Former Jewish Ghetto in Venice where the mortal sinners used to lend money to earn interests.

# Bankers, Physicists, and their Space-time Approaches

## Time Variable for Bankers

Before Medici's time, it was a mortal sin to charge interest on borrowed money. These days, those who control the interest rate rates are among the most powerful people in the world. How did this happen?

 Federal Reserve Building in Washington, and Einstein Monument one block away.

Italians spoke and still speak the same language, but Italy used to be a collection of kingdoms with different currencies. If a Italian man went to Venice with 100 Florentine Euros, he could get 200 Venetian Euros if the exchange rate if one-to-two. If he comes back to Florence after the exhange rate became one-to one, his money became 200 Florentine Euros. This mechanism is illustrated in this figure.

How could he predict the change in the exchange rate? The rate is determined by money-loving politicians. It is a matter of sharing profits with them.

Let us write Karl Marx's formula for surplus values.

G' - G = W ,

where G means money, and W is for manual work. For this person who made one excursion

G' - G = G (times) T,

where T is the time interval in an approtpriate unit.

If this person makes repeated trips, he could end up with the formula

G' - G = G {exp(T) - 1 } .

Then the bankers and politicians realized that one did not have to make trips from one region to another. All they had to do was to fix the interest rate. This is how the rate-fixing people became so powerful.

These days, the interest rate is determined (a matter of chaning it by 0.25 %) by the people in this building, which is known as the Fedreal Reserve Building in Washinton, DC, U.S.A. Some people call it Hatshepsut's Palace.

One block away from this building is a bronze momument of Einstein. Here is a Washinton webpage telling where these places are. They are within a walking distance from the White House.

## Galileo's Time

 Roman engineering did not require the time variable, but Galileo recognized it is essential in understanding physics.
The name of this museum was
changed in 2010 to Museo Galileo.

Time is an essential variable in physics, but physicists did not realize this until Galileo. The reason is very simple. There were no physicists before Galileo.

Of course, Egyptians and Romans produced engineering miracles, but they did not have anything to do with time variable.

In 2004, I visited Florence to study Galileo. I was very happy to learn that he had financial and political supports from the Medici family. In Forence, there was a museum called the Muesum of History of Science, where many of Galilio's instruments were diplayed.

After coming back, I constructed a webpage telling that the City ant the Univ. of Florence should to more to express their respect of Galileo Galileni. When I was there in 2014, I noticed that the Museum name was changed to Museo Galileo. I do not think my 2004 wepage had any influence on the name change, but I said the right thing.

I was inside the museum with a digital camera, but I was not allowed to take photos. There were many telescopes and other precision instruments, but I was most interested in his inclined plane. This is my sketch of the instrument.

The unsusual aspect of this instrument is that a pendulum is attached to the inclined plane. I do not know how accurate this clock was. This is not the point.

The point is that this instrument measures both the space and time variables. With this inclined plane with a pendulum, Galileo brought the time variable into physics.

However, the space and time variables are orthogonal. This remains so even for moving obeservers. We call this this the Galilean system.

## Time variable in the 20th Century

• In 1905, Einstein discovered that space and time varibles become entangled for moving obserbers.

 Einstein's Observation Galilean Lorentzian
 Newtonian Mechanics Yes No
 Maxwell's E & M No Yes
While attempting the harmony between Newtonian mechanics and Maxwell's theory, he had to entangle the time and space variables. He ended up with his E = mc2.

• In 1913, Bohr started talking about the discrete energy levels of the hydrogen atom.

• In 1927, quantum mechanics was formally inaugurated based on the principle of wave-particle duality. The hydrogen atom consists of a standing wave of the electon around the proton.

Einstein and Bohr met occasionally before and after 1927. We can assume that they discussed physics. While Bohr was worring about the shape of the hydrogen atom, Einstein should have worried about how the hydrogen atom appears to moving observers. How the time variable gets entangled with the Bohr radius? I do not know whether they raised this question. In either case, this is a metaphysical question at that time, because the moving hydrogen atom was beyond the scope of their imagination at that time, because the moving hydrogen atom was beyond the scope of their imagination. at that time. It is still impossible to accelerate the hydrogen atom to a relativistic speed. Click here to see how we changed our view toward since then.

• It was Paul A. M. Dirac who realized this problem as early as 1927, and used the Gaussian function to solve this problem in 1945. However, he failed to state that he was using the time-separation variable, not the time variable appearing in the time-sependent Schrödinger equation.

In 1971, Feynman and his students used a Lorentz-invariant oscillator equation to tackle this problem. Yes, they make a distinctin between the Schrödinger time and the time-separation between the constituents. However, they ended up with a non-sense wave function in terms of this time-separation variable.

 Dirac Feynman Dirac Feynman
 Time Separation Undefined Defined
 Wave function localized Yes No
This problem is similar to the problem Einstein had before he came to