Is the traditional explanation of why moving clocks run slow correct?

Question

Like most people I struggle to get my head round special relativity. I read a superficially-plausible explanation for why a moving clock runs slow from the point of view of an observer in a rest frame - this is the light clock that bounces light perpendicularly to the direction of travel between two mirrors: because the mirrors are moving, from the point of view of the rest frame, but not the moving frame, the light path is longer and each 'tick' takes longer. But what happens if the light is bouncing parallel to the direction of travel? If the mirrors were sufficiently far apart to measure it, would the rest-frame observer see alternating long ticks and short ticks? Surely not, but what am I missing??

Answer 1

If there was a difference in the transverse and longitudinal light-clock, then large Michelson interferometer would be able to detect the direction of the Earth's motion.

They can't. Just ask the LIGO guys.

So why do all the explanation use the transverse version? Because it is easy, and it doesn't require that you already know about length contraction.

The use of a light clock, in particular, is attractive because it couples directly to the speed of light postulate: the distance traveled and the (invariant) speed of light fix the time it took

There are other ways to introduce the subject which avoid exhibiting that particular construct. Tatsu Tacheuchi's little book is a brilliant example.

Answer 2

Time dilation is widely misconceived and many of the explanations of it are simply misguided.

The common misconception is that clocks slow down in some absolute sense when they move- they do no such thing.

Time dilation in SR arises because the temporal distance between a pair of events is frame dependent. Suppose in one frame two events occur ten seconds apart- in another frame the time between the same two events might be eleven seconds, while in a third frame the time might be twenty seconds. Clocks noting the times of the events in the first frame will tick off ten seconds, while identical clocks in the other two frames will tick off eleven and twenty seconds respectively- it is not that the clocks are running at different speeds to each other, but simply that they are measuring different durations between the same pair of events.

There is a very simple everyday analogy you might consider. Suppose you walk 100 metres along a street and then back again, each of your paces being a metre long. If you have a smart watch with a pedometer it will tell you that you have walked 200 metres. Now imagine your walk in the frame of a train passing along a track at right angles to your street. In that frame, your walk consists of two angled paths, and the distance you have covered is greater than 200 metres. In that frame each of your paces is more than a metre long, and your pedometer in your smart watch will seem to be ticking slow. If a helicopter is following the railway track at a faster speed than the train, each of your paces will be even longer in that frame- and your pedometer will seem to be ticking off the distance even more slowly.

More generally, the length of your pace will vary as a function of the speed of the frame of reference in which it is measured- if the reference frame is moving at right angles to the street, the 'dilation' of each of your paces and the extent to which your pedometer seems to be running slow, can be calculated using Pythagoras' theorem, just as you would calculate the 'dilation' of time in an SR thought experiment about a light clock.

In each of the three frames we have considered, namely your frame and those of the train and the helicopter, you have walked a different distance using the same number of paces, and your pedometer has shown the distance to be 100m. It is not because your pedometer is somehow running slow, or that you have made an effort to stretch the length of your paces- it simply reflects the fact that the distance between two events is frame dependent.

In SR, the temporal distance between two events is frame dependent owing to the relativity of simultaneity. Two frame moving relative to each other have tilted planes of constant time. If I am moving at a fixed speed through your frame, a plane of constant time for me is a sloping slice through time in your frame, the slope rising up through time in my direction of travel. So if it is now 6pm everywhere in my frame of reference, and 6pm where I am in your frame of reference, everywhere else in your frame of reference my 6pm equates to a different time- namely to progressively later times ahead of me and progressively earlier times behind me. Two events that are simultaneous for me happen at two different times in your frame. Clocks in my frame will show 0s have elapsed between the two events, while clocks in your frame will show that some longer interval has passed.

More generally, the time between any two events I can be present at in my frame will be shorter than the time between them in your frame, because our respective baselines of zero time are tilted, so in your frame an event I am travelling to is always later in your frame than it is in mine. Time dilation follows, not because my clock is ticking slow but because it has a shorter duration of time to tick-off.