Last year I wrote an article for the AIP (Australian Institute of Physics) magazine Australian Physics – Volume 56, Issue 1. The article is about special relativity (SR) and is titled *Moving clocks do not run slow* (**Important note**: the article is about pedagogy, i.e. how we teach SR, and it’s not claiming there’s anything wrong with SR!)

This is one of a series of posts related to the article. You can read the introductory post here. As I said in that introduction, one of the things I’ll do in this series of posts is take the opportunity to provide my response to readers’ comments which were posted on the AIP website.

I’ve already responded to one reader’s comments (Jim Hodges) here. This post is a response to comments by Don Koks.

# Response to Don Koks Comments

First Don writes:

I am concerned that Australian Physics published “Moving clocks do not run slow” by Theo Hughes in the Jan-Feb 2019 issue. Its title is incorrect and its content obfuscates a straightforward subject. In this space allowed, I can do little more than prove that Hughes’ “proof” of his title is invalid. I’ll first establish my position with some correct statements:

That’s the first time I’ve heard special relativity (SR) called a straightforward subject. If Don has taught SR to high school, or university students, and they all “just got it” than hats off to Don, and I wish he would let the rest of us in on the secret!

As to whether the title of the article is correct… well, trivially it’s correct in the sense that, that’s the one I decided on and that’s the one the editors accepted and published. Apologies, I know that’s being flippant, but Don’s tone here makes me feel like being a little flippant.

As to whether the statement is correct, that was the thesis of the article. Though hopefully the abstract of the article makes it clear that the title refers to the way we teach SR, rather than referring to any claim that SR is incorrect. I’ll repeat the abstract here for convenience:

“Moving clocks run slow” is an oft-used phrase in the teaching of, and discussions about, special relativity. However, it is conceptually confusing, operationally useless and, worse, misleading. It also has the potential to slow the development of a broader, deeper and more advanced understanding of relativity. So please stop using it, and encourage others to stop using it. Seriously, stop it!”

With that in mind, I’ll respond to the rest of Don’s comments.

## Measuring time

So Don then says:

(1) Measurements are made in relativity in the same intuitive way that they are made in nonrelativistic physics. Thus, the tick rate of a moving clock in frame X can be measured by comparing its reading at two moments to the clock in frame X that is currently closest (hence eliminating the need to account for signal-travel times), where all clocks in X are synchronised. (In analogy, the Australian Government does something similar to track speeds of road trains between checkpoints.)

One of Einstein’s (and others) insights in developing relativity was that we needed to reconsider how we make measurements. In particular, how we consistently and coherently allocate time coordinates to spacetime points (events) in different (relatively moving) inertial reference frames (IRFs)… and therefore how we measure the time interval between events from different IRFs. From Einstein’s 1905 paper:

“We have to take into account that all our judgments in which time plays a part are always judgments of simultaneous events. If, for instance, I say, “That train arrives here at 7 o’clock,” I mean something like this: “The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events.

On the electrodynamics of moving bodies – Einstein

It might appear possible to overcome all the difficulties attending the definition of “time” by substituting “the position of the small hand of my watch” for “time.” And in fact such a definition is satisfactory when we are concerned with defining a time exclusively for the place where the watch is located; but it is no longer satisfactory when we have to connect in time a series of events occurring at different places, or—what comes to the same thing—to evaluate the times of events occurring at places remote from the watch.”

The basis of SR is that, **contrary **to how time is considered in nonrelativistic physics the time coordinates of a sequence of events is assigned differently in different IRFs. The idea that:

…the tick rate of a moving clock in frame X can be measured by comparing its reading at two moments to the clock in frame X that is currently closest…

Seems to indicate a basic misconception about allocating time coordinates to events in different IRFs. It attempts to circumvent the foundations of SR, and yet somehow say that SR still applies.

I would hope that any instructors in SR would be able to see this… but for any that are not sure of the point I’m making, and for anyone who’s in the process of learning relativity, I’ll be more explicit.

## Measuring time from different IRFs

Consider a ticking clock T. Let’s take two “ticks” of this clock. This is then two events.

- Event 1 = the first tick
- Event 2 = the second tick

In the clocks’ IRF these two events occur at the same location i.e. where the clock is located. As Einstein said:

“such a definition is satisfactory when we are concerned with defining a time exclusively for the place where the watch is located”

On the electrodynamics of moving bodies – Einstein

However, let’s assume the clock is moving relative to another IRF in which we want to measure this “tick rate”. As the clock is in motion relative to this other IRF then the two events occur at different locations P and Q in this other IRF. as in the diagram below.

For those who are familiar with Minkowski diagrams, the related Minkowski diagram is shown to the left of the event diagram.

### The light clock

If T were a “light clock” then this just becomes the standard set-up for deriving time dilation. The tick of the clock being the light beam bouncing off the top mirror and returning to its starting point, as in the diagram below:

The use of a light clock to derive time dilation can be found in many textbooks (and on the web). For example, see the popular undergraduate text Fundamentals of Physics by Halliday, Resnick and Walker (often just known as HRW), p1116 in the 10th edition.

You can also find a version of this derivation, that I wrote, in the Biobrain Physics app!… I can’t resist a plug!

HRW discusses the importance of a single clock in one IRF and two clocks in the other. The text states (my bold):

Sam, watching from the station as the events occur,

Fundamentals of Physics – Halliday, Resnick and Walkerrequires two synchronised clocks, C1 at event 1 and C2 at event 2, to measure the time interval between the two events.

(**Note**: interestingly HRW uses the scenario of a platform and train as I do in the article!… a coincidence, as at the time I wrote the article I was teaching from a different textbook. Not an unlikely coincidence though because Einstein used a lot of trains in his examples so people tend to follow this in their SR examples.)

In the same way, in our scenario to measure the “tick rate” in the IRF of P and Q we must evaluate the time coordinate at P and at Q. Similar to HRW, this is the same as locating a clock at P and a second clock at Q (the time coordinate at P being the reading on a clock at P…the time coordinate at Q being the reading on a clock at Q).

It’s unfortunate that some textbooks do not explicitly include the clock at each event in the diagram. This can lead to people thinking that (similar to Don’s comment) one is simply comparing a single clock in one IRF to a single clock in the other IRF. For example, the diagram in Physics for Scientists and Engineers by Knight does not explicitly show the two clocks.

On the other hand Knight clearly mentions the importance of one location vs two (one clock vs two) in the text (his italics):

Only one inertial reference frame measures the proper time and it does so with

Physics for Scientists and Engineers – Knighta single clock that is present at both events. An inertial reference frame [in relative motion] must use two clocks to measure the time interval, one at the position of the first event, the other at the position of the second event.

Also, textbooks often only show the two events in the same diagram, as in HRW, rather than showing the two events independently as in *Figure 3* above. Of course, it’s necessary to show the events in the same diagram to show the distances etc. that we’re using if we’re deriving the time dilation equation. Which is how the diagram is usually used, as in HRW.

However, I would recommend initially showing the light clock in its own frame of reference (as HRW does), then showing a diagram with the two events separate (as in *Figure 3* above) to emphasise how the different IRFs are measuring the time interval, and finally show the diagram with both events in it for the purposes of aiding with the derivation of the time dilation equation.

Not coincidentally, this is what I’ve done in the Biobrain Physics app!

### Grids of rods and clocks

Einstein referred to this sort of process as setting up a grid of measuring rods and clocks in each IRF. We can imagine that in each IRF we have a clock at whatever location we wish, which keeps track of the time coordinate at that location. The distance between one clock and another can be determined by relatively stationary measuring rods between the clocks as depicted in the diagram below.

All the clocks in a particular IRF are synchronised in that IRF via Einstein sycnhronisation. The foundation of SR is how the grids of rods and clocks in different IRFs are related to one another.

However, from a practical point of view, in any diagram, we only show the particular clocks we’re interested in. Any diagram would be an unintelligible mess if we placed a clock at every point of the diagram! So, for example, in *Figure 3*, we’re only showing T (which belongs to one IRF), and P and Q (which belong to a different IRF).

### Time dilation

In the IRF of T, the time interval between the events is the “proper time”, *t*_{0}, and in the PQ IRF the time interval is the dilated time *t*. The two times are related by the Lorentz factor *γ* in the time dilation equation:

*t* = *γt*_{0}

One can derive the expression for *γ* by, for example, considering T as a light clock (as mentioned, I won’t do this here as it can be found in many other places).

Now while the events happen in both IRFs the “story” about the events from each IRF differ.

- From PQ’s IRF they would claim the clocks at P and Q are synchronised and T is therefore “running slow”.
- From T’s IRF, the clock is not running slow. The difference in the measurement is due to the fact that P and Q are not synchronised.

So the fact that P and Q are not synchronised in T’s reference frame is intimately related to time dilation. It’s not a “problem” (I’ve already extensively commented on this in my response to Jim Hodges, but I wanted to repeat this from another point of view i.e. Don’s “tick rate”. Understanding often comes from discussing a particular concept from various perspectives.)

Now, dear reader, if you’re happy with this set up (I’m hoping you are as it’s analogous to a basic starting point in many textbooks) then we can make some “trivial” rearrangements (to anyone who’s familiar with SR) to show that this situation is equivalent to Figure 1 from the article.

**Step 1**: It should be clear that it makes no difference if we swap P and Q to the top on our event diagram on the right (this makes no difference to the Minkowski diagram as we’re assuming that P and Q are horizontally in line with T, we’re only showing them vertically separated so they’re not sitting on top of each other on the diagram… common practice).

**Step 2**: Motion is relative. If we switch to viewing the situation from T’s IRF, with P and Q in relative motion, this makes no difference to the relationship between the measured time intervals (the time dilation equation) or the explanation of the time dilation equation. In the Minkowski diagram this just means the axes for T’s IRF are now orthogonal.

**Step 3a**: A similar relationship holds between T, and two clocks X and Z travelling in the opposite direction. The direction of travel doesn’t affect the results of SR. The blue axes on the Minkowski diagram are just angled in the opposite direction.

**Step 3b**: Figure 8 is just Figure 1 from the article but with different labels on the objects, and in Figure 1 we are embedded in a familiar everyday situation of trains and platforms.

The whole point of Figure 1 is that it is “trivially” the same as the standard “light clock” scenario (or any similar scenario in which we are comparing the measurement of the time interval between two events from different IRFs).

If one really understands SR one should realise this. The phrase “moving clocks run slow” obscures this for the learner and so it’s not useful for this reason and other reasons discussed in the article.

## Do we really need two clocks?

Considering *Figure 3* again, one could stand with a clock at Q, for example, and (taking into account how long it took the light from the event at P to reach you) determine the time interval between the two ticks in PQ’s IRF.

However, this obscures the fact that what one is doing is evaluating the time coordinate at P (which can be represented by a clock at P). It obscures the foundation of the origin of the difference in measurement i.e. the requirement that to have a coherent set of time coordinates in PQ’s IRF (or similarly in any IRF) we synchronise the clocks at P and Q using Einstein synchronisation, and it obscures the fact that what’s important to the differing perspectives of the two IRFs is that T’s IRF does not agree that P and Q are synchronised.

## Seeing time dilation

Now, there are situations in which one can “look” at a clock and “see” time dilation. For example, a clock moving in circular motion around another clock (as in the time dilation article on wikipedia). However, this is (a) accelerated motion and (b) in more than 1 dimension. Further, we wouldn’t start with this scenario to try and derive or understand time dilation – just as, historically, Einstein and others didn’t and just as the wikipedia article doesn’t, it derives the time dilation equation from the “light clock” – though it does this poorly, hiding the fact that it’s a comparison of one clock vs two.

When we introduce SR we work in one dimension and non-accelerated motion. Accelerated motion is introduced later though, most of the time, we continue to work in one dimension. We can understand and explain most of the effects of SR in one dimension (except for effects such as the transverse doppler effect).

## In complete agreement

Don then says:

(2) A set of clocks, synchronised in the frame in which they are all at rest, is unsynchronised in a frame in which they move. This item is shown correctly in Hughes’ Figure 2.!

Great! I’ve mentioned the importance of this multiple times, so clearly we see eye to eye on this, As I’ve mentioned extensively, this is really important to understanding time dilation and SR in general.

## Slowing of time?

Next, Don says:

(3) In an inertial frame, all physical processes “onboard a moving vehicle” evolve slower than they would if that vehicle were at rest. E.g., all clocks that move (even accelerate) in any inertial frame tick slower in that frame than their factory setting.!

OK, so let’s make this situation explicit. We have two spaceships A and B. They’re in relative motion at some constant velocity, *v*, which is a significant fraction of the speed of light. They pass right next to each other and at that time set their clocks to read the same. They are then moving directly away from each other at the same constant velocity.

In the IRF of A, then B is Don’s “moving vehicle”. In the IRF of B, then A is Don’s “moving vehicle”.

- Neither the occupants of A or B “feel” that time is moving any differently.
- While they were moving towards each other, if they were able to look at what was going on aboard each other’s ships they would both see that time would appear to be going faster (relativistic doppler effect)!
- Once they are moving away from each other if they were able to look at what was going on aboard each other’s ship then they would both see that time appears to be moving slower (relativistic doppler effect again)!… but note this “slowing” is more than that described by the time dilation equation.
- We could choose two events for which A would measure the proper time interval between them and so in B’s IRF the time interval between the two events would be dilated. Similarly, we could choose a different two events for which B would measure the proper time and in A’s IRF the time interval between the two events would be dilated.
- If they were
*really*long spaceships passing each other and they had each synchronised a set of clocks along their length in their reference frame, then as the various clocks on the ships were opposite each other they would variously see the times of their clocks behind or ahead of each other depending on how the origin of each coordinate system had been defined. Effectively this is a version of Figure 2 from the article.

How, considering all this, is it useful to claim (or can we claim) that the physical processes on one of the spaceships are evolving more slowly than on the other? To emphasise this further we’ll consider what happens if the two spaceships later meet up.

## “Twin Paradox”

(This section is effectively an analogy of the Twin Paradox.)

The spaceships keep moving away from each other for some time (years, say). Then we imagine the following two scenarios.

- Spaceship A briefly accelerates in the direction of B so that they are now moving directly towards each other at a relative velocity of
*v*, until they meet again. - Spaceship B briefly accelerates in the direction of A so that they are now moving directly towards each other at a relative velocity of
*v*, until they meet again.

Consider the clocks that they set to be the same when they passed each other.

In scenario 1, spaceships A’s clock would have recorded less time than spaceship B’s. In scenario 2, spaceship B’s clock would have recorded less time than spaceship A’s.

So in one of the scenarios it turns out that the physical processes on spaceship A were “running slower” and in the other scenario it’s the physical processes on spaceship B. We don’t know which until they meet again. So when they were travelling away from each other, until we decide on how they should meet again, there’s no sense in which we can say the physical processes on either spaceship were evolving slower than the other… because the first part of the journey is the same in each scenario but the end result depends on who undergoes acceleration.

The final time difference depends on a comparison of the complete journey (the complete path through spacetime of each spaceship) from the first spacetime point where the met to the second.

(Of course, there’s a lot more to say about these scenarios e.g. one should not try and ascribe the time dilation to the acceleration period… one could consider a longer journey before they meet and then the difference in time would be greater but with the acceleration period having remained the same. But much has been written elsewhere on the Twin Paradox, so I’ll leave it here for now.)

So unless one references a specific measurement (such as a particular choice of two events, or a particular way they are to meet up) there is no sense in which the time in one IRF can be said to be “moving slower” than that in another. And different measurements will give you different answers! As usual in SR, it’s dependent on the perspective of which IRF you are viewing a situation from, and each perspective is correct for that IRF.

## Factory Setting?

The mention of a “factory setting” (a term which I’ve only seen mentioned in relation to SR in articles that Don has written) is odd to me but potentially indicates the source of Don’s confusion.

Don’s background, as far as I understand, mainly relates to working in a practical / engineering setting at the Australian Department of Defence Science and Technology.

So, for example, if one is considering sending a GPS satellite into orbit the clock on the satellite will be set to “run slow”. This is to compensate for the different rate at which the clock on the satellite will run in orbit (compared to the ground stations) due to the combined difference in relative gravitational field and relative motion **relative to the IRF chosen in which to synchronise the GPS system of clocks**.

(**Note**: the “gravitational effect” is larger than the “relative motion” effect and hence the clocks have to be set “slow”, rather than “fast”).

However, this does not mean that the clock on the satellite (or any other process on the satellite) is “running slow” in any absolute sense. It’s only “running slow” relative to the IRF that’s been chosen in which to evaluate time for the GPS system. For example, someone on board the satellite would not “feel” time running slower (partly because the relative difference is very small, but they still would not notice even if the relative difference was very large… just like someone falling into a blackhole doesn’t experience time moving slower, even if it would appear that it was to an external observer).

As it is, between the ground stations themselves it’s non-trivial to synchronise their clocks due to, for example, the oblate shape of the earth and resulting variation in gravity across the Earth’s surface, and the sagnac effect (though there turn out to be some happy coincidences in terms of the earth’s shape). For details see the very interesting article by Neil Ashby Relativity in the Global Positioning System.

Any “slowing” of the clocks on the satellites due to their relative motion is only **relative to** the IRF we’ve chosen in which to synchronise the clocks of the GPS system. And this slowing is the same “slowing” as when we were trying to measure the ticks of clock T. It’s relative.

For example, if we considered one of the satellites over a short period of time (so we could consider it as being in an IRF and ignore it’s acceleration… we’ll also, for the moment, ignore the gravitational effects) then just as with any other IRF in SR, whether it measured the time between two events as being more or less than another IRF would depend on the particular choice of those two events.

There is nothing different about the IRF of the satellite compared to any other IRF. it just so happens our choice of IRF in which to synchronise the system of GPS clocks means we have to make adjustments to the satellites clocks because, for practical reasons, we don’t choose an IRF related to one of the satellites.

The reference frame of any “factory” where the clocks have been built (which is likely not an IRF anyway due to it being on a rotating planet in a gravitational field) is no more special than any other reference frame. If a clock were to leave the factory and take a path through spacetime that ended up back in the factory, then whether the clock read ahead or behind a similar clock that had remained at the factory would depend on the relative paths of the factory and the clock through spacetime to meet up again. Just like our spaceships A and B.

An example of this is the Hafele-Keating experiment where the travelling clocks were sometimes behind and sometimes ahead of the “stay at home” clocks.

This is because identifying either set of clocks as “moving” is not a valid description of the relative path of the clocks through spacetime.

When we move to General Relativity (GR) and more arbitrary paths through spacetime, which include acceleration and gravitational fields, we move away from the more simplistic comparisons that we make in SR to the more more general concept of geodesics – the path along a geodesic between two spacetime points being the maximum “proper time” between those two points. We cannot distinguish any particular path between the spacetime points as one that is a “moving clock”.

## Acceleration

(4) In an accelerated frame, such processes can run slowly or quickly, depending on the vehicle’s location and speed in the frame. (This little-known fact helps explain the Twin Paradox.)

I am struggling to respond to this as I’m not quite sure what is meant here. Also, to claim that there is a “little known fact” about SR (or even if the reference is to something in general relativity) is quite strange. I would guess that whatever fact Don might mention about relativity is known to many physicists or, at the very least, to the many physicists who use relativity extensively. This is especially true if it’s some fact related to the Twin Paradox which is a well worn example. There are various ways of viewing the Twin Paradox (e.g. spaceship A and B discussed previously) and I don’t know any of them that rely on a “little known fact”.

Hughes’ analysis is restricted to the inertial frames of item (3) above; his mention of acceleration on page 15 is only an aside.

(As an aside here, I have to say I dislike the use of referring to people’s surnames in relation to articles, even if it is common practice, hence my use of “Don” rather than “Koks”.)

Yes. The article is focussed on IRFs (“non-accelerating reference frames”).

Item (3) is traditionally shortened to “Moving clocks run slow”. This applies only to inertial frames; but with that understood, it’s a correct, useful statement.

The whole article was that the phrase does not apply as Don describes in (3) and is not a useful phrase. So there’s nothing additional to respond to here – just read the article and the rest of my response to Don.

Hughes might argue that he includes item (4) in his title; but he can’t, because his “proof” applies only to inertial frames. Even if item (4) is included, his title is still wrong, because in an inertial frame all moving clocks do run slow.!

As already mentioned, and pointed out by Don, I was focusing on IRFs. However, as I’ve mentioned, the phrase is also not useful if we include acceleration and gravity.

Interestingly Don’s statement here that

“in an inertial frame all moving clocks do run slow”

Is starting to do what I said would need to be done if we were to try and save the phrase. Already rather than just “moving clocks run slow” he has added “in an inertial reference frame”. Though hopefully a reading of the article, and other comments here (such as the discussion of spaceships A and B) will indicate why it still does not capture the richness of SR, and is confusing to learners.

I get what he’s trying to say because I have an understanding of SR. Just because I get it (having already spent a significant amount of time grappling with SR) does not make it useful.

Hughes’ “proof” of his title statement appears in the section called “Operationally useless, and misleading”.

My “proof” is various points that I make in the article Not just one. And, as mentioned, I had limited word count and could not write about it as extensively as I otherwise might have done. These blog posts are a chance to remedy that (though there’s always more to say in such a vast topic). There are a variety of reasons why the phrase is not a good one. If there were only one, we could probably easily adjust the phrase. As it is, this is not the case.

## Proper time

His argument mis-uses the concept of proper time…

Don does not specify how I have misused the term “proper time”. So unfortunately I can’t respond to this comment. I can only say that I have only used it as it is used extensively elsewhere in textbooks etc.

Though, having said that, I have pointed out to others (and did so at a recent Workshop on teaching relativity.. that’ll need another blog post!) that there is a potential point of confusion for learners in moving from SR to GR in the use of the term “proper time”.

In SR “proper time” is the minimum time in the time dilation equation. This is because In SR we are comparing a “proper time” (the time recorded on a single clock) to the “non-proper time” in another IRF (the dilated time, which is measured at two locations / with two clocks).

However in GR the comparison we usually make is different i.e. we focus on a comparison of various “proper times” between two spacetime points i.e. we compare the readings on clocks that have taken different paths between those two spacetime points (as in the Twin Paradox) with the “proper time” along a geodesic being the maximum “proper time” interval.

So in one case we are referring to a “minimum” and in another case a “maximum” – perhaps Don is confused by this point?

## Symmetry and time dilation

…to conclude, incorrectly, that the phenomenon of one frame measuring the other’s clocks to be ticking slowly is not symmetric between train and platform. The rest of the article is built on this wrong conclusion, and yet elsewhere in it he seems to say that the situation is symmetric.

This is something I can clarify for Don, and anyone else who has the same confusion. It would seem that Don has not understood the point in the article that while the time dilation equation itself is **not **symmetric, the phenomena of time dilation **is **symmetric.

The time dilation equation is (as in any textbook, wikipedia etc.):

*t* = *γt*_{0}

where *t*_{0} is the proper time, *t* the dilated time and *γ* (the Greek lower case letter gamma) is the Lorentz factor. The equation refers to the time interval between two events as measured in different IRFs e.g. the two events as pictured in Figure 1 of the article.

*t*_{0} is the time interval between the two events as measured in one frame of reference (the frame of reference in which the two events happen at the same location) and *t* is the time interval measured in the other frame of reference (in which the events happen at two different locations). Clearly this is **not** symmetric i.e. they are not the same value, the two IRFs do not measure the same time for the time interval.

I hope that makes it clear what I mean by “the time dilation equation is not symmetric”.

The time dilation equation on its own is **not **symmetric in that there is one IRF in which the time is greater than the other IRF. This doesn’t change even if you depict the situation from the perspective of a different IRF e.g. we can draw the same situation as Figure 1 but this time depict the train as stationary and the platform in motion. The values measured by the different IRFs for the time interval (*t*_{0} and *t*) are not affected simply by how we depict the situation.

So how *is* time dilation symmetric?

It **is **symmetric in the sense that we can choose two **different events **(say Events 3 and 4 shown in the diagram below) and this time the smaller time interval is measured in the other IRF (the IRF of the train). The IRF of the train is now measuring the “proper time” because these two events occur in the same place for the IRF of the train.

So for any **single pair of events** the symmetry of time dilation is not apparent.

However we can see the symmetry by choosing different pairs of events to show that either IRF can measure a “proper time” and the other IRF will then measure the related “dilated time”.

*In that sense* time dilation is symmetric i.e. all IRFs are equivalent.

So time dilation is a symmetric concept only if we look at the “bigger picture” (all pairs of events) not if we focus on a single pair of events.

Not understanding this point causes a lot of confusion in people trying to learn SR. One example of this is a reference I provided in the article to a website where the author is confused about SR in relation to this point.

The author refers to two clocks not being able to measure each other as being both faster and slower (the author is correct, this not possible) and therefore the author of the website claims SR is incorrect.

**However**, the websites author is mistaken about what a measurement of time dilation entails i.e. it relates to a particular measurement of the time interval between a pair of events, not two individual clocks “measuring” each others time (which is not possible, as discussed in terms of T, P and Q i.e. to measure the tick of a clock from a different IRF we need two clocks in that other IRF).

Ironically, if the author was talking about the clocks “looking at each other” (rather than a “measurement” of each other’s time) then when approaching each other they “see” each other as running faster, and when receding, they see each other as running slower (in both cases this is just the relativistic doppler effect).

## A point already covered

Part of the confusion seems to result from his seeming not to accept item (1) above.

I’ve covered item (1) earlier, so I won’t comment again here.

## Clock synchronisation

In his Figure 1, Hughes is essentially comparing the initial reading on clock R with the final reading on clock L (although he might not realise that);

Absolutely I realise that. This is how time dilation (the difference in the measurement of the interval between the two events in the two IRFs) arises.

but he fails to correct for item (2), that these clocks are out of sync in the platform frame. If he did make that correction, or if the platform were to record two successive readings on the same clock (either L or R will do), these clocks would be found to be running slow in the platform frame. And ditto for clock Y by train observers.

In calculating the time interval measured in both reference frames one doesn’t “correct” for this… it’s the basis of time dilation! The measurement of the time interval is correct from both reference frames, there is no way to measure it differently that is consistent with SR.

I wonder if this way of looking at the situation comes from Don’s “Engineering” background (i.e. Australian Department of Defence Science and Technology) where the main concern he has with a practical realisation of some timing system within a particular IRF, and not an exploration of IRFs etc. to understand SR.

For example, if one was setting up a timing system in the IRF of the platform, like that required for GPS, one would “correct” the clocks L and R so that they were synchronised not in their IRF but in the IRF of the platform (similar to the corrections of the clocks in GPS satellites).

However, setting up a timing system in the platform frame of reference is not what we’re doing here. And the choice of either the platform or the train in which to set up a timing system is arbitrary i.e. it’s not fundamental to the theory of SR (though there might be a practical choice for those setting up a timing system, just as the choice of IRF in the GPS system is chosen for practical reasons).

## All OK?

One minor caveat is that in at least one spot where Hughes makes an incorrect statement, a reread suggests that he is actually saying “A confused person might think that the following incorrect statement is true.”!

I’m assuming Don means there was something in the article he initially thought was incorrect, but actually he now thinks it’s correct. If so, great!

## Clock synchronisation again

A last point: in the section “Yet more complications”, Hughes “recommends” that in introductory relativity, we should avoid discussing item (2). And yet, most of special relativity follows from that item—and it’s precisely what Hughes was unaware of in his “proof” above. Hence, we do well by demonstrating this lack of synchronisation at the very start of an introductory course, because from it, all else follows, and without it, nothing can be understood.

I would encourage Don to reread this part of the article. I did **not **say that we should avoid discussing clock synchronisation. I was saying that something like *Figure 2* was too complicated a point from which to start (with multiple frames and multiple clocks).

Hopefully it’s clear from my response to Jim Hodges, and this response, that I understand and communicate to others the importance of clock synchronisation.

It’s something that I have always discussed when teaching, and if you use the Biobrain Physics app to learn or teach SR (I couldn’t resist another plug!) you’ll see that it includes a discussing of clock synchronisation.

## Final comment

I urge Australian Physics to vet articles that clearly contradict established physics.

Well, considering the article doesn’t contradict established physics (and it calls out those who do e.g. the reference to the website where someone is claiming SR is incorrect) then the urging is unnecessary.

The editors published the article because they understood it was an article about pedagogy (how we talk about SR and how this can impact teaching SR) and that I was not challenging the validity of SR in any way. This was discussed prior to the article being written.

## Final thanks

Again, thanks to Don for his interest in my AIP article. I hope this post clarifies certain points for him, as well as for anyone else who has read (or reads) my AIP article and Don’s related comments.

Don, as others, is free to continue the discussion in the comments section of this blog and clarify what he said, or simply comment further on the article or my response to his comments.