Is Relative Simultaneity Real?

[andromeda]

One problem in understanding Special Relativity is that it is intuitively hard to agree with relative simultaneity.

My major problem is that I cannot quite answer the question:

Is relative simultaneity a real effect or only a mathematical artifact of Lorentz transformation?

I am not the only one who has this kind of cognitive problems. This is quite common as well documented in peer reviewed journals [1].

The real or apparent contradiction arises in the following situation:

Lorentz transformation of two simultaneous distant events in a stationary system as defined by Einstein in [1] Part I § 1, without any doubt produce non simultaneous events in a moving system.

This is because the calculated times t1’ and t2` for events E1 and E2 at t1=t2(in the stationary) are not equal after transformation to the moving system. And that is the well known demonstration of relative simultaneity.

However if you have two particles approaching X axis in a manner that they are always on a parallel line to X, or simply a rigid rod descends in a motion parallel to X, both distant points cross X axis simultaneously by assumed arrangement in the stationary system.

If both points are aligned on X, they are automatically aligned on X’ which is the same line albeit moving.

How it is then possible that two points are both aligned with the axis and yet the times of alignment are different?

Where is the other point when one of them is on the axis at some time t'?

Is relative simultaneity real? Has it been experimentally proven?
Its not the question of time dilation which we know is real, but how does that relate to simultaneity? The equations alone do not provide these answers.

Any guidance will be highly appreciated.


[1] R., E. Scherr, P., S. Shaffer, S. Vokos "Student understanding of time in special relativity: Simultaneity and reference frames" Am. J. Phys. 69, S24 (2001);
[2] Albert Einstein, “On the Electrodynamics of Moving Bodies” (translation from original Annalen der Physik, 17(1905), pp. 891-921) published on the internet in http://www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf

 

[Fredrik]

The distinction between "real" and "mathematical" isn't as clear as you seem to think. In fact, I'm not sure it's meaningful at all.

If time dilation and length contraction are real, then so is relativity of simultaneity. They are all things that show up when we compare how two different coordinate systems describe the same thing. So they all have the same status in the theory.

I don't understand the scenarios you describe. A line parallel to the x-axis that crosses the x axis? If it's parallel to the x axis, it either is the x-axis or never crosses it.

 

[andromeda]

The distinction between "real" and "mathematical" isn't as clear as you seem to think. In fact, I'm not sure it's meaningful at all.

Thanks for your answer. Its a valid point do define real. Need to think about it a bit

If time dilation and length contraction are real, then so is relativity of simultaneity. They are all things that show up when we compare how two different coordinate systems describe the same thing. So they all have the same status in the theory.

I know the theory is internally consistent but the meaning of "real" (which I need to define better if possible) would lie outside the mathematical construct. Do not want to elaborate without thinking.

I don't understand the scenarios you describe. A line parallel to the x-axis that crosses the x axis? If it's parallel to the x axis, it either is the x-axis or never crosses it.

Sorry, confusing wording on my part. A line crosses the x-axis is in the same sense as the bumper of my car crosses the rails on railway crossing. Moves parallel to them then aligns with them, and I called it "crosses the line". Should find a better word for this. I am not a native English speaker.

 

[ghwellsjr]

"Relative Simultaneity" results from observers in _different inertial reference systems_ viewing the same space-time event ... perhaps a supernova.

If everybody shares a reference system their clocks are synched together, and when they take into account their local time of observation, plus the distance ... they should agree on the time of the event.

But if your clocks don't agree (due to time dilation) then the best you can do is to figure out what time _the other guy_ saw it. There are many other things which you will agree upon - the relativistic invariants.

This is totally wrong for the following reasons:

1) Simultaneity has to do with the Coordinate Times of two events in one Inertial Reference Frame (IRF), not one event as "viewed" from two different IRF's.

2) Simultaneity has nothing to do with the local time of observation, it has only to do with the Coordinate Time of events. If you're considering the time of observation of a distant event as the second event, then those two events can never be simultaneous.

Relative Simultaneity refers to the fact that two events that are simultaneous in one IRF may not be simultaneous in another IRF.

 

[andromeda]

This is totally wrong for the following reasons:

1) Simultaneity has to do with the Coordinate Times of two events in one Inertial Reference Frame (IRF), not one event as "viewed" from two different IRF's.

2) Simultaneity has nothing to do with the local time of observation, it has only to do with the Coordinate Time of events. If you're considering the time observation of a distant event as the second event, then those two events can never be simultaneous.

Relative Simultaneity refers to the fact that two events that are simultaneous in one IRF may not be simultaneous in another IRF.

Thank you all for the response.

Hope we can now agree on facts such that we do not need to repeat them again and use in subsequent reasoning.

1) Coordinate time is fully equivalent to clocks readings at arbitrary positions relative to origin of a
3D coordinate system, given the clocks are adequately synchronised.

2) It is clear now that if one event is detected and recorded in one place, it has the clock reading
at this place. The other one detected and recorded elsewhere, has the reading of a similar clock
at that clock's position.

3) The clocks have been synchronised in accordance with the procedure given by Einstein in his
1905 work assuming forward and backward speed of light being the same and constant in all
inertial frames.

4) Lorentz transformation is the consequence of the speed of light assumption and the
synchronisation procedure.

5) The simultaneity can be proven after the events by gathering event records from remote
locations. If the time of detected events in their respective places have the same numerical
values, then the events are called simultaneous. Otherwise they are successive.

I hope this is correct, and if not please indicate.

I hope to return to the thread in a day or two to rephrase my dilemma based on your comments and common understanding of terms and scientific facts described above.

 

[Dale]

One problem in understanding Special Relativity is that it is intuitively hard to agree with relative simultaneity.
...
[1] R., E. Scherr, P., S. Shaffer, S. Vokos "Student understanding of time in special relativity: Simultaneity and reference frames" Am. J. Phys. 69, S24 (2001);

I also like this article by Scherr, Shaffer, and Vokos:
http://www.aapt.org/doorway/TGRU/articles/Vokos-Simultaneity.pdf

In it they present some pedagogical approaches for teaching this concept. Unfortunately, very few students are lucky enough to be taught with this method, myself included and you also I assume.

 

[Dale]

If both points are aligned on X, they are automatically aligned on X’ which is the same line albeit moving.

X' is not parallel to the x' axis. I will assume that you know four-vector notation, and I will use units such that c=1.

The worldsheet of X is given by $X=(t,a,ut,0)$ where -1<u<1 is the velocity of X in the unprimed frame, t is coordinate time in the unprimed frame and a is a parameter which picks out a given point along the line at any given t.

Transforming to the primed frame we get $X'=(\gamma(t-av),\gamma(a-tv),ut,0)$. Now, taking $t'=\gamma(t-av)$ and $a'=\gamma(a-tv)$, solving for t and a, and substituting back and simplifying we get:

$X'=(t',a',u't'+a'u'v,0)$ where $u'=\gamma u$

Note that the distance to the x-axis is no longer $ut$, but $u't'+a'u'v$ where the second term means that it is not parallel to the x' axis.

Is relative simultaneity real?

I agree with Fredrik that the question about "real" requires a good rigorous definition of "real". If you come up with such a definition, whether it is a generally accepted definition which could be discussed here or a personal one which would have to be analyzed elsewhere, I would expect that you would find that simultaneity itself is not real.

In other words, the Lorentz transform shows that the universe "cares" about causality. Things that are causally related in one frame share the same causal relationship in any other frame. But the universe simply does not "care" about simultaneity. As soon as you realize that you can stop being distracted by things that are physically unimportant (simultaneity) and focus on what is physically important (causality).

Has it been experimentally proven?

The relativity of simultaneity is a consequence of the Lorentz transforms, which are well-established, scientifically:
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

The experimental evidence is overwhelming.

 

[andromeda]

This thread is getting interesting.
Before I come back with something worth publishing, I have to say that the only thing one needs to reconcile with the common sense in order to accept Einstein theories, is just one single concept of relative simultaneity.
All the rest is easy (relative to how much math one can handle).

 

[georgir]

I think a useful step in coming to terms with relativity is not trying to categorize events as "simultaneous" or "not simultaneous", as that is obviously dependent on reference frame, but instead "space-like separated" (i.e. simultaneous in some reference frame) and "time-like separated" (i.e. co-located in some reference frame), and the edge-case of "light-like separated" which are always absolute, frame-independent relations between any two events.

 

[andromeda]

X' is not parallel to the x' axis. I will assume that you know four-vector notation, and I will use units such that c=1.

To clarify the issue: in my original post I (rightly or wrongly) referred to X as an axis, that is a straight line, and now in your argument you use X as a 4 dimensional vector representation of a traveling line (in old fashion 3D terminology, when you drop first coordinate and t is a variable scalar parameter).

I understand that your argument can be verbalised in a notation tolerant manner like this:

A line descending towards "x axis" in the stationary system such that it remains parallel to "x axis" at all times (t), it remains not parallel to "x' axis" at all times (t') in the moving system.

Naturally, X axis is always parallell to X' axis (using my original notation).

Perhaps for further discussion I will keep your capital X as you use it and refer to x,y,x in lower case as axes, but then it will be difficult to refer to x,y,z as coordinates based on those axes although it can be avoided using indexed notation.
Please comment.

 

[jkl71]

Using a rigid rod was one way of describing the setup in the original post, however you cannot have a rigid rod.

Using the rigid rod version of your setup, the issue is essentially the same as the manhole paradox, e.g.

http://www.physics.oregonstate.edu/coursewikis/GSR/book/gsr/manhole

 

[Dale]

Perhaps for further discussion I will keep your capital X as you use it and refer to x,y,x in lower case as axes, but then it will be difficult to refer to x,y,z as coordinates based on those axes although it can be avoided using indexed notation.
Please comment.

Feel free to use whatever notation you prefer. I may have misinterpreted your intended usage of x vs X, and if you wish to alter your notation for clarity then that is certainly fine. I will do my best to use your notation or I will try to clearly define any notation that I employ.

The notation doesn't change the geometry. A line which is parallel to the "boost" axis and moving in one frame will not be parallel to the "boost" axis in another frame.

 

[andromeda]

Thank you DaleSpam for supporting the parallel lines argument.

The reason of this reply is that I do not fully agree with your conclusion although your mathematical presentation is correct. Its all about the interpretation not just only maths. Furthermore my main question whether relative simultaneity is real or apparent hinges on understanding of parallel line translation in the lateral direction to x axis

This post will be a bit long but I cannot do it any simpler at this stage.

Notation Remark:
The coordinates are expressed in positional association form and the notation $X=(t,x1,y1,z1)$ represents a point in the space time or in 3d mentality a point in euclidean 3d sub-space which is associated with "coordinate 1" when its value is equal to t.

Let the traveling straight line parallel to x axis be represented by:

$X=(t,a,ut,0)$​

where:

t is a scalar parameter representing a value of "time coordinate 1" in the unprimed frame​

X[1]=ct where c is the speed of light set to 1 for convenience.​

a is a scalar parameter which picks out all values of spatial "coordinate 2" comonly referred as x coordinate.​

-1<u<1 is the velocity component of X in the direction of spatial "coordinate 3" commonly referred as y coordinate in the unprimed frame,​

spatial "coordinate 4" commonly referred as z coordinate is permanently set to 0

Lorentz Transformation matrix $L$ can be written as:

| γ,-vγ,0,0|
|-vγ, γ,0,0|
| 0, 0,1,0|
| 0, 0,0,1|​

The transformation from unprimed to primed is represented by matrix multiplication as follows

$X'=LX$​

where $X$ should in fact be a column vector but to conserve space we show it in text horizontally dropping the transposition notation.

Transforming to the primed frame we get $X'=(\gamma(t-av),\gamma(a-vt),ut,0)$.

Up to this point I assume everyone would agree.

Before going further, the above equations can be interpreted as follows:

$X$ represents an instant of a traveling line in the unprimed system such that when $X[1]=t$ the instant of this line in 3d space is $(a,ut,0)$, where ut is a fixed instance of coordinate y at clock time t while a (as assumed before) represents "all x'es". Coordinate z remains 0.

Note that at t=0 which is the synchronisation time appropriate for the above form of $L$ Lorentz transformation matrix, the $X$ at t=0 is identical with the x axis.

Similar but not identical reasoning can be used about $X'$


$X'$ represents an instant of a traveling line in the primed system such that when $X'[1]=\gamma(t-av)$ the instant of this line in 3d space is $(\gamma(a-vt),ut,0)$ where ut is a fixed instance of coordinate y at clock time t. Coordinate z remains 0. Coordinate x' is obviously different than x because of the motion of the system.
The difference is that the "time coordinate 1" is different for every value of a that represents arbitrary position in x direction, which is not the case in the unprimed system. This means clocks in the primed system are synchronised that way.

At time t=0 $X$ is exactly aligned with x axis so it is aligned with x' axis because x ad x' axis are on the same straight line.
The fact that the "time coordinate 1" varies in the primed system is because of choice Einstein's synchronisation method.

My conclusion is:
the traveling line is parallel to x axis and to x' axis at each instant of its existence including t=0 and (t'=0 at x'=0) when it fully coincides with both.

We have to live with the fact that clocks in the moving system are phase shifted and running at different rate than in the uprimed system and equal time at distant locations does not mean temporal coincidence. Unfortunately all dictionaries agree that simultaneous means equal times so the usage of "temporal coincidence" is justified although it is used as a synonym of simultaneity.

That situation would be similar to a degree, if we used time of the primed system as an output of a precise sundial synchronised at 0 GMT and traveling along the equator east-west and reasoning about kinematics perceived while in motion. At each instant of the traveling line motion form the perspective of the moving system every point of that line would have different sundial time.

Continuing with the originator's argument:

Now, taking $t'=\gamma(t-av)$ and $a'=\gamma(a-tv)$, solving for t and a, and substituting back and simplifying we get:

$X'=(t',a',u't'+a'u'v,0)$ where $u'=\gamma u$

Note that the distance to the x-axis is no longer $ut$, but $u't'+a'u'v$ where the second term means that it is not parallel to the x' axis.

My Answer:
This is all correct mathematically when you wish to express $X'$ in a consistent set of parameters. The grouping by t' parameter for phase shifted clocks will show the line as not parallel because for the same t' in extreme case one point would be say "now" the other where the line was yesterday and this is definitely not parallel line.

There is a little known publication in an official academic peer reviewed journal dating back to 1972 which describes time phase shift extensively but I am afraid I would be banned for referring to something not adhering to majority views.

 

[Dale]

The reason of this reply is that I do not fully agree with your conclusion although your mathematical presentation is correct.

Then your disagreement is illogical.

If the math is correct (as you concede) and if the premises are correct (the Lorentz transforms are presumed correct on this forum) then the conclusion is correct. The only way to dispute the conclusion is by showing the math incorrect or by disputing the premises.

I will go through your reply in detail, but it is rather lengthy so it may take some time, and the outcome is guaranteed by the rules of logic.

 

[Dale]

Actually, it took less time than I anticipated.

Notation Remark:
The coordinates are expressed in positional association form and the notation $X=(t,x1,y1,z1)$ represents a point in the space time or in 3d mentality a point in euclidean 3d sub-space which is associated with "coordinate 1" when its value is equal to t.

Presumably then $X'=(t',x1',y1',z1')$ would be the notation for a point in the primed frame.

Transforming to the primed frame we get $X'=(\gamma(t-av),\gamma(a-vt),ut,0)$.

Then, by your own notation in the primed frame $t'=\gamma(t-av)$, and all of the rest of my previous post follows.

$X'$ represents an instant of a traveling line in the primed system such that when $X'[1]=\gamma(t-av)$

This simply incorrect. An "instant" by definition is a single value of time in the given system. $X'[1]=\gamma(t-av)$ is not a single value in the primed system, it is potentially all time in that system depending on the range of t and a. Now, it is possible for you to fix a relationship between t and a such that the expression above evaluates to a single value. However, if you do this you will either wind up with a single point (which cannot be parallel to anything) or you will wind up with a line which is not parallel to the x axis.

This is the logic error. You called something an "instant" in the primed frame which does not meet the definition of "instant" in the primed frame. All of the rest of your logic from this point on fails. I encourage you to work through the math to see that if you fix a and t such that you do get a single instant then you do indeed not obtain a parallel line.

 

[andromeda]

You called something an "instant" in the primed frame which does not meet the definition of "instant" in the primed frame. All of the rest of your logic from this point on fails. I encourage you to work through the math to see that if you fix a and t such that you do get a single instant then you do indeed not obtain a parallel line.

I am happy that the discussion is progressing and I accept the challenge. It may take me a while in order to write something free from errors and ambiguities or at least significantly better.

I see the traveling line problem we are discussing can be resolved to mutual satisfaction this way or another in finite time. Either outcome will satisfy my internal curiosity department. This is possible because of the simplicity of the stated problem, only linear algebra and all framework of Special Relativity unchallenged.
The reason two intelligent people disagree while acting in good faith is they either do not understand each other or at least one fails to recognise his own mistakes.
All this can be improved gradually.

 

[Dale]

Sounds good. I look forward to the next installment whenever you get around to it.

 

[darkhorror]

How about look at it simply, take 4 clocks, 2 in a stationary FOR, 2 in a moving FOR. Let's put these clocks on a train and a platform. One on left side of train one on right, one on left side of platform, one on right. In the platform's FOR, the train and the platform are the same length, the clock distance is also the same. So in the platform's FOR when the left two clocks are at the same point, the right two clocks are also at the same point. Yet in the train's frame the distance between it's clocks and the platforms clocks is different. So in the train's FOR, when the left pair of clocks are in the same place the right pair of clocks can not be in the same place.

So if the left clocks read 0 when they line up, and the right clocks also read 0 when they align. In the train's frame of reference when the left clocks both read 0, the right clocks can't also read 0 since they aren't aligned. Since the math alone isn't convincing you, draw out an actual example of what it would look like in reality, take time dilation, length contraction, and that both frame needs to agree on events. Draw the clocks, draw them moving towards other clocks, look at how time must behave, and what "now" would have to be in different frames.

 

[andromeda]

...the universe simply does not "care" about simultaneity. As soon as you realize that you can stop being distracted by things that are physically unimportant (simultaneity) and focus on what is physically important (causality).
The relativity of simultaneity is a consequence of the Lorentz transforms, which are well-established, scientifically

It may seem that I am a bit picky and going off-side from my main challenge, but I have to disagree with your low rating of simultaneity although such opinion is shared by many.
If I was to rate simultaneity and causality I would agree the later seems a little bit more important, but to disregard simultaneity as a non-issue?
Simultaneity in descriptive terms is the boundary that separates before from after and cause from effect(locally). How is that the boundary is not important?
My words may not be convincing however we should take note that there are quite different views:
According to M. Jammer [1] Einstein[2] stated that relativity of simultaneity “is the most important, and also the most controversial theorem of the new theory of relativity. It is impossible to enter here into an indepth discussion of the epistemological and ‘naturphilosophischen’ assumptions and consequences which evolve from this basic principle.”

In another place Jammer [1] states: "Reichenbach had already recognized that the notion of simultaneity plays an important role in the metrical geometry of special relativity when he defined the length of a moving line segment as the distance between simultaneous positions of its end points".

I can rest on Lorentz transformation to calculate what happens in the primed system but I cannot understand how “at once” becomes before and after. Being in this thread I want to understand just that rather than move the controversial issue away from me.

[1] Jammer, M. Concepts of Simultaneity: From Antiquity to Einstein and Beyond . Baltimore : Johns Hopkins University Press, 2006.

[2] A. Einstein, “Vom Relativitäts-Prinzip,” Vossische Zeitung, 26 April 1914 (no. 209), pp. 1–2;
The Collected Papers (1996), vol. 6, p. 4; English translation (1997), vol. 6, pp. 3–5.

 

[andromeda]

How about look at it simply, take 4 clocks, 2 in a stationary FOR, 2 in a moving FOR. Let's put these clocks on a train and a platform...

Thanks. I will look at this example as well. It is good to have different angles on the same problem

 

[Nugatory]

My words may not be convincing however we should take note that there are quite different views:
According to M. Jammer [1] Einstein[2] stated that relativity of simultaneity “is the most important, and also the most controversial theorem of the new theory of relativity. It is impossible to enter here into an indepth discussion of the epistemological and ‘naturphilosophischen’ assumptions and consequences which evolve from this basic principle.”

That's relativity of simultaneity that's the most important and (then - it's not controversial any more) most controversial result of SR. And seeing as how the relativity of simultaneity is basically saying what DaleSpam said, that nature cares about causality not simultaneity, I'm not finding a lot of support for your position there.

The second Jammer quote is best understood as a statement about the impact of relativity of simultaneity: the assumption of simultaneity is buried in such deceptively simple concepts as distance and relativity of simultaneity requires us to form more rigorous definitions of these concepts.

 

[darkhorror]

Then there is a similar example when I was trying to figure out what length contraction and time dilation would mean for the universe. Single clock on a train, and two clocks on a platform. When the clock on the train is at the first clock on the platform let's say they both show zero, and the other clock on the platform is synchronized with it's other clock so on the platform they both show zero. Give the train a certain velocity. Calculate from the platform's FOR what the clocks will read when the train is at the first clock then at the second. Then look from the trains FOR, look at when the first clock and the train clock are at the same point and both read zero. Then look how far you have to go and how long it will take to get there, and how much time will tick on the platform's clock. You will see that the only way you will agree on the events is if the platform's clock are not synchronized in the trains frame of reference.

 

[Nugatory]

Simultaneity in descriptive terms is the boundary that separates before from after and cause from effect(locally)

That description doesn't work, not even locally. Although two simultaneous events cannot be causally related, the same is true of many pairs of non-simultaneous events.

You are right that there is a boundary, and that it matters a lot. However, that boundary isn't defined by the planes of simultaneity because there's nothing interesting that we can conclude from knowing that one event is on one side of a plane of simultaneity and another event is on the other side. Instead, the boundaries that matter are the light-like surfaces that determine causality - it matters which side of these you're on.

 

[pervect]

Simultaneity in descriptive terms is the boundary that separates before from after and cause from effect(locally). How is that the boundary is not important?

In relativity, cause and effects are determined by light cones. Here's an ascii diagram of a light cone for special relativity, time runs up the screen, space runs horiziontally. The orgin as at event O The diagonal lines represent the path that a light beam emitted from O.

 \.../
  \../
   \/
---O--- 
   /\
  /xx\
 /xxxx\

Events in the dotted region are in the future lightcone of O
Events in the "x" region are in the past lightcone of O
Events on the dashed line "---O---" are simultaneous to event O in a frame in which O is at rest.
Events outside the lightcone are space-like separated. Every event space-like separated from O is simultaneous to O for some moving observer.

So "past" and future are separated not by a line, but a region, the region being the region of space-like separated events, the region outside the lightcone.

The notion of simultaneity is observer dependent, only events on the dashed line are simultaneous for the observer at O. If you consider the set of events which is simultaneous for some observer in arbitrary motion, this set is not observer dependent and includes all events outside the forwards and backwards lightcones.

Rather than "past, future, and present" events can be categorized as "Past, future, and space-like separated".

 

[WannabeNewton]

Simultaneity is simply a necessary component of the construction of a coordinate system. Being that a coordinate system is merely a calculational tool, there is no reason to expect simultaneity to be any more fundamental than a mere calculational tool as well. Physical measurements and physical observables depend not on simultaneity as they are influenced only by events in the local light cones.

 

[Dale]

If I was to rate simultaneity and causality I would agree the later seems a little bit more important, but to disregard simultaneity as a non-issue?

You need to note my wording, which was carefully chosen. I said that simultaneity is "physically unimportant". Regardless of the philosophical, emotional, or computational importance that you may attach to "the boundary that separates before from after" there is no physical importance.

In other words, there is no physical experiment you can perform whose measured outcome will depend on whether or not two events were simultaneous.

Simultaneity in descriptive terms is the boundary that separates before from after and cause from effect(locally).

This is incorrect even locally. Simultaneity is indeed the boundary that separates before from after (by definition), but the light cone is the boundary that separates cause from effect. Even locally causes cannot be outside the past light cone of their effects and effects cannot be outside the future light cone of their causes.

 

[AnssiH]

Just stumbled on this thread while I was looking for something else, but I had to comment because I don't see much communication happening here.

Andromeda, I'm sure you notice that everyone are refusing to communicate under your specific conceptualization of the meaning of "simultaneity". (e.g. see DaleSpam's previous post).

Might as well; it is always possible to conceptualize these things under all kinds of semantics, whatever one can establish as "logically valid" is good to go, regardless of philosophical connotations.

But there is one very critical detail here that most people tend to stumble on. Almost everyone attempt to conceptualize - i.e. interpret the meaning of relativity - under some idea regarding what reality is "really" like, overlooking the fact that all the definitions associated with relativity (or any theory for that matter) are a human representation of reality.

I think you are doing yourself a big favor when seriously thinking about the question you are thinking about. Dale's comment "Simultaneity is physically unimportant" is basically valid comment if one is not interested of such questions, but I doubt it clears out any questions in your mind. I do not get the sense that Dale has quite figured out himself why exactly it is physically unimportant, apart from the fact that it is unimportant from an observational point of view, and wishes not to get too entangled into unknowable ontological speculations more than necessary.

But let me take a step back and explain some important epistemological aspects ("what can be known") behind this issue;

Is relative simultaneity real? Has it been experimentally proven?

No, there is no reason to believe it is "real" in the usual meaning of the word "real". That is to say, if you conceptualize simultaneity plane as representing a "real momentary state of actual reality", then no, relative simultaneity cannot be said to be "now" in "real" sense, it is more accurately just a valid way to represent reality.

Obviously so, as if it was "real now", then we would also be saying that the state of Andromeda (or anything at all) is affected by our choice of reference frame. It's safe to say that reality doesn't "really change" when someone chooses to represent reality in different reference frame. Note that this idea is exactly what led some physicists to argue that reality is a static spacetime block; another rather childish ontological speculation on unknowable things. Note the flip-side of this same coin is, relative simultaneity can be said to be a representational feature of our world view. That much we know, while ontological nature behind it is unknowable.

So, assuming you are not interested of arbitrary ontological speculation, what you want to understand is, what does relative simultaneity represent epistemologically? The must succint answer is, it represents a kind of ignorance, arising from a particular unobservable aspect of reality, which allows its valid use (valid as in "it works"). This is in fact one of the most important things to understand regarding relativity, but often appears to be quite poorly understood (even among some physicists) leading to rather ridiculous philosophical perspectives about relativity.

A full analysis is far beyond a scope of a forum post, but I will give you a little hand-wavy argument. Walk through the following, and see if you can build up personally satisfactory understanding along every step.

Fact #1
C is not a measurable property of reality. It is often implied in scientific dialogue that C is well measured quantity, but what they are actually talking about is what C is under relativistic clock synchronization convention. This has caused a lot of people to loose perspective on the actual facts behind the issue;

1a: Measuring two-way speed of light is possible via the fact that you can measure it with single clock.
1b: Measuring one-way speed of light is fundamentally impossible, because you need two clocks, which you cannot synchronize without already knowing the speed of light. Note that you cannot take clock measurements to be unaffacted by motion of the clocks as long as you take clocks to be macroscopic devices held together by electromagnetic phenomena. Try to get around that and you should understand the fundamental nature of this problem.

This is actually a rather trivial issue to understand if you really think about it for a bit, and it was also well known by the physicists pre-relativity. Some reference material;
http://en.wikipedia.org/wiki/One-way_speed_of_light

Fact #2
Fact #1 leads directly to Fact #2; if you can't measure one-way speed of light, you cannot possibly establish factual notion of any "real momentary state of reality". Although it may be valid to think such a state exists, it is simply not possible to measure what it is. This leads into a rather interesting fact that, we are quite free to arbitrarily choose different conventions for one-way speed of light, as long as they also yield the measured two-way speed of light. Different conventions would lead to different ideas of "real now". Note also that, as long as you take macroscopic objects to be collections of elements held together via electromagnetic forces, you can't assume them to be unaffected by different one-way speeds of C.

This was also well known pre-relativity. Note especially that Lorentz transformation did not arise from special relativity, it arose from a particular ontological speculation by Hendrik Lorentz; exactly where it got its name;
http://en.wikipedia.org/wiki/Hendrik_Lorentz#Electrodynamics_and_relativity
http://en.wikipedia.org/wiki/History_of_Lorentz_transformations

The significance of which is that while such ontological speculation may be true, but it cannot possibly be proven due to fact #1.

Fact #3
If you read Einstein's original paper about SR in the above context (which is close to the context he wrote it in), you should be able to see that what he is really getting at is not that isotropic C is a fact of nature, but rather that we are completely free to define C as isotropic across all reference frames, as long as we perform a self-consistent transformation between those frames; that very transformation which Lorentz had already established.

English translation of that paper;
http://www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf

You will not find him talking about spacetime or none of that ontological speculative nonsense. He is talking about a convention that is available to us. That is also why the people who understand this issue often refer to this as "Einstein CONVENTION". All the spacetime speculation became later as an interpretation to the paper by Minkowski (google "Minkowski spacetime" if you wish). It is popular nowadays because the further developments were developed under that terminology. But Einstein's confidence to the validity of his argument is in fact directly related to his understanding that he is use definitions that he is free to use, due to very specific ingnorance forced on us by our fundamental inability to measure one-way speed of light.

Fact #4
Maxwell's equations of electromagnetism contain an inconsistency called "The moving magnet and conductor problem". If you look at that Einstein's paper on SR, you have seen him referring to this problem in the very opening.

More reference material;
http://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem

The significance of this fact is that Maxwell's equations (i.e. the underlying definitions to his equations) already implicitly contain the requirement for Einstein's convention for relative simultaneity, via requiring C to be defined as isotropic. Meaning, if Maxwell's equations can be taken as valid representation of real phenomena, then so can special relativity. That is one of the major sources of Einstein's confidence to his definitions; exactly the reason he opens with this issue.

So, if you can follow the above issues and trace them to the definitions of relativity, you should be able to see clearly how relativity arises from a specific ignorance; it is rather a representation form that is valid, and available for us, but its ontological status remains as unknown as any other. If you can see this, you will also start to see how most people actually have a rather naive perspective towards relativity philosophically.

As one little side note, notice that special relativity has to do with principle of relativity in terms of defining physical laws. But from an ontological/cosmological perspective, the cosmic background radiation - if you presume it to be a residual effect from the big bang - it does in fact establish a cosmological reference frame (a frame where the background radiation does not doppler shift in any direction). Also note that all the macroscopic objects that we observe are almost stationary relative to each others in relativistic terms (a homogeneous distribution would appear from any reference frame as if most things are moving arbitrarily close to C). But this last paragraph is not to be confused with anything above related to definitions of special relativity, just thought you might find it interesting to think about.

-Anssi

 

[andromeda]

Simultaneity is simply a necessary component of the construction of a coordinate system. Being that a coordinate system is merely a calculational tool, there is no reason to expect simultaneity to be any more fundamental than a mere calculational tool as well. Physical measurements and physical observables depend not on simultaneity as they are influenced only by events in the local light cones.

I think that this answer summarises all replies to my question about importance of simultaneity.

Thank you all who contributed to this sub-thread.

Seeing my thoughts in perspective is a valuable experience and possibly brings me closer to resolution of the main question of my thread: "Is relative simultaneity real?". One possible answer I was not aware of so far is that such question may even not be worth asking.

 

[andromeda]

Obviously so, as if it was "real now"...

-Anssi

Thanks for an interesting explanation from a different angle. I hear from everywhere there is no "now" after Einstein, which I find hard to comprehend. I think mathematically the time coordinate applies everywhere rather than propagating at the speed of light so instance of t=whatever is "now". That is explained in another message in this thread.
For me there is "now" for any instant of my existence as it is for you on the other side of the globe I presume.
If My wife is at work she is elsewhere then she comes back. For each instance of my existence when she was away I had my "now" and she had her "now" then we met. Therefore I conclude there was my "now" mapped to her "now" even though we could not communicate instantaneously.
I better stop now :) , because this is not the kind of discussion people would be interested in this thread.

 

[andromeda]

The first installment

Sounds good. I look forward to the next installment whenever you get around to it.

I believe that the problem of traveling parallel line should be resolved algebraically using analytic geometry and Lorentz transformation. I am working towards this goal which many of the readers would call futile and I am not there yet. I think however it would be interesting to try pure geometric proof as an exercise and opportunity to clean up traditional way of thinking in the context of relativity. I would be interested in arguments against the following reasoning:

Assumptions:

1) Let there be a coordinate system K as defined in [1] part 1 § 1 also referred as “stationary”
with axes named X,Y,Z
2) Let there be a coordinate system k moving relatively to K with a constant velocity as defined
in [1] part 1 § 3. with axes named X’,Y’,Z’
3) Let us assume the coordinate systems are representative to the physical world in a region of
negligible gravity in every detail, as described in [1] part 1 § 1,3.
4) Let the axes X and X’ coincide and Y,Y’ and Z,Z’ axes respectively be parallel.
5) Let a straight line T referred thereafter as “travelling line” that exists on the plane XY be
parallel at all times in K while in motion at constant velocity towards X from a remote
location.
6) At any stage of motion, the traveling line in T momentarily coincides with a statically defined persistent line on XY plane that is parallel to X
7) The traveling line T defined in K is persistent and therefore it exists in the system k and it is denoted as T’.
8) Both K and k systems can be regarded as stationary and rules of Euclidean geometry apply in their respective spaces.

Proposition:

If the traveling line T is parallel to X the line T’ cannot be oblique or perpendicular to X’

Proof:
1) System K axes X,Y Z are perpendicular straight lines as defined in Euclidean geometry and intersect in one point.
2) System k axes X’,Y’ Z’ are perpendicular straight lines as defined in Euclidean geometry and intersect in one point.
3) At any stage of motion of k axes X and X’ are the same straight line.
4) The traveling line T in K does not have any common point with X axis unless it fully coincides with X axis and then all points of T belong to X
5) If the line T’ were oblique or perpendicular to X’ while wholly contained within X’Y’ plane it would have exactly one common point with X’ at all times.
6) Since T is parallel to X (while X fully coincides with X’), it has no common points with X and therefore X’, unless it fully coincides with X, hence T’ cannot be oblique or perpendicular Q.E.D

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[1] Albert Einstein, “On the Electrodynamics of Moving Bodies” (translation from original Annalen der Physik, 17(1905), pp. 891-921) published on the internet in http://www.fourmilab.ch/etexts/einst...el/specrel.pdf