Thereís no Such Thing as Gravity:
The World Just Sucks!

A slightly different approach to general relativity
for high school physics students

By Mark Sowers

Table of Contents

Chapter 5:
Clock-Rate

Time itself flows at different rates in different locations. This concept can be difficult to understand or accept at first, but once you do, you will see that it explains a lot.

Time flows more slowly in the presence of energy. As we saw earlier from E=mc2, a lantern battery is made up of a tremendous amount of energy in the form of matter. And since time flows more slowly in the presence of energy, time near that lantern battery flows ever-so-slightly more slowly than it does several feet away from it. Even though there is a lot of energy in that lantern battery, the effect on time is so small, modern-day tools are not sensitive enough to measure it directly.

To actually measure the degree to which time slows down, you need a much larger object with much more energy. You need something like the Earth.

In 1959 a group of scientists at Harvard University did an experiment to determine just how much of an effect the Earth has on changing the clock-rate, and they got really close to the answer they were expecting. They placed two devices that kept very accurate time in a tower: one at the top and one in the basement 74-feet below. It turns out that at the top of the tower, time flows approximately 0.00000000000000245 times faster than it does at the bottom.

We now have an exchange rate, and the currency is Ďsecondsí. One second at the bottom of the tower equals 1.00000000000000245 seconds at the top.

This difference is so small that no one would ever notice it in daily life. But if you apply that tiny difference to every atom, to every electron, proton, and neutron, to every quark, each moving at the speed of light, it adds up to a significant effect.

When we calculated the inherent energy (or rest energy) of the lantern battery we assumed that the clock-rate for both the observer and the object were the same; that the observer was in the same frame of reference as the battery. Thatís how we got away with writing c2. But this is not always the case.

Remember when we discussed E=mc2 we noted that the two cs actually represent two different things. So back up one step to the equation E=m1c1c2 where c1 is the speed of light at the objectís location and c2 is the speed of light at the observerís location. Then lets use this equation to find the energy of a 1kg rock sitting on a tower 74-feet above our observer.

At the bottom of a tower sits our observer where the speed of light is 299,792,458m/s(c2 ). At the top of the tower sits a 1kg rock where the speed of light is 299,792,458.0000007345m/s relative to the observer (c1) (We got this by multiplying 299,792,458m/s times 1.00000000000000245). Solving for E we find that the inherent energy of that rock relative to the observer is 89,875,517,873,681,984 joules.

When we drop the rock, it moves to a region where times flows more slowly. We can calculate its energy again, this time using 299,792,458m/s for both c1 and c2 as they are both in the same location. Solving for E we find that the inherent energy of that rock relative to the observer is now 89,875,517,873,681,764 joules, a difference of 220 joules.

Where did those 220 joules go?

It took the rock just over 2 seconds to fall to the bottom of the tower. In that time it accelerated (relative to the observer) to a speed of 21m/s (about 47mph). According to the equation a 1kg object moving at 21m/s has 220 joules of kinetic energy. Some of the inherent energy of the rock changed into kinetic energy.

But how does such a transformation happen? What process is occurring within the rock to make this happen?