Quantum Gravimeter: Exploiting the Born rule

[my_wan]

Among the last of the classical tests of general relativity was the Pound–Rebka experiment performed in 1959. This experiment employed a variation of Mössbauer spectroscopy in which a moving emitter was used to counteract a gravitational redshift. The idea here is to exploit QED to measure the same frequency shift with a far higher resolution and sensitivity. In fact, by exploiting the Born rule with partial reflection, it is apparently possible to obtain a power law gain in subwavelength sensitivity within a tuneable upper and lower bound without employing any external clock reference.

To draw the connection between QED and GR first note that a gravitational redshift can be characterized by QED as a change in the rotation rate of a unit vector. Since the change in rotation rate corresponds to the change in the relative clock rate between the emitter and detector it contains its own relative clock reference. Given a dual surface partial reflector of a specific thickness the unit vector rotation rate determines the reflection statistics. Or more specifically the rotational offset of the unit vector as it passes from the front to the back surface. Which means sensitivity is constrained to 1/2 wavelength, or 1/2 rotations of a unit vector, before the signal reverses direction.

The baseline effect is extraordinarily tiny. But this is where exploiting the Born rule saves the day. Given a dual surface partial reflector with a thickness that equals the wavelength of a 10 watt red light reference beam for instance it will take about a month just to get one extra photon reflection from this beam falling one meter at Earths surface on a one wavelength thick dual surface partial reflector. Not statistically relevant. If you double the thickness of this particular partial reflector it should have no effect on the reflection statistics with this unshifted reference wavelength. But because the reflection statistics is determined by the square of the rotational offset, $theta^2$, any increase in the rotational offset of this reference beam will effectively induce a power law gain in sensitivity up to the min/max limit. Care must be taken not to over-amplify the signal in this manner because amplification in this manner is also subject to exceeding the min/max, 1/2 rotation, range after which the signal direction reverses. Though another gravimeter may be used in tandem to determine when and by how much the primary bandwidth has been exceeded.

So how would you define the fundamental limits of sensitivity?

 

[azntoon]

Well, it turns out that the fundamental limit of sensitivity is determined by the uncertainty principle. In other words, the uncertainty principle sets a limit to the time available for observation, which in turn sets a limit to the resolution of the experiment. So, if you want to achieve the highest possible resolution you must reduce the time available for observation as much as possible. This means that you must reduce the total amount of time that the reference beam takes to travel from the emitter to the detector. This can be achieved by increasing the frequency of the reference beam (i.e. by using higher frequency light). Thus, the higher the frequency, the higher the resolution and the greater the sensitivity.