As you view the motion of this pendulum can you decide whether this video is playing forward in time or in reverse? The problem with the arrow of time is its apparent reversibility. That is to say, if this system is reversible then it can proceed in either the forward or reverse temporal directions without breaking physical law. Lets take a look at another simple system; a planet in orbit.
By reversing this video we would find that at every corresponding position the velocity of the planet would also be reversed (-v) and the acceleration would remain constant. This completely agrees with physical law and in neither clip can we discern whether we pressed play or rewind. Thus, Newton's equation for the force of the gravity (F = GMm/r^2) between these 2 planetary bodies is time reversible and in fact this entire system works just as well in reverse as it does in the forward direction. Actually, all of Newton's laws and equations happen to be time reversible.
Whether or not these simple systems are time reversible, we are still able to maintain our previous perception of time. There are many events in our daily lives that are apparently irreversible. For example, here's a glass breaking.
And here's it breaking in reverse...
Surely this situation is different since glass does not put itself back together in such a manner by the laws of physics. In a complicated system such as this our original perceptions are justified and we find that there must be some difference between the past and the future. It is a seemingly irreversible event. Now consider another complicated system where gas, which is held in a bottle, is released into a room. As time goes by, the gas exits the bottle and evenly distributes itself throughout the room. Again, it is seemingly impossible for this situation to reverse itself and for all the dispersed molecules of gas to gather and enter the bottle once again. However, this event is dictated entirely by Newton's laws, which are time reversible. How can a situation described by time reversible equations produce such apparently irreversible results? One might even argue that perhaps if we were able to obtain data on each molecule of gas, including its position, velocity, and the results of their elastic collisions, that the entire system could be described in time reversible simple states.
To determine the validity of this claim let us consider a third event. You stand at the edge of a pool. The water is completely still. You take your finger and touch the water, creating a series of circular ripples emanating outwards. Laws determining the propagation of waves are time reversible and therefore, at a fundamental level this event should be completely reversible. This means it is possible to design boundary conditions at the edges of the pool such that you create waves emanating inward to a single point. Additionally, at the moment those waves converged it would be necessary for your finger to come into contact with the water to absorb the momentum. For all practical purposes, this is impossible. Therefore, in principle these three events are not irreversible. Rather, the chances that the reverse of these situations may occur(in reality) by accident or design are extremely low. Why is this?
The thing is...ALL the fundamental laws of Physics are time reversible. This includes Newton's laws, the laws of electromagnetism, and even the wave equation of quantum mechanics. How can we reconcile this fact with our macroscopic observations and interpretations of time and reality? Why does the process of time and the processes of the universe appear so irreversible? I will attempt to answer this question in my next post...
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