Is the Changing Clock Rate in Relativity Directionally Dependent?

[Hurkyl]

Hurkyl - The transforms relate time and distances

No they don't!

The transforms relate (inertial) coordinate systems, which most certainly are "abstract mathematical artifact".

E.g., IIRC, Einstein made a big deal about showing how to construct what he called an inertial reference frame, via a hypothetical network of clocks, each of them "at rest" with a given inertial observer, and "synchronized" with his clock. I put those terms in quotes because those are also terms in need of construction.

If coordinate systems were physical things, Einstein would have just said "measure it".

 

[RandallB]

I have no agenda Randall - my interest in SR goes back many years - I pose questions that come to mind - if those questions lead to a different view ...one I have overlooked - great. Usually what happens on these boards is an attack - either I don't understand it or I am not qualified to question it - but for a few posters, the attitude is always one of condesention.

Fine – I’ll let your condescension towards me pass as a result of the above.

I understand I don’t have the “pro” tag, banner or ribbon of the mentors & advisors on this board - so you don’t have to take my encouragements to heart.

As to reciprocal views being relative – Based on how you pose those questions as conclusions, from the frame of reference of many trying to respond, it can often be seen as attacks on SR as they know it to be. So that part seems to be the same from both views.

 

[Hurkyl]

No they don't!

The transforms relate (inertial) coordinate systems, which most certainly are "abstract mathematical artifact".

I guess I should qualify this...

The transforms do relate coordiante position, and coordinate time, so in some sense they can be said to relate times and distances.

But my point still stands -- coordinate position and coordinate time are derived from coordinates, which are not physical things.



Case in point: the Julian and Gregorian calendars are not the same -- they¹ assign different time coordinates to events. Would you say that the transformation between these calendars is a physical thing?


1: I'm assuming any usual² method of identifying spatial position. A calendar, by itself, is unable to assign time coordinates to almost every event!


2: Notice I said usual, and nothing such as "intrinsic" or "determined by reality" -- it's a convention we use as humans. And it's even changed over time, such as when time zones were instituted, and when calendars were changed!

 

[pervect]

Randall - you are obviously going to have a difficult time undertanding the Gravity" book you borrowed - you are having a difficult time with my several statements to the effect that the resolution of the question doesn't involve anything but SR - first you accuse me of saying Relativity is Broken - title of another post - they you allege I am making a claim about GR - my reference to GR is strictly an analogy - nothing to do with it other than the fact that SR has in common with GR the fact that in some experiments things are not reciprocal.

Since I've had some run-ins with RandallB in the past, I didn't and don't consider it an enjoyable use of my time to respond to his response.

Hopefully the point I wanted to make has been made, though.

 

[yogi]

Pervect - I appreciate your comments and frequently read your posts although a cannot always make a sensible response. See Below

 

[yogi]

Pervect - I appreciate your comments and frequently read your posts although often cannot make a worthwhile response.

I do recall at one time in another thread you made a statement that the time discrepancy is physically explainable - but then the direction of the thread veered off along other lines as is often the case - so i wasn't able to get back to the subject

In my previous posts on this thread I have tried to target the situation Einstein created when he combined the relationships that were obtained from observations in another frame - specifically to my way of thinking there is a quantum jump from the notion of two observers in relative motion drawing identical conclusions about lengths and clock rates in the other frame - as opposed to the idea that one of two synchronized clocks put in motion will run slower than the one that was not moved. There is a real loss of time between the clocks when they are later compared - in other words, did Einstein get the right answer for the wrong reason - or by intuition. He does not attempt to justify or even rationalize this - it works to explain the experiments - but it doesn't follow from the initial postulates of SR - in one sense it seems to require its own special postulate and - i guess what i am saying is that something is missing.

 

[yogi]

So to pick up the thread - it seems there is a discontinuity in the development of the notion of real time dilation - for example if we explore what Einstein asserts in part 4 we could imagine the following scenerio - we plan a trip to Altair but first we draw a line connecting the Earth and Altair and at the center point of this line we place a clock C - we also place a clock E on the Earth and a clock A on Altair. All are initially synchronized. Now from the center point (location of clock C) we draw a large circle that intersects both the Earth and altare. This is the trajectory the spaceship will follow. The spaceship has a clock R also initially synced with A, E and C. The spaceship is quickly accelerated to its crusing velocity v wrt Earth and steered to maintain a uniform velocity tangent to the circular path it will follow during the entire voyage (there will of course need to be some lateral thrust to correctly follow the path - this radial acceleration however does not enter into the accumulated time on clock R because acceleration per se does not affect clock rates as has been determined many times in centrifuge experiments). Einstein tells us that the R clock will read less than the A clock when R passes by A, and that it makes no difference what path is followed so long as the velocity remains constant - this is simply the first half of the twin thing - and since the second half is dynamically the same as the first half, half the time is lost in arriving at Altair and half is lost on the return trip.

The three clocks A, E and C remain in sync since they are not moved - if the gamma factor is 0.5 the R clock should read half that of the A clock at the time R passes A - during the return trip the R clock will again lose the same amount of time - so it will read half the E clock time when R returns to earth.

The issue is whether in real time dilation experiments there is symmetry - either the R clock runs at the same rate as A,C and E or it runs at a different rate - and if it runs at a different rate how does it know physically at what rate to move its hands. We can interrogte the R clock from C at each and every mile along the way just as we can interrogate the GPS clock from the Earth tower. We know from GPS data, unless a GPS clock is corrected for its velocity relative to the tower clock, the Earth clock and the satellite clock will run at different rates at all times while they are in relative motion.

A possible query is whether the R clock is a good reference frame - true it has slight radial component - but not one that would influence its rate in a measurable manner - so if we assume R is at rest in an approximate inertial platform - would we expect measurements made in the spaceship frame using R to determine the rate of time passage on clocks , C, E and A to be the same as measurments made by C, E and A to measure R. In other words, if we sent interrogation radio signals from R to C, what conclusion could R arrive at from the signals received from C

 

[yogi]

lets take it a step further - we will have C send out interrogation signals every hour - they are received by tansceiver on the spaceship and they immediately transmit the time reading on clock R - now we presume c is constant and we have defined the radial distance to be always constant - so we know the over and back time is always the same - so after each transmission is received by C, C should be able to say that R is always running at 1/2 the rate of C (for gamma = 0.5). In a like manner, R can send interrogations to C and R should be able to determine from what it receives from C that C is running at double the rate of R.

If this really occurs - then do we not have a reference frame problem - if there is an intrinsic difference in the rate of uniformly moving clocks - it cannot be said that two clocks meeting in empty space with uniform relative motion will each judge the other clock to be reciprocally slow as measured by a local clock at rest. How does one distinguish between two clocks meeting in empty space and R flying by A after several thousand years of travel in deep space?

 

[Hurkyl]

Let's take it one step further: let's have R periodically send interrogations to E. (instead of to C)

Everything stated below is as seen by R.

(I'm using units in which the distance between A and E is 2, and c = 1)

I've written a program to run this experiment -- R is sending a signal every 0.01 units of time. E receives the signal and immediately broadcasts its time. R receives the return signal. R then takes the average of the send & receive times, by his clock, and compares it with the transmitted E-time.

R-time : E-time
---------
0.0 : 0.0
0.073 : 0.037
0.141 : 0.074
0.202 : 0.111
0.256 : 0.149
...
1.8 : 3.585
1.81 : 3.616
1.82 : 3.647
1.83 : 3.678
1.84 : 3.708
...
3.602 : 7.242
3.607 : 7.245
3.612 : 7.247
3.618 : 7.25
3.623 : 7.253
3.645 : 7.264

The first group is, of course, as R is leaving Earth.
The second group is when R passes Altair. (at 1.813 R-time)
The third group is when R passes by Earth again. (at 3.628 R-time)

Compare the rates of the R and E clocks by this reckoning:

As R leaves Earth, R-time is running twice as fast as E-time.
As R passes by Earth again, R-time is once again running twice as fast as E-time.

In other words, it is exactly what one would expect from "reciprocosity".


Also, note that R is passing by Altair that E-time is running three times as fast as R-time. (As opposed to C-time, which is only running twice as fast as R-time)

 

[yogi]

Hurkyl - Thanks for your interest and the time taken. Your approach is however, what I endeavored to avoid - I cannot help but feel that to find an explanation in the symmetry of the transforms is a bootstrap argument - it leads to a nummerical solution (albeit a correct one as far as the numbers go) but what is missing is an appreciation of what is really going on in the moving frame. Treating the clock frames of R and E as equal casuses a shift from apparent observations to an actual time dilation - I am not sure Einstein was not guilty of the same methodology - What I tried to do was set up the simpliest scenerio possible - with a central clock C that is always the same distance from R ...the three clocks in the earth-Altare (ECA clocks) frame will always read the same - so if you are getting different relationships between R and E at different points in the journey - they can only be apparent because the C clock always runs at a constant rate and since the R clock is following a circle - it too must run at the same rate for the entire trip - so any statements to the effect that the R clock observes E to be running fast at the beginning and ending, and slow in the middle, must of necessity be apparent. What I am trying to do is disect the problem by proposing the simpliest geometry possible ... one which is free from any challenges that could be raised as to changing conditions (e.g., accelerations, turn around stress etc) as is frequently done depending upon how the twin paradox is rationalized to a non-paradox). Run your programe using only signals between C and R and vice versa - if you arrive at a time discrepancy when R returns to E, tell where and when the R clock runs fast wrt to C and where it runs slow.

 

[Hurkyl]

I didn't use the transforms at all, actually.

I did the entire problem in the coordinates of the ECA-rest frame. I placed Earth at spatial coordinates (1, 0), and Altair at spatial coordinates (-1, 0).

Since R travels with uniform speed in a circle (as measured by the ECA frame -- most inertial frames would disagree on both counts), its worldline has to look something like:

r(s) = <ks, cos s, sin s>

for some k. (The parameters are time, x, y) You gave the condition that the rate of the R-clock should be one-half that of its ECA-time coordinate. I used that to solve for k, and then I reparametrized the worldline by R's proper time:

<br /> \vec{r}(\tau) = \langle 2 \tau, \cos (\tau \sqrt{3}), \sin (\tau \sqrt{3}) \rangle<br />

So, I'm now armed with the knowledge of how to find the ships ECA-coordinates if I know what R's clock reads.

Using this, if I decree that the ship emits a signal at R-time \tau, I could determine the ships ECA-coordinates when the signal is emitted. I can then compute when the signal arrives on Earth. I then numerically solve for the R-time \tau&#039; when R receives Earth's reply.

That is how I generated the chart.


I certainly agree that if I add a C-column via the above methodology, the C-times will always read exactly twice that of the R-times.


I also certainly disagree that the problem is free of acceleration. While the ship may be accelerating gently, we are also looking at the problem over very large scales -- small * large = indeterminate, so we cannot brush away the effects of acceleration as being irrelevant.

 

[JesseM]

If this really occurs - then do we not have a reference frame problem - if there is an intrinsic difference in the rate of uniformly moving clocks

Why do you think your example shows an intrinsic difference in the rate of uniformly moving clocks"? "Uniformly moving" means uniform velocity, not just uniform speed, so R doesn't qualify.

Any thoughts on the questions I asked in my previous post?

 

[Hurkyl]

I think one of the important lessons that was learned from Einstein is that a concept is only relevant if we can determine it experimentally.

The big, overarching point is that you cannot talk about what time something happened way over there -- what you can talk about are the results of some sort of "timing experiment".

One way to give meaning to a phrase like "E observes that R's clock is running half as fast as his own" is to say that E is continually performing timing experiments to assign E-times to the readouts of R's clock. The results of these experiments yield E-times that are increasing twice as fast as the R-times to which they're assigned.


It is somewhat of a miracle (or more accurately, an assumption) that it is possible for E to perform this timing experiment on C, and find that the assigned E-times are equal to the readouts on C's clock. And conversely, that C performs this timing experiment on E to find that the assigned C-times are equal to the readouts on E's clock. The concept of a reference frame is an abstraction of this miracle.


When R performs this timing experiment on E's clock, and finds that the result is not that the assigned R-times are always half as much as E's clock, it shouldn't be a surprise.

All it means is that the amazing string of coincidences that allowed some of these experiments to agree with each other have finally come to an end. There's no inherent reason to think that any of these coincidences could be possible! In fact, according to GR, they are not: they can only be approximately possible on small scales. (Okay, I should point out that my confidence in this very last sentence isn't nearly as much as the rest of my post)

 

[yogi]

Jesse - Hurkyl Let me address part of what you have both said - it has to do with the propriety of R as a reference frame - here i will again direct you to Einstein's statement (1905 Part 4) - that it doesn't make any difference what path is followed - the equation for the time difference only concerns the relative velocity v between the clock that remains at rest after sync and the clock that is put in motion - I interpret this to mean that the moving clock (in our case R) could zig zag all over the place as long as its heading velocity remains v - if we believe Einstein's statement then should we not be able to disregard any radial acceleration that R incurs during the round trip flight - we all agree (I think) that we get the right answer by considering only C and R, and when we do that we arrive at the same result as Hurkyl gets using the chart methodology - so if arriving at the right numbers is the primary object - either approach is of equal utility.

Now if we follow hurkyl's logic that we will see R running at half the assigned C rate if we continue to use timing experiments between R and C at all points of the path, and vice versa, can we not conclude that the spaceship is a good inertial frame - it shouldn't really make a difference in the outcome if the path were comprised of many straight segments that approximate the circle and the readings were always taken at the midpoint of the seqments - we wouldn't really expect the total time difference between a circular path and a segmented path to be any different so long as the total distance traveled was the same - what I am trying to do is eliminate any affect of acceleration.

Now I do not see that this experiment leads to the notion of a universal time - but if both R and C run at the same speed at all times as a necessary consequence that they are not being acted upon by any forces or factors that would change the rate at which they run - then we do have a condition where they run at different rates as judged by each other - but unlike apparent time dilation - R judges C as fast and C judges R as slow ...in other words, they are running at intrinsically different rates, The question that follows is whether its permissible to ignor this difference when using the LT or some other methodolgy to make measurements in a ralativly moving frame. Again are we getting the right numerical answer for the wrong reason. Does not R have to take into account that it is running slow wrt to C when setting up its local clocks to make mesaurements in C's frame - for example let us say that prior to launch someone fiddles with the R clock so it doesn't keep the same time as C before launch - we would not expect that R would be able to get correct results when it is used to measure E and A rates.. More later

 

[yogi]

Jesse - I assume you were asking about the questions posed in your post 120 which referred to your Epistle posted in 110. If I have given the impression that I have any doubt about physical experiments producing different results in different frames - I did not intent to - Nor am I taking issue with the lorentz group of symmetries as a mathematical principle, although it is not always easy to see what is being conserved.

At this juncture however, I cannot say whether such mathematical constructs always represent the real world - we use them as though they were God given - just as we once used Newtonian mechanics w/o question.

 

[JesseM]

Jesse - Hurkyl Let me address part of what you have both said - it has to do with the propriety of R as a reference frame - here i will again direct you to Einstein's statement (1905 Part 4) - that it doesn't make any difference what path is followed - the equation for the time difference only concerns the relative velocity v between the clock that remains at rest after sync and the clock that is put in motion - I interpret this to mean that the moving clock (in our case R) could zig zag all over the place as long as its heading velocity remains v - if we believe Einstein's statement then should we not be able to disregard any radial acceleration that R incurs during the round trip flight

Are you referring to this part of section 4 of the 1905 paper?

It is at once apparent that this result still holds good if the clock moves from A to B in any polygonal line, and also when the points A and B coincide.

If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the traveled clock on its arrival at A will be 1/2*tv^2/c^2 second slow. Thence we conclude that a balance-clock7 at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions.

If you're saying that this justifies treating the circular-moving clock as having its own rest frame, you misunderstand what he was saying there. Einstein was saying that time dilation as seen in an inertial reference frame is dependent only on velocity in that frame. So if something moves on a curved path at constant speed as seen in an inertial frame, you can calculate the time elapsed just by multiplying the coordinate time in that frame by \sqrt{1 - v^2/c^2}. But Einstein is not claiming there that the object moving on the curved path itself has its own rest frame where the usual rules of relativity apply; these rules only apply in frames "in uniform translatory motion", ie no acceleration (and changing direction always involves acceleration).

Now if we follow hurkyl's logic that we will see R running at half the assigned C rate if we continue to use timing experiments between R and C at all points of the path, and vice versa, can we not conclude that the spaceship is a good inertial frame - it shouldn't really make a difference in the outcome if the path were comprised of many straight segments that approximate the circle and the readings were always taken at the midpoint of the seqments

But making the path into a series of straight line segments wouldn't help either, because R would not have a single inertial rest frame throughout the journey, it would have a series of different inertial rest frames. This is just like the twin paradox, where for convenience you usually assume that the traveling twin's path is just made up of two straight line segments.

Now I do not see that this experiment leads to the notion of a universal time - but if both R and C run at the same speed at all times as a necessary consequence that they are not being acted upon by any forces or factors that would change the rate at which they run - then we do have a condition where they run at different rates as judged by each other - but unlike apparent time dilation - R judges C as fast and C judges R as slow

Usually in the context of relativity, when people say things like "A judges B to be running slow" they just mean that in the inertial frame where A is at rest, B is running slow. But again, R does not have a single inertial rest frame throughout the journey. It is certainly true that in any frame where R is momentarily at rest, then in that frame C will be running slower than R at that moment, but then that frame will see R's velocity change throughout the journey and at some point it will have to see R running slower than C. And again, there is no physical reason to prefer one inertial frame's description of the whole situation to another's, so you cannot say that R was running slower than C at every moment, you can only say that R's average rate of ticking over an entire orbit was slower than C's (this will be true in every inertial frame).

Again are we getting the right numerical answer for the wrong reason.

WHY do you think it is wrong? You keep objecting to the idea that every frame is equally valid but you never spell out any reasons, and you seem to have agreed in your last post that as long as all the laws of physics have equations with the mathematical property of lorentz-invariance, this insures that every inertial frame will see the same laws of physics and will make the same predictions about all physical questions like what two clocks read at the moment they meet. If you agree with this, it seems that you must agree that no inertial frame's analysis is physically preferred over any other's, so all you're left with is some kind of aesthetic preference for one frame's description over all others, no different than someone who prefers cartesian coordinates to polar coordinates.

 

[Hurkyl]

in other words, they are running at intrinsically different rates

Well I have two responses:

(1) R interrogating C and R interrogating E are exactly the same experiment. What do you find so special about the former experiment that allows you to justify calling it "intrinsic" and the latter "apparent"?

(2) There is no "intrinsic" difference. The observer on R, using the R-clock to measure all relevant times, still finds that his heart is beating at 120 bpm, still finds that middle A is 440 Hz, still finds that the half-life of a pion is 26 ns, et cetera.

 

[jtbell]

it shouldn't really make a difference in the outcome if the path were comprised of many straight segments that approximate the circle and the readings were always taken at the midpoint of the seqments

But making the path into a series of straight line segments wouldn't help either, because R would not have a single inertial rest frame throughout the journey, it would have a series of different inertial rest frames.

In order to predict what C's (or E's or A's) clock reads in the inertial frame that R happens to be instantaneously at rest in, at any point along R's path, you need to perform a series of Lorentz transformations, from one straight segment to the next in yogi's approximation. Then, ideally, you would take the limit as the number of segments increases towards infinity and their length each approaches zero. Mathematically, this is of course an integral. But yogi's example is a two-(space)-dimensional problem so you need to use a two-dimensional version of the Lorentz transformation.

 

[JesseM]

In order to predict what C's (or E's or A's) clock reads in the inertial frame that R happens to be instantaneously at rest in, at any point along R's path, you need to perform a series of Lorentz transformations, from one straight segment to the next in yogi's approximation. Then, ideally, you would take the limit as the number of segments increases towards infinity and their length each approaches zero. Mathematically, this is of course an integral. But yogi's example is a two-(space)-dimensional problem so you need to use a two-dimensional version of the Lorentz transformation.

Well, if the speed as a function of time is v(t), the integral would be \int_{t_0}^{t_1} \sqrt{1 - v(t)^2/c^2} \, dt regardless of how many dimensions the problem is, no? Anyway, yogi specified that R was moving at a constant speed in the rest frame of the other clocks, and in any frame where speed is constant you shouldn't need to do an integral.

 

[yogi]

My use of the word intrinsic is of course undefined in SR - - it is not the observed time - it is the difference between what two clocks that are in uniform relative motion will determine to have accrued on each clock when they are compared in the same frame. Let us proceed to use R and E as Hurkyl has chosen to illustrate - as long as they are in relative motion, we make measurements and get different results because relative velocity and distances are changing But what is being measured is a distortion - If R quickly stops halfway to Altare and interrogation signals are sent from E to R and from R to E - what do they report - after comparison R has fallen behind E by 1/2 - the comparison is being made in the same frame and there is no doubt that they have been physically running a different rate. But the result would be no different if we made the same inquiry while R is moving. But we must ask the question "What does your clock read" and not set up a Lorentz grid or some other formalism that can only lead to a distorted answer as to how fast time appears to be moving in the other frame. We can make this determination at any point we wish during the trip - and by asking the question: "What does your clock read" rather than: "how fast does time appear to be passing while we are in relative motion" we arrive at the correct physical reality...at all times during the voyage, proper time in the R frame accrues twice as fast as it does in the E, C, A frame. The result would be no different if R is in an orbit around some great attractor which C happended to be the center of - and it is no different on any other experiment - the invariance of the interval assures us that it is the high speed pion and not the Earth clock that runs slow - real time dilation is a one way thing.

 

[yogi]

Jesse - yes I was referring to the polygonal line statement - and i agree Einstein did not go further - what I am saying that every motion has some curvature most likely - but it does not show up in the results - why because acceleration per se does not affect clock rates - as i have said about 50 times. So the slight curvature is of no moment - if you were on that spaceship with such a low curvature you would feel perfectly justified in claiming yourself to be on an inertial platform (you could even straighten it out if you desired, as you passed A - it wouln't make any difference - when you attempted to use your slowly running clock to try to make measurments of the A clock as you passed by ...you would get the wrong answer - because the proper rate of the A clock in the A frame and the proper rate of the R clock in the spaceship frame is different by a factor of 2 whether you momentarily straighten out the spaceship path or not.

 

[JesseM]

My use of the word intrinsic is of course undefined in SR - - it is not the observed time - it is the difference between what two clocks that are in uniform relative motion will determine to have accrued on each clock when they are compared in the same frame. Let us proceed to use R and E as Hurkyl has chosen to illustrate - as long as they are in relative motion, we make measurements and get different results because relative velocity and distances are changing But what is being measured is a distortion - If R quickly stops halfway to Altare and interrogation signals are sent from E to R and from R to E - what do they report - after comparison R has fallen behind E by 1/2

Only if R "stops" in the inertial frame that E is at rest. But what if both R and E "stop" in some other inertial frame? If R has only made 1/4 of a full circle, I'm not sure if all inertial frames will agree that its average rate of ticking was slower than E (they would definitely agree on this if it made a full circle), and in any case it certainly won't be true that all frames agree that its average rate of ticking was 1/2 of E's. So what if, at the moment R has made it halfway to Altare both R and E stop in some inertial frame where R's average rate of ticking was 3/4 that of E's--in this case when they compare non-doppler-shifted signals, they will indeed find that during the journey R only elapsed 3/4 the time of E. Why should the comparison after both clocks "stop" in this frame be considered any less real than the comparison after R "stops" in the rest frame of E?

But we must ask the question "What does your clock read" and not set up a Lorentz grid or some other formalism that can only lead to a distorted answer as to how fast time appears to be moving in the other frame. We can make this determination at any point we wish during the trip - and by asking the question: "What does your clock read" rather than: "how fast does time appear to be passing while we are in relative motion" we arrive at the correct physical reality...at all times during the voyage, proper time in the R frame accrues twice as fast as it does in the E, C, A frame. The result would be no different if R is in an orbit around some great attractor which C happended to be the center of - and it is no different on any other experiment - the invariance of the interval assures us that it is the high speed pion and not the Earth clock that runs slow - real time dilation is a one way thing.

Well, see above, there is no reason to consider the time comparison in E's frame any more of a "physical reality" than the time comparison in any other. No matter what frame you choose, if both clocks "stop" in that frame then when they compare non-doppler shifted signals they will conclude that one clock is behind by exactly the amount that frame's coordinate system would predict.

Let me ask you this, if you had an object moving inertially at 0.99c relative to the Earth and another object traveling in a circle at constant speed in the first object's rest frame, then would you consider the earth-frame's analysis of this problem to be "distorted"? Note that if the circular-moving object came to rest relative to the inertial one, and in their new rest frame they agreed that the circular-moving one had elapsed 1/2 the time of the inertial one, in the earth-frame the signals between them would still appear to be extremely doppler-shifted since one object is moving towards the other's signals at 0.99c while the second is moving away from the first one's signals at 0.99c. So we would not conclude that the circular-moving one had elapsed 1/2 the time of the other, you only get that conclusion if you assume that the relative velocity between each object and their signals is c, which is not true in our frame.

 

[yogi]

Only if R "stops" in the inertial frame that E is at rest. But what if both R and E "stop" in some other inertial frame? If R has only made 1/4 of a full circle, I'm not sure if all inertial frames will agree that its average rate of ticking was slower than E (they would definitely agree on this if it made a full circle)

I think you have a hang up on the necessity of a round trip - there is a physical thing going on - 1/8 of a circle is as good as a half which is as good as 3/4 which is as good as a whole. Look at the physical reality of what is actually taking place - there is no way that any of the clocks can change the rate at which time progresses in their own frame after R reaches crusing velocity - the A, C and E clocks remain in the same frame from beginning to end, the R clock rides on a spaceship that changes direction at a continuous rate but the tangent velocity remainst constant (there is no energy added or subtracted to or from the spaceship) What could possibly cause R to run a different rate at different parts of the voyage. if you prefer we can consider R tied to C by a long teather - there is unchanging continuity during the journey

Think about each clock as being powered by a frictionless flywheel which has been cranked up to speed and geared to drive the hands of the clock - it spins on for years at the same rate - when the R clock is launced, the angular momentum of the flywheel should not change (or perhaps you think it does - if so how and why) In any event - if it does not change, the hands should keep moving at the same pace as those of E, C and A - but SR tells us that the hands now go slower - something physical has occurred - this is the crux of the SR puzzle.

 

[yogi]

Jesse - As to some of your other questions - go back again to Part 4 - Einstein puts both clocks in the same frame and then moves one - when you introduce other moving frames you will again be mixing real time events with apparent measurments - we can only have two frames if we are going to follow Einsteins scenerio - obviously if we ever come to an agreement on something then we could extrapolate to other situations - in fact that was what I tried to do in my original statement of this thread -i then shifted to the orbiting GPS clocks and then the big voyage centered on clock C to make it easy to illustrate how REAL values could not be any other way - obviously I did not do such a good job - so I will restate what i am convinced to be correct - namely - it doesn't make any difference if the R clock travels in a circle or in orbit in a G field (freely floating fame) or a straight line or a polygonal path - the reality of the situation is that the clock which is accelerated to reach a constant magnitude velocity after initial synchronization will run at a constant slower rate than the one which remains fixed - we can only find out by how much if we ask the question - what does the moving clock read when interrogated - we can pose this question at any time during the travel period or we can ask it when the moving clock is brought to rest in the same frame from which it was launched - if we try to predict the results in third frames - it obscures the issue.

 

[JesseM]

I think you have a hang up on the necessity of a round trip

Only because that's the only case where all frames will agree on the time elapsed on both clocks.

there is a physical thing going on - 1/8 of a circle is as good as a half which is as good as 3/4 which is as good as a whole.

But with less than a full circle, there is no reason to prefer one frame over another. If you disagree, what reason do you think there is?

Look at the physical reality of what is actually taking place - there is no way that any of the clocks can change the rate at which time progresses in their own frame after R reaches crusing velocity - the A, C and E clocks remain in the same frame from beginning to end, the R clock rides on a spaceship that changes direction at a continuous rate but the tangent velocity remainst constant (there is no energy added or subtracted to or from the spaceship)

The tangent speed remains constant in C's rest frame, but the tangent velocity does not, because velocity is a vector, and the tangent velocity vector points in different directions as R moves along the circle. And in a frame where C is not at rest, the tangent speed isn't constant either.

What could possibly cause R to run a different rate at different parts of the voyage.

The fact that its speed is changing (in some frame other than the rest frame of A, C and E), and rate of clock ticking depends on speed.

Again, yogi, you didn't address my questions. When I ask you questions, can you please not just ignore them? Do you agree that if R and C both "stop" in some other frame other than C's original rest frame, and afterwards they compare their times using radio signals, they will get a different answer to how much R fell behind then if R "stopped" in C's original rest frame and they compared times with radio signals? And what about the question about the clock that is moving at 0.99c in the Earth's frame, with another clock moving in a circle relative to the first--is the earth-frame's perspective on this situation an incorrect one, according to you?

Think about each clock as being powered by a frictionless flywheel which has been cranked up to speed and geared to drive the hands of the clock - it spins on for years at the same rate - when the R clock is launced, the angular momentum of the flywheel should not change (or perhaps you think it does - if so how and why) In any event - if it does not change, the hands should keep moving at the same pace as those of E, C and A - but SR tells us that the hands now go slower - something physical has occurred - this is the crux of the SR puzzle.

Again, as long as the laws of nature obey equations which have the mathematical property of lorentz-invariance, then it's inevitable you'll get relativistic phenomena like time dilation. For example, since Maxwell's laws of electromagnetism have this property, if you built a "clock" which could be understood totally in terms of electromagnetic laws--say, a charge which oscillates back and forth at a regular rate, which can occur in EM--then it's necessarily going to be true that if are moving inertially and this clock moves away from you and then comes back, it will have elapsed less time than yours. No need to have a specific theory of relativity, this is guaranteed to happen just based on the equations of electromagnetism, and would have to be true even if you believed in an ether theory which obeyed the same equations in the rest frame of the ether.

Anyway, if you admit your own intuitions tell you a clock should not change its rate just because it moves, but you can see these intuitions are somehow incorrect, then why do you feel so comfortable trusting your intuitions about which reference frame's perspective is the "correct" one and which frame's is "distorted"?

 

[JesseM]

Jesse - As to some of your other questions - go back again to Part 4 - Einstein puts both clocks in the same frame and then moves one - when you introduce other moving frames you will again be mixing real time events with apparent measurments

What is a "real time event" and what is an "apparent measurement"?

we can only have two frames if we are going to follow Einsteins scenerio

No, his scenario is only that you have two clocks at rest relative to each other, and then one accelerates towards the other. He chooses to analyze this situation in the frame where they are originally at rest, but this is not part of the "scenario", it is fundamentally no different from a choice of where to place the origin of the coordinate axes or a choice of whether to use cartesian or polar coordinates.

the reality of the situation is that the clock which is accelerated to reach a constant magnitude velocity after initial synchronization will run at a constant slower rate than the one which remains fixed

But for an object moving in a circle, "constant magnitude velocity" itself depends on your reference frame. Likewise, "initial synchronization" of separated clocks also depends on your choice of reference frame. These things are entirely coordinate-dependent, there is no rational reason to treat one frame's view of them as more valid then another's, so your own preferences can only be aesthetic ones.

 

[Hurkyl]

But we must ask the question "What does your clock read" and not set up a Lorentz grid or some other formalism that can only lead to a distorted answer as to how fast time appears to be moving in the other frame.

Aha! You have confessed to belief in absolute time. You have now unequivocally confirmed my suspicion that you are selecting one reference frame to be the preferred frame, and that all other reference frames are considered to be "distorted".

This is exactly what it means for one to consider time to be "absolute", or "universal", or such.


The question is why should that particular frame be preferred? It is just as much as "formalism" as any other reference frame.

Why isn't, say, the Andromedra frame the preferred one? (In which ECA are all moving) Can you write down an experiment that would prove the ECA is the preferred frame, whereas the Andromeda frame is not?

(No)

 

[yogi]

Hyrkyl - There may be many preferred frames in a particular experiment if we define preferred frame as a frame where we can determine reality at all times - For example let's take the case where we have our spaceship tethered to C and halfway out on the rope we add another clock - say J. Now J moves at half the speed of R. J moves at a constant velocity wrt to C. J is a preferred frame in the sense that it will always measure the R clock to be running at 1/4 the speed of light - each and every time it interrogates R and C it will find that the time lapsed on R is 1/2 that of C. In theory we can have an infinite number of these types of frames - all strung out along the rope joining R and C.

When Einstein made the shift from observational results to real time dilation in part 4 he implicitly made the rest frame a preferred frame - this is the bases of the twin thing and every other counterintuitive aspect of SR - if SR were nothing but an abstract theory of how things appear distorted in moving frames it would be of little use - in actuality, I see no justification for Einstein combining the equations as he did to arrive at the conclusion that one clock gets physically ahead of the other - it would seem that he should have said: The traveling clock appears to run behind the at-rest clock from the perspective of the at-rest clock and the at-rest clock appears to run behind the traveling clock when judged from the moving clock, and that both clocks read the same when the traveling clock is stopped so that it is at rest in the original frame. But he didn't say that - he went out on a limb and predicted a physical result that has fueled a 100 year debate. Actual time dilation does not follow from the mathematics - it is in fact a new postulate - couched in the mathematics of apparent observations, but not a logical consequence thereof. Einstein created a preferred frame thought experiment which results in the answer he had arrived at by intuition - as he said in one of his biographies - he had worked on the problem off and on for ten years - but it was always with me ... gradually I began to suspect time as the culprit. in actuality, Einstein turned a problem into a postulate. To get real time dilation, one frame had to be different from the other. If you choose to call it preferred - fine with me.

 

[yogi]

Jesse: "But with less than a full circle, there is no reason to prefer one frame over another. If you disagree, what reason do you think there is? "

There is every reason - because the C point I have chosen always gives the same value for the rate of the moving clock R. This is the same reason we choose the non rotating Earth centered reference system for GPS. The R clock should not change the pace at which it logs time during the voyage - the C clock measures this rate - i suppose you will say this is just its a convenience. True. Any clock on the ACE frame could be used to send and receive signals to R and as long as they ask the question "what does your clock read" we have an experiment that
comports with Einsteins 2 frame scenario. A third frame passing the whole experiment would raise the further issue - were the clocks in teh new frame ever properly synchronized in the ACE frame - that situation is undefined in Einsteins scenario

 

[JesseM]

Hyrkyl - There may be many preferred frames in a particular experiment if we define preferred frame as a frame where we can determine reality at all times - For example let's take the case where we have our spaceship tethered to C and halfway out on the rope we add another clock - say J. Now J moves at half the speed of R. J moves at a constant velocity wrt to C. J is a preferred frame in the sense that it will always measure the R clock to be running at 1/4 the speed of light

J is not a frame in the first place. And how can J "measure" the speed of the R clock at all, without using some coordinate system? Presumably you just mean how fast J will see R ticking using light signals, but all inertial frames will make the same prediction about this, so it makes no sense to treat this as evidence for a "preferred frame".

When Einstein made the shift from observational results to real time dilation in part 4 he implicitly made the rest frame a preferred frame

No he didn't, because he'd get the same answer if he analyzed the situation in some other inertial frame.

Actual time dilation does not follow from the mathematics

Yes it does. Given laws whose equations have the mathematical property of Lorentz-invariance (which, remember, is not a statement about relativity at all, it's just a purely mathematical property of certain equations, like saying a given equation is a 'polynomial'), it is logically impossible that clocks obeying these laws would fail to show genuine time dilation as in the twin paradox. Do you agree with this or not?