Blog of Veikko M.O.T. Nyfors, Hybrid Quantum ICT consultant

Quantum Mechanics demystified, a try

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Principle of Equality

Think of a person in a space ship accelerating away from earth. If the acceleration is 1g ~ 9.81m/s^2, i.e. the same as gravitational acceleration as on earth, astronaut inside could be standing at the back just as if the ship was sitting still on the ground. How would astronaut without any external help know, whether ship was on the ground or accelerating in the space?
According to Einstein’s equivalence principle: No Way.

On the ship, there is a photon emitter in the front and an absorber in the back. A photon is emitted and then another one in a second’s time. First photon is received at the absorber and the other one shortly afterwards. But the time difference between first and second reception is somewhat less than a second.

Take a guess in which ship this took place? The one accelerating or the one on the ground?

Looking at the accelerating space ship, the ship had accelerated it’s speed a bit in between absorber receiving the first and second photon, and thus the distance to travel for the second photon was a bit shorter.

What about the ship on the ground then?
Nowadays there is available precision clocks, e.g. optical Al⁺ clocks, that can measure time is running faster on a table than on floor.
If the space ship was sitting on the ground, such a precision clock certainly will show a difference in rates of clocks high up and down on the floor. Right in accordance to equality principle.

How much would the difference in rate be then?

Per a series of experiments described in the September 24 issue of Science, formula for the rate difference at Earth surface for clocks in height h would be

$\frac{\delta f}{f_0}=\frac{g\Delta h}{c^2} \implies $

$\delta f=\frac{9.81\frac{m}{s^2}*33m}{(299792458 \frac{m}{s})^2} * f_0 \sim 3.6 * 10^{-15} * f_0 $

I.e. upper clock would advance one second in $\frac{10^{15}}{3.6}$ seconds, about 9 million years.
No human would notice ;-)

If clocks were separated vertically by 1 km near the surface of Earth, the higher clock emits about three more second-ticks than the lower one in a million years.