How does time work? Pt II Special Relativity.

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

Post by uwot »

Noax wrote:...they count a different number because it takes time to get to the destination by one route than by another.
I'm sure this was just a slip, but this is not what H-K were testing.
Noax wrote:One cannot accurately read the time of a clock from any distance since the time that it reads 'now' is completely frame dependent.
I don't mean reading the clock, I mean literally, although in practise impossibly, counting the actual vibrations of the atoms.
Noax wrote:
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.
There is no separation between the hypothetical observer and himself. In the unlikely event that he could actually see the atoms of either of the clocks, from the moment it left, to the moment it returned, he would count a different number of vibrations.

A version of the twins paradox, is less cluttered:

There are two synchronised clocks next to each other.
One is flown around the world.
When they are put back next to each other, they are no longer synchronised.
The clocks work by counting vibrations.
Since they are not synchronised, they didn't count the same number of vibrations.
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attofishpi
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Re: How does time work? Pt II Special Relativity.

Post by attofishpi »

uwot wrote:A version of the twins paradox, is less cluttered:

There are two synchronised clocks next to each other.
One is flown around the world.
When they are put back next to each other, they are no longer synchronised.
The clocks work by counting vibrations.
Since they are not synchronised, they didn't count the same number of vibrations.
..and what of the Higgs Field, if time and gravity are so intrinsically linked?

If the Higgs Field gives mass to some particles, and the greater the mass the slower the time, or the greater the speed the slower the time but greater the mass?

I wish there was an emoticon for crossed eyes.
uwot
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Re: How does time work? Pt II Special Relativity.

Post by uwot »

attofishpi wrote:..and what of the Higgs Field, if time and gravity are so intrinsically linked?
I'm on the case.
attofishpi wrote:I wish there was an emoticon for crossed eyes.
Pretty much all I can see.
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Noax
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Re: How does time work? Pt II Special Relativity.

Post by Noax »

I read your new page. Difficult since the size of the panels is so small that the font leaves some words illegible. I expanded it to fill the screen, but that doesn't add resolution.
Contents of the page is totally accurate.
uwot wrote:
Noax wrote:...they count a different number because it takes time to get to the destination by one route than by another.
I'm sure this was just a slip, but this is not what H-K were testing.
I missed a word there. It takes more time to get to the destination (the second comparison event) by one route than the other. That is what relativity says, and H-K was testing predictions of relativity. What special relativity doesn't say is that velocity affects the accuracy of a clock. It cannot, because velocity cannot be a property of a thing. This is opposed to the gravity effect. The absolute depth on an object in a gravity well IS a property of a thing, so it is more open to interpretation if gravity alters the accuracy of a clock.
Noax wrote:One cannot accurately read the time of a clock from any distance since the time that it reads 'now' is completely frame dependent.
I don't mean reading the clock, I mean literally, although in practise impossibly, counting the actual vibrations of the atoms.
Reading a clock cannot be done from a distance. The reading that you get is dependent on your arbitrary choice of frame. The atomic clock actually literally counts vibrations, so I'm not contesting that ability. But it is impossible to read (or synchronize) a clock on say Pluto to even the correct hour. Given any arbitrary selection of frame, we have the technology to sync a Pluto clock to within a second. For the same reason, your thing at the pole must assume a frame before it can take those measurements.

Now presumably we would select the frame of the axis itself, in which case it would note that the westbound clock runs fast, and the eastbound clock runs slow, and it all happens at a pretty steady pace assuming the clocks are in reasonably constant motion. Given a different selection of frame, the steady-pace thing goes away, but the results at the end are unaffected.
There is no separation between the hypothetical observer and himself.
He isn't watching himself. You have him watching the aircraft from a distance.
In the unlikely event that he could actually see the atoms of either of the clocks, from the moment it left, to the moment it returned, he would count a different number of vibrations.
It is not unlikely. There was a device counting the vibrations exactly, and they did count a different number of vibrations, and didn't need the axis viewpoint to do it. That has been my point: The axis viewpoint isn't necessary for the result. Arbitrary numbers for intermediate states does not affect the final state, the only one that counts.
A version of the twins paradox, is less cluttered:

There are two synchronised clocks next to each other.
One is flown around the world.
When they are put back next to each other, they are no longer synchronised.
The clocks work by counting vibrations.
Since they are not synchronised, they didn't count the same number of vibrations.
Agree. Don't think I ever said otherwise, but perhaps you interpreted one of my comments as a deviation from this.
uwot
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Re: How does time work? Pt II Special Relativity.

Post by uwot »

Noax wrote:I read your new page. Difficult since the size of the panels is so small that the font leaves some words illegible.

Sorry about that. I forgot to enlarge the images, which I have since done.
Noax wrote:What special relativity doesn't say is that velocity affects the accuracy of a clock. It cannot, because velocity cannot be a property of a thing.
This is where I think you and I differ. How I interpret SR is that it accepts that there is a finite limit to velocity, c, and that your velocity relative to that will determine the dilation you experience. I think we agree though, that there is no way of telling in your own frame how fast you are moving relative to c, because everything that is in your frame is dilated by exactly the same factor. Nor can you tell by observing other frames, within the confines of special relativity, because within SR there is no acceleration and therefore no way of bringing two frames together to compare them. However, tacked onto this strictly mathematical treatment of SR, is this claim by Einstein that in the real world, where acceleration abounds, by bringing two clocks (in the form of twins) together, you will be able to tell which has been travelling at a greater proportion of the speed of light, faster, in other words, because less 'time' will have passed for them.
Noax wrote:
uwot wrote: There are two synchronised clocks next to each other.
One is flown around the world.
When they are put back next to each other, they are no longer synchronised.
The clocks work by counting vibrations.
Since they are not synchronised, they didn't count the same number of vibrations.
Agree. Don't think I ever said otherwise, but perhaps you interpreted one of my comments as a deviation from this.
Right. Well, this is no longer a scenario that is confined by SR, because it includes acceleration. All I am saying is that in this circumstance, if it were possible for observers at each clock to count the other's vibrations, the one in orbit around the other, would not see the equivalent dilation in the one at the axis, because even from their orbital point of view, the atoms at the axis are vibrating on the same spot.
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Noax
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Re: How does time work? Pt II Special Relativity.

Post by Noax »

uwot wrote:
Noax wrote:What special relativity doesn't say is that velocity affects the accuracy of a clock. It cannot, because velocity cannot be a property of a thing.
This is where I think you and I differ. How I interpret SR is that it accepts that there is a finite limit to velocity, c, and that your velocity relative to that will determine the dilation you experience. I think we agree though, that there is no way of telling in your own frame how fast you are moving relative to c, because everything that is in your frame is dilated by exactly the same factor. Nor can you tell by observing other frames, within the confines of special relativity, because within SR there is no acceleration and therefore no way of bringing two frames together to compare them. However, tacked onto this strictly mathematical treatment of SR, is this claim by Einstein that in the real world, where acceleration abounds, by bringing two clocks (in the form of twins) together, you will be able to tell which has been travelling at a greater proportion of the speed of light, faster, in other words, because less 'time' will have passed for them.
OK, I see what you mean. Velocity as a property, despite it being immeasurable, and time itself being immeasurable, since a clock or any other physical device only measures 'time', which only matches actual time if the device has no actual velocity. The guy at the Earth axis does not play that role. Just sayin...
uwot
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Re: How does time work? Pt II Special Relativity.

Post by uwot »

Noax wrote:...a clock or any other physical device only measures 'time', which only matches actual time if the device has no actual velocity. The guy at the Earth axis does not play that role. Just sayin...
Well, if I haven't made it clear that I understand that terms like "actual time" are simply mathematical constructs, then I haven't been expressing myself very well. It is very difficult to do, since it is natural to think that there is some actual time, against which everybody's local time is somehow measured and is the judge of "the accuracy of a clock". In my view, the accuracy of a clock is simply how well it counts the events it is designed to count; it's up to the human operators to decide whether the reading it gives is something they can operate with.
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Noax
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Re: How does time work? Pt II Special Relativity.

Post by Noax »

uwot wrote:Well, if I haven't made it clear that I understand that terms like "actual time" are simply mathematical constructs, then I haven't been expressing myself very well. It is very difficult to do, since it is natural to think that there is some actual time, against which everybody's local time is somehow measured and is the judge of "the accuracy of a clock". In my view, the accuracy of a clock is simply how well it counts the events it is designed to count; it's up to the human operators to decide whether the reading it gives is something they can operate with.
Both kinds of time are mathematical constructs. Question is if either references anything real. As for clocks that count regular events, those measure the time as appears in local physics like all of Newton's and Einstein's work. If global (frame independent) time exists, it is used only in cosmology and is called comoving time.
Under the comoving coordinate system, all of classical and relativistic physics must be rewritten. A physical tape measure can measure proper distance between two events but not between two stationary objects. There are no inertial frames, so there is no constant speed of light. But the system can be used to describe distant places beyond the Hubble sphere, places that don't exist in any inertial frame containing Earth. In the comoving coordinate system, being stationary cannot be determined by any local tests, so we go non-local and observe the cosmic microwave background. At any given point, there is a frame where the CMB is isotropic, and that frame is different depending on your location, so it does not define any inertial frame.
Comoving time is measured not by counting anything, but more like sticking a thermometer up the arse of the big bang and measuring the age of the universe by how much it has cooled. In this way one can order all events in the universe objectively: A comes before B is the universe appears younger in the isotropic frame at A than it does for B in B's isotropic frame.

Such a system is great for cosmology, but seems to serve no purpose to the physics of why accelerated clocks don't match less accelerated clocks. For that you need to use the kind of time that counting-clocks measure. The H-K experiment results would not benefit from being expressed in comoving terms. It is a local experiment (anything that can be performed in an arbitrary size box) and should use local physics.
uwot
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Re: How does time work? Pt II Special Relativity.

Post by uwot »

I'll save cosmological time for the sequel, but thank you for the image of a universe with a thermometer up its arse.
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