# Could you slow time using a tuning fork?

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Just an odd thought that occurred to me seconds ago.

Time slows, for objects under acceleration. The tip of a tuning fork is constantly accelerating one way, then the other. The g forces must be very high. Could you set up an experiment to slow the ageing of a radioactive isotope right down, by putting it on the tip of a similar spring, and maintaining it's vibration?

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DrP    355

How/why would the oscillations of the material atoms have any effect on the sub atomic particles in the nucleus?

I also suspect that the speeds and accelerations involved would be negligible compared to what is going on inside the atoms themselves.

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"Time slows down" for an object in motion, relative to another object.  Acceleration is not necessary nor are "g- forces".  Yes, a sub-atomic particle would experience "slower time" compared to the "laboratory" time, but as DrP says, that would be a negligible effect.  The "aging of a radioactive isotope"" has been demonstrated by moving the isotope at high speeds in a cyclotron.

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swansont    6208
21 minutes ago, mistermack said:

Just an odd thought that occurred to me seconds ago.

Time slows, for objects under acceleration. The tip of a tuning fork is constantly accelerating one way, then the other. The g forces must be very high. Could you set up an experiment to slow the ageing of a radioactive isotope right down, by putting it on the tip of a similar spring, and maintaining it's vibration?

It's the speed, not the acceleration, that matters.

How fast is the tip moving? Let's use 300 m/s; the actual number is probably smaller. But that's a millionth the speed of light, and for speeds this small the dilation factor is about  v^2/2c^2, or 5 parts in 10^13, for the maximum speed. Less than that overall, because it doesn't move that fast all the time.

That's not going to slow a decay by any noticeable amount. A part in 10^12 is a picosecond per second. Several microseconds per year.

17 minutes ago, DrP said:

I also suspect that the speeds and accelerations involved would be negligible compared to what is going on inside the atoms themselves.

Correct. Hundreds of m/s for a gas at room temperature. (Slower as the mass goes up, of course)

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geordief    53

Is there any connection at all between the time effects of being higher or lower  in a gravitational well  and any (or no?) time effect caused by acceleration per se?

There seems to be a close connection between gravity and acceleration in GR (the equivalence principle) but the former does have time effects and I am not sure if the latter does except for the fact that relative motion is involved.

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So are you saying that the acceleration doesn't come into the equation? I thought that in General Relativity, time dilation occurs in a gravitational field, and acceleration is not distinguishable from gravity.

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Janus    687

g- forces have no effect on aging, or put another way, there is no time dilation factor due to acceleration forces.  The only time dilation effect that would be seen would be from the speed of the vibrating ends of the tuning fork.    That acceleration forces have no time dilation effect has proven by spinning radioisotopes up to extremely high speeds in centrifuges so that they experience 1000's of gs. By varying the size of the centrifuge, you can vary the ratio of speed and g force experienced. Such experiments show that the only factor that determines the time dilation is the speed at which the sample travels.

This is no different than Gravitational time dilation.  Gravitational time dilation is related to the amount of work it takes to move a test mass from one height to another, not to the difference in g force felt by this test mass at the two heights.  In the same way, with the centrifuge, it is related to the work needed to move the test mass in from the end of the spinning arm to the axis of rotation, and this is directly related to the speed at which the end of the arm is moving, and not the g force difference between the end of the arm and the axis.

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swansont    6208
7 minutes ago, geordief said:

Is there any connection at all between the time effects of being higher or lower  in a gravitational well  and any (or no?) time effect caused by acceleration per se?

There seems to be a close connection between gravity and acceleration in GR (the equivalence principle) but the former does have time effects and I am not sure if the latter does except for the fact that relative motion is involved.

6 minutes ago, mistermack said:

So are you saying that the acceleration doesn't come into the equation? I thought that in General Relativity, time dilation occurs in a gravitational field, and acceleration is not distinguishable from gravity.

For something in motion, you can do either. You'll get the same answer. The folks who did a followup to the Pound-Rebka experiment by putting the radioactive material in a centrifuge showed this. You get the same answer by using the kinematic time dilation formula, or using the centripetal acceleration in place of g in the gravitational potential. It works for the reasons Janus points out above.

edit: reference at the end of this
http://blogs.scienceforums.net/swansont/archives/1426

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geordief    53
5 minutes ago, mistermack said:

So are you saying that the acceleration doesn't come into the equation? I thought that in General Relativity, time dilation occurs in a gravitational field, and acceleration is not distinguishable from gravity.

And we got two answers from Janus and Swansont.

I am going to try and digest them now....

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4 minutes ago, Janus said:

Gravitational time dilation is related to the amount of work it takes to move a test mass from one height to another, not to the difference in g force felt by this test mass at the two heights.

I thought that it was related to the strength of the gravitational field at the point in question, and that that was directly related to the g force at that point, which is directly comparable to the g force of an accelerating body.

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geordief    53

I am fascinated that the time dilation in a gravitational well would be due to the work involved in placing it there (if I understood that right) . Is there a link where this is explained ?

(not that I expect to be able to understand it for now)

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Janus    687
3 minutes ago, mistermack said:

So are you saying that the acceleration doesn't come into the equation? I thought that in General Relativity, time dilation occurs in a gravitational field, and acceleration is not distinguishable from gravity.

Consider the following example:

You have a rocket which is accelerating. There is a clock in the nose and tail.  As far as anyone in the rocket is concerned, they are accelerating at the same rate.  Relativity predicts that the clock in the nose will run faster than the clock in the tail, even though there is no difference in the acceleration felt.  In the same way,  two clocks at different heights in a uniform gravity field (one that does not change strength with height.) will run at different rates even though they feel no difference in gravity.   While you need acceleration or gravity for these differences to show up, it is not the difference in acceleration/ gravity that causes the difference.

To go back the the centrifuge.  If you are in the lab frame, you have a sample traveling at a high speed and you expect it to show a time dilation effect from it. If you are in the centrifuge frame, it is like there is a gravitational force acting outward from the axis and which gets weaker as you move towards the axis.  You would expect a time dilation effect that would be related to the potential difference between the end of the arm and the axis. (the aforementioned work needed to move in to the axis).  This will work out to be the same factor as that expected in the lab frame.   The two time dilation effects, as seen in the lab and as seen by the centrifuge are just two different views of the same thing.  What you cannot do is "double up" by applying both.

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8 minutes ago, Janus said:

two clocks at different heights in a uniform gravity field (one that does not change strength with height.) will run at different rates even though they feel no difference in gravity.

That does strike me as pretty amazing. What physical difference can there be, between the two clocks?

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Janus    687
5 minutes ago, geordief said:

I am fascinated that the time dilation in a gravitational well would be due to the work involved in placing it there (if I understood that right) . Is there a link where this is explained ?

(not that I expect to be able to understand it for now)

It is implicit in the gravitational time dilation formula.

For example, use it to work out the time dilation for the surface of the Earth vs. the surface of Uranus, and then compare the surface gravity of the two. You will note that, for a far off observer, clocks will tick slower on Uranus than on Earth, but the surface gravity of Uranus is less than that of Earth.   This is because even though you are starting from a point where the gravity is locally weaker while on Uranus, the amount of energy needed to lift a mass far away from Uranus is greater than that needed to lift an equal mass as far away from Earth.

4 minutes ago, mistermack said:

That does strike me as pretty amazing. What physical difference can there be, between the two clocks?

This is the problem, you are trying to assign the difference in tick rates as being due to some local physical effect acting on the clocks.  It is due to the fact that the clocks simply measure time differently.   This is a much more abstract concept, than a "physical cause".

Let's describe it this way.

You have your two clocks, and they are sending signals to each other at 100,000hz.  This means that for every sec ticked off by a clock, its sends out 100,000 complete waves of electromagnetic radiation.  The light going up from the lower clock to the upper clock is fighting the gravity the whole way and loses energy in doing so.  Light's energy is tied to its frequency, so it exhibits this as a decrease in the signal frequency as it climbs to the upper clock.

So let's say that by the time it reaches the upper clock it has a frequency of 99,999 hz.  This means that the upper clock receives 99,999 waves every second, and thus will take a tad bit more than 1 sec to receive the 100,000 waves, the lower clock sent in its measured sec.  Since the number of waves sent off by the lower clock between each second it ticks off is fixed, The upper clock must also "see" the lower emit 100,000 waves between each second it sees the lower clock tick off one sec.  Since we have established that it takes longer than one sec by its own clock for the upper clock to receive 100,000 waves, it must also take longer for it to see the lower clock tick off 1 sec.  The longer we let these clock run, the greater their difference in reading grows.

If after some time, we stop both clock and bring them together again, they will show different times.  (Imagine the top clock has seen the lower clock stop and then stops itself. Then it approaches the lower clock, while watching it. at no point during the approach will the top clock see either the lower or itself change time readings. so when they meet they will show different times.  Now its is true that some time will pass between the lower clock stopping and the upper clock seeing this, so we must account for this offset.  But this is a fixed amount and doesn't change depending on how long we let the clocks run before stopping them.  It could be 1 microsecond, and we could let the clocks run until the upper clock saw the lower one 1 sec behind. When brought together, that 1 microsecond only accounts for a small amount of the difference.

If we turn things around and watch the upper clock from the lower, the signal gains frequency as it travels down and increases its frequency.  The lower clock sees the upper clock as running faster than itself.  And when the clocks are brought together again this difference in clocks will remain.

Nothing is physically acting differently on the two clocks, they are just measuring each other across a gravity potential.

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swansont    6208
58 minutes ago, geordief said:

I am fascinated that the time dilation in a gravitational well would be due to the work involved in placing it there (if I understood that right) . Is there a link where this is explained ?

(not that I expect to be able to understand it for now)

The first two references in my blog post link, I think. And many discussions of the Pound-Rebka experiment are out there.

1 hour ago, mistermack said:

I thought that it was related to the strength of the gravitational field at the point in question, and that that was directly related to the g force at that point, which is directly comparable to the g force of an accelerating body.

Near the surface of the earth (where we can assume g is constant) it's given by gh/c^2. gh is the gravitational potential , which is the potential energy per unit mass for a massive object, and the PE is also the work done.

So it depends on g, but is not solely due to g, and requires having clocks at different positions in the field.

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Thanks Janus. I have got my head around some of that, thanks to the mental picture you provided. So the deeper in the gravity well you are, the slower your clock is running, even if there is no increase in the actual pull of gravity. That's counter-intuitive at first thought, but I think I get it now.

So the event horizon of a black hole is as much  to do with position, as the force at that point. It's the point from where the frequency of a photon would drop to zero, before it could escape. A combination of field strength and position in the field.   ??

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MigL    511

I'm sorry if this confuses you further but...

"the deeper in the gravity well you are, the slower YOUR clock is running"

is incorrect. Your clock never runs slower ( or faster ).
It is only in comparison to another clock ( or an observer ) at a different height in the potential well, that a difference is noted.
The timing signal ( or frequency of light ) will decrease as it expends energy to climb to a higher position, or increase as it gains energy falling to a lower one.
( and I apologize if this is actually what you meant )

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Mordred    884
4 hours ago, MigL said:

I'm sorry if this confuses you further but...

"the deeper in the gravity well you are, the slower YOUR clock is running"

is incorrect. Your clock never runs slower ( or faster ).
It is only in comparison to another clock ( or an observer ) at a different height in the potential well, that a difference is noted.
The timing signal ( or frequency of light ) will decrease as it expends energy to climb to a higher position, or increase as it gains energy falling to a lower one.
( and I apologize if this is actually what you meant )

Even if he/she does, this is a key detail to fully understand. +1

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12 hours ago, MigL said:

I'm sorry if this confuses you further but...

"the deeper in the gravity well you are, the slower YOUR clock is running"

is incorrect. Your clock never runs slower ( or faster ).
It is only in comparison to another clock ( or an observer ) at a different height in the potential well, that a difference is noted.
The timing signal ( or frequency of light ) will decrease as it expends energy to climb to a higher position, or increase as it gains energy falling to a lower one.
( and I apologize if this is actually what you meant )

No apology needed, all comments are warmly welcomed.

I did mean that. It appears that time is relative in a similar way to space, in that a clock is only faster or slower, relative to another clock, just as you can only detect movement, relative to another body.

So I was really assuming that the deeper in the gravity well you are, the slower your clock is running, RELATIVE to a clock that is somewhere out in deep space, unaffected by the gravity well. Which corresponds to a clock at the very top of the gravity well.

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geordief    53

Yes ,the twin paradox (as an example) does invite one to mistakenly imagine that the outgoing twin is actually experiencing some kind of a "slow time" . You feel you have  done so well in the first place by reluctantly  accepting that clocks can counter intuitively run slower in certain circumstances  and imagine that things surely can't really be so mundane as that time passes in exactly the same way for all  observers regardless of where they happen to be or  what is happening to them (1 second per second as it is described perhaps simplistically) .

Ca we also blame our subjective experience of time  for this misunderstanding? The way time is supposed to slow down  when we are in great danger ,like falling off a cliff....

Are there any examples to give where paradoxes occur if time did not (as we intuitively believe) slow down but was an absolute feature of our experience... any "reductio ad absurdum" scenarios based on that premise?

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Mordred    884

The car in garage paradox with regards to the length contraction.

3 hours ago, geordief said:

Are there any examples to give where paradoxes occur if time did not (as we intuitively believe) slow down but was an absolute feature of our experience... any "reductio ad absurdum" scenarios based on that premise?

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Thanks for all of the comments. I've learned more than I expected from this thread, and as far as I'm concerned, the answer is no.

You may be able to slow time with a tuning fork, but only by an incredibly small fraction, that would never be measurable.