How does the Twins Paradox challenge our understanding of ageing?

[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.

 

[Dale]

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.

How is it supported by the experimental results? You have not given an equation yet that we can compare to experimental results.

I repeat my earlier request for the equation describing this relationship between acceleration and tick rate. The SR formula has been given, is well supported by the evidence, and depends only on velocity and not on higher derivatives of position.

 

[jadgerz]

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


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


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.]

I am amazed at how people are (still) such slaves to dogma. And how "nasty" they get when you "dare" disturb their locked minds. The experiment done back in 1971... if my memory serves me right... the Hafele and Keating experiment (?) was later torn to shreds after a review, one being the inventor of atomic clocks themselves (or some important association) if I recall. I neither deny or accept the theory of time dilation. I read it myself and although I don't proclaim to be an expert my response would be: "I wouldn't pay money for it". My point is that there is some reasonable doubt, or at least serious unanswered questions in regards to time dilation and for those who say: "This is how it is" are a total bore. I was hoping for an intelligent discussion on the matter but I find myself confronted with people possessed with a conditon known as "Doctrinaire Loyale". This condition usually afflicts religious zealots who still believe the world is flat, or the Earth was created in October 6006 BC. or that the Earth is the center of the universe. They flinch in pain when you say something contrary to their beloved dogma. Do I risk being burned at the stake for daring to question the validity of "time dilation"? (Oh, the ghost of Bruno!). Some greeting this is to "the new kid on the block". Please, I am a degreed person, well studied in physics, science and engineering. I'm seriously looking for people who can discuss this matter with an open, logical mind. May I start afresh and ask you "learned" folks again my questions?

 

[russ_watters]

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...

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.

[separate post]May I start afresh and ask you "learned" folks again my questions?

Sure, you may start again. We don't hold grudges here. However, we also recognize when we're pumping a dry well: Sylas's response to your first post was not in the least bit condescending, but your posts are dripping with attitude. Your ability to learn - and our willingness to teach you - will require that you drop your attitude and really start trying to understand what people are explaining to you. Please understand, we're not here for the fun of arguing with crackpots or beating down people who know less: this forum is here to help teach people physics and the people who make significant contributions are sincere in their desire to teach people. So you can decide which you are - someone who wants to learn or a crackpot who just wants to berate the dogmatic establishment - and choose to start fresh... or not.

 

[atyy]

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.

Not exactly, but close. Velocity is frame dependent, acceleration is absolute - in loose language, there is no such thing as velocity, whereas acceleration really exists. In that sense, time dilation thought of as clocks running slow or fast is relative, since the rate of a clock would have the form dT1/dT2, where one of the Ts is a coordinate time, which is frame dependent. So in that sense, there is not really such a thing as time dilation - we think of differences in clock readings as differences in integrals, not derivatives. Since there is not really such a thing as time dilation, the rest of your argument is moot.

 

[atyy]

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

But we already know that acceleration affects the "rates" of some clocks, such as pendulum clocks.

Acceleration does not affect the rate of an ideal clock, by definition. So we will never find that acceleration affects the rate of an ideal clock, since if acceleration affects the rate of a clock, then the clock is not ideal.

BTW, what do you mean by the rate of a clock? To define the rate of a clock, don't you need some other clock or clocks to compare it with?

 

[matheinste]

I am amazed at how people are (still) such slaves to dogma. And how "nasty" they get when you "dare" disturb their locked minds. The experiment done back in 1971... if my memory serves me right... the Hafele and Keating experiment (?) was later torn to shreds after a review, one being the inventor of atomic clocks themselves (or some important association) if I recall. I neither deny or accept the theory of time dilation. I read it myself and although I don't proclaim to be an expert my response would be: "I wouldn't pay money for it". My point is that there is some reasonable doubt, or at least serious unanswered questions in regards to time dilation and for those who say: "This is how it is" are a total bore. I was hoping for an intelligent discussion on the matter but I find myself confronted with people possessed with a conditon known as "Doctrinaire Loyale". This condition usually afflicts religious zealots who still believe the world is flat, or the Earth was created in October 6006 BC. or that the Earth is the center of the universe. They flinch in pain when you say something contrary to their beloved dogma. Do I risk being burned at the stake for daring to question the validity of "time dilation"? (Oh, the ghost of Bruno!). Some greeting this is to "the new kid on the block". Please, I am a degreed person, well studied in physics, science and engineering. I'm seriously looking for people who can discuss this matter with an open, logical mind. May I start afresh and ask you "learned" folks again my questions?

The problem with accusations of dogma is that those accused are allowed no argument in reply as any arguments they use will also be labelled as dogmatic.

You say you are looking to discuss issues with an open and logical mind, that's what we all want to do. But when people have looked at the evidence with "open and logical minds" and have come to conclusions other than those you want, you label them as dogmatic. Mistaken maybe, (though I do not believe so) but dogmatic no.

Matheinste.

 

[jadgerz]

The problem with accusations of dogma is that those accused are allowed no argument in reply as any arguments they use will also be labelled as dogmatic.

You say you are looking to discuss issues with an open and logical mind, that's what we all want to do. But when people have looked at the evidence with "open and logical minds" and have come to conclusions other than those you want, you label them as dogmatic. Mistaken maybe, (though I do not believe so) but dogmatic no.

Matheinste.

I agree. Let's just say that "ruffled feathers have been smoothed" and let's start afresh. Good, that done, let's continue our discussions in a civilized manner.

The one honorable and learned gentlemen earlier implied that the tests done by Hafele & Keating in 1971 gave results that were "exactly" what would be predicted by GR. Well, that is not so. For the eastbound flight the predicted (calculated) time dilation was (-40 +/- 23) nanoseconds. The H&K experiment had an observed time dilation of (-59 +/- 10) nanoseconds. Hardly exact. An interesting read on this experiment is by Dr. Kelly (PhD), which I suggest you read, and another critique by the inventor of the atomic clock. Quite frankly, if the H&K experiment was introduced as evidence in a court of law I believe it would be summarily rejected.

What does such a variance in the predicted and the "observed" results of the H&K experiment imply? It implies doubt. Look at the range of the predicted dilation. It could be from 17 to 63 nanoseconds. Not quite the accuracy mentioned by the other honorable and learned gentlemen. If it were as precise as mentioned then it would be "exact"

 

[jadgerz]

But we already know that acceleration affects the "rates" of some clocks, such as pendulum clocks.

Acceleration does not affect the rate of an ideal clock, by definition. So we will never find that acceleration affects the rate of an ideal clock, since if acceleration affects the rate of a clock, then the clock is not ideal.

BTW, what do you mean by the rate of a clock? To define the rate of a clock, don't you need some other clock or clocks to compare it with?

At the risk of appearing to take sides, let me make a comment in support of ThomasT's assertion. If you study the Hafele & Keating's experiment from 1971 you will see it was necessary to predict the time dilation effect of both Special and General Relativity. Special Relativity being the Kinematic Relativity and General being the Gravitional. Now, correct me if I'm wrong but Gravity, to my understanding, is a Force, correct? Well, to invoke the name of Newton, he said that Force (F) is equal to mass times acceleration (ma). F = ma. Of course you know all this and I don't mean to suggest you don't. Just a reminder of the point for the argument at hand. The presence of gravity implies acceleration and since gravity (so it is said) affects the rate of an ideal clock in General Relativity then so does acceleration.

If Thomas T is asserting that acceleration affects the rate of the clock as opposed to an actual dilation of time then he has my vote for now. May I suggest (as have others more knowledgeable than myself) that this time dilation phenomena in a gravitational field (accelerration) is analoguous (spelling?), but not exactly, to a chemical rate of reaction in varying temperature regimes.

I hope I haven't offended either of you in bringing this up. God Bless all of you.

 

[Dale]

For the eastbound flight the predicted (calculated) time dilation was (-40 +/- 23) nanoseconds. The H&K experiment had an observed time dilation of (-59 +/- 10) nanoseconds. Hardly exact.

True, the H&K experiment had a relatively low precision, as you would expect at such low velocities. But despite the low precision the result does agree with SR and does not agree with Newtonian physics.

However, time dilation is well established to very high precision in a wide variety of experiments at many laboratories using many different techniques. The data is overwhelmingly in support of time dilation. All of the reputable scientific data points to the correctness of the SR prediction, some to within several percent, and some to within a few parts per million. Here is a sampling:

G. Gwinner, Mod. Phys. Lett. 1, 20, no. 11 (2005), pg 791.
H.E. Ives and G.R. Stilwell, J. Opt. Soc. Am. 28 pg 215–226 (1938);
H.E. Ives and G.R. Stilwell, JOSA 31 pg 369–374 (1941).
Otting, Physik. Zeitschr. 40, 681 (1939).
Hasselkamp et al., Z. Physik A289 (1989), pg 151.
Rossi and Hoag, Physical Review 57, pg 461 (1940).
Rossi and Hall, Physical Review 59, pg 223 (1941).
Rasetti, Physical Review 60, pg 198 (1941).
Redei, Phys. Rev. 162 no. 5 (1967), pg 1299.
Durbin, Loar and Havens, Physical Review 88, pg 179 (1952).
D. Frisch and J. Smith, Am. J. Phys. 31 (1963) 342.
Terell, Nuovo Cimento 16 (1960) pg 457.
Greenberg et al., Phys. Rev. Lett. 23 no. 21 (1969), pg 1267.
Ayres et al., Phys. Rev. D3 no. 5 (1971), pg 1051.
Burrowes et al., Phys. Rev. Lett. 2 (1959), pg 117.
Kaivola et al., Phys. Rev. Lett. 54 no. 4 (1985), pg 255.
McGowan et al., Phys. Rev. Lett. 70 no. 3 (1993), pg 251.
Hay et al., Phys. Rev. Lett. 4 (1960), pg 165.
Kuendig, Phys. Rev. 129 no. 6 (1963), pg 2371.
Olin et al., Phys. Rev. D8 no. 6 (1973), pg 1633.
Mandelberg and Witten, Journal Opt. Soc. Amer. 52, pg 529 (1962).

 

[sylas]

The one honorable and learned gentlemen earlier implied that the tests done by Hafele & Keating in 1971 gave results that were "exactly" what would be predicted by SR. Well, that is not so. For the eastbound flight the predicted (calculated) time dilation was (-40 +/- 23) nanoseconds. The H&K experiment had an observed time dilation of (-59 +/- 10) nanoseconds. Hardly exact.

Certainly there were measurement errors; there always are in this and any other experiment. You should not read that remark as saying the experimental result was exact, but rather that the experiment was completely consistent with relativity, and that it falsified the Newtonian view of an absolute time.

The actual comment was by DaveC426913, and in his own words it is as follows:

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.

Dave is correct, and it is a rather strange reading of his words to think he means that the lag was actually measured exactly. A more natural understanding of this phrase is that the actual lag -- which we can measure only to a limited precision, of course -- is completely consistent with the exact value given by relativity. But if it is confusing, no doubt he would rephrase.

What is definitely INCORRECT, however, is to say that measurements of clocks on jets can be explained as a natural variance analogous to the variance between the multiple clocks (45?) used to keep track of a reference time for Earth's surface.

The consideration of measurement uncertainties is enough to show that time dilation exists, and that it matches the relativistic exact solution within measurement precisions. The evidence proves that time dilation is real, and lends strong experimental support to the relativistic formulae.

Some details that may be of interest.

• The original 1971 experiment used four clocks on the jet flights, to give a check on natural variations between clocks.
• In 1971, there was already no credible doubt of the result. It would have been a stunning upset had the result been anything else, but give that the clocks of sufficient accuracy were available, and also the technology to fly them around the world, it was inevitable that some scientist was going to make this test.
• Since then the experiment has been repeated with more and more accurate clocks; and always the results are consistent with relativity in the sense used by Dave. I wouldn't use the qualifier "exact" myself, since the measurement itself is obviously not exact, but Dave's wording is still okay because the correspondence itself is exact up to allowed precision.
• Now, the corrections for relativity are routinely used not as something to check with experiment, but as a necessary correction that must be applied because time dilation is real, and the relativistic equations do tell you with complete accuracy what correction factor is required for it. (There's a difference between accuracy and precision.)

This is more than enough to prove that the idea of no time dilation is wrong. Science never gives final proof of a new theory; that's why the notion of "falsification" is used so widely. The relativistic formulae for time dilation have been consistent with all attempts to test them, even as tests of greater and greater precision are applied.

Cheers -- sylas

 

[Dale]

The presence of gravity implies acceleration and since gravity (so it is said) affects the rate of an ideal clock in General Relativity then so does acceleration.

This is a common misconception. Gravitational acceleration is not what affects ideal clocks in GR, it is the gravitational potential.

"http://en.wikipedia.org/wiki/Gravitational_time_dilation" is the effect of time passing at different rates in regions of different gravitational potential; the lower the gravitational potential (closer to the center of a massive object), the more slowly clocks run."

This distinction becomes important e.g. in determining the gravitational time dilation at the center of a spherical mass where the gravitational acceleration is 0 but the gravitational time dilation is maximum because the gravitational potential is minimum.

 

[jadgerz]

Certainly there were measurement errors; there always are in this and any other experiment. You should not read that remark as saying the experimental result was exact, but rather that the experiment was completely consistent with relativity, and that it falsified the Newtonian view of an absolute time.

The actual comment was by DaveC426913, and in his own words it is as follows:


Dave is correct, and it is a rather strange reading of his words to think he means that the lag was actually measured exactly. A more natural understanding of this phrase is that the actual lag -- which we can measure only to a limited precision, of course -- is completely consistent with the exact value given by relativity. But if it is confusing, no doubt he would rephrase.

What is definitely INCORRECT, however, is to say that measurements of clocks on jets can be explained as a natural variance analogous to the variance between the multiple clocks (45?) used to keep track of a reference time for Earth's surface.

The consideration of measurement uncertainties is enough to show that time dilation exists, and that it matches the relativistic exact solution within measurement precisions. The evidence proves that time dilation is real, and lends strong experimental support to the relativistic formulae.

Some details that may be of interest.

• The original 1971 experiment used four clocks on the jet flights, to give a check on natural variations between clocks.
• In 1971, there was already no credible doubt of the result. It would have been a stunning upset had the result been anything else, but give that the clocks of sufficient accuracy were available, and also the technology to fly them around the world, it was inevitable that some scientist was going to make this test.
• Since then the experiment has been repeated with more and more accurate clocks; and always the results are consistent with relativity in the sense used by Dave. I wouldn't use the qualifier "exact" myself, since the measurement itself is obviously not exact, but Dave's wording is still okay because the correspondence itself is exact up to allowed precision.
• Now, the corrections for relativity are routinely used not as something to check with experiment, but as a necessary correction that must be applied because time dilation is real, and the relativistic equations do tell you with complete accuracy what correction factor is required for it. (There's a difference between accuracy and precision.)

This is more than enough to prove that the idea of no time dilation is wrong. Science never gives final proof of a new theory; that's why the notion of "falsification" is used so widely. The relativistic formulae for time dilation have been consistent with all attempts to test them, even as tests of greater and greater precision are applied.

Cheers -- sylas

Keeping our focus with the H&K experiment in 1971 I recommend you read Dr. A. Kelly's critique of the test. The "errors" weren't just a result of usual experimental errors but bad science. I'll let the work speak for itself. Atomic clocks are always drifting, falling out of time, etc. etc. and have to constantly be updated, pulled from service, etc. due to these reasons. I'm not crying "conspiracy" but due to the fact the GPS system is run through a military organization we can not investigate or corroborate the topic as we can in a civilian environment. Their explanations, motivation, information, etc. that the military gives out to the public on these matters are, by the very nature of a military establishment, done so for reasons which must always be taken as suspect whether true or not. As Winston Churchill called it: "A bodyguard of lies". Your "details of interest" are more rhetorical than factual. I would respond to them in detail but that would be a bit lengthy. Dr. Kelly's critique did not claim falsification, just a critique of technique. Have you read it? Please do. He doesn't deny time dilation, he simply states the particular experiment by H&K proves nothing and after reading it I find the critique very plausible. Of course some snide-*** out there will say so what or something worse but hey, that's their problem, not mine.

 

[Dmitry67]

I'm not crying "conspiracy" but

Yes, you are :)

 

[ThomasT]

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.

Note that 1 = accelerating the traveling clock.

There's an invariant relationship between accelerating the traveling clock and the difference between the two clocks when they're reunited back on earth.

I'm not sure what you're saying above.

In Earth's frame, the ship's clock ticks at the same (slow) rate after acceleration as it did before the acceleration.

So the Earth twin will see no change in the tick rate of the traveling clock during the trip?

A change in v may or may not coincide with acceleration of the clock, but will affect its tick rate equally either way.

I thought that "change in v" = "acceleration".

 

[Janus]

At the risk of appearing to take sides, let me make a comment in support of ThomasT's assertion. If you study the Hafele & Keating's experiment from 1971 you will see it was necessary to predict the time dilation effect of both Special and General Relativity. Special Relativity being the Kinematic Relativity and General being the Gravitional. Now, correct me if I'm wrong but Gravity, to my understanding, is a Force, correct? Well, to invoke the name of Newton, he said that Force (F) is equal to mass times acceleration (ma). F = ma. Of course you know all this and I don't mean to suggest you don't. Just a reminder of the point for the argument at hand. The presence of gravity implies acceleration and since gravity (so it is said) affects the rate of an ideal clock in General Relativity then so does acceleration.

If Thomas T is asserting that acceleration affects the rate of the clock as opposed to an actual dilation of time then he has my vote for now. May I suggest (as have others more knowledgeable than myself) that this time dilation phenomena in a gravitational field (accelerration) is analoguous (spelling?), but not exactly, to a chemical rate of reaction in varying temperature regimes.

I hope I haven't offended either of you in bringing this up. God Bless all of you.

Just to add a little to what DaleSpam has already noted about GR time dilation being due to potential not acceleration. One example would be a uniform gravitational field (one that does not change strength with height). In such a field two clocks at different heights would run at different speeds even though they experience the same acceleration.
While it would be difficult to find a perfectly uniform field, the argument can still be used to examine fields generated by different masses. For example, the while the surface gravity of Uranus is slightly less than that of the Earth, the depth of the of the field is greater, and a clock on Uranus would run slower than a clock on the Earth.

A more practical example would be GPS satellites. In order to remain accurate, they have to have their clocks pre-adjusted to account for both SR and GR time dilation, the higher the orbit, the greater the GR adjustment. If GR time dilation were due to experienced acceleration, then a clock in a free fall orbit experiences none, and it wouldn't matter what the altitude of the satellite was in terms of the GR part of the dilation.

You just can't make "time dilation by acceleration" match up with the time dilation factors we actually see under real circumstances.

 

[ThomasT]

How is it supported by the experimental results? You have not given an equation yet that we can compare to experimental results. I repeat my earlier request for the equation describing this relationship between acceleration and tick rate.

What about this:

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.

When the velocity of the traveling clock changes (when it's accelerated), then its tick rate (wrt the stationary earthbound observer) changes.

 

[jadgerz]

Yes, you are :)

You must be that snide-*** I was referring to. Disinformation is part and parcel for military. They, and with good reason, never give out the truth. Never, never, always remember that.

Forgive me if I can't respond to everyone's comebacks on the topic. Some of your responses simply don't make sense by the grammar used and I simply can't respond. Here's an example which I hope sylas will forgive me for using but it typifies what I am saying:

•In 1971, there was already no credible doubt of the result.

Now what does this mean? Before or after the test? What does "...already no credible doubt" mean? What's "credible"? Does he mean "already" in 1971? Of course not, that's when the test was performed. If you read Dr. A. Kelly's critique he shows H&K were doubtful of their own results. Does the sentence really mean that in 1971 there were already no credible doubt as to what the result would be? "Credible" is one of the most subjective words in the English language.

Forgive me sylas but many of your comments are "ambigious" but I do appreciate your responses. Anyways, here's a question for you learned folks. Simple answer please and I'll be your best friend if you do.

If time dilation is a fact, which many here say it is, then is it "Time Travel"? In other words does an object leave the present (relative present of course) and travel into the future or past?

 

[jadgerz]

If GR time dilation were due to experienced acceleration, then a clock in a free fall orbit experiences none, and it wouldn't matter what the altitude of the satellite was in terms of the GR part of the dilation.

Janus, you really need to rethink this statement. Are you saying a clock in a free fall orbit does not experience acceleration? I'll give you the opportunity to reconsider this one. See what I nice guy I am?

 

[Dmitry67]

If time dilation is a fact, which many here say it is, then is it "Time Travel"? In other words does an object leave the present (relative present of course) and travel into the future or past?

Time dilation does not help to time travel

But thank you, I've never heard of such conspiracy before. Americans never landed on the Moon - yes, alien corpses - yes, but military hiding the correct equations from physics - that made my day :)

 

[edpell]

This is a common misconception. Gravitational acceleration is not what affects ideal clocks in GR, it is the gravitational potential.

Yes, and since gravitational potential goes as 1/r and the amount of matter "out there" goes as r^2 my local gravitational potential is mostly set by "the distant stars". Yes, we must take into account the finite speed of propagation of the gravitational potential, it is not instantaneous action at a distance.

 

[Dale]

What about this:

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.

When the velocity of the traveling clock changes (when it's accelerated), then its tick rate (wrt the stationary earthbound observer) changes.

That is the same as the equation I gave in https://www.physicsforums.com/showpost.php?p=2531754&postcount=160". So if that is what you mean, then we are obviously in agreement. I am glad we straightened that out.

 

[Janus]

If GR time dilation were due to experienced acceleration, then a clock in a free fall orbit experiences none, and it wouldn't matter what the altitude of the satellite was in terms of the GR part of the dilation.

Janus, you really need to rethink this statement. Are you saying a clock in a free fall orbit does not experience acceleration? I'll give you the opportunity to reconsider this one. See what I nice guy I am?

We are not talking coordinate acceleration. We are talking proper acceleration, or the acceleration measured by an accelerometer. An accelerometer attached to a clock in orbit would read zero no matter the altitude of the orbit.

 

[jadgerz]

Time dilation does not help to time travel

But thank you, I've never heard of such conspiracy before. Americans never landed on the Moon - yes, alien corpses - yes, but military hiding the correct equations from physics - that made my day :)

Did I say that? Not me!

 

[jadgerz]

We are not talking coordinate acceleration. We are talking proper acceleration, or the acceleration measured by an accelerometer. An accelerometer attached to a clock in orbit would read zero no matter the altitude of the orbit.

Try again Janus. Are you saying all those inertial guidance systems carried on all those spacecraft (mercury, gemini, apollo, etc.) were just for looks?

 

[DaveC426913]

Did I say that? Not me!

You did conclude that time travel exists. You equated time dilation with time travel. Since we see time dliation every day, your logic tells you that time traveling is indeed occurring.

Which it is - if you accept that as a definition of time travelling. That family on the top of Mt. Rainer experienced a few more microseconds than we did. If you want to look at that as time travel, so be it.