The Relativity of Simultaneity: A Fundamental Concept in Special Relativity

[harrylin]

Does the clock synchronisation rely on the constancy of the one way speed of light?

The clock synchronisation defines the one-way speed of light. However, and as I tried to clarify, the assumption that the clock synchronisation method is consistent with a constant speed of light relies on the two-way speed of light being the same in all directions. Thus you could say that the clock synchronisation of SR relies on the constancy of the two way speed of light.

 

[mangaroosh]

It may be useful to highlight a subtle point that has perhaps not been brought up. Some of the replies can look contradictory because "relativity of simultaneity" has a technical meaning as well as an extended meaning (just like for example "democracy"):

- there is technical relativity of simultaneity, as illustrated by dalespam. Such relative simultaneity does not necessarily imply the PoR.

- there is relativity of simultaneity in the context of relativity theory, implying the PoR.
The expression then acquires the additional meaning that no Newtonian "absolute simultaneity" can be established ("simultaneity is relative"). That is explained by SR with such effects as length contraction and time dilation.

Does that help?

Harald

thanks Harald, it helps to clarify the issue a little further.

In the context of the OP, or perhaps Einsteinian relativity, is it the latter that we are interested in, because the PoR is implied?

Or is it accurate to say that under the Einsteinian interpretation of relativity, RoS is a consequence of time dilation and/or length contraction?

EDIT: also, is the reasoning in the above posts, relating to RoS being a consequence of the constancy of the speed of light, accurate; namely that RoS is a consequence of TD and/or LC?

 

[mangaroosh]

The clock synchronisation defines the one-way speed of light. However, and as I tried to clarify, the assumption that the clock synchronisation method is consistent with a constant speed of light relies on the two-way speed of light being the same in all directions. Thus you could say that the clock synchronisation of SR relies on the constancy of the two way speed of light.

Thanks again Harald, that was my understanding, I just wasn't sure how to interpret post #91

 

[harrylin]

Note also the remark by Einstein (1905) "We assume that this definition of synchronism is free from contradictions".

By starting with a definition of which the applicability only appears later he put IMHO the chart before the horse in his 1905 presentation (his 1907 presentation does not have that weakness). Also, he first defines c as equal to the two-way speed of light. For a careful reader, this can be a bit confusing. Here's how I would present it (afterwards it's always easier!):

Physical assumptions of the theory, based on observations:

1. the laws of nature which describe physical phenomena are the same in all reference systems that are in linear uniform motion
2. the two-way speed of light (defined as distance/time) in such a reference system is the same in all directions, independent of location and independent of the motion of the source

A measurement convention for distant time will be required (see the long explanation in Einstein-1905). The following one allows for the simplest description (compare Einstein's 1907 formulation*):
- we may synchronize clocks such that the one-way speed of light becomes equal to the two-way speed of light.

It directly follows that the simultaneity of reference systems that are in relative motion and use that convention is relative.

PS. in answer to the next question by mangaroosh: how that relative simultaneity fits with the PoR is explained by the combined effects of length contraction and time dilation. In such matters, what you call "cause" and what you call "consequence" is often reversible and thus a matter of opinion.

Harald

*We now assume that the clocks can be adjusted in such a way that the propagation velocity of every light ray in vacuum - measured by means of these clocks - becomes everywhere equal to a universal constant c, provided that the coordinate system is not accelerated. - Einstein 1907

 

[PhilDSP]

In order for RoS to arise, something would have to happen. What is that something?

Doesn't RoS arise because the definition of simultaneous in SR is based on considerations of causality AND because the flow of information is limited in speed AND because the definition of time and therefore the lapse of time varies in different situations? If the limiting speed for whatever information causing some effect is not c but not infinite then RoS would still arise.

Some further development of LET might posit a universal time keeper whose knowledge spans space and so could act in such a capacity, i.e. would know all the details about how clocks function in different situations and could integrate them all to produce a unified time. But that would seem to require either omniscience or a structure that distributes what we call information across space without requiring a delay of time. Certain aspects of Quantum Mechanics start to point to such things.

 

[mangaroosh]

Doesn't RoS arise because the definition of simultaneous in SR is based on considerations of causality AND because the flow of information is limited in speed AND because the definition of time and therefore the lapse of time varies in different situations?

quite possibly, I'm not sure I've heard it formulated as such before; however, I don't think a limited speed of information flow, by itself, would lead to RoS, but would I be right in saying that it pertains directly to the considerations of causality? I think those however would be secondary and wouldn't, lead to RoS, but rather affect what can occur under the conditions of RoS. I think that the lapse of time varying in different situations is probably what would, ultimately, give rise to RoS (under Einsteinian relativity). Would I be right in saying that, that phenomena, would be referred to as time dilation?

Some further development of LET might posit a universal time keeper whose knowledge spans space and so could act in such a capacity, i.e. would know all the details about how clocks function in different situations and could integrate them all to produce a unified time. But that would seem to require either omniscience or a structure that distributes what we can information across space without requiring a delay of time. Certain aspects of Quantum Mechanics start to investigate such things.

Alternatively it might go the other way, and question whether time itself actually exists, such that there would be no need for a universal timekeeper, because there would be no universal time; just clocks whose repetitive process can provide a standard unit of comparison, for the purpose of expressing the duration of other processes.

Instead of requiring omniscience, what would be needed would be to define a rest frame for standard units of measurement, the Earth for example, such that any motion relative to this [non-absolute] rest frame would be ascribed to the reference frame moving relative to the earth, and any contractions would necessarily be ascribed to that reference frame. The Earth wouldn't need to be considered at rest in the ether, it could either be in motion or at rest, it wouldn't matter, all that would matter is that the units for expressing experimental results are defined with a standardised rest frame.

 

[Dale]

I'm not sure that I am unwittingly using them;

You are using them. Specifically, the comment which kicked off this whole discussion was your statement that due to LC and TD the measured c should be frame variant. The measured c is frame invariant for the Lorentz transform, therefore you were not using the Lorentz transform. You were, instead, using some other transform which contained LC and TD, but not RoS and thus led to a non-invariant c.

EDIT: the point being made by a number of people is that RoS is a consequence of the constancy of c; but the constancy of the speed of light does not cause length contraction and time dilation, length contraction and time dilation must occur in order for all observers to measure the speed of light to be c - hence RoS is a consequence of them - in terms of real world phenomena, as opposed to hypothetical mathematics that doesn't correspond to physical phenomena.

You have it backwards. The principle of relativity and the postulate of c lead to TD, LC, and RoS. The postulates are simply assumed. To make an assumption, draw some conclusions, and use those conclusions to explain the assumptions would be circular reasoning.

Now, it is possible to switch up which statements are postulates and which are derived. If you do that, then postulating TD and LC does not lead to the principle of relativity and the invariance of c. You need to add RoS as a separate third postulate to do that. Either way, RoS is a separate feature of the Lorentz transform, not a simple consequence of TD and LC.

 

[PhilDSP]

Alternatively it might go the other way, and question whether time itself actually exists, such that there would be no need for a universal timekeeper, because there would be no universal time; just clocks whose repetitive process can provide a standard unit of comparison, for the purpose of expressing the duration of other processes.

That doesn't seem to work for QM which studies not only local interactions but so-called non-local interactions or dependencies also. To get an idea of what's at stake you might consider one particular interpretation of QM that provides a workable model - Bohm Mechanics. To simply radically, a single wave equation is initiated in the beginning of time that contains all causes for every effect everywhere until the end of time or the end of the universe. That could only work if there is an absolute order of effects when evaluated for the entire universe.

 

[James_Harford]

Now, it is possible to switch up which statements are postulates and which are derived. If you do that, then postulating TD and LC does not lead to the principle of relativity and the invariance of c. You need to add RoS as a separate third postulate to do that. Either way, RoS is a separate feature of the Lorentz transform, not a simple consequence of TD and LC.

This point is so important it deserves an example:

Suppose your friend departs at 4/5 the speed of light. You will note that he has shortened by 3/5 and his clock runs 3/5 slower. Nothing in this description requires your friend to perceive himself at rest relative to the speed of light. Nor has he any reason to disagree with you about the simultaneity of events.

Given these assumptions of yours, a logically correct conclusion can be made that your friend will see you moving away from him at 4/5 the speed of light, but lengthened by a factor of 5/3 and your clock speed increased by the same factor. This is an intuitive and logically correct consequence of working without Einstein's 2n'd postulate. But as a description of reality, we all know it is wrong, yes?

To correct it, you need Einstein's 2'nd postulate.

 

[harrylin]

This point is so important it deserves an example:

Suppose your friend departs at 4/5 the speed of light. You will note that he has shortened by 3/5 and his clock runs 3/5 slower. Nothing in this description requires your friend to perceive himself at rest relative to the speed of light. Nor has he any reason to disagree with you about the simultaneity of events.

Given these assumptions of yours, a logically correct conclusion can be made that your friend will see you moving away from him at 4/5 the speed of light, but lengthened by a factor of 5/4 and your clock speed increased by the same factor. This is an intuitive and logically correct consequence of working without Einstein's 2n'd postulate. But as a description of reality, we all know it is wrong, yes?

To correct it, you need Einstein's 2'nd postulate.

Almost correct. The last factor has a glitch and your account went a little wrong in the end: the operator is free how to synchronize clocks - that has nothing to do with a "wrong description of reality". I already mentioned this in my last few posts, as I elaborated on Agerhell's comments. Also kmarinas86 brought this up.

 

[James_Harford]

The last factor has a glitch and your account went a little wrong in the end: the operator is free how to synchronize clocks - that has nothing to do with a "wrong description of reality".

Thanks for the correction. And, yes, "reality" is a loaded term. Better to say it is "a wrong description of SR", instead. But the point stands.

 

[mangaroosh]

You are using them. Specifically, the comment which kicked off this whole discussion was your statement that due to LC and TD the measured c should be frame variant. The measured c is frame invariant for the Lorentz transform, therefore you were not using the Lorentz transform. You were, instead, using some other transform which contained LC and TD, but not RoS and thus led to a non-invariant c.

You have it backwards. The principle of relativity and the postulate of c lead to TD, LC, and RoS. The postulates are simply assumed. To make an assumption, draw some conclusions, and use those conclusions to explain the assumptions would be circular reasoning.

Now, it is possible to switch up which statements are postulates and which are derived. If you do that, then postulating TD and LC does not lead to the principle of relativity and the invariance of c. You need to add RoS as a separate third postulate to do that. Either way, RoS is a separate feature of the Lorentz transform, not a simple consequence of TD and LC.

ah, I think I get the point now; thanks DS.

In the second transform you used, where there was RoS but no LC or TD, does c remain invariant?

 

[Dale]

In the second transform you used, where there was RoS but no LC or TD, does c remain invariant?

Yes, in that one c is invariant, but the principle of relativity is violated.

 

[mangaroosh]

you are using them. Specifically, the comment which kicked off this whole discussion was your statement that due to lc and td the measured c should be frame variant. The measured c is frame invariant for the lorentz transform, therefore you were not using the lorentz transform. You were, instead, using some other transform which contained lc and td, but not ros and thus led to a non-invariant c.

Just going back to the comment and reply which kicked off the discussion.

just on that point, and this is somewhere i might lack clarity, but if someone uses a slower clock and a smaller ruler (than similar instruments at rest on earth) and if they measure the speed of light to be 300,000 km/s with those instruments, would it not mean that the speed of light in both frames is actually different; because it would mean that the light in the reference frame moving relative to the Earth actually took longer than a second to travel a distance shorter than 300,000 km?

what you say would be correct except that you are forgetting the relativity of simultaneity. The lorentz transform is not just length contraction and time dilation, but it also includes the relativity of simultaneity. You cannot just ignore it and get correct conclusions.

Is that not circular reasoning, to say that Ros was forgotten about, because it is using the conclusion to support the assumption [of the invariant speed of light]?

Just from the discussion, it looks like RoS is a consequence of an invariant actual speed of light, as opposed to an invariant measured speed of light, because the point of the above was that the measured c would remain invariant, but that the actual speed represented by those measurements would be different. In the examples of the transforms, RoS only seems to result when the [actual] speed of c remains invariant.

If Lorentzian relativity uses the same transform, but it doesn't involve, or give rise to, RoS then it suggests that RoS is not necessarily a consequence of the Lorentz transform, rather a consequence of the actual speed of light remaining invariant. Am I right in saying that Lorentzian relativity allows for the measured c to be invariant but for it to represent a variant actual c?

You have it backwards. The principle of relativity and the postulate of c lead to td, lc, and ros. The postulates are simply assumed. To make an assumption, draw some conclusions, and use those conclusions to explain the assumptions would be circular reasoning.

Now, it is possible to switch up which statements are postulates and which are derived. If you do that, then postulating td and lc does not lead to the principle of relativity and the invariance of c. You need to add ros as a separate third postulate to do that. Either way, ros is a separate feature of the lorentz transform, not a simple consequence of td and lc.

Is that not what happens though; are the conclusions not used to explain how the assumptions are possible?

The thing is, the aforementioned assumptions can only lead us to reason that such phenomena occur; however, in the physical world, the assumptions cannot give rise to the phenomena of TD and LC; that is, the invariant speed of light does not cause length contraction and time dilation, LC and TD must occur in order for the speed of light to remain invariant. RoS, then, is not a third and separate phenomena which can be used to explain the invariance of the actual c, it is a consequence of the actual speed of light remaining invariant.

 

[Dale]

Is that not circular reasoning, to say that Ros was forgotten about, because it is using the conclusion to support the assumption [of the invariant speed of light]?

You were going the other way. You said "LC + TD ≠ invariant c". I merely pointed out that you were missing the RoS.

Is that not what happens though; are the conclusions not used to explain how the assumptions are possible?

The conclusions can certainly be analyzed to show how they are internally consistent as well as consistent with the assumptions.

 

[mangaroosh]

You were going the other way. You said "LC + TD ≠ invariant c". I merely pointed out that you were missing the RoS.

Invariant c might help us to deduce that LC & TD are necessary, but invariant c cannot cause LC & TD; LC & TD must occur in order for c to be invariant. However, if LC & TD occur, it should mean that c is variant, for the reasons outlined. RoS is a consequence of c remaining invariant, so, to say that it is missing would be circular reasoning.

The conclusions can certainly be analyzed to show how they are internally consistent as well as consistent with the assumptions.

But LC & TD, which you mentioned are the conclusions, are necessary for c to remain invariant; so that would be circular reasoning, wouldn't it?

 

[Dale]

invariant c cannot cause LC & TD

Why not?

LC & TD must occur in order for c to be invariant.

This is not true. You can have a transform with invariant c, but no LC or TD.
$$t'=t+\frac{v}{c^2}x$$
$$x'=vt+x$$

 

[mangaroosh]

Why not?

Accoridng to Einsteinian relativity, LC & TD are caused by the relative motion of a reference frame; if LC & TD occur then it should mean that c is invariant; using RoS as a reason why that isn't the case is circular reasoning.

This is not true. You can have a transform with invariant c, but no LC or TD.
$$t'=t+\frac{v}{c^2}x$$
$$x'=vt+x$$

Is that a transform used in Einsteinian relativity?

 

[Dale]

Accoridng to Einsteinian relativity, LC & TD are caused by the relative motion of a reference frame; if LC & TD occur then it should mean that c is invariant; using RoS as a reason why that isn't the case is circular reasoning.

Your language here is a little confused, so I am concerned that your thoughts are also a little confused. When we are talking about the different postulates and conclusions in relativity we are not talking about a "cause and effect" effect relationship, but rather a "logical implication" relationship.

A cause and effect relationship involves more than a logical implication relationship, specifically it also implies a temporal ordering where the cause preceeds the effect. There is no such temporal ordering between LC, TD, RoS, the principle of relativity (PoR) and the invariance of c (C), so you cannot speak of causes or effects amongst them.

So, what we have is properly "implies" and not "causes". The proper way to express this formally is:
$(\text{PoR} \cap \text{C})\leftrightarrow (\text{LC} \cap \text{TD} \cap \text{RoS})$
Notice that the relationship is bidirectional (i.e. "if and only if").

If the above statement is true then all of the following statements are true and non-circular:
$(\text{PoR} \cap \text{C})\rightarrow (\text{LC} \cap \text{TD} \cap \text{RoS})$
$(\text{PoR} \cap \text{C})\rightarrow (\text{TD} \cap \text{RoS})$
$(\text{PoR} \cap \text{C})\rightarrow (\text{LC} \cap \text{RoS})$
$(\text{PoR} \cap \text{C})\rightarrow (\text{LC} \cap \text{TD})$
$(\text{PoR} \cap \text{C})\rightarrow \text{LC}$
$(\text{PoR} \cap \text{C})\rightarrow \text{TD}$
$(\text{PoR} \cap \text{C})\rightarrow \text{RoS}$
$(\text{LC} \cap \text{TD} \cap \text{RoS})\rightarrow (\text{PoR} \cap \text{C})$
$(\text{LC} \cap \text{TD} \cap \text{RoS})\rightarrow \text{C}$
$(\text{LC} \cap \text{TD} \cap \text{RoS})\rightarrow \text{PoR}$

As with any iff relationship you can, of course, make circular statements such as $(\text{PoR} \cap \text{C})\rightarrow (\text{LC} \cap \text{TD} \cap \text{RoS})\rightarrow \text{C}$. But that does not imply that either $(\text{PoR} \cap \text{C})\rightarrow (\text{LC} \cap \text{TD} \cap \text{RoS})$ or $(\text{LC} \cap \text{TD} \cap \text{RoS})\rightarrow \text{C}$ are circular.

This whole conversation began when you correctly pointed out that $(\text{LC} \cap \text{TD})\rightarrow \text{C}$ is false. I responded by correctly pointing out that $(\text{LC} \cap \text{TD} \cap \text{RoS})\rightarrow \text{C}$ is true and you had neglected RoS which is an essential part of SR. You then followed up with the incorrect assertion that $(\text{LC} \cap \text{TD})\rightarrow \text{RoS}$ to which I gave a counter-exmaple. The rest of the conversation has basically been follow-up to that.

I hope this clarifies things.

Is that a transform used in Einsteinian relativity?

No, it is merely a counter example to your claim of post 121 that "LC & TD must occur in order for c to be invariant" i.e. $\text{C}\rightarrow (\text{LC} \cap \text{TD})$

 

[nitsuj]

From reading some of this thread I realize that I don't have a good understand ing of RoS.

I would have assumed that time dilation / length contraction would account for RoS, invariance of c ect.

Is / was RoS an issue or noticed pre-SR / LET? Why not if it's exclusive of time dilation / length contraction?

Even in post #42, there is relative motion involved. I can't think of a scenario (visual) demonstrating RoS, where there is no relative motion. (amongst the event, and the two observers)

 

[Dale]

Is / was RoS an issue or noticed pre-SR / LET? Why not if it's exclusive of time dilation / length contraction?

That is an historical question. I simply don't know.

I can't think of a scenario (visual) demonstrating RoS, where there is no relative motion.

I agree, $RoS \rightarrow M$ where M is relative motion. RoS is when two different frames disagree on whether or not two events are simultaneous or not. So this implies at least two events and at least two reference frames. And two reference frames implies relative motion.

In fact, everything we have discussed, LC, TD, RoS, PoR, and C all imply M. It is part of the definition of each.

 

[nitsuj]

Thanks for the reply Dalespam.

Maybe if I pose my question differently it will become more apparent where my confusion is.

In what scenario would two observers have the same measure of length / time, but not agree on simultinaity?

To your point in the last comment, when I think of relative motion, I immediatly consider their measure of length / time to not be equal "parts/units" comparatively.

If RoS includes relative motion, how can length / time measure the same (comparatively) for each observer?

Lastly, sure you know now that I don't know math, can this demonstration of RoS without LC / TD be concluded with thought?

 

[Dale]

In what scenario would two observers have the same measure of length / time, but not agree on simultinaity?

If you are assuming special relativity then there is no such scenario since SR implies all three (LC, TD, and RoS). If you are not assuming SR then the last transform of post 2 is an example.

To your point in the last comment, when I think of relative motion, I immediatly consider their measure of length / time to not be equal "parts/units" comparatively.

If you assume SR that is correct.

 

[nitsuj]

Ah okay and phew!

 

[harrylin]

From reading some of this thread I realize that I don't have a good understand ing of RoS.

I would have assumed that time dilation / length contraction would account for RoS, invariance of c ect.

I think that it was mentioned in this thread that "RoS" has slightly different meanings.
RoS in the sense that we can't determine absolute simultaneity relates to the PoR, and the basic features that enable the PoR despite constant c are TD and LC.
Note that Einstein's constant c (independent of the motion of the source) should not be confused with invariance of c (relativity principle for light propagation).

Is / was RoS an issue or noticed pre-SR / LET? Why not if it's exclusive of time dilation / length contraction?

What's your meaning of RoS in that sentence?

Even in post #42, there is relative motion involved. I can't think of a scenario (visual) demonstrating RoS, where there is no relative motion. (amongst the event, and the two observers)

RoS refers to measurements in reference systems that are in relative motion. It is always possible to apply Galilean simultaneity based on a Master reference system - as is common practice.

 

[nitsuj]

Ah okay, I didn't (nor have I ever) seen that mentioned. There is always something new in SR from my perspective, this one is particularly suprising given what I do know of SR concepts.

I can't make the distinction you mention with "Note that Einstein's constant c (independent of the motion of the source) should not be confused with invariance of c (relativity principle for light propagation)."

Is there a simply way to make that distinction more clear (for me)? Maybe I should just consider scenarios of each, maybe that's where my confusion is. If so wow, good eye Harrylin!


I only have the one understanding of RoS, where two events separated spatialy could be measured as occurring simultaniously depending on relative motion.

 

[harrylin]

Ah okay, I didn't (nor have I ever) seen that mentioned. There is always something new in SR from my perspective, this one is particularly suprising given what I do know of SR concepts.

Yes, and in this thread: see post #105.

I can't make the distinction you mention with "Note that Einstein's constant c (independent of the motion of the source) should not be confused with invariance of c (relativity principle for light propagation)."

Is there a simply way to make that distinction more clear (for me)? Maybe I should just consider scenarios of each, maybe that's where my confusion is. If so wow, good eye Harrylin!

Sure.

1. Just look up "invariant" on Wikipedia:
http://en.wikipedia.org/wiki/Invariant Note that (at least today!) the word "constant" doesn't appear on that page. In the context of SR, people mean with "invariant" that a frame transformation doesn't change it.

Then look up "physical constants" on Wikipedia:
http://en.wikipedia.org/wiki/Physical_constant Note that (at least today!) the word "frame" doesn't appear on that page.

According to SR, such physical constants are not affected by a frame transformation; and that may be the reason that the distinction is often blurred. However, in classical physics it was assumed that the speed of light is a constant that is independent of the motion of the source ("the speed of light is a constant c"). Maxwell assumed that the speed of light could only be exactly c relative to a light medium - just like the speed c of sound in air. Consequently, in classical optics it was though that the speed of light is a constant but not invariant.

Similarly, Einstein's second postulate of SR refers to a single inertial frame. The speed of light is assumed to be a constant c: the same in all directions, and independent of the motion of the source. That postulate seemed incompatible with the relativity principle according to which all physical constants should be invariant (the speed of sound is variant, so how can the speed of light be invariant?).

Is that clearer?

I only have the one understanding of RoS, where two events separated spatialy could be measured as occurring simultaniously depending on relative motion.

"depending on relative motion" sounds like it merely involves the standard synchronization procedure. That was already applied before SR, but it was thought (because of the above) that the laws of physics only worked in good approximation in moving frames.

 

[mangaroosh]

your language here is a little confused, so i am concerned that your thoughts are also a little confused. When we are talking about the different postulates and conclusions in relativity we are not talking about a "cause and effect" effect relationship, but rather a "logical implication" relationship.

A cause and effect relationship involves more than a logical implication relationship, specifically it also implies a temporal ordering where the cause preceeds the effect. There is no such temporal ordering between lc, td, ros, the principle of relativity (por) and the invariance of c (c), so you cannot speak of causes or effects amongst them.

This is one thing that I have trouble with, and it might be down to my lack of understanding of the nuances of the concepts; but my understanding is that that light is physical, and when the speed of light is measured a physical effect is being measured; I'm also of the understanding that LC & TD are physical effects. For that reason I don't understand how we can't speak in terms of cause and effect.

I have not trouble with the idea that the postulates of relativity allow us to reason what should be the case, if the postulates are assumed to be true; and what effects must occur, in order for the assumptions to hold true; but insofar as they relate to the physical world, then I think we have to be able to discuss cause and effect at some point; reasoning alone, as far as I am aware, doesn't cause physical effects (of the sort we are talking about).

So, what we have is properly "implies" and not "causes". The proper way to express this formally is:
$(\text{PoR} \cap \text{C})\leftrightarrow (\text{LC} \cap \text{TD} \cap \text{RoS})$

This whole conversation began when you correctly pointed out that $(\text{lc} \cap \text{td})\rightarrow \text{c}$ is false. I responded by correctly pointing out that $(\text{lc} \cap \text{td} \cap \text{ros})\rightarrow \text{c}$ is true and you had neglected ros which is an essential part of sr. You then followed up with the incorrect assertion that $(\text{lc} \cap \text{td})\rightarrow \text{ros}$ to which i gave a counter-exmaple. The rest of the conversation has basically been follow-up to that.

I hope this clarifies things.

Apologies, I'm not overly familiar with the formal notation, although I think I understand the above; I just can't write a full response using the correct operators.

It might be worth drawing the distinction, again, between an invariant measurement of c $\text{(mC)}$ and an invariant actual c $\text{(aC)}$; where
$\text{mC}$ does not necessarily imply $\text{aC}$ ; as per the example where two reference frames measure the speed of light to be c, but because the instruments used are of different lengths, the actual speed represented by the measurements is different.


You mentioned that I had neglected RoS, and so had drawn the wrong conclusion; however, RoS is a consequence of the actual speed of light (c) remaining invariant, not necessarily of an invariant measurement of ca 300/000 km/s.

$(\text{PoR} \cap \text{mC})$ does not necessarily imply $(\text{LC} \cap \text{TD} \cap \text{RoS})$

but
$(\text{PoR} \cap \text{mC})\leftrightarrow (\text{LC} \cap \text{TD})$


If we consider, that we can only ever, really, speak about the measurement of c, and not the actual speed", then:
$(\text{PoR} \cap \text{mC} \cap \text{RoS})\leftrightarrow (\text{aC})$


Which leaves us with the formulation:
$(\text{PoR} \cap \text{mC} \cap \text{RoS})\leftrightarrow (\text{LC} \cap \text{TD} \cap \text{RoS})$


which appears to be circular.

No, it is merely a counter example to your claim of post 121 that "lc & td must occur in order for c to be invariant" i.e. $\text{c}\rightarrow (\text{lc} \cap \text{td})$

OK; again, I'm not 100% sure of the relevance of an unrelated transformation. It might be best to just assume that the context is Einseinian relativity.

 

[Dale]

I'm also of the understanding that LC & TD are physical effects. For that reason I don't understand how we can't speak in terms of cause and effect.

Physicalness is neither a necessary nor sufficient condition for causality. Indeed, you can speak of psychological effects in terms of causality, e.g. his delusions of grandure caused his risk-taking behavior. But there must be a temporal ordering, the cause always comes chronologically before the effect. That is not the case here.

It might be worth drawing the distinction, again, between an invariant measurement of c $\text{(mC)}$ and an invariant actual c $\text{(aC)}$;

I don't think it is worth drawing the distinction; consider all of my previous statements to refer to measurements. Scientifically, all that matters is the measurements. If there is a hidden actuality that cannot be measured then it is irrelevant to physics.

OK; again, I'm not 100% sure of the relevance of an unrelated transformation. It might be best to just assume that the context is Einseinian relativity.

I am fine with that. Then the whole discussion goes away since in Einsteinian relativity there is C and PoR and LC and TD and RoS. We are left with only my original response that you had forgotten about RoS.

 

[harrylin]

[..] I'm also of the understanding that LC & TD are physical effects. [..]

I agree, insofar as those effects are independent of clock synchronization (in fact they are, but the description isn't!).

[..] RoS is a consequence of the actual speed of light (c) remaining invariant [..]

Perhaps you mean that no absolute simultaneity can be measured because of how the universe works, as expressed by the relativity principle. I agree with that.

Harald

 

[mangaroosh]

Physicalness is neither a necessary nor sufficient condition for causality. Indeed, you can speak of psychological effects in terms of causality, e.g. his delusions of grandure caused his risk-taking behavior. But there must be a temporal ordering, the cause always comes chronologically before the effect. That is not the case here.

But psychological effects have a physical manifestation.

As for the temporal separation, that would probably be a more philosophical discussion on the nature of "cause" and "effect".

I don't think it is worth drawing the distinction; consider all of my previous statements to refer to measurements. Scientifically, all that matters is the measurements. If there is a hidden actuality that cannot be measured then it is irrelevant to physics.

I think it is worth making the distinction, because, as mentioned above, an invariant measurement of c does not imply RoS; it is an invariant measurement of c plus RoS which results in RoS; with the latter being circular in nature.

I am fine with that. Then the whole discussion goes away since in Einsteinian relativity there is C and PoR and LC and TD and RoS. We are left with only my original response that you had forgotten about RoS.

I should, more precisely, have said, I don't see the relevance of using a transformation that is not the Lorentz transformation. As there are two interpretations of the Lorentz transformation, one which incorporates RoS and one which doesn't; with one of those being, arguably, circular in nature.

 

[mangaroosh]

I agree, insofar as those effects are independent of clock synchronization (in fact they are, but the description isn't!).

Apologies har, I don't fully understand the point being made.

Perhaps you mean that no absolute simultaneity can be measured because of how the universe works, as expressed by the relativity principle. I agree with that.

Harald

That's not really what I was trying to get at. As outlined above, an invariant measurement of c does not necessarily imply RoS; RoS is a consequence of the actual speed of light remaining unchanged. This requires us to assume RoS, which is the conclusion being drawn.

I think that saying that no absolute simultaneity can be measured is somewhat of a category mistake, because absolute simultaneity is not a physical object. However, a consequence of RoS, I believe, is that for each individual observer, their "past" state continues to exist in some reference frame, and their "future" state also "exists" in some reference frame; this requires each observer to make unverifiable assumptions about the existence of "past" and "future"; absolute simultaneity, however, doesn't require such assumptions, it simply requires us to accept the empirical evidence that an ever changing present moment is all that exists - this is because, I'm pretty sure, no observation of "past" or "future" can be made by an observer.

 

[harrylin]

Apologies har, I don't fully understand the point being made.

For example a change of clock rate in a train due to a change of velocity can be detected with clocks along the railway, but depending on clock synchronisation one can measure an increase or a decrease. Thus that the detection of the effect is independent of synchronisation, but not the description of the effect.

That's not really what I was trying to get at. As outlined above, an invariant measurement of c does not necessarily imply RoS; RoS is a consequence of the actual speed of light remaining unchanged. This requires us to assume RoS, which is the conclusion being drawn.

Sorry, I don't know what you mean with "the actual speed of light": what do you mean with "actual", and do you mean the 2-way speed of light?

I think that saying that no absolute simultaneity can be measured is somewhat of a category mistake, because absolute simultaneity is not a physical object.

Time is not a physical object, but it can be measured. Do you have a problem with that?

However, a consequence of RoS, I believe, is that for each individual observer, their "past" state continues to exist in some reference frame, and their "future" state also "exists" in some reference frame [..]

?? Not at all! As measured with every inertial reference system, everyone's present corresponds to a certain present event (x, t) in that system...
Perhaps you mean that an observer who is using a certain reference system can attribute certain distant events that he/she has not yet seen, to the past or future while using another reference system, the contrary would be attributed to those events.

 

[GeorgeDishman]

The best way to understand SR is geometrically. Take a sheet of paper and draw a simple spacetime diagram: put two dots on the sheet horizontally aligned to represent two events which are simultaneous in the frame of the drawing and spatially separated. Now get some transparent film, draw graph lines on it and place it over the paper so one grid line passes though the two events. Rotate the film a few degrees to represent a different frame and the events can no longer lie on the same gridline, they are not simultaneous in the new frame. What special relativity says is that there is no intrinsically preferred frame in reality, any choices of frame is equally valid.

Note that this is jut an analogy, to get an accurate picture you have to rotate the vertical and horizontal lines in opposite directions (e.g clockwise and anti-clockwise).

Length contraction and time dilation are just names for the effect of changing coordinate separations resulting from frame rotation.

 

[harrylin]

[..]
As there are two interpretations of the Lorentz transformation, one which incorporates RoS and one which doesn't. [..]

The Lorentz transformation incorporates RoS and no interpretation can alter that. Perhaps that's the cause of the confusion?