“Moving clocks do not run slow” – Part 2

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.

This post is a response to the comments by Jim Hodges. Posts will follow, with responses to the other two readers’ comments. The order of these responses is simply related to the length of the readers’ comments i.e. shortest first.

Response to Jim Hodges Comments

Jim made comments on clock synchronisation and the CMB (Cosmic Microwave Background). I’ll address these comments separately, clock synchronisation first.

Clock synchronisation

First, Jim refers to Figure 1 in my article (reproduced here for convenience):

Figure 1 – this is Figure 1 from the original article.

When dealing with SR, we usually make the assumption that any clock in an inertial reference frame (IRF) is synchronised with all the other clocks in that IRF using Einstein synchronisation. So the assumption should be that L and R have synchronised their clocks in this way.

However, a key point in SR is that clocks synchronised in one IRF are not synchronised relative to any other IRF. The platform is a different IRF (it’s in relative motion to L and R’s IRF) so from the IRF of the platform, L and R’s clocks are not synchronised.

So Jim’s comment about the readings on the clocks is correct. In the IRF of the platform, the clocks L and R are not synchronised. He’s also correct in identifying that, in the platform’s IRF,  L will show a time ahead of R.

However, Jim states that this is a “complicating factor”, he suggests that it’s a problem with the situation, which is misleading.

The disagreement between IRFs about clock synchronisation is not a “complicating factor”, rather it’s the basis for the effect of time dilation. The disagreement arises from Einstein’s postulates and clock synchronisation. It’s something students need to get to grips with to really understand concepts such as time dilation and length contraction.

Let’s consider two different events:

  • Event 3 – Clock R is opposite clock X
  • Event 4 – Clock R is opposite Clock Z

As in the diagram below. (We’ll call this diagram Figure 3 to distinguish it from Figures 1 and 2 in the article.)

Figure 3 (Figure 2 is in the original article) – we’re considering two different events such that the “proper time interval” between the events is now measured in the train’s IRF.

Events 3 and 4 happen at different locations on the platform and at the same  location in the IRF of the train (two clocks on the platform, and one on the train).

This is what one might call a “standard” point of view, the one an instructor is likely referencing / has in their head if they state “moving clocks run slow”. However, in terms of how we explain the difference in the measurement of the time interval between Events 3 and 4, there’s no difference to Figure 1 from the article.

Each IRF has it’s “story” about the events.

  • From the IRF of the platform, based on this particular measurement, the clock R on the train is “running slow”.
  • However, similar to Jim’s point about Figure 1, from the perspective of the IRF of the train, R is not running slow but rather, the two clocks on the platform (X and Y) are not synchronised.

It is equally valid to draw this diagram showing this situation from the IRF of the train (the train stationary and the platform moving to the left):

Figure 4 – showing the same situation as Figure 3 but now shown from the perspective of the train’s IRF (so the train is shown as “stationary” and the platform is shown “in motion”).

It doesn’t matter that we’ve changed how we depict the situation, the smaller interval is still measured on the platform. Whether the train or platform is “moving” simply depends on which IRF we depict the situation from. The whole point of SR is that “motion is relative”!

Similarly, it doesn’t matter how we depict the situation in Figure 1 (platform stationary or train stationary). So, for example, we could show the train stationary with the platform moving past it, as in the diagram below. The smaller interval between the two events is still measured on the platform.

Figure 5 – the same situation as depicted in Figure 1 but now shown from the perspective of the train’s IRF (so the train is shown as “stationary” and the platform is shown “in motion”).

Again, a fundamental point of SR is that “motion is relative”. It’s neither the platform nor the train that’s “moving”. What matters is that if we measure the interval between two events, the smaller time is measured in the IRF in which the two events happen at the same location in that IRF.

This is fairly basic and is, for example (as mentioned in the article) the definition of the “proper time” as described in the VCE (Victorian Certificate of Education) Physics Study Design – which is the Victorian high school curriculum.

[Note: we haven’t even discussed aspects such as, for example, there’s not always a “proper time” between two events i.e. there’s no “proper time” between “spacelike separated” events. Another point that anyone teaching SR hopefully understands.]

The Minkowski diagram version

For any physicist who’s not used to working with diagrams drawn as we have done so far (event diagrams). I’ll show the related Minkowski diagrams.

Figure 6 – showing Figure 1 and 5 again (which depict the same situation, just shown from the perspective of the different IRFs) with the associated Minkowski diagrams.

I’ve coloured the IRFs blue and red in each Minkowski diagram and related event diagram so that it’s easier to relate the two.

  • In the top pair of diagrams the axes of the platform (red) are orthogonal (we’re taking the perspective of the platform being stationary).
  • In the bottom pair of diagrams the axes of the train (blue) are orthogonal (we’re taking the perspective of the train being stationary).

Whichever perspective we take, the smaller interval between the events is measured in the IRF of the platform. This is NOT because the platform is “moving”. It’s because the platform is the IRF in which the events happen at the same location.

We could draw similar diagrams for Events 3 and 4. For Events 3 and 4 the smaller interval between the events is measured in the IRF of the train (rather than the platform). This is not because the train is “moving” but because the events happen in the same location in the IRF of the train.

So, to reiterate, the reference frame which measures the smaller time interval is not determined by which IRF is “moving”. There’s no sense in which we can pick out any particular IRF as moving… this is the whole point of SR! The smaller time interval is measured in the reference frame in which the events happen at the same location.

Student’s need to understand this. The phrase “moving clocks run slow” is not useful in conveying this, or other aspects related to time. It obscures these concepts… and students make mistakes in questions, based on using the phrase “moving clocks run slow”.

So I would agree with Jim in that we should be showing students how the disagreement on the interval of time between the two events arises from Einstein’s postulates and the synchronisation of clocks. However, this is not a problem with the scenarios we’ve discussed. It’s the reason for the discrepancy between the measurements.

Back to the article

Now to get back to the article, and Figure 1. The article was aimed at those who are teaching relativity and, one would hope, already have an understanding of the role of clock synchronisation. So, as I was discussing other ideas at this point in the article, I did not mention it – it’s impossible to mention everything at every point.

Additionally, the concept of clock synchronisation is referenced later in the article e.g. Figure 2 (reproduced here for convenience).

Figure 2 – Figure 2 from the original article

This is a more general illustration of the fact that if we take the perspective of an IRF with a set of synchronised clocks (Frame S) then clocks that are synchronised in other frames will not be synchronised relative to this frame.

So, for example, we could take Frame S (black) to be the platform from Figure 1, and Frame S’ (green) to be the train (because it’s shown moving in the same direction, relative to S, as the train is to the platform in Figure 1). Then if we consider two of the green clocks we can see that the one to the left is ahead of the one to the right – which was one of Jim’s points about Figure 1.

So while this particular comment of Jim’s is correct, and of interest, it doesn’t have any impact on the thesis of the article.

Saving the phrase

Jim’s subsequent suggestion on how to save the phrase “moving clocks run slow” supports one of the main points of the article i.e. that the phrase “moving clocks run slow” is insufficient to usefully convey in a meaningful way what SR is about. As Jim’s attempt shows, if we try to save this phrase, the phrase becomes overly complicated and is still not particularly useful.

I don’t think Jim’s phrase would bring any greater clarity to students trying to understand what’s going on, than the original phrase. That’s not to say that Jim’s version is particularly worse than any other, but just that the idea of trying to capture the concepts involved in time dilation in a single phrase is not a useful exercise.


Finally Jim discusses the CMB (Cosmic Microwave Background):

When it comes to the matter of when clocks are really running slow, the student should be made aware that astrophysicists are now telling us that all motion is absolute. Which is to say, the Earth has an absolute speed of 370 km/sec in the direction of the constellation Leo, plus or minus 30 km/s, according to the time of year.

Jim Hodges https://aip.org.au/wp-content/uploads/2019/08/AP-56-1-Reader-response-Jim-Hodges.pdf

This is a misconception. The CMB is not an absolute frame of reference. This misconception is possibly due to astrophysicists not being careful about the language they use (hopefully it’s not due to misconceptions that any astrophysicist holds). Potentially, it’s an additional reason for needing to be careful about the language we use in describing these phenomena.

I recommend googling “CMB absolute reference frame” to quickly and easily find multiple discussions about this issue, and some good explanations from reliable sources e.g. this reference from the University of British Columbia (UBC).

The UBC page is a FAQ about the CMB and, as such, answers a number of questions about the CMB. This includes whether the CMB is an absolute reference frame, which can be found under the heading How come we can tell what motion we have with respect to the CMB? Given this, I won’t seek to explain it further here, but if there’s any remaining confusion on this point, I’m happy to write an additional post about it.

A final thanks

Again, thanks to Jim 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 Jim’s related comments.

Jim, 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.

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