Interpreting the observations from a moving clock in special relativity

Question

Consider a clock in motion and another at rest with respect to us, both frames are inertial. The moving clock will measure the time differently than ours, let's say for every 2 seconds that we measure only 1 second is gone in the moving clock. Now, when we see that the moving clock shows 1 second what do we infer from this observation? Do we say that the mechanism of clock is somehow affected by motion and thus it's showing 1 second when in reality 2 seconds have passed, that is all physical processes happen at the same rate in both frames? But since the ticking of a clock itself is a physical process this contradicts our claim. Thus the other option is to say that time does slow down in a moving frame and all the physical processes too.

From another point of view we can define a time interval as the duration between two ticks, then it becomes clear that time must slow down in a moving frame, and since this is a physical process all other physical processes must slow down as well.

The essential difference between these two views is that for the first one we are saying that when clocks aren't in motion then the numbers they show are always equal at each instant, whereas in the second one we are defining what the differences between these numbers mean.

From above paragraph it seems as if the first procedure is more general than the second one since it doesn't explicitly mention the way by which we are measuring time but since we use the word "instant" to explain it, it loses its generality.

So is this view correct?

Answer 1

It's a mistake to think of time as something that flows or "slows down". It's better to think of it geometrically, as a dimension, one of the 4 of spacetime, and to think of objects as moving through spacetime.

In this view the "time axis", or direction of spacetime motion, of the moving clock is tilted relative to the time axis of the stationary clock -- in other words the moving clock goes through both space and time, whereas the stationary clock goes only through time. In this picture it's perfectly understandable to see why the clocks disagree, just as rulers that are placed at an angle to each other both measure the other as being "short" along their axis.

Answer 2

You misunderstand time dilation. It doesn't mean that clocks tick more slowly in a moving frame. Suppose you are sitting at rest and two people pass you in turn, each carrying a clock synchronised in their frame. If you compare the elapsed time on your watch with the times shown on the clocks, you will find that your watch has recorded a shorter time between the two encounters than the readings on the clocks would suggest. It is your watch that seems to be running slow, even though you are at rest, and the moving clocks seem to be running faster, not slower.

That is because time-dilation is actually a synchronisation effect. All good clocks tick at the same rate, measuring a second every second. However, the geometry of spacetime means that the actual time between two events is frame dependent. Specifically, the time dilation formula applies where you have two events that occur at the same place in one frame and at two different places in another- in that case, the time between the events is always shorter in the frame where they occur in the same place, and good clocks will accurately record that to be the case.

To return to the example where you are sitting in your chair and two people pass you in turn at high speed. Suppose the time between the two encounters recorded by your watch is 4s while the time suggested by the moving clocks is 5s, then that is because the actual time between the two events is 4s in one frame and 5s in the other. It is not because your watch has been impaired in some way so that it under-reports time.

Answer 3

Different inertial frames of reference are different views of the same reality. We are used to this in classical physics. But relativity violates our classically trained intuition and takes some getting used to.

Alice sits beside a road, occupying a certain position now. Later she is in the same position. She watches Bod drive drive by. Bob occupies Alice's position now, but a different position later. What Alice sees as one position at different times, Bob sees as a series of different positions at different times. We are not confused by this.

This is the kind of difference you get from relativity. Except that you have an incorrect classical understanding of what time is. You see the universe as a $3$D block that changes state as time flows. The present is all that exists. The past is over and gone. The future hasn't happened yet. An instant of time identifies the state of the entire universe at that instant. Every place in the universe is experiences the same instant together. This is called Presentism. All very straight forward, but this isn't the way the universe works.

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Alice sits by the side of the railroad track. She has clocks spaced out along the tracks at regular intervals. All are synchronized. If you turn on a light halfway between any two clocks, they will record the same time when the light arrives at their location.

Bob rides by in a train at relativistic speed. He has the same kind of clock arrangement spread out in different cars. He has been in communication with Alice. He has spaced his clocks so that Alice agrees they have the same spacing as her own clocks. When the Bob passes Alice, each of Bob's clocks will be at the same position on one of Alice's clocks.

Bob has synchronized all of his clocks to his own satisfaction. If a light is turned on halfway between any two of his clocks, both will report the same time when the light arrives.

Furthermore, Alice and Bob have arranged it so that when Bob passes Alice, their wristwatches agree.

As each pair of clocks pass each other, each records its own time.

Our classical intuition tells us that all the clocks must record the same time.

• Alice has synchronize her clocks and arranged Bobs clocks to have the same spacing as her own. She expects all the clock pairs to pass each other at the same instant. And she is right. All of her clocks record the same time.
• As each pair of clocks pass, they are certainly in the same place at the same time. Therefore, if Bob's clocks are correct, surely each must report the same time as Alice's clock.

But Bob's clocks disagree with this. Bob still says they are synchronized, but they record different times of passing Alice's clocks. Clocks at the front of the train record an earlier time than clocks at the tail.

Alice and Bob both agree that these are the numbers that were recorded, all clocks and trigger mechanisms are in good working order, all spacings are as they were intended to be, and the train is moving as expected. This is not an experimental error.

What Alice says is one time in different places, Bob says is a series of different times in different places. Time is working something like how space works.

This is impossible to understand with time from Presentism. Time must work differently than we always thought it did. Understanding this and getting used to a different idea of time is the biggest conceptual hurdle in special relativity.

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The standard way of reimagining time is the Block Universe.

The road before us and behind us continues to exist, even though those points are out of reach at the moment.

In the same way, the past and future exist even though those times are out of reach from here.

In this view, time does not flow. The past, present, and future simply exist. Time and space form a $4$D block, as in a space-time diagram. The present is a $3$D slice of space-time.

Different people can have a present that slices in a different angle. This means that Alice's present can use parts of Bob's past and future.

This correctly gives all the right answers, but it isn't very intuitively satisfying. It clashes to much with the appearance that an instant doesn't happen until its appointed time, and then it is immediately over and gone.

It can help to think of us as a reel of film in a movie. Each frame experiences its moment of play, but the whole film is permanent.

This leaves a question. Why does time appear to flow always forward? People have ideas, but this question is still debated. We don't really know.

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Another way to reimagine time is that it does flow. Every world line progresses forward. But there is no universal way of matching up times for different world lines.

This does less violence to the everyday understanding of time. At least it flows normally for me. My past is gone and my future hasn't happened yet.

But you still have to let go of the idea that the entire universe is happening right now the way I match up world lines.

Again, this does not explain why time flows. It just does. We had the same question in classical physics. We are no better off now.

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The difference between these two ways of thinking about time is purely philosophical. They correctly describe the same experimental results. They use the same space time diagrams.

Use whichever you prefer.

For more on the Block Universe, see What is time, does it flow, and if so what defines its direction?