Chapter 16: The Duality of Matter

(Press the TAB key to position the cursor at the beginning of the first blank and type what you believe completes the thought. Then press the TAB key for feedback and to move to the next blank. If you miss it, delete all of the word by positioning the cursor with the mouse and backspacing over all of the letters and try again. You should be able to complete this exercise without error before completing this chapter.)

If light, which had been interpreted in the 19th century as a wave, in fact turns out to act like a stream of particles (photons), could it be possible that what we have traditionally thought of as particles (e.g. atoms, protons, etectrons) in fact act like waves? Louis deBroglie concluded that the answer to the question was (yes, no?) and subsequent experiments by (last name?) confirmed his answer. wavelength = (Planck's Constant)/[(mass) x ( )] For all material objects except the very (most, least?) massive (such as electrons and protons), the wavelength is so unmeasurably (long, short?) that it can be completely ignored. Electrons, protons, and photons behave in their own inimitable way, which technically could be called a quantum mechanical way...it is like nothing that you have ever seen before! The two-slit experiment helps us to understand the strange behavior of electrons. We describe three versions of the experiment in detail: one is for real, honest-to-goodness particles, the second is for real, honest-to-goodness waves, and the third is for electrons. For bullets fired from a machine gun at slits in a battleship-steel target, we measure a mathematical (probability, wave amplitude?) curve. This curve has (how many?) humps located behind the open slits or hump(s) if one slit is closed. The humps in the probability curve locate the places where the bullets have a high probability of striking the backdrop behind the slits. For waves, on the other hand, that encounter two slits, it does not make sense to measure a probability curve because the wave does not just arrive at one place or the other. Instead, for waves we measure a wave intensity curve (which is obtained from the square of the of the waves at each point behind the slits.) The wave intensity curve is an interference pattern with many humps and valleys because the waves interfere with one another as they come through the slits. When we do the two-slit experiment with electrons, we believe we will get the two-hump probability curve because we think of them as particles (like bullets), but nature instead gives us a curve that looks like a wave intensity curve for a probability curve. This is very surprising. Principle of Wave-Particle Duality: Matter and light have a dual wave/particle nature. Matter in its finest state is observed as (waves, particles?) but when unobserved is described by waves of . The probability curve is the wave! Where the probability curve has humps, that is where the probability is (high, low?) for observing an electron with a detector. Where the probability curve is flat and low, that is where the probability if (high, low?) for finding an electron. The wave is only a mathematical description of probability, but the law that describes how the wave of probability moves in time and space is known (Schroedinger's Equation.) Does the electron in the two-slit experiment go through one slit or the other (like a particle)? The answer is (yes, no?) if you watch it, but you can't say at all if you don't watch it. Watched electrons behave differently than unwatched electrons! ("Watching" includes detection with instruments.) Wave-particle duality puts limits on what we can know. The Heisenberg Principle says that we cannot know simultaneously both the exact and the exact of a particle, so we cannot predict its exact future. This contradicts the philosophy of rigid .

Click here to return to the Table of Contents