# The mystery of the arrow of time

2013/9/28
Published 2004/12/26

Do you know a problem of the arrow of time? Time has one problem that has been troubling for physicists. I would like to explain this problem this time.

## Daily arrow of time

This world is full of irreversible phenomena when we look around our surroundings.

For example, I would like to consider the phenomenon that a glass cup with water falling from a table. It is a natural phenomenon that the glass cup breaks and is scattered and the water spills. On the other hand, it is a strange phenomenon that all pieces of the broken glass cup stick together. In the phenomenon, a glass cup is generated, and the spilled water converges into the glass cup.

It is very natural that the time of the future direction and the time of the past direction are different definitely in this way. However, this way of thinking becomes different when we think physically.

## Physical arrow of time

Surprisingly the time of the past direction and the time of the future direction make no difference when I think about time physically.

For example, I would like to think about the state that two balls collide. Two balls come close to each other, collide and go away. We photograph this phenomenon on a video. If you play it backwards, it does not contravene a physical law. All physical theories are symmetric about time.

A time symmetric minute gap exists in the collapse phenomenon of the elementary particle called the K meson. However, it does not generate the difference of the direction in the past and future time we watch routinely.

## Thermodynamic arrow of time

Thermodynamic has the second law of thermodynamics. The law states that the quantity of the entropy indicating the degree of the disorder increases towards the future. Some person might think it is a cause of the asymmetry of the past and future. However, this is a rule of thumb and it is not well understood why the entropy increases.

## The world such as the tape of the movie

Why does the time go by only in the future direction? For example, I would like to think that this world is the world such as the tape of the movie. Then one question arises. Why will asymmetry exist in two directions like this? Big Bang exists at the end of one direction, and the other direction continues infinitely.

## Many-worlds interpretation and arrow of time

I think about the relationship between many-worlds interpretation and the arrow of time as follows.

The world belonging to different times is regarded as a kind of multi-world in the many-worlds interpretation. In addition, a world does not have one history like the tape of the movie in the many-worlds interpretation. Various histories open like a spider's web. An index called the time is not assigned to each world. Only differences of each world exist.

For example, I would like to think about the world that the world's clock points at the time t. We think various worlds of the world transition from this world as possible. Though most world's clock points at the time t + 1, some worlds may point at t - 1.

However, we observe the progress of the time in most cases because there are predominantly much worlds that have clocks pointing at the time t+1. This is the explanation of the arrow of time by the many-worlds interpretation. Because the number of the worlds that has big entropy is more than the number of the other worlds that has small entropy, the world that has big entropy easily transits.

However, we may not observe the progress of the time, even if the transition between such worlds occurred when entropy showed the maximum in the future. In other words, I think that the clock does not keep correct time in the world that has the greatest entropy.

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