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Picture a situation with clock A at the centre of a circle while clock B travels round it in circles at 0.866c. Clock B ticks at half the rate of clock A on average for lap after lap after lap, and all observers agree that it is doing so.

We can now run a bunch of other clocks along tangents to that circle and have them take turns to move alongside clock B for a short time while ticking at the same rate as clock B.

These other clocks which never accelerate and just follow straight paths likewise tick at half the rate of clock A on average

we cannot pin down which clocks are running fastest or slowest, but the fact that all those clocks on tangents tick half as fast as clock A on average tells us that some clocks do tick more slowly than others

Clock B must be ticking slower than clock A some of the time, and whenever it is doing so, the clock on a tangent to the circle which accompanies it for a short while must also be ticking at a fundamentally slower rate than clock A.

We just can't tell which clocks are ticking slower than clock A at any moment, but some of them certainly are. That is what mathematics actually tells us about this. There's a difference between symmetry of possibility and symmetry of probability.

We can point at any of the clocks moving along a straight path and say, "that could be the fastest ticking one," and it's just as possible that it is the fastest ticking one as any other of them that we might point at.

However, we can point at any of the clocks on tangents to the circle and say, "that is probably ticking at a lower rate than clock A, " and that is correct because the clocks on tangents are ticking at half the rate of clock A on average, as is proved by the fact that clock B is certainly ticking at half the rate of clock A on average.

Physicists have simply misapplied mathematics to this and come to an incorrect conclusion.

QuoteWe can now run a bunch of other clocks along tangents to that circle and have them take turns to move alongside clock B for a short time while ticking at the same rate as clock B.They would not necessarily tick at the same rate since one is inertial and the other not.

QuoteThese other clocks which never accelerate and just follow straight paths likewise tick at half the rate of clock A on averageAgain, each of these tangential clocks ticks twice as fast as A in its own frame of reference. So I bolded the statement since you seem to be talking about time relative to the preferred frame, not relative to each other.

QuoteClock B must be ticking slower than clock A some of the time, and whenever it is doing so, the clock on a tangent to the circle which accompanies it for a short while must also be ticking at a fundamentally slower rate than clock A.How is the some clock (U say, opposite T the fastest clock) running slower than clock A different than clock U running fundamentally slower than A? In other words, what does the adjective 'fundamentally' add to your statement?

Now you've introduced probability into the mix, which I've bolded since SR theory is in no way a probabilistic theory, but with the addition of your unstated premise, yes, one can speak meaningfully of the probability of one inertial frame being closer to the preferred one than another. Not very meaningfully mind you since there is no test that can affect that probability.

Mathematics says otherwise. Clock B is ticking at half rate because it is accelerating, so it isn't a candidate for 'fastest clock'.

Any of the tangential ones (let's say X this time) has equal probability as clock A, per your prior statement above. By symmetry, a clock could circle X in the same way, and clock A would become one of those tangential clocks, which you are asserting here is probably ticking slower than clock X. So now A is probably faster than X (your statement), and also probably slower than X (symmetrical logic). That's a direct contradiction.

Just because the average speed of all those tangential clocks is less than (not half, but yes, less than) clock A,...

... it doesn't imply that a random one is likely slower than A. Otherwise you could pick a random frame, abstractly spin some stuff around it, and declare the random frame to likely be more stationary than a second random frame. You've suggested no meaningful empirical test, yet logically concluded that your random choice is better than a different random choice, and by invoking symmetry no less.

QuotePhysicists have simply misapplied mathematics to this and come to an incorrect conclusion.It seems that you're the one who has done exactly this. Where exactly have physicists misapplied their mathematics, and which conclusion of theirs do you think you've shown incorrect?

Could it be their conclusion that in Minkowski spacetime, there is no empirical meaning to the premise of a preferred frame?

We have all observers agreeing that clock B ticks at half the rate of clock A on average. We have a set of T clocks which all observers agree tick at the same rate as clock B while they accompany it,

and that's an important bit you've missed: their conversation is the proof that they are ticking at the same rate and that there is no possibility of them somehow getting in enough extra ticks in anywhere to tick collectively at a higher average rate than clock B.

QuoteHow is the some clock (U say, opposite T the fastest clock) running slower than clock A different than clock U running fundamentally slower than A? In other words, what does the adjective 'fundamentally' add to your statement?The "fundamentally" is there to make the point that there have to be some T clocks which are ticking at a lower rate than clock A

How is the some clock (U say, opposite T the fastest clock) running slower than clock A different than clock U running fundamentally slower than A? In other words, what does the adjective 'fundamentally' add to your statement?

because there have to be times when clock B is ticking at a fundamentally lower rate than clock A

This is where people get the maths wrong.

We have a certainty here that clock B ticks at a lower rate than clock A some of the time. That certainty has ramifications which lead to the necessary involvement of probabilities. If you select a T clock at random, it is probably ticking slower than clock A.

We can take that T clock and make it the central clock of another system of clocks in which it serves as a clock A, and if we do that, clock A in the original set serves as a T clock in the new system. If you pick a T clock at random in the new set, that clock is probably ticking at a lower rate than the central clock of that system

This is mathematicians' mathematics rather than physicists' mathematics. Physicists don't do mathematics in full, so they miss important things.

It's most certainly half.

Quote and that's an important bit you've missed: their conversation is the proof that they are ticking at the same rate and that there is no possibility of them somehow getting in enough extra ticks in anywhere to tick collectively at a higher average rate than clock B.Wrong.

Your mathematics is faulty, mostly because you’ve not actually shown any of the mathematics and you’re guessing incorrectly at the result.

It isn’t known, so the distribution of your measurement points similarly cannot be objectively determined.

I want verification of what ‘tick collectively at a higher rate’ means. I assume you mean adding the ticks of n clocks and dividing by n, but if all of them are bunched preferentially on the fast or slow side of the non-circular circuit as you are suggesting, I can make that average be above or below the total ticks for B in one circuit, in contradiction of your claim to the contrary above.

So you meant nothing by that except emphasis. Italics would have said it better.

QuoteThis is where people get the maths wrong.I’m pointing where you your guesses do not match the maths. If you were to actually do said maths, I could point out the error more specifically, but you’ve not actually shown any.

Again, this makes sense only with your additional premise which introduces said probabilities. SR has none, and your statement, lacking frame references, makes no sense at all under SR. Hence my pointing out that probabilities are only meaningful (ish) in your model, not everybody else’s.

QuoteWe can take that T clock and make it the central clock of another system of clocks in which it serves as a clock A, and if we do that, clock A in the original set serves as a T clock in the new system. If you pick a T clock at random in the new set, that clock is probably ticking at a lower rate than the central clock of that systemClearly wrong. You suggest a symmetry, and yet you suggest an asymmetry, contradicting yourself, which shows that it’s probably good to look closer.

In this case, a random clock chosen relative to A (assuming A is stationary) is probably one of the closely-spaced clocks on the actually-slow side of the circuit, so T is indeed ‘probably slower’ than A, but that makes A on the fast side of the T clock and thus less likely to be chosen as a random tangential clock about T.

QuoteThis is mathematicians' mathematics rather than physicists' mathematics. Physicists don't do mathematics in full, so they miss important things.I’m pointing out the things being missed, and it isn’t the physicists missing them. The theory would have fallen apart long ago if it wasn't mathematically consistent.

QuoteIt's most certainly half.… says the guy biasing the average by bunching most of the samples on the slow side. Don’t be so certain of things. You cannot learn if you’re not open to being mistaken.

is this related to the expansion of the Universe?

Not so. Each T clock passes a virtual baton to the next while they are at the same location, so we know exactly how many times they've ticked for their leg of the trip. We can count up all the ticks for all those legs and it comes to the exact same number of ticks as the circling clock on its lap. This is something which any maths teacher looking at it would confirm.

It never ceases to amaze me how people can fail to recognise correct mathematics as correct mathematics. I don't guess: I calculate and prove.

Make it a regular polygon in the frame in which the central clock is at rest

I assumed you'd picture it that way rather than taking all the clocks at one side and halving the leg they do so that you can put extra clocks in there to bias the results.

The issue is with whether physics is about reality or voodoo. Reality says that some clocks are certainly ticking at a lower rate than others, even in cases where no acceleration is involved.

If STR has any relevance to reality, it has to follow the rules of reality and not break them at every turn.

You've misinterpreted it and got it wrong as a result. You're loading it with a bias and you're failing to recognise that you have done so. My point was that if you choose that original T as the new A in such a way that this T is the first clock you consider, then the status of whichever of its T clocks you randomly select will be that it is probably ticking at a lower rate than the A clock.

That's a case where such a bias in favour of my argument has to be balanced to remove its bias, just as there are ways of looking at this which put a bias your way which must likewise not be allowed to interfere with the conclusion. When you remove the biases of that kind, perhaps by biasing the selection process to cancel out the original bias (so that a clock moving faster relative to the system [which means slower through space and ticking faster] is more likely to be selected), you still have a probability that the randomly chosen clock is ticking at a lower rate.

A better way to deal with that bias though is to restate the claim to say that if the randomly chosen clock isn't ticking at half the rate of the central clock, then it is equally probable that it is ticking faster than half the rate of the central clock as that it is ticking slower than half the rate of the central clock.

There are all sorts of time-wasting games that you can play with such biases to try to derail a correct argument, but the important fact is that in all frames the T clocks are ticking on average at half the rate of the central clock and that the most probable ticking rate for a randomly chosen T clock will be half that of the central clock. That's maybe the best way to phrase it as it avoids any possible bias.

QuoteIt never ceases to amaze me how people can fail to recognise correct mathematics as correct mathematics. I don't guess: I calculate and prove.No numbers in any post so far, so hard to comment on what calculations you are doing.

QuoteMake it a regular polygon in the frame in which the central clock is at restBut this would actually be an irregular polygon.

Your maths should include frame translations to some hypothetical preferred frame, which the B clock probably never becomes even momentarily stationary no matter how fast you spin it around.

QuoteThe issue is with whether physics is about reality or voodoo. Reality says that some clocks are certainly ticking at a lower rate than others, even in cases where no acceleration is involved.Your biases are showing. I’d have agreed if you were talking about the average rate of B vs A, but you didn’t specify that, so without your additional premises, the statement is not even wrong.

QuoteIf STR has any relevance to reality, it has to follow the rules of reality and not break them at every turn.Reality is not necessarily your view of reality.

As I said above, in actual reality, all one has to do is look out the window to determine the cosmological frame, which is most often proposed as being this preferred frame despite it not being an inertial one. There are problems with that which prevent me from accepting the needless premise, but it often suffices for those with the need for such a thing. The lack of it defining an absolute time is one of those problems.

Show the maths please. Maybe, but this seems unlikely. Haven’t run those numbers myself, but I think I see what you’re saying. It’s not like the B clock is actually moving on any polygon in reality, but rather a squashed helix of sorts. We can divide up the circuit into equal chunks of real time (by some secret mechanism privy to the absolute frame).

I think I’ve lost track of exactly what the goal of the exercise is. The way I suggested dividing it up (equal time segments) would seem to result in a probability of even less than 50% of the central clock rate.

QuoteA better way to deal with that bias though is to restate the claim to say that if the randomly chosen clock isn't ticking at half the rate of the central clock, then it is equally probable that it is ticking faster than half the rate of the central clock as that it is ticking slower than half the rate of the central clock.Can you show that? My gut says most will be less than 50%, but again, a lot depends on how the choices are determined. I should write a little program, since these sorts of assertions are easily tested.

They’ll all be ticking at a different rate, so how can any one rate be more probable than another one? The odds of randomly hitting a clock at exactly 50% rate is zero, but likewise for any other specific rate, so I think you need to qualify your statement more clearly.

It's really very simple: each of the clocks on tangents spends the same number of ticks as each of the others when doing its leg of the relay race. That isn't arbitrary.

There are no biases in what I said there: the clocks in question are following straight paths at constant speed, and some of them are certainly ticking at a lower rate than the central clock

The absolute frame of relevance is the local absolute frame in which light travels at c in all directions relative to an object at rest in that frame. That is the one I'm working with here.

QuoteI think I’ve lost track of exactly what the goal of the exercise is.The point is to look at the asymmetry of probability.

I think I’ve lost track of exactly what the goal of the exercise is.

If we have clock A as the stay-at-home twin, clock B as the travelling twin, clock C moving to the right and clock D moving to the left, then we use clock B like the circling clock to prove that either clock C or clock D must be ticking at a lower rate than clock A.

On average, clocks C and D tick at half the rate of clock A.

If we start with clock A and then pick randomly between clocks C and D, we will probably choose a clock that's ticking at a lower rate than clock A.

There are as many possible cases where clock C is ticking faster than clock A as there are possible cases where clock D is ticking faster than clock A, but there are extra possible cases where clock A is ticking faster than both clock C and clock D.

Quote... if the randomly chosen clock isn't ticking at half the rate of the central clock, then it is equally probable that it is ticking faster than half the rate of the central clock as that it is ticking slower than half the rate of the central clock, but again, a lot depends on how the choices are determined.Can you show that? My gut says most will be less than 50%...

... if the randomly chosen clock isn't ticking at half the rate of the central clock, then it is equally probable that it is ticking faster than half the rate of the central clock as that it is ticking slower than half the rate of the central clock, but again, a lot depends on how the choices are determined.

The fastest ticking clock is arguably over-represented in that it's involved for the shortest length of time. The straight line, four clock alternative scenario is easier to handle as there's no room for such biases.

If you have eight clocks, you can pick a pair such as 1&5, 2&6, etc. and be sure that picking one of that pair at random will probably lead to you choosing a clock that ticks at a lower rate than the central clock.

I still probably haven't found the right wording for a scenario with all the biases removed, but there will be one. It's much easier just to save a lot of time though and use the alternative case where all the action takes place along a straight line.

QuoteThere are no biases in what I said there: the clocks in question are following straight paths at constant speed, and some of them are certainly ticking at a lower rate than the central clockThat’s a bias, just to point one out. Relative to any given clock, the central one is not ticking faster. The bias is the assumption that there is an actual tick rate, without which the frame-ambiguous statement above is not meaningful. I’m not saying it’s necessarily wrong, but I’m saying it’s a bias of yours to which I’ve become accustomed. All your proofs seem to rely heavily on this assumption, so any inconsistency you find is probably evidence against this new assumption.

QuoteThe absolute frame of relevance is the local absolute frame in which light travels at c in all directions relative to an object at rest in that frame. That is the one I'm working with here.Why local?

You’re the one that says LET maintains Euclidean geometry, which sounds like you meant Minkowskian. Are you saying the absolute frame does not order all events in reality, only the local ones? Didn’t you say that any theory should be discarded if it isn’t a model of the universe? I don’t agree with that, but here you are pushing something that only works locally and then turning around and rejecting the validity of SR when it doesn’t describe the entire universe (something it never claims to do).

QuoteIf we have clock A as the stay-at-home twin, clock B as the travelling twin, clock C moving to the right and clock D moving to the left, then we use clock B like the circling clock to prove that either clock C or clock D must be ticking at a lower rate than clock A.Taken as an absolute statement, it seems wrong. C could be moving at .1c left, D at .1c right, and A moving at .2c in any direction since it is completely unspecified above. So I cannot agree.

Taken as a statement relative to the assumed frame in which A is stationary, A by definition is stationary, and any clock in motion in any direction relative to that frame is going to tick slower relative to the A clock. The speeds and direction don’t matter. So it is true pretty much by definition, without need for all the extra details.Taken any other way and you’re mixing frames without explicit references, and the whole scenario is meaningless. Try again, but with care to say it precisely.

B isn’t described well at all in your statement, but I assume B is going left-right relative to A and not some other direction. He’s got 3D of directions from which to choose after all.

The point was to demonstrate asymmetry of probability. Have yet to see mention of that.

Assuming C and D are moving at .866c relative to A (you didn’t say it), then they’re both ticking at half rate relative to frame A and there's no average or probability involved.

Relative to an arbitrary frame, this isn’t so. Let’s suppose for simplicity that C is stationary. Relative to that frame, A is ticking at 0.5, C at 1.0 and D (moving at .99c) ticks at at a rate of 0.14 for a C-D average of 0.57 which is actually higher than the A rate of 0.5, not half of it.Did you even get out a calculator? This is what I mean about you guessing.

So ‘calculate and prove’ means guess, and incorrectly at that. I can’t call it incorrect mathematics because I didn’t see any, rigorous or otherwise.

QuoteIf we start with clock A and then pick randomly between clocks C and D, we will probably choose a clock that's ticking at a lower rate than clock A.No frame reference again.

Hand waving and talking of biases aside, you’ve not shown what I asked. What does ‘involved in the action’ mean?

From A’s viewpoint, why would any clock arranged evenly in a circle be ‘represented’ more than another? It’s faster than the threshold absolute speed or not. There’s nothing else to it.

I thought you were choosing a ‘random clock’, which from frame A sounds like a choice of completely arbitrary direction to for .866c of velocity. Correct me if you mean something else by your words.

Still, my gut is moved after thinking about it. I think it is 50%. I thought of a little proof. I’m willing to accept the statement, despite your lack of rigorous demonstration of it. I’ll share the thinking if you don’t want to give it a shot yourself. Your guesses are not always wrong.

You still haven’t demonstrated ‘asymmetry of probability’.

Because the universe is expanding, so the absolute frame shifts as you move around.

The absolute one (which we should maybe call the local absolute frame)

is the [frame] in which the an object is at rest in if light moves at c in all directions relative to it (or at a reduced speed locally measured as c, if we take into account gravity wells slowing light).

QuoteQuoteIf we have clock A as the stay-at-home twin, clock B as the travelling twin, clock C moving to the right and clock D moving to the left, then we use clock B like the circling clock to prove that either clock C or clock D must be ticking at a lower rate than clock A.Taken as an absolute statement, it seems wrong. C could be moving at .1c left, D at .1c right, and A moving at .2c in any direction since it is completely unspecified above. So I cannot agree.You can assign any speeds you like and it will remain correct, once you take into account that B moves at the same speed as C (and in the same direction) during one leg of its trip, and then at the same speed and direction as D during the other leg.

C and D are forced to tick at the same rate as B, one on each leg of B's trip, and that forces one of them to tick at a lower rate than A too.

To have it tick at a faster rate you have to change frame, but that means changing the speed of a light pulse (travelling through the system along the line all the action takes place on) relative to the clocks, so it's you that mixes frames when you try to have your cake and eat it.

I referred to it as the straight-line case because all the action takes place along that line. …If you pick a clock randomly from C and D, the odds are that you have picked a clock that's ticking slower than clock A.

because you're making a mathematically illegal move every time you mix frames

QuoteQuoteIf we start with clock A and then pick randomly between clocks C and D, we will probably choose a clock that's ticking at a lower rate than clock A.No frame reference again.That's because it's all frames of reference being considered here: the whole lot of them collectively.

You're taking a random speed for clock A and choosing randomly between clock C and clock D to compare with it. Do that with a large enough sample and you will choose more cases where clock A is ticking faster than your chosen clock than the opposite.

QuoteYou still haven’t demonstrated ‘asymmetry of probability’.I did in the previous post, and again here: go up three answers.

The fact that won't be overturned by any tinkering with biases is that there are as many possible cases where clock C is ticking faster than clock A as there are possible cases where clock D is ticking faster than clock A, but there are extra possible cases where clock A is ticking faster than both clock C and clock D. That's the only thing you need to consider to see the asymmetry in the probabilities: in a large enough sample size of cases when you choose a random clock C or D to compare with their clock A, you will more likely choose a clock that's ticking at a lower rate than that clock A. We can discard all the other stuff about this in the discussion about the probabilities as none of them can override this no matter how much they're biased.

Quote from: David Cooper on 20/02/2021 06:07:06Because the universe is expanding, so the absolute frame shifts as you move around.Then it would be a curved frame, not a different frame. There can only be one objective ordering of events in the universe. If you deny that, then you’re pushing something not absolute. If said ordering does not correspond to an inertial frame of reference, so be it.

Quote is the [frame] in which the an object is at rest in if light moves at c in all directions relative to it (or at a reduced speed locally measured as c, if we take into account gravity wells slowing light).And this of course is a lousy definition since light moves at c relative to the inertial frame in which any object is a rest. Your definition should not be relative to anything, and I would suggest the wording mentioning the objective ordering of all events. Maybe not. There’s no way to demonstrate that light moves locally at c relative to any such frame, only a subset of such orderings.

Imagine two objects moving at 0.5c relative to each other along a straight line. We introduce a pulse of light which moves along the same line at c relative to the first object. The speed of that light is 0.5c or 1.5c relative to the second object (depending on which direction along the line that object is moving in). STR denies that measurement and insists that the correct relative speed for the light and second object is c, but if the relative speed of the light to both objects is c, the two objects cannot be moving at 0.5c relative to each other: their relative speed to each other would have to be zero.What’s going on here? Well, Einstein bans you from accepting some measurements between light and objects that travel at lower speed than c. He requires you to change frame to make the second object stationary, and only then will he accept the relative speed for the light and that object. In that new frame, the relative speed between the light and the first object is now 1.5c or 0.5c, but again he bans you from accepting that measurement. So, he mixes frames to get the two measurements which he wants to make so that they conform to his theory, and he rejects all measurements that disagree with his ideology. In the course of changing frame, he changes the speed of the light relative to both objects. In doing so and mixing frames, he is making an illegal mathematical move.

QuoteYou can assign any speeds you like and it will remain correct, once you take into account that B moves at the same speed as C (and in the same direction) during one leg of its trip, and then at the same speed and direction as D during the other leg.I gave an example where the statement was wrong.

You can assign any speeds you like and it will remain correct, once you take into account that B moves at the same speed as C (and in the same direction) during one leg of its trip, and then at the same speed and direction as D during the other leg.

So yea, I think I know the scenario you have in mind, but your wording is so inconsistent (mixing absolute and relative references) that it’s not even wrong.

QuoteC and D are forced to tick at the same rate as B, one on each leg of B's trip, and that forces one of them to tick at a lower rate than A too.Assuming your additional premise, agree. Assuming (omitted) relative references, the statement is meaningless because tick rates are a frame dependent.

I’ll have to keep saying things like this because you refuse to state your bias, which is something like: “Premise: There is a preferred ordering of all events relative to which all unqualified temporal statements are measured”.Without that or something equivalent, the unqualified statements are meaningless. If you make the statement above, it becomes an acknowledged premise, and not an unstated bias.

QuoteTo have it tick at a faster rate you have to change frame, but that means changing the speed of a light pulse (travelling through the system along the line all the action takes place on) relative to the clocks, so it's you that mixes frames when you try to have your cake and eat it.And there’s the bias in all its color. I was wondering when you’d finally word it this way.

You seemingly have either zero grasp of the principle of relativity, or you’re deliberately trolling. In the latter case, yes, this is why your threads end up in the lighter-side.

In the case with all the action taking place in a straight line, the odds are even (one faster, one slower) except in the case where A is already nearly stationary. Hence my clarifying about the directions from which the choices can be made. The odds are even in a 1D case.

QuoteSee my previous answer: there are more cases in which a random choice will lead to a clock ticking at a lower rate being selected than there are for a higher rate being selected.You said this about clocks C and D, not about some B going back and forth. Pick any random direction. Only in the impossibly improbably case that they go exactly perpendicular (relative to A) to the absolute motion of A will the average between them be as low as half of A. In every other case, the average of the two is higher. Try it in any direction. Oh wait, you don’t actually do any mathematics.

See my previous answer: there are more cases in which a random choice will lead to a clock ticking at a lower rate being selected than there are for a higher rate being selected.

Quotebecause you're making a mathematically illegal move every time you mix framesWant me to count all the times you mix frames without references?

Hence all the meaningless statements above.

You talk about A having some absolute velocity and then C and D going off in opposite directions, which is a frame change since they’re moving in opposite directions only in one frame, and it isn’t the one you used before.

It isn’t mathematically illegal, but the references need to be there so the correct transformations can be applied.

QuoteQuoteQuoteIf we start with clock A and then pick randomly between clocks C and D, we will probably choose a clock that's ticking at a lower rate than clock A.No frame reference again.That's because it's all frames of reference being considered here: the whole lot of them collectively.The tick rate is frame dependent, so it can’t be relative to all of them at once.

QuoteYou're taking a random speed for clock A and choosing randomly between clock C and clock D to compare with it. Do that with a large enough sample and you will choose more cases where clock A is ticking faster than your chosen clock than the opposite.Assuming your bias, agree, but I’ve agreed to that long ago.Without the assumption, the statement is meaningless.

I presume this is perhaps the 3D case where C and D are random but opposite directions relative to A. You don’t say this, so let me know if I’m wrong about it.

QuoteThe fact that won't be overturned by any tinkering with biases is that there are as many possible cases where clock C is ticking faster than clock A as there are possible cases where clock D is ticking faster than clock A, but there are extra possible cases where clock A is ticking faster than both clock C and clock D. That's the only thing you need to consider to see the asymmetry in the probabilities: in a large enough sample size of cases when you choose a random clock C or D to compare with their clock A, you will more likely choose a clock that's ticking at a lower rate than that clock A. We can discard all the other stuff about this in the discussion about the probabilities as none of them can override this no matter how much they're biased. You’re saying that given a small relative velocity change in a random direction relative to a fast moving object A, the change will more often than not result in a speed greater than the original speed of A. Yes, that’s true. I think to make the odds even, you’d have to choose a random absolute direction for your acceleration vector, not a random direction relative to A.

It’s not asymmetrical.

There’s symmetry to it. Picture a golf ball with a sand grain in each of the pits. The ball is moving at relativistic speed to our preferred frame and explodes, sending the grains at moderate speed in an even distribution of directions relative only to A. Most of the grains will be going faster relative to the preferred frame, but the line dividing the faster ones from the slower ones will be a neat symmetrical circle covering say 1/4th the area of the golf ball (the area depends on the speed of A and the relative speed at which the grains are ejected). It’s completely symmetrical, not some weird wavy border between the slower ones and the faster ones.

You're creating some other kind of frame by doing that and it is not an absolute absolute one either

When I refer to absolute speeds here, those are speeds relative to the local space fabric given in proportion to that local speed of light.

Light is merely hypothesised as moving at c relative to that object for that frame

I didn't mix anything - you simply failed to interpret it the way it was intended to be understood.

QuoteAssuming (omitted) relative references, the statement is meaningless because tick rates are a frame dependent.It refers to all frames, so it's the opposite of meaningless.

Assuming (omitted) relative references, the statement is meaningless because tick rates are a frame dependent.

QuoteIn the case with all the action taking place in a straight line, the odds are even (one faster, one slower) except in the case where A is already nearly stationary. Hence my clarifying about the directions from which the choices can be made. The odds are even in a 1D case.No maths teacher would agree with you there. C is slower than A in more than half of all possible cases.

None. I never mix frames at all....Obviously that refers to them moving in opposite directions relative to A.

The fact that C and B's ticking rates are dependent on B's ticking rates is also frame independent.

Any frame you choose, and you're getting an infinite number of free choices from all possible frames, if after making your choice you pick randomly between C and D you will probably choose a clock that's ticking at a lower rate than A. No amount of irrelevant objections can overturn that fact.…That B ticks half as often as A is an established fact agreed on by all observers, and that constrains the possible ticking rates of C and D in a manner which means that a random choice of frame followed by a random choice of C or D will probably lead to you selecting a clock that's ticking slower than A. You're not going to be able to break that.

QuoteIt’s not asymmetrical.For it to be symmetrical it would also have to be the case that that A would probably be ticking slower than your randomly chosen clock (C or D), but that is not also the case.

Quote from: David Cooper on 22/02/2021 05:01:00You're creating some other kind of frame by doing that and it is not an absolute absolute one eitherI’m not creating anything. I’m trying to understand what you think you’re creating, and you’re essentially saying.

You criticize SR by only describing spacetime sufficently local to approximate Minkowskian spacetime, for not being a model of the universe, but then you go on and do the same thing for your idea, which is contradicting yourself.

Do you or do you not agree that a premise of absolute time requires an absolute ordering of all events in the entire universe? If so, you still don’t know what that ordering is, or for that matter, if it corresponds locally to an inertial frame. I can think of some models where it doesn’t.

You also are chronically mixing proper time, coordinate time, and absolute time (and associated speed/velocity), to the point where none of your comments are clear, which I think is deliberate on your part since obfuscation seems to be one of your goals.

I’ll give you a clue then since you think it doesn’t concern you: Absolute time is infinitely fast (relative to any clock), and thus all absolute velocity is zero. It is easily shown even in Newtonian mechanics that the gravitational potential of an infinite uniform distribution of matter in 3D (or even 2D or 1D) is infinitely negative. The universe’s absolute age is thus infinite regardless of coordinate system of choice, and thus useless for any comparisons.

QuoteWhen I refer to absolute speeds here, those are speeds relative to the local space fabric given in proportion to that local speed of light.That would not be absolute speed, but rather coordinate speed relative to your coordinate system (unspecified) as measured by a clock at some unspecified relative potential. See the difference? I’m willing to talk about coordinate speed, except you refuse to propose a coordinate system, or at least the nature of it even if it cannot be known.

QuoteLight is merely hypothesised as moving at c relative to that object for that frameStrawman. Try quoting the actual premise.

QuoteIt refers to all frames, so it's the opposite of meaningless.Then we cannot communicate, because relative tick rates are very much frame dependent and you did not specify that we were not using relative rates. See the pattern? Specify when you’re using coordinate tick rates and not relative tick rates. Be the physicist for a moment, and not the layman.

It refers to all frames, so it's the opposite of meaningless.

There are only two choices for acceleration in the 1D case: this way or that. One of them slows you down, the other speeds you up. What misfortune of a maths teacher have you had, that he would disagree?

Relative to A, when the absolute references were used elsewhere in the same description. That’s mixing frames. ‘Obviously’ doesn’t cut it. State the frame reference when you reference more than one in a description. Mixing frames is fine. Doing so without reference is not.

QuoteThe fact that C and B's ticking rates are dependent on B's ticking rates is also frame independent.They don’t depend on B at all. They’d not tick at a different rate (relative to any frame) if B were not there.

Relative to an unknown arbitrary frame, C and D are not moving in opposite directions, but are probably both moving in a direction similar to A, so acceleration in those directions is bound to result in a faster velocity than A (for both of them). It’s no big surprise that such acceleration in a non-random direction will result in faster speed relative to said unknown arbitrary frame.

OK, it’s asymmetrical as defined that way. The choice of C and D are not random, but probably both pointed in the direction of motion relative to the unknown frame, so this is to be expected. For the direction relative to the unknown frame to be random, the selected velocity change needs to be made relative to the unknown frame, not relative to A. If you did that, then the tick rate of your randomly selected C would have a 50/50 shot at being faster or slower than A, again, assuming that A is moving faster than our selected speed difference of C and D. If A is already nearly stopped (probability zero), then acceleration in any direction will result in a faster speed.

This works for any selection of unknown frame, so the symmetry is completely preserved.

So what do you think you’ve demonstrated by this probability upon which we agree? Can you determine the absolute frame by repeated experiment? You have nobody taking a measurement of anything in your scenario, so probably not.

it is sufficient here to restrict the idea of the absolute frame to the local one in which the speed of light is c relative to the local fabric.…The only part of the idea of an absolute frame that matters here is that it supports local absolute speeds relative to the space fabric.

Whenever you pick the time of a particular frame, that is a coordinate time and a clock at rest in that frame has its proper time tick out coordinate time.

QuoteAbsolute time is infinitely fast (relative to any clock), and thus all absolute velocity is zero. It is easily shown even in Newtonian mechanics that the gravitational potential of an infinite uniform distribution of matter in 3D (or even 2D or 1D) is infinitely negative. The universe’s absolute age is thus infinite regardless of coordinate system of choice, and thus useless for any comparisons.That is mere philosophy and not physics.

Absolute time is infinitely fast (relative to any clock), and thus all absolute velocity is zero. It is easily shown even in Newtonian mechanics that the gravitational potential of an infinite uniform distribution of matter in 3D (or even 2D or 1D) is infinitely negative. The universe’s absolute age is thus infinite regardless of coordinate system of choice, and thus useless for any comparisons.

They have been referred to as absolute speeds throughout the history of physics.

QuoteQuoteLight is merely hypothesised as moving at c relative to that object for that frameStrawman. Try quoting the actual premise.What I said is 100% correct.

It's a shortcut in a description which a few years ago wouldn't have caused you any difficulty.

QuoteQuoteThe fact that C and B's ticking rates are dependent on B's ticking rates is also frame independent.They don’t depend on B at all. They’d not tick at a different rate (relative to any frame) if B were not there.(Typo in the bit I wrote: should have been "C and D" rather than C and B.)

They do depend on B's ticking rate because they each travel alongside B for a while and tick at exactly the same rate as B while they do so, and they never change that rate of ticking at all - only B changes its ticking rate.

QuoteRelative to an unknown arbitrary frame, C and D are not moving in opposite directions, but are probably both moving in a direction similar to A, so acceleration in those directions is bound to result in a faster velocity than A (for both of them). It’s no big surprise that such acceleration in a non-random direction will result in faster speed relative to said unknown arbitrary frame.Again, acceleration and faster speed is irrelevant: I don't know why you keep dragging it in there. There's a random choice being made between C and D which doesn't change any of the action.

There are two random choices being made. The first is to select a random A out of an infinite number of possible ones, and the next choice is between that A's C and D friends.

The symmetry is not preserved: you can make a billion random choices of which A to use, and more than half of them will lead to A ticking faster than the randomly selected C and D for the chosen A.

The point is that while there is a symmetry of possibility, there is not a symmetry of probability.

Even that symmetry of possibility breaks down though in an expanding universe though.

Quote from: David Cooper on 24/02/2021 04:33:03it is sufficient here to restrict the idea of the absolute frame to the local one in which the speed of light is c relative to the local fabric.…The only part of the idea of an absolute frame that matters here is that it supports local absolute speeds relative to the space fabric.Ohh, I like how you mix absolute and relative in the same sentences. What if the local fabric isn’t stationary (so called aether-wind)? The the light would have a different absolute speed if it was c relative to the moving fabric.

QuoteWhenever you pick the time of a particular frame, that is a coordinate time and a clock at rest in that frame has its proper time tick out coordinate time.Not so, since I can have two clocks both stationary relative to the same frame, and they tick at different rates.

It's unassailable mathematics. Show where the maths allow otherwise.

Told you you wouldn’t like it. No, I don’t have absolute time in my models precisely because such a premise leads to this kind of problem.

No clock can be put at zero gravitational potential of course since there’s nowhere in the universe that hasn’t got matter all around it. You need a king clock. “How do you know it’s king? A: It’s the only one that hasn’t got sh1t all around it”.

You still need an arbitrary choice of location to put your clock that measures ‘absolute time’ since picking one at zero gravitational potential leads to the above unworkable results. Is it Earth then? Don’t mind light moving at an absolute speed faster than c from here to the moon and back?

QuoteQuoteQuoteLight is merely hypothesised as moving at c relative to that object for that frameStrawman. Try quoting the actual premise.What I said is 100% correct.Quote Einstein then, not some children’s textbook.

You assert that if B were not there, then the tick rates of C and D (relative to any given frame, presumably the absolute one) would be different?

That seems to be what you’re asserting, but I want to make sure. C and D would tick no differently relative to a given frame if they lacked a momentary traveling companion.

Can you demonstrate a way to determine the absolute frame from this or some other observation that occurs only when one of C or D happen by chance to actually be going slower?

If not, then the symmetry is perfectly preserved in my book since empirical physics behaves identically for all random choices.

You think that given an arbitrary reference frame to measure tick rates, that C should have an even shot of being faster or slower than A? Just not true given our laws of physics. That only works (almost works actually) under Galilean relativity and Galilean transforms.

QuoteEven that symmetry of possibility breaks down though in an expanding universe though.The above discussion has nothing to do with expansion.

Given observation of the expansion, there’s only one coordinate system (not an inertial frame) where the rate of expansion is the same everywhere at a given time. For some reason, you resist this obvious choice for an absolute foliation of spacetime.

QuoteIt's unassailable mathematics. Show where the maths allow otherwise.It would only be physics if there was an infinite uniform distribution of matter

(or the expansion cuts off the ability of the mass that's beyond range of detection to influence space here):

nothing would have been able to happen to get things into the state it's in now.

You can simply calculate on the basis of what's close enough to affect us here - if the light is never going to get here because of the expansion of space between us and that stuff, its no longer has any power to slow our clocks.

Any theory that says our time is running infinitely slow compared to that king clock is wrong.

Mathematics dictates that light is merely hypothesised as moving at c in every direction relative to an object that's at rest in a chosen frame.

What happens? You've frozen the action, but when you change frame, events unhappen, and when you change back again they rehappen, over and over again.

QuoteQuoteThe fact that C and B's ticking rates are dependent on B's ticking rate ...…They do depend on B's ticking rate ... You assert that if B were not there, then the tick rates of C and D (relative to any given frame, presumably the absolute one) would be different?I haven't made any such assertion.

QuoteThe fact that C and B's ticking rates are dependent on B's ticking rate ...…They do depend on B's ticking rate ... You assert that if B were not there, then the tick rates of C and D (relative to any given frame, presumably the absolute one) would be different?

The fact that C and B's ticking rates are dependent on B's ticking rate ...…They do depend on B's ticking rate ...

We're simply replacing the A and B twins paradox with an A, C and D clocks paradox

If you try to have as many As tick faster than their C than as there are Cs which tick faster than their A, you'll find that you necessarily have more As tick faster than their D than there are Ds which tick faster than their A.

This applies to our actual universe.

QuoteGiven observation of the expansion, there’s only one coordinate system (not an inertial frame) where the rate of expansion is the same everywhere at a given time. For some reason, you resist this obvious choice for an absolute foliation of spacetime.That doesn't tell you how fast the content of space might be moving through space.

It could all be going that way (I'm pointing at Polaris) at 10% the speed of light relative to the fabric

I don't see how that would make the apparent rate of expansion different in different directions.

For any content of space that's at rest relative to the fabric, it should look to its observers as if the expansion is even in all directions too.

The only disagreement (if none of them has run an experiment that can pin down actual speeds through the fabric) would be on how old the universe is.

...a figure that would be meaningless if there was not a uniform distribution of matter as you seem to suggest.

...but it seems to rely that gravity is something that travels and that the potential is something that radiates away. Gravity waves do travel like that, but a gravitational field, by definition, is just a description of what is already there.

Quotenothing would have been able to happen to get things into the state it's in now.This assumes a finite rate for absolute time (a singularity) and a choice of coordinate system in which such singularities necessarily exist. It’s a similar argument to one asserting that nothing can fall into a black hole, which makes it difficult for the guy who’s done so to explain his presence beyond the event horizon. The better answer is to simply use a different coordinate system in which such singularities don’t exist. The failure of one coordinate system to describe a situation doesn’t imply that the situation (falling into a black hole) cannot take place.

QuoteAny theory that says our time is running infinitely slow compared to that king clock is wrong.Non-sequitur, which is good news for you, else your theory is wrong.

If our time is running infinitely slow relative to a clock that runs infinitely fast relative to us, that’s just a circular relation, not something necessarily wrong.

Again, I can bring up the clock at the black hole event horizon to illustrate that. That clock runs at an infinitely slow coordinate rate, but that doesn’t affect the guy falling in, who notices nothing amiss as he crosses over. The conclusion that the theory is wrong just doesn’t follow, and hence I’m not asserting that your theory is necessarily wrong just because of this relation.

If time stops at the horizon of a black hole, how can a black hole orbit anything? Wouldn’t that require anything stuck near the horizon to move large distances in zero time? It simply isn’t a contradiction for one clock to run infinitely faster than another relative to a given coordinate system.

QuoteMathematics dictates that light is merely hypothesised as moving at c in every direction relative to an object that's at rest in a chosen frame.Mathematics says no such thing since there is no light in mathematics.

Reference to light is physics, and the mathematics is only what can be derived from the premises of a physical theory.

SR does not list the premise you quote above, so the mathematical implication of the premise is irrelevant to the theory.

You want to bash SR, then use the premise as worded.

QuoteWhat happens? You've frozen the action, but when you change frame, events unhappen, and when you change back again they rehappen, over and over again.Your choice of simulation assumes additional premises not even assumed by LET, but only nLET. Lorentz never posited a preferred moment in time. The theories that do are commonly grouped under neo-Lorentz-Ether-Theory.

We’ve been over this before. I know you also assert this 4th premise. You use it to demonstrate an inconsistency in a theory that doesn’t posit it.

QuoteQuoteQuoteThe fact that C and B's ticking rates are dependent on B's ticking rate ...…They do depend on B's ticking rate ... You assert that if B were not there, then the tick rates of C and D (relative to any given frame, presumably the absolute one) would be different?I haven't made any such assertion.I put the quotes back that seem to suggest otherwise, but OK, just checking.

QuoteIt could all be going that way (I'm pointing at Polaris) at 10% the speed of light relative to the fabricNo it cannot. The expansion if the universe would be different everywhere if our motion was that way. It’s fine if you allow the universe to expand higher and higher rates in one direction and consistently lower rates in the other, but if you suggest that it should be the same everywhere at a given moment in time, then there’s only one choice of coordinate systems, and relative to that coordinate system, we’re not moving north at .1c.

QuoteI don't see how that would make the apparent rate of expansion different in different directions.Then trust those that understand frame translations. I can’t make you learn the mathematics.

It's the word "infinite" in "infinite uniform distribution of matter" that's in question

Any theory that runs time and advances events must conform to this approach of analysis if it is to be valid.

Quote from: David Cooper on 28/02/2021 07:59:33It's the word "infinite" in "infinite uniform distribution of matter" that's in questionSo LET suggests a bounded model of the universe? Does it have an ‘edge’? I was unaware that it was in denial of the cosmological principle.

So anyway, I asked about the gravitational depth thing, and it turns out that we’re both wrong on the issue. The idea of absolute gravitational potential is not meaningful at all in the geometry of our universe. Neither SR, GR, LET etc describe the geometry of the universe, they only describe the physics.

QuoteAny theory that runs time and advances events must conform to this approach of analysis if it is to be valid.Possibly so, but STR doesn’t ‘run’ time or ‘advance’ events.

The discussion seems to have gone completely off track. Not one comment pertaining to whatever you think you were trying to demonstrate with A, C and D except some brief thing talking about something ‘forcing’ (frame references absent) the various tick rates.