On Tuesday, December 28, 2021 at 9:11:11 AM UTC-8, tjrob137 wrote:
> In GR proper time does advance at the same rate along every worldline.

Again, the rate of proper time is a quantity of the form dtau/dt where t is the time coordinate of some specified system of coordinates. If you do not specify a system of coordinates (or at least a temporal foliation), you can't talk about the *rate* of proper time, you can just talk about proper time. Now that you understand this, you should be able to see what is wrong with your statement.

> The physical situation in this thread is an experiment to
> measure gravitational redshift of EM signals; it is NOT about "relations
> between the rates of proper time along separate worldlines"

Yes it is, because gravitational redshift consists of the relations between the rates of proper time along separate worldlines, as explained to you in detail many times. Do you understand this?

> You keep changing your "argument". Initially it was a machine gun...

No, it was never a machine gun. (In different threads discussing a different topic with different individuals I have used a machine gun to illustrate the Doppler effect, but in this discussion from the very start I referred to two bullets fired a year apart.

> Within your [clear explanation], such an interval between bullets does not
> meet the requirement I EXPLICITLY gave that "the time interval between [bullets]
> is very much shorter than any other time scale".

Right, which is precisely why I specified that lengthy interval, so debunk your ridiculous "reasoning". The point is that none of your idiotic "parallel transport of intervals" is relevant, as shown by the fact that relativistic time dilation is fully exhibited by the bullets one year apart. Once again, the clock at the top simply measures the elapsed proper time at the top between arrivals of consecutive bullets, and the clock at the bottom measures the elapsed proper time between departures, and even though these have the same elapsed coordinate times, the elapsed proper times are different, because dtau/dt is different at the top and bottom.

> Sure. But to do that the clock must project the displacement 4-vector...

Ideal clocks, by definition, measure the elapsed proper time along their world line. Again, your gibbering about displacement vectors is completely pointless, as shown by the bullets one year (or a thousand years) apart.

> You are ignoring HOW the clocks perform such measurements...

Nope, the functioning of clocks is well known, and the concept of an ideal clock as one that indicates elapsed proper time along its world line is well known.

> > Those elapsed times are different, because in terms of the essentially unique
> > stationary coordinate system the rate of proper time at the top is faster than
> > the rate at the bottom. If you agree with this, then all you need to do is stop
> > denying it whenever anyone says it.
>
> I agree with that, and have never denied that...

Not true... in fact, here you go again:

> What I object to is claiming "clocks tick at different rates", implicitly discussing
> their INTRINSIC rates, not their rates compared to a stationary coordinate system.

This is the nub of your lunacy. The implicit context of statements like "clocks tick at different rates at different elevations" is the obvious single stationary coordinate system that everyone uses every day. It is completely insane to imagine that scientists are referring to the rates of two clocks in terms of two different local inertial free-falling coordinate systems, in which they are respectively at rest momentarily. Saying all clocks run at the same rate is exactly like saying "All objects are motionless", referring to the fact that every object is always at rest in its own rest frame. Duh. Please do not project your own lunacy onto rational people.

> Describe an experiment to compare tick rates of clocks following
> different worldlines...

Already done. See above. Countless others can be described just as well. You need to clarify your objection, i.e., are you denying that dtau/dt for any given foliation is generally different for different worldlines? Or are you denying that dtau is given by the integral of the line element along any specified path? Or do you semi-accept these things, but claim that these facts must be placed in "scare quotes" because they only seem to be true but are actually false? The actual analysis of the simple situations does not involve "parallel transport of displacement vectors", it is simply noting the secular accumulating difference in elapsed proper times between separate locations, which can be as large as we like by extending the duration, even though the pigeons flying from one to the other a million years from now are no different than the pigeons today.

On 12/27/21 4:15 PM, Townes Olson wrote:
> we were discussing the bullets in another thread, and when Tom
> realized he couldn't explain the bullets scenario, he ran away and
> started this new thread,

Your attempt to state what I think is wrong. DON'T DO THAT.

I started this thread because I realized I was repeating its content
over and over in many different threads. I wanted a definitive
description of how GR models such experiments, so I could refer to it
elsewhere in this newsgroup.

Given the assumptions I gave in the original post of this thread, both
calculations I gave apply to the interval between bullets. You keep
changing your scenario so the assumptions don't apply, and then
attempting to ridicule what I wrote. That's disingenuous, and the fault
is YOURS.

Tom Roberts

On 12/28/21 8:26 AM, Paparios wrote:
> The clocks used in the Tokio tower experiment are working at a
> frequency uncertainty of the order of 10^-18. These are real clocks
> used to measure time, but clearly they are not perfect clocks. To
> validate the gravitational redshift, predicted by GR, the Tokio tower
> experiment used two of these optical lattice clocks. One was located
> at the top of the tower, the other was located at the bottom of the
> tower (therefore separated by 450 meters). The gravitational redshift
> is given (to first order) at location 1 by:
>
> (f2-f1)/f1 = (1 + α)(U2-U1)/c^2
>
> where f2 is the clock frequency at location 2, f1 is the clock
> frequency at location 1 and (U2-U1) is the gravitational potential
> difference between locations 1 and 2. In order to compare the
> frequencies f1 and f2, an optical fibre link was used to transport
> the information from the top to the bottom of the tower. α is the
> violation from GR. α=0 denotes the case when GR is valid. The
> experiment result is that α=(1.4 +/- 9.1)x10^-5 meaning the
> experiment found "almost" the result predicted by GR. The frequency
> difference (f2-f1), measure at the bottom of the tower, amounts to
> around 21.177 mHz (as shown in figure 3a of the paper).
>
> These are facts!!!

The coordinate-free calculation I gave in the first post of this thread
applies to this experiment (the calculation is completely general, and
does not specify details). The second calculation does not apply,
because the parallel transport of the displacement 4-vector is not
vertical, but rather inside the fiber. But for the signal presented to
the receiver clock, the difference is only in the spatial components of
D', and those are irrelevant as D' is dotted into U' in which the
spatial components are all zero. So the final result of the second
calculation is the same as a complete calculation using the fiber.

Tom Roberts

> ... "grown-up scientists" don't discuss "different rates of proper time",
> they discuss "different rates of proper time relative to the specified
> coordinates"

That's what I've been explaining to you, and any adult scientist is quite happy, if asked, to stipulate the obvious intended system of coordinates to anyone who is dense enough not to know that they are talking about the normal stationary coordinates. There is only one idiot here who insists, in Humpty Dumpty fashion, that one can talk about the rate of proper time without reference to a specific system of coordinates, and that idiot is you. You insist that "the rate of proper time" for a world line can only mean the rate in terms of local inertial coordinates in which that world line is momentarily stationary... even when comparing the rates of two different clocks moving along separate world lines, which is idiotic, like saying all objects are motionless.

> The phrase "tick rate of clock A" refers to clock A only...

No, it does not, because the word "rate" refers to the ratio of two things. You have just one hand clapping. A rate of proper time is a quantity of the form dtau/dt, so it unavoidably involves some coordinate time t. Whenever someone talks about the rate of a clock they are (whether they know it or not) referring to some coordinate basis, or else expressing the empty tautology dtau/dtau=1. Duh.

> The tick rate (of a clock) is different from motion -- a clock's tick
> rate is INTRINSIC, while its motion is not. Your analogy is flawed and
> useless.

Nope, the rate of proper time is a coordinate-dependent quantity, just as is velocity. If you define the word intrinsic to mean "in terms of the object's rest inertial coordinates", then the intrinsic velocity of every particle is always zero. So saying that all objects move at the same speed (have dx/dt=0 in terms of their respective rest frames) is exactly like saying all clocks tick at the same rate (have dtau/dt=1 in terms of their respective rest frames). This was explicitly explained previously. Remember?

> I have said many times that I put "time dilation" and "length contraction" in
> quotes because those names are poor, and lead all too many people to
> misinterpret the actual phenomena to which they refer.

But we've seen here that it is you who misinterpret the phenomena.

> I started this thread because I realized I was repeating its content
> over and over in many different threads.

Right, that's the problem. You seem determined to spread your misunderstandings, rather than actually learn and understand the subject.

> You keep changing your scenario so the assumptions don't apply, and then
> attempting to ridicule what I wrote.

Nope, the bullets separated by a year have not changed, and the point is that this has nothing to do with parallel transport of displacement intervals, it just has to do with the variations in dtau/dt for different worldlines (i.e., different locations and states of motion) for a suitable (i.e., stationary) foliation.

> The coordinate-free calculation I gave...

The rate of proper time is a coordinate-dependent quantity, so there can be no coordinate-free calculation of it. Of course, for these purposes, only the temporal foliation of the coordinate system is relevant, since that establishes the mapping between the worldlines.