an aesthetic choice, none is more right then the other, I understand. When I say the world is in certain state around me, I DO understand it is so only around me (and those who are at rest with me).


Ok, I understand, that the statement, "things must move backwards if I start moving away from the fast enough" can be understood in MANY different ways. Most of which are not how I mean it.

Is there ANY way at all for you to interpetate that statement so that it would seem correct for you? Can you see how I am only referring to how my plane of simultaneity is tilting in such a manner that somewhere there are events moving through it backwards? Can you assume that I might actually understand block time exactly the way you do, and that the meaning of the statement is the one that actually makes sense in SR?

Again, you can adopt the convention that each observer at a given moment uses the inertial coordinate system in which they are at rest, but this is purely a convention, you could equally well adopt the convention that each observer uses the inertial coordinate system in which they are currently moving at 0.7c along the x-axis, and that would define simultaneity "for them". In the block time view these are purely conventions, there is no physical or ontological reason for a given observer to say that one coordinate system represents his "point of view" while another doesn't.

Is there not a way to interpetate the information of block time in such manner that it actually tells what the state of the universe is around one observer? I mean, the universe must be in some state? Even if this information is invalid* for observers moving to other directions, and even if every observer can choose to think about the world as a block view, there still exists such a thing as "now" in which things are in certain state.

*And by invalid I don't mean non-existent, I mean "not the state of the world around them".

 

[JesseM]

When referring to POV, I mean the state of the universe around the observer whose POV I'm talking about. I am assuming there actually is a universe around me in certain state.

But that assumption is meaningless in the block time view! There is an actual spacetime "around" the observer in a 4D sense, but there is no "state of the universe" in the sense of a single 3D spatial slice through this 4D spacetime that somehow is ontologically preferred as that observer's "POV" than any other choice of slices. How a given observer chooses to slice up spacetime is a totally arbitrary matter of choice, just like the choice of how to orient the x and y axes in his coordinate system, there is no ontological truth about which choice should represent his "POV" and which shouldn't.

In spacetime diagrams, my plane of simultaneity is expressing this state that I am talking about.

But it is only "your" plane of simultaneity if we adopt the arbitrary linguistic convention that each observer defines "his" coordinate system to be the one in which he is currently at rest.

Yes, exactly, it is an aesthetic choice, none is more right then the other, I understand. When I say the world is in certain state around me, I DO understand it is so only around me (and those who are at rest with me).

No, you miss the point of what I meant by "aesthetic convention". My point was that even for a single observer, it is a matter of aesthetic convention as to what coordinate system, and which definition of simultaneity, he terms to be "his own". There is no intrinsic reason to attach one particular coordinate system to one particular observer. So there is no natural truth about what the world's present state "around you" is, we could equally well adopt the convention that the state of the world "around you" is defined to be whatever's on the surface of simultaneity of the coordinate system that is moving at 0.93c along the axis from the tip of your nose to a spot on the back of your head. Aesthetically this might be a lot uglier, but its not "incorrect" in any ontological sense. Also, note that even if you want to associate each observer with a coordinate system where they're at rest, it's still a matter of aesthetic choice to adopt the Einstein clock synchronization convention which results in different coordinate systems having different definitions of simultaneity; with a different clock synchronization convention you can have different inertial coordinate systems in motion with respect to each other which nevertheless all agree about simultaneity, although this is also uglier aesthetically because it means the equations of the laws of physics don't look the same in different frames (this would be true if you use the Mansouri-Sexl transformation instead of the Lorentz transformation, for example).

Ok, I understand, that the statement, "things must move backwards if I start moving away from the fast enough" can be understood in MANY different ways. Most of which are not how I mean it.

Is there ANY way at all for you to interpetate that statement so that it would seem correct for you? Can you see how I am only referring to how my plane of simultaneity is tilting in such a manner that somewhere there are events moving through it backwards? Can you assume that I might actually understand block time exactly the way you do

Not if you think there is any intrinsic, non-arbitrary reason to associate a particular definition of simultaneity with a particular observer, no.

Again, you can adopt the convention that each observer at a given moment uses the inertial coordinate system in which they are at rest, but this is purely a convention, you could equally well adopt the convention that each observer uses the inertial coordinate system in which they are currently moving at 0.7c along the x-axis, and that would define simultaneity "for them". In the block time view these are purely conventions, there is no physical or ontological reason for a given observer to say that one coordinate system represents his "point of view" while another doesn't.

Is there not a way to interpetate the information of block time in such manner that it actually tells what the state of the universe is around one observer? I mean, the universe must be in some state?

Not as I understand the "block time" view. If reality is just a 4D block, I can't see why there would be any intrinsic reason to associate certain ways of laying coordinate systems on this block with certain observers, any more than there is reason to associate certain spatial coordinate systems layed on a diagram on a piece of paper with lines that are part of that diagram. Aesthetically it might be simpler to use a coordinate system where the observer is at rest or a spatial coordinate system where the y-axis is parallel to the line in the diagram you're focusing on, but in neither case would I say there's any ontological reason you must make this association between coordinate systems and worldlines/lines in the 4D block/2D diagram.

 

[leandros_p]

So now what is puzzling is simply the immediate history of your worldline, right before the moment you finally observe the event. Since the moment the observed event "actually happened" is in the raw logics decided by the inertial coordination system you are in WHEN you observe it, this leaves it unexplained what was happening to the information while it was propagating and you were NOT yet in the inertial coordination system in which you made the observation.

It seems that in the raw logics there is this sort of causal connection between "the moment of something being observed" and "the moment of the information being dispatched from the source". Only that the direction of this causality is running from the observation (future) to the dispatching (past).

I.e. even if someone messages you 10 light seconds away, "I will send a test signal towards you 5 seconds after sending this", you may think then that this test signal must be following the message 5 seconds afterwards -> it must be halfway on its way towards you already. Only this is not true in the case you decide to change your direction rapidly into inertial coordination system that is receding from the source.

AnssiH, First, I apologize for the long post.

An event does not carry any physical information. For example, the light coming from the sun does not carry any physical information, as an event, other that of a position on space-time map of reality.

The measurements made from physical events help us to map reality, but they do not explain reality neither do they provide a causal connection for physical information, other than providing information for changes of the map of reality. In an analogy, an event that is happening at your neighbourhood has a “place” for the map of your neighbourhood, but when you change neighbourhood the same event is meaningless on the map of your new neighbourhood. (I will use the analogy of “neighbourhoods” and “maps”, for the rest of this message)

Therefore the created information of two flashes of light, as two physical events, traveling in the same direction separated by the time of 5 seconds have a meaning of created information of an event for an observer, but this information does not define the reality by which this physical information was produced by a physical agent, nor does it define the reality of the physical messenger of the information. Actually, it is the other way around: the reality defines both the production and the messenger of the information. The reality is the "causal connection" between the event and the observer . This "causal connection" is defined by Einstein in the constancy of space/time ratio, which is expressed by the constancy of speed of light.

Now, it seems odd to say that the omission of the observation of the second flash of light (which is the concomitant of changing the relative inertial frame of the observer after the reception of the first flash) carries the same physical information to the observer, as the physical information that is carried by the observation of the first flash. The carried physical information is not the production of the flash of light or the transmission of the flash of light in space-time. The presence of flash of light and its absence are both providing physical evidence of the same physical information about the reality of space-time, which is the consistency of the reality of the observer. In an analogy to the above example of moving between neighbourhoods, the presence and the absence of observation of events from your maps when you move from the one neighbourhood to another does not makes you to lose faith neither in maps nor in reality. You know what maps are good for, and you know that for each neighbourhood you need to use different map which is describing different events, appropriate for the reality of each neighbourhood.

But an observer is not obliged to observe everything, no matter how much space or how long time the observation covers. An observer is not obliged to receive all created information by events produced from the raw material of reality. This is due to certain “limit” that is introduced by the finite nature of the velocity by which the information of physical events travels towards the observer. The absence of observation of created physical events does not negate reality.

On the contrary, the example of the two flashes of light bonds the observer with the reality of space-time regardless of created events. The absence of the observation of the second flash of light when we change reference frame means that our “map” is the proper one for our new “neighbourhood”. The absence of observation of the second flash of light is an absence of a position of an event on the space-time map of reality of the new reference system.

The "history of my worldline" is not the history of present and of past events, but it is the history of my present and of my past reference systems. It is a history of present and past “maps” of my reality. When these references are chained in succession then the reality of space-time defined by the two axioms of Einstein "traverse" through them, producing a consistent reality for the observer through which light is always present as a physical constant for all reference systems, but it may be either present or absent as an event depending on the relative position of the observer.

In this context, the reality (the raw material of space-time) is consistent for the observer, but it is inconsistent for the events depending on the "position" of the observer. In an analogy, the reality of moving between neighbourhoods is consistent for an observer but when he moves to the new neighbourhood the map of the previous neighbourhood is inconsistent.

PS: Unforunately we do not know how to construct a global/universal map. We only know how to construct local maps.

Leandros

 

[mitchellmckain]

... what I've picked up is that while the speed of light is the absolute speed limit, one could still travel hundreds of light years in a fraction of a second because near the speed of light, hundreds of light years could turn into few hundred meters. (of course hundreds of years of time has passed in the destination)

That is correct. Though you should modify the parenthetical: (of course hundreds of years will have passed at the destination according to the interpretation of simultaneity used by an observer at the destination, assuming the desination is not itself moving relativistically with respect to your starting location).

So now what is puzzling is simply the immediate history of your worldline, right before the moment you finally observe the event. Since the moment the observed event "actually happened" is in the raw logics decided by the inertial coordination system you are in WHEN you observe it, this leaves it unexplained what was happening to the information while it was propagating and you were NOT yet in the inertial coordination system in which you made the observation.

It seems that in the raw logics there is this sort of causal connection between "the moment of something being observed" and "the moment of the information being dispatched from the source". Only that the direction of this causality is running from the observation (future) to the dispatching (past).

I.e. you cannot decide when some information begins to propagate, UNTIL you know for certain which way you are moving at the moment of observation. Obviously you don't know "which way you are moving" for certain until you actually observe the information, and thus you also know the moment of dispatching ONLY once you have observed the information.

I.e. even if someone messages you 10 light seconds away, "I will send a test signal towards you 5 seconds after sending this", you may think then that this test signal must be following the message 5 seconds afterwards -> it must be halfway on its way towards you already. Only this is not true in the case you decide to change your direction rapidly into inertial coordination system that is receding from the source.

I think you are confusing the observers conclusions with the raw information. Yes his interpretation of data will depend on the inertial frame in which he will make the observation but not the the raw data (the photons) which is traveling toward him.

Lets follow through on your example and say that after receiving the message you accelerate to 86.60254% of the speed of light away from him. When you do that then according to the coordinate system appropriate to your new inertial frame the first light signal arrived 2.68 seconds after he sent it from a distance of 2.68 light seconds away (using the lorentz transformations on t = 10s and x = 10 ls). After that due to time dilation you determine that he actually sends the second signal 10 seconds after he sent the first on your clock (in your new space-time measure) and during that time he has traveled 10(.866) = 8.66 light seconds away so that the signal must travel 8.66+2.68 = 11.34 light seconds requiring 11.34 seconds to reach you.

From his point of view he does wait only 5 seconds but after the light travels only 5 light seconds, the first signal reaches you, and you start moving away from him at 86.60254% of the speed of light. This means that the light will take an additional time t = 5 + .8660254 t to get to you. Solving this equation you get that t = 37.32 seconds, the time between the arrival of the two signals at your location according to the sender.

This agrees with time dilation because for you the time between the two signals was 10 s - 2.68 s + 11.34 s = 18.66 s which is only half the 37.32 seconds according to the sender. This is half rather than twice because these two events occur in the same place only in your coordinate system not his. The time between the events of sending the light signals takes half as long for the sender because these two events occur in the same place only in his coordinate system not yours (in your new inertial frame).

 

[AnssiH]

Not if you think there is any intrinsic, non-arbitrary reason to associate a particular definition of simultaneity with a particular observer, no.

So you really don't think there is any definition of simultaneity for an observer that might be more meaningful for him than the other definitions? You don't see any meaning in the phrase "there is a light signal approaching me now" at all? You have no idea what one could possibly mean by saying that? Because world is a stationary 4D block, not something where we could say things are actually happening?

I'm not asking "can you see how it might be wrong to say it THIS way", I'm asking if you can see ANY sense at all in that? Yet you answered "not if..." what does the "if" imply, do you mean there is some tiny opening for such interpetation that it might make sense to you?

Should I take it that block time is the ontological interpretation of the world according to SR? No sense of simultaneity exists at all, not even subjectively? The simultaneity planes don't mean anything at all, and I've been incorrectly thinking they represent "the present" for a single point in a world line? Are you are saying that that's not the case?

I mean, I'm sorry, but this just seems like technical nit-picking to the degree of trolling, it really does... Or then we just don't understand each others at all...

 

[AnssiH]

AnssiH, First, I apologize for the long post.

No problem at all. Thank you for bothering :)

On the contrary, the example of the two flashes of light bonds the observer with the reality of space-time regardless of created events. The absence of the observation of the second flash of light when we change reference frame means that our “map” is the proper one for our new “neighbourhood”. The absence of observation of the second flash of light is an absence of a position of an event on the space-time map of reality of the new reference system.

Yes I understand the nature of spacetime. You seem to be pointing out basically the same concern that Jesse is. Perhaps I better just modify my question so that it makes better sense in SR terminology.

Can your plane of simultaneity change its orientation in relation to events?

If so, does this mean that events (or "dots that represent events" whatever), pass through it backwards? Backwards in the sense that usually they pass through it other way around.

If the answer is "yes", then we are basically there.

As for if it is ok to say that "events can occur backwards", I think is completely a semantical issue. If I say it, it is not wrong per se, is it? Unless you want to make it wrong by pointing out something about the nature of time, or about the nature of simultaneity, or about the nature of events, or about light or information propagation or about what you can actually see when receiving photons or something. None of this matters as long as you DO accept there actually is a world around you, and there is a semantical meaning in the phrase "things happen", or in "motion". I don't care about how many different semantical meanings someone can think for words like time and motion.

 

[AnssiH]

I think you are confusing the observers conclusions with the raw information.

No.

I am simply assuming there is world around us where things are in motion even when we are not witnessing it. I'm starting to get the feeling that this is very unorthodox idea.

And by motion I mean the very ordinary meaning of motion that everybody use in their everyday life. I don't care if motion is not actually motion when drawn on paper.

Believe me, I understand that even if the tilting of a plane of simultaneity implies that events are occurring in backwards order, no one can actually SEE something moving backwards. That's not the point at all.

Oh man, I hope I never need to get a physicist to "move" his car, because it would be a looooong day... ;)

 

[leandros_p]

Can your plane of simultaneity change its orientation in relation to events?

If so, does this mean that events (or "dots that represent events" whatever), pass through it backwards? Backwards in the sense that usually they pass through it other way around.

If the answer is "yes", then we are basically there.

If I understand your question correctly, the answer is absolutely yes.

An observer calculates the positions of the events in his space-time map. The positions of events on the map are picturing the physical reality. There is an iconic relation between the ontology of reality and the calculation of positions of events: the space-time map of events depicts physical reality.

We have to understand that space-time reality is both finite and at the same time without limits. This antinomy/paradox of unlimited, but yet finite, physical reality is obliging us to produce a space-time map, constituted from observations/calculations of physical events that has a horizon. The “horizon” of the map of space-time means that there are real physical events that are “beyond” physical interaction with the reference system of the observer. Physical reality allows the observer to picture the physical events on a space-time map, but there is a limitation on simultaneous depictions. This limitation forms a boundary which acts like a horizon for the observation. I would say that “the plane of simultaneity change its orientation in relation to events” which are depicted on the space-time map of the observer, If I am allowed to use your phrase.

If you combine both axioms of Einstein:

1)The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion.

2)Any ray of light moves in the "stationary" system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body.

then you get the result that the observer of physical events is able to observe physical reality bounded in a horizon of events, although he can move within an infinite space-time reality. This is, according to my understanding, the physical meaning of time/space relativity.

You can also check the following presentation "[URL 9: Special Relativity II"]"simultaneity and causality"[/URL] for the terms: “causally connected events” and for “causally discounted events”


Leandros

 

[JesseM]

So you really don't think there is any definition of simultaneity for an observer that might be more meaningful for him than the other definitions?

Some coordinate systems might have more aesthetic or practical value to the observer, but their definition of simultaneity is not "more true" for that observer in any ultimate physical or ontological sense, no.

You don't see any meaning in the phrase "there is a light signal approaching me now" at all?

I can see what it might mean if you reject block time and take the view tha time "really flows", but not if you accept block time.

Because world is a stationary 4D block, not something where we could say things are actually happening?

According to the block time view, yes.

I'm not asking "can you see how it might be wrong to say it THIS way", I'm asking if you can see ANY sense at all in that? Yet you answered "not if..." what does the "if" imply, do you mean there is some tiny opening for such interpetation that it might make sense to you?

Again, the "if" is if you accept block time. You don't have to, of course--this is philosophy, not physics. But there can be no empirical reason to favor one definition of simultaneity over another in relativity.

Should I take it that block time is the ontological interpretation of the world according to SR?

No, like I said, block time is a philosophical viewpoint, you can accept SR without accepting block time.

No sense of simultaneity exists at all, not even subjectively? The simultaneity planes don't mean anything at all, and I've been incorrectly thinking they represent "the present" for a single point in a world line? Are you are saying that that's not the case?

It's not the case that physicists see these definitions of simultaneity as anything other than a convention. Remember, they are based on what is commonly referred to as "Einstein's clock synchronization convention", where each observer assigns coordinates based on a network of rulers and clocks which are at rest relative to himself, and where he synchronizes clocks based on the assumption that light should travel at the same speed in all directions in his coordinate system, so if a flash is set off at the midpoint of two clocks in his system, they are considered "synchronized" if they both read the same time when the light from the flash reaches them. The fact that this is referred to as a "convention" shows that physicists would not say there is any physical reason why you must synchronize your clocks in this way. Certainly things will be a lot more elegant if you do it this way, though, since this convention means that the laws of physics will obey the same equations in each inertial coordinate system, whereas if you use some other convention you will have to use different equations in each coordinate system. Still, nothing is stopping different observers from each using a set of clocks and rulers which are at rest relative to themselves but synchronizing their clocks in such a way that all observers agree on simultaneity (as I mentioned earlier, this would result in the transformation equations derived by Mansouri and Sexl rather than the Lorentz transformation for mapping different observer's coordinates to each other's), and likewise nothing is stopping different observers from defining "their own" coordinate system to be one that is measured by rulers and clocks which are not at rest with respect to themselves.

I mean, I'm sorry, but this just seems like technical nit-picking to the degree of trolling, it really does...

I'm confident that if you asked any physicist, they would agree with what I've said here, there's nothing physical that requires any observer to use a particular coordinate system or a particular definition of simultaneity. They wouldn't say there's anything incorrect (although it is less elegant) about using the set of inertial coordinate systems provided by Mansouri and Sexl, for example, as long as you made sure to find the correct equations for the laws of physics in each coordinate system. And remember, in general relativity, with the laws of physics stated in terms of tensors, there is even less reason to prefer one set of coordinate systems over any other, because the laws of physics will obey the same tensor equations in any coordinate system you can think up, a property known as diffeomorphism invariance (unlike in SR stated without using tensors, where only when you use the set of inertial coordinate systems provided by the Lorentz transform do the equations of the laws of physics look the same in every coordinate system).

 

[mitchellmckain]

No.

I am simply assuming there is world around us where things are in motion even when we are not witnessing it. I'm starting to get the feeling that this is very unorthodox idea.

You were "confusing the observers conclusions with the raw information" in the what you said in the portion I quoted, but perhaps this is only a problem with how you were trying to express yourself and that this is not the real source of confusion. So forgive me if I am wrong but I am going to make a guess, based on the statement which you just made, about what may be the real trouble.

No one is denying that there is a real world out there, it is only that in special relativity this real world is a four dimensional one that is not Euclidean. Given all four coordinates of an event, that event will be found precisely at those coordinates. However, these coordinates are not constants but are a functions of an inertial vector and for numerical coordinates an inertial vector (or inertial frame) must be selected and plugged into the coordinate functions. This does not make them or the world any less real. What it does do is strongly change is how that world is put together. It completely isolates events from each other, which are not causally connected because they have a spacelike distance between them. Eventually they reach out and touch each other in some later event and through that later event they become connected in a definite way, but before that happens, they might as well be in different universes, because they cannot affect each other in anyway. They cannot even say whether the other event has or has not happened yet. They are truly independent of each other.

If there is such a thing as clairavoyance then to bridge that space-like gap would be equivalent to an ability to see the future and all the difficulties, puzzles, paradoxes and contradiction which that involves. Restricted small region of space like the Earth the limitation of a tenth of a second hardly presents any problem. If a clairavoyant can see what is happening on the other side of the Earth it would be difficult to detect a less than a tenth of a second delay in what he or she sees, don't you think. If this ability does exist then by all accounts it is no where near clear or reliable enough to be bothered by such a time delay.

Anyway, back to our previous example of the two signals, I suspect that what may bother you is that before you accelerate, you interpret that the second signal is already 5 seconds into its journey and after you accelerate (if you really could supply the truly astronomical energies and forces to accelerate that fast), the message has not been sent yet, but that you have to wait an additional 7.32 seconds after you received the first signal before the second signal will even be sent. Yes, this is a startling result. But the truth is that both of these, are interpretations only with no definite reality, because there is no already happened or not yet happened in relation to events which are separated from us by space-like distances. The event is real and out there with its four inertial vector dependent space-time coordinates, but until those 10 seconds (or 11.34 seconds if you run away from it as in the example) have elapsed that event is practically in a different universe. It could have been an enormous antimatter explosion which will vaporize the Earth but for those initial 10 seconds it is in another universe.

Did you know that two equal sized asteroids hitting each other at a relative speed of 94.3% of the speed of light would produce as much energy as a non-relativistic collision if the one of the asteroids was pure antimatter? At a distance of only 10 light seconds and asteroids big enough to be noticed, that would be just such an Earth vaporizing event. The forces in the universe are enormous and destructive beyond belief and the way that special relativity keeps them apart from us is very comforting.

Believe me, I understand that even if the tilting of a plane of simultaneity implies that events are occurring in backwards order, no one can actually SEE something moving backwards. That's not the point at all.

Oh man, I hope I never need to get a physicist to "move" his car, because it would be a looooong day... ;)

NOTHING occurs in any backwards order, EVER! There is for example (our previous example) no inertial frame in which the two signals are sent in a different order. There is no inertial frame in which the signals are going back to the person who sent them. There is in fact no inertial frame in which the signals are traveling anything less than the speed light towards you. If events are separated by space-like distances there is no order, period. If events are separated by a time-like distance they are causally connected and the order is absolutely unchangeable in any way whatsoever! You cannot say that you accelerating makes the signal go back to the sender, that is pure imagination. Before you receive the signal any idea that the signal is already sent is also pure imagination. It is only in setting up problems this by simultaneously set up events separated by space-like distances, that we can create this illusion of a reversal of events, and this is pure imagination as well. When time has advanced to the point where a later event is connected to two separate events, which are themselves separated by a space-like distance then and only then can those two events, mutually, both be said to have already happened and are in the past, even though which happened first is a matter of opinion and much like who hit who first in a fight between squabbling children, it doesn't really matter.

As for moving moving his car, who better than the physicist, who can tell you what methods will be a complete waste of time because it is physically impossible. You may wish to keep warm exerting effort to feel like you are doing something useful, while the physicist freezes trying to think of something that will really work. But then, who is doing the real work in that case?

 

[AnssiH]

Some coordinate systems might have more aesthetic or practical value to the observer, but their definition of simultaneity is not "more true" for that observer in any ultimate physical or ontological sense, no.

Again, the "if" is if you accept block time. You don't have to, of course--this is philosophy, not physics. But there can be no empirical reason to favor one definition of simultaneity over another in relativity.

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.

All that matters is that isotropic nature of information propagation absolutely requires events to sometimes move from the so-called "future" back to the "past".

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.* 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. Lorentz-contraction belongs to the same class of phenomenons as "events moving backwards", and a host of other effects. We cannot pick and choose here.

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.

*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...

Thank you leandros for your post too. I agree with you, and I would add that at every moment there exists one plane of simultaneity for any given observer that has more meaning that the other planes of simultaneity; it describes the actual state of the real world around the observer at that moment.

 

[AnssiH]

Given all four coordinates of an event, that event will be found precisely at those coordinates. However, these coordinates are not constants but are a functions of an inertial vector and for numerical coordinates an inertial vector (or inertial frame) must be selected and plugged into the coordinate functions. This does not make them or the world any less real. What it does do is strongly change is how that world is put together. It completely isolates events from each other, which are not causally connected because they have a spacelike distance between them. Eventually they reach out and touch each other in some later event and through that later event they become connected in a definite way, but before that happens, they might as well be in different universes, because they cannot affect each other in anyway.

Yes, this is exactly the way I've understood it.

When I said "I am simply assuming there is world around us where things are in motion even when we are not witnessing it" it means that the world around me does possesses a definite state that is more true to me than to an observer moving to another direction. That is, in my coordinate system there exist events that are simultaneous for me. And this is the state on which my observations are eventually based on.

Perhaps I should not call what the plane of simultaneity describes a "reality", since in SR something like block time is in many ways more objective than that, but I really cannot think of any other words to express this "reality" that is "meaningful for the experience" of a single observer. (I understand it is not actually "the experience" of a single observer)

Anyway, back to our previous example of the two signals, I suspect that what may bother you is that before you accelerate, you interpret that the second signal is already 5 seconds into its journey and after you accelerate (if you really could supply the truly astronomical energies and forces to accelerate that fast), the message has not been sent yet, but that you have to wait an additional 7.32 seconds after you received the first signal before the second signal will even be sent. Yes, this is a startling result. But the truth is that both of these, are interpretations only with no definite reality, because there is no already happened or not yet happened in relation to events which are separated from us by space-like distances.

Yes, that is the startling result I got too, and my intention was to get an ontological interpetation to such a thing. I take it that your interpetation is that the different inertial coordination systems are, in a sense, "detached" from each others. So that you don't need to assert that the light signal had been sent twice from the "point of view of a single world line". (And I still don't mean about what the observer actually sees)

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.

We hear about Lorentz-contraction all the time, but never about how SR also predicts that when changing direction, the actual state of the world around us undergoes such a transformation that some events must move back and forth between our subjective past and future. It seems to me that the reason we don't hear about this is that it sounds so absurd that people don't really want to interpetate it like that.

But really, it can be said that length contraction for an object occurs simply because the "far end" of the object "swoosh" forwards or backwards in time more than the "near end". How is that any more fantastical than events moving forward and backward in time? How can we accept the other but not the other?

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; it just occurs further away from your position. If the length of the plane of simultaneity is thought to be infinitely long, then even the most miniscule change of direction causes it to cross its own history at some finite distance from here.

Did you know that two equal sized asteroids hitting each other at a relative speed of 94.3% of the speed of light would produce as much energy as a non-relativistic collision if the one of the asteroids was pure antimatter? At a distance of only 10 light seconds and asteroids big enough to be noticed, that would be just such an Earth vaporizing event. The forces in the universe are enormous and destructive beyond belief and the way that special relativity keeps them apart from us is very comforting.

No I didn't know that, that is very interesting.

NOTHING occurs in any backwards order, EVER! There is for example (our previous example) no inertial frame in which the two signals are sent in a different order. There is no inertial frame in which the signals are going back to the person who sent them.

Yeah, Jesse made this point too, it leads to the idea of detached inertial frames, which is kind of interesting.

I mean I understand that nothing occurs backwards for a single inertial frame nor do any signals arrive to different inertial frames in different order.

The question was whether the "actual (subjective) state of the universe around a single world line" can proceed in such a manner that things "move" backwards. And obviously here we are talking about such a world line that changes from one inertial coordination system to another.

Of course I understand that the signals could never arrive to this observer in a backwards manner, that's not the point. The point is simply to comprehend what is occurring to the real state of the world around me when I change direction.

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.

Obviously things are not moving in backwards manner anymore when they are actually observed by a natural observer. The same objects that are moving backwards "temporally" are also moving closer to us "spatially", and causality is preserved. (I am aware that there are many semantical pitfalls in the previous sentence. Let's try to get over them)

But in order to achieve this feat of working causality together with the second postulate of SR, things MUST move backwards for the clairvoyant observer. And since it is the clairvoyant observer who sees "the world which springs the experience of the natural observer", this should tell us something about the actual ontological nature of the world around us (as described by SR)?

You cannot say that you accelerating makes the signal go back to the sender, that is pure imagination. Before you receive the signal any idea that the signal is already sent is also pure imagination.

That is true, but then we face the problem that I described in the last thought experiment in this thread, regarding blue and purple observer. The world must possesses some state around the observers when they were making their bet.

We must assert that the state of the world around the purple observer must have been such that the light signal WAS on its way.

Can we now assert that the state of the world around he blue observer was such that the light signal was NOT on its way yet? Because he was going to change direction?

It would be hard for the blue observer to stay as friends with the purple observer :(

That is to say, it seems that in SR we must "imagine" things really move backwards that way, or then we need to come up with another ontological interpetation of the actual "subjective" world around us. What other choices do we have?

 

[leandros_p]

I agree with you, and I would add that at every moment there exists one plane of simultaneity for any given observer that has more meaning that the other planes of simultaneity; it describes the actual state of the real world around the observer at that moment.

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. It means that reality as a physical term is transcendental, it is beyond elaboration. But, at the same time we can elaborate a plan/map of reality. I think that the other forum members participating in this thread describe this difference, in their own responses.

The "actual" state for the real world can be described only as relative information arranged and classified by a scientific methodology. This is the result of communicating with reality through physical consciousness.

The observer does not come in direct ‘contact’ with a physical event. The observer is always using a messenger in order to access the message of a physical event. The only way that could provide to the observer the reality of the actual state of the real world is to unite the observer with the essence of the world. Of course this is not how the science of physics works. This is the work of metaphysics.

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, therefore "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". The ‘map’ is information arranged and classified by a scientific methodology which administers ratios of quantities and qualities.

Having said that, I wonder how a map of the actual state of the real world can be useful for an observer. This question was answered by the two axioms of Special relativity. Einstein invented and provided for us a scientific mapping methodology that is the same for every observer and for every position of space-time world. According to Einstein's axiomatic proposition the scientific ratio of information is defined by the constancy of speed of light. The emerging maps of physical reality through Einstein's proposal are different for each observer, who is following this methodology, but this not paradox.

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.

But, Einstein accepted as an axion that we can not find a common reference system for two observers, under certain space-time positions.The normalization of classical physics according to a common reference system is an illusion.

That is to say, it seems that in SR we must "imagine" things really move backwards that way, or then we need to come up with another ontological interpetation of the actual "subjective" world around us. What other choices do we have?

Let me give you another point of view, trying to answer your question (which was not addressed to me, but I find it very interesting. I apologize to Mitchell McKain for intervening. I am looking forward for his reply on this.)

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.

In this context, it is not that “some events must move back and forth between our subjective past and future”, but the messengers that carry the information about the events are moving back and forth in relation to our space-time variable position. So, there is no ontological subjectivity of the actual world around us, there is only informational subjectivity of the mapping of the actual world around us. In an analogy, our ‘map service’ is waiting for the messengers of the universe, which travel with a velocity no greater than the speed of light, to arrive at our space-time position to register the information that they carry for each objective physical event. The succession of registration of this information on the map of reality produces our subjective interpretation of the map of reality. But we must understand that we can not produce ontological conclusions by looking at a map of reality.

Unfortunately, scientific methodology does not produce ontological data. It merely produces subjective information of measurements and calculations which we call physical observations.

Finally let me say that from my point of view, ontological reality is not observed. It is experienced from within, for that ontological reality is not the subject of science.

Leandros

 

[mitchellmckain]

Yes, this is exactly the way I've understood it.
Perhaps I should not call what the plane of simultaneity describes a "reality", since in SR something like block time is in many ways more objective than that, but I really cannot think of any other words to express this "reality" that is "meaningful for the experience" of a single observer. (I understand it is not actually "the experience" of a single observer)

You can call it whatever you like but it has no objective reality. Regions of space time separated from you by space-like distance are in a gray area between already happened and not happened yet. Already happened because nothing you do can change them in any way and not happened yet because they cannot affect you in any way. So everything in this region of space-time could be said to be simultaneous with your current moment. For example, on a planet 10 light years away all events between those which you can now conceivably see with a telescope and the time on that planet when they could conceivably see your current moment with a telescope, all those events are simultaneous with your current moment. Yet these events take time to leave this extended region of simultaneity.

Yes, that is the startling result I got too, and my intention was to get an ontological interpetation to such a thing. I take it that your interpetation is that the different inertial coordination systems are, in a sense, "detached" from each others. So that you don't need to assert that the light signal had been sent twice from the "point of view of a single world line". (And I still don't mean about what the observer actually sees)

No it is not the inertial coordinate systems that are detached from one another they are all just in our head anyway. It is the regions of space-time separated by space-like distances which are detached from one another. You simply cannot say that a signal "has been already sent" until you receive the signal, for then and only then does it pass from "simultaneous" to "already happened". Likewise you cannot say that it has "not been sent yet" unless a light signal can reach that location from yours before it is sent.

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. When I say that the coordinate system associated with an inertial frame is not real, what I mean is that we construct them to aid in calculation but that it has nothing to do with what events have already happened and what events have not happened yet. When we say that Lorentz contraction is real it means that it does not for example block the light of stars passing in front of it or stars passing behind it as if it were such a length. On the other hand, the contraction is not real in another sense because we are simply seeing the back end after it has already traveled towards its front end.

We hear about Lorentz-contraction all the time, but never about how SR also predicts that when changing direction, the actual state of the world around us undergoes such a transformation that some events must move back and forth between our subjective past and future. It seems to me that the reason we don't hear about this is that it sounds so absurd that people don't really want to interpetate it like that.

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.

But really, it can be said that length contraction for an object occurs simply because the "far end" of the object "swoosh" forwards or backwards in time more than the "near end". How is that any more fantastical than events moving forward and backward in time? How can we accept the other but not the other?

Because it is not really a matter of what sounds reasonable to the scientifically unititiated but a matter of what is consistent with our scientific observtions. As crazy as special relativity sounds to the non-scientist it makes perfect sense to the scientist, not like quantum physics where scientists are even more confounded and flabbergasted than the non-scientists.

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; it just occurs further away from your position. If the length of the plane of simultaneity is thought to be infinitely long, then even the most miniscule change of direction causes it to cross its own history at some finite distance from here.

I do not understand what you are saying. to accelerate to 86.6% of the speed of light not only requires energy equivalent to your mass energy (or to put it another way it requires half your mass in antimatter fuel with an equal part of regular matter to annihilate it with). And to accelerate to this speed even if you have this amount of energy is no laughing matter. At a reasonable acceleration which we know will not kill us of one g it would take a year and eight months to get to 86.6% of the speed of light. To do so in a few seconds would require a few hundred million gees which is way beyond what solid steel could endure let alone the human body.

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. It has a relativity of simultaneity demo but it does not run things backwards and forward to make everything conform to coordinate system of the inertial frame of the the ship. Instead, time passes everywhere in agreement with the inertial frame of the sun, which in my program does not yet move around the center of the galaxy. This means that everything just speeds up when the ship travels at relativistic speeds. My program does not even have the ability to adjust the date at all. The trouble is that it has objects which move freely under the influence of gravity and is constantly integrating their motion.

But in order to achieve this feat of working causality together with the second postulate of SR, things MUST move backwards for the clairvoyant observer. And since it is the clairvoyant observer who sees "the world which springs the experience of the natural observer", this should tell us something about the actual ontological nature of the world around us (as described by SR)?

But physicists do not believe in clairavoyance and in fact only believe in local reality, something which quantum physics has now made very difficult. 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.

But anyway, like most physicists, I accept the Minkowsky structure of space-time as quite real and it troubles me no more than it troubles them. I simply accept that events separated by space-like distances cannot be put into any real temporal order.

That is true, but then we face the problem that I described in the last thought experiment in this thread, regarding blue and purple observer. The world must possesses some state around the observers when they were making their bet.

Ah yes but these two are just exercising their mouths without any real meaning coming out of them. They can bet on and argue about nonsense until they are blue or purple in the face if they want, but what they are arguing about is not in fact a state of the world around them but only a state of their own minds. The signal has neither "already left" nor has it "not left yet," or both of these at the same time if you like. So both blue and purple are, in fact quite incorrect, and both would lose their bet, if the truth prevails, or, if you like, both are correct and both win the bet equally.