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

==========
[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

 

[Dale]

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

Number 5 is true, no "if" involved. T' does always have exactly one common point with X' at all times in k.

The "and therefore" in number 6 does not follow, just because T has no points in common with X at some instant in K does not imply that T' has no points in common with X' at some instant in k. The instants in K are not the same as the instants in k.

Without loss of generality, suppose that T fully coincides with X at time t=0 in K, then any event where a K clock located at the X-X' axis reads 0 is an event where T crosses X. Due to the relativity of simultaneity at any time in k there is always exactly one K clock which reads t=0 on the X' axis. This K clock identifies the single point where T' intersects X' at that instant in k.

This is the third time that you have made the same argument in one guise or another. It is false. Please move on.

 

[Dale]

If you like geometric arguments then you may be well-served to try to understand the situation in 4D spacetime. Think of time as being up and down, X and being horizontally forward and backwards, and Y being horizontally left and right, and ignore Z.

In spacetime the X-X' axis is not a 1D line, but rather a 2D plane (sometimes called a worldsheet), specifically it is a vertical plane that is edge-on to you. T-T' is also a 2D plane that is edge-on to you, but at an angle rather than vertical. These two planes intersect, and the intersection is a single 1D line in spacetime running forward and backward.

An instant in X is a horizontal plane, and this horizontal plane intersects the X-X' plane in a 1D line and the T-T' plane in a 1D line. These two lines are parallel, and at one instant they are the same line.

An instant in X' is a plane which slopes upwards as it stretches out in front of you. Note that the intersection of the sloped plane with the X-X' axis is still a 1D line, and that the intersection of the sloped plane with the T-T' plane is also still a 1D line. However, because of the slope those two lines are no longer parallel inside the sloped plane and they intersect in one point.

Thus geometrically, simply because two given planes intersect with a third plane in parallel lines does not imply that the intersection of the two given planes with a fourth plane must also result in parallel lines.

 

[andromeda]

Partial Answer to the problem

Facts which at first seem improbable
will, even on scant explanation,
drop the cloak which has hidden them
and stand forth in naked and simple beauty.
Galileo Galilei[1]​

I think I have received enough good answers to many questions and my main problem whether relative simultaneity is real can be partially answered.

Firstly, what is real, philosophers do not agree, but for a scientific realist it is sufficient that if confirmed by an experiment that is set to test a theory, then it is real. I agree with this statement

Secondly, simultaneity has to be defined. There are many definitions to chose from

If simultaneity is defined as the same numerical indication of two clocks that have been synchronised in accordance with Einstein's procedure[2] part I § 1 , then we are ready for an answer.

I have no doubt two clocks placed on X and X' axes that would coincide with two ends of a rod passing through the X axis being parallel to X axis would record times in primed and non primed as calculated by Lorenz transformation

For such defined word "simultaneity" and the word "real" I hereby declare:
Relative Simultaneity is Real

The controversies which started to build up in my discussion arise in general from the fact that there may be different definitions of simultaneity which may or may not have some physical meaning.

The majority opinion in this thread is that simultaneity's physical significance is nothing in particular.

I no longer intend to continue discussion on parallel lines as it is not going to go anywhere and the full answer to my question will remain unresolved.

Thank you all participants for valuable contributions.

[1] from www.brainyquote.com
[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/einst...el/specrel.pdf

 

[Dale]

For such defined word "simultaneity" and the word "real" I hereby declare:
Relative Simultaneity is Real

Under those definitions, I agree. I am glad that you have that resolved.

I no longer intend to continue discussion on parallel lines as it is not going to go anywhere and the full answer to my question will remain unresolved.

I am sad that you think this is unresolved. It was proven algebraically, several counter-arguments were debunked, and it was demonstrated geometrically. To me that seems incredibly well resolved. However, if that is insufficient for you, then I agree that an internet forum is probably not a viable mechanism.

 

[andromeda]

Under those definitions, I agree. I am glad that you have that resolved.
I am sad that you think this is unresolved. It was proven algebraically, several counter-arguments were debunked, and it was demonstrated geometrically. To me that seems incredibly well resolved. However, if that is insufficient for you, then I agree that an internet forum is probably not a viable mechanism.

Hi DaleSpam,

That was the nicest comment about my completely illogical way of thinking.

I really wanted to stop that parallel line thing but you have encouraged me to comment again, possibly for the last time.

Firstly I have no intention to challenge Special Relativity and I assume it is a scientific fact
with at least two unquestionable experimental effects the E=Mc2 equivalence together with mass variation with speed, and direct time dilation confirmation from muon experiment.

Your proofs were not wrong when considered in t' domain.

My geometric "proof" had no concept of time and had infinitely long lines moving laterally which is natural in geometry. The laterally moving line or a segment in stationary system could be seen as means to synchronise clocks instantaneously without violation of the speed of light limit.

Without even considering another relatively moving system k this fact alone is remarkable.

All I can say about your refutation is that my geometric problem cannot be resolved within
Euclidean Geometry alone because you need to invoke special relativity. And in my somewhat provocative (as to provoke/stimulate free discussion) point of view I saw the common line X or X' the same for both systems k and K' and the parallelism is a transitive property.

You have to break the temporal connection between moving and stationary system to achieve non parallel situation. Perhaps using 3D Classic Geometry in the context of relativity is simply inappropriate and that point could be agreed upon.

If I have a rigid rod in the stationary system moving laterally, the ends of the rod move simultaneously so each time it coincides with line with clocks it can synchronise them instantaneously. I am talking a thought experiment not the actual physical implementation.

So it seems quite naively to me that even without possibility of speed greater than light you can still achieve instantaneous synchronistion accomplished by to ends of a line segment and that what I thought was interesting to discuss here, but it obviously is not.

I have already pointed out that Lorentz transformation which in my examples require two steps:
a) LX matrix/vector multiplication which preserves parallell lines which is a fundamental theorem in linear transformation theory.
b) algebraic elimination of t in favour of t' which naturally lingers there after step a).

When you do a) and b) there is no doubt traveling line is not parallel

I was interested in step a) after which the line is still parallel, and the meaning of such fact. Then suddenly this becomes controversial and inappropriate issue in this thread.

I agree then "an internet forum is probably not a viable mechanism" to resolve controversies.

I still consider all responses without exception very inspiring and I have learned a lot. At the end only discussions of opposing views bring progress in science.

Regards from andromeda, for the last time

 

[Dale]

My geometric "proof" had no concept of time and had infinitely long lines moving

As soon as you have something moving you have a concept of time. Your proof didn't get away from any notion of time, it simply used a Galilean notion, which is perfectly fine geometrically, but disagrees with experiment.

The laterally moving line or a segment in stationary system could be seen as means to synchronise clocks instantaneously without violation of the speed of light limit.

Certainly. Although Einstein's synchronization convention uses light pulses, there are a few other equivalent synchronization mechanisms. Slow clock transport is the most famous, but I agree that this is another.

All I can say about your refutation is that my geometric problem cannot be resolved within
Euclidean Geometry alone because you need to invoke special relativity.

I agree that the problem cannot be resolved within Euclidean geometry alone, in fact, the problem cannot even be stated within Euclidean geometry alone. You need time to have moving lines, so you must have a geometry that includes time. Euclidean geometry does not, so you can pick Galilean or Minkowski geometry.

Perhaps using 3D Classic Geometry in the context of relativity is simply inappropriate and that point could be agreed upon.

I agree. However, to be clear, at any single instant in any frame the 3D space is Euclidean. All of Euclid's axioms and geometry apply at a single instant in any frame.

This can be seen directly from the metric: $ds^2=-dt^2+dx^2+dy^2+dz^2$. In a single instant we have $dt=0$ which clearly leaves the metric for Euclidean geometry.

So it seems quite naively to me that even without possibility of speed greater than light you can still achieve instantaneous synchronistion accomplished by to ends of a line segment

Certainly. But it is only "instantaneous" in one reference frame. This procedure is equivalent to Einstein's method.

I have already pointed out that Lorentz transformation which in my examples require two steps:
a) LX matrix/vector multiplication which preserves parallell lines which is a fundamental theorem in linear transformation theory.

Yes, the Lorentz transform can be represented as a linear transform, and the standard rules of linear algebra apply, and parallel lines do remain parallel in a linear transform. If you take any pair of worldlines which are parallel in one frame and perform a Lorentz transform then they will remain parallel in every other frame.

However, that is not relevant to the discussion here, because in the space where that linear transform exists (Minkowski spacetime) the X-X' axis is a plane, not a line, and that plane is not parallel to the T-T' plane. Please refer to my geometric description in post 32 above.

I was interested in step a) after which the line is still parallel, and the meaning of such fact.

It means that you are still using t, and t is coordinate time in the frame where they are parallel.

Then suddenly this becomes controversial and inappropriate issue in this thread.

There remains plenty to discuss, if you wish. The idea of the line as an equivalent synchronization procedure is interesting, possibly novel. As long as you don't repeat the disproven assertion that it is parallel in other reference frames, then there is nothing otherwise inappropriate with it.

 

[andromeda]

There remains plenty to discuss, if you wish. The idea of the line as an equivalent synchronization procedure is interesting, possibly novel. As long as you don't repeat the disproven assertion that it is parallel in other reference frames, then there is nothing otherwise inappropriate with it.

The idea is not novel although I have come up with it myself.
My later research found publication of Jackson and Pargetter [1] which of course attracted criticism in [2],[3],[4], however I remain unconvinced that the last word was said on this issue. But until I find sufficient presentable argument otherwise, I will shut up.

The good thing in this thread is that you get down from your ivory tower and face the real world and see the points of view different than your own, and if you think your point of view is sound and matters, you have to find the way to convince even the harshest critics.


[1] Jackson, F. and Pargetter, R. Relative Simultaneity in Special Relativity. Phil. Sci. 1977, Vol. 44, 3.
[2] Giannoni, C. Comment on "Relative Simultaneity in the Special Theory of Relativity". Phil. Sci. 1979, Vol. 46, 2.
[3] Torretti, R. Jackson and Pargetter's Criterion of Distant Simultaneity. Phil. Sci. 1979, Vol. 46, 2.
[4] Øhrstrøm, P. Conventionality of Distant Simultaneity. Found. Phys. 1980, Vol. 10, 3/4.
12.

 

[Dale]

The idea is not novel although I have come up with it myself.

Ahh, I know how frustrating that can be!

My later research found publication of Jackson and Pargetter [1] which of course attracted criticism in [2],[3],[4], however I remain unconvinced that the last word was said on this issue.

The fact that there was criticism and the expectation that there will be more discussion can be taken as a given since you are looking in the philosophy literature.

 

[andromeda]

Taking a break

As promised twice already I do not intend to add more to this thread unless there is a significant comment or some new really relevant issue comes to my attention.
The defence and the prosecution have rest their case and the jury is out.

However, if readers wish to comment in any way they can use the forum private messaging mechanism that remains open (I hope). I find every bit of critique or support (if any) very valuable,
and that is why I put this post despite my previous promise.

 

[andromeda]

Need some opinion

While digesting my apparent failure of the parallel line arguments I came to some issue that is related.

I would like an opinion about the following:

Given a long (say one light second long) straight rigid rod and an observer near one end of the rod.

If the observer moves away from the end of the rod in the immediate vicinity, does he instantaneously moves away from the other end or the change of distance is delayed due to speed of light.
More precisely, can the observer moving away from one end of the rod can assume he moves away instantaneously from the other end?
Is the problem formulated properly? Is there a valid explanation in agreement with STR where nothing can happen faster than at the speed of light?

 

[Nugatory]

Is there a valid explanation in agreement with STR where nothing can happen faster than at the speed of light?

"Happen faster than the speed of light" makes no more sense than "happens faster than I can walk" - "happens" isn't a speed so it can't be faster or slower than the speed of light or the speed of anything else.

You mean the observer is standing next to one end of the rod, and at time zero starts moving away from the rod with speed $v$? This is no different than if I take a step to the left and everything to my right is immediately one meter further away, even the remote star that went from being fifty light-years away to being fifty light-years plus one meter away. There's nothing faster than light going on here, our observer just started moving while the rod sits there.

 

[Fredrik]

All you have described is a person moving away from an object. There's an event where that person begins to move away, but to discuss simultaneity, you would have to specify at least two events. And if you're only going to move the person and not the rod, why does the rod need to be rigid?

I suspect that what you were trying to ask is this: Suppose that that guy pushes himself away from the rod by kicking it, so that he moves in one direction, and every part of the rod is simultaneously nudged in the other direction. Will an observer comoving with the rod describe the two events "my end of the rod starts to move" and "that guy starts to move" as simultaneous?

The problem with this scenario is that a perfectly rigid rod contradicts relativity. What would actually happen when you push the rod is that you would only be moving the first layer of atoms, which interacts electromagnetically with the second layer, which interacts with the third, and so on. This creates a longitudinal wave in the rod. Longitudinal waves in a solid are, by definition, sound. So the disturbance propagates at the speed of sound. The other end may not move at all, since the wave loses energy by heating the rod.

It looks like the reason why you asked about this is that you want to know if the observer at the other end will consider the event where your guy started to move, simultaneous with the time when the light from that event reaches him. The answer is no. He will assign time coordinates to these events that differ by L/c, where L is the length he assigns to the rod.

 

[andromeda]

Thanks Nugatory and Fredrik for the response. And you have understood the issue that I have presented in a casual language.

My question in more precise language was like this:

1) Observer is standing next to one end of a very long rod, and at time zero starts moving away from the rod on the straight line designated by the rod with a speed $v$.

2)The rod is rigid in the sense that its length is constant in its own rest frame.

3) The issue is that when visualising close and far ends together and making a step away from them , the observer seems to change the distance to both ends simultaneously no matter how far is the end and I was interested in your opinion about distant simultaneity in such case. The rod would not be disturbed, only the observer moves.

4)I was not yet considering the issue of the rod being moved but that would be the next thing to analyse.

It seems we have no objection to say that the range to every part of the rod or any distant object for that matter changes instantaneously when the observer starts moving.

I find it interesting but not unexpected that to accomplish the same relative motion of the rod by kicking it in one end without touching the observer creates a range of relativity issues including rigid rod contradicting relativity.

I understand the nature of Fredrik's argument such that we have elastic bodies not rigid ones, yet rigid rods are theoretical objects of importance in relativity as can be guessed from Einstein's 1905 paper[1], and declaring rigid rod a contradictory concept may be not right even though a lot of people including Pauli have said that.

I partially question the statement that disturbance propagates at the speed of sound in elastic bodies in classical physics.
Although fully formed disturbance appears to move at the speed of sound, the actual mechanism is that the disturbance builds up rather than moves and all parts of the elastic body act simultneously upon tension force changes as per general solution of the simplified 1D form of the wave equation:
A=F(x-c*t)+G(x+c*t) where A is generalised amplitude and c is the speed of sound.
Tension forces are instantaneous in classical physics and various distant parts of an elastic body slowly accelerate right from the start. Relativistic wave is something I would not go into at this stage.

It looks like the reason why you asked about this is that you want to know if the observer at the other end will consider the event where your guy started to move, simultaneous with the time when the light from that event reaches him. The answer is no. He will assign time coordinates to these events that differ by L/c, where L is the length he assigns to the rod
.

That was not the reason and agree with the above explanation. Many people mix observation delays with simultaneity issues, I do not.
My reason was to get some perspective in the problem of asymmetry in the case when observer moves and the rod moves which plays role in my goal to understand simultaneity. Thanks to you guys I have gained a bit more perspective.

It would be interesting to do some Lorentz transformations in each case to get some definite answers. Acceleration to speed v may be an issue outside of the STR.

______________________________________________________________________________
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

Just above section I. KINEMATICAL PART:
The theory to be developed is based—like all electrodynamics—on the kinematics
of the rigid body, since the assertions of any such theory have to do
with the relationships between rigid bodies (systems of co-ordinates), clocks,
and electromagnetic processes. Insufficient consideration of this circumstance
lies at the root of the difficulties which the electrodynamics of moving bodies
at present encounters.

 

[Dale]

2)The rod is rigid in the sense that its length is constant in its own rest frame.

3) The issue is that when visualising close and far ends together and making a step away from them , the observer seems to change the distance to both ends simultaneously no matter how far is the end and I was interested in your opinion about distant simultaneity in such case. The rod would not be disturbed, only the observer moves.

Regarding 2. There is a standard sense of the word "rigid" in relativity. It is also called Born rigid, and it describes rigid motion rather than rigid material. So you could say something like "an inertial Born-rigid rod".

Regarding 3. When you use a word like" simultaneously" in relativity, don't forget to specify the reference frame. I assume that you mean the frame of the rod, but it is unclear. In this case you could be asking about the non inertial frame of the observer.

 

[Nugatory]

2)The rod is rigid in the sense that its length is constant in its own rest frame.

That is not physically possible if the rod is being accelerated by pushing on one end. Check out the third paragraph of Fredrik's post 42 in this thread to see the mechanics of what's going on.

Even in classical Newtonian mechanics it's not possible to maintain a constant length of a body that's being pushed at one end. The perfect rigid body that you see in textbook problems is an approximation, but in the real world if you nudge one end of a meter stick it will contract by a nanometer or so before the other end starts to move.

That's small enough that people seldom notice or care, but the effect is still there - and that's one of many reasons why careful authors insist on infinitesimal test particles when describing gravitational and electromagnetic fields.

 

[andromeda]

For he record and convennience of the reader.
A new thread "Confusion over length contraction" that someone has just created:
https://www.physicsforums.com/showthread.php?t=750525
seems to reveal some issues which are relevant to this thread, so my responses there are somewhat complementary.

 

[ghwellsjr]

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.

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

Since you have expressed an interest in darkhorror's example, I have decided to make the diagrams he suggested.

The first one is the FOR (Frame Of Reference) in which the platform is at rest and the train is moving to the right at 0.6c. I have depicted the two ends of the platform where there are two clocks in blue and green and the two ends of the train where there are two more clocks in red and black.

At the Coordinate Time of zero, the red and blue clocks are colocated and have a time of zero on them and the black and green clocks are colocated at a different place 8 feet to the right with a time of zero on them. The dots mark off 1 nanosecond increments of Proper Time on all the clocks. You can determine the Proper Time on any clock by counting the number of tick marks above or below the point of colocation. The red and black clocks start at -4 nsec (at the bottom) and go up to +7 nsec (at the top) while the blue and green clocks start at -5 nsec (at the bottom) and go up to +6 nsec (at the top). Please understand that the platform and train existed before and after the brief intervals depicted in the diagram. The speed of light is taken to be 1 foot per nanosecond:

You will note that the Proper Times on the blue and green clocks are synchronized with each other and with the Coordinate Time of the FOR but this cannot be said for the red and black clocks. Note also that the distance between the ends of the train is 8 feet, the same as the distance between the ends of the platform.

Now we transform to the FOR in which the train is at rest and the platform is moving to the left at 0.6c:

Note, as darkhorror mentioned, the distance between the train's clocks is different. It has gone from 8 feet to 10 feet. And the distance between the platform's clocks is also different. It has gone from 8 feet to 6.4 feet. So, he concludes, when the left pair of clocks are in the same place (at the Coordinate Time of 3 nsecs) the right pair of clocks cannot be in the same place (they are separated by 3.6 feet).

Also note, as darkhorror advised, that we have properly taken into account Time Dilation, Length Contraction, and the Relativity of Simultaneity (or as he said, what "now" would have to be in different frames).

He also said that both frames need to agree on events and they do, they just have different coordinates for the events in the two frames as determined by the Lorentz Transformation process.

Now I want to show you another way in which frames need to agree on events and that is how light travels between each pair of events. This is the real significance of doing the transformation between frames. I have drawn in a whole bunch of random light signals going from an event on one line to an event on another line. Note that each of these thin lines (in the color of the thick source line) travels upwards to the left or to the right on a 45-degree diagonal between events. Here is the first FOR with those light signals drawn in:

And here is the second FOR with the same light signals drawn in going at 45-degree angles. You should confirm that both frames depict exactly the same pattern of lines going between the same pairs of events at 45-degree angles:

And there is nothing magic about rest frames. Here is a frame in which both the platform and the train are traveling at the same speed (0.333c) but in opposite directions:

Same results for light traveling between events.

And let's do one for a frame traveling at -0.333c with respect to the first one:

One other aspect of these light signals is to show that an observer located with anyone of the clocks sees exactly the same thing in all frames. The light signal carries the information of how each observer sees the other clocks. So, for example, when the red clock is at +4 nsec, it sees the black and green clocks colocated with zero on both of them. Another example: when the blue clock is at +4 nsecs, it sees the red clock at +2 nsec, the black clock at -2 nsecs and the green clock at -4 nsecs. Veryify that this is true in all frames.

Does this all make sense to you? Does it help? Any questions?

 

[andromeda]

Does this all make sense to you? Does it help? Any questions?

I will respond as soon as I can.

Thank you very much for help and for going to such length in your presentations here and in another thread.

The pictures are worth thousand words. It will take me a while to come up with a meaningful response to this and the other related thread posts. Unfortunately I cannot do relativity for living and right now I need to attend my less glamorous yet still interesting daily job, where distant things appear simultaneous no matter what (small) speed, where twins talk over radio with no delay

 

[PAllen]

I will respond as soon as I can.

Thank you very much for help and for going to such length in your presentations here and in another thread.

The pictures are worth thousand words. It will take me a while to come up with a meaningful response to this and the other related thread posts. Unfortunately I cannot do relativity for living and right now I need to attend my less glamorous yet still interesting daily job, where distant things appear simultaneous no matter what (small) speed, where twins talk over radio with no delay

But every magnet you have ever held demonstrates a relativistic effect ...

 

[Nugatory]

where twins talk over radio with no delay

As long as they aren't Apollo astronauts... Dunno if you were around for that, but the time delay in in radio conversations between Earth and moon was very clearly perceptible. No relativistic effects were involved here, but the demonstration that radio doesn't travel instantaneously was very convincing.