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:

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

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?