How does the Twins Paradox challenge our understanding of ageing?

[Evolver]

I called mirrors 'ideal' to assume that 100% of light is reflected.
You can replace that system with 2 lasers, detector, so when one side detects a signal it sends a light splash back. In such case no ideal mirrors are required. But for the discussion it is irrelevant.

Ok I understand this and agree with it... Now comes my confusion:

In the twin paradox, both twins would be using said ideal clock to measure their time... but as they separated away from one another near the speed of light, to the opposite twin the opposing twin's clock would read at a different rate, and each twin would say the others clock has changed. Each twin would experience a different rate of time relative to the others perspective.

 

[ThomasT]

No, of course.

Say, you have a stationary twin. The second one is
1. Accelerating distance L with acceleration a;
2. Then moving distance B without any acceleration;
3. breaks with the same acceleration (-a) the same distance B
4. accelerates back (B)
5. Moves distance B back without an acceleration
6. Breaks

Total distance traveled (in a frame of stationary observer) is 2*(L+B+L)=4L+2B
Now you repeat the experiment keeping the same a and L but varying B
If it was the acceleration which caused the time dilation then the effect would not depend on B which is wrong

? I didn't say that acceleration causes time dilation.

I said that acceleration alters the periods of oscillators.

 

[Dmitry67]

Period of oscilator IS proper time.
If you don't agree, then you are denying the axiom or special relativity: that speed of light is always c.

Of course you can deny it if you want, but then it must belong to some other thread.

 

[Mentz114]

ThomasT:

I said that acceleration alters the periods of oscillators.

maybe, but not clocks. For instance, a mechanical clock worn on the wrist undergoes lots of accelerations but still keeps time. The clocks used on spacecraft undergo great accelerations during launch but still keep time.

 

[matheinste]

No, we're talking about the same thing.

The net effect of the clock hypothesis is that you disregard accelerations and calculate in terms of instantaneous velocities.

But just consider the simple two-clock scenario I outlined a few posts ago. From it, we can deduce that it's during intervals of acceleration that changes in the tick rate of the accelerated clock are occurring.

The clock rates of each clock do not change. Their perceived rate is different between frames. That is normal time dilation. During changes of velocity the accelerating body moves through a sequence of different instantaneous comoving frames and so its ideas of simultaneity alters sequentially and the other clock's rate is appears to run differently due to this, in addition to the time dilation effect.

Matheinste.

 

[ThomasT]

The tick rate does not alter with acceleration.

You believe that the tick rate of the traveling clock isn't altered. Right?

You believe this because the spacetime geometric interpretation of SR provides an explanation (altered spacetime path) which precludes the alteration of tick rates vis accelerations. Right?

But remember that we're not using this interpretation of SR, because we want to see if there might be a more physical (and, yes, intuitive) approach to actually understanding the deep physics of differential aging.

So, with that in mind, is it logical to conclude that tick rate changes are occurring during periods of acceleration?

 

[matheinste]

You believe that the tick rate of the traveling clock isn't altered. Right?

You believe this because the spacetime geometric interpretation of SR provides an explanation (altered spacetime path) which precludes the alteration of tick rates vis accelerations. Right?

No, I believe the click rates are not altered because there is experimental evidence that this is the case.

Matheinste.

 

[Dmitry67]

So, with that in mind, is it logical to conclude that tick rate changes are occurring during periods of acceleration?

No,
I showed the example which proves that this hypotesis is wrong few posts above

 

[tryceo]

First of all, all the chemical process and the brain activity and everything that is going on in a human body would slow down RELATIVE to the twin on earth. The twin traveling at the near speed of light would not notice this change. So what seem to be 1 second to the light-speed moving twin would be years for the non-moving twin on earth.

 

[Dale]

ThomasT, you have stated that acceleration causes a change in the tick rate of clocks. What is the equation describing this relationship between acceleration and tick rate?

 

[jadgerz]

Things to ponder:
1. If velocity is relative then, between two moving objects, there is no faster or slower and thus time is not slower or faster for either one, i.e. the Twins Paradox is nada.
2. If an object were entirely alone in the universe it could never possesses "velocity".
3. Velocity cannot be measured internally but acceleration can thus, if between two objects that are accelerating from each other, it would be possible to determine which one is doing the accelerating and how much.
4. From the above, if there really is such as thing as time dilation, then I would put my money on acceleration as the "culprit". Anything that goes in a circle is accelerating even if it keeps a constant velocity. Anything circling the Earth or not going in an absolutely straight line such as shuttles and airplanes at a constant velocity are accelerating.
5. Even when acceleration stops the speed of the two objects is still "relative" to each other and if one object vanished from the Universe the remaining object would have no speed or velocity.
6. Amazing how all these movings objects return back to the same point in time when they come back together. What a cosmological book-keeping job that must be.
7. An object in the present does not exist in the future nor in the past so if one object beside another slowed down in time or sped up in time then "never the twain shall meet in the present". Funny how all those atomic clocks come back to the present.
8. Test: If we can ever get a space probe to achieve a significant portion of the speed of light it should possesses a radio beacon which "beeps" at a known, precise interval. If we measure the interval of the "beep" and it is what it should be then we will know there is no time dilation aboard the probe (think about it). If there is an increase or decrease in the interval then maybe there is something weird going on.
9. If there is something to the theory of "time dilation" then my bet, as I said before, is that it is due to acceleration and not velocity. I also would suspect that the phenomena is more analogous to temperature affecting chemical reaction rates rather than any actual disturbance of time.
10. Electrons have mass and they often reach near light speed velocities. When they do they don't possesses "near infinite" mass.

 

[sylas]

1. If velocity is relative then, between two moving objects, there is no faster or slower and thus time is not slower or faster for either one, i.e. the Twins Paradox is nada.

It is better to say, because velocity is relative, it is also relative which of two clocks is ticking faster.

The twins "paradox" simply helps explain that this is not in fact paradoxical at all. Many people find it paradoxical that identification of a faster or slower clock is relative. Examination of the twins thought experiment is used to show this is only an apparent paradox, to those who don't yet understand the theory of relativity very well.

3. Velocity cannot be measured internally but acceleration can thus, if between two objects that are accelerating from each other, it would be possible to determine which one is doing the accelerating and how much.
4. From the above, if there really is such as thing as time dilation, then I would put my money on acceleration as the "culprit". Anything that goes in a circle is accelerating even if it keeps a constant velocity. Anything circling the Earth or not going in an absolutely straight line such as shuttles and airplanes at a constant velocity are accelerating.

Yes, you can determine accelerations (in the absence of gravity) internally. That is, this is NOT relative in the same sense as velocity is relative.

Your notion of the culprit is mistaken, I am afraid. The time dilation is precisely the same for particles moving in a circle at some speed, or moving in a straight line at the same speed. Yet the acceleration only applies in the first case. Einstein used this very example to show that the dilation is associated with speed, not with acceleration. His discussion of this point is a topic we explain here regularly for people who find it confusing.

8. Test: If we can ever get a space probe to achieve a significant portion of the speed of light it should possesses a radio beacon which "beeps" at a known, precise interval. If we measure the interval of the "beep" and it is what it should be then we will know there is no time dilation aboard the probe (think about it). If there is an increase or decrease in the interval then maybe there is something weird going on.

This test is done, and with accurate clocks you don't even need to get within a significant fraction of the speed of light. The effect can be measured using accurate clocks on a flights with a regular commercial airline, and this test was first performed in 1971.Welcome to the forum, jadgerz. There are people here who can help you get expectations that are more consistent with what we know about relativity. You have a ways to go on that, but its worth learning about.

Cheers -- sylas

 

[atyy]

You believe this because the spacetime geometric interpretation of SR provides an explanation (altered spacetime path) which precludes the alteration of tick rates vis accelerations. Right?

But remember that we're not using this interpretation of SR, because we want to see if there might be a more physical (and, yes, intuitive) approach to actually understanding the deep physics of differential aging.

So, with that in mind, is it logical to conclude that tick rate changes are occurring during periods of acceleration?

Yes, it is logical, a pendulum clock provides an example. In the twin paradox using ideal clocks, an ideal clock is defined to be one whose tick rate does not change. In recognition that the possibility you mentioned is logical, the definition of an ideal clock is an additional axiom of special relativity (if I interpret Fredrik correctly, this "clock hypothesis" is his favourite axiom).

 

[sylas]

... But remember that we're not using this interpretation of SR, because we want to see if there might be a more physical (and, yes, intuitive) approach to actually understanding the deep physics of differential aging.

So, with that in mind, is it logical to conclude that tick rate changes are occurring during periods of acceleration?

Yes, it is logical, a pendulum clock provides an example. [...]

Guys, just to keep this discussion on track, I'm going to lay down a strong statement on the substance of this discussion.

ThomasT has some misconceptions about relativity and time dilation, and there has been a useful discussion with good input from a number of regulars in trying to help sort this out.

In fact, ThomasT's conclusion is not logical, in the sense that it does not follow formally, except possibly by a hidden presumption of things we know to be incorrect. Hence atyy's reply may be confusing. Almost always in these discussions the error comes back to failing to realize that simultaneity is relative. You cannot use the notion of "at the same time" and presume it means the same thing for all observers.

The pendulum tick rate depends on the local gravitational field strength, which by the principle of equivalence is the same as a dependency on acceleration. The association is not the same as the gravitational time dilation of general relativity. A pendulum is not a "clock" in the sense used in relativity discussions, or in ThomasT's post. It is rather an accelerometer. You can measure acceleration by comparing a clock with a pendulum.

Special relativity can handle acceleration just fine; but you need general relativity to properly consider the effects of gravity on spacetime. The physics of differential aging due to motions of any kind, acceleration included, is explained with special relativity.

Other members are doing a good job in trying to help explain this, and so carry on by all means. But for readers wondering, this discussion will have been most useful when all participants can get a clearer understanding of conventional physics and standard relativity.

Getting a deeper understanding of differential aging is a good thing. ThomasT, you have the benefit here that you are talking with a number of members who do have a deeper understanding of differential aging.

Cheers -- sylas

 

[Dale]

I guess my confusion then stems from the idea of how an ideal clock can exist. Because if SR says there is no absolute reference frame, then how can their be one clock to measure absolutely?

There doesn't need to be one clock to measure absolutely, any good clock will do regardless of its state of motion.

I understand that they may exist, but my confusion is concerning how is that possible? And perhaps you could give me an example as simply saying that an ideal clock measures time for all reference frames does not help my confusion about what you're saying.

Certainly I can provide an example and some details. The Wikipedia article on proper time is decent:
http://en.wikipedia.org/wiki/Proper_time

Basically, proper time is the integral of the spacetime interval over the path of the clock. You can think of this interval as "distance" or "arc length" in spacetime. So a clock is simply a device which measuring the length of timelike intervals in spacetime.
$$\tau = \int_P ds$$
where the spacetime interval s is given by
$$ds^2 = g_{\mu\nu} \, dx^\mu \, dx^\nu$$
where x is the coordinate of the clock in some arbitrary reference frame (can be non-inertial) and g is the metric in that reference frame. For standard special relativity (inertial reference frame, flat spacetime, Minkowski metric) this can be explicitly written as:
$$\tau = \int_P \sqrt{dt^2-\frac{dx^2}{c^2}-\frac{dy^2}{c^2}-\frac{dz^2}{c^2}}$$
and if the spacetime path is parameterized by some parameter $\lambda$ then we can write this integral as
$$\tau = \int \sqrt{\left(\frac{dt}{d \lambda} \right)^2-\frac{1}{c^2} \left( \left(\frac{dx}{d \lambda} \right)^2 + \left(\frac{dy}{d \lambda} \right)^2 + \left(\frac{dz}{d \lambda} \right)^2 \right)} \, d \lambda$$

So, let's say that we have a clock undergoing uniform circular motion at 0.6 c in some inertial reference frame such that its coordinates (in units where c=1) are given by:
$$x(t) = cos(0.6 \, t)$$
$$y(t) = sin(0.6 \, t)$$
$$z(t) = 0$$
plugging this into the equation above gives:
$$\tau = \int \sqrt{\left(\frac{dt}{dt} \right)^2- \left( \left(\frac{dx}{dt} \right)^2 + \left(\frac{dy}{dt} \right)^2 + \left(\frac{dz}{dt} \right)^2 \right)} \, dt$$
$$= \int \sqrt{1 - \left( \left(-0.6 sin(0.6t) \right)^2 + \left( 0.6 cos(0.6t) \right)^2 \right)} \, dt$$
And integrating this from t=0 to t=1 gives 0.8, which is exactly what you would expect for a clock moving at v=0.6c.

Now, if we boost this to an inertial reference frame moving at 0.5 c in the x direction wrt the unprimed frame we get:
$$t'(t) = 1.15 t - 0.58 cos(0.6 t)$$
$$x'(t) = -0.58 t + 1.15 cos(0.6 t)$$
$$y'(t) = sin(0.6 t)$$
$$z'(t) = 0$$
plugging this into the equation above gives:
$$\tau = \int \sqrt{\left(\frac{dt'}{dt} \right)^2- \left( \left(\frac{dx'}{dt} \right)^2 + \left(\frac{dy'}{dt} \right)^2 + \left(\frac{dz'}{dt} \right)^2 \right)} \, dt$$
$$= \int \sqrt{ (1.15 + 0.35 sin(0.6 t))^2 - \left( (-0.58 - 0.698 sin(0.6 t))^2 + (0.6 cos(0.6 t))^2 \right)} \, dt$$
And integrating this from 0 to 1 also gives 0.8

 

[atyy]

Roughly speaking, if SR is true, an ideal clock exists, because (i) proper time is absolute ("really exists"), and (ii) acceleration is also absolute and can be measured and corrected for. Of course, in real life, we have to figure out what clocks are ideal, and what not.

 

[matheinste]

Roughly speaking, if SR is true, an ideal clock exists, because (i) proper time is absolute ("really exists"), and (ii) acceleration is also absolute and can be measured and corrected for.

A quote along those lines

Rindler- Essential Relativity. Page 43.

""If an ideal clock moves through an inertial frame, we shall assume that acceleration as such has no effect on the rate of the clock i.e., that its instantaneous rate depends only on its instantaneous speed------.
---This we call the clock hypothesis. It can also be regarded as the definition of an “ideal” clock. By no means all clocks meet this criterion----.
----on the other hand, the absoluteness of acceleration ensures that ideal clocks can be built, in principle. We need only take an arbitrary clock, observe whatever effect acceleration has on it, then attach it to an accelerometer and a servomechanism that exactly cancels the acceleration effect. By contrast, the velocity cannot be eliminated.""

Matheinste.

 

[ThomasT]

ThomasT, you have stated that acceleration causes a change in the tick rate of clocks. What is the equation describing this relationship between acceleration and tick rate?

What's the equation relating the instantaneous tick rate of a clock with its instantaneous speed?

Instantaneous tick rate and instantaneous speed do vary proportionally, don't they?

If so, then that would seem to support the idea that accelerations (changes in speed) affect the periods of oscillators -- despite the fact that acceleration has been more or less formally structured out of consideration.

 

[ThomasT]

ThomasT has some misconceptions about relativity and time dilation ...

I'm just not satisfied with "different spacetime paths" as an explanation for differential aging.

 

[Dale]

What's the equation relating the instantaneous tick rate of a clock with its instantaneous speed?

$$\frac{d\tau}{dt} = \sqrt{1-v^2/c^2}$$
where v is actually speed, not velocity.

Instantaneous tick rate and instantaneous speed do vary proportionally, don't they?

No. It is a non-linear relationship, see above.

If so, then that would seem to support the idea that accelerations (changes in speed) affect the periods of oscillators -- despite the fact that acceleration has been more or less formally structured out of consideration.

How so? As given above, the tick rate is not a function of acceleration or any higher derivatives of position, so I don't see how it would support that idea at all.

I'm just not satisfied with "different spacetime paths" as an explanation for differential aging.

That is a personal bias, not an argument.

 

[vela]

Instantaneous tick rate and instantaneous speed do vary proportionally, don't they?

No, but you're probably misusing the word "proportionally," so you're not asking what you really mean.

If so, then that would seem to support the idea that accelerations (changes in speed) affect the periods of oscillators -- despite the fact that acceleration has been more or less formally structured out of consideration.

Obviously, if the clock's speed increases or decreases, the stationery observer will see its tick rate change. So in that sense, yes, acceleration affects the period of oscillators, but acceleration itself does not directly do so. Mathematically, you'd say

$$\frac{dt}{d\tau} = f(\beta)$$

where $\beta$ is the velocity, not

$$\frac{dt}{d\tau} = f(\beta,\beta')$$

To say that acceleration affects the period of oscillators in the way I suspect you mean it is really just playing word games.

I'm just not satisfied with "different spacetime paths" as an explanation for differential aging.

That's the fundamental problem. The difference is a consequence of the geometry of spacetime, and you're saying, "I don't accept the correct answer. What's another correct answer?" I do get what you're saying though. The Lagrangian formulation of mechanics doesn't provide one with an intuitive feeling for why a projectile follows the path it does whereas thinking in terms for forces does. But that's really not the case here with SR.

 

[jadgerz]

Sylas,

You are a bit condescending in your response, however, I need to take issue with your statements. You made one statement which tells me that maybe you'd need a bit more education in physics.

Your statement: "Yes, you can determine accelerations (in the absence of gravity) internally. That is, this is NOT relative in the same sense as velocity is relative." is a bit of a "babble" and a bit "non sequitir". Maybe unbeknownst to you there is this thing called "inertial guidance" which works quite well in gravity. Submarines use it and before GPS aircraft used it quite extensively. Acceleration is not RELATIVE at all in any sense.

Answer me this: If there are but two objects, A and B, in a hypothetical universe and object A observes B moving at a certain velocity x and object B sees object A moving at a certain velocity x who is moving faster? If the time dilation hypothesis says the faster moving object experiences greater time dilation which one takes the honor?

The theory of relativity simply states that there is no "fundamental" frame of reference. Velocity is dependent upon an outside reference and acceleration is not. Paradoxes are mental constructs and do not exist in the real world.

Atomic clocks: To my understanding there are 45 atomic clocks working to determine "official" time. All these clocks have a variance and real time (sic) is an average of them all. Atomic clocks on airplanes and GPS satellites experience this variance and must be adjusted from time to time to correlate with the "official" average. The fact that these clocks on airplanes, etc. show a variance with the average of the 45 atomic clocks is no proof of "time dilation". Time dilation is not proven or demonstrated.

I'll pause here and let you ponder my statements. I don't claim to have an answer to the universe but I know one thing for sure, no one else does either.
"

 

[sylas]

Your statement: "Yes, you can determine accelerations (in the absence of gravity) internally. That is, this is NOT relative in the same sense as velocity is relative." is a bit of a "babble" and a bit "non sequitir". Maybe unbeknownst to you there is this thing called "inertial guidance" which works quite well in gravity. Submarines use it and before GPS aircraft used it quite extensively. Acceleration is not RELATIVE at all in any sense.

Inertial guidance works because accelerations are not relative. They rely on measurements of acceleration, which are unaffected by velocity; only by change in velocity.

Answer me this: If there are but two objects, A and B, in a hypothetical universe and object A observes B moving at a certain velocity x and object B sees object A moving at a certain velocity x who is moving faster? If the time dilation hypothesis says the faster moving object experiences greater time dilation which one takes the honor?

Velocity is relative, and so there is no absolute answer to this. Which one is moving faster, and which one has the greater time dilation, depends on the observer. That is, there is no fundamental frame in which to give the answer.

Atomic clocks: To my understanding there are 45 atomic clocks working to determine "official" time. All these clocks have a variance and real time (sic) is an average of them all. Atomic clocks on airplanes and GPS satellites experience this variance and must be adjusted from time to time to correlate with the "official" average. The fact that these clocks on airplanes, etc. show a variance with the average of the 45 atomic clocks is no proof of "time dilation". Time dilation is not proven or demonstrated.

The effects of time dilation are several orders of magnitude greater than the tiny random variations which exist because of an atomic clock's intrinsic accuracy. This has allowed time dilation to be demonstrated many times by measuring differences that are well within the accuracy of atomic clocks to determine.

The clocks of a GPS system on satellites, for example, have a constant small shift, which can be calculated using relativity. They end up running slightly faster than when on Earth, by about 38 μs per day. To account for this, the on board atomic clocks have their frequency deliberately reduced from 10.23 MHz to 10.22999999543 MHz. It is not comparable to the much much smaller random shifts in an ensemble of clocks, due to variations between them.

But my favourite example by far is of a physicist with a young family. He took his kids on a camping trip up Mt Rainer along with some atomic clocks, while Mum stayed home with clocks in the kitchen. See Clocks, Kids, and General Relativity on Mt Rainier. Here is a picture of the kids in a van carrying three clocks (using an ensemble to deal with the small drifts that do occur).

The clocks up the mountain run faster. By going up the mountain with his kids, this Dad got to spend an extra 22 nanoseconds with his kids that he'd have missed by staying home. As he says: It was the best extra 22 nanoseconds I've ever spent with the kids. This is much less dilation than in the GPS satellite, but still easily within the capacity of an off the shelf atomic clock to demonstrate.

I'll pause here and let you ponder my statements. I don't claim to have an answer to the universe but I know one thing for sure, no one else does either.
"

We don't have the complete answer to the universe, but we do have answers on basic physics questions that students are learning about.

This is primarily an education site, and your questions are ones that are normal as people learn about relativity. None of this will be easy to grasp straight off. All of us here have had the experience of working through the initially counter intuitive notions and learning about physics. Some have learned more than others. I've learned more about about relativity than you have, and others here have learned a lot more about it than I have.

People are going to give you confident answers to your questions when they know the answers to them. No insult is intended in this and there's no reason to take offense. The whole idea of the site is to encourage learning about the details of modern physics.

Cheers -- sylas

 

[Dale]

Time dilation is not proven or demonstrated.

Yes, it is: http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#Tests_of_time_dilation

 

[DaveC426913]

You made one statement which tells me that maybe you'd need a bit more education in physics.

Uh well, if he does it won't be coming from you...

The fact that these clocks on airplanes, etc. show a variance with the average of the 45 atomic clocks is no proof of "time dilation".

Do you have an alternate explanation? The actual lag experienced by these jets is exactly in accordance with GR.

Time dilation is not proven or demonstrated.

It is one of the most demonstrated phenomena in physics. Every particle fired through an accelerator exhibits this effect; every airplane with a clock in it, and every GPS satellite. Much of our modern navigation technology is built upon it. If the technology did not compensate for this effect, it would not work.


And yeah. That Mt. Rainer experiment is awesomely awesome.

[ EDIT: Ah. I see Sylas has already dealt with you. And more diplomatically than I, especially considering he was the one you were being so condescending to.]

 

[Al68]

In the experiment where you have two identical clocks, with identical tick rates sitting side by side, and you accelerate one to wherever, then bring it back to rest beside the unmoved clock, it's obvious that the tick rate of the traveling clock has been altered during the trip. It follows that the tick rate of the traveling clock was altered due to velocity changes (during intervals of acceleration) during its round trip.

And of course it follows that accelerations affect the periods of oscillators. This is all I want to say ... really.

This simple experimental scenario seems to falsify the clock hypothesis.

Why? The result you obtained is the result that would be obtained by assuming the clock hypothesis to be true.

But the tick rate of the accelerated clock wasn't "altered due to velocity changes". The clock's rate being frame dependent isn't an alteration. An unaccelerated clock's rate is frame dependent, too.

 

[ThomasT]

To say that acceleration affects the period of oscillators in the way I suspect you mean it is really just playing word games.

I mean that the periods of oscillators (the tick rates of clocks) change during intervals when their (the oscillators, the clocks, etc.) velocities are changing. I don't think this is an ambiguous statement, and it's supported by the outputs of accelerometers and accelerated clocks.

However, the mainstream interpretation of SR is as odds with this, and attributes differential aging to different paths in a spacetime geometry. Wrt this formulation, the tick rates of clocks, the periods of oscillators, don't change. This is what I'm disagreeing with.

I don't think that the mainstream interpretation of SR should be taken as a literal description of reality. It's an invention -- for calculation, and visualization of a sort.

That's the fundamental problem. The difference is a consequence of the geometry of spacetime, and you're saying, "I don't accept the correct answer. What's another correct answer?"

Well, there are correct answers, and then there are correct answers. If one doesn't want to accept the spacetime geometric interpretation of SR as the final word (and one certainly isn't required to), then one might want to look at what's happening during intervals of acceleration.

My guess is that when more science is done, it will be found that accelerations do affect tick rates.

Thanks to everyone who commented.

 

[vela]

I mean that the periods of oscillators (the tick rates of clocks) change during intervals when their (the oscillators, the clocks, etc.) velocities are changing. I don't think this is an ambiguous statement, and it's supported by the outputs of accelerometers and accelerated clocks.

Actually, it is an ambiguous statement as I explained in my earlier post. You can interpret it two ways, and you're interpreting it the way everyone disagrees with and which disagrees with experimental evidence.

Well, there are correct answers, and then there are correct answers. If one doesn't want to accept the spacetime geometric interpretation of SR as the final word (and one certainly isn't required to), then one might want to look at what's happening during intervals of acceleration.

My guess is that when more science is done, it will be found that accelerations do affect tick rates.

You don't have to accept the geometric interpretation of spacetime. You can just take the equations of SR, which have been verified countless times, at face value. Simply put, time dilation only depends on the relative velocity, not on the acceleration.

 

[Al68]

I mean that the periods of oscillators (the tick rates of clocks) change during intervals when their (the oscillators, the clocks, etc.) velocities are changing. I don't think this is an ambiguous statement, and it's supported by the outputs of accelerometers and accelerated clocks.

It's ambiguous because you omitted the word "relative" before the word velocity. The tick rate of a clock depends on the relative velocity between clock and reference frame, regardless of the clock's acceleration.

A change in this relative velocity can mean three things:

1. The clock accelerated.
2. The reference frame accelerated.
3. Both 1 and 2.

The tick rate of a clock changes with a change in relative velocity independently of which of those 3 things happened, ie independently of the acceleration of the clock.

Your statement would equally apply to an unaccelerated clock: The tick rate of a clock on Earth will change relative to an observer on a spaceship that accelerated away from earth, because the relative velocity between clock and reference frame changed, the exact same reason that the above clock's rate would change, despite the fact that the clock in this case didn't accelerate.

The tick rate of an ideal clock is always T*sqrt(1-v^2/c^2) where T is the at rest tick rate of the clock and v is the relative velocity between the clock and the reference frame.

If the clock accelerates, it's tick rate before, during, and after after acceleration is T*sqrt(1-v^2/c^2). If it isn't, then it's not a valid clock in SR.

My guess is that when more science is done, it will be found that accelerations do affect tick rates.

Do you think future experiments will contradict the many already performed, or that future experiments will use faulty clocks that are affected by acceleration? So far, if the clocks used were affected by acceleration, the deviation was too small to detect, indicating that the clocks were close enough to ideal, even if not perfect.

An ideal clock would have no mechanism to detect acceleration, would have no way to "know" whether it accelerated, and would be incapable of altering its tick rate in any way even if it did.

 

[ThomasT]

You can interpret it two ways:

... the periods of oscillators (the tick rates of clocks) change during intervals when their (the oscillators, the clocks, etc.) velocities are changing.

Seems pretty clearly stated to me. What are the two ways that you'd interpret the above?

Simply put, time dilation only depends on the relative velocity, not on the acceleration.

As a general statement, yes of course that's true. But if you introduce an acceleration anomaly into an otherwise uniform dilation pattern, then what?

 

[ThomasT]

It's ambiguous because you omitted the word "relative" before the word velocity. The tick rate of a clock depends on the relative velocity between clock and reference frame.

A change in this relative velocity can mean three things:

1. The clock accelerated.
2. The reference frame accelerated.
3. Both 1 and 2.

The tick rate of a clock changes with a change in relative velocity independently of which of those 3 things happened, ie independently of the acceleration of the clock.

Ok, thanks for clarifying. I've only been dealing with, 1. the clock accelerated, for this entire discussion. I thought that was assumed, since this is a thread about the twin clocks and differential aging. I thought it was assumed that velocity of the traveling clock meant velocity wrt at rest beside the other clock on earth.

That should take care of any ambiguities. The rest is a matter of science.

 

[ThomasT]

If the clock accelerates, it's tick rate before, during, and after after acceleration is T*sqrt(1-v^2/c^2). If it isn't, then it's not a valid clock in SR.

This seems to support my statement. Per the above, the tick rate will show an anomalous variance as v varies.

 

[Al68]

Ok, thanks for clarifying. I've only been dealing with, 1. the clock accelerated, for this entire discussion. I thought that was assumed, since this is a thread about the twin clocks and differential aging.

Yes, but your statements indicate that a resulting change in tick rate is caused by 1, even though we would get the same exact resulting tick rate without 1. That indicates the resulting tick rate wasn't caused by 1.

I would also note that in the twins case, differential aging isn't the same thing as a clock's instantaneous tick rate. In Earth's frame, the ship's clock ticks at the same (slow) rate after acceleration as it did before the acceleration.

So the tick rate varies with v, is that correct?

Yes, where v is the relative velocity between the clock and a given reference frame. A change in v may or may not coincide with acceleration of the clock, but will affect its tick rate equally either way.

Edit: Sorry, I edited my previous post after you responded. I have to stop doing that.

 

[sylas]

So the tick rate varies with v, is that correct?

Yes. It would be best to omit "the", and just say "tick rate depends on v", because different observers considering the same clock will have different tick rates, depending on the observer.

The tick rate is r(1-(v/c)²)^0.5, where v is the relative velocity of the clock and the observer determining a tick rate, and r is the tick rate of the clock at rest. Note that it is non-linear, so "depends on" is better than "varies with".

 

[Al68]

This seems to support my statement. Per the above, the tick rate will show an anomalous variance as v varies.

Sure, but I wouldn't call it anomalous. But it's only the change in v that matters. It's irrelevant whether or not the change in v was caused by acceleration of the clock.

How about this analogy: Two equal mass cars crash head on. The severity of the crash depends on the relative kinetic energy which varies with the relative velocity between the cars.

Sure the relative velocity between the cars was affected by the previous acceleration of one or both cars, but the relative kinetic energy and therefore the severity of the crash, depends only on the relative velocity between the cars, regardless of whether one car or the other or both previously accelerated.