The Relativity of Simultaneity: A Fundamental Concept in Special Relativity

[mangaroosh]

I don't think that anything productive will come from a discussion of Lorentzian relativity. It is a defunct interpretation which asserts the reality of undetectable entities. All of the confusion with LET comes from the simple fact that the aether is undetectable, so in LET you continually have to make careful distinctions between measurements and what is happening in (undetectable) reality. It is a rabbit hole not worth going down.

DS, just wondering if you would agree with what George said was accurate, that Lorentzian relativity had been divested of all the trappings except for the absolute rest frame?

 

[mangaroosh]

It would probably be fair and correct to say that the mathematics going into and coming out of the Lorentz Transformation and their usage is very different comparing Einstein-Minkowski and Lorentz-Poincare relativity. While the Lorentz Transformation itself is obviously common. For the most part, Lorentz worked with vectors, differential equations and their initial and boundary conditions. Einstein and Minkowski built a platform where those things were abstracted away in which tensors and 4-vectors are preferred.

Thanks Phil.

The points being raised appear to pertain to the Lorentz transformation; does it make sense then to ask why the transformation under one interpretation has RoS while under the other interpretation has absolute simultaneity?

 

[mangaroosh]

Then, evidently, you did not understand it. As Dalespam suggests, you can simply re-post the reformulation of your question without including a link to a crank(?) site.

I could be completely wrong Harry, but based on your posts and the fact that you mentioned you prefer to base your understanding on Einstein's original German paper I would guess that either English or German is your native language - of course you could be form a bilungual family. But if one of them isn't your native language, then you presumably have experience in learning a foreign language. If so, I'm sure you will have noticed that there is usually a disconnect between how much a person can understand and how much they can express themselves, such that it is possible to understand something without necessarily being able to express it [adequately] in your own words. The inability to express it in your own words wouldn't necessarily mean that you haven't understood something that has been said.

The post has been re-posted without the link. As to whether or not the site is a "crank" site, I prefer to examine the content and judge it on that basis.

 

[Dale]

I'm not sure the specific example of the transform you gave fully addresses the question, because the question is more general. It might be the case that length contraction and time dilation do not lead every single event to be relatively simultaneous, but if time dilation and/or length contraction never occurred at all, anywhere, would RoS still prevail?

I specifically addressed that in the math above. In one transform I showed there can be no length contraction nor time dilation at all, anywhere, and there is still RoS.

The opposite claim is that the RoS is a consequence of length contraction and time dilation, and I disproved that claim also by providing a transform that had length contraction and time dilation, but no RoS.

Both claims have been disproven by counter-example. I don't know why you persist in them.

 

[Dale]

DS, just wondering if you would agree with what George said was accurate, that Lorentzian relativity had been divested of all the trappings except for the absolute rest frame?

He and I disagree about LET, but it is such a useless topic that I do not intend to dispute it, neither with him nor with you.

 

[mangaroosh]

I specifically addressed that in the math above. In one transform I showed there can be no length contraction nor time dilation at all, anywhere, and there is still RoS.

The opposite claim is that the RoS is a consequence of length contraction and time dilation, and I disproved that claim also by providing a transform that had length contraction and time dilation, but no RoS.

Both claims have been disproven by counter-example. I don't know why you persist in them.

I have a few questions relating to that, so if it is possible to proceed from here I might be able to get my head around it.

Were the transformations you gave for just one event EDIT: between two reference frames?

Would the same transformations be used in Lorentzian relativity and not include RoS in any of them?

In the example of the transform where there was no RoS, would we conclude that absolute simultaneity prevails, right across the universe, under the Einsteinian interpretation?

 

[Dale]

Were the transformations you gave for just one event?

They were for all events.

Would the same transformations be used in Lorentzian relativity and not include RoS in any of them?

Those transforms are not the Lorentz transform, so it is not used in LET.

In the example of the transform where there was no RoS, would we conclude that absolute simultaneity prevails, right across the universe, under the Einsteinian interpretation?

Again, those transforms are not the Lorentz transform, so it is not used by SR.

 

[mangaroosh]

They were for all events.

Those transforms are not the Lorentz transform, so it is not used in LET.

Again, those transforms are not the Lorentz transform, so it is not used by SR.

sorry, you've thrown me with the last 2 comments; I thought we were talking about Lorentz transformations under Einsteinian relativity.

EDIT: that might be where the confusion is arising from.

 

[James_Harford]

Apologies DS, ... I can understand how it might be frustrating to read the same point repeated, particularly when you are under the impression that you have already answered it, but, as mentioned, I had subsequent questions which were taken up by someone else; this lead me to repeat and/or reformulate the point for the purpose of that discussion.

Repeating a question that has already been answered to your satisfaction "for the purpose of that discussion" is puzzling, to put it mildly.

...the purpose of bringing up Lorentzian relativity here, was solely to juxtapose it with Einsteinian relativity for the purpose of clarification; namely that it appears that the same transformations can result in both absolute simultaneity and RoS. The question that is begged from that is, what is the difference between the two; why RoS under one interpretation, but absolute relativity in the other?.

In terms of predictive capability, there is no difference between the two. The only difference is of interpretation. Lorentz assumed, in accordance with the conventional belief of that time in the aether, that a preferred frame of reference existed. Einstein' noted that since no such frame was detactable, it is a superfluous assumption. That, in a capsule, is all you need to know about Lorentz Ether Theory (LET).

... but if time dilation and/or length contraction never occurred at all, anywhere, would RoS still prevail?

Yes. A simple example of your hypothetical question is a Euclidean space spacetime. It also has RoS, but unlike Minkowski spacetime of SR, moving objects undergo the opposite effects, i.e. time contraction and space dilation. So if you want to insist that such effects "explain" RoS, you must include these as well. Learning Euclidean spacetime is, relatively speaking (!), a snap, so you might want try out your questions on this spacetime first, perhaps with pencil and paper. Hint : the axis of every coordinate system in a Euclidean spacetime are at right angles. You will see exactly how RoS interacts with space dilation and time contraction, and having done this, you will have some idea of how to adapt what you have learned to actual relativistic, or Minkowski, spacetime.

It's not so much that I'm confused, rather I haven't made the logical connection yet as to how RoS is separate, stand-alone aspect of Einsteinian relativity and not just a consequence of Lorentzian contractions.

You don't know that it is a consequence, so why assume that it is? That no one can explain your belief should tell you that maybe this duck can't fly. Indeed, it cannot.

- Regards

 

[James_Harford]

Hi James, if possible I'd like to change the first question; I didn't formulate it in reply to yourself, but did in reply to Agerhall.

Then you should have done so.

Your explanation was based on the second postulate, the constancy of c in every reference frame, regardless of the motion relative to the source. The question that arises from that is, what phenomena have to occur to allow for this possibility? Ordinarily, with the addition of velocities we would expect the moving observer to measure a different speed of light; what phenomena occur that leads to him measuring the speed of light to be the same as the other observer?

The general phenomena that you are looking for is that every object defines a proper reference frame in which all of the laws of physics, including the speed of light, are the same as that of a stationary observer. These frames are related by the Lorentz transformations derived from Einstein's postulates. All relativistic effects can be obtained from these transformations. Therefore learn about these transformations and their derivation.

 

[mangaroosh]

Repeating a question that has already been answered to your satisfaction "for the purpose of that discussion" is puzzling, to put it mildly.

The issue is that it hadn't been answered to my satisfaction, in the sense that I didn't fully understand it; hence I repeated the question and/or reformulated it in discussion with someone else, to see if they could highlight where my misunderstanding lay.

Addressing subsequent questions by referring back to the original answer which lead to those subsequent questions doesn't address those subsequent questions - yes that sounds complicated, but that is precisely what appears to me to be happening.

In terms of predictive capability, there is no difference between the two. The only difference is of interpretation. Lorentz assumed, in accordance with the conventional belief of that time in the aether, that a preferred frame of reference existed. Einstein' noted that since no such frame was detactable, it is a superfluous assumption. That, in a capsule, is all you need to know about Lorentz Either Theory (LET).

According to George and wikipedia

the last vestiges of a substantial ether had been eliminated from Lorentz's "ether" theory, and it became both empirically and deductively equivalent to special relativity. The only difference was the metaphysical[C 7] postulate of a unique absolute rest frame, which was empirically undetectable and played no role in the physical predictions of the theory

current status

It is probably even possible to get rid of the notion of an absolute rest frame also, which appears to be an oft cited reason why Einsteinian relativity is preferred.

Yes. A simple example of your hypothetical question is a Euclidean space spacetime. It also has RoS, but unlike Minkowski spacetime of SR, moving objects undergo the opposite effects, i.e. time contraction and space dilation. So if you want to insist that such effects "explain" RoS, you must include these as well. Learning Euclidean spacetime is, relatively speaking (!), a snap, so you might want try out your questions on this spacetime first, perhaps with pencil and paper. Hint : the axis of every coordinate system in a Euclidean spacetime are at right angles. You will see exactly how RoS interacts with space dilation and time contraction, and having done this, you will have some idea of how to adapt what you have learned to actual relativistic, or Minkowski, spacetime.

I'm not sure I understand the point re: Euclidean spacetime; it appears to suggest that RoS prevails because effects very similar to time dilation and length contraction occur. I have difficulty seeing how that demonstrates that RoS under Einsteinian relativity is not a consequence of Lorentz contractions.


Quite a few explanations have been provided thus far as to how RoS prevails without length contraction and time dilation, but I'm not sure of the relevance to the question being asked. I thought I was discussing Lorentzian transformations according to Einsteinian relativity, but the answers being provided appear to relate to anything but that. Unfortunately I don't immediately see the relevance of such answers to the question in hand, so that may be part of the reason for the general frustration and annoyance in this thread; people are answering a question in a manner they believe addresses the question, but I am having trouble seeing how it does.


If we stick with Einsteinian relativity, however, would RoS still prevail if time dilation and length contraction didn't manifest anywhere?

You don't know that it is a consequence, so why assume that it is? That no one can explain your belief should tell you that maybe this duck can't fly. Indeed, it cannot.

The impression I got was that it was a consequence and thus far I haven't encountered an explanation which clarifies why that impression is inaccurate.


For example, if we take your explanation involving the pulse operator and the moving observer, your explanation was based on the constancy of c, but, to my understanding, in order for the speed of light to be c in all reference frames regardless of the motion relative to the source, then length contraction and/or time dilation have to occur; which again would suggest that RoS, under Einsteinian relativity is a consequence of contractions.

 

[mangaroosh]

Then you should have done so.

The general phenomena that you are looking for is that every object defines a proper reference frame in which all of the laws of physics, including the speed of light, are the same as that of a stationary observer. These frames are related by the Lorentz transformations derived from Einstein's postulates. All relativistic effects can be obtained from these transformations. Therefore learn about these transformations and their derivation.

I'll try a more direct question: if length contraction and/or time dilation did not occur, would an observer moving relative to another observer, and a light source, measure the same speed of light as the other observer?

 

[mangaroosh]

They were for all events.

Those transforms are not the Lorentz transform, so it is not used in LET.

Again, those transforms are not the Lorentz transform, so it is not used by SR.

hey DS, I'm just wondering if you could explain how this pertains to the question about RoS under Einsteinian relativity, because I can't make the connection.

 

[James_Harford]

I'll try a more direct question: if length contraction and/or time dilation did not occur, would an observer moving relative to another observer, and a light source, measure the same speed of light as the other observer?

Length contraction, time dilation, and RoS are all consequences of the Lorentz transformations, which in turn are derived from Einstein's postulates, which includes the constancy of the speed of light. Therefore, if any of these effects did not occur, Einstein's postulates would be violated.

Time dilation and Lorentz contraction lack the completeness of Einstein's postulates. They cannot be used as postulates to derive the RoS, constant speed of light, etc.

-Regards

 

[harrylin]

[..]

again, YES! Let's get the proper theory explained, then it
will become clear why older theories were inadequate. [..]

The older theory that you seem to refer to is Lorentz theory of electrons; and this is rather well explained in Einstein's 1907 paper which is discussed in a parallel thread. And there is already a parallel thread about other theories. So yes, please let's not mix those topics!

 

[mangaroosh]

Length contraction, time dilation, and RoS are all consequences of the Lorentz transformations, which in turn are derived from Einstein's postulates, which includes the constancy of the speed of light. Therefore, if any of these effects did not occur, Einstein's postulates would be violated.

Time dilation and Lorentz contraction lack the completeness of Einstein's postulates. They cannot be used as postulates to derive the RoS, constant speed of light, etc.

-Regards

Thanks James, this is somewhat clearer. There are still a few questions arising for me though, one which I have repeated but haven't really had a discernable answer to yet.


You say that Length contraction, time dilation and RoS are all consequences of the Lorentz transformations; but Lorentzian relativity uses the same transformations doesn't it? If so, then RoS is not necessarily a consequence of the Lorentz transformations, because RoS is not a part of Lorentzian relativity, which includes length contraction and clock retardation, due to mechanical effects; clock retardation appears to be almost the exact same thing as time dilation except for a different metaphysical explanation.


The differences appear to be:
- time dilation in Einseinian relativity; but mechanical retardation of a clock in Lorentzian
- RoS in Einsteinian relativity; absolute relativity in Lorentzian.


There appears to be some correlation between time dilation and RoS, is that a fair assessment?

 

[harrylin]

Does this not just verify the point of the OP that RoS is just a consequence of Lorentz contractions, and isn't necessarily a separate, third aspect of Einsteinian relativity?

No - and that answer is already contained in my posts #31 and #34.

 

[James_Harford]

The impression I got was that it was a consequence and thus far I haven't encountered an explanation which clarifies why that impression is inaccurate.

Consequence means "derivable from". RoS is not derivable from the "lorentz contraction" and/or "time dilation", without also assuming the constancy of the speed of light.

For example, if we take your explanation involving the pulse operator and the moving observer, your explanation was based on the constancy of c, but, to my understanding, in order for the speed of light to be c in all reference frames regardless of the motion relative to the source, then length contraction and/or time dilation have to occur; which again would suggest that RoS, under Einsteinian relativity is a consequence of contractions.

Correlation means little. By this one can equally argue that contractions are a consequence of RoS.

 

[mangaroosh]

No - and that answer is already contained in my posts #31 and #34.

I referenced post #31 in #48.

 

[mangaroosh]

Consequence means "derivable from". RoS is not derivable from the "lorentz contraction" and/or "time dilation", without also assuming the constancy of the speed of light.

Is it possible to assume the constancy of the speed of light without assuming "lorentz contraction" and/or "time dilation"?

Correlation means little. By this one can equally argue that contractions are a consequence of RoS.

I would say not, if the simultaneity of an event is contingent on the time co-ordinate provided by a clock.

 

[James_Harford]

You say that Length contraction, time dilation and RoS are all consequences of the Lorentz transformations; but Lorentzian relativity uses the same transformations doesn't it? If so, then RoS is not necessarily a consequence of the Lorentz transformations, because RoS is not a part of Lorentzian relativity, ...

Stop right there! RoS is most assuredly an effect of Lorentzian relativity. The predictions of the two theories are exactly the same. In either theory two observers can disagree on the order of two distant events. LET claims that one observer is wrong and the other right, but doesn't know which. LET claims that one definition of now is the "right one" but doesn't know which. In other words, the differences between the two theories are non-physical, or metaphysical. LET is SR with metaphysical baggage.

- Regards

 

[harrylin]

Hi James, if possible I'd like to change the first question; I didn't formulate it in reply to yourself, but did in reply to Agerhall.

Your explanation was based on the second postulate, the constancy of c in every reference frame, regardless of the motion relative to the source. The question that arises from that is, what phenomena have to occur to allow for this possibility? Ordinarily, with the addition of velocities we would expect the moving observer to measure a different speed of light; what phenomena occur that leads to him measuring the speed of light to be the same as the other observer?

The combination with the first postulate leads to the conclusion that the operationally defined speed of light must be the same constant in every inertial reference system (did you carefully read Einstein's description?). And most textbooks as well as some already given replies here provide the answer to your question. I'm afraid that you think that a theory can be learned from merely having discussions on a discussion forum; however, that's just a waste of time of the people here. It's even not an efficient use of your own time.

 

[James_Harford]

Is it possible to assume the constancy of the speed of light without assuming "lorentz contraction" and/or "time dilation"?

Of course it is. And from that follows,

1. the lorentz contraction
2. time dilation
3. and RoS (as shown in post 42) .

I would say not, if the simultaneity of an event is contingent on the time co-ordinate provided by a clock.

Simultaneity requires no clock!
Again, see post 42.

 

[harrylin]

Hi Harry, the conversation with DaleSpam is in reference to mathematical transformations, while your reply in post #28 was with respect to clocks; unfortunately I don't have the nous to make the connection between the two, [...]

I find that an astonishing comment; for it means that you did not understand (if you indeed read) the introduction in Einstein's 1905 paper to which I referred earlier.

I had a quick glance at the reference in post #31, but statement immediately following the link was something you had mentioned before, with respect to detecting absolute simultaneity (or the time on a distant clock) and which I had addressed in #18;
[..]
so that affected my judgement of the necessity to go through it in detail. Is there a specific part that I can jump to that would address the issue?

It addresses how and why "local" simultaneity first emerged, independent of the concept of time dilation (of which the possibility also is suggested); and I already pointed to it. I would have to look up another paper to direct you to how this next lead to the concept of "relative" simultaneity. However only reading one part is not the correct way to surely understand a discourse - and jumping around between text fragments and parts of explanations of people here isn't a good way to learn a topic. The proper way would be to first study a textbook, do some exercises, and check out the explanations in some of the original papers.

Post #20:

The issue being raised appears to be the idea of detecting absolute simultaneity; but that isn't necessarily an issue that needs to be addressed. We don't need to figure out how to synchronise clocks to say that if all clocks remained synchronised then there would be absolute simultaneity; it's somewhat of a tautology. [...]

Only if with you mean "absolute simultaneity" in an operational sense without the implication of "true" simultaneity. I would call that "universal simultaneity", and it's what one effectively does in descriptions of the universe as a whole.
ADDENDUM: Perhaps you meant with " remained", the method of slow clock transport. Then my last remark doesn't apply. Instead, the clarifications of PAllen apply: slow clock transport is a way to naturally approximate the same outcome as is achieved with the Poincare-Einstein synchronization. And it illustrates in which way time dilation and relativity of simultaneity are not fully independent in SR. However, this will hardly be possible to understand without first learning SR; and we can't do that for you.

 

[mangaroosh]

Einstein's 1905 paper

I find that an astonishing comment; for it means that you did not understand (if you indeed read) the introduction in Einstein's 1905 paper to which I referred earlier.

It addresses how and why "local" simultaneity first emerged, independent of the concept of time dilation (of which the possibility also is suggested); and I already pointed to it. I would have to look up another paper to direct you to how this next lead to the concept of "relative" simultaneity. However only reading one part is not the correct way to surely understand a discourse - and jumping around between text fragments and parts of explanations of people here isn't a good way to learn a topic. The proper way would be to first study a textbook, do some exercises, and check out the explanations in some of the original papers.

Only if with you mean "absolute simultaneity" in an operational sense without the implication of "true" simultaneity. I would call that "universal simultaneity", and it's what one effectively does in descriptions of the universe as a whole.
ADDENDUM: Perhaps you meant with " remained", the method of slow clock transport. Then my last remark doesn't apply. Instead, the clarifications of PAllen apply: slow clock transport is a way to naturally approximate the same outcome as is achieved with the Poincare-Einstein synchronization. And it illustrates in which way time dilation and relativity of simultaneity are not fully independent in SR. However, this will hardly be possible to understand without first learning SR; and we can't do that for you.

I am acutely aware that I might be exhausting peoples' patience here, but I am genuinely trying to understand this. I appreciate your advice that consulting a textbook would be a good place to start, and if you could recommend a worhtwhile one, I would eagerly consult it. I do however believe that people on here, and indeed elsewhere, give a relatively relaible representation of the concepts and phenomena contained in many textbooks, because from discussions I've had with people, the information they've presented has been almost entirely representative of the textbook-like resources that I have encountered - through their references. The added benefit of discussing it in a forum is that it offers the chance to question what is meant by certain terminology, something that isn't possible with a textbook.

I appreciate people taking the time to post detailed replies, but because of my lack of a scientific or mathematic background, I am not always able to make the logical connections between points that some people might think is obvious - for example, DaleSpams non-Lorentzian transformation example, which didn't pertain to Einsteinian relativity, when I was working on the assumption that it was Lorentzian transformations, under Einsteinian relativity, that we were talking about. Unfortunately, in such instances, unless it is spelled out for me, I can't see the logical connection between the two.


the 1905 Paper
I did indeed read, and understand, the introduction to the paper you posted; but I'm still unsure as to how DaleSpams example relates to it; it is more the maths used by Dalespam that I don't understand than the introduction to the paper, I would say.

If it would be possible to proceed slowly on the basis of Einstein's definition of simultaneity in that paper, I can give my understanding and if everyone hasn't put me on ignore by then, maybe, just maybe, someone can point out where it is I'm going wrong.

 

[mangaroosh]

Of course it is. And from that follows,

1. the lorentz contraction
2. time dilation
3. and RoS (as shown in post 42) .

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.

Simultaneity requires no clock!
Again, see post 42.

Is it not required for assigning the time co-ordinate of an event?

 

[mangaroosh]

Stop right there! RoS is most assuredly an effect of Lorentzian relativity. The predictions of the two theories are exactly the same. In either theory two observers can disagree on the order of two distant events. LET claims that one observer is wrong and the other right, but doesn't know which. LET claims that one definition of now is the "right one" but doesn't know which. In other words, the differences between the two theories are non-physical, or metaphysical. LET is SR with metaphysical baggage.

- Regards

Neo-Lorentzian theory appears to have been divested of a lot of that metaphysical baggage, as George mentioned and as the person who posted the widipedia enty also maintains (assuming they're not one and the same person):

the last vestiges of a substantial ether had been eliminated from Lorentz's "ether" theory, and it became both empirically and deductively equivalent to special relativity. The only difference was the metaphysical[C 7] postulate of a unique absolute rest frame, which was empirically undetectable and played no role in the physical predictions of the theory. As a result, the term "Lorentz ether theory" is sometimes used today to refer to a neo-Lorentzian interpretation of special relativity

The remaining metaphysical baggage appears to be the "postulate of a unique absolute rest frame", which could probably be done away with, without the assumption that reference frames are at rest in the ether, as George has suggested Einsteinian relativity has.

 

[Dale]

sorry, you've thrown me with the last 2 comments; I thought we were talking about Lorentz transformations under Einsteinian relativity.

EDIT: that might be where the confusion is arising from.

hey DS, I'm just wondering if you could explain how this pertains to the question about RoS under Einsteinian relativity, because I can't make the connection.

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?

 

[harrylin]

[..] the 1905 Paper
I did indeed read, and understand, the introduction to the paper you posted; but I'm still unsure as to how DaleSpams example relates to it; it is more the maths used by Dalespam that I don't understand than the introduction to the paper, I would say.

If it would be possible to proceed slowly on the basis of Einstein's definition of simultaneity in that paper, I can give my understanding and if everyone hasn't put me on ignore by then, maybe, just maybe, someone can point out where it is I'm going wrong.

Yes it may be better if you restart on that basis!

 

[Agerhell]

Thanks James, this is somewhat clearer. There are still a few questions arising for me though, one which I have repeated but haven't really had a discernable answer to yet.


You say that Length contraction, time dilation and RoS are all consequences of the Lorentz transformations; but Lorentzian relativity uses the same transformations doesn't it? If so, then RoS is not necessarily a consequence of the Lorentz transformations, because RoS is not a part of Lorentzian relativity, which includes length contraction and clock retardation, due to mechanical effects; clock retardation appears to be almost the exact same thing as time dilation except for a different metaphysical explanation.


The differences appear to be:
- time dilation in Einseinian relativity; but mechanical retardation of a clock in Lorentzian
- RoS in Einsteinian relativity; absolute relativity in Lorentzian.


There appears to be some correlation between time dilation and RoS, is that a fair assessment?

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.