Simple Nature - Light and Matter

close are the electrons to the limit imposed by the uncertaintyprinciple?⊲ If we assume the electron moves in all directions with equalprobability, the uncertainty in its momentum is roughly twice itstypical momentum. This only an order-of-magnitude estimate, sowe take ∆p to be the same as a typical momentum:∆p∆x = p typical ∆x= (m electron )(0.01c)(0.1 × 10 −9 m)= 3 × 10 −34 J·sThis is on the same order of magnitude as Planck’s constant, soevidently the electron is “right up against the wall.” (The fact thatit is somewhat less than h is of no concern since this was only anestimate, and we have not stated the uncertainty principle in itsmost exact form.)self-check FIf we were to apply the uncertainty principle to human-scale objects,what would be the significance of the small numerical value of Planck’sconstant? ⊲ Answer, p. 929Measurement and Schrödinger’s catOn p. 847 I briefly mentioned an issue concerning measurementthat we are now ready to address carefully. If you hang around alaboratory where quantum-physics experiments are being done andsecretly record the physicists’ conversations, you’ll hear them saymany things that assume the probability interpretation of quantummechanics. Usually they will speak as though the randomness ofquantum mechanics enters the picture when something is measured.In the digital camera experiments of section 13.2, for example, theywould casually describe the detection of a photon at one of the pixelsas if the moment of detection was when the photon was forced to“make up its mind.” Although this mental cartoon usually worksfairly well as a description of things they experience in the lab, itcannot ultimately be correct, because it attributes a special role tomeasurement, which is really just a physical process like all otherphysical processes. 4If we are to find an interpretation that avoids giving any specialrole to measurement processes, then we must think of the entirelaboratory, including the measuring devices and the physicists themselves,as one big quantum-mechanical system made out of protons,neutrons, electrons, and photons. In other words, we should takequantum physics seriously as a description not just of microscopic4 This interpretation of quantum mechanics is called the Copenhagen interpretation,because it was originally developed by a school of physicists centeredin Copenhagen and led by Niels Bohr.864 Chapter 13 Quantum Physics