The idea of “time dilation” comes from H.A. Lorentz’s 1895 electrodynamics theory as published in his book, “Versuch Einer Theorie Der Elektrischen Und Optischen Erscheinungen In Bewegten Körpern.”

He was talking specifically about “atomic clocks,” i.e. the internal harmonic oscillation rates of atoms. The first mention that I can find of an atomic oscillation rate working as a “clock” is in an 1873 book by Maxwell.

Lorentz’s theory involves “forces” being placed on atoms when they movie through fields. The faster they move through the fields, the slower their oscillation rates become. Einstein later, in 1905, thought that all clocks would act that way and he attributed the clock slow-down just to “relative motion” alone. However, since the two clocks in his 1905 thought experiments are moving only “relatively”, both clocks should slow down at the same rate, therefore they should both have the same reading when they are united and become stationary relative to one another. But in his 1905 examples, only one clock has a reading that lags behind the other when the two unite. This created the famous “clock paradox”.

Later, around 1911, during Einstein’s work on his own electrodynamics theory, which he preferred to call his “relativity” theory, he discovered that atomic clocks would slow down when near the surface of a massive body, and they would speed up when they are a long distance from the massive body.

In a paper published in 1918 Einstein corrected the “relative motion” error of his 1905 paper and he added “forces” and “atomic clocks” to his thought experiments. He changed the reason for the single clock slow-down from “relative motion” to “forces” exerted on the oscillating atoms in the single atomic clock that slowed down, and thus he basically returned to Lorentz’s basic electrodynamics concept of 1895, and Einstein's own 1911 gravitational redshift theory.

So, atomic clocks do slow down when they are near the surface of the earth and they speed up when they are away from the surface, and there is also some evidence that they slow down when they move rapidly around the earth. When they do that, they are moving rapidly through the gravitational field of the earth, and this kind of slow-down was predicted by Lorentz in his 1895 book. In a 1907 paper Einstein credited Lorentz's book for providing the basic information for his own time-dilation ideas, but later he modified those ideas so that they provided real physical reasons and forces for the atomic oscillation rates in the atomic clocks to slow down.

When talking about atomic clocks, both Einstein and Lorentz were talking about the fundamental oscillation rates of basic atoms. For example, in a 1911 paper, Einstein said, “Let Vo be the vibration-number of an elementary light-generator, measured by a delicate clock at the same place.”

The “elementary light-generator” is an atom, and the “vibration-number” is its internal harmonic oscillation rate.

The devices we know today as “atomic clocks” were not invented until the early 1950s, but they use the same basic principle of measuring the oscillation rates of the atoms contained inside their timing mechanism. This is why they are known as hydrogen clocks, cesium clocks, etc. The clocks monitor the internal oscillation rates of these kinds of atoms. There are various environmental conditions, such as motion and elevation above the earth, that affect their internal harmonic oscillation rates.

One reason the “clock paradox” is still debated today is, in my opinion, because not enough people have conducted research about the origin and development of the earliest atomic-clock slowdown electrodynamics theories. A lot of people read only Einstein’s 1905 relativity theory, which has been readily available in a popular Dover book since 1952, but the original Lorentz book has been extremely rare and difficult to find, and the 1918 Einstein paper had not be re-published or translated into English until 2002, when Princeton Press released a copy of it in English. In that paper you can see where Einstein adds "forces" to the clock that slows down and he has that clock existing in a stronger gravitational field than the clock that doesn't slow down. Of course gravitational fields were not considered in the original 1905 paper that led to the clock paradox in the first place. So Einstein did away with the clock paradox by modifying the terms of his 1905 paper and adding "forces" on an atomic clock that results from the clock being in a stronger gravitational field than the clock that doesn't slow down. It seems to me that most people who talk about the "clock paradox" have never read Einstein's 1918 paper and they don't know how he finally solved the problem

The original Lorentz book is so rare today that a copy sold recently in Holland for $8,000 Euros (more than $8,000 US dollars). Finally a small company in Boston scanned a copy of the book in a library archives and they have made it available in a photocopy form, but it hasn’t yet been translated into English. The book is available here:

http://www.elibron.com/english/other...sg_id=10017783

Einstein's 1918 paper is available in Volume 7 of "The Collected Papers of Albert Einstein," Princeton Press.