the Atemporal Universe - Resolving the Problem of Time

Fourier wrote: »

Why is the observer you're denoting as stationary here correct? You're basically already assuming the existence of a preferred frame whose conclusions are the "correct" ones, then obviously an absolute time emerges and is identified with how they measure time.

Einstein's point was that there is no reason to prefer the point of view of a given observer (what physically measurable property singles out their frame?), thus the different notions of simultaneity are equally valid.

There might be some confusion here. The thought experiment, as laid out, is simply Einstein's thought experiment on clock synchronisation. In his 1905 paper he designates one frame as the "stationary system", so as to distinguish it from the relatively moving system. That convention is simply followed here. Basically, both observers label their own reference frames as "stationary".

Relativity of Simultaneity is the idea that events which are simultaneous in one frame are not simultaneous in a relatively moving reference frame. The point being made is that the simutaneity of events in the first frame is presupposed. In actual fact, there is no way of determining if events are actually simultaneous, in any frame. This can be seen as an extension of the Galilean Principle of Relativity i.e. there are no experiments which can determine simultaneity/synchronisation.

To see this, we just need to consider the thought experiment. Let's say we have (good ol') Alice and Bob - Alice on the Platform, Bob on the train. Both are wearing bodycams.

Alice sets up her synchronisation procedure, clocks are equidistant from the emitter, mirrors to reflect the light pulses back to her at the midpoint.
She sees that Bob has the exact same set-up: clocks are equidistant and mirrors to reflect the light pulses back to Bob at the midpoint.

Alice sends the light pulses and sees Bob do the same.
Alice sees the clock at the rear of the train move towards the light pulse while the clock at the front moves away. She oberves that Bob's clocks fail to synchronise.

The light pulses reflect from each clock and return to Alice simultaneously. She assumes her clocks are synchronised.
However, she also sees the light pulses return to Bob simultaneously, despite his clocks failinng to synchronise. Bob also assumes that his clocks are synchronised.

Alice, being capable of self-reflection, wonders if it is possible that the same thing has happened in her synchronisation procedure. What if one of her clocks was moving toward the light pulse while the other was moving away, with the opposite happening on the return leg to the midpoint, exactly canceling out and ensuring the light pulses return simultaneously?

She recalls the Galilean Principle of Relativity and realises she has no way of determining this.

Then, she receives a video file from Bob, it's his bodycam footage. The bodycam footage shows that her clocks failed to synchronise.

So, she is left with her assumpion that the clocks synchronised versus the obervational evidence to the contrary.

Indeed, the Einseinian interpretation requires that a single observer must stick dogmatically to their assumption about the simultaneity/synchronisation in their own "stationary system" while an infinite number of relatively moving observers provide observational evidence to the contrary.

Sounds more like religion than science.


One might try to point to the 2nd postulate, the constancy of the speed of light, but this too can be interpreted more parsimoniously - as outlined above.


Without this assumption of simultaneity in a particular frame, the conclusion of reativity of simultaneity cannot be reached - bcos the circle is broken. This leaves us with absolute simultaneity and absolute time.

Absolute time is effectively indistinguishable from a timeless universe. As per Lee Smolin, "were it not for the external clock, one could already say that time has disappeared" (https://www.edge.org/conversation/lee_smolin-stuart_a_kauffman-a-possible-solution-for-the-problem-of-time-in-quantum).

If there is no time, then there is no background dependence in QM, which is [apparently] one of the major issues with marrying QM and GR in a theory of Quantum Gravity

Fourier wrote: »

I know Relativity and Einstein's original argument and who the stationary observer refers to. However for all experimental purposes Alice has no reason to distrust her notion of simultaneity. It fulfills all necessary conditions of a definition of time for her, so she is free to use it. What seeing Bob's video shows her is that simultaneous for her is not simultaneous for Bob.

Your argument just shows that there is no "true" simultaneity, as everybody's attempt at defining it will not be so in another frame. Thus Alice's time is simply a coordinate definition, not an objective demarcation of time. So it is for all observers. This is all compatible with Relativity.

Alice assumes that her clocks are synchronised. She cannot determine the validity of this. Bob sends her observational evidence to the contrary. This challenges the validity of Alice's assumption.

Only if Alice sticks to her assumption - of the simultaneity of clock synchronising events - inspite of the contradictory obserational evidence, will she conclude that what is "simultaneous for her is not simultaneous for Bob". But that is simply assuming the conclusion.

Alternatively, Alice could look at the observational evidence - Bob's bodycam footage - and conclude that she was mistaken in her assumption. Of course, Bob would do the same.

That is an alternative interpretation that frees each observer from clinging dogmatically to an assumption, in the face of observational evidence to the contrary [from an infinite number of relatively moving observers]. It doesn't change the mathematics - so makes the same predictions - it's more intuitive, it doesn't rely on circular reasoning, and it isn't based on a principle that assumptions rank above observation, or at least, that both are on an equal footing.

It is also an interpretation whiich aligns the concepts of time in both GR and QM, one of the issues in developing a theory of Quantum Gravity.

Fourier wrote: »

The issue with the concept of time in QM has nothing to do with this issue. The issue of time in QM is that QM is a "single user" theory, i.e. about managing expectations for observational outcomes for a single observer and thus its time is the time of the observer in that application of the theory. This is present even if QM is formulated in a Galilean background.

You may, of course, be correct however, the opposing viewpoint can also be found in the literature on the subjecct:
The Problem of Time is, in greater generality, a consequence of the mismatch between Background Dependent and Background Independent Paradigms of Physics. Newtonian Physics, SR, QM, and QFT are all Background Dependent,
whereas GR is Background Independent and many approaches to Quantum Gravity expect this to be Background Independent as well. (Anerson, 2017 - The Problem of Time: Quantum Mechanics versus General Relativity

Fourier wrote: »

First Alice's method of establishing her time parameter via this method fulfills the definitions of a coordinate, along with her definitions for her spatial coordinates she has a full 4D coordinate system. Comparing her results with Bob however she likes, she will see he uses a different set of coordinates but will find the coordinates are related by a transformation that shows they are different coordinates on a single 4D manifold. This is all Special Relativity claims ultimately. The fact that your own method of establishing a coordinate and having it obey the correct axioms, but that others will disagree with said definition, is exactly what you would expect if you lived on a 4D manifold.

I hope you don't mind, I'm going to repost what I reeplied to Morbert because they are effectively the same point. If they aren't, I apologise, let me know and I will reply in kind.

Indeed, she adopts a reference frame for her observations that relies on the Einsteinin clock synchronisation. Herr method of establlishing her time parameter involves defining "a common “time” for [two clocks] A and B, [which] cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A." So, she establishes her co-ordinate frame on the assumption of simultaneity of clock synchronisation events.

Essentially, this boils down to an assumption that the distance traveled by light pulses - from emitter to clock - in her "stationary system", equals the distance that she measures from the emitter to each clock. Her own observations of Bob's synchronisation attempt demonstrate to her that this is not a reasonable assumption.

Bob's observational records are then juxtaposed with her bare assumption. If she tries to maintain this assumption in the face of observational evidence - from a potentially infinite number of relatively moving observers - she will of course conclude that simultaneity is relative i.e. frame dependent. But that is because, in the statement: Events which are simultaneous in one frame are not simultaneous in a relatively moving frame, she is simply assuming the former, while everyone else provides observational evidene of the latter.


Indeed, it seems to be a quirk of nature that she can adopt this convention and make sense of her observations. But what the above shows is that she cannot ascribe any physical meaning to her choice of mathematical co-oridinates and she cannot make metaphysical claims about simultaneity or "the speed at which time ticks". In a basic sense, she cannot say that "events in her frame are simultaneous". It' simply not a justifiable assumption.

Fourier wrote: »

Secondly your objection applies to all observer's, you can see that nobody's time is agreed upon by anybody else. Who has the objective time?

As per the title of the thread, there is no objective time. Time is a system of measurement, like the metric system is a system of measurement. Neither of which are fundamental or emergent.

EDIT: "Time" is still relational in the Machian sense i.e. it is an abstraction from change. We take examples of regularly repeating systems and use them as a unit of comparison, in a similar manner to how a metre stick is used as a unit of comparison.

Fourier wrote: »

QM and QFT can be formulated in a background independent manner for example in QFT in curved spacetimes. SR is about the general physics of a large class of backgrounds or of one fixed background (Minkowski space) but it's not background dependent in the same way Newtonian physics is.

This seems like an invalid classification to me.

As regards trading absolute structures, one has gone from separate absolute t and δij to a unified absolute ημν. We also recognize that this comes with a metric connection, and then notice that Newton and Galileo’s Paradigms also happen to possess a different type of connection. So we pass from four absolute structures in Newton’s own view (the fourth is Vi relative to absolute space) to three in Galileo’s (Vi removed) and to a single but larger one in SR. We subsequently detail how GR removes this last one.
The new privileged structures are underlied by SR’s Minkowski spacetime M4 possessing suitable Killing vectors (Anderson, 2017)

"Passing from Newtonian physics to SR is just trading one set of absolute or background structures for another" (Anderson, 2019)

If QM and QFT can be formulated in a background independent manner then that obviously removes that issue. Removing time altogether removes any problem of time.

Fourier wrote: »

It's not just a "quirk" of nature. That "quirk" is the entire point. Yes in Special Relativity there is as such no physical meaning to her choice of coordinates, they seem to be entirely that: simply a choice of coordinate. In fact anyway of attempting to define one's time will have the same problem due to the constancy of the speed of light. Any notion of time will be relative and revealed to be just a coordinate and no more.

However the relations between the coordinates of different observers are agreed upon and an objective observational fact for all. The relations form a Lie Group called the Poincaré group. This group is the symmetry group of a four dimensional manifold of a certain type. Thus when comparing everybody's definitions of time you are forced to conclude:
(a) That they are coordinates and no more
(b) They are coordinates on a 4D manifold

I presume you are familiar with the empirically equivalent Lorentz-Poincare interpretation of Relativity? Maybe not with the notion that it can be formulated without reference to an ether, such that it just makes reference to an absolute reference frame. This reference to an absolute reference frame can be removed simply by removing the need for an absolute time - an atemporal universe does this.

That represents an alternative to the Einsteinian interpretation, that is not based on the Relativity of Simultaneity, not dependent on an Ether and with no absolute reference frame. It's basically Einsteinian Relativity without the assumption of Simultaneity in any given frame.

Given that Simultaneity/Synchronization - in the frame of the stationary system- is assumed in the Einsteinian interpretation i.e. his synchronization convention, the conclusion of Relativity of Simultaneity is thereby assumed. This is because there are an infinite number of relatively moving observers providing observational evidence that [clock synchronization] events ae not simultaneous in the given frame, and that solitary observer clinging to their assumption that their clocks are synchronised.

So, of course: [infinite] observational evidence of non-simultaneity, plus one assumption of Simultaneity = the Relativity of Simultaneity

Morbert wrote: »

Simultaneity isn't assumed. Simultaneity is a description that follows from a choice of reference frame.

Similarly:


This isn't assumed. This is a description that follows from a choice of reference frame.

Reference frames aren't established or refuted by some prior metaphysical assumptions about simultaneity or the speed of light. They're a mathematical tool for characterising physical observations.

In the Einsteinian clock synchronization convention, as laid out in his 1905 paper, the Simultaneity of clock synchronization events is assumed.

[A "common time"] cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A.

Here we have the assumption of the Simultaneity of clock synchronization events.


The thought experiment outlined to demonstrate this - and the alleged consequences- only serves to demonstrate that such an assumption is not valid, because an infinite number of relatively moving observers provide empirical evidence that the clocks are not synchronised, while one observer tries to maintain the assumption [that their clocks are synchronised] in the face of the contradictory, observational evidence.

If that observer drops their assumption about the Simultaneity of the clock Synchronisation events then the Relativity of Simultaneity disappears.

If the assumption is dropped, then an alternative interpretation remains that is empirically, and mathematically equivalent to the Einsteinian interpretation, but with fewer assumptions.

Morbert wrote: »

You're still putting the cart before the horse here. The clocks are only considered to be synchronised under the standards of observations defined by the appropriate frame of reference.

It's not a case of "the clocks are synchronised therefore a reference frame is established". It's a case of, "the reference frame in which the system is described as stationary will describe the clocks as synchronised by the appropriate procedure"

I'm not sure if you remember in our previous discussions, but that is precisely how outlined the establishing of a reference frame; it involved populating the universe with synchronised clocks at rest relative to the observer - I think the point I was arguing was how an observer could be at rest relative to a set of imaginary, mathematical co-ordinates. It's not necessarily a point we need to get back into

Morbert wrote: »

This is stipulated by the reference frame. It is a definition established by our choice of reference frame. It is not an assumed metaphysical fact upon which we establish the reference frame.

This would seem to suggest that the set of [imaginary] mathematical co-ordinates [chosen to describe physical events] bestows metaphysical properties upon the universe in the form of the Relativity of Simultaneity; together with the physical structure necessitated to accommodate it.

Morbert wrote: »

It is one thing to suggest some Lorentz-Poincaire-type dynamics as an explanation for relativistic phenomena. It is another to suggest that the orthodox geometric account of relativistic phenomena is inconsistent.

Some key points here:

1) I'm not arguing [anymore] that the Einsteinian interpretation is inconsistent, I'm arguing that its self-consistency stems from its assuming its conclusion, an assumption which I am arguing is contradicted by [implied] obervational evidence - implied by the thought experiment used to explain it.

2) We don't need to rely on dynamics in a Lorentz-Poincare style interpretation; bcos an LP style formulation can be derived in an entirely kinematical manner, following the Einsteinian approach - as I will try to outline below.

Somewhat separately, but entirely related, the LP interpretation can be divested of an undetectable Ether - given it plays no [detectable] role in anything. This leaves us with an absolute reference frame. Essentially, we don't need an absolute reference frame, we need a privileged referece frame that defines "true time". There are 2 posssible approaches to removing the need for this privileged reference frame; my preferred route is simply removing the idea that there is a "true time" - an atemporal interpretation does this. Altternatiely, we can simply use a privileged reference frame for the definition of our units of measurement. As a matter of operational necessity, the rest frame of the Earth plays this role because that is how we have defined our units of measurement.

This is not the kinematical derivation, but it addresses some possible "background" issues.

3) The clock synchronisation thought experiment can be taken to represent a possible real-world, experimental set-up that can be used to test the assumption of Einstein's clock synchronisation convention - if the assumption is determined to be invalidated, then we are left with an alternative interpretation that has been derived kinematically.



As per the the Synchronisation Convention, the journey time for a light signal from clock A to clock B is assumed to be the same as the journey time from B to A. This equates to assuming the simultneity of clock synchronisation events. In the thought experiment with Alice and Bob, their emitters and their 2 clocks, we effectively have 3 examples of this in the one set-up.

The thought experiment can be seen as a testing of this assumption, so what is the outcome? Basically, every relatively moving observer provides observational evidence that the clocks are not synchronised i.e. that the clock synchronisation events were not simultaneous. This is juxtaposed with Alice's assumption - in the face of contradictory empirical evidence - that her clocks are synchronised.

Maintaining this assumption leads, by way of necessity, to the conclusion of relativity of simultaneity but only because the "events which are simultaneous in one frame...." part of the definition is assumed i.e. the conclusion is assumed.

Maintaining this assumption requires us to accept a position where observers can be both right and wrong about oberved physical; a seeming paradox in anyone's language but not in the Einsteinian interpretion of relativity; however, it's self-consistency is entirely based on its circularity.

The alternative is one where we equally have to accept that observers are both right and wrong, but it is the infintiely more palatable case where obervers are mistaken in their assumptions and it is the observational evidence which is correct.

Upon dropping the assumption of simultaneity of clock synchronisation events we are left with a purely kinematical derivation of the theory which extends the Galilean Principle of Relativity to simultaneity/synchronisation because, when you think about it, there is no way to determine that two events are simultaneous. We can determine that light signals from two events arrive at a detector simultaneously, but this cannot be used to determine the simultaneity of those events.

Fourier wrote: »

It's not see:
Peskin and Schroeder, Introduction to Quantum Field Theory
Weinberg, The Quantum Theory of fields
Zee, Quantum Field Theory in a Nutshell
Itzykson and Zuber, Quantum Field Theory

These are actual textbooks on Quantum Field Theory used by generations of particle physicists and thus reflect standard usage.

On a personal level, having actually worked in Quantum Field Theory general usage is not as you claim.

Ok, I'll take your point. I'll check out those references, thank you!

Fourier wrote: »

In the Minkowskian view they are a consequence of geometry and hence in that view are analogous to "left" and "right". Even how left and right function is a "simple fact of existence", but it is explained in terms of Euclidean geometry.
The whole point of Minkowski space is how it explains these facts and their relations.


Once again though this isn't evidence to the contrary this is what I have been saying over and over again. It's exactly what you would expect from living in Minkowski space. Empirical evidence to the contrary would be actual observations differing from that predicted by the Minkowski picture, this is not the case here.

I think you're slightly missing the point. I'm not sayinng that it is evidence contrary to the EM interpretation.

As mentioned, the thought epxeriment can be taken to represent a [potential] real-world experimental set-up and as such, it allows us to make a number of deductions about our competing interpretations; that is, we can learn something about the interpretations by considering it.

The EM interpretation is fully consistent with the observational evidence. The contention is that it applies an assumption, along with that observational evidence, which the observational evidence itself renders unjustified.


For a moment, try to shelve any thoughts about Minkowski spacetime - bear in mind, I am saying that Minkowski spacetime is consistent with the obervational evidence - and lets consider the thought experiment solely on its own merits. We can view it as an empirical test of Einstein's clock synchronisation convention.

Without going through the whole thing again, Alice performs the synchronisation procedure. The light signals return simultaneously to her and she assumes her clocks are synchronised that is, she assumes the simultaneity of [clock synchronisation events] in her "stationary system".

All other, relatively moving, observers provide empirical evidence that the [clock synchroonisation] events were not simultaneous and that her clocks are not synchronised. This empirical evidence doe not support her attempt to establish a "common time" for her clocks ; her attempt to "establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A" is not supported by the empirical observations.

So, Alice is at a crossroads, two possible interpretations, leading in opposite directions.

She can maintain her insistence that the clock synchronisation events, in her "stationary system", were simultaneously. She can maintain that all other observers are wrong/mistaken and that it is her assumption that is correct. If she chooses this route, she will arrive at the conclusion that simultaneity is relative. This is a conclusion necessitated by maintaining that both her assumption and the observational evidence are correct - despite the observational evidence contradicting her assumption. Incidentally, she must also accept that she is mistaken and that the others are correct.

To reiterate, the Relativity of Simultaneity says that events which are simultaneous in one reference frame [the frame of the "stationary system"] are not simultaneous in a relatively moving frame. The observational evidence says that the [clock synchronisation] events in Alice's frame were not simultaneous, while Alice assumes that they were. Hence, the conclusion is assumed.

Down this route lies Minkowski spacetime.


Back at the crossroads, the other road - the other interpretation - simply involves Alice dropping her assumption.

Fourier wrote: »

Alice doesn't assume she is correct though in the standard Minkowskian view though. She assumes she has a working definition of a time coordinate, but not that it is absolutely correct and everybody else is wrong. Doing that would be to assume absolute time. She simply assumes it is a functioning way of defining time for her own purposes and she will be able to demonstrate that it and every other method of defining time will be disagreed with by others. In the Minkowskian view this is fine since all such definitions are ultimately just coordinates so you wouldn't expect anything else.

There is no assumption that she is right and others are wrong.

Again, the contention isn't that the above isn't fine with the Minkowski view. As you highlight above, the Minkowski view is predicated on certain assumptions about the working definition of the time co-ordinate. The thought experiment allows us to investigate alternative interpretations and some of the consequences of those interpretaions.

Also, I didn't necessarily state that she assumes that it is absolutely correct and everybody else is wrong, I mentioned at the end that she must also accept that she is wrong and everyone else is right. In anyones language, this would represent a contradiction, but this is taken to be a feature, not a bug, of the Einsteinian interpretation.

Just for the sake of clarifying a point, let's label the implements that Alice uses in her synchronisation set-up. Let's label the emitter as A, the clock on one side as B1 and the clock on the other as B2.

In the real-world experimental set-up, as represented in the thought experiment, she assumes that the time the light signal takes from A to B1 equals the time from B1 to A, as well as assuming that the time the light signal takes from A to B2 equals the time from B2 to A, together with the assumption that the time for A to B1 equals A to B2, and the assumption that B1 to A equals B2 to A.

These assumptions are encoded in her choice of co-ordinate system and working definition of a time coordinate.

The observational results from the experiment do not support the above assumptions.

Fourier wrote: »

She simply assumes it is a functioning way of defining time for her own purposes and she will be able to demonstrate that it and every other method of defining time will be disagreed with by others.

This is essentially agreeing with the point being made. Yes, she assumes - assumes being the operative word - that it is a functioning way of defining time for her own purposes and she also knows that others will disagree with it. The whole point being made is that Alice assumes it is functioning way of defining time, while others base their disagreements on emprical observations.

Essentially, this disagreement IS the Relativity of Simultaneity. Alice assumes her definition of time is valid, while all other observers disagree on the basis of empirical observation. It is Alice's continuing insistence that her assumption is valid that gives rise to the conclusion of RoS - without her assumption all that is left is the observational evidence that the events were not simultaneous.



Can you, at the very least, see the alternative interpretation that doesn't rely on the Relativity of Simultaneity, and that equally explains all the evidence? One in which the matematics of Poincare/Minkowski are taken to be just a mathematical construct?

Morbert wrote: »

I'll try and avoid treading old ground. You made an important statement here:

There's nothing problematic with her assuming that her frame of reference offers a functioning way of defining time for her own purposes (as opposed to her assuming some metaphysical fact about her synchronised clocks, which she does not do). Others will not disagree though. They will have no problem acknowledging that her frame of reference is suitable for her purposes.

Again, the internal consistency of the Einsteinian interpretation is not being challenged here. The above is all fine as it is simply a statement as to what the Einsteinian interpretation is.

While you suggest that she is not making a metaphysical assumption about her synchronised clocks, she is making the assumption that her clocks are synchronised - whether this is a metaphysical claim or not is irrelevant. Well, apart from the fact that her assumption that her clocks are synchronised has metaphysical consequences pertaining to simultaneity. To put it more plainly, while her choice of a mathematial co-ordinate system might not [strictly] be a metaphysical claim, its description of the physcial world certainly has metaphysical implications. It is not the only possible interpretation, however.


As I've asked Fourier, do you at least acknowledge that there are [at least] 2 mutually exclusive, interpretations of the evidence?

Also, do you agree that regardless of how the discussion is framed, the thought experiment represents a plausible, real-world experimental set-up that can be used to examine the competing interpretations - even if there were only one interpretation, the thought experiment could be used to to examine it. Examining this plausible, real-world set-up, allows us to draw conclusions and make inferences about the competing interpretations, what they necessitate, and how they interpret experimental results.

Fourier wrote: »

There are a few different versions of the Lorentz-Poincaré interpretation, I don't want to get into discussing them while we're still talking about the standard interpretation.

That's fair enough. I think, for now, it should probably suffice to say that there are [at least] 2 mutually exclusive interpretations.

Fourier wrote: »

The Minkowski metric cannot satisfy the axioms because it is a metric, not a coordinate system.

Apologies, I have a tendency to sometimes use collocations imprecisely. Nevertheless, the contention isn't that the Einstein/Minkowski interpretation employs co-ordinates that don't satisfy the axioms of co-ordinate systems. That is to say, it's internal consistency is not being questioned.

Indeed, Poincaré anticipated the seminal work of Herman Minkowski on the four-dimensional formulation of special relativity. However, unlike relativity in four-dimensional space-time, in the ether theory these properties represent mere mathematical niceties that do not have a physical meaning. (Acuna - On the Empirical Equivalence between  Special Relativity and Lorentz’s Ether Theory). So  presumably the same is true for the Lorentz-Poincare interpretation.

Fourier wrote: »

Yes, although within limits. In some cases what are initially interpretations actually lead to different predictions. In some cases they're purely a different conceptualisation of the symbols of the mathematics.

We can try to stick within those limits.

Fourier wrote: »

As Morbert says above, she's not assuming anything about her clocks. She's simply defining her coordinate system through a well-defined procedure that results in four coordinates satisfying the usual axioms for such systems. Other observers will not hold the same notion of simultaneous but they will agree that hers is a valid coordinate system.
Then all coordinates are related by a group which has the Minkowski space as its homogeneous space, homogeneous here meaning it is the simplest space with that group as its symmetry group.

The choice of mathematical co-ordinates does not determine whether or not her physical clocks are synchronized with each other - regardless of whether they satisfy the axioms or not. That is to say, clocks in the physical world are not synchronised using mathematics.

The co-ordinate system- and the choice thereof - can only serve as a description of the physical world. Indeed, in certain cases - as per Poincare's four-dimensional formalism - those co-ordinate systems can be viewed, not as descriptions of the physical world  but, as mathematical tools.

Fourier wrote: »

Thus if you have a bunch of observers all holding valid coordinate systems and all of those coordinates are related via a well-defined group, the simplest thing to do is just to conceptualise this as being due to everybody living on the simplest space carrying that group as a symmetry. In this case Minkowski space.

This is one possible interpretation.

Fourier wrote: »

She's not.

She can check if her definition of t,x,y,z (or however she paramterises space) satisfies the definition of a coordinate system. They do. Then she simply can check if under such a definition are the t values of those two events equal.

Thus purely mathematically she has a coordinate system with two events at times t_1 and t_2 obeying t_1 = t_2. She hasn't been forced to assume anything. Her notions of time and space form a consistent set of coordinates and those different events occur at the same time value. No different from somebody setting up "forward-back" and "left-right" coordinates for the land about them and concluding two things are directly left.

In the [plausible] real-world, experimental set-up, Alice does not perform the synchronisation procedure purely mathematically. She performs it using physical equipment and physical clocks.


We can use the time labels you use above - times t_1 and t_2 - and see if we can make progress. Obviously times t_1 and t_2 refer to readings on physical clocks, as opposed to being purely mathematical labels.


Imagine the thought experiment again: Alice is located at the mid-point between her two clocks ( call them B1 and B2); she is co-located with her emitter and a clock (clock A - used to provide timestamps for events).
t_0 is the time she sends the light signals. Imagine that the clock ticks uniformly with increasing increments: t_1, t_2, t_3, etc.

Let's also label the events:
B1 = light pulse making physical contact with clock B1
B2 = light pulse making physical contact with clock B2


At t_0, Alice sends a light pulse in the direction of each clock. How does she determine:
a) the reading on her physical clock A, that co-incides with event B1
b) the reading on her physical clock A, that co-incides with event B2
c) that events B1 and B2 have the same timestamp i.e. that they are simultaneous

How does she determine the readings on her physical clocks? Bearing in mind that her choice of mathematical co-ordinates doesn't determine what she observes.

Fourier wrote: »

They are completely different concepts and I've never known anybody familiar with Relativity to mix them up. Can I ask what books you have read on the subject? This might provide a better path for discussion. I suspect you are not familiar enough with Special Relativity to see the point being made here.

I haven't read any books on that specific topic, I've encountered the term in my [self study] of Relativity. But, there is no contention of the point. I'm content that it does obey the axioms of co-ordinate systems and that it is internally consistent.

It represents one of [at least] 2 contradictory interpretations. So, the point is moot, unless your contention is that the Lorentz-Poincare interpretation doesn't obey the axioms of a co-ordinate system.

Fourier wrote: »

You're making an artificial division between physics and mathematics. Defining something as simultaneous experimentally necessarily involves mathematics because you need to define a parameter t, assign values of t to two events giving you t_1 and t_2 and then check that t_1 = t_2 from your recordings.

The thought experiment represents that checking of recordings. It is entirely the case in point.

At t_0, Alice sets the light pulses off towards clocks B1 and B2; clock A is ticking uniformly - at any rate it is the same for both signals; how does Alice determine what reading on clock A co-incides with event B1 and the reading on clock A that co-incides with event B2?

I'm not asking for you to tell me what the reading is, rather how she determines what it is. Bearing in mind that light must travel from the clocks to her so that she can actually make an observation.

Fourier wrote: »

Once again this is an artificial division. What is "purely mathematical"? You've stated this above and I believe this is exactly why you are missing the point. Alice's operational definition of time from her equipment combined with similar definitions of the spatial directions obeys the mathematical axioms of a coordinate system. There is no division between "pure mathematics" and "physics" of the sort you are using here. Mathematics is simply the precise symbolic language with which we discuss physics. Your objection is analogous to:
Obviously "Alice's clock" refers to an actual physical clock not to purely lexemic English language labels

How does she determine the reading on her physical clock A that co-incides with event B1 and the reading on clock A that corresponds to event B2 - bearing in mind the travel time/distance for light signals involved in making observations.

Fourier wrote: »

I asking what books have you read on Relativity in general, textbooks specifically so that I can refer to them.

I generally tend to download textbooks and go straight to the parts that are of interest, without necessarily taking note of the name. At the moment I've got books by Feynman; Physics: principles and applications by Giancoli; the Problem of Time by Anderson; and an uncountable number of online material. Oh, and @Morbert =D

Fourier wrote: »

Even here I think you don't understand. The Lorentz-Poincaré interpretation doesn't "obey the axioms of a coordinate system", neither does the standard interpretation. Alice's operational definition of her four spatio-temporal parameters does.

while I don't fully understand the point, I can deduce that it isn't enough to decide between mutually exclusive interpretations. I know that if it satisfies the axioms for a co-ordinate system that essentially just means it is a valid - in terms of the axioms - co-ordinate system. Since it's robustness as a co-ordinate system isn't in question - I clearly wouldn't know where to start in that regard - it's not a decisive point.

Fourier wrote: »

We all know the procedure. What is the purpose in asking this? It's based solely on the constancy of the speed of light ultimately.

As it pertains to Einstein's clock synchronization convention, which states that the synchronisation of clocks [in "the stationary system"] must be established by definition i.e. clocks must be assumed to be synchronized, in "the stationary system".

Fourier wrote: »

This indicates to me you haven't read an account of Relativity systematically. It's actually hard to conduct this conversation because you're clearly (and I don't mean this in a rude way) not fully conversant in the theory or its mathematics.

I'd recommend working through Ray d'Iverno's "Introducing Einstein's Relativity".

I don't take it in a rude way at all. I do undestand that this places limitations on my ability to discuss certain aspects of the theory. It is also why I am appreciative of people like yourself and Morbert taking the time to discuss this. While it does place limitations on my ability to discuss certain aspects of the theory, I believe that sufficient deductions can be made while sticking within those limits.

The thought experiments represent one such avenue through which deductions and inferences can be made. Within limits, yes, but we can stick within those limits.

Thank you for the recommendation. I'm always on the lookout for resources like that.

Fourier wrote: »

You've mixed up things like metrics and coordinate systems. This is very basic to the theory and I don't fully understand why one wouldn't just learn the theory first before attempting to argue against it.

I haven't necessarily mixed them up. I'm more familiar with coordinate systems than I am with the idea of metrics. Not fully knowing what the latter was, I misapplied the term thinking the terms were somewhat interchangable. While I don't know what the axioms of a coordinatee system are, I undertand what it means to satify the axioms of something. I knew, therefore, that I wasn't arguing the proposition that Alice's chosen coordinate system disobeyed the axioms.

That is an important point when we have mutually exclusive interpretations, both of which employ a coordinate system which satisfy the axioms of a coordinate system - both, I'm inferring, using the same coordinate system.

Fourier wrote: »

The purpose isn't to decide between two interpretations, it's to demonstrate that the standard one is non-circular. Coordinate systems are a fundamental part of Relativity and not knowing them properly does hinder this discussion.

Given the limitations imposed by my limited understanding of this point, I can't argue against it. What I can do however, is examine the tought experiments and make inferences and deductions within the aforementioned limits

It's by examining the thought experiment that we can deduce, that circular reasoning is employed and is a matter of necessity for that particular interpretation. So, while the construction of the coordinate system might follow certain axioms, which make it non-circular (in the context of constructing coordinate systems), circular logic mut be applied to the interpretation of the observational evidence, it would seem, in order to reconcile it with the mathematical description; or rather, to reconcile it with one particular interpreation of the mathematics.

Just to reiterate, we have [at least] two mutually exclusive interpretations which are mathematically identical, both of which employ a cordinaate system which satisfy the axioms of a coordinate system, so the two cannot be distinguished on that basis. We can however, make inferences and deductions about the differnt interpretations (of the mathematics and evidence) by means of the thought experiments.

Fourier wrote: »

It doesn't assume this. If you look up treatments of this in textbooks that assumption is never made because it is unnecessary to assume. If you knew the mathematics this would be easier to demonstrate (and that is the point of the coordinate system argument) however I will attempt a simpler one.

Light always travels at a constant speed

Bear in mind that there is more than one interpretation of "the constancy of the speed of light".

It can be taken in the Einsteinian sense or it can be taken to mean that the average speed of light is constant i.e. the two-way speeed of light is constant, as opposed to the one way speed of light.

=wiki: onee-way speedd of light wrote:

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,

It could be taken to mean that the speed of light is always measured to be the same. This could be the result of some form of Lorrentzz-Poinccare conspiracy of dynamics, or it could be a quirk of nature that can be described kinematically [by following the reasoning of Einstein but offering a different interpretation] and could be illustrrated through the thought experiments used to demonstrate the Einsteinian interpretation..

Fourier wrote: »

From this we know that a specific travel time for light is associated with a specific distance and vice versa, i.e. if light travels for t seconds it must have covered ct meters. It also means if light travels a distance d, then returns along d the travel time to d must be half that of the total journey.

When Alice receives the light back from B1 at time T, it must have reached the reflectors at T/2 since the speed of light is constant. For B2 she receives it at T, thus it must have reached B2 at T/2.

Hence from the constancy of the speed of light she concludes that they were simultaneous, not from an assumption of simultaneity.

It is precisely the idea that "it must have reached the reflectors at T/2" that Einstein says must be estabished by definition i.e. that must be assumed. Therein lies the assumption of simultaneity of [clock synchroonisation] events.


Alice's own observations [should] demonstrate [to her] why this assumption is not justfied. She observes Bob, with the exact same set-up, attempt the exact same synchronisation procedure, with the exct same obervational results. As observed by Alice, the light signal for Bob also returns simultaneously to him, corresponding to time t_1 on Bob's clock. However, Alice makes the obsservation that the evnts were not simultaneous and Bob's clocks are not ssynchhronised.

This should give Alice pause for thought.

On the basis of this obervational evidence, Alice should be able to deeduce that just because the light signals return to her simultaneously at t_1, it doesn't necessarily mean that both reached the clocks/reflectors at t/2. It's possiblle that the journey time to one was not equal to the journey time to the other and that this difference was canceled out on the return journey.

This is a possible, alternative interpretation for her actual observations i.e. the signals returning simultaneouusly at t_1. Alice canot determinee, by way of experiment, which scenario is the correct one - both are possible.

The cruciall point, and the point that has been argued, is that within the totality of observational evidence, there is no empirical observation of her clocks being synchronised. All the evidence shows that her clocks are not synchronised.

So, all other observers make the observation that Alice's [clock synchronization] events were not simultaneous (this is what they observe). If Alice assumes that the [clock synchronization] events are simultaneous, the conclusion of relativity of simultaneity follows as amatter of necessity. This is solely on the basis of Alice's assumption that her the [clock synchronisation] events were simultaneous, in spite of the observational evidence not supporting this assumption.

If Alice drops her assumption, then the conclusion, that simultaneity is relative, disappears - thus demonstrating that it is the assumption of the observer, in the "stationary sysstem" (Alice), that the [synchronisation] events [of her clocks] are simultaneous, which leads to the conclusion that simultaneity is relative i.e. the conclusion is assumed - with regard to the interpretation of the empirical evidence.


To reiterate, yes, the obserrational evidence - that the events are not simulttaneous - is consisent with the Einteinian interpretation. It represents the "are not simultaneous in relatively moving frames" part of the conclusion.. That part on it's own, however, doesn't lead to the conclusion that simultaneity is relative. For that, the first part of the conclusion - "events which are simultaneous in one frame" - is also required. It is this first part that must be assumed. Thus, for the observational evidence (non-simultaneous events) to lead to the conclusion of the relativity of simultaneity, it requires the additional assumption that events in a given frame are simultaneous i.e. the conclusion must be assumed.

To summarise, while the coordinate system employed in the Einsteinian interpretation may satisfy the axioms of a coordinaate system, the interpretation of [plausible] real-wold, empirical observations requires the application of circular reaoning, in order to reconcile it with that particular interpretation of the mathematics.


The map is not the territory. Where there are different interpretations of the map, we must look to the territory for additional information. In doing so, we see that one interpretation relies on/incorporates/necessitates/however you want to phrase it/requires the assumption of its conclusions.

Fourier wrote: »

The fact that it occurs at T/2 follows from the constancy of the speed of light.

And that the clock reads T/2 at the moment the light signal makes physical contact with the clock can be verified by observation, as opposed to being "established by definition"? I'm sure you know that the answer to this is, simply, that it cannot. Hence, it must be "establlished by definition" i.e. it must be assumed.

Thus is the simultaneity of clock synchronisation events in the "stationary system", assumed, along with it the conclusion that "events which are [assumed] to be simultaneous in one frame, are [obseerved as being] not simultaneous in relatively moving frames".


You probably didn't miss it, but just for posterity in case it is pressumed that the above response somehow addressed the points below:

Bear in mind that there is more than one interpretation of "the constancy of the speed of light".

It can be taken in the Einsteinian sense or it can be taken to mean that the average speed of light is constant i.e. the two-way speeed of light is constant, as opposed to the one way speed of light.

wiki: one-way speedd of light wrote:

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,

It could be taken to mean that the speed of light is always measured to be the same. This could be the result of some form of Lorrentzz-Poinccare conspiracy of dynamics, or it could be a quirk of nature that can be described kinematically [by following the reasoning of Einstein but offering a different interpretation] and could be illustrrated through the thought experiments used to demonstrate the Einsteinian interpretation..

Fourier wrote: »

Yes, it is assumed that the speed of light (as opposed to the average speed of light over a two way trip) is constant. That's what implies the reading is T/2. The assumption is not one of simultaneity as you original posited, nor is there a circularity.

It is an assumption of simultaneity though!

The assumption that the time for the signals to reach each clock is the same, necessarily means that the events - the signals reaching each clock - are simultaneous, in the "stationary system". Hence the timestamp for each event is assumed to be T/2. This is an assumption of simultaneity.

Fourier wrote: »

Of course that's where the different interpretations come in. I'm not sure what is your actual point. That there is an assumption? Naturally there is otherwise one could not make any statements about observations at all aside from the brute fact of their occurrence. One has to propose something in some form in order to model the observations. The assumption is not circular though.

However Einstein's assumption strikes most physicists as the most natural one. It is very difficult to believe this quirk of nature or conspiracy of dynamics that allows all of nature to appear as if the structure of spacetime is Minkowskian.

If one constantly sees light return from a distance d in time 2d/c, no matter how small or large d is made, it seems the simplest assumption to say this is because light is always moving at c. Otherwise why would the physical constituency of all objects make it appear to be the case. Think about it, you are claiming that the world deludes one into thinking light is always travelling at one speed. Since different physical objects reflect light via completely different dynamics this requires a vast fine-tuning over all chemical substances so that the reflected speeds match this assumption. Specifically one needs a different ether-material coupling for each material in order to replicate that speed in the Lorentz-Poincaré case.

The simpler assumption than assuming every material has a specifically fine-tuned and unique coupling to give the appearance of the constancy of the speed of light is to just assume that yes in fact light speed is constant. One assumption replacing multiple coupling assumptions.

There is no need to depend on any sort of dynamics. I'm not sure if you're familiar with the following idea pertaining to the Lorentz-Poincare interpretation:

wiki LET wrote:

By this point, most 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 main difference was the metaphysical postulate of a unique absolute rest frame, which was empirically undetectable and played no role in the physical predictions of the theory

My contention is that even the absolute reference frame can be divested.

Essentially, we can take Einstein's kinemtical formulation and examine it through the aforementioned thought experiments to see the possible interpretions of the empirical evidence.

The Einstein/Minkowski interpretation is one possible interpretation but it does require the assummption of simultaneity of events in "the stationary system".

An alternative interpretation of the evidence would see the extension of the Galilean Principle of Relativity to the concepts of simultaneity/synchronisation - given that there is no experiments that can be conducted to determine these (yet). Simply dropping the assumption that the simultaneity of events "in the stationary system" can be determined.

Without such an assumption RoS simply disappears and we are left with absolute simultaneity - despite the fact that we cannot actually determine which events are simultaneous. This is done without reference to an absolute reference frame or conspiratorial dynamics, simply from following Einstein's kinematical description and looking at the alternative interpretation. Einstein's thought experiments actually show us how nature "conspires" to ensure that we always get the same measurement for the speed of light.

I do realise that it would be need to be formalised a touch more rigorously than that, but that is the reasoning.