# Time dilation an illusion

1. Aug 1, 2010

### Nickelodeon

One commonly quoted example of speedy things ‘living longer’ is the accelerated Muon. If you accelerate a beam of muons in a circular synchrotron and accelerate them to .99c then the muon lifetime is increased by a factor of 100. Quite a significat value and not one that could be fobbed off as experimental error. As I see it, you may be forgiven if you argued that the accelerated muons are really living longer compared to the stationary twin one you are keeping metaphorocally in your pocket.

I can't help thinking it is a relative thing and really an illusion caused by the limitations of the data carrier.

This time, leave one of the twin muons on the laboratory bench and start accelerating the other in the synchrotron. Instead of observing the accelerating muon from the laboratory floor, get in the synchrotron and accelerate yourself to .5c allowing the other muon to increase its velocity to .99c as before. In effect, both muons are moving relative to you at more or less .5c . You will see that they die together, am I right or am I right?

2. Aug 1, 2010

### Dmitry67

No
Check relativistic velocity addition

3. Aug 1, 2010

### yossell

Also, since the observer is travelling in circular motion, he is accelerated and not in an inertial frame, so he can't conclude that the muon left on the floor, which is inertial, lives longer relative to him. In effect, he's like the returning twin of the twin paradox.

4. Aug 1, 2010

### Nickelodeon

Yep, I know activity in this example is circular so not so good but if you forget that bit and think of it all happening in a straight line ...

5. Aug 1, 2010

### Rasalhague

Assume linear motion, as you said, and, to take into account relativistic composition of velocities, accelerate to 0.8676 c after the muon that's moving with respect to the lab. Then both muons will be travelling at the same speed relative to you:

(.99-.8676)/(1-.99*.8676) = 0.8676

(0-.8676)/(1-0*.8676) = -0.8676

Now the scenario is nicely symmetrical, and muons going one way should last as long as muons going the other at the same speed.

6. Aug 1, 2010

### Nickelodeon

Thanks for that. So I think we have established that in this new found symmetry the muons die at the same time. What happens when we reverse the process and accelerate the .99c muon back to the beginning again to join its twin in the laboratory? Do they still die at the same time?

7. Aug 1, 2010

### Rasalhague

If you have two curves through spacetime which intersect twice, and one of those curves is the path through spacetime of a particle moving inertially at all points between the intersections, and the other is the path of a particle that accelerates between the intersections, then the particle that accelerates ages less. This is an objective difference, not dependent on an arbitrary choice of reference frame, unlike the observation that a "moving clock runs slow", which depends on what velocity you choose to define as zero (out of the infinitely many equally good velocities there are to choose from).

8. Aug 1, 2010

### yogi

Most of us have read the wild endorsements that proclaim SR simply can't be wrong because it has survived every test conceivable - interestingly, there do not seem to be any tests actually measuring things from the standpoint of observers moving relative to the earth centered reference frame - normally we set up two clocks a distance d apart as measured in the earth frame and we note other clocks that move wrt to our earth frame accumulate less time (ignoring GR)- we then conclude that if two clocks were spaced apart a fixed distance x in space, an earth clock would be measured to be running slow as it traversed the distance X between the two clocks in free space - I don't have much doubt that it would be seen as running slow - but do we ever really confirm this experiment? This has led to speculation that SR time dilation is like GR, that is, it isn't reciprocal. The argument is that there is something going on wrt the G field that affects the outcome - anyone know of a free space experiment that refutes these musing?

9. Aug 2, 2010

### Nickelodeon

So in practicality, we have two time variables, the significant one due to an illusion and the other real and due to relative acceleration (presumably this includes gravitational effects)?

Could it be possible that if you accelerate time slows down but when you decelerate it speeds up again, ie. reversing the process?

Last edited: Aug 2, 2010
10. Aug 2, 2010

### Bussani

I think you're asking the same thing I asked in https://www.physicsforums.com/showthread.php?p=2549150". Deceleration doesn't reverse the time dilation or make time "catch up".

Last edited by a moderator: Apr 25, 2017
11. Aug 2, 2010

### Austin0

That would seem to be the case wrt the returning twin. Having returned to earth his "clock"
is now running at the same rate as his brother's. SImultaneously too! :-)

12. Aug 2, 2010

### Rasalhague

Proper time is a useful term. It's a property of a timelike curve (also called a world line) through spacetime. A timelike curve represents the possible path of an object through spacetime. If you think of points in spacetime as events, the proper time between two events on the curve is the spacetime analogy of arc length in space. It represents the amount of time experienced by an object "travelling" through spacetime along the curve from one of those events to the other.

A geodesic is the most direct path between two points; in spacetime between two events. Examples of geodesics in space: a straight line in Euclidean space, a segment of a great circle on a sphere (such as the equator). A material object on a spacetime geodesic is in freefall.

With no gravity, we have what's called flat spacetime. This is the geometry that special relativity describes. In flat spacetime, you can have curves that are straight lines. These are the geodesics of flat spacetime. In space, a geodesic is the shortest path between two points; it's the curve with least arc length. But in spacetime, between a given pair of events, if it's possible for a material object to travel between them, the geodesic path between those events is the one with most proper time. In flat spacetime, straight world lines represent motion with constant velocity: clocks record most time along these. Curved world lines represent accelerated motion: clocks record less time along these, less and less the more acceleration there is. Velocity is relative, since it depends on an arbitrary choice of coordinate system, but acceleration, in this sense, is absolute, since it doesn't depend on the choice of coordinates. There is a special, "favoured" state of acceleration, a natural choice of what to call zero acceleration (inertial motion, constant velocity).

Gravity curves spacetime itself. It causes geodesics to be curved too. This makes the definitions of velocity and acceleration more complicated, and there are people here far better qualified than me to talk about this. In curved spacetime, something on a geodesic is still in freefall. There's still something special about geodesic motion. Locally (meaning in the limit, as you examine smaller and smaller regions of spacetime) an object in freefall experiences less time between two events than an object taking a non-geodesic (i.e. a more roundabout) path between those same events. But on a large scale, the curvature of spacetime itself also contributes to the amount of proper time along a world line, so this has to be taken into account too, as well as the amount of deviation from freefall.

I think this might be open to more than one interpretation. One way to answer might be that deceleration is acceleration by another name. Taken in isolation, there's no natural way to say which of two accelerations is "speeding up" and which "slowing down"; you'd have to first make an arbitrary choice of velocity as your baseline, zero velocity. It's not as if there's a special absolute velocity (with respect to time dilation) that you move further and further away from the more you accelerate, and then have to decelerate to get back down to. All velocities, except c, are physically equivalent.

Last edited: Aug 2, 2010
13. Aug 2, 2010

### Staff: Mentor

Gravity provides an error that makes the experiment come out correct? That doesn't make logical sense. Besides, gravity does have an effect all its own and experiments exist (clocks on towers, clocks in GPS satellites) that provide for different mixes of the SR and GR components as well as SR tests that don't travel with the earth's surface. So it would be an awfully small place for an awfully large error in both theories to think that all of these experiments have just the right errors that they cancel each other in all cases yet devised.

Why would a scientist humor such musings? It violates Occam's razor and it is basically saying that scientists should disregard confirming experiments and assume that the confirmation is based on sneaky errors not found or even conceived of. Again, that makes no logical sense.

Last edited: Aug 2, 2010
14. Aug 3, 2010

### yogi

Hi Russ

That isn't really the way the argument goes - for example, you can get the correct answer to the SR time dilation in the classical twin scenario by using GR - you also get exactly the same time dilation using a centrifuge and computing the acceleration G force on the accelerating clock that you would get if you used the tangent velocity and applied the SR transform - so the thinking is that both involve energy (one in the form of potential, the other kinetic). These are not freeky errors that coincidentally arise - they seem to correspond precisely in all experiments involving energy - so the thinking is that because GR is not reciprocal, SR may not be either. Specifically earth based clocks are endowed with a different energy by virtue of their potential and the clocks moving relative to earth based clocks have a kinetic energy and the difference determines the rate at which time passes. To really falsify the arguement it would seem to require a free space experiment - for example two spaceships each one mile long could be arranged to have a clock at both ends - They are prepared in the same inertial frame and each is taken to a different free space environment and put into motion wrt to the other so they pass nearby in opposite directions on parallel paths at constant relative velocity v - The observers in each spaceship measure the clock rate of one of the clocks on the oppositely moving spaceship to determine its relative rate - SR states each should measure the other clock to be running slow - but this experiment is never performed - all verification has been done by using the earth centered reference frame as a bases and then proclaiming that it is not privileged.

15. Aug 3, 2010

### starthaus

This is falsified (on a daily basis) by a continously running experiment: the GPS.

16. Aug 3, 2010

### yogi

No it is not - the non moving earth centered reference system is taken as the proper frame. Correction for the altitude and velocity are then made wrt to the earth's surface potential and velocity with respect thereto - to eliminate the potential error arising from our choice of the earth one needs to do the experiment in free space

17. Aug 3, 2010

### starthaus

Doesn't matter, what you are denying is the very existence of a test for time dilation, I gave you an experiment that does this every second of every day. The frame of reference chosen for calculations is immaterial, any other frame would have worked just as well as ECI. The rate differential between the GPS transmitter and the receivers exists independent of the frame chosen to perform the computation. The only reason ECI has been chosen is that it makes the computations easier.

Last edited: Aug 3, 2010
18. Aug 6, 2010

### yogi

To verify the earth clock is running slow when measured by two satellites in circular orbit at the same height where one is, for example, half an orbit behind the other - you need to perform the experiment by measuring a single earth clock using the two satellites clocks and their separation distance taken as the proper length interval. You have asserted the outcome, and accompanied it with the usual comment that the earth is taken as the proper frame for convenience - which is true but does not address the claim of the critics that the situation is not reciprocal. Perhaps there is some data that that can be processed to establish the experiment ... but the GPS satellites are preset to correct for altitude and the velocity relative to the non-moving earth centered reference frame, so I am not aware whether the data can be processed to verify reciprocity

19. Aug 6, 2010

### matheinste

Hello Nickelodeon,

Experiments which measure the transverse Doppler effect are also often quoted as a confirmation of time dialation. I am not totally familiar with the details but it might be worth your looking it up if you are not already aware of its consequences with respect to time dilation. I am going to familiarize myself with it later

Matheinste.

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