The Relativity of Simultaneity: A Fundamental Concept in Special Relativity

[harrylin]

Special Relativity basically says:

1. There is no way to measure the one-way speed of light, one can only measure the two way speed of light.
2. The two way speed of light is the same for all inertial observers.

Length contraction and time dilation is then used to explain how the two way speed of light is the same for all observers.

That is all there is to it.[...]

That's almost all there is to it. However some people here find it important to state "the obvious" and it does relate to the topic of this thread: the one-way speeds in an inertial reference system can be made equal to the two-way speeds by means of appropriate clock synchronization (and next one can "measure" that they are indeed equal. ). That can be easily understood as a mathematical theorem about averages.

 

[James_Harford]

The connection is that, by considering LC and TD but neglecting RoS, you are unwittingly using one of these alternate transforms, instead of the Lorentz transforms. Thus you are reaching incorrect conclusions.

Is that clear?

Well stated.

 

[mangaroosh]

You have repeatedly made the mistaken assertion that RoS is not a separate feature of the Lorentz transform, but rather is somehow automatically implied by LC and TD. You have even made incorrect conclusions based on that assumption by considering LC and TD and assuming that RoS was included and your conclusions were identical to what the Lorentz transforms would predict.

IF your assertion were correct, then all transforms which included LC and TD would automatically also include RoS and would therefore be equivalent to the Lorentz transform. I have provided counter examples which demonstrate that there are transforms (which are not the Lorentz transform) which have TD and LC but not RoS and vice versa.

The connection is that, by considering LC and TD but neglecting RoS, you are unwittingly using one of these alternate transforms, instead of the Lorentz transforms. Thus you are reaching incorrect conclusions.

Is that clear?

Ah, sorry, I understand your rationale now, but I still don't understand the maths.

the part I don't understand is the initial equations; I read t'=t-vx as meaning t' equals t minus the velocity along the X-axis, but I don't understand why the velocity comes into it.

and x'=x-vt I read as x' equals x minus the velocity multiplied by the time - which makes a bit more sense to me [without understanding how it demonstrates length contraction]

While I don't doubt that your examples demonstrate transformations which include LC and TD but not RoS, and RoS but not LC and TD I can't discern how they do so. I also have difficulty relating them to the physical phenomena which they represent. That is why I find it easier to discuss the physical phenomena affecting clocks than the maths.

You mentioned that the example of the transform you gave wasn't a useful one in physics, but was useful for demonstrating that RoS wasn't a consequence of LC and TD; I'm just wondering if the examples you gave correspond to physical phenomena, that might help with understanding them?

Just on the point "by considering LC and TD but neglecting RoS, you are unwittingly using one of these alternate transforms, instead of the Lorentz transforms". Are the transforms you used based on the assumption of the constancy of c, as with Einsteinian relativity?

 

[mangaroosh]

Special Relativity basically says:

1. There is no way to measure the one-way speed of light, one can only measure the two way speed of light.
2. The two way speed of light is the same for all inertial observers.

Length contraction and time dilation is then used to explain how the two way speed of light is the same for all observers.

That is all there is to it.

Yes in LET you assume a universal preferred frame and there is no "relativity of simultaneity".
"Relavity of simultaneity" occurs when you decide that all inertial observers should get the same result when they measure the speed of light.

It has nothing to do with time dilation per se.

Yes LET uses the same formulas for time dilation and length contraction but it does not state that the speed of light is the same in all inertial systems and thus has no need for relativity of simultaneity.

Thanks Ager.

My understanding of that explanation would be:

RoS is a consequence of the assumption that the speed of light is the same for all inertial observers.

The assumption about the constancy of c requires Length contraction and/or time dilation to explain it, therefore RoS is a consequence of length contraction and/or time dilation.

If Length contraction or time dilation didn't occur, then the speed of light would not be c for all observers and there would be no RoS.

i must stress, that's just according to that explanation.

EDIT: to summarise, it appears as though length contraction and time dilation are a necessary intermediate step before we can arrive at the conclusion the RoS is a consequence of the constancy of c.

 

[mangaroosh]

That's almost all there is to it. However some people here find it important to state "the obvious" and it does relate to the topic of this thread: the one-way speeds in an inertial reference system can be made equal to the two-way speeds by means of appropriate clock synchronization (and next one can "measure" that they are indeed equal. ). That can be easily understood as a mathematical theorem about averages.

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

 

[kmarinas86]

What on Earth is a two-way speed of light?

Speed is the magnitude of velocity. Speed is the velocity SANS the directional component.

Edit: HMMM. WEIRD:

http://en.wikipedia.org/wiki/One-way_speed_of_light

One-way vs. two-way speed of light
[edit] The two-way speed

The two-way speed of light is the average speed of light from one point, such as a source, to a mirror and back again. Because the light starts and finishes in the same place only one clock is needed to measure the total time, thus this speed can be experimentally determined independently of any clock synchronization scheme. Any measurement in which the light follows a closed path is considered a two-way speed measurement.

Experiments have shown within tight limits that in an inertial frame the two-way speed of light is independent of the closed path considered.

Since 1983 the meter has been defined as the distance traveled by light in vacuum in 1⁄299,792,458 second.[11] This means that the speed of light can no longer be experimentally measured in SI units, but the length of a meter can be compared experimentally against some other standard of length.
[edit] The one-way speed

Although the average speed over a two-way path can be measured, the one-way speed in one direction or the other is undefined (and not simply unknown), unless one can define what is "the same time" in two different locations. To measure the time that the light has taken to travel from one place to another it is necessary to know the start and finish times as measured on the same time scale. This requires either two synchronized clocks, one at the start and one at the finish, or some means of sending a signal instantaneously from the start to the finish. No instantaneous means of transmitting information is known. Thus the measured value of the average one-way speed is dependent on the method used to synchronize the start and finish clocks. This is a matter of convention.

The Lorentz transformation is defined such that the one-way speed of light will be measured to be independent of the inertial frame chosen.[12]

wow... -They- really don't want to show this stuff very often, do -they-?

 

[mangaroosh]

What on Earth is a two-way speed of light?

Speed is the magnitude of velocity. Speed is the velocity SANS the directional component.

I think it refers to the round-trip speed of light.

 

[Dale]

I also have difficulty relating them to the physical phenomena which they represent. That is why I find it easier to discuss the physical phenomena affecting clocks than the maths.

You mentioned that the example of the transform you gave wasn't a useful one in physics, but was useful for demonstrating that RoS wasn't a consequence of LC and TD; I'm just wondering if the examples you gave correspond to physical phenomena, that might help with understanding them?

They do not correspond to physical phenomena, that is precisely why they are not useful and why your unwittingly using them is such a problem.

 

[kmarinas86]

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

No. The following is why:

http://en.wikipedia.org/wiki/One-way_speed_of_light

The "one-way" speed of light from a source to a detector, cannot be measured independently of a convention as to how to synchronize the clocks at the source and the detector. What can however be experimentally measured is the round-trip speed (or "two-way" speed of light) from the source to the detector and back again. Albert Einstein chose a synchronization convention (see Einstein synchronization) that made the one-way speed equal to the two-way speed. The constancy of the one-way speed in any given inertial frame, is the basis of his special theory of relativity although all experimentally verifiable predictions of this theory do not depend on that convention.[1][2][3][4][5][6][7][8]

Experiments that attempted to probe the one-way speed of light have been proposed, but none has succeeded in doing so.[9] It was later shown that these experiments are in fact measuring the two-way speed.[1][10]

The 'speed of light' in this article refers to the speed of all electromagnetic radiation in vacuum.

Other clock synchronization conventions need not hold this assumption.

References [1] through [8]:

^ a b Yuan-Zhong Zhang (1997). Special Relativity and Its Experimental Foundations. World Scientific. ISBN 9789810227494.
^ Anderson, R.; Vetharaniam, I.; Stedman, G. E. (1998), "Conventionality of synchronisation, gauge dependence and test theories of relativity", Physics Reports 295 (3-4): 93–180, Bibcode 1998PhR...295...93A, doi:10.1016/S0370-1573(97)00051-3
^ Conventionality of Simultaneity entry by Allen Janis in the Stanford Encyclopedia of Philosophy, 2010
^ Mathpages: Conventional Wisdom and Round Trips and One-Way Speeds
^ a b Edwards, W. F. (1963). "Special Relativity in Anisotropic Space". American Journal of Physics 31 (7): 482–489. Bibcode 1963AmJPh..31..482E. doi:10.1119/1.1969607.
^ Winnie, J. A. A. (1970). "Special Relativity without One Way Velocity Assumptions". Philosophy of Science 37: 81–99, 223–38. JSTOR 186029.
^ Rizzi, Guido; Ruggiero, Matteo Luca; Serafini, Alessio (2004). "Synchronization Gauges and the Principles of Special Relativity". Foundations of Physics 34 (12): 1835–1887. arXiv:gr-qc/0409105. Bibcode 2004FoPh...34.1835R. doi:10.1007/s10701-004-1624-3.
^ Sonego, Sebastiano; Pin, Massimo (2008). "Foundations of anisotropic relativistic mechanics". Journal of Mathematical Physics 50 (4): 042902-042902-28. arXiv:0812.1294. Bibcode 2009JMP...50d2902S. doi:10.1063/1.3104065.

 

[mangaroosh]

They do not correspond to physical phenomena, that is precisely why they are not useful and why your unwittingly using them is such a problem.

I'm not sure that I am unwittingly using them; maybe my reply to Agerhell can clarify what I was trying to get at

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.

 

[James_Harford]

Of course, that should have been obvious. I can see how 1 & 2 follow, but I can't yet see how 3 is separate from 1 & 2.

Since, 3, Relativity of Simultaneity [RoS] can be demonstrated simply and directly without requiring the introduction of Lorentz contractions, time dilations, measuring rods, or clocks, it is explained most simply without them.

Is [RoS] not required for assigning the time co-ordinate of an event?

Yes. But simultaneity is not, as you said, "contingent on the time coordinate of a clock", as I showed in the earlier post.

- Regards.

 

[mangaroosh]

Since, 3, Relativity of Simultaneity [RoS] can be demonstrated simply and directly without requiring the introduction of Lorentz contractions, time dilations, measuring rods, or clocks, it is explained most simply without them.

Is that in relation to hypothetical maths that don't correspond to real world phenomena though?

Rather than repeating the point, I'm just wondering if the clarification of my point in post #100 makes any more sense?

Yes. But simultaneity is not, as you said, "contingent on the time coordinate of a clock", as I showed in the earlier post.

I could be wrong, but that sounds a bit like a category mistake.

Is RoS not the term applied when the time co-ordinates of an event are different across reference frames; and are those time co-ordinates not supplied by local clocks? My understanding is that if the time co-ordinate of an event, as supplied by a local clock, is different than the time co-ordinate for the same event, supplied by a remote clock, then the events are not absolutely simultaneous, but relatively simultaneous.

To refer back to an earlier comment, that "simultaneity requires no clock", that is of course true, but given that there are clocks, and if we assume that they measure time, then if absolute simultaneity prevailed, all "reliable" clocks should measure the same time - is that accurate enough? I think that is roughly what the introduction to [the English translation of] Einstein's 1905 paper said, or at least I think it can be deduced from it.

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


As mentioned, hopefully the clarification of the point pertaining to the constancy of the speed of light is clearer in post #100.

 

[James_Harford]

Is that in relation to hypothetical maths that don't correspond to real world phenomena though?

No, because the demonstration that RoS is relative uses no "hypothetical math". Just Einstein's postulate. You can answer this question and the others in your post yourself. Again, no clock is required. You don't seem to believe me. Go back, look at the post and see for yourself.

It's a really simple demonstration: post #42 (42 = The Answer to Life, the Universe, and Everything).

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

Einstein's postulate. All else follows. You are unlikely to find a simpler answer anywhere. :-)

- Regards.

 

[mangaroosh]

No, because the demonstration that RoS is relative uses no "hypothetical math". Just Einstein's postulate. You can answer this question and the others in your post yourself. Again, no clock is required. You don't seem to believe me. Go back, look at the post and see for yourself.

It's a really simple demonstration: post #42 (42 = The Answer to Life, the Universe, and Everything).

Einstein's postulate. You are unlikely to find a simpler answer anywhere. :-)

Thanks James, I've read post #42 and others have also raised the issue of the second postulate, of the constancy of the speed of light, most recently Agerhell. Indeed, Ager's formulation was quite simple and straight forward, and so the point is probably most easily addressed from that formalism.

The contention appears to be that RoS is a consequence of the constancy of the speed of light. The issue, as I see it is, that the speed of light doesn't cause length contraction and/or time dilation; rather, the observation of the speed of light to be constant, by all observers, is a consequence of length contraction and/or time dilation; that is, if length contraction and/or time dilation did not occur, then observers would not measure the speed of light to be the constant c; and so RoS is a consequence of length contraction and/or time dilation. That is solely based on the explanation using the constancy of the speed of light.

Saying that RoS is a separate and distinct aspect of Einsteinian relativity appears to be a category mistake.That would be my understanding anyway, am I going wrong somewhere there?DaleSpams examples didn't, I don't think, refer to real world phenomena, so I'm not immediately able to see their relevance.

 

[harrylin]

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

 

[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.