Speaker
Description
The effect of the noise induced by gravitons in
the case of a freely falling particle from the viewpoint of an
external observer has been recently investigated. The quantum gravity modified Newton’s law of free fall was obtained.
We extend this work by calculating the variance in the
velocity and eventually the momentum of the freely falling
massive particle. From this simple calculation, we observe
that the product of the standard deviation in the position with
that of the standard deviation in momentum picks up a higher
order correction which is proportional to the square of the
standard deviation in momentum. We also find out that in
the Planck limit (both Planck length and Planck mass), this
uncertainty product gives the well-known form of the generalized uncertainty principle. A similar uncertainty product is obtained when the graviton is in a squeezed state. The analysis is then extended for the gravitons being in a thermal state. Here we obtain a temperature dependent uncertainty product. If one replaces this temperature with the Planck temperature and the mass of the particle by the Planck mass, the
usual generalized uncertainty product appears once again.
| Field of contribution | Theory |
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