Alternatively, from Eq.(11), we may say that for a region that is roughly spherical, of size l , and contains a mass M the fractional distortion is of order Even for rather strong gravitational fields this generally holds at least roughly. The above results Eq.(13) will be basic to our arguments in future sections. Our first road to the Planck scale is based on the same thought experiment as the Heisen- berg microscope used to obtain the UP in section II and shown in Fig.1, but it includes the effects of gravity to obtain a generalization of the UP. 27,28 According to the UP in Eq.(4) there is no limit on the precision with which we may measure a particles position if we allow a large uncertainty in momentum, as would result from using arbitrarily short wavelength light. But this does not take into account the gravitational effects of even a single photon. As noted in section II a photon has energy hν and thus an effective mass M$_{ef}$ = hν/c 2 = h/cλ , which will exert a gravitational force on the particle. This will accelerate the particle, making the already fuzzy particle position somewhat fuzzier. Using classical Newtonian mechanics we estimate the acceleration and position change due to gravity as roughly where r$_{ef}$ and t$_{ef}$ denote an effective average distance and time for the interaction. The only characteristic velocity of the system is the photon velocity c, so we naturally take r$_{ef}$/t$_{ef}$ ≈ c , and obtain for the gravitational contribution to the uncertainty According to the UP Eq.(4) the position uncertainty neglecting gravity is about Δ x ≈ $_{ℏ}$/ Δ p ; we add the gravitational contribution in Eq.(15) to obtain a generalized uncertainty principle or GUP, Spacetime fractional distortion ≈ GM lc 2 (13b) Δ a$_{g}$ ≈ GM$_{ef}$/r 2 ef = G ( h/λc ) /r 2 $_{ef}$, (14) Δ x$_{g}$ ≈ Δ a$_{g}$t 2 ef ≈ G ( h/λc )( t 2 $_{ef}$/r 2 $_{ef}$) Δ x$_{g}$ ≈ Gh/λc 3 ≈ ( G$_{ℏ}$/c $^{3}$) /λ = l 2 $_{p}$/λ (15) Δ x ≈ ( ℏ Δ p$^{)}$ + l 2 p ( Δ p ℏ ) (16) 8 III. THE GENERALIZED UNCERTAINTY PRINCIPLE