Philosophy Discussion Forums | A Humans-Only Philosophy Club

[David Cooper]

You know full well what I mean by acceleration because I've spelt it out clearly.

You have absolutely not spelled it out at all. I have succinctly stated numerous times that the definition of acceleration is rate of change of velocity with respect to time.

There are actual accelerations and actual decelerations, and these relate to the absolute frame. There are also apparent accelerations and decelerations which relate to other frames. When we know that we're talking within the context of a specific frame, we can drop the word "apparent" as it can be assumed, and in theories where there's no absolute frame, we can even drop that assumption. However, when I'm asked absolute questions, I will answer using descriptions that relate to valid theories rather than invalidated ones, but you complain when I do that because you want me to give absolute answers using descriptions that relate to an invalidated theory, and that is something I refuse to do. If you ask me to give SR answers to absolute questions, I will give you SR answers.

I prefer my usage of the word because it is less ambiguous than yours - this leads to greater clarity.

This is the opposite of the truth. The reason why terms like "acceleration" have well defined specific meanings in physics is so that they are absolutely unambiguous. It is impossible to mistake the short, simple definition of acceleration for anything else. But generally, in everyday life, words are used ambiguously, meaning different things in different contexts.

They are not absolutely unambiguous in physics - they are only unambiguous in SR/GR.

Everyone is entitled to use words in they way they want to so long as they spell out how they intend to be interpreted, and I have done so.

No you haven't. I have said many times "acceleration means...". You have not.

I have spelt out exactly what I mean by them.

The "man in the street" has numerous different purposes for words and generally isn't concerned with precision of language.

The man in the street will call something a deceleration something that looks to him like a deceleration, but when you point out to him that the Earth is moving round the sun, the sun round the galaxy, and that the galaxy too is moving towards M31, his natural response is to think of all this movement being relative to space, and that a deceleration will naturally mean slowing down relative to space, or slowing towards a speed (or lack of speed) where light passes at a relative speed of c in all directions. That is the way people naturally think, until the SR people start messing with their minds.

When discussing physics we don't have that luxury. As a software engineer, like me, you should know this. You don't talk to your computer using vague, ambiguous English, do you? You use precisely defined, unambiguous computer languages that are defined according to agreed published standards that anybody who is interested can look up. If you want to be properly understood you need to apply similar standards here.

My work involves programming computers to understand natural language so that it will be possible to program them using normal words the way normal people use them while the computer interprets what they mean and asks for clarification if it isn't sure - it will not force them to speak in any way other than the way that is natural to them. Almost everything can be done with full precision using normal words, and where specialist vocabulary is essential, it can be learned by the person who needs it at that point. If it isn't essential, there is no reason why the person's existing way of talking should be banned. There should be no difficulty whatsoever in an expert understanding the words of the man in the street when they're discussing a subject where the expert knows alternative wordings for things but where ordinary words are good enough. The inability of the expert to cope with ordinary wordings shows a lack of capability on his part which makes it harder for him to communicate with normal people.

In this case here, it is particularly important to use language that is as open as possible to the man in the street because we are taking on in philosophy something that physicists supposedly consider to be outside their remit and beyond their expertise. We are not bound by the language of physicists, and we want to express things so clearly that anyone can follow what's being said without needing any expertise. This matters, because we're asking non-physicists to judge theories and we want to strip away all the jargon and just say directly in normal language what everything is and does. There is nothing in SR, GR or LET that can't be described and discussed in normal language, apart from the key idea of frames of reference, the names of different models (which had never been catalogued properly by anyone until I did it), and an understanding of what a block universe is.

[David Cooper]

The definition you give here is one used by the two of us and by Einstein and physics in general. David has a different one, which is more or less 'rate of increase of objective speed', which isn't even a vector.

If it's clear that you're talking about vectors, then an acceleration is a vector and (it may be a deceleration). In the case of a gravity simulation with things orbiting each other, an acceleration is repeatedly applied as a vector, adding it to the movement vector for the thing the force is acted on. For the man in the street though, it's better just to call it a pull, or a force being applied.

David's definition fits with any theory that has a concept of objective speed, but is meaningless in a theory that doesn't. The physics definition is not thus dependent on a specific view, which is why physics uses it.

But when an absolute question is asked about whether something is accelerating, the answer "yes" can be misleading.

The man in the street isn't talking absolute speed. He is giving an implied reference, and that makes it correspond to the physics definition.

When the man in the speed has it in mind that the Earth is moving, he is thinking about what is happening relative to space, and he will use the words "accelerate" or "decelerate" accordingly, if he thinks he knows how something is moving relative to space. Even when he's introduced to the idea of something moving at relativistic speed and being length-contracted, he's imagining it moving through space at very high speed, and he may not be imagining anything else in that space to compare its speed to. He automatically thinks in absolute accelerations and decelerations (relative to space).

[David Cooper]

As an example of the way that the simple definition of the word "acceleration" is, in David's mind, all wrapped up with this idea that everyone has been brainwashed by the establishment, look again at what he said to you here:

viewtopic.php?p=318925#p318925

Interesting. Acceleration is a vector rate of change in velocity, not a change in speed. There is no difference between acceleration and deceleration. The ISS for instance is always accelerating, yet its speed remains constant (relative to Earth). This is high-school physics, not even touching on relativity.

It's a contradiction that you've been heavily brainwashed into believing is acceptable, but the part about clocks speeding up and slowing down at the same time takes it a much more obvious step into the irrational.

Your simple statement of a fact of physics, that has nothing at all to do with Einstein and is simple high school Newtonian mechanics, is seen to be all part of this "brainwashing" process. The result is that you can't simply use words in accordance with their standard definitions without being accused of being "brainwashed".

This illustrates precisely what's wrong with the way you use the word: "there is no difference between acceleration and deceleration". There is a very clear difference between the two things, and the man in the street knows it. You are referring to a technical usage in which you don't distinguish between accelerations and decelerations because all you're thinking about are vector additions. That's fine in that context, but it does not fit with normal usage and comprehension of the word(s).

[Steve3007]

viewtopic.php?p=320617#p320617

viewtopic.php?p=320619#p320619

The definition you give here is one used by the two of us and by Einstein and physics in general.

One thing I've considered it important to point out is that "acceleration" has nothing, in itself, to do with Einstein or SR. If we say that, I think we feed the bizarre idea of his that the whole of physics is corrupted by the evil dogma of SR, including the physics that existed before SR was born.

I think that what I said in the above two posts (and in some previous posts) is further illustrated by comments such as these:

They [terms like "acceleration"] are not absolutely unambiguous in physics - they are only unambiguous in SR/GR.

The man in the street will call something a deceleration something that looks to him like a deceleration, but when you point out to him that the Earth is moving round the sun, the sun round the galaxy, and that the galaxy too is moving towards M31, his natural response is to think of all this movement being relative to space, and that a deceleration will naturally mean slowing down relative to space, or slowing towards a speed (or lack of speed) where light passes at a relative speed of c in all directions. That is the way people naturally think, until the SR people start messing with their minds.

So, apparently, 300 years before Einstein was born, when Galileo was doing his experiments to establish the character of acceleration due to gravity and, 200 years before Einstein was born, when Newton created his laws based on such things as those experiments and the findings of Kepler and Tycho Brahe, making precise unambiguous use of the concept of acceleration, both of them were brainwashed by a theory that hadn't yet been invented. We're told that it came back in time to mess with their minds. A clever trick.

[Halc]

David's definition fits with any theory that has a concept of objective speed, but is meaningless in a theory that doesn't. The physics definition is not thus dependent on a specific view, which is why physics uses it.

But when an absolute question is asked about whether something is accelerating, the answer "yes" can be misleading.

On the contrary. Acceleration is quite absolute given the physics definition. There is nothing misleading about the answer.
Velocity and speed on the other hand are relative terms, and when an absolute question is asked about something's speed, the answer has no meaning in the standard definition.

[Steve3007]

viewtopic.php?p=320651#p320651

It's a good example of you not getting your head around the thought experiment, as will soon become clear.

I hope so, as I'd like to know if I've missed something. To be clear: In the post to which you're replying my point was that the three experiments you describe are physically identical. Let's see if you've shown me to be wrong in saying that. To be clear, here are the three experiments:

1. You stand still throughout. I move away from you and then turn around and come back. At speeds v and -v relative to the Earth frame and you.

2. You move at speed v relative to the Earth frame throughout. I move at speed 2v, then I stop and wait for you to catch up.

3. You move at speed v relative to the Earth frame throughout. I stand still for a while then start moving and catch you up by travelling at speed 2v, relative to the Earth frame.

In all cases, you remain in one inertial reference frame throughout. In all cases, between legs 1 and 2, I switch between two inertial reference frames that are moving at speed 2v relative to each other. The only different thing about experiment 3 is that I am initially moving away from you to the left instead of the right. i.e. it's a mirror image of the first two. I presume you agree with this?

Fine. We can also have someone else travel with you on the way out who doesn't undergo any accelerations, and someone else come back with you who doesn't undergo any accelerations, and they can confirm that your clock ticks at the same rate as theirs while they are travelling with you, thereby removing any magical role for the accelerations to affect the timings - this shows that the way the clocks tick relative to each other is entirely controlled by their speed of movement through space.

We can indeed. And those two people will be in two different inertial reference frames, travelling at speeds v and -v, respectively, relative to you. This will be true in all three experiments. And this has nothing to do with the point I was making in the post to which you are replying, which is that the three experiments you describe are physically identical. But carry on.

Fine (ignoring the relativistic speed addition aspect which reduces the 2v speed by a fraction).

True.

Of course, but there is a hidden difference.

What's the hidden difference?

And yet there's a hidden difference.

What's the hidden difference?

Yes they have. If my clock was ticking faster than yours during the first leg of the first experiment, when we do the third experiment, your clock must be ticking faster than mine during the first leg. You deny that...

I note that whatever happens during the first leg of the first experiment must also happen during the first leg of the other two versions of the experiment, because all three experiments are physically identical. In all three cases the separations, relative velocities and accelerations of you and me are identical.

...but I know it to be true because I had the wit to leave a third clock behind which was with me throughout the first experiment, and you were stationary relative to it throughout the fist leg of the third experiment. That third clock hasn't accelerated at any time, so it was ticking at a constant rate throughout all three experiments.

OK, so you leave a third clock stationary relative to the Earth at your original location on the Earth. As you correctly state, it doesn't accelerate in any of the experiments. In the first experiment it stays with you throughout. At the start of the 2nd and 3rd experiments you are moving relative to it at speed v. At the start of the third experiment it is stationary relative to me. So in the first experiment it is your clock. In the 3rd experiment it is my clock for the 1st leg. In the 2nd experiment it is neither of our clocks.

In the same way, during the first experiment, you were accompanied by a fourth clock on the first leg, and it kept on going when you turned back, moving at a constant speed which it maintained right through the second and third experiments. Throughout the first leg of the third experiment, that fourth clock and I were co-moving, so it was ticking at the same rate as my clock.

Ok, here's where you start to fudge things. You say that in the first experiment I was accompanied by a 4th clock that carried on when I turned back. If that clock also accompanies me in the first leg of experiments 2 and 3 then obviously it's not co-moving with you, is it? So it's not clear what you're saying here about the 4th clock. Be clear. What does the 4th clock do in experiments 2 and 3? Are you saying that this 4th clock carries on moving at speed v relative to the Earth while we both come back and do experiments 2 and 3? If so, what does that prove? Are you saying that, in each experiment, the 4th clock moves with me on the 1st leg? You can't be, because then your last sentence in the above quote would be false.

This proves what I said at the start of this paragraph: if my clock was ticking faster than yours during the first leg of the first experiment, when we do the third experiment, your clock must be ticking faster than mine.

It proves nothing of the sort. You haven't been clear what this 4th clock is doing in each of the 3 experiments, and you haven't specified what you hope to demonstrate by bringing in clocks 3 and 4. When you say of the 3rd clock "it was ticking at a constant rate throughout all three experiments", ticking relative to which other clocks?

If you don't nail the details like this, you accidentally change the proposed speed of light relative to the system without realising that you're doing so, but we need to analyse these experiments with greater rigour than that to avoid making careless mistakes.

Yes, you do need to do that. Look again carefully at the relative positions and movements of you and me in these three experiments and look at your wording as I've broken it down above. Do you see that those relative movements and positions are the same in all 3 experiments?

And it is no surprise to me that you do make such careless mistakes, because almost everyone in the SR camp makes the exact same mistakes every time due to their abject failure to check what they're doing to the speed of light relative to the system. The third and fourth clocks show up their error.

The 3rd and 4th clocks don't yet show anything. You haven't said what you mean when you say that the 3rd clock is "ticking at a constant rate", (constant relative to what?) and you haven't been clear about how the 4th clock moves in each of the 3 experiments. Try again. Be precise. Remember throughout that the only way to tell if a clock is "ticking at a constant rate" is by comparison with another clock.

[Steve3007]

In the same way, during the first experiment, you were accompanied by a fourth clock on the first leg, and it kept on going when you turned back, moving at a constant speed which it maintained right through the second and third experiments. Throughout the first leg of the third experiment, that fourth clock and I were co-moving, so it was ticking at the same rate as my clock.

OK, I've looked at this passage again and I think I know what you intend the 4th clock to be doing. I think you're saying that the 3rd clock stays stationary relative to the Earth throughout all 3 experiments and the 4th clock moves at speed v, to the right, relative to the Earth throughout all 3 experiments. Yes?

If so, then the following is true for all 3 experiments:

At the end of the 1st leg I accelerate, changing my speed relative to clocks 3 and 4 by 2v.

Agree?

(Note again: Throughout all of this I'm using the standard definition of the word "accelerate", as Newton used it.)

[Steve3007]

viewtopic.php?p=320659#p320659

This illustrates precisely what's wrong with the way you use the word: "there is no difference between acceleration and deceleration"...

David, please don't casually misquote me. If you think I have said that then find it in my posts and quote the relevant part of the relevant post. Whenever I quote you I do it directly from your posts and try to make the context clear, typically by adding a link to the original post for reference, and/or including the comment to which you were replying.

Here is the post that you may or may not be thinking about (although I can't tell for certain because you didn't quote me):

viewtopic.php?p=318815#p318815

By denying an absolute frame, you automatically have contradictions in that every acceleration is also a deceleration, and every such change in speed leads to a clock both running slower and speeding up at the same time. These are contradictions that cannot be tolerated by anyone rational.

Obviously every acceleration is a deceleration. You will have learnt that in high school physics. A ball thrown into the air and in free fall is accelerating in a coordinate system in which the positive direction points towards the Earth (down). Therefore it is decelerating in a coordinate system in which the positive direction points away from the Earth (up).

Note: I didn't say what you misquoted me as saying. If I'd quoted Paul Simon when he said "one man's ceiling is another man's floor" and you'd quoted him as saying "there is no difference between ceilings and floors" that wouldn't convey the meaning of what he'd said, would it? If you're going to quote somebody, always actually quote them.

It is true by definition that deceleration (reduction in speed) is an instance of acceleration (change in velocity), and it is true by definition that an acceleration with respect to one inertial reference frame is a deceleration with respect to another (one man's ceiling is another man's floor). If I jump out of a moving car I rapidly decelerate with respect to the road, and I rapidly accelerate with respect to the car, and to the other cars on the motorway. I feel that the "man in the street" would get that.

...There is a very clear difference between the two things, and the man in the street knows it.

And you can't keep using this "man in the street" defense for your inaccuracies, because when you say this...

You may be capable of imagining an acceleration to be a deceleration at the same time, even though it can't really be

...shortly after the comment of mine that you misquoted, you make it clear that you still haven't got your head around the above simple definitions. I think "the man in the street" would have no trouble with them. So, as a student of advanced physics and an expert in language, why do you?

[Tamminen]

With the numbers I proposed (5 years out and 5 back for T, 20 elapsed at D), at the halfway point, just before acceleration in frame T1, D clock would read 2.5 years, and just after acceleration, D clock would read 17.5 years. This assumes acceleration is done in a brief time.

And during this brief time in T clock 15 years have elapsed in D clock seen from T. Simultaneity is a strange thing. But this is the solution for the paradox. There is no contradiction. The "underlying reality" is there: the D clock ticks for 20 years and the T clock ticks for 10 years. But the part of this period of 20 years in D clock that is simultaneous with a given part of the 10 years in T clock as seen from T's perspective depends on the current frame and the changing of frame by accelerating. I think the case is closed. Except perhaps not for everyone.

[Halc]

With the numbers I proposed (5 years out and 5 back for T, 20 elapsed at D), at the halfway point, just before acceleration in frame T1, D clock would read 2.5 years, and just after acceleration, D clock would read 17.5 years. This assumes acceleration is done in a brief time.

And during this brief time in T clock 15 years have elapsed in D clock seen from T.

We seem to not be clear what what all the labels are. T is the traveler, or the ship, or the clock on it. T1 is the frame of the ship going from D (home) or D0 (departure event) to a turnaround event (did we pick a label for that?? U for U-turn let's say. I think you're talking about U here).
T2 for the frame of the return trip back to D. D is also the frame in which 'home' is stationary. D20 is the event at home when the ship T returns. The D clock reads 20 then. T clock reads 5 at event U in any frame. T clock reads 10 when it gets back home, so event T10 is the same event as D20.

Back to your comment then. I am going to rewrite your comment using the terms I just spelled out above:

And during this brief time at U, 15 years have elapsed in D clock seen from T.

My correction of the wording of this: At event U, in frame T1, the D clock simultaneously reads 2.5 years. At event U, in frame T2, the D clock simultaneously reads 17.5 years. The difference is not 'elapsed', but merely a declaration of which events are simultaneous with event U in the two different frames. Yes, there are 15 years difference between them. Very good. Finally, this is 'as computed by T, not as seen. At U, if T looks back at D from that distance, he 'sees' a clock reading 1.34 years, and he sees this from either frame, as that is the light from D getting to event U at that time.
In frame of D, U is 8.66 light years away. The ship departs at time 0 moving at .866c, and the light from the clock reading 1.34 'departs' at lightspeed 1.34 years later. They both get to U at the same time, so that's what T 'sees', but T computes a different time for what that clock currently reads since he knows the distance to D when the clock said 1.34, and thus the time it took for that light to get to him. That computation is quite different in frames T1 and T2, and hence the discrepancy of 15 years between them.

Simultaneity is a strange thing. But this is the solution for the paradox. There is no contradiction.

Just so.

The "underlying reality" is there: the D clock ticks for 20 years and the T clock ticks for 10 years. But the part of this period of 20 years in D clock that is simultaneous with a given part of the 10 years in T clock as seen from T's perspective depends on the current frame and the changing of frame by accelerating. I think the case is closed. Except perhaps not for everyone.

Not everyone posits that same underlying reality.

[Tamminen]

My correction of the wording of this: At event U, in frame T1, the D clock simultaneously reads 2.5 years. At event U, in frame T2, the D clock simultaneously reads 17.5 years. The difference is not 'elapsed', but merely a declaration of which events are simultaneous with event U in the two different frames. Yes, there are 15 years difference between them. Very good. Finally, this is 'as computed by T, not as seen. At U, if T looks back at D from that distance, he 'sees' a clock reading 1.34 years, and he sees this from either frame, as that is the light from D getting to event U at that time.
In frame of D, U is 8.66 light years away. The ship departs at time 0 moving at .866c, and the light from the clock reading 1.34 'departs' at lightspeed 1.34 years later. They both get to U at the same time, so that's what T 'sees', but T computes a different time for what that clock currently reads since he knows the distance to D when the clock said 1.34, and thus the time it took for that light to get to him. That computation is quite different in frames T1 and T2, and hence the discrepancy of 15 years between them.

Fine. Let us be precise.

[David Cooper]

That is the way people naturally think, until the SR people start messing with their minds.

So, apparently, 300 years before Einstein was born, when Galileo was doing his experiments to establish the character of acceleration due to gravity and, 200 years before Einstein was born, when Newton created his laws based on such things as those experiments and the findings of Kepler and Tycho Brahe, making precise unambiguous use of the concept of acceleration, both of them were brainwashed by a theory that hadn't yet been invented. We're told that it came back in time to mess with their minds. A clever trick.

What I said remains true: it is the way people naturally think until the SR people start messing with their minds. That doesn't preclude other physicists from using words in unnatural ways before SR came along.

[David Cooper]

But when an absolute question is asked about whether something is accelerating, the answer "yes" can be misleading.

On the contrary. Acceleration is quite absolute given the physics definition. There is nothing misleading about the answer.
Velocity and speed on the other hand are relative terms, and when an absolute question is asked about something's speed, the answer has no meaning in the standard definition.

It is ambiguous when used as an answer to an absolute question - if you say something accelerates in that context, you imply that it is accelerating relative to space and reducing the relative speed at which light races away ahead of it. I always have that in mind when absolute questions are asked. SR people don't. That is the difference, and it's the SR people who are getting it wrong.

[David Cooper]

1. You stand still throughout. I move away from you and then turn around and come back. At speeds v and -v relative to the Earth frame and you.

2. You move at speed v relative to the Earth frame throughout. I move at speed 2v, then I stop and wait for you to catch up.

3. You move at speed v relative to the Earth frame throughout. I stand still for a while then start moving and catch you up by travelling at speed 2v, relative to the Earth frame.

I wasn't thinking in terms of an Earth frame - we want to eliminate the rotation, so the experiments need to be done in deep space as a space walk.

In all cases, you remain in one inertial reference frame throughout.

Throughout the first experiment, I'm at rest in the frame being used. In the other two experiments, I'm moving relative to that frame. In the third experiment, you are at rest in that frame during the first leg. Clock 3 is at rest in that frame at all times. Clock 4 is moving at v through the frame at all times.

i.e. it's a mirror image of the first two. I presume you agree with this?

It looks like one if you change frame to look at each experiment, but if you do that, you're changing the speed of light relative to clocks 3 and 4.

And this has nothing to do with the point I was making in the post to which you are replying, which is that the three experiments you describe are physically identical. But carry on.

I put in the bit about other people moving clocks and staying in inertial frames for the sake of other readers who might think the accelerations have a magic roll.

What's the hidden difference?

The speed of light relative to clocks 3 and 4 reveals an asymmetry if clock 3 is ticking faster than clock 4 (or the reverse).

Yes they have. If my clock was ticking faster than yours during the first leg of the first experiment, when we do the third experiment, your clock must be ticking faster than mine during the first leg. You deny that...

I note that whatever happens during the first leg of the first experiment must also happen during the first leg of the other two versions of the experiment, because all three experiments are physically identical. In all three cases the separations, relative velocities and accelerations of you and me are identical.

Except that they aren't physically identical - that's where you're making your error. They only look identical if you change the speed of light relative to the arena in which we're carrying out the experiments, but that's cheating.

OK, so you leave a third clock stationary relative to the Earth at your original location on the Earth.

A rotating Earth would interfere with the experiments, so we're doing this in deep space. The arena in which we're doing the experiments has clock 3 at rest in it throughout.

In the same way, during the first experiment, you were accompanied by a fourth clock on the first leg, and it kept on going when you turned back, moving at a constant speed which it maintained right through the second and third experiments. Throughout the first leg of the third experiment, that fourth clock and I were co-moving, so it was ticking at the same rate as my clock.

Ok, here's where you start to fudge things.

No - it's where you start to fudge things. If set it out with absolute clarity and precision.

You say that in the first experiment I was accompanied by a 4th clock that carried on when I turned back. If that clock also accompanies me in the first leg of experiments 2 and 3 then obviously it's not co-moving with you, is it?

Which part of "Throughout the first leg of the third experiment, that fourth clock and I were co-moving" is not correct? How could it be accompanying you in the first leg of experiments 2 and 3 when it kept going in experiment 1 when you turned back? You aren't reading carefully.

So it's not clear what you're saying here about the 4th clock. Be clear.

It's absolutely clear what I'm saying about the 4th clock.

What does the 4th clock do in experiments 2 and 3? Are you saying that this 4th clock carries on moving at speed v relative to the Earth while we both come back and do experiments 2 and 3?

It keeps on moving at v relative to clock 3 throughout the three experiments.

If so, what does that prove? Are you saying that, in each experiment, the 4th clock moves with me on the 1st leg? You can't be, because then your last sentence in the above quote would be false.

The fourth clock moves with you on the first leg of the first experiment. It keeps going, but you turn back.

This proves what I said at the start of this paragraph: if my clock was ticking faster than yours during the first leg of the first experiment, when we do the third experiment, your clock must be ticking faster than mine.

It proves nothing of the sort.

It proves exactly what I said it proves. If my clock was ticking faster than yours during the first leg of the first experiment, then your clock was ticking faster than mine during the first leg of the third experiment. This is (for rational people) an undeniable conditional truth.

You haven't been clear what this 4th clock is doing in each of the 3 experiments, and you haven't specified what you hope to demonstrate by bringing in clocks 3 and 4.

I've been fully clear about what's doing what, and I've told you exactly what clocks 3 and 4 reveal. You're just taking a long time to get your head around this kind of thinking, but it's something you need to get on top of if you want to test SR properly. What I'm doing is stopping you changing the speed of light relative to the arena between experiments. Clock 3 ticks at a constant rate throughout, and clock 4 ticks at a different constant rate throughout. In experiment 1, my clock ticks at the same rate as clock 3, and in experiment 3 my clock ticks at the same rate as clock 4. In leg one of the first experiment, your clock ticks at the same rate as clock 4, and in the first leg of experiment 3 your clock ticks at the same rate as clock 3. Every competent mathematician in the world will agree with this, and they'll also agree that if my clock was ticking faster than yours during the first leg of the first experiment, then your clock was ticking faster than mine during the first leg of the third experiment.

When you say of the 3rd clock "it was ticking at a constant rate throughout all three experiments", ticking relative to which other clocks?

It was ticking at the same rate as my clock during the whole of the first experiment, and it was ticking at the same rate as yours throughout the first leg of the third experiment.

If you don't nail the details like this, you accidentally change the proposed speed of light relative to the system without realising that you're doing so, but we need to analyse these experiments with greater rigour than that to avoid making careless mistakes.

Yes, you do need to do that. Look again carefully at the relative positions and movements of you and me in these three experiments and look at your wording as I've broken it down above. Do you see that those relative movements and positions are the same in all 3 experiments?

I've checked it again to make sure my wording was right, and it was. Clock 3 is always stationary relative to the arena in which we're doing the experiments - we never accelerate it. Clock 4 moved at v relative to clock 3 at all times - we never accelerate it either.

The 3rd and 4th clocks don't yet show anything.

They show a lot. If clock 3 is ticking faster than clock 4 during the first experiment, it is ticking faster than clock 4 during all three experiments. My clock is ticking at the same rate as clock 3 during the first experiment and your clock is ticking at the same rate as clock 4 during the first leg of the first experiment. Your clock is ticking at the same rate as clock 3 during the first leg of the third experiment and my clock is ticking at the same rate as clock 4 throughout the third experiment. How much clearer than that do I need to spell it out?

You haven't said what you mean when you say that the 3rd clock is "ticking at a constant rate", (constant relative to what?)

It is at rest in the arena where we're doing the experiments throughout - it is ticking at a constant rate because it never accelerates.

and you haven't been clear about how the 4th clock moves in each of the 3 experiments. Try again. Be precise.

I've been absolutely clear. You just need to load the experiments into your head more carefully and then process them with equal care.

Remember throughout that the only way to tell if a clock is "ticking at a constant rate" is by comparison with another clock.

The way to tell if a clock is ticking at a constant rate is to see if it's being accelerated. We do the experiment in deep space with more or less equal amounts of distant matter in all directions sitting in galaxies, so any tiny acceleration force that might be acting on the arena is too small to make any significant change to the ticking rates of clocks sitting in or moving through the arena at constant speed (relative to it).

[David Cooper]

OK, I've looked at this passage again and I think I know what you intend the 4th clock to be doing. I think you're saying that the 3rd clock stays stationary relative to the Earth throughout all 3 experiments and the 4th clock moves at speed v, to the right, relative to the Earth throughout all 3 experiments. Yes?

Yes, but we do this well away from the Earth to prevent rotation accelerating clock 3.

If so, then the following is true for all 3 experiments:

At the end of the 1st leg I accelerate, changing my speed relative to clocks 3 and 4 by 2v.

Agree?

Nearly 2v (taking into account relativistic velocity addition), although in some cases it could be exactly 2v. We're initially most interested in what this reveals about relative ticking rates during the first leg of experiments 1 and 3, before you accelerate. Further conditional truths can then be made about the relative ticking rates of the clocks after you've accelerated, but we'll get on to that once/if you can reach the point where you agree with mathematics about the first part.