# Time dialation formula

David
Originally posted by Peterdevis
the Rollex

I think a Rolex will probably tick a little faster in space, since there are no gravitational forces pulling down on its gears and their shafts, so they won’t experience as much friction in space. But the speed up will not match the same speed-up rate as an atomic clock, because the Rolex speed up is a large-scale “mechanical” function, while an atomic oscillation speed up operates by quantum mechanics rules.

Regarding a Rolex or any kind of balance-wheel watch or clock, think of it this way: Put the watch inside a rapidly spinning centrifuge, and notice that the higher the g forces, the more friction is placed on the bearings and the gear shafts. This will tend to slow the watch down a little. However, if you put an electronic watch in your refrigerator freezer, that will slow it down a little, for thermodynamic and quantum mechanics reasons. Put a pendulum clock high on a mountain and it will slow down. Put an atomic clock in a valley and it will slow down.

These different types of clocks will slow down and speed up for different reasons, because different laws of physics apply to the different types of clocks.

David
Originally posted by mikesvenson

I fully understand the concept that if you travel at .99c for an extended time relative to Earth that upon your return to Earth you will actually be re-entering into the future time of Earth (relative to the elapsed time you experianced while out in space traveling at .99c).

No clock slows down due to “relative motion” alone, since no physical force is placed on the mechanism of the clock. Different kinds of clocks will slow down and speed up if you add forces to them or take forces away from them.

Your biological time while you are traveling in space is determined by your molecular vibration rates. This is “thermodynamic” time.

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. SR theory just doesn’t work. You can’t have your clocks and your aging rate slow down, while your molecular vibration rates don’t change at all. If you remain warm during your trip, that means your molecular clocks, your molecular vibration rates are not slowing down.

Go read some Lorentz stuff. That’s what the SR theory was based on and modeled from, but unfortunately Einstein neglected to include acceleration, fields, and real physical forces, so the SR theory does not work in real life.

russ_watters
Mentor
[Peterdevis]
...the natural time for the traveler would be an ellapsed 7 months, and the syncronized Earth watch(impossible throuth SR) would only have read an ellapsed 1 month! What the heck do they mean by "natural time" Wouldnt this be the same thing as the 1 month time? This doesnt make sense to me.
The specific link might help, but from the context given, "natural time" appears to be the time shown by your watch in your frame of reference.
Originally posted by David
Maxwell mentioned “sodium” in his 1873 comments.
So then which is the type of atomic clock that Einstein used in his books (did he always use the same kind?) and what are the transformation equations for converting time between different atomic clocks?
I think a Rolex will probably tick a little faster in space, since there are no gravitational forces pulling down on its gears and their shafts, so they won’t experience as much friction in space.
Analog watches have used frictionless springs for several hundred years and and since the spring is where the frequency comes from, they are not mechanically affected by gravity. If friction due to weight mattered, they'd tick at different rates upside down and right side up.
These different types of clocks will slow down and speed up for different reasons, because different laws of physics apply to the different types of clocks.
All laws of physics apply in all cases. The effects are only relevant in certain cases. But the law of physics for the last case is relevant to all of them.
No clock slows down due to “relative motion” alone, since no physical force is placed on the mechanism of the clock.
Then explain GPS. The engineers who make GPS satellites use the predictions of SR (motion related time dilation) in the calibration of the satellites' clocks.
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.
No. From your frame of reference if you shut your eyes, nothing has changed. You don't understand the relevance of frame of reference.
SR theory just doesn’t work.....so the SR theory does not work in real life.
Scientists, engineers, and laypeople who don't even know it, use Einstein's Relativity every day in real life. It hasn't let them down yet. Maybe I was wrong in the other thread: the problem here appears to be you just plain don't understand it.

David
Originally posted by russ_watters
So then which is the type of atomic clock that Einstein used in his books

He called them “elementary light generators” in the 1911 theory. You need to read Maxwell’s book and Steinmetz’s book so you will know what he was talking about. You really need to read the original theories, the original books, and not get all your information out of mass-media popular books designed for junior high school kids. You need to also read the old major science books of that era, such as Maxwell’s work, which was still fresh and new when the original theories were developed in the late 19th and early 20th Century. That will give you more background information so you can understand the newer theories from the early 20th Century. For example, I’ve never seen a modern book that says exactly what Einstein meant by “elementary light generators”. However, I did find the information in Maxwell’s book and Steinmetz’s book from 1923.

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.

Originally posted by russ_watters

Then explain GPS. The engineers who make GPS satellites use the predictions of SR (motion related time dilation) in the calibration of the satellites' clocks.
Read Lorentz’s theory and some of Dr. Su’s papers. They explain it. It has nothing to do with SR theory. The atoms in the clocks don’t know they are “moving relatively”. They only know they are “moving” if they feel some kind of motion-related force.

David
Originally posted by russ_watters
From your frame of reference if you shut your eyes, nothing has changed. You don't understand the relevance of frame of reference. Scientists, engineers, and laypeople who don't even know it, use Einstein's Relativity every day in real life. It hasn't let them down yet. Maybe I was wrong in the other thread: the problem here appears to be you just plain don't understand it.

Einstein tried to work thermodynamics into the SR theory in his 1907 paper, “On the Relativity Principle and the Conclusions Drawn From It,” but he got all mixed up. When he wrote the SR theory in 1905, he didn’t consider the thermodynamic implications.

See, if “all of time” slows down inside a “moving” frame, then the vibration rates of all the molecules slow down too, since they are, in effect, molecular clocks, and everything inside the frame freezes, based on the "time slowdown" rules of SR theory itself. He just didn’t think of that when he wrote the paper. I thought of it, and I finally tracked down his 1907 paper in which he tried to introduce thermodynamics into the SR theory. But it never worked out. His 1905 theory was based on his misunderstanding of the 1895 Lorentz book.

You really need to get a copy of his 1918 correction paper, in which he adds fields, acceleration, and atomic clocks to the SR theory. When he does that, then it becomes the 1895 Lorentz theory that he tried to copy in the first place. You need to get a copy of Lorentz’s book too, to see the original of the Lorentz Transformation and many of the ideas that were copied for the SR theory. Modern books won’t tell you this stuff. You’ve got to do your own research.

The Lorentz book is so rare, I saw a copy offered for sale in Holland for 6,750 Euros. That’s more than \$6,750 dollars. Some day the book with be translated and published in English, and everyone will see where the SR theory originally came from, and how the 1905 errors occurred.

Here is a page from my copy of the 1895 Lorentz book:

He introduced atomic time dilation on page 49, when Einstein was just 16 years old and still in high school.

Last edited by a moderator:
russ_watters
Mentor
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
Mentor
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

Last edited:
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
Mentor
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.

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' dont 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
Mentor
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' dont 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 arguement 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.

Last edited:
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
Staff Emeritus
Gold Member
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
Staff Emeritus
Gold Member
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.

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
Staff Emeritus
Gold Member
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
Staff Emeritus
Gold Member
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
Staff Emeritus
Gold Member
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.