“Moving clocks do not run slow” – Part 4

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 posted responses to two reader’s comments (Jim Hodges here, and Don Koks here). This post is the final response to comments posted about the article on the AIP website. In this post I’m responding to comments by Vivian Robinson.

Response to Vivian Robinson’s Comments

The first thing to do is thank Vivian for reading the article, and taking the time to write some comments. In Vivan’s case those comments are extensive and formatted similar to the original article, kudos to Vivian for that!

Motion is relative

In Vivian’s first paragraph he states:

There is no absolute frame of reference – all measurements are made relative to the observer. That is why Einstein’s theories were labeled “relativity”. Whether, an observer is moving or stationary with respect to another observer, he/she will have no concept that time is other than moving at his/her normal experience of time.

Yes! I couldn’t agree more! This is the basis upon which I point out that the phrase “moving clocks run slow” is misleading.

So I then find it surprising that the first sentence of Vivian’s abstract is:

Time going slower on moving clocks than stationary clocks…

when we seemed to be in agreement that we can’t identify clocks as “moving” or “stationary” in any absolute sense. I’ll come back to this in a second.

Experimental evidence

Vivian mentions that there is significant experimental evidence supporting SR.

I couldn’t agree more! Yes, there is. But considering I was not challenging the correctness of SR but discussing a point of pedagogy (i.e. how we teach SR) the experimental evidence is not directly relevant.

However, the whole of the first sentence of Vivian’s abstract says:

Time going slower on moving clocks than stationary clocks has been experimentally verified for decades.

As I’ve mentioned, I agree that SR has been extensively verified experimentally, but then how we talk about this evidence as indicating “time going slower” is what the original article is discussing.

Choosing a “practical” IRF

While the first sentence of Vivian’s abstract is superficially contrary to the first paragraph of his comments, from the rest of the abstract I assume Vivian is talking about “moving” or “stationary” relative to some “appropriate” or “practical” inertial reference frame IRF.

So, with that understanding, in the abstract Vivian goes on to state:

Although there is no absolute rest reference frame there are some practical rest reference frames.

Sure. So, for example, in deciding on an IRF in which to synchronise the clocks of the GPS system a particular “practical” IRF is chosen. However, when someone is learning SR, to help them get to grips with the idea that all motion is relative, all IRFs are equivalent etc. we don’t focus on the choice of a practical IRF. Also in the case of the GPS system, the decision of which IRF to choose in which to synchronise various moving clocks is complicated. I would refer readers to the same article Vivian later does, Neil Ashby’s Relativity in the Global Positioning System, as evidence of the fact that the particular choice of IRF in which the GPS system of clocks is synchronised, is non-trivial.

Vivian goes on to say:

When the appropriate rest reference frame is chosen,

In SR there is no definition of “appropriate” IRF Sure, if we’re setting up some specific system like the GPS system then there is an “appropriate” choice of IRF in the sense of it being practical for technical reasons. However, this practical choice is defined from an earthbound human-centric point of view and is not in anyway fundamental to SR.

If we’re studying the theory, and trying to understand the fundamental concepts of SR, there is no “appropriate” IRF. We’re trying to get learners to understand that all motion is relative etc. Then can then learn how to apply this to a particular practical / engineering situation such as how we set up synchronised time for GPS, or similarly apply it to the relativistic collisions of particles – which requires a different choice i.e. usually the centre of moment (CoM) IRF. There’s no single way of choosing a “practical” IRF and what’s “practical” can change depending on what your’re trying to do.

As we do with any area of physics one learns the abstract details of a theory and learn to apply the same concepts to multiple situations (one of the great powers of physics, maths and other sciences). In particular, the concepts of SR are incredibly powerful as they apply to all motion – and all processes involve relative motion!

In theoretical work about relativity the whole point is to be able to look at any situation from multiple IRFs to really comprehend what’s going on i.e. does time really slow down? The claim of my article is that to say “time is slowing down” is misleading, in the sense of viewing a situation from multiple IRFs. So when Vivian says:

clocks moving with respect to that rest reference pass time slower than those at rest in that reference frame.

This is supporting the claim of my article in the sense that Vivian is expanding on the phrase “moving clocks run slow” in an attempt to communicate what instructors are usually trying to convey with this phrase. Vivian’s comment supports the fact that the phrase itself is inadequate. The original article argues, further, that even trying to expand the phrase in this way is not useful in teaching SR.

Contradictions

I am slightly confused by Vivian’s comments as a whole as they contain contradictory statements later on, when compared to his first paragraph. For example:

There is no confusion about whether it is the cosmic rays or Earth that is travelling the fastest. Cosmic ray protons have higher mass than terrestrial protons. SRT indicates they are the faster travelers, not Earth.

As I already pointed out, in his first paragraph Vivian emphasises the relativity of motion. Whereas here, and elsewhere in his comments, he seems to be insisting that there is such a thing as “absolute motion”. While I understand that Vivian originally seemed to be referring to a “practical” choice of IRF, here (and definitely by the end of his comments – see later in this response) he seems to have gone further than this to asserting that there are some absolutes.

SR does not indicate that cosmic rays “are the faster travellers”. What SR tells us is that we can equally view the cosmic rays from the reference frame of Earth, in which case the cosmic rays are in relative motion at a significant fraction of the speed of light, OR we can view the cosmic rays in the reference frame of the cosmic rays, in which case the cosmic rays are stationary and Earth is in relative motion at a significant fraction of the speed of light.

Mass

The mass of the cosmic ray protons is the same as that of protons on Earth. All protons have the same mass irrespective of their relative motion. Mass is an invariant quantity (takes the same value in every IRF).

So let’s assume that by “mass” Vivian means “relativistic mass”. The term “mass” is now commonly taken to mean what was once often referred to as “rest mass”. However, now, If one wants to refer to the term “γm” as some sort of “mass” one needs to at least use the term “relativistic mass”. In addition, “relativistic mass” is no longer a common term (e.g. in terms of its use in textbooks and by physics researchers).

If Vivian is referring to “relativistic mass” then the cosmic rays only have a higher relativistic mass in the Earth’s reference frame. In their own IRF they have a lower relativistic mass than protons on Earth. Relativistic mass is, like other specific quantities in SR, relative.

Figure 1

As others have, Vivian comments on Figure 1. Vivian says:

Consider the situation of a relativistic traveling train and observers with superhuman reactions making the time measurements suggested by Hughes [1]. The first feature to realize is that it is an unrealistic situation. We can’t even get rockets in free space to travel at much more than 10–4 c.

This is why such situations are called thought experiments, or commonly in SR, gedanken experiments (because Einstein was German and this means “thought experiments” in German).

Einstein, and many people since, and numerous textbooks etc. etc. have used such thought experiments to investigate concepts in SR. I was not going to use the word count of my article to explain this commonly understood point. The mention of “superhuman reactions” was an implicit reference to this.

If I had spent significant word count on explaining such a basic aspect of teaching SR in an article about teaching SR I would likely, and rightly, have been accused of wasting peoples’ time.

OK, so moving past that, I found the rest of Vivian’s analysis of Figure 1 confusing. As far as I can tell he’s saying that both Y and RL would measure the time interval between the events as t’:

Y would measure the train traveling a shorter distance S’, which would pass it in time t’. Instruments R and L would measure time interval according to equation 1, also measuring time t’.

(Vivian’s equation 1 is just the usual time dilation equation.)

As mentioned in my response to Don Kok’s comments, Figure 1 is a simple situation that is analogous to the “light clock” derivation of time dilation. The only conclusion I can draw from this comment is that Vivian has a fundamental misconception about time dilation in SR.

In Figure 1:

  • Y measures the proper time t0 (t or Δt in Vivian’s varying notation) because in Y’s IRF the events happen at the same location.
  • In L and R’s IRF the events happen at two locations and so in their IRF they measure the dilated time t (or t’ or Δt’ in Vivian’s varying notation).

Vivian goes on to say:

Consider the reversed situation. Instruments R and L were fixed on the platform, separated by distance S and instrument Y was moved past them at a relativistic speed.

I’m assuming what Vivian means by this is as shown in the following diagram:

Figure 3 (I’m starting at 3 as Figure 1 and 2 are in the article)

And I’ll show Figure 1 from the article here for ease of comparison:

Figure 1 – from the article

Figure 3 is not, in the sense of the physics of SR, any different to the original situation. Again, this indicates that due to Vivian’s focus on an “appropriate” choice of IRF he seems to be misunderstanding some basics about all IRFs being equivalent etc.

Someone who understands SR should be able to see that the situation in Figure 3 is analogous to that in Figure 1. In Figure 3, just as in Figure 1, we’ve got one IRF in which the proper time is being recorded (which will now be in the train’s IRF) and one IRF in which the dilated time will be recorded (which will now be in the platform’s IRF).

To emphasise this I’ve put both figures together in the diagram below and shown the associated Minkowski diagrams.

Figure 4 – emphasising that FIgure 1 and FIgure 3 depict the same situation in terms of the physics, by showing the similarity of the associated Minkowski diagrams.

By choosing:

  • the axes of the IRF in which the proper time will be measured to be the orthogonal axes in both Minkowski diagrams, and,
  • keeping the colour the same for the IRF in which the proper time is measured i.e. the IRF with one clock (and hence keeping the same colour for the IRF in which the dilated time is measured i.e. the IRF with two clocks),

then one can more easily see that the Minkowski diagrams for both situations are the same. (Which axes we choose to show as orthogonal, and the colour we choose to depict an axes, does not make any difference to the physics!)

I go back to what Vivian states in his first paragraph, that a fundamental concept in SR is that motion is relative. The only important point in Figure 1 is that the platform and train are in relative motion. We can equivalently analyse the situation considering the IRF of the platform stationary (the platform’s coordinate axes orthogonal on a Minkowski diagram) or the train stationary (train’s coordinate axes orthogonal on a Minkowski diagram).

Changing Y to the train and L and R to the platform and making a similar measurement makes no difference to the physics (except as to “which IRF” records the “proper time”). The fact that we are labelling the IRFs “platform” and “train” is just putting the situation in an “everyday” setting. And which IRF we label “platform” and which IRF we label “train” is irrelevant to the physics. We could simply swap the labels in Figure 1 to get the situation Vivian wants for Figure 3. We could equally label the IRFs S and S’ (or similar). What label we apply to the IRFs is irrelevant and arbitrary in relation to the physics of the situation.

Despite the situations being the same Vivian seems to be saying that the situation is now different, that Y would now record a shorter time. Vivian’s confusion is potentially explained by his statement that:

In both experiments the “fixed” reference frame is the Earth’s rotating surface.

No! The “fixed” (by which I assume he means “stationary”?) reference frame is whichever IRF we choose to view the situation from. The whole point of SR is to learn that we can analyse any situation from any IRF. What’s important is the relationship between the values measured in those different IRFs. This is what Vivian said in the first paragraph of his comments. However, throughout the rest of the comments Vivian seems to keep wanting to assert some particular IRF as more important (fundamentally) than other IRF.

Vivian next states:

As such, there does not seem to be anything wrong with a definition of time as “the interval between two events that occur at the same point in space“.

Well, that’s the definition of a “proper time” interval. The time dilation equation then relates this proper time interval to a “non-proper” time interval between the same two events as measured in a different IRF. This is not a “definition of time” as such.

In light of this, Vivian potentially has some confusion about the details of time, and time dilation, in SR.

GPS Again

So! Do moving clocks really run slower? As mentioned above, it has been measured that clocks in satellites orbiting Earth run slower than those stationary on it.

First, if anything, the satellites clocks “run faster” due to the “gravitational effects” being larger than any “relative motion” effects.

OK, so let’s assume Vivian is talking about just the “relative motion” effects then, as with all other examples, this is only because we’ve picked a particular IRF in which to synchronise the GPS system of clocks. It’s similar to taking the train as the IRF in Figure 1 and considering the reading of clock Y on the platform compared to clock L and R. Taking that particular measurement then, yes, one could talk about Y “running slow”. However, the whole point is that SR is about more than this one situation and more than this one possible measurement from the perspective of the one IRF.

Muons

Students are supposed to understand about the decay of atmospheric muons for VCE (Victorian Certificate of Education) Physics – part of the Victorian high school certificate. As such I know high school students who understand that we can equally view the situation from the IRF of the physicists, or the IRF of the muons. Neither perspective is the “correct one”. Both are equally correct related to their particular choice of IRF.

  • In the physicists IRF they make two measurements of the flux of atmospheric muons (commonly at the top and bottom of a mountain). This is essentially the physicists using two clocks at two different locations in order to measure the muons’ one clock passing them by. From their IRF they could say the muons clock (decay time) is “running slow”.
  • From the IRF of the muons their clocks are not “running slower”, the physicists two “clocks” are not synchronised (and the mountain is “shorter”).

I would recommend watching a really good black and white video by Frisch and Smith who made the first precise measurements of atmospheric muon decay. In it they demonstrate how they made the measurements and discuss the related theory. MIT has kindly made it available on YouTube. At the 1.17 mark one of them gives a nice explanation of the one clock (one location) vs two clock (two location) comparison that is involved in the measurement of the decay time of the muons.

Vivian states (in relation to the muons):

That can only happen if their time reference frame slows down at their high velocity and the distance they travel appears shorter.

This is sort of correct, but it’s difficult to tell if Vivian understands what’s going on (when considering Vivian’s other comments such as in relation to Figure 1 and time intervals). Hopefully Vivian is saying something like:

“In the physicists IRF it appears as if the muon’s time has “slowed down”. In the Muon’s IRF it appears as if the mountain that’s passing them by is shorter than is measured in the IRF of the physicists.”

However, equally, from the perspective of the muon’s IRF their time moves normally and the physicists have not made a correct time measurement as their “clocks” are not synchronised.

Further, in the muons IRF if a measurement was made of, say, the physicists clock at the top of the mountain the muons could conclude (if muons could do such a thing!) that time is “slowing down” for the physicists. All IRFs are equivalent. The phenomena of time dilation is symmetric. Both IRFs can make a measurement which seems to imply that time is “moving slowly” in the other IRF. There is nothing “absolutely” special about the physicists IRF or the muon’s IRF. It’s all relative!

Sure, being Earthbound we have a bias towards the IRF of the Earth. However, for a student to understand, in this particular situation, who will measure the shorter, “proper time” it’s important (in terms of understanding SR as a whole and applying the same principle to other situations) to be able to understand this from fundamental principles (i.e. that it’s the IRF in which the events happen at the same location) rather than just rattling off a memorised answer.

The correct reference frame?

It’s again confusing, given Vivian’s first paragraph, that he then goes on to state:

The answer is yes! Moving clocks run slower than stationary clocks when the correct rest reference frame is chosen.

The whole point of getting someone to learn SR is that there is no “correct” IRF. All IRFs are equivalent. The whole point, in relation to time dilation, is to ensure someone can identify which IRF measures the proper time and which IRF measures the dilated time. This is not helped by talking about the “moving” IRF. It does not identify one IRF over another. What is correct is that the proper time is measured in the IRF in which the events happen at the same location.

Then Vivian says:

There is no reciprocity! All motions start from one of a small number of rest reference frames.

This is what I meant earlier that by the end of Vivian’s comments it seems he has abandoned all notion of what he said in his first paragraph. “There is no reciprocity” seems to imply that Vivian does not think that, for example, the phenomena of time dilation applies equally to all IRFs. For example, in the case of the muons, that from the muons reference frame we can view the physicists time as “slowing down” in the same way we can view the muons time as “slowing down” from the reference frame of the physicists.

Discussions of experimental evidence

I’ve skipped over the discussions of experimental evidence in the middle of Vivian’s comments because, while they are interesting and important in relation to SR as a whole, they’re not relevant to the discussion here, which is about pedagogy, and helping students understand the fundamentals of SR.

Also, I’m well aware of a whole raft of experimental evidence that supports SR and, I’ve never claimed SR is incorrect.

As an aside, I’ve not checked whether the details of what Vivian says in that part of his comment is correct. I’ll assume they are. Others are free to respond to check that section of Vivian’s comments.

A final thanks

Again, thanks to Vivian 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 Vivian’s related comments.

Vivian, 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.

A final, final thanks

Also, as this is the last response to the comments that were published on the AIP website I’ll take the opportunity to thank all three commenters again, and I’ll repeat what I said in the introductory post to these responses.

And again, thanks to everyone who has shown, or shows, an interest in the article or these posts… or contributes to any ongoing discussion on this blog.

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