Photon Clock & Time Dilation: Rotating the Clock 90 Degrees

[peterspencers]

In the case where you have a photonic clock bouncing a photon between 2 mirrors, if the mirrors are alligned on the vertical axis, bouncing the photon up and down and the overall clock traveling along the horizontal axis, then the whole thing makes sense to me. However, if you were to rotate the clock 90 degrees, so that the mirrors are alligned on the horizontal axis, in line with the direction of travel of the overall clock, then surely as the photon bounces back, the motion of the overall clock would effectively counter the distance it needs to travel to complete one cycle (increment of time) and negate the effects of time dilation?

 

[Dale]

It doesn't negate it, but the effect you mention is one way to derive length contraction.

 

[Bill_K]

peterspencers, We often have posters here who describe rather complex situations in relativity and then say, "I want to understand this intuitively." Well, ofttimes intuition is not sufficient, and it's not just because relativity is a hard subject. Even simple situations become clear only when we pick up a pencil and do some arithmetic.

The question you ask is a good example of this, where intuitively it seems that the time difference encountered on the forward trip will exactly cancel the difference on the trip back. But a little high school algebra will show you this is not the case. if the distance I measure between the moving mirrors is L, then the time to go forward is L/(c-v) while the time to come back is L/(c+v). The sum of these is 2Lc/(c²-v²) -- they don't cancel.

 

[bcrowell]

The transeverse (up-down) photonic clock is one type of clock. The longitudinal (forward-backward) photonic clock is another type of clock.

It's perfectly reasonable to imagine that clocks would be affected by motion, and that different types of clocks would be affected differently. For example, a pendulum clock will be affected if you take it on a sailing ship across the Pacific. So will a mechanical spring clock, and the effects on the two clocks will be unequal.

However, we think that all inertial frames of reference are equally valid, so we only expect such effects due to accelerations, not inertial motion. Both the transverse light clock and the longitudinal one are moving inertially, so we expect them to agree. (A person aboard the spaceship also sees the spaceship as being at rest, so in this frame there is no meaningful distinction between the longitudinal and transverse directions.)

If SR is to be interpreted as describing spacetime itself, and time dilation as an effect on time itself, then it's necessary for *all* clocks to agree (once we eliminate trivial reasons like random error and accelerations that jar their mechanisms).

All of these considerations are independent of the details of the two clocks, but there's also a simple way to see that the two light clocks must give consistent results, without doing any algebra. In the spaceship's rest frame, let's say that two rays of light are emitted at the same time in perpendicular directions, from the same location. That is, the two clocks are synced, and they also touch at one end. The emission of the two rays is event A. If the two clocks have equal lengths, then the rays are clearly received again after one trip at exactly the same time and place, at event B. Applying a Lorentz transformation can change the time from A to B, but it can't change the fact that the times taken by the rays are equal to one another.

 

[peterspencers]

Ahh ok, thanks:)

so if the 2 different clocks give different amounts of time dilation for the same velocity then what do we use when calculating the effects of time dilation on the ageing of a human on a long high speed space voyage, or say the half life of matter?

 

[Austin0]

Ahh ok, thanks:)

so if the 2 different clocks give different amounts of time dilation for the same velocity then what do we use when calculating the effects of time dilation on the ageing of a human on a long high speed space voyage, or say the half life of matter?

No, both the up and down and the longitudenal versions of the light clock tell the same time.

The L (going up)/c + L (going down)/c= L (going forward)/c +L (going backwards)/c for any possible relative velocity.

 

[bcrowell]

so if the 2 different clocks give different amounts of time dilation for the same velocity then what do we use when calculating the effects of time dilation on the ageing of a human on a long high speed space voyage, or say the half life of matter?

Experiments show that two different clocks don't give different amounts of time dilation. (The biological effects are too small to measure presently, but the effect on radioactive half-lives has been accurately verified.) If a hypothetical future experiment did show some such discrepancy, then special relativity would be invalidated and we'd have to find a new theory.

 

[phyti]

The poster (#1) wanted to know how the light clock explains time dilation.
All he got was 'the theory requires it'.

 

[Dale]

I didn't get that from reading the OP. He already seemed to understand how it explains time dilation in the perpendicular orientation, and simply had a misconception about the parallel orientation.

 

[phyti]

I didn't get that from reading the OP. He already seemed to understand how it explains time dilation in the perpendicular orientation, and simply had a misconception about the parallel orientation.

He still doesn't grasp it in post 5.
You mentioned length contraction in post 2, but not its cause and how it corrects the x clock so as to agree with the y clock. It's another case of 'Euclid said so' for the poster.

 

[Dale]

You mentioned length contraction in post 2, but not its cause and how it corrects the x clock so as to agree with the y clock.

Fair enough.

peterspencers, let's consider a slight variation on the usual light clock. In its rest frame, this one has two equal-length arms perpendicular to each other, the clock starts one "tick" by a single flash of light which goes down both arms, is reflected from mirrors at the end of both arms, and returns to a detector which is calibrated to end the "tick" only if it receives both flashes (reception is at the same place and same time so relativity of simultaneity is not an issue).

In its rest frame this clock ticks off time as any other clock.

In the frame where the clock is moving parallel to one of the arms, I assume that you already understand how the perpendicular arm becomes time dilated. Therefore, the parallel arm must also be time dilated by the same amount, otherwise the clock would tick in one frame and not in the other (voilating the principle of relativity).

Since we know the speed of the clock, the speed of light, and the duration of the forward and back reflection, we can calculate the length of the parallel arm (the algebra is left as an exercise to the interested reader). That length is shorter than the length in the clock's rest frame, which is known as length contraction.

 

[Janus]

Here's an animation to go with DaleSpam's explanation:

We compare a "stationary" Light clock to one in "motion". The expanding circles demonstrate how the pulses for each clock travel at the same speed in the frame of the animation.

 

[phyti]

Hoping posts 11 & 12 improve peterspencers understanding.

Dale said

we can calculate the length of the parallel arm

How does that change the length of the parallel arm in the clocks frame where it's needed?

 

[Dale]

How does that change the length of the parallel arm in the clocks frame where it's needed?

It doesn't. That is the length of the parallel arm in the "moving" frame.

 

[phyti]

It doesn't. That is the length of the parallel arm in the "moving" frame.

Back up to the MM experiment. The arms/paths are equal. Using only constant c and an arbitrary speed v, i.e. rules of physics, the calculated times are different. The explanation is length contraction in the lab frame. How does the x arm become shorter? It's not accomplished via a calculation, and especially by a remote observer!

 

[Dale]

Back up to the MM experiment. The arms/paths are equal.

In the interferometer's rest frame, yes.

Using only constant c and an arbitrary speed v, i.e. rules of physics, the calculated times are different.

Only if you incorrectly assume that the length in the moving frame is the same as the length in the rest frame.

The explanation is length contraction in the lab frame. How does the x arm become shorter? It's not accomplished via a calculation, and especially by a remote observer!

The x arm, like all material bodies, is held together internally by EM fields which obey Maxwell's equations (or rather QED). It isn't the calculation which holds them together, it is the fields. We can calculate how those fields behave, and the fields behave by length contracting (among other things).

Btw, phyti, this is a fairly common complaint, and I never really understand it. Why is there this apparent assumption that if scientists can describe something mathematically that they must believe that it is the mathematical calculation that causes the thing described? Perhaps you can explain to me where that thought process comes from, because I just don't get it, and yet I see it voiced disturbingly often.

 

[schaefera]

Even more simply, though, think of this:

We know that two events happening at the same time AND place in one frame happen that way in all frame. So wherever you have a clock different from a light clock, just imagine placing a light clock at the same place with that other clock, and synchronize the two of them. The light clock we know works for time dilation, so the other clock must also since they are in the same time and place.

We can do this for any clock (theoretically, at least), so we should be sure time dilation works for all them.

 

[phyti]

In the interferometer's rest frame, yes.

Btw, phyti, this is a fairly common complaint, and I never really understand it. Why is there this apparent assumption that if scientists can describe something mathematically that they must believe that it is the mathematical calculation that causes the thing described? Perhaps you can explain to me where that thought process comes from, because I just don't get it, and yet I see it voiced disturbingly often.

In the few years of visiting forums and reading posts, reading papers and books on SR, I have never seen a graphical or math derivation of a physical length contraction. It's always stated as if a postulate, i.e. Euclid/Einstein/Homer... says so. The object moves and it contracts, or the Anaut blasts off and space contracts, i.e. it just happens. The inquisitive mind will next ask,"how/why".
Every step has to be supported by known effects, otherwise you can't lead them from the initial condition to the end result. In the current topic you will typically get: if the Anaut's ship contracts as a result of his initiating his motion, "why should the remainder of the universe contract without any (apparent) cause?". I've shared the frustration of the poster who leaves with little or no more understanding than when he entered. I viewed length contraction as the effect of motion on the measuring process. Now with a demonstrable (em) explanation for a physical length contraction, there are two modes.

The inquiring mind is looking for explanations in terms of things they understand, not abstract descriptions of conceptual things. They are not so naive that they would believe the calculation did it. It's more likely skeptiscism if you can't demonstrate a physical cause, i.e. what do the calculations represent.
If a person wants a ride in a plane, it doesn't mean they want to be a pilot. If a poster wants to understand time dilation, it doen't mean they want to be a physicist. If you've studied the history of science then you're aware that many of the 'scientists' were doctors, lawyers, clergyman, etc. Logical thinking or reasoning isn't exclusive to science.

 

[Dale]

The basic physical explanation is the Lorentz invariance of Maxwells equations (and QED). If you accept Maxwells equations as a correct description of EM and accept EM as the basic force in holding "stuff" together then length contraction follows easily.

The wikipedia page does both a math and a graphical derivation from the Lorentz transform:
http://en.m.wikipedia.org/wiki/Length_contraction