Galileo's Synchronization and Its Implication in Quantum Physics
There are many well-known museums in Florence, and there are also some
unknown places. One of those neglected museums is the History of Science
Museum. In this museum, there are many scientific instruments which Galileo
used to formulate his physical ideas. Of course, one of the most important
items is his inclined plane.
After seeing it, I realized how I used to be stupid when I was teaching physics. When I drew inclined planes to illustrate gravitational acceleration in the past, I never included Galileo's clock attached to the plane. You will note that the inclined plane without the clock looks very dumb. Without the time dimension, physics is meaningless. Let us see the the two inclined planes (one with and one without) into one webpage.
The time variable is also important in quantum mechanics. Yet, we do not worry too much about this variable because we seldom deal with the time-dependent Schroedinger equation. Furthermore, there are no quantum excitations along the time-like direction.
There is another point. You are often asked how old you are, and when you were born. Are they the same question? No. One year later, you will be one more year old, but the birthday remains invariant. As the time progresses, your age increases. This is a progressive time. Your birthday specifies the time interval between the birthday of Jesus and your birthday. This interval does not change.
The Bohr radius is an important spatial distance in quantum mechanics. It measures the distance between the proton and electron in the hydrogen atom. According to Einstein, there must also be a time-like separation, but we do not talk about this variable in quantum mechanics. The time-separation variable does not exist according to the Copenhagen school of quantum mechanics.
Then, is the present form of quantum mechanics wrong. Not necessarily because there is a mechanism which allows us to bury this variable. In his book on statistical mechanics, Feynman introduces the concept of Rest of the Universe. Feynman states that the universe can be divided into two parts, namely the world in which we make observations, and the rest of the universe which does not tell us anything. We can hide this time-separation variable in Feynman's rest of the universe.
Then is the time-variable completely buried in the rest of the universe? The answer is clearly No, according to Einstein. The Bohr-radius is a clearly defined quantity in quantum mechanics. It specifies a spatial separation between the particles. If we look at this from a moving frame, the Bohr radius picks up its time-like component. If the speed of the frame is close to the light speed, the time separation becomes as prominent as the spacial separation.
So what? Can we reason this quantitatively? You are invited to a recent paper dealing with this problem.