Time is defined operationally to be that which is measured by clocks

Question

A light clock is a mechanism that produces (and counts) equal time intervals.

Yes, but, do we understand correctly what the light clock is showing?

Since we don't know what the time exactly is, we can say that time is represented by a series of events (this event is not a point in Minkowski space-time). For example, this event can be a transition of photons from one point of space to the next as well as a mirror reflection.

In case in which we look at the time as a series of events, there must be an elementary event through which we can describe any complex event. So we can say that elementary event must be a permutation of points (switching places of two points) in space-time continuum.

So, instead of counting time intervals, we can say that a clock measures or counts permutations of points. Since it takes some time for two neighboring points to switch places, the clock simultaneously counts equal time intervals.

The definition of time remains correct.

Said permutation of points is also not time, but in a space-time continuum there is a posibility of movement that does not exist in Euclid's flat space.

Then we can say:

Time: Time is a posibility of permutation for points of space in space-time continuum.

Flow of time: Every new time period is represented by a new permutation.

Arrow of time: Since the reverse permutation is a new permutation, time moves in one direction only.

Is this view correct? Or does it violate any known rule in physics?

Answer 1

You need to be clear about what you mean by time, and in particular the difference between time and the flow of time. I go into this in What is time, does it flow, and if so what defines its direction? and that is really essential pre-reading for this question.

Any object traces out a world line in spacetime, which is just the set of all points that the object passes through. The length of the world line is given by the metric. That is suppose the position along the world line changes by distances in space $dx$, $dy$ and $dz$ and a difference in time $dt$ then the total distance moved along the world line is (assuming flat spacetime):

$$ c^2d\tau^2 = c^2dt^2 - dx^2 - dy^2 - dz^2 \tag{1} $$

where $c$ is the speed of light and $\tau$ is called the proper time. Equation (1) is a very important equation in special relativity and is called the Minkowski metric.

To understand the significance of the proper time suppose we are using the rest frame of the observer. In this frame the observer is not moving in the $x$, $y$ or $z$ directions because by definition in the rest frame the position in space is constant. That means $dx=dy=dz=0$ and only $dt$ is non-zero. Equation (1) simplifies to:

$$ c^2d\tau^2 = c^2dt^2 $$

or:

$$ d\tau = dt $$

So in the observer's rest frame the proper time is just the time measured on the observer's clock. That is, the observer's clock measures the distance travelled along the observer's world line. The flow of time just corresponds to motion along the world line.

So what about these light clocks? Well light has the property that its proper time is always zero i.e. $d\tau = 0$. If we go back to equation (1) and plug this in we get:

$$ 0 = c^2dt^2 - dx^2 - dy^2 - dz^2 $$

or:

$$ dt = \frac{\sqrt{dx^2 + dy^2 + dz^2}}{c} = \frac{dr}{c} \tag{2} $$

where I'm using $r$ for the total distance travelled in space, which using Pythagoras' theorem is simply:

$$ dr^2 = dx^2 + dy^2 + dz^2 $$

Equation (2) shouldn't be any great surprise, because it's just telling us that time is velocity divided by distance. It's importance is that it gives the coordinate time $dt$ in terms of a distance, and since we've already decided that proper time and coordinate time time are the same in our rest frame that means we can measure our motion along our world line by measuring how far light travels. That is, if we measure light to travel a distance $dr$ then we know we have moved a distance $cd\tau$ along our world line.

And this is why a light beam acts as a clock. Its motion in space tells us our motion in time.

Light clocks typically bounce the light beam between mirrors simply because that's a convenient way to do the the measurement. If the mirror spacing is $\Delta r$ then after each bounce we've moved a distance $c\Delta\tau = \Delta r$ along the world line. But there is no special significance to the bouncing. A light beam that just headed off to infinity would measure our time in the same way.

Answer 2

I think the term spacetime is just a source for confusion. It should be space movement, if anything. Any measurement of time, including your light clock example, takes a predictable repetitive movement pattern and uses it to measure other movements. So no, time does not exist. There is only movement. We can measure movement, and call the unit of measurement time, but that does not mean that time itself exists. Matter does, and movement does.

And I think that means thinking of time as a series of events is not really helpful. Maybe your observation of movement may not be continuous, but the underlying movement absolutely is.