How does time work? Pt II Special Relativity.

How does science work? And what's all this about quantum mechanics?

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Noax
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Re: How does time work? Pt II Special Relativity.

Post by Noax »

uwot wrote:Kinematic time dilation is a consequence predicted in SR, but real world kinematic time dilation is not a result of the idealised situations described in SR. Clocks really do show that they have run slower or faster, when compared to clocks they have been moving relative to.
How can that be demonstrated if they can only be compared once, which is when they pass each other? To do a comparison, a second comparison must be taken which, if done at a distance, is completely dependent on arbitrary selection of frame. So at least one of the clocks needs to alter the frame in which it is at rest for them to be compared a second time in each other's presence.
There is no physical slowing of a clock that results from velocity since velocity is not a property of a thing, velocity is a mathematical relation with an inertial reference frame which is a mathematical thing, not a real thing I can put in a box. No clock actually changes because of a mathematical designation of how fast it is going. It can't actually have the property of velocity since that is not a measurable property of something.

Physical distance between two points J and L is accurate only if the tape measure is pulled straight from J to L and does not take a detour to K way off to the side first. Clocks work the same way, measuring the temporal distance between P and R, but the clock that takes a non-straight path from P to R, detouring to Q along the way, gives an inaccurate result. It doesn't mean the clock measured wrong any more than the tape measure stopped measuring actual meters. The measurement of temporal distance from points P to Q and from Q to R are completely accurate (not some inaccurate dilated figure), but adding them does not yield the correct measurement from P to R if the three points are not all on the same line, which they're not.
Noax wrote:I took a couple days to proofread and get it right, but maybe I messed up somewhere. The names and numbers are my own. I did not copy this story from anywhere.
I will look at it again to do it justice and make sure I haven't messed up, but it is nothing to do with my blog.
Agree, you haven't gotten into it yet, but the title suggests it is about relativity and it hinted that it would get into this sort of experiment.

Remember the distant object billions of light-years away? In it's frame, right now, the universe is actually about 50 billion years since the big bang, a good deal of the stars have burned out, and our Solar system is moving at say .96c and we still have a burning star, and it looks like only 13.7 billion years since the big bang from here because all the clocks and the star consumption are dilated down to .27 of the pace we would get if stationary. Einstein noted this sort of thing (that there is a place right now that is any arbitrary point in time you want), and thus it makes no sense to declare only one of them to be the actual current age of the universe. Hence he discarded the model of 3D space in which the state of things change, in favor of 4D spacetime that has no external arrow pointing into it defining the preferred location 'here' which just happens to be where we are. If there was an arbitrary place that was the 'stationary one', odds are we'd be moving at least that fast relative to it. Almost all the arbitrary places in the universe are at least that far away from us.
uwot
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Re: How does time work? Pt II Special Relativity.

Post by uwot »

Noax wrote:
uwot wrote:Kinematic time dilation is a consequence predicted in SR, but real world kinematic time dilation is not a result of the idealised situations described in SR. Clocks really do show that they have run slower or faster, when compared to clocks they have been moving relative to.
How can that be demonstrated if they can only be compared once, which is when they pass each other?
You and I are talking at cross purposes. When I was looking at your description of relativity, I was assuming that you were referencing some privileged inertial frame, in which all the different events were resolved. You weren't, because, as you say, at no point do you compare Oscar vs Irving. That was my mistake. However, I am not trying to explain Special Relativity, and have conceded as much; rather I am trying to explain the difference that occurs in atomic clocks if you fly them around the world, as Joseph Hafele and Richard Keating did.
Noax wrote:There is no physical slowing of a clock that results from velocity since velocity is not a property of a thing...
Ok. So how do you explain Hafele-Keating?
Noax wrote:Remember the distant object billions of light-years away? In it's frame, right now, the universe is actually about 50 billion years since the big bang, a good deal of the stars have burned out, and our Solar system is moving at say .96c and we still have a burning star, and it looks like only 13.7 billion years since the big bang from here because all the clocks and the star consumption are dilated down to .27 of the pace we would get if stationary. Einstein noted this sort of thing (that there is a place right now that is any arbitrary point in time you want), and thus it makes no sense to declare only one of them to be the actual current age of the universe.
Well, that is essentially John McTaggert's block universe interpretation of time. For all I know, that is the case, but I think you are massively over egging it by insisting that it is.
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Re: How does time work? Pt II Special Relativity.

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uwot wrote:You and I are talking at cross purposes. When I was looking at your description of relativity, I was assuming that you were referencing some privileged inertial frame, in which all the different events were resolved.
You weren't, because, as you say, at no point do you compare Oscar vs Irving.
I thought I was repeatedly emphasizing the nonexistence of any privileged frame. I can compare Oscar vs Irving, but it doesn't clarify anything:

Oscar's frame:
At event P Oscar's clock reads zero. Irving is 192 light minutes away and moving towards Oscar at .98974c and his clock reads 166.3 minutes. 194 minutes later, Oscar has gone nowhere and Irving passes by, and both their clocks read 194.
Irvings frame:
Irving's clock reads about -1164 minutes. That moment is simultaneous with event P that takes place 1344 light minutes away where Oscar and Edgar pass each other. Oscar and Edgar's clocks both read zero at that event. 1358 minutes later, Irving has gone nowhere and Oscar passes by and both their clocks read 194.

Similar figures for the interval between events Q and R.
Noax wrote:There is no physical slowing of a clock that results from velocity since velocity is not a property of a thing...
Ok. So how do you explain Hafele-Keating?
Some clocks are accelerating more than others. The ones that accelerate the most (to be more precise, the ones that effect the greatest moment-of-acceleration) take the least straight path between the two comparison points, and thus yield the least accurate temporal distance between the points. The westbound aircraft actually attempts to minimize that acceleration as much as possible, letting the Earth spin below it, and thus that one yields the longest measurement.
Well, that is essentially John McTaggert's block universe interpretation of time. For all I know, that is the case, but I think you are massively over egging it by insisting that it is.
McTaggert says there is no present and all the other times exist. Einstein just stated that there is no way to measure the actual time. The actual age of the universe cannot be determined by any means since the actual velocity of the measurement device cannot be known.
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Re: How does time work? Pt II Special Relativity.

Post by uwot »

Noax wrote:I thought I was repeatedly emphasizing the nonexistence of any privileged frame. I can compare Oscar vs Irving, but it doesn't clarify anything...
The point about the privileged frame is that while there isn't one in your story, there is in Hafele-Keating; all three clocks are moving relative to the axis of the Earth. In theory, it would be possible to place a mirror above the north pole so that each of the clocks can be monitored from the three locations they are in. By doing so, the different observers would be able to see the clocks all ticking at different speeds. That in essence is what I am trying to portray, and I accept that this is not a situation that can be expressed in the conditions imposed by your story, but it is what actually happens.
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Re: How does time work? Pt II Special Relativity.

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uwot wrote:The point about the privileged frame is that while there isn't one in your story, there is in Hafele-Keating; all three clocks are moving relative to the axis of the Earth. In theory, it would be possible to place a mirror above the north pole so that each of the clocks can be monitored from the three locations they are in. By doing so, the different observers would be able to see the clocks all ticking at different speeds. That in essence is what I am trying to portray, and I accept that this is not a situation that can be expressed in the conditions imposed by your story, but it is what actually happens.
The frame of Earth's axis is a more stable one, certainly for the duration of the H-K experiment. But it is also the frame of the westbound aircraft that does its best to deviate from that frame as little as possible, so no that clock does not move relative to the axis. The other clocks are under continuous acceleration where GR rules apply, and no, I'm not up to those computations.
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Re: How does time work? Pt II Special Relativity.

Post by uwot »

Noax wrote:The frame of Earth's axis is a more stable one, certainly for the duration of the H-K experiment. But it is also the frame of the westbound aircraft that does its best to deviate from that frame as little as possible, so no that clock does not move relative to the axis.

As it happens, the flights took a total of about three days each, so there was a fair bit of movement relative to the axis, even for the westbound plane, but I take your point that it is less than for the other two. For simplification it is convenient to assume that the flights took place over 24 hours, which is what I did in a much earlier version of the current blog. ( http://willibouwman.blogspot.co.uk/2014 ... plane.html if you are interested.)
Noax wrote:The other clocks are under continuous acceleration where GR rules apply...
True, but even in your story the clocks are subject to dilation as a result of their relative velocity.
Noax wrote:...and no, I'm not up to those computations.
You're not alone. Any computation is necessarily an approximation, because while there are privileged frames, there is no absolute one.
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Re: How does time work? Pt II Special Relativity.

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uwot wrote:As it happens, the flights took a total of about three days each...
Oh... Well they can keep up with what they fly today. One can always get closer to the poles if it is desired to keeps it below supersonic speeds.
Noax wrote:The other clocks are under continuous acceleration where GR rules apply...
True, but even in your story the clocks are subject to dilation as a result of their relative velocity.
That's true in any story, including the H-K one, and including the velocity of the stable clock in relation to any of the others.
... while there are privileged frames, there is no absolute one.
I think our terminologies differ there. I consider the absolute frame to the the privileged one. They're the same frame, and there is no way to detect it, so why bother positing its existence? What you call a privileged frame I call a stable one, a frame in which the clock present at the beginning and at the end of the experiment has not accelerated. Edgar is my stable frame in my story since he is present at both P and R, unaccelerated. But the story can be told from any of the frames with the same numbers (388, 776) being compared at R. The frame is just a mathematical framework and has no actual effect on any of the physics. No clock is making inaccurate measurements.
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Re: How does time work? Pt II Special Relativity.

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Noax wrote:
uwot wrote:As it happens, the flights took a total of about three days each...
Oh... Well they can keep up with what they fly today. One can always get closer to the poles if it is desired to keeps it below supersonic speeds.
If you get close enough to the poles, you can walk it, but you would need increasingly sensitive clocks to register the dilation, as the relative speed becomes negligible, and ultimately zero. Even in 1971, when the experiment was conducted, flying around the world in under 24 hours was no big deal. Even with refuelling it was a piece of cake at the latitude chosen by H-K. I could dig into why they couldn't procure funding to charter military aircraft; airspace, air fields, politics, who knows? But frankly, who cares? (One day it will be someone's PhD thesis.) H-K took the commercial airliner route and were subject to scheduling. Even today, getting half way round the world takes a day.
Noax wrote:
...even in your story the clocks are subject to dilation as a result of their relative velocity.
That's true in any story...
Yes. And without getting into vectors and scalars, the simplest interpretation, which happens to be concomitant with the empirical data, is that kinematic time dilation is not simply a function of velocity, but of speed.
Noax wrote:...including the H-K one, and including the velocity of the stable clock in relation to any of the others.
There is no stable clock.
Noax wrote:I think our terminologies differ there.
They do.
Noax wrote:I consider the absolute frame to the the privileged one.
You can attach any label to anything you like. It's what people do, but the general consensus is that a privileged frame is one from which an observer can look on others' from a view to which they are not party. An absolute frame is effectively a god's eye view to which even people in privileged frames are not party. But then a rose by any other name...
Noax wrote:They're the same frame, and there is no way to detect it, so why bother positing its existence?
I'm not a big Popperian, but 'Conjectures and Refutations' was worth reading.
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Re: How does time work? Pt II Special Relativity.

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uwot wrote:Yes. And without getting into vectors and scalars, the simplest interpretation, which happens to be concomitant with the empirical data, is that kinematic time dilation is not simply a function of velocity, but of speed.
Well, without getting into vectors and scalars, what do you consider to be the difference between the two?
You can attach any label to anything you like. It's what people do, but the general consensus is that a privileged frame is one from which an observer can look on others' from a view to which they are not party. An absolute frame is effectively a god's eye view to which even people in privileged frames are not party. But then a rose by any other name...
As for the general consensus, This from https://en.wikipedia.org/wiki/Special_relativity :
wiki wrote:Galileo Galilei had already postulated that there is no absolute and well-defined state of rest (no privileged reference frames), a principle now called Galileo's principle of relativity.
That was how I was using the word.
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Re: How does time work? Pt II Special Relativity.

Post by uwot »

Noax wrote:
uwot wrote:Yes. And without getting into vectors and scalars, the simplest interpretation, which happens to be concomitant with the empirical data, is that kinematic time dilation is not simply a function of velocity, but of speed.
Well, without getting into vectors and scalars, what do you consider to be the difference between the two?
For me velocity is speed without acceleration. In my view, it is a purely mathematical quantity, for the simple reason that nothing is ever going in a straight, Euclidean line. Which is not to say that It isn't a very useful concept for everyday calculations relative to a given frame. Speed is the stuff that actually happens, basically how fast you are going with whatever change of direction you fancy.
Noax wrote:As for the general consensus, This from https://en.wikipedia.org/wiki/Special_relativity :
wiki wrote:Galileo Galilei had already postulated that there is no absolute and well-defined state of rest (no privileged reference frames), a principle now called Galileo's principle of relativity.
That was how I was using the word.
Like I said, a rose by any other name, but note that 'absolute' is singular and 'privileged' is plural.
I really don't want to get into semantics, to my mind, meaning is demonstrably contextual. The whole point of the exercise is to express ideas that some people think they cannot possibly understand, in ways that might make sense to a few people. As I said before, I don't think it will make its way onto the reading list of physics courses.
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Re: How does time work? Pt II Special Relativity.

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uwot wrote:The point about the privileged frame is that while there isn't one in your story, there is in Hafele-Keating; all three clocks are moving relative to the axis of the Earth. In theory, it would be possible to place a mirror above the north pole so that each of the clocks can be monitored from the three locations they are in.
I thought about this sort of referee monitoring point at the north pole. I don't think it would work unless the experiment started and ended there, which it doesn't. One cannot monitor such experiments from any remote location due to the ambiguity of where everything is at any given moment. Yes, mirrors or whatever communication equipment you like is in place, but it takes time for information to get to the monitoring point, and the distance traveled by that information is frame dependent.
wiki wrote:Galileo Galilei had already postulated that there is no absolute and well-defined state of rest (no privileged reference frames), a principle now called Galileo's principle of relativity.
Like I said, a rose by any other name, but note that 'absolute' is singular and 'privileged' is plural.
Good catch on that one. That is definitely an error in the wiki statement of the principle.
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Re: How does time work? Pt II Special Relativity.

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Noax wrote:I thought about this sort of referee monitoring point at the north pole. I don't think it would work unless the experiment started and ended there, which it doesn't.
Ok. So hypothetically, suppose the two jets started at the North Pole, took the same flight path to Washington, commenced their circumnavigations from there, and returned to the North Pole by the same route. Do you think that will alter the results?
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Re: How does time work? Pt II Special Relativity.

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uwot wrote:Ok. So hypothetically, suppose the two jets started at the North Pole, took the same flight path to Washington, commenced their circumnavigations from there, and returned to the North Pole by the same route. Do you think that will alter the results?
No change to the results. But my point was that the stable polar observer added nothing to the experiment. The results are known when the clocks being compared are in each other's presence. The observer at the pole does not serve any purpose in that capacity. I could be an observer that goes to Venus and finally stopping at Pluto, and the results would be unaffected: The eastward clock logs 59 fewer nanoseconds than the one that didn't leave home. The complete instability of the observer I just described had no effect on that result.

I read up on details of the experiment, and it seems the altitude of the aircraft has almost as much positive effect as the motion has a negative effect on elapsed time. If you fly slow and high enough, the more-accelerated clock logs more time. Clocks on different floors of any building run at different rates.

Yes, the original experiment was done as cargo on public flights, and they spent plenty of the time on the ground on layovers. This should not effect results too much so long as the latitudes and altitudes of the layovers stay reasonably similar for the duration.
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Re: How does time work? Pt II Special Relativity.

Post by uwot »

Noax wrote:... my point was that the stable polar observer added nothing to the experiment.
Well it's completely implausible, but the idea was that the observer would be able to watch the clocks 'ticking'. Caesium beam clocks, which Hafele and Keating used, are the ones which define the SI unit 'second'. You can read the details here: http://tycho.usno.navy.mil/cesium.html , but basically the clocks count the vibrations; 9,192,631,770 of them is a second. I may be crazy, but it is my belief that the reason the clocks differed is that they counted a different number of vibrations. Like many thought experiments it is impractical, but in theory a privileged observer would be able to simultaneously watch the atoms in the air bound clocks vibrate a different number of times over the same period; slower or faster, in other words.
Noax wrote:I read up on details of the experiment, and it seems the altitude of the aircraft has almost as much positive effect as the motion has a negative effect on elapsed time.
Yes, but the effect was only significant in comparing the airborne clocks with the ground based one. It was assumed that the airborne clocks both flew at a constant altitude and the only reason GR had a bearing in comparing the two airborne clocks is that one set was airborne slightly longer than the other.
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Re: How does time work? Pt II Special Relativity.

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uwot wrote:
Noax wrote:... my point was that the stable polar observer added nothing to the experiment.
Well it's completely implausible, but the idea was that the observer would be able to watch the clocks 'ticking'. Caesium beam clocks, which Hafele and Keating used, are the ones which define the SI unit 'second'. You can read the details here: http://tycho.usno.navy.mil/cesium.html , but basically the clocks count the vibrations; 9,192,631,770 of them is a second. I may be crazy, but it is my belief that the reason the clocks differed is that they counted a different number of vibrations.
Yes, they count a different number because it takes time to get to the destination by one route than by another. But I don't see how an extra observer changes any of that or measures something that otherwise wasn't being measured. One cannot accurately read the time of a clock from any distance since the time that it reads 'now' is completely frame dependent.
Like many thought experiments it is impractical, but in theory a privileged observer would be able to simultaneously watch the atoms in the air bound clocks vibrate a different number of times over the same period; slower or faster, in other words.
My bold. There is no 'simultaneously' if there is any spatial separation. That is completely ambiguous for events at which the measurement is not present with the thing measured. For two clocks going this way and that way, I may arbitrarily choose the one that is faster by my selection of frame. Of course we know where the experiment will start and stop and can select our observer to watch from the frame in which those two events are at the same place, and even gather said telemetry data if it seems to help. A different choice of frame will not alter the experiment but it will alter the intermediate telemetry. But the frame was still one arbitrarily chosen by the experimenter or perhaps by an arbitrary object like Earth.
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