The key to UNDERSTANDING (at least for me) is the ability to "picture" the information, almost as if you had a physical model you could "touch and feel".

In my talk, I discussed several techniques, including animation, "blick" graphics, and others, and used them to illustrate:

- Einstein's Relativity (based on his 2005 theories of "Special Relativity" and 2015 "General Relativity"),
- A "Nash Bargain" (if you saw the 2001 hit movie "A Beautiful Mind", you know that John Nash earned the 1994 Pulitzer prize in Economics in despite having paranoid schizophrenia),
- Bayesian "Inverse Probability" (based on the work of Rev. Thomas Bayes, published in 1763), and
- Global Warming (Real but not a big Deal).

**EINSTEIN'S RELATIVITY**

How to UNDERSTAND the relativistic effects of Kinetic Energy (Special Relativity) and Gravitational Potential Energy (General Relativity)?

One of the relativistic effects is "Time Dilation". Clocks (of all kinds, including biological clocks) slow down when they are at high levels of either Kinetic or Gravitational Potential Energy.

**Yes, I said it was CLOCKS that slow down (not TIME), and "Kinetic Energy" and (not "Speed"), and "Gravitational Potential Energy (not "Gravity") that cause these relativistic effects. Some readers may think it is TIME that slows down and that it is Relative Speed and Gravity/Acceleration that cause it, but I plan to motivate you otherwise!**

Please refer to the above graphic

The image above is a screen capture from an animated "thought experiment" involving four identical, extraordinarily accurate clocks and an idealized Earth that has a conveniently-located, friction-free Tunnel, cut through the Center, from the left Surface to the right Surface.

Initially, all clocks are "at rest". The RED and BLUE clocks are at the left edge of the image, very far from the gravitational attraction of the Earth. The GREEN clock is fixed in position at the Earth Surface, and the GREY clock is fixed at the Center.

OK, let us set the BLUE and RED clocks to zero. Keep the BLUE clock fixed in place and release the RED clock.

Release the RED clock

The RED clock slowly "falls" towards the Earth, accelerating as it gets closer. As the RED clock enters the left end of the Tunnel and passes the GREEN clock at the Surface, each clock makes a record of its reading and that of the other. As the RED clock passes the GREY clock at the Center, they each record both readings. The RED clock continues out the right end of the tunnel, decelerates as it gets further from the Earth, momentarily stops moving very far from the Earth, and then "falls" back to the Earth.

Compare Intervals recorded by each clock

As the RED clock it passes the GREY and GREEN clocks, and as it stops momentarily next to the BLUE clock they exchange readings and figure out the interval between their first encounter and this one. According to Einstein, the RED clock will measure a shorter interval than the GREY clock, the GREEN clock, and the BLUE clock.

This difference may be expressed as picoseconds per second (picosec/sec), that is how many trillionths of a second less the interval indicated on the RED clock, divided by the time interval, is less than the interval measured by the other clocks.

Using the BLUE clock as a reference, the table in the image above indicates that the GREEN clock, at the Earth Surface, will measure a Time Dilation" of 696 picosec/sec, and the GREY clock, at the Surface, will measure 1044 picosec/sec. (These values agree with data found on Wikipedia and other sources.)

*So, is it Gravity or Gravitational Potential Energy that causes Time Dilation?*As the graph above shows, Gravity is about zero at the far left, when the RED and BLUE clocks are far from the gravitational attraction of the Earth. Gravity increases to a maximum (negative) value of 32 feet per second squared (32 ft/s2) at the Surface, and then DECREASES to zero at the Center. Gravity is considered negative because it points to the center of the Earth.

Gravitational Potential Energy (also considered negative) is about zero at the far left, continually increases in (negative) magnitude as the RED clock passes the Surface, and continues to increase in magnitude, reaching a maximum (negative) magnitude at the Center (unlike Gravity which decreases in magnitude to zero at the Center).

In mathematical terms, Gravitational Potential Energy increases "monotonically" from the far left to the Center, while Gravity increases and then decreases, so it is "non-monotonic" between these points.

**Well, Time Dilation is about zero at the far left, and MONOTONICALLY increases in magnitude from the far left to the Center. Therefore, Time Dilation is more like Gravitational Potential Energy than it is like Gravity. So, it is not Gravity, per se, that causes Time Dilation but it is Gravitational Potential Energy.**

The graph indicates that the speed of the RED clock is about zero at the start, increases to 25,000 mph at the Surface, and then to 31,000 mph at the Center. (These values agree with data found on Wikipedia and other sources.)

**Kinetic Energy increases and decreases more like Time Dilation than does Speed. (Kinetic Energy varies as the square of the Speed as does Time Dilation). So, it is not Speed, per se, that causes Time Dilation but it is Kinetic Energy.**

(NOTE: This topic is not complete, I intend to add more material)

*Ira Glickstein*

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