In fact, there is no “visible” boundary between physical and mathematical time. Moreover, there is no generally accepted term “physical time” and “mathematical time”. But there is some contradiction here and it is quite scientific. Let’s talk about it.
Let’s first put things in order in the terminology we will be using.Mathematical time , although it is not actually called that, implies a cesium clock.Cesium clocks are the most accurate clocks in the world, but they don’t measure time like a regular clock with gears and hands. They rely on a fundamental property of cesium-133 atoms to tell how much time has passed.
Imagine a pendulum. To get it to swing, it needs a push. The cesium atoms inside the clock also have their own “pendulum” – electrons spinning around the nucleus. These electrons can only be at certain, strictly defined energy levels.
Cesium clocks do not measure time, but use cesium atoms as a highly accurate standard – a “tuning fork” tuned by nature itself. The accuracy of cesium clocks is such that they can lose or gain just one second in millions of years.
The principle, in short, is obvious – the cesium atom is excited, and the time of transition of electrons to the standard is always the same. We measure the number of transitions, and when it reaches the control number, one second passes. There is nothing magical about this. In fact, this is the exact mathematical time.
We defined the second as a unit of time. The ancients said that a year had passed when the Earth (the Sun in the sky) returned to where it was when the count began. For them, that was their unit of time. Native Americans lived by the full moon. Time is very slow for hummingbirds. They could see a bullet fly by.
And then Einstein appeared. In fact, the question of the relativity of anything, and especially time, had been raised long before him, but it was Einstein who worked out the logic of relativity in detail. As a result, it turned out that there is still some physical time.
Such a term does not exist in the literal sense, but all conversations about the relativity of time and its real essence can be attributed to this understanding of the question. What is time from a physical point of view? Is it a measurement or just a metric? Does time have its own matter? Questions of this kind border rather on a philosophical understanding of the problem and intersect here with physics.
Real physical time is subjective for every living being. Time can go very quickly for an elderly person or very slowly for someone stuck in an elevator between floors. This perception is described by the specifics of the work of human consciousness. There have even been studies on this subject and it has been established that if a person takes the metro to work every day for 10 years on the same route, then the consciousness perceives it as “fast”, and if he takes it for the first time, then it will seem like an eternity has passed. This is why children, who are constantly learning about the world, see that time drags on for a long time, and older people already perceive it as a moment. They have already done standard actions many times in their lives and it is simple for them.
Added to this are purely physical aspects related to Lorentz transformations and different reference systems. It probably won’t be news that time seems to freeze at the event horizon of a black hole, and an observer from this point will see the world flying past at breakneck speeds. The influence of gravity and the distortion of space-time, which Einstein so carefully described, are to blame.
This might lead one to believe that different observers experience different times. But no. These are identical indicators, linked by relativity . Within their own system, both a space shuttle astronaut traveling faster than light and a railcar driver perceive time in the same way. Artifacts occur when these systems overlap and move relative to each other.
It turns out that there is one obstacle for physical time – the effects of relativity. At the same time, they do not affect time directly and no change in the “matter of time” occurs. The conclusion suggests itself. Even what we understand by physical time, capable of transforming in an interesting way, in fact does not transform into anything. All this is subjective perception and the work of the theory of relativity (where this issue is even more complex and implies the play of space-time).
This means that even if we admit that there is such a thing as “mathematical time” and “physical time”, they will not differ from each other. It is one entity, it is just that in one case we are talking about a calculated value that is compared with the course of the process, and in the other case we are considering the course of the process itself in relation to reality. This does not create two different times.
