# Can someone explain time dilation w.r.t following experiment?

1. Jul 21, 2009

### venuz

Hi all,

I am not so good in physics. Plz forgive me if i am totally wrong. However, i just want to understand the time dilation thing. I referred the net, but couldn't get a convincing answer.

Please explain how the time in two clocks in different inertial frame of reference can show different times? Explain in the context of following experiment.

Assume that:
1) There are only 2 axes X and Y
2) I have a clock that measures time using a particle (inside it) oscillating along Y axis. Say 1 oscillation(up+down) happens in 1 second.
3) There are 2 persons(P1 and P2) each with one clock.
4) both are at (0,0) initially
5) Assume, there are no gravitational or electromagnetic forces acting on the experimental objects.

Now,
1) P1 is stationary with his clock and P2 is moving along +X.
2) After 10 oscillations in P1s clock, say P2 is at (+d,0).
3) Here even P2s clock would have oscillated only 10 times right?
But according to time dilation it says that time in P2s clock will be slower. How is it possible ?
By time, here i mean number of oscillations along Y.

Lets not bring into this discussion, the following concepts
1) that speed of light is constant in whatever frame of reference. (im using oscillation of particle with solid mass for measuring time)
2) that moving objects increase in mass

Thanks for ur patience. Now answer.

2. Jul 22, 2009

### vin300

The clock measures lesser time because of the second point that is not to be discussed.
F=-kx{F=force, k=constant, x=displacement}
a=-k/m(x)
So increase in mass decreases the acceleration
k/m=w^2, so increase in mass decreases the square of frequency(implies time dilation).
That means you icrease the mass and The square of time measured by clock decreases
Curious It should have been time

Last edited: Jul 22, 2009
3. Jul 22, 2009

### venuz

All right then. Here P2s clock actually has an error factor. Let's consider that the clock is error corrected during the calculation, then P2s actual time = P2 oscillations + error(calc using mass change). However, twin paradox states that the travelling person is YOUNGER. Means while the resident has grown beard, the traveller is still young. How is it possible for human growth to decelerate relating to clock error. If however someone is let to travel like that, will he be physically younger? If so, plz explain why.

4. Jul 22, 2009

### vin300

No, it is not due to clock error.The time really goes slower at places close to massive bodies and trips at relativistic speeds
For explanation and detailed derivation, seehttp://en.wikipedia.org/wiki/Time_dilation" [Broken]or
I am curious to know what is the possible explanation that says increase in mass is inversely proportional to time measured and not square of time as derived above

Last edited by a moderator: May 4, 2017
5. Jul 22, 2009

### Staff: Mentor

OK.
No.
Where do you see a problem? Realize that according to P2's frame:
(1) The distance traveled is less than d.
(2) The clocks (note that multiple clocks are needed in P1's frame to measure the time interval) in the P1 frame are not synchronized.
(3) The clocks in the P1 frame run slow.

6. Jul 22, 2009

### Staff: Mentor

This is due to the first postulate of relativity, that the laws of physics are the same in all reference frames. If the clocks are identical and the twins are identical and the laws governing clock ticking and beard growth are identical then the number of clock ticks required to grow a beard are identical. Therefore since the clock ticked less the beard grew less.

7. Jul 22, 2009

### vin300

And an answer for the proportionality of mass and time as derived in the second post?

8. Jul 22, 2009

### Bob S

Brookhaven National Laboratory recently completed a precision experiment on relativistic muons stored in a magnetic storage ring at a relativistic gamma of about 29.4 (beta ~ 0.9994). See
http://arxiv.org/PS_cache/hep-ex/pdf/0102/0102017v3.pdf
The natural lifetime of stopped muons in the laboratory is about 2.197 microseconds. This is their "clock". In the ring, the observed lifetime of the relativistic muons was about 64.4 microseconds (our "clock"), time dilated by a factor of 29.4.

9. Jul 22, 2009

Staff Emeritus
Bob, how is this relevant?

10. Jul 22, 2009

### venuz

People,

Sorry for calling the oscillation difference as clock error.
I ACCEPT that mass increases in moving objects. I AM NOT CONTRADICTING THAT EQUATION.

What i am trying to say is..... "what we define as TIME" is always being related to the clock and since clock has oscillating mass => mass increase => frequency reduxn => clock's slow.

Lets assume a different way for measuring time. Assume P1 and P2 mentally know what is the gap for 1 sec and they close their eyes and imagine "tik tik" in their mind which is the clock. Lets NOT USE MASS TO MEASURE TIME. In THIS case, tell me what will affect the mental frequency? (dont say that neural synapse will be slow, hence their imagination of tik tik will differ).

Every calculation i see talks about atomic clock frequency as time, but freq is just motion of mass, where mass itself is changing. Here what i see changing is mass and its movement, not the way we measure tik tik. Do you get my point?

11. Jul 22, 2009

### Bob S

Posted by Bob S
Brookhaven National Laboratory recently completed a precision experiment on relativistic muons stored in a magnetic storage ring at a relativistic gamma of about 29.4 (beta ~ 0.9994). See
http://arxiv.org/PS_cache/hep-ex/pdf/0102/0102017v3.pdf
The natural lifetime of stopped muons in the laboratory is about 2.197 microseconds. This is their "clock". In the ring, the observed lifetime of the relativistic muons was about 64.4 microseconds (our "clock"), time dilated by a factor of 29.4.
This validates that the muon's clock has slowed down by afactor of 29.4 relative to the observer's clock, and that the distance traveled, as measured by the observer, is 29.4 times longer than measured by the muon.

12. Jul 22, 2009

### jambaugh

This is where Einstein started. "Time is what a clock reads". Now consider different types of clocks; Swinging pendulums which depend on mass and gravity, celestial clocks depending on rotation or orbits of planets or moons, Spring-mass clocks, electronic clocks depending on the harmonic capacitor-inductor tank circuit, etc.

Now start with the idea that each type of clock defines its own type of time. Forget about moving frames and special relativity for now.

How each clock works gives us a measurement of physical laws. Springs rely on the electromagnetic interactions between atoms. Pendulums depend on the mass of the earth, the radius of the earth, and the gravitational constant. Electrical clocks depend on Maxwell's equations and the permeability and permittivity of the materials (or of vacuum). Atomic clocks likewise and also on the masses of electrons, and atomic nuclei and on the Planck constant. Decaying atoms depend on strong and weak force coupling constants as well as fundamental masses and on c.

We can talk about the dynamics of a mass-spring system using atomic-clock time or using resonant em-cavity time or decaying-muon time. And vis versa et cetera.

In the end (within a given inertial frame) it seems we can always make different types of clocks equivalent assuming basic fundamental constants are constant. Among these and ubiquitous among these is c, the speed of light in a vacuum.

Consider how we measure the speed of light. We basically clock the time it takes light to travel a measured distance. We must have a clock and a measuring rod each of which must be calibrated to some standard. However if two measurements of the speed of light yield different values we may ask if the speed is really different or did the clocks differ or did the measuring rods? Or all three? How could you tell? At best you can only tell if one of the three vary relative to the other two. Of these we prefer to fix the speed of light as a constant and define distance in terms of how far light travels in a given time. We then measure time with an atomic clock (which in turn depends on constancy of the Plank value and of the masses of electrons and atoms and again on the constancy of c.)

You can decide to do otherwise but you aren't really conceiving of new physics...only a new definition of "what is fundamentally constant". You could also consider asking whether certain fundamental constants are not so constant but you can only do so relative to other fundamental constants and not in any absolute sense. (Quite a fun undertaking.)

Now we again bring up relative motion. Two main possibilities can be conceived:
a.) The speed of light is (an isotropic) constant only in some single stationary frame and all observers can see their own motion relative to that frame by comparing the speed of light in different directions?
b.) The speed of light constant for all frames and every observer regardless of his motion relative to other observers sees identical physical laws (though of course different versions of a commonly observed physical phenomenon.)

Position (a.) was tested via the Michelson-Morley experiment and we failed to see absolute motion due to variations in the speed of light in different directions.
Explanations were attempted by invoking new phenomena (shrinking of physical objects relative to their motion through the aether, slowing of clocks and increasing effective masses). In short the Lorentz transformations were derived which if valid would imply position (b.) as a practical consequence. Position (b.) was then adopted by Einstein as a fundamental principle in his special theory of relativity.

(There are many more conceivable possibilities but not as many distinct possibilities as you might at first think.)

Now where I say "speed of light" this also includes the various laws of physics we've observed which depend on this constant which include atomic interactions and thus mechanical forces as well as mental processes

Thus you can look into the details of various types of clocks but you won't get away from that pesky c constant in their dynamics. As seen by one observer all the moving observer's clocks will slow by the same amount be they mass-spring clocks, atomic clocks, electromagnetic cavity clocks, particle decay clocks, or biological clocks.

It is instructive to consider these different types to see how "length contraction" and "relativistic mass" and "time dilation" all interplay but I think you can get caught up in the details and loose sight of the basic principle of relativity. You need to start with light signals and the relativity principle and work through the Lorentz transformations in various examples.

13. Jul 22, 2009

### Staff: Mentor

Hi venuz,

Again, this is due to the first postulate. If any clock is slowed and if the laws of physics are the same in all frames then all clocks must be slowed.

14. Jul 22, 2009

### darkhorror

The mass in it's own frame does not change, it's when you look at it from another frame. Just look at acceleration, you could get on a rocket and accelerate at a constant acceleration forever. But when we were to look at you from earth we would see your acceleration slowing.

15. Jul 22, 2009

### Eli Botkin

You probably readily accept without question that the square of the spatial distance between 2 points, x^2+y^2+z^2, is invariant with respect to a coordinate rotation. Why is that so? Because that is the structure of space.

Now you need also to accept that the spacetime interval, (ct)^2-x^2-y^2-z^2, is invariant with respect to a velocity boost. Why is that so? Because that is the structure of spacetime.

There is no other reason. Every other offered reason (mass increase, constancy of light, etc) is itself a consequence of this spacetime structure.

16. Jul 22, 2009

### Staff: Mentor

Your point is that you don't think the definition of "clock" is correct. You don't think clocks really measure time. But they do. We know this because there are many types of clocks that measure time in many different ways (and the good ones do not rely on moving mass) and all of them agree on the rate of the passage of time, assuming they have the precision required to make the comparison.

So the answer to your question "what affects the mental frequency?" is nothing. Your "mental frequency" is fixed to the rate of the passage of time. And time in your reference frame always flows at the same rate. Time measured from two different frames may pass at different rates, but that should not be thought to imply some physical change is happening in one of those frames because you can choose any frame to compare yours to and thus come up with any of an infinite number of possible time dilation factors between them.

17. Jul 22, 2009

### Staff: Mentor

Good point.

18. Oct 7, 2009

### Grimble

Hi Venuz, I think I can see what you are asking -- and it isn't concerned with clocks!
Are you not wanting to remove clocks from the question about time dilation?
And yes, you were right in your original post in that P1 and P2 would experience identical time! The difference is that when either 'looks' (by whatever means he has available) at the passage of time for the other he will see a difference in the time passed, i.e. a difference in the rate that time is passing for his moving friend.
I prefer not to use terms like faster and slower, younger and older as they are very much dependent on what is being viewed from where! Even the formula for time dilation is given in conflicting terms by different people though, in reality they are saying the same thing, just perhaps, standing in a different place to say it.

I have been going over much the same ground myself https://www.physicsforums.com/showthread.php?t=333112"

It is confusing that so many 'experts' don't agree on what they are saying or, perhaps, how to say it.

Grimble

Last edited by a moderator: Apr 24, 2017
19. Oct 7, 2009

### yuiop

Hi Venuz,

anything you can think of that can be timed, slows down with relative motion. For example it takes about 1 second for a ball to fall 10m to the surface of the Earth. Now, imagine that the Earth is accelerated to near lightspeed relative to you. You will see that it now takes say 100 seconds for the same ball to fall the same height. Even the acceleration due to gravity slows down! The heart rate of a person on the Earth speeding past you will be 100 times slower than yours. A sandwich that normally takes a week to become inedible now stays fresh for nearly 2 years at room temperature. TV.s will be displaying 1 frame every 2 seconds rather than the usual 50 frames per second. Global warming and rate of population increase will be 100 times slower and yes, the people on the Earth speeding past you are thinking 100 times slower than you are and do not notice anything unusual about the rate of change of things happening local to them.