Steve3007 wrote: ↑September 28th, 2018, 2:23 amMy point is that it refers to time (whether it's an instant or a period is not the issue) and that therefore, for completeness, the clock being used to measure that time needs to be clearly specified.
We have two clocks comparing themselves with each other. How is that unclear?
As I've said many times, I think that propositions in physics (and science generally) always, one way or another, however indirectly, have to relate to something that can be observed/measured. They have to be falsifiable/verifiable.
If you can't do something as simple as comparing two clocks, I don't see how you can measure anything.
Based on all your talk of things happening in an "underlying reality" without apparent reference to how they could be empirically verified to be happening, I suspect you disagree.
You walk away from me with your clock, and then you return. You say that your measurements tell you that your clock was ticking more quickly than mine during both legs of your trip. The clocks tell you though that your clock ticked more slowly than mine. Do you really want to dismiss the measurement that reveals an underlying reality that conflicts with the naive measurements you made while travelling?
But when I suggested previously that this is the cause of our disagreement you disagreed. In the context of my description of what the laws of physics are, you said we were simply using different words to describe the same thing. I don't think so. If that were the case, we would not be accusing each other of self-contradiction. If two people are describing the same thing but just using different language, either they're both being logically consistent or neither of them are.
Most of the time we're understanding things the same way, but you're simply denying the existence of the clear contradictions that show up. You may be doing that because you're not seeing them as contradictions in one model that lacks running time where they have no relevance, but you're being asked to look for the contradictions in the context of a model with running time where they are highly relevant. Different models fail in different ways, but you can't cure a fault in one broken model by pointing to a different broken model and pointing out that it isn't a fault there. Suppose you have two cars, one with no wheels and the other with no engine. If someone complains that one of the cars doesn't work because it has no wheels, you don't prove him wrong by pointing at the other car and showing him that it has wheels, and if he complains that the car with wheels has no engine, you don't prove him wrong by pointing back at the first car and showing him that it has a engine - both cars are broken.
And, in the absence of other clocks, the only way that we establish how much time they've recorded as passing is by comparing them to each other. Your language (such as the use of the word "apparent") always suggests to me that you have another, universal time in the back of your mind, and that you don't appear to believe that time to be associated with any actual clock. But I could be wrong. Let's see.
We compare them with each other on two occasions when they are together, and we find that while they were apart, one of them ticked more than the other. That is one measurement. We have other measurements which conflict with that, because you also made two measurements while you were travelling which informed you that your clock was ticking faster than mine. If those measurements were the only reality, they would agree with the other measurement that says that your clock ticked more slowly than mine, but they don't agree. That shows that there is an underlying reality which doesn't match up to some of the measurements, and that means that some of the measurements are giving you apparent relative ticking rates rather than actual ones.
OK. Various examples of observers carrying clocks moving relative to each other. And you've specified (below) that, in all cases, one of them changes the inertial reference frame WRT which it is stationary (changing speed) and one stays stationary WRT the same inertial reference frame throughout.
Indeed.
In each case, the clock that didn't change speed ticked at a constant rate while the other clock ran slow on average.
What do you mean by "ticked at a constant rate"? Relative to what? The only way I can assess whether any clock is ticking at a constant rate is by comparing that clock's ticks with those of another clock which I deem to be ticking at a constant rate. As I sit here and look up at the clock on my wall, I deem the second hand of that clock to be ticking at a constant rate. How? By comparing it to my own internal sense of time - my biological clock. Or by comparing it to some other clock. How else would I make that judgement?
We don't technically know that any clock is ticking at a constant rate. The speed of light could be going down all the time as the universe expands, for example, and the only sign we'd see of that is an apparent increase in the rate of expansion of the universe which we would likely attribute to dark energy. There are numerous ways in which a clock's ticking rate could change without us realising it (including an alien that created the universe fiddling with the controls), but whatever slowing might be happening for that clock is clearly also slowing the other clock too in equal measure, because whenever we do experiments, everything behaves as if a clock that remains at rest in an inertial frame ticks at a constant rate. Any interference with it is universal to the clocks that we're comparing, so we can ignore it and treat the system as if clocks at rest in inertial frames tick at constant rates.
When the clocks are reunited, if one clock is found to have ticked more relative to the other clock, then, unless the observers also observed their respective clocks in transit, via signals sent between them, we know nothing of the details of what happened there. Although, if we wish, we could discuss doing such an experiment and see what happens. We just know the number of elapsed ticks at the two points when they meet.
We can measure the relative ticking rates while the clocks are moving relative to each other, correcting for the 100% predictable Doppler effect. This gives us measurements which make out that our clock is ticking faster than the other at all times throughout the trip.
Remember, in the absence of other clocks, there is no other meaningful sense in which we can say "it ran fast".
Yes there is - to each clock, the other clock appears to be ticking at a lower rate.
The analysis using different frames provides accounts proposing whether a clock ran fast or slow on different legs of the trip, and different frames produce contradictory accounts. They are simply not compatible.
And here is the nub of our disagreement, once again. It really is essentially the same as our disagreement over the movements of observers WRT various reference frames, despite you saying that is a distraction.
No - this time we have an absolute answer which tells us that one clock ran slower (on average) than the other, and that gives us a glimpse in the direction of the underlying reality, demonstrating that there is one. We also know that while you were moving your clock away from me, that clock was at rest in an inertial frame, and that while you were bringing it back, it was again at rest in an inertial frame. We can assume that it was ticking at a constant rate throughout each of those periods in which it was at rest in an inertial frame. [Let's do the experiment in such a way that you move away from me at the same speed relative to me as you do on the return leg.]
This gives us five possibilities for the underlying reality (if we assume that time runs):-
(1) Your clock was ticking more slowly than mine during both legs of the trip.
(2) Your clock was ticking more slowly than mine during the first leg of the trip, and at the same rate as mine during the second leg.
(3) Your clock was ticking at the same rate as mine during the first leg, and more slowly than mine during the second.
(4) Your clock was ticking more slowly than mine during the first leg, and more quickly than mine during the second.
(5) Your clock was ticking more quickly than mine during the first leg of the trip, and more slowly than mine during the second.
Each of these possible accounts of the action ties in with accounts generated from frames of reference, but they are rival accounts which are incompatible with each other because they contradict each other. For any two of them to be true, a clock would have to be ticking at two different rates relative to the other clock at the same time.
If we repeat the experiment in the opposite direction (meaning that you set out in the opposite direction from the one you did the previous time), the same five possibilities apply, but we can then combine the results of the two experiments to derive further truths such as:-
(A) If (2) applies to the first experiment, then (3) must apply to the second experiment.
(B) If (3) applies to the first experiment, then (2) must apply to the second experiment.
There are many other such truths that can be derived in the same way, particularly if we consider how much slower or faster one clock might have ticked on one of the legs compared with the other clock, and we can carry out the experiment in many different ways by changing the speed that my clock is moving at, but we already have more than enough here to work with. There is a frame of reference that generates claim (2) for the first experiment, and there's another frame that generates claim (2) for the second experiment. For both of the claims from these rival frames to be true, we'd have to accept contradictions. Rational people don't accept contradictions though, so we can say: if (2) for the first experiment, not (2) for the second experiment. Contradictions pop out all over the place unless we recognise that for one claim to be true, others that contradict it would necessarily need to be false.
So, what exactly are the claims that are generated from different frames? My clock's rest frame produces claim (1), that your clock runs slow on both legs. Your clock's rest frame during the first leg produces claim (5). Your clock's rest frame during the second leg produces claim (4). These are incompatible claims, so we can't take them all to be true. They need to be taken as truths about how things appear rather than how they actually are, so we are
forced to recognise that there's an underlying reality which is not accurately described by these claims. The frame in which my clock's at rest therefore produces the claim that (1)
appears to be the underlying reality. The frame in which your clock is at rest throughout the first leg produces the claim that (5)
appears to be the underlying reality. The frame in which your clock is at rest throughout the second leg produces the claim that (4)
appears to be the underlying reality. These are the LET wordings, whereas the previous wordings are the ones that have become SR dogma. Attempts to disassociate SR from the former wordings will either require it to take on the LET wordings and accept that there's an absolute frame, OR you can try to sit on the fence and leave your options open, but how do you gain anything by keeping your options open in such a way that you're taking up the LET position with one sole difference, that you aren't ruling out the other option which generates contradictions that rule it out? If you rule out the former wording, you logically have to shift to the latter wording (of LET). This is why the set 2 models are no longer in play - they're gone.
If, on reuniting the two clocks, clock A is found to have ticked more times than clock B and therefore clock B is found to have ticked fewer times than clock A, there is obviously no contradiction in that. The only possible reason why you might see a contradiction appears to be that you always implicitly assume that there is some absolute sense in which one clock ran fast and the other ran slow.
There clearly is an absolute sense in which one clock ran faster than the other - the most direct measurement that can be made tells us precisely that one clock ran faster than the other.
So you're effectively imagining some "absolute clock" against which they can both be compared. i.e. you're assuming the existence of what you refer to elsewhere as Newtonian Time.
We're comparing two clocks that we can see and touch. Where are you dragging another time into the measurement?
You're assuming the existence of that which you wish to demonstrate. A "begging the question" fallacy.
Are you trying to make out that one of our two clocks doesn't exist? Which one doesn't exist?
And you think that there is some sense in which the number of ticks recorded by Newton's clock (as it were) is "right" and one or both of our two clocks are therefore "wrong".
We can do everything with our two physical clocks. They tell us everything we need to know for us to understand that we can't trust either of them to record actual time.
That's the only reason I can think of as to why you would see a contradiction where obviously none exists.
Oh sure - there's obviously no contradiction in two clocks each ticking faster than each other, for people who are irrational.
Let's do something else with our clocks. We repeat the first experiment and see that your clock ticked more slowly than mine (on average). I then move my clock at the speed you carried your clock at during the first leg of that first trip and you race on ahead of me with yours, then wait for me to catch up. Again my clock has ticked more than yours, so we don't learn much from that. But let's try it again with me walking at the same speed, but this time you stop for a while, then race after me. Again, your clock has run slower than mine. But look at what's just happened. During this third experiment, my clock was moving through space at the same speed as yours was during the first leg of the first experiment, and your clock was moving through space during the first leg of the third experiment at the same speed as my clock did during the first experiment, so they've swapped places. Is my clock ticking faster than yours during the first leg in the first experiment and then ticking faster than yours during the first leg of the third experiment? No - it cannot be doing so without contradiction. If my clock was ticking faster than yours during the first leg of the first experiment, it must be ticking slower than yours during the first leg of the third experiment. Alternatively, if my clock was ticking faster than yours during the first leg of the third experiment, it must have been ticking slower than yours during the first leg of the first experiment. These are incompatible possibilities - if one of them is true, the other is necessarily false. SR makes out that both possibilities are true, or at the very least, it denies that if one is true the other must be false. However, all competent mathematicians and logicians say that if one is true the other is false. They understand contradictions, and they reject them. The only reason they're tolerated in SR is that they don't apply to set zero models (in which no clocks tick at all), but when we're looking at set 2 models, they absolutely do apply and those models are invalidated by them.
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