Time Dilation Formula: Calculating Rel Speed Diff b/w Objects

[russ_watters]

Originally posted by David
He called them “elementary light generators” in the 1911 theory.

In fact, the reason he didn't identify any by specific name/type is that they weren't invented until 1952. Einstein makes no mention of specific clocks and their particular sources of error/rate because they are not relevant to his theory. Einstein's theory is about time itself.

All mechanical watches have shafts and bearings. That’s what a 23 jewel watch used to be. They used hard ruby or other jewels as the bearing pivot points, since the jewels were harder than metal and didn’t wear out as often. Gravity increases friction in the bearings of mechanical watches.

Certainly. But if that friction affected the rate, it would badly throw off the accuracy of the watch every time you moved or changed the watch's orientation.

Something I didn't point out/ask before, but you do know the mechanical difference between a spring-mass and a pendulum, right? Both are simple harmonic motion, but they are not affected by gravity in the same way. In a pendulum, the force of gravity is the driving force. In a spring-mass system, the force of gravity may be part of the driving force or not depending on the type of spring-mass system and its orientation. As a result, the rules that apply to a pendulum are different from the rules that apply to a mechanical watch. For this reason, when talking about clock rate variations, you must specify what type of clock you are talking about. There is a reason Einstein did not.

 

[David]

Originally posted by russ_watters
In fact, the reason he didn't identify any by specific name/type is that they weren't invented until 1952.

No, sorry, you are wrong. Maxwell, in 1873, recognized natural atoms as being natural “clocks”. Einstein used this idea in his 1911 theory.

“Natural atomic clocks” with numerical clock-face read-outs and installed in self-contained boxes weren’t invented until the 1950s. Before that, the oscillation rates of natural atomic clocks had to be measured by spectrometers. You should have been taught that in physics class.

 

[russ_watters]

Originally posted by David
No, sorry, you are wrong. Maxwell, in 1873, recognized natural atoms as being natural “clocks”. Einstein used this idea in his 1911 theory.

“Natural atomic clocks” with numerical clock-face read-outs and installed in self-contained boxes weren’t invented until the 1950s. Before that, the oscillation rates of natural atomic clocks had to be measured by spectrometers. You should have been taught that in physics class.

None of that contradicts what I said. Clearly they recognized the possibility it could be done, but neither Maxwell nor Einstein ever used an actual atomic clock when formulating their theories.

That fact is more important than you are admitting and I think you know it. With your talk of clocks, you are mixing several fundamentally different and unrelated sources of variation and calling them equivalent. You used the example of a pendulum clock, which slows down if the driving force (gravity or a centrifugal force) is lowered. But for other clocks, you talk about fricton. Setting aside that you haven't said what kind of friction affects an atomic clock and how, friction isn't even close to the same issue as how gravity affects a pendulum clock. Thats easy enough to see when you realize that a pendulum clock does not work at all in orbit, but the wearer of a mechanical spring-driven watch would not even notice a variation during a quick trip to orbit and back.

Also, while friction does play a part in rate for some mechanical clocks, it differs quite a bit from one clock to another, yet you are applying a blanket equation to a large but undefined set of atomic clocks. You're contradicting yourself.

Also, while gravity can be simulated in a centrifuge, a centrifuge does not produce gravity. As a result, it is easy enough to test whether its the force/acceleration itself or the field that is creating the dilation. And guess what: it's been done. And no, acceleration force does not produce the same effect on an atomic clock as GR time dilation.

On the SR side, something I just read about - another way to see SR time dilation: particle decay. Particles moving at high velocity (supercollider experiements) show SR time dilation induced changes in their lifespans.

I've just started looking into those last two, so I should have more later, but for a start: http://www.lns.cornell.edu/spr/2002-01/msg0038144.html

 

[mikesvenson]

Originally posted by russ_watters
Thats easy enough to see when you realize that a pendulum clock does not work at all in orbit, but the wearer of a mechanical spring-driven watch would not even notice a variation during a quick trip to orbit and back.

Does this mean that a pendulum clock operates on kinetic and potential energy driven by the force of gravity?

 

[russ_watters]

Originally posted by mikesvenson
Does this mean that a pendulum clock operates on kinetic and potential energy driven by the force of gravity?

Precisely. When the bob is at the bottom of its swing, its all kinetic and at the top of its swith all potential. The excange of the two is what causes the simple harmonic motion.

 

[Peterdevis]

Also, while gravity can be simulated in a centrifuge, a centrifuge does not produce gravity. As a result, it is easy enough to test whether its the force/acceleration itself or the field that is creating the dilation. And guess what: it's been done. And no, acceleration force does not produce the same effect on an atomic clock as GR time dilation.

is this really true? Then it's violating the EEP (einsteins equivalence principle): In a closed box you can't make out if you are excelarating or moving in a gravitational field (I' don't love the word gravitational field, but everybody use it)

 

[David]

Originally posted by russ_watters
Clearly they recognized the possibility it could be done, but neither Maxwell nor Einstein ever used an actual atomic clock when formulating their theories.

Maxwell did. You just don’t know enough about the history of science. The old timers could calculate the oscillation rates of specific atoms by studying spectrographs of their light. That led to the invention of the self-contained atomic clock with a digital read-out.

Einstein studied other people’s books and papers to get his ideas.

 

[David]

Originally posted by russ_watters
Clearly they recognized the possibility it could be done, but neither Maxwell nor Einstein ever used an actual atomic clock when formulating their theories.

Here’s the way Charles Steinmetz explained Einstein’s 1911 theory about atomic clocks, in his own book of 1923:

”We cannot carry a clock from the Earth to Betelgeuse, but we do not need to do this, since every incandescent hydrogen atom, for instance, is an accurate clock, vibrating at rate definitely fixed by the electrical constants of the hydrogen atom and showing us the exact rate of its vibration in the spectroscope by the wave length or frequency of its spectrum lines. Thus in a strong gravitational field the frequency of luminous vibrations of the atoms should be found slowed down’ in other words, the spectrum lines should be shifted towards the red end of the spectrum.”

Look, you need to go out and buy these books yourself. I don’t have time to tutor you in physics or type up all the text from all my books for you. You need to go to a good university somewhere and take some physics courses.

 

[russ_watters]

Originally posted by Peterdevis
is this really true? Then it's violating the EEP (einsteins equivalence principle): In a closed box you can't make out if you are excelarating or moving in a gravitational field (I' don't love the word gravitational field, but everybody use it)

Hmm, good question: perhaps I misunderstood the experiment. I think though, the difference isn't in what you are seeing, but in what an outside observer sees. You can only measure time dilation by comparing dis-similar frames of reference. And in seeing the dilation, you'll also see the reason for it.

Maxwell did.

Again, if no atomic clock existed, he couldn't have used one. He certainly speculated on/theorized on how they might work, but that is not the same thing.

Here’s the way Charles Steinmetz explained Einstein’s 1911 theory about atomic clocks, in his own book of 1923:

”We cannot carry a clock from the Earth to Betelgeuse, but we do not need to do this, since every incandescent hydrogen atom, for instance, is an accurate clock, vibrating at rate definitely fixed by the electrical constants of the hydrogen atom and showing us the exact rate of its vibration in the spectroscope by the wave length or frequency of its spectrum lines. Thus in a strong gravitational field the frequency of luminous vibrations of the atoms should be found slowed down’ in other words, the spectrum lines should be shifted towards the red end of the spectrum.”

Looks good to me: that description is consistent with the pervasive view that atomic clocks accurately measure time and that GR affects time, not just certain types of clocks.

Look, you need to go out and buy these books yourself. I don’t have time to tutor you in physics or type up all the text from all my books for you. You need to go to a good university somewhere and take some physics courses.

Hehe, you learned your current opinion in school? And you passed? Impossible. Again: what you are saying is not consistent with the current accepted view. Even if you want to argue that the current accepted view is wrong or (you are very careful about avoiding directly saying that, but you do agree with Einstein in one breath while saying he's wrong with the next), its the one taught in school and you can't pass without at least being able to regurgitate it. I'm glad you finally said it though.

You like regurgitating quotes and taking them out of context. Ok, fine, here's one from page 35 of "Relativity" (1916):

As a consequence of its motion the clock goes more slowly than when at rest.

The chapter is 2 pages long and he never once specifies which type of clock it applies to. Why? Because he's assuming we'll realize by "clock," he means 'any instrument that measures time with sufficient accuracy to notice the SR effects discussed in that chapter.' There are also several nuggets in there about C being an unattainable speed.

Look, I'm an engineer, not a physicist, which is why I harp on practical uses (which you brush aside or ignore). In our every day lives, we use things that would not work if SR and GR didn't work the way I (and others) am telling you it does.

Your tactics are quite good (you appear to have been practicing this argument for quite some time): you press a point until its clear that you're backed into a corner you can't get out of, then ignore it like it has never been discussed. Fear not: people reading these threads notice when you drop the ball.

 

[David]

Originally posted by russ_watters
Looks good to me: that description is consistent with the pervasive view that atomic clocks accurately measure time and that GR affects time, not just certain types of clocks

You said they didn’t have atomic clocks in the old days, and I just proved to you that they considered natural atoms to be atomic clocks. You apparently didn’t know this because you said atomic clocks weren’t invented until 1952.

Anyway, the vibration rates of the atoms tells us the vibration rates of the atoms. They do not tell us what the vibration rates of pendulum, mechanical, or thermodynamic clocks will be in the same places.

Look, I don’t have time to tutor you in physics or the history of atomic clocks and other timekeeping devices. Go out and buy some classic books on the subject.

 

[David]

Originally posted by russ_watters

Look, I'm an engineer, not a physicist,

Well that’s just great. You need to be on an engineering board, because you sure don’t know much about physics. Go out an build a bridge or something.

 

[Phobos]

Warning #2, David. Discuss the topic at hand. Do not flame.

 

[David]

Originally posted by Phobos
Warning #2, David. Discuss the topic at hand. Do not flame.

I didn’t flame anybody. You don’t say anything at all about Russ’ constantly flaming of me. He’s been posting personal insults directed at me the whole time I’ve been on this board. You are just setting me up so you can ban me, because you don’t like my opinions. You should be ashamed of yourself.

 

[Janus]

Originally posted by russ_watters


Also, while gravity can be simulated in a centrifuge, a centrifuge does not produce gravity. As a result, it is easy enough to test whether its the force/acceleration itself or the field that is creating the dilation. And guess what: it's been done. And no, acceleration force does not produce the same effect on an atomic clock as GR time dilation.

Okay, you have to be really careful here. Yes, acceleration in of itself does not cause time dilation, but neither does gravity. What is happening depends upon whether you are rotating with the Centrifuge or not.

If you are sitting next to the centrifuge, you measure a Time dialtion in the sample at the end of the arm due to simple SR effects of velocity. And there is no additional effects due to acceleration.

If you were sitting at the axis of the centrifuge and turning with it, you can consider both yourself and the end of the arm as stationary, but you will measure a time dilation at the end of the arm due to the difference in potential caused by the apparent gravitational field that exists between you and the arm. This dilation behaves exactly like was caused by "real" gravity.

The main thing to remember is that this dilation is due to the difference in potential and not due to the difference in force felt. For instance, One could build two centrifuges, one with an arm twice as long as the other, and spin both such that the ends of the arms of each experience the same g force. If you were sitting on the axis of the one with the longer arm you would note a greater time dilation between you and the end, then you would if you were sitting on the centrifuge with the shorter arm, even though both arms are experiencing the same g force.

You could even arrange things such that the arm end that feels less g-force undergoes a greater time dilation.

This is like the fact that even though the surface gravity of Uranus is less than that of the Earth's, the time dilation on the surface of Uranus is greater than that on the Earth's.

 

[Peterdevis]

The main thing to remember is that this dilation is due to the difference in potential and not due to the difference in force felt. For instance, One could build two centrifuges, one with an arm twice as long as the other, and spin both such that the ends of the arms of each experience the same g force. If you were sitting on the axis of the one with the longer arm you would note a greater time dilation between you and the end, then you would if you were sitting on the centrifuge with the shorter arm, even though both arms are experiencing the same g force

I don't think there is a difference between force and potential, (it are two mathematical descriptions of the same phenomena for me)

The greater time dilitation of the centrifuge with the long arm,is the result of the greater velocity (for getting the same centrifugal acceleration).

When you measure the time dilitation of a clock in a centrifuge (simulating gravity 10 km above Earth surface) or you measure time dilitation of a clock in an airplane (10 km above Earth surface) with the same velocity as the clock in the centrifuge, you must see the same result.

 

[Janus]

Originally posted by Peterdevis
I don't think there is a difference between force and potential, (it are two mathematical descriptions of the same phenomena for me)

The formula for gravitational force is
$$F_{g}= \frac{GMm}{r^{2}}$$

For gravitational potential, it is

$$PE_{g} = -\frac{GMm}{r}$$

A difference in relative force between two points in a field is just the difference in force felt by an object at those two points.

A difference in relative potential is a measure of the amount of work it would take to move an object from one point to the other. (IOW, the amount of work it would take to lift the object the distance between the two points.

These particular formulas are for your standard "mass generated" gravity which follows the inverse square rule.

Now let's imagine a uniform gravity field. (One which does not fall offf with distance) In this case, the force remains the same no matter where you are in the field, so the relative force between two points is always zero. But the potential between two points depends on their height difference in the field.

If we assume that the strength of the field causes an acceleration ofg, then the relative potential difference between two points is related to gh, where h is the height difference between the two.

Now in GR, time dilation is tied to relative potential, Thus two clocks at elevations h1 and h2 would be at different potentials, even though they would feel the same exact force, and they would run at different rates (as measured by anyone within that field).

This is the important difference between force and potential.

The greater time dilitation of the centrifuge with the long arm,is the result of the greater velocity (for getting the same centrifugal acceleration).

Again, this depends upon whether you are measuring from the reference frame that is rotating with the centrifuge or not. If you aren't, then you will measure a time dilation due to relative velocity alone.

If you are, you will measure a time dilation due to the apparent gravity field alone, ( As there is no relative velocity difference within the rotating frame.)

The time dilation works out to be the same, but each reference system sees it for a different reason.

 

[Phobos]

Originally posted by David
I didn’t flame anybody. You don’t say anything at all about Russ’ constantly flaming of me. He’s been posting personal insults directed at me the whole time I’ve been on this board. You are just setting me up so you can ban me, because you don’t like my opinions. You should be ashamed of yourself.

Reread that previous post. It was a personal attack intended to only cause anger and was not part of any technical debate.

Russ can be tough, but he's fair. I'll take another look through the posts and I'll talk to Russ if I see anything that is as you say.

I've never banned anyone because of differing opinions. I'm just asking that the debate be kept civil. The irony here is that I've been asking the mentors to give you more chances.

 

[ahrkron]

Originally posted by David
No clock slows down due to “relative motion” alone, since no physical force is placed on the mechanism of the clock.

They do, as it is measured every day in particle accelerators, communications with space probes, the use of GPS, etc., and was also measured directly using jets and atomic clocks.

Different kinds of clocks will slow down and speed up if you add forces to them or take forces away from them.

"Take forces away from them"?
The point is not if a Rolex will speed up or slow down, but what effects need to be considered when doing a real analysis of a physical situation.

Indeed, complex mechanisms may be affected by tempreature and other conditions, but when doing precise measurements, you need to take into account all real effects that contribute significantly to what you are measuring. Relativistic time dilation does affect any mechanism. The amount to which it does depends on specific conditions.

If you are measuring how a Rolex is affected in an passenger flight, many factors will affect your measurement much more than relativity. On the other hand, when measuring lifetimes of heavy mesons, you surely need to consider time dilation.

If the SR theory were true, and if you traveled at .99c, your molecular vibration rate would slow down to near zero and you would freeze to death.

Wrong. In order to say "if the SR theory were true", you first need to understand what SR actually says about the situation.

What it says is that, even at 0.99999c, you won't notice any change in yourself, since your speed relative to you is still 0.

SR theory just doesn’t work.

Funny how the GPS, nuclear reactors, QFT, GR and the standard model of particle physics
(all of which depend on SR) keep producing extremely accurate results. *That's* the heck of a lot of good luck!

You can’t have your clocks and your aging rate slow down, while your molecular vibration rates don’t change at all.

True, which means that your interpretation of what SR says is wrong.

On the other hand, that is perfectly in agreement with the predictions of SR (i.e., your clocks and your molecular vibrations stay in tune).

Go read some Lorentz stuff. That’s what the SR theory was based on and modeled from,

And, after nearly a century of accumulating experimental evidence and testing devices based on both, we are keeping the version that best describes all data we have. Nobody really cares if it is called "Einstein's" or "Lorentz's", but now that you bring it up, it is Einstein's.