# Time dilation

1. Dec 9, 2003

### David

Re: Re: Re: time dilation

Let me tell you a little secret. There is an error in the 1905 Special Relativity theory that Einstein corrected with the General Relativity theory. There is no time or clock paradox in General Relativity because only one clock slows down at a time. In the original 1905 theory, Einstein had both clocks slowing down at the same rate at the same time, and that turned out to be an error, which he corrected later in the GR theory.

2. Dec 9, 2003

### Ambitwistor

Re: Re: Re: Re: time dilation

Untrue. General relativity does not correct special relativity, it merely treats a greater variety of situations than SR can. All SR results are GR results too.

3. Dec 9, 2003

### David

Re: Re: Re: Re: Re: time dilation

That is a common belief, but the reason for time dilation in SR is completely different from the reason in GR. The reason atomic clocks slow down in GR and in real life is because of acceleration. There is a “force” placed upon the atoms of the clocks and this causes the internal harmonic oscillation rates of their atoms to physically slow down.

The reason the clocks slow down in SR is due to Einstein’s thought-experiment use of two “light clocks” and because of the peculiar way he synchronized them and caused them to dilate. Essentially this is an illusional kinematical phenomenon caused by an error in his thought experiments.

The dilation in GR involves only the clock that experiences the acceleration, while a reference clock does not slow down (unless it’s experiencing acceleration too). In GR, the slow clock sees the fast clock as ticking fast, while the fast clock sees the slow clock as ticking slow.

But in SR, both clocks “see” each other as ticking only slow, never fast, and slow in both directions of relative travel, and slow by the same rate. In SR theory, the clocks can either run normally or slower, but they can’t speed up. In GR theory the clocks can run slow or fast depending on the gravitational potential at or the acceleration level of the clocks.

In GR the time dilation can be caused by accelerated motion or stationary acceleration (gravity). But in SR the time dilation is causes only by “relative motion”, while acceleration is left out of the theory altogether, and no “force” of any kind is felt by the clocks.

In SR theory all clocks can “slow down” at the same rates due only to the “v” of their relative motion, but in GR theory atomic clocks slow down due to acceleration, while under the same acceleration, pendulum clocks speed up.

So SR is not a “special case” of GR. The time dilation of the kinematical part of the SR theory is completely different from the atomic clock rate slowdown of the electrodynamical part of GR theory.

4. Dec 9, 2003

### Ambitwistor

Re: Re: Re: Re: Re: Re: time dilation

Not only is that incorrect, it's logically impossible. SR is a special case of GR, so any GR explanation has to apply to SR as well.

No. Gravitation has no mechanical effect on clocks; it has a geometric effect on spacetime. Moreover, time dilation is not determined intrinsically by acceleration in GR.

In either GR or its subset, SR, you work out the time dilation between two events as measured by two observers knowing their instantaneous 4-velocities (not their 4-accelerations) and the spacetime curvature between them along some path. (The time dilation is not well-defined unless you also specify an arbitrary path.)

Sometimes their accelerations are related to their 4-velocities or the spacetime curvature (such as in the case of a static observer in Schwarzschild spacetime), so the time dilation factor can depend indirectly on the acceleration, but in general it does not.

Wrong. Not only is Einstein's reasoning correct, is has been verified by experiment: time dilation due to relative motion is not illusory.

That's overly simplistic. For instance, two clocks, neither of which is experiencing (proper) acceleration, can experience time dilation relative to each other.

Maybe in the static Schwarzschild case, but not in general.

You can set up symmetric situations in GR, too.

This is just wrong. If you disagree, please post a GR calculation of how you calculate the time dilation between two events as measured by two observers, for a generic metric (not just Schwarzschild), and show where that calculation makes use of the acceleration (proper or coordinate) of either observer.

Don't be absurd. Simply set the metric to the Minkowski metric, and you have recovered SR as a special case. Set the metric to something else, and you get special cases corresponding to non-flat spacetimes.

What does "completely different" mean? The time dilations arise from the same general formula, though of course they are not the same because they describe different physical situations.

Incidentally, there is no "electrodynamical part" of GR.

5. Dec 10, 2003

### GijXiXj

David

Like some of your arguments, on the other hand have to agree at least partly with ambitwistor's critique of them:

Summing over all possible values of i & j:

S² = Ó GijXiXj, i,j run 1 to 2, Pythagoras in 2-D he say! (eg: X1 = 'normal' X coordinate length, X2 = 'normal' Y coordinate length, S = hypotenuse)

S² = Ó GijXiXj, i,j run 1 to 3, Pythagoras in 3-D he say!

S² = Ó GijXiXj, i,j run 1 to 4, Gij = 0 when i not=j, else Gii = ±1 (kinda), hello to the Special Theory of Relativity.

S² = Ó GijXiXj, i,j run 1 to 4, Gij = Gji, hello to the General Theory of Relativity. (Ok, I missed out the d's).

Darn it that funny Ó symbol was supposed to come out as capital Greek SIGMA, meaning sum over all combinations of i & j. Nevermind.

Pythagoras he say! So there's a progression in generality from Pythagoras, (where Gij = 0 when i not = j, and Gij = 1 for i = j), to SR (4-D) with Gij's sticking to those 'Pythagoras rules', except one of the Gii's is opposite sign to all the others, to GR (also 4-D) where there is no such restriction on the Gij's, just a much looser one as far as I remember, rusty as hell, that Gij = Gji. So there are 16 Gij's, because i & j take the values 1-4 independently but only 10 of them are independent because Gij = Gji.

Ambitwistor will probably tear me into bone gaping shreds for this, but, ahem, the Gij kind of defines gravity through the warping of space time (the four dimensions, Xi to Xj, one of them's 'time', kinda). If none of the 16 (or 10, take your pick) Gij's differ from 0 or ±1, you get 'flat' space-time, or GR 'collapses' into 'SR'. Gij's differing from 0 or ±1, gives you the 'full' GR. Of course, there is no such thing as flat space-time, and so really no such thing as SR.

:-)

Useful approximation though.

;-)

But in the sense of a mathematical generalisation from ( ... Pythagoras ... ) --> SR --> GR, Ambitwistor's got a very good point.

... if Pythagoras had just stuck at it a bit harder ...

;-)

All that said, like you I've always felt a bit uncomfortable with the SR 'explanation' of the Twin Paradox, and talking about this and other Relativity things on another forum quite a while ago now, caused me to fiddle about with it a bit, to produce THIS. See if it helps.

( ... goes away and tries to think of rebuffs to Ambitwistor perhaps shredding offering to pieces ... ;-)

Last edited: Dec 10, 2003
6. Dec 10, 2003

### chroot

Staff Emeritus
GijXiXj,

We use the lowercase g to represent the metric, and lowercase x to represent coordinates.

In special relativity,

$$g_{ij} \equiv g_{ji} \equiv \eta_{ij} \equiv \left(\begin{array}{cccc} -1&0&0&0\\ 0&1&0&0\\ 0&0&1&0\\ 0&0&0&1 \end{array}\right)$$

i.e. it is not 0 in special relativity, as you indicated. It's a generalized identity matrix. Also, in both special and general relativity, the metric is symmetric.

- Warren

7. Dec 11, 2003

### GijXiXj

Warren, you said:

" We use the lowercase g to represent the metric, and lowercase x to represent coordinates. "

Yes, I know, but then the subscripts look less like subscripts for us lazy sods who can't be bother latexing.

By, the way, as far as I know, latexing also isn't a verb, at least in the sense I use it.

You go on:

"In special relativity,

.... some matrix ....

i.e. it is not 0 in special relativity, as you indicated.
"

Nope, I never did so indicate. Read what I posted again. I indicated pretty much exactly as you did in your matrix, but in "words", that's all: Pythag & SR: Gii = 1, except SR has one Gii = -1, i not= j then Gij = 0; GR: Gij = Gji.

Last edited: Dec 11, 2003
8. Dec 11, 2003

### David

Re: Re: Re: Re: Re: Re: time dilation

Well, gravitation does cause an "effect" on some clocks. In this case, whether we call it a "mechanical" effect on atoms or an "electrodynamical" effect, I won't quibble about what we call it.

I want to show you something very interesting in “On the Influence of Gravitation on the Propagation of Light”, A. Einstein, 1911. In the paper, Einstein predicted that atomic clocks would slow down in stronger gravitational fields, such as in a valley on earth or at the sun. But he did this in a very long convoluted roundabout way that is a little difficult to follow.

In the paper he said:

”It follows, then, that a ray of light emitted in S2 with a definite gravitational potential, and possessing at its emission the frequency v2, compared with a clock in S2, will, at its arrival in S1, possess a different frequency v1, measured by an identical clock in S1.”

Then he says:

”Let v0 be the vibration-number of an elementary light-generator, measured by a delicate clock at the same place. Let us imagine them both at a place on the surface of the Sun (where our S2 is located).”

His “elementary light-generator” is basically a vibrating “atom”, which is a fundamental “atomic clock”, and the frequency of the light it emits is tied to its vibration rate.

Then he says that when we measure the frequency of the sunlight at the earth:

”Thus according to our view the spectral lines of sunlight, as compared with the corresponding spectral lines of terrestrial sources of light, must be somewhat displaced toward the red....”

What we basically have here in the “elementary light-generator” on the sun is an elementary atomic clock that is vibrating more slowly than the same kind of atom on earth and is emitting light of a lower frequency at the sun because the atom is experiencing the force of the stronger gravitational potential at the sun. Its light frequency can be calculated by its shift when received at the earth, and the sun-atom’s vibration frequency shift can also be calculated. Both kinds of frequency shifts can be shown to be lower at the sun than their counterparts here on earth, because the earth atoms experience less gravitational forces.

He is essentially saying that atomic clocks “tick more slowly” at the sun than at the earth, which I think he should have come right out and stated as simply as that. But he didn’t. He went into a long description about what “time” is at the sun and what “time” is at the earth, and he introduced two completely superfluous “delicate clocks” of no particular kind or description, which he designated as “U” clocks.

He already has the most basic and accurate clocks in the “elementary light-generators”, which are the atoms on the sun and the same kinds of atoms on earth, ie “atomic clocks”, so the introduction of the “U” clocks is not at all necessary, since they are totally imaginary and their rates are different at the sun and at the earth in exactly the same amount as the “vibration-number of an elementary light-generator” is different at the sun and at the earth.

But he goes on to say:

“What v2 denotes is the number of periods with reference to the time-unit of the clock U in S2, while v1 denotes the number of periods per second with reference to the identical clock in S1. Nothing compels us to assume that the clocks U in different gravitational potentials must be regarded as going at the same rate.... Therefore the two clocks in S1 and S2 do not both give the ‘time’ correctly. If we measure time in S1 with the clock U, then we must measure time in S2 with a clock which goes 1 + Φ/c^2 times more slowly than the clock U when compared with U at one and the same place.”

So he’s basically saying here that the “U” sun clock (which I designate U2) ticks slower at the sun than the other “U” clock (which I designate U1) ticks at the earth. So the “U” clocks themselves are nothing other than “atomic clocks”. And he says that if we want to accurately note the U2 tick rate at the sun, and duplicate that rate in a clock here on earth, then we must adjust the rate of any other kind of earth clock by purposely slowing it down to the U2 rate, and then we compare that slower rate to the earth’s U1 clock rate. That’s what he means by, “we must measure time in S2 with a clock which goes 1 + Φ/c^2 times more slowly than the [earth] clock U when compared with U at one and the same place [at the earth].”

But this is extremely confusing in the way he words it. What he is basically saying is that on earth, we adjust and slow down a third clock, of a different kind than “U”, to the rate of the Sun’s U2 clock, and then we compare the rate of the adjusted and purposely slowed down clock with the rate of U1.

So? What did he accomplish by introducing the “U” clocks?

Nothing at all.

We already know the rate of the Sun’s U2 clock by observing the sunlight’s spectral line shift, and this gives us the vibration rate of the sun’s atoms that emit the light. Since that vibration rate is tied directly to the rate of the U2 clock, we don’t even need the U2 clock. And since the earth’s U1 clock rate is tied directly to the vibration rates of the same kinds of atoms on earth, we don’t need the U1 clock. So there is absolutely no need for any imaginary “U” clocks, since the atoms themselves are “delicate clocks” that “tick” at different rates at the sun and on the earth because of the gravitational potential differences in both places.

So Einstein in 1911 was saying that atomic clocks slow down under strong gravity and speed up under weak gravity, but he said it in such a confusing way, that’s why in 1911 “only 12 people in all the world” could understand what he was talking about. If he had used simpler wording instead of what he did use, then most people in all the world could have easily understood what he was talking about.

So, yes, gravitation does cause an “effect” in atomic clocks. You can call it a “mechanical” effect, or an “electrodynamical” effect, or whatever you want to call it. It is a physical effect caused by a gravitational “force” being placed on the atoms. But this is not “time dilation”, its an “atomic harmonic oscillation rate slowdown”.

Yes, true, my computer clock and my wall clock constantly disagree. In aerospace, that’s called “clock drift”, and there are several causes for it. In my post I was speaking specifically of atomic clocks and acceleration.

9. Dec 11, 2003

### Ambitwistor

Re: Re: Re: Re: Re: Re: Re: time dilation

It's neither one. Even if electrodynamics didn't exist, gravitational time dilation still would exist. Nor is time dilation restricted to clocks that operate by mechanical means, or to vibrating atoms, or whatever. Time dilation has nothing to do with how the clocks are physically constructed.

That's wrong. It is time dilation, it has nothing to do with a force being exerted on anything, and it has nothing in particular to do with harmonic oscillation or any other mechanical or electromagnetic process.

I was speaking of clocks (atomic and otherwise) and acceleration, too. You missed my point, which had nothing to do with inaccuracies in clocks.

10. Dec 11, 2003

### David

Re: Re: Re: Re: Re: Re: Re: Re: time dilation

I don’t think you can say that unless you can show some observational or experiment evidence of what you say. Electrodynamics does exist and that’s why atomic clocks slow down in a greater gravitational potential.

Although it is commonly called “time dilation,” it’s actually a “clock rate change” (a slowdown or speedup) caused by some sort of force placed on or removed from the fundamental mechanism of the clock, or a changing force being felt by the clock mechanism.

Do you know of any kind of clock that doesn’t measure time by means of some kind of physical vibration or motion taking place inside or at the clock or a motion of the clock relative to something else?

I understand that a high gravitational potential speeds up pendulum clocks while it slows down atomic clocks at the same location, so here we have two different kinds of clocks changing rates in opposite directions at the same place, so this phenomenon is obviously a “clock rate change” phenomenon at each clock, not a “time rate change” phenomenon at the place.

11. Dec 11, 2003

### David

Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: time dilation

So will atomic clocks.

I don’t see how you can say these things. A pendulum clock clearly speeds up where an atomic clock slows down.

Where do you get your ideas from? Why would you say that gravity slows down a pendulum clock just like it slows down an atomic clock, when 500 years of observational evidence reveals that a larger gravitational potential speeds up a pendulum clock? On what are you basing your refutations of direct observational evidence?

12. Dec 11, 2003

### Ambitwistor

Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: time dilation

No, they won't.

That a pendulum clock ticks at different rates at different locations in a gravitational field has nothing to do with gravitational time dilation. Pendulum clocks have to be constructed to work at a specific gravitational potential.

If I construct a pendulum clock to tick off a 1-second period at one height, according to an observer at that height, then I have to construct a different pendulum clock (with a different pendulum length) to tick off a 1-second period at a different height, according to an observer at that different height. (This is unlike atomic clocks; the same atomic clock will work at any height.)

Assuming that I have two pendulum clocks constructed to work at the heights they are at, they will tick at exactly the same rate in Newtonian gravity. That means there is no time dilation. But if you put the same two clocks into a general relativistic gravitational field, they will not tick at the same rate, and the rate difference will be the same as for two atomic clocks at those locations, or any two other kinds of clocks.

Einstein.

Last edited: Dec 11, 2003
13. Dec 11, 2003

### David

Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: time dilation

High quality pendulum clocks are adjustable for different elevations and some atomic clocks are too. The large pendulum clocks of past generations were completely adjustable for use all over the earth, at different elevations. In the 19th Century, some pendulum clocks were used to measure elevation. If you move a pendulum clock up in elevation, it will tick more slowly, and if you move an atomic clock up in elevation it will “tick” more rapidly. That appears to be a clear law of nature.

He said that atomic clocks will slow down when placed under a large gravitational potential, and observational evidence says that idea turned out to be true. But just as with the ideas of any other theorist, you need to compare everything he said to actual experiment and observation to determine what different things he said were true or untrue. In 1915 he said all stars were “fixed” and the universe was “static”. That turned out to not be true. He said in 1911 that we need the “U” clocks in his thought experiments, but that turned out not to be true.

14. Dec 11, 2003

### Ambitwistor

Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: time dilation

Yes, but once you have adjusted them for the local gravitational field and synchronized them with each other, two pendulum clocks (or any other two clocks) at different elevations will keep the same time in Newtonian gravity --- but they won't in general relativity. That's what is meant by gravitational time dilation.

Gravitational time dilation in general relativity has nothing intrinsically to do with atomic clocks, or the properties of atoms. (For that matter, what we call "atomic clocks" today weren't even invented in 1911.)

15. Dec 11, 2003

### David

Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: time dilation

Maxwell talked about vibrating atoms being used as clocks as early as the 1870s. Vibrating atoms are "atomic clocks". They don't have to be enclosed in a manufactured case that is labeled "Atomic Clock" before they can be "atomic clocks".

You are talking about ancient theories as opposed to observation data, and some of those theories are now obsolete.

16. Dec 11, 2003

### Ambitwistor

Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: time dilation

I'm talking about general relativity and the gravitational time dilation which is predicted by that theory, as well as the experimental evidence for that time dilation.

17. Dec 11, 2003

### Janus

Staff Emeritus
Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: time dilation

Pendulum clocks depend on gravity to work, thus the local gravitational strength will affect their operation. If you move both an atomic clock and pendulum clock up in elevation, yes the atomic clock will tick more rapidly, and the pendulum clock more slowly. BUT, If you measure the pendulum clock tick rate very carefully, you will note that it doesn't tick quite as slowly as you would expect(as compared to a pendulum clock at a lower elevation), and that difference will be exactly equal to the amount that the atomic clock ran fast (again, as compared to a clock at a lower elevation).

The pendulum clock is effected by both the lessening of local gravitational strength and gravitational time dilation, it is just that the first has the greatest effect.

The atomic clock however is not sensitive to local gravitational stength but does note time dilation due to relative difference in gravitational potential (Not the same thing as local gravitational strength).

The other difference is that a person standing next to the clocks would notice that the pendulum clock was running slow, but would see the atomic clock as running at proper speed, and would not be be aware of any speeding up of the clock. (He would note, however, that the atomic clock at the lower elevation was running slow)

18. Dec 11, 2003

### David

Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: time dilation

Yes, but I’m talking about reality.

The reason I got into this is because all my life I worked with variable time-flow rates of different kinds, and all kinds of Doppler effects, and when I retied I wanted to read some physics books and find out what “time” is.

I was shocked to learn that most physicists don’t know what “time” is, and they have made up some of the wildest and most outrageous claims and superstitions about it. I’ve read things such as Stephen Hawking claiming that a person will “live longer” on top of a mountain because Einstein said so, and stuff like you’ve just said about pendulum clocks “time dilating” at the same rates as atomic clocks in high gravitational potentials, even though they clearly “speed up”, and stuff about relative motion causing clocks millions of miles away to “slow down”. “Relative motion” alone can’t possibly cause any clock to slow down or speed up.

These old and incorrect “time” theories have become urban legends. I’ve worked with and interviewed scientists in different fields who don’t pay any attention to them. In fact, many scientists use the observed rules of “thermodynamic time”. In fact, doctors, medical researchers, and biologists don’t pay any attention to the Einstein time superstitions. They mainly use the rules and laws of thermodynamic time.

19. Dec 11, 2003

### master_coda

Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: time dilation

Doctors, medical researchers, and biologists are unlikely to ever work in a situation where the affects of time dilation are significant. So why would they use a more complicated theory when the additional accuracy it provides isn't necessary? In fact, it's unlikely that most of them will even learn about relativity at all.

20. Dec 11, 2003

### David

Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: time dilation

Can you post some links to some precise experiments that prove this conclusively?