light ranging is about the Planck length. The energy and gravitational field of the photon prevents us from doing better. A final note is in order. We have here assumed implicitly that we have access to a perfect classical clock for timing the light pulse. However if the clock is assumed to be a small quantum object then there will be a further contribution to the uncertainty due to the spread of the position wave function of the clock during the travel of the light pulse. Some authors suggest that such a quantum clock should be used in the thought experiment, and arrive at a larger uncertainty estimate for light ranging, one involving the size of the system l . 9,31 However other authors point out that such a quantum clock may not be appropriate since it could suffer decoherence and behave classically. 10 Predictions of this nature may be testable with laser interferometers constructed as gravitational wave detectors. 32 In this thought experiment we shrink a volume containing a mass M as much as possi- ble, until we are prevented from continuing. We assume the volume is intrinsically three- dimensional, about l in all of its spatial dimensions, as shown in Fig.4. A difficulty occurs due to gravity when the size approaches the Schwarzschild radius, The system may then collapse to form a black hole as discussed in section II and cannot be made smaller. There is of course no lower limit to this size if we choose an arbitrarily small mass M . A different difficulty occurs due to quantum effects. From the UP the uncertainty in the momentum of the material in the volume is at least of order Δ p ≈ $_{ℏ}$/l . Since the energy in the volume is given by E 2 = M $^{2}$c4 + p $^{2}$c2 the uncertainty in the energy is roughly If l is made so small that this energy uncertainty increases to about 2 Mc 2 then pairs of particles can be created and appear in the region around the mass M, as shown in Fig.4. 33 The localization is thereby ruined and the volume cannot shrink further. This limit happens V. SHRINKING A VOLUME l ≈ GM/c 2 (22) Δ E ≈ c Δ p ≈ $_{ℏ}$c/l (23) 11