1 The behaviour of a clock in a linear accelerator versus a centrifuge

In Sci.Physics.Relativity In the thread "A suggested time dilation experiment"

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Yes, within limits. Here we meet those limits and can consider the rotating centrifuge to be "generating" an equivalent gravitational field in its rotating frame. Note that in these coordinates the centrifuge clock is not moving; let's place the lab clock at the center of rotation, so it is also not moving relative to these coordinates (and is also not moving relative to the lab). Note that this is GR, in which gravity is not a force. The only force exerted on any clock is the force from the outer centrifuge wall pushing radially inward on the centrifuge clock. Note also that forces do not affect clocks (as long as they are not broken). (I am neglecting the upward force from the floor, as I am ignoring earth's gravity.) As I said before, since everything is supported against the earth's gravity, and because the lab clock is at the same altitude as the centrifuge clock, earth's gravity makes no contribution. This implies that we can consider the lab to be a locally inertial frame. Here are three calculations of the difference in elapsed proper time between the centrifuge and lab clocks: 1. Centrifuge clock's "time dilation" relative to the lab frame: sqrt(1-v^2/c^2), with v the clock's speed relative to the lab, measured in the lab. Integrate this over 22 hours and one gets 0.93 ns over 22 hours. 2. Centrifuge clock's "equivalent gravit...

2 The behaviour of a clock in a linear accelerator versus a centrifuge

In SR, "time dilation" does not depend on the type of clock -- it is a geometrical projection caused by the fact that clocks in relative motion have non-parallel 4-velocities. This is pure geometry and simply CANNOT depend on the type of clock.

The actual equation is:

>	For certain clocks: Yes. For other clocks: NO.

Nope. Somewhere you goofed. The above equation holds for all types of clocks.

Your simulation is wrong.

Tom Roberts

3 The behaviour of a clock in a linear accelerator versus a centrifuge

>	The actual equation is: t' = \integral sqrt(1-v^2/c^2) dt

> >	For certain clocks: Yes. For other clocks: NO.

The clock I'm simulating is described at page 12 in the book SpaceTime Phyisics. The clock consists of two parallel mirrors in horizontal direction. The eye piece is towards the right side in horizontal direction. You can also depict the eye piece at the center between the two parallel mirrors. There are two ways to move this clock:
1) in veritical direction. That is done at page 69 of the book, inside a rocket. However 90 degrees rotated. The equation that describe this movement is the same as above mentioned. From the rocket point of view, in the direction of movement, the signal is reflected against the ceiling and the floor. My simulation shows exactly the same in a linear acceleration.
2) in horizontal direction. The equation that describes this behaviour is:

>

Nope. Somewhere you goofed. The above equation holds for all types of clocks. Note that t and v MUST be associated with an INERTIAL FRAME. That could be your mistake. etc. Note that no rotating system is an inertial frame, so if you ever used rotating coordinates in any way you almost surely introduced an error.

I fully agree. Any clock in a centrifuge is not in an inertial frame. My point is to simulate the behaviour of a clock undergoing acceleration. What the simulation shows is that the behaviour is very complex using the clock as described on page 12 (as a function of v) My point is also that allmost all clocks in principle have this problem. This is the case When for a clock in front of you on a table. For a clock in circular motion around the earth, around the Sun or around in our Galaxy. In the simulation this is done for one revolution. My point is also that accelaration is the primary influence of the behaviour of a clock.

>	Your simulation is wrong. Tom Roberts

Nicolaas Vroom.

4 The behaviour of a clock in a linear accelerator versus a centrifuge

IIRC that is a light clock with a light pulse bouncing between two mirrors. Remember that the mirrors are accelerated but the light is not -- the light pulse moves in straight lines between bounces (relative to any INERTIAL frame).

>	My point is also that allmost all clocks in principle have this problem.

I doubt it: SR predicts that NO clock has this "problem", and I see no reason to doubt that prediction. For instance, muons in a "relativistic centrifuge" (aka storage ring), undergoing the enormous proper acceleration of 10^18 g, are observed to decay at the rate SR predicts; that prediction depends on only their speed relative to the lab and their proper lifetime (see equation given earlier in this thread); in particular it is completely independent of their acceleration.

Not in SR. (Also not in GR.) And apparently not in the world we inhabit.

As I said before: your simulation is wrong.

Tom Roberts

5 The behaviour of a clock in a linear accelerator versus a centrifuge

Tom,

Unless I am misinterpreting your argument, I believe the last statements about acceleration not affecting the period of the clocks is incorrect. Let me describe a counter example that I believe makes this clear:

-Consider the two mirrors to be at the same radius in the centrifuge, but displaced along the axis of the centrifuge so the light pulses are describing a zig-zag along a cylinder at that radius. There is also a slight radial component, which gets larger as the centrifuge spins faster. -At very low speeds the distance the light travels between reflections is basically the axial separation of the mirrors. At very high speeds there is a substantial circumferential component to the light path and it is significantly extended. This happens when the mirrors are experiencing a very high acceleration. This the ticking of this light clock slows down with high accelerations. -Certainly much, if not most, of this slowing can be attributed to the tangential velocity of the mirrors. However because of the increase in radial motion of the light paths with increasing acceleration/velocity there will also be a component of the slowing that is due to the radial acceleration.

HOWEVER, I do agree with your basic position that acceleration itself does not affect the "rate of clocks" because this affect of acceleration can be recognized by the local observer. He can make clocks with shorter and longer paths between the mirrors and will see that these clocks run at different rates (even after compensating for the longer light paths). As the mirrors are put closer and closer together the rate will asymptotically approach the "normal" rate of time for that observer. Thus the observer could use this set of clocks to measure his acceleration. This puts this effect in a completely different category from the SR and GR time dilation effects.

Rich L.

6 The behaviour of a clock in a linear accelerator versus a centrifuge

In principle my clock consists of 6 mirrors (3 pairs of parallel mirrors) The center of the clock is the most important point. This is point where a light flash is emitted. This is also the point where the photon is observed or 'measured' and where a new flash is created after one cycle. The light flash is a sphere of photons emitted in all directions. If the clock is at rest then a photon emitted in vertical direction upwards, will be reflected at the ceiling, move downwards, is reflected at the bottom and is measured at the center. This is one cylce. Next a new flash will be emitted in all directions. etc. etc. The same can be done in all 6 directions.

7 The behaviour of a clock in a linear accelerator versus a centrifuge

For a centrifuge with a fixed radius, the speed of the mirrors relative to the lab is directly related to their acceleration, making it easy to confuse the dependence.

That said, a more careful analysis shows my statements are indeed wrong:

Consider two centrifuges with vertical axes and different radii, but the same tangential speed relative to the lab; they have different accelerations. Let each have a light clock with mirrors separated vertically (along the axis of rotation). Plot the bounce points (in 3-d) in the lab for each centrifuge, and project them onto a single horizontal plane -- each centrifuge's points all lie on a circle, and the tangential speed of the centrifuge is related to the arc of the circle between the projected points (which is equal for the two centrifuges). Since the radii are different, the chords of the circle between projected points are different, and Pythagoras' theorem (applied to the chord and the vertical separation of the mirrors) implies the light path lengths are different -- the two light clocks tick at (slightly) different rates.

This leads us to a rather different lesson: in relativity, clocks are considered to be pointlike [#]. These light clocks are pointlike, and behave as relativity predicts, ONLY when their internal light path is much smaller than their acceleration between bounces (i.e. only when the two chords above differ by a negligible amount). They do, of course, behave as relativity predicts for all INERTIAL motions, even when they are not really pointlike.

In retrospect, this should have been obvious, especially for a light clock in a centrifuge oriented with its mirrors along the radius (i.e. at different "heights" in the equivalent "gravitational field").

>	-Consider the two mirrors to be at the same radius in the centrifuge, but displaced along the axis of the centrifuge so the light pulses are describing a zig-zag along a cylinder at that radius.

NO! In the lab, the points of the bounces are all on that cylinder, but the light rays follow STRAIGHT LINES between the bounce points. You sort of talk around this, but it OUGHT to be clear that the light follows straight-line paths between bounces (i.e. on the faces of a many-sided polygon, not a cylinder).

>	[... description of what appears to be similar, using very different words]

Bottom line: clocks must be pointlike or their behavior can differ from what relativity predicts.

Tom Roberts

8 The behaviour of a clock in a linear accelerator versus a centrifuge

See my recent post in this thread, which shows an effect -- my earlier claims were wrong and a light clock can deviate from the predictions of relativity when it is not pointlike. That is, when its movement between bounces due to acceleration is not very much smaller than its internal light-path length.

>>	For instance, while they are being accelerated you must tilt the mirrors so the light pulse continues to bounce between them. Parallel mirrors work only when they are moving inertially.

>	I definitive do not want to change anything inside the clock as part of the experiment. The whole clock functions as a fixed box, all the angles are 90 degrees.

Then it won't work when accelerated.

For instance, in a centrifuge with a vertical axis and a light clock having a light path along the vertical axis and parallel mirrors, the light pulse will remain at a fixed azimuth in the lab, and the clock will rotate away from it. That is, motion of a mirror parallel to its surface does not affect light bouncing from it.

You MUST tilt the mirrors when the clock is accelerated, or the light pulse won't remain inside the clock. This applies to all orientations except when the acceleration is parallel to the clock's internal light path.

>	What is science? Do you adjust an experiment to fit the mathematics or Do you adjust the mathematics to fit the experiment?

Neither. In this case, PHYSICS (geometrical optics) requires that one tilt the mirrors when the light clock is accelerated, or it does not remain a light clock.

This is, of course, a GEDANKEN, not a real experiment. The conditions required are not achievable in the real world.

Tom Roberts

9 The behaviour of a clock in a linear accelerator versus a centrifuge

In physics nothing physically can be treated as a point. It always has a size. Under Newtons Law a physical object can be treated as a point in the sense that all its mass is 'contracted' in a point. As such a distance between two objects is the distance between the center of each object. Following that reasoning the behaviour of a clock can not be explained when the clock is considered pointlike. In the book SpaceTime physics all the clocks have a 3D Dimension. Nothing is considered pointlike.

My whole point is that when a clock (Using lightsignals) undergoes acceleration (its speeds increases) its behaviour changes. These changes are different, and are a function, of how the clock is build. (This difference depents about the direction of the mirrors relatif to the direction of movement of the clock)

>	You MUST tilt the mirrors when the clock is accelerated, or the light pulse won't remain inside the clock. This applies to all orientations except when the acceleration is parallel to the clock's internal light path.

My simulation shows that when the lightsignal follows a continuous path and is reflected against the mirrors of the clock than the light signal will not stay inside a clock. This is what I call a Long simulation. Such a simultion needs an initial angle.

10 The behaviour of a clock in a linear accelerator versus a centrifuge

Here the clock is clearly not treated as pointlike i.e. it has a size. My simulation calculates the bounces at the exact moment (event) when the lightflash reaches a mirror. The speed of the mirror is of no importance. The position (direction) is important.

> >	Unless I am misinterpreting your argument, I believe the last statements about acceleration not affecting the period of the clocks is incorrect.

>

For a centrifuge with a fixed radius, the speed of the mirrors relative to the lab is directly related to their acceleration, making it easy to confuse the dependence. That said, a more careful analysis shows my statements are indeed wrong: Consider two centrifuges with vertical axes and different radii, but the same tangential speed relative to the lab; they have different accelerations.

11 The behaviour of a clock in a linear accelerator versus a centrifuge

12 The behaviour of a clock in a linear accelerator versus a centrifuge

Rather, any accelerated system may be viewed as disturbed somehow with particle and fields constituting it as a seemingly solid state device, not following their time evolution at rest or at constant velocity.

In the extreme case the atomic clock at the head and tail of an accelerated rocket will not show the same time, if they were synchronized before accelearation at rest.

What happens to the H-atom at constant acceleration is long known as gravitational shift of the s-state

13 The behaviour of a clock in a linear accelerator versus a centrifuge

The only way to find out is by performing an experiment. The results of my simulations show that not all clocks behave the same.

>	One could argue that a grandfather clock is driven by gravity and thus, due to the equivalence principle, would be affected by acceleration,

Also this should part the experiment. As you expect such a clock will read differently and if that is the case you find the reason by investigation how this clock is build and operates.

>	(but what about the other three?) What about two partially-silvered mirrors with a light pulse bouncing between them which beeps when a photomultiplier behind one of the mirrors is activated?

14 The behaviour of a clock in a linear accelerator versus a centrifuge

Given that all of the (other) clocks are pointlike, as well as the box [#], then GR certainly predicts they all read the same. I see no reason to doubt this prediction -- after all, it is based purely on geometry, not on any construction details of the clocks.

As my earlier discussion showed, this applies only to the accuracy with which the clocks and box [#] can be considered to be pointlike (not being pointlike affects the geometry). And of course the gedanken is limited to accelerations that do not break any of the clocks.

(I'm willing to discuss the geometry of GR; I'm not interested in construction details of clocks.)

Tom Roberts

15 The behaviour of a clock in a linear accelerator versus a centrifuge

The clocks used in the book SpaceTime Physics are not pointlike and the reason that tick is also because they are not pointlike. The reason that they behave differently is because the mirrors can be parallel or pendicular to the direction of motion. My simulation assumes the same.

>	As my earlier discussion showed, this applies only to the accuracy with which the clocks and box [#] can be considered to be pointlike (not being pointlike affects the geometry). And of course the gedanken is limited to accelerations that do not break any of the clocks.

How can I understand a thought experiment when in reality a clock has 3 dimensions and in the thought experiment not. (only 1)

>	[#] The box must be pointlike, or clocks higher in the acceleration's equivalent "gravitational field" will not remain in sync with clocks that are lower. This is also geometry.

That clocks don't remain in sync is also because they can behave differently even when gravity is not considered.

>	Note that arguments about "nothing being truly pointlike" are valid MATHEMATICALLY, but in physics such approximations are used all the time, when the error involved is smaller than the measurement resolution.

IMO it only makes sense to assume that a clock is pointlike when you consider the time of a pointlike object in space. My simulations of the movement of the planet mercury (using Newton's law) assume the same time at each iteration for all the planets considered. The position of the clock, in theory, is considered fixed.

16 The behaviour of a clock in a linear accelerator versus a centrifuge