Simplified Quantum Physics Theory:

A Non-Mathematical Introduction
to The Physics of Wave-Particles

by Craig Rusbult, Ph.D.

      This page is adapted, with minor revisions and major excisions (...snip...), from Chapter 17 of a book — Physics: Power Tools for Problem Solving — that I wrote in the late-1980s.  It introduces basic concepts that show the strangeness of wave-particle duality and the mysteries of quantum physics, which is an essential foundational theory of modern science that — since all of its theory-based predictions have been verified by observations — has very strong scientific support.
      In this page, most links (those in italics) are inside-the-page and are fast;  non-italicized links open a new page in a new window, so this page remains open in this window.
      This is the first of two pages.  The second page — Quantum Physics - New Age Religion & Schrodinger's Cat — critically examines speculative metaphysical claims about quantum physics.  { And a third page looks at The Joy of Science illustrated in the history of quantum physics. }


      The purpose of this chapter [about Wave-Particle Duality and Quantum Physics] is to help you become comfortable with the radical ideas of quantum physics (which is also called quantum mechanics, or wave mechanics), to help you combine creativity and critical thinking so you can be freely imaginative without being silly and illogical.

      Sections 17.1 and 17.2 explain wave-particle duality, and try to convince you that "yes, things really are strange."  Section 17.3 describes what quantum physics is and isn't, and why things are stable and dependable.  Then Section 17.4 discusses quantum uncertainty, and 17.5 shows that "no, things are not as strange as some people say they are."
      <...snip...>  { note: This snip-symbol indicates the omission of material that was in the original chapter. }


      17.1  Wave-Particle Duality: Photons

      An example of a particle is a bullet.  It has mass and velocity, participates in collisions, follows a definite trajectory that can be analyzed using Newton's Laws, is countable (you can say "there are 4 bullets on the table"), and has definite boundaries and volume (two bullets cannot both occupy the same volume at the same time).
      The properties of a wave aren't as obvious.  For two common waves (light and sound), with our eyes and ears it is easy to observe what they do, but these waves are invisible so it isn't easy to observe what they are.   Section 9.1 [in Chapter 9] uses easy-to-visualize water waves to describe characteristics that all waves have: velocity, frequency, wavelength, and amplitude.  Unlike particles, two or more waves can simultaneously occupy the same volume;  the interference this produces is discussed in Sections 9.2 and 15.1-15.3.

      Before 1905 the scientific model of light was simple, logical, easy to understand, and wrong.  A long-running argument about whether light is a wave or a particle was apparently settled in 1801 when the double-slit experiments of Young, described in Section 15.1, provided convincing evidence for the wave nature of light.  In 1864, Maxwell developed a set of equations describing light as an electromagnetic wave.  But our knowledge of light was not yet complete*, as shown by the Michelson-Morley experiment (in 1887) and the photoelectric effect.  {* And we don't know it all now, either! }
      In 1905, Einstein published papers explaining the Michelson-Morley experiment (with the special theory of relativity described in Chapter 16) and the photoelectric effect (by answering the question "Is light a wave or a particle?" with "yes, yes").

      The Photoelectric Effect
      In the late 1800's, experimenters discovered that when light shines on metals, electrons are ejected from atoms at the surface of the metal.  For example,... <...snip...>
      These observations cannot be explained satisfactorily using the pre-1905 model of light, which predicts that... <...snip...>  The observed results are just the opposite of the predictions based on a classical theory of light.  Why?
      To answer this question, Einstein proposed that light is emitted, transmitted, and absorbed as particles he called photons, whose energy depends on their wave-frequency:  E (of photon) = h f
      Notice the wave-particle duality within this equation:  the energy of a photon (a particle of light) equals h (a constant of nature) multiplied by f (the photon's frequency, which is a wave-characteristic).

      17.2  Wave-Particle Duality: Electrons

      In 1923, Louis DeBroglie reversed Einstein's wave-particle logic of 1905 by reasoning that if something we had previously considered to be a wave (light) has particle-like properties, maybe things we usually think of as particles (like electrons, neutrons, bullets,...) have wave-like properties.
      He introduced the concept of matter waves, and... <...snip...>
      In 1927, experiments showed that a beam of electrons interacted with a "multiple-slit grating" to produce wave-interference effects similar to those described for a light beam in Section 15.1.  Later experiments confirmed the wave-like properties of neutrons, protons, and other particles.

      note:  The following subsection (until "Sometimes Analogy is Inadequate") is a radically revised summary of the corresponding section in the original Chapter 17.  It shows the extremely strange behavior of wave-particles.

      Wave-Particles in a Two-Slit Experiment

      As described in Section 15.1, wave-diffraction [or wave-diffraction plus wave-interference] occurs when light passes through one slit [or two slits] in an opaque screen, to produce a distinctive one-slit pattern [or two-slit pattern].  When analogous experiments are done with electrons, analogous results are obtained, showing that the basic behavior of waves is the same for all wave-particles: for photons, electrons,...  { historical summary of two-slit experiments with photons and electrons }
      In a two-slit experiment, shown below, moving electrons can pass through two slits in a thin barrier, and when an electron hits the wall its location is detected.


      Below are four experiments and the resulting observations.

      T:  When we cover the bottom slit so electrons can pass through only the top slit (T), electrons form a one-slit pattern (the T-pattern) on the wall in front of the top slit.  This pattern, caused by diffraction of the electron waves, is due to the wave-like nature of electrons.

      B:  When we cover the top slit, so electrons pass through only the bottom slit (B), we observe a one-slit pattern (the B-pattern) similar to the T-experiment, except that now the pattern is lower because it's now centered in front of the bottom slit.

      TB:  When both slits are open, so each electron can pass through both T and B, we observe a two-slit pattern (the TB-pattern).
      What happens if we do this two-slit experiment with the intensity of the electron beam turned down very low, so low that only one electron at a time passes through the slits?  If we let this run for a long time, we observe the same TB-pattern as when the intensity is high and many electrons are simultaneously going through the slits.
      Based on our everyday expectations, the result of the low-intensity experiment is surprising, since it shows that each single electron is passing through "both T and B" (not "either T or B") and the wave-like nature of a single electron will interfere with itself.
      But even though it passes through both slits, each electron hits the wall as a whole electron. 
      Each electron has electrical charge, and if this charge was "smeared out" when the electron moves through both slits simultaneously, we would expect different parts of this smeared-out electron to repel itself.  But there is no term for electrical self-repulsion in the quantum physics equations for an electron that is moving through the slits and toward the wall.
      a summary:  An electron goes through both slits (like a wave) but interacts with the wall as a whole electron (like a particle);  and it has self-interference (like a wave) but (like a particle) no self-repulsion.  Yes, this is very strange.  In some ways the behavior is what we might expect from a wave (but not a particle), while in other ways it is behaving like a particle (but not a wave).

      T+B:  Imagine that — in response to the crazy claim being made for TB, that when both slits are open "each electron goes through both slits" — you say, "This is impossible; I want to know which slit it really goes through."  To gain this knowledge, you do an experiment that is more sophisticated (I'll omit the details) by adjusting the intensity of the electron source so only one electron is moving through the slits at any time, and shining lights in front of T and B so you can discover which slit each electron actually passes through.  When you do this experiment, you find that the electrons passing through T form a one-slit pattern (the T-pattern) when they hit the wall, and those passing through B form a B-pattern.  Overall, what you see is a sum of the T-pattern and B-pattern, so I call this a T+B experiment.  The two-slit pattern (TB) has been destroyed, since interaction with a photon of light occurs when an electron has gone through "either T or B" instead of going through "both T and B" as in the TB-experiment above.
      a variation:  If we reduce the intensity of light, so that some electrons don't interact with any photons and thereby pass through undetected (*), these electrons form the two-slit pattern of TB.
      * Notice that detection depends on whether an electron has interacted with a photon, not whether humans have "observed" this and have thereby gained knowledge.  The same experimental results (re: the mixture of T, B, and TB patterns) will occur whether or not a human is observing, since photon-electron interactions are the causal factor.  The meaning of "observation" is a central theme of another paper whose goal is to show that "things are not as strange as some people say they are."

      Sometimes Analogy is Inadequate
      An electron does not behave like a particle, like a wave, or like a combination of wave-and-particle.  Its type of behavior depends on the situation; during interaction with the slits an electron behaves exactly as if it was a wave, and during interaction with the wall an electron behaves exactly as if it was a particle.
      To describe the quantum behavior of matter (or light) we use either a wave-explanation or a particle-explanation, depending on the situation.  The wave and particle aspects are complementary because both are needed to reach a complete understanding.
      The usual reaction to wave-particle duality is amazement-and-confusion.  Why?  Because all of your experience has been with things that act like particles, or like waves, but never both.  There is no familiar object or phenomenon that can serve as a total analogy.  To understand electrons or other wave-particles you must accept this fact:  pictures and descriptions that are adequate for everyday experience may not be adequate for areas beyond everyday experience.  When you consider that a tennis ball has 1032 times more mass than an electron, the fact that their behavior isn't totally analogous shouldn't be too surprising!

      The same kind of wave-particle duality occurs for electrons (or other types of matter: neutrons, protons, atoms, ...) and photons.  To understand this dual nature, you must have imagination and a freedom from preconceived bias.  In Chapter 6 of The Character of Physical Law, Nobel Prize winning physicist Richard Feynman does an excellent analysis of the double-slit experiment, and offers this advice:
      Now we know how the electrons and light behave.  But what can I call it?  If I say they behave like particles I give the wrong impression; also if I say they behave like waves.  They behave in their own inimitable way, which technically could be called a quantum mechanical way.  They behave in a way that is like nothing that you have ever seen before. ...  Our imagination is stretched to the utmost, not, as in fiction, to imagine things which are not really there, but just to comprehend those things which are there. ...  It will be difficult.  But the difficulty really is psychological and exists in the perpetual torment that results from your saying to yourself, "But how can it be like that?" which is a reflection of uncontrolled but utterly vain desire to see it in terms of something familiar.  I will not describe it in terms of an analogy with something familiar; I will simply describe it. ...  Do not keep saying to yourself, if you can possibly avoid it, "But how can it be like that?"...  Nobody knows how it can be like that.  { excerpts from pages 127-129 }
      And we should be thankful it is "like that" because, as explained in Section 17.3, this strange wave-particle duality is necessary for atomic stability and for life.

      17.3  Quantum Physics

      Here is a brief history of quantum physics: ... <...snip...>

      Wave Equations

      Equations can be written for many types of waves: water, string, sound, light, matter,...  In 1925, Erwin Schrodinger wrote the appropriate equation for an electron in an atom.  The solution of this equation gives valuable information about the atomic electron, including its energy, angular momentum, and probable location.
      Standing Waves and Quantization:  As discussed in Section 9.2, the superposition of waves moving back and forth on a guitar string produces standing waves with quantized frequencies: the string can vibrate with only certain frequencies.  In a similar way, an electron moving within an atom forms a standing wave, which leads to quantization of the electron's energy.  <...snip...>

      Quantum Physics and Probability

      The equations of quantum physics1) predict numerical values for some attributes,  2) make probability-predictions for some attributes, and  3) answer some questions with "I don't know" or "it may be impossible for anyone to ever know."
      1) The first type of predicting is the same as predicting in classical physics.
      But the last two categories require some explanation:
      2) Classical physics makes definite predictions about motion.  For example, in Problem 2E it predicts the path followed by The Human Cannonball and the spot where he dives into the whipped cream.  But if quantum physics is asked to describe the motion of an electron in a double slit experiment, it doesn't try to predict the electron's path or wall-hitting spot.  But it can predict the probability that an electron will hit a certain location on the wall, and it correctly predicts the pattern that is formed when a large number of electrons hit the wall.   { This is analogous to predicting the results of rolling two dice.  We can predict probabilities (there is a 1/36 chance of getting "2", a 2/36 chance of getting "3", and so on) and the probable distribution of results after 1000 throws, but unless the dice are "fixed" there is no way to predict with certainty the result of any individual dice-roll. }  <...snip...>
      3) Here is one illustration:  If you ask quantum physics to trace the path of an electron as it moves around inside a hydrogen atom, the theory says "I'm sorry, I can't do that."  But this is better than giving a definite answer — like the "planetary model" of an electron orbiting around the nucleus — that is wrong.  { Or if you ask, for an electron in a p-orbital, how the electron gets from the top half to the bottom half even though there is a probability of zero for the electron being at the boundary between the top and bottom, quantum physics simply says "I don't know." }

      A few philosophers and scientists don't think quantum physics is a complete-and-satisfactory theory because it answers some questions with probabilities or says "I don't know."  But most scientists think these limitations are necessary because, as discussed in Section 17.4, there do seem to be limitations on "what we can know" about how things behave on the microscopic level.  <...snip...>

      Strangeness and Normality
      Chapter 16 and Section 17.2 emphasize that you must "stretch your imagination" to understand the behavior of nature in extreme situations, for objects that are very fast or very small.  But it is also important to recognize the limits of strangeness.  In everyday situations, relativity theory and quantum physics both predict the normal behavior that experience has taught us to expect.
      For example, a rocket at 24300 miles/hour is fast by normal standards, but slow compared with the speed of light.  For this rocket, most relativistic calculations differ from those of classical physics by a factor of only... 1.000000007, so the two theories predict almost identical results.
      And quantum effects are significant only for extremely small microscopic objects like electrons, protons, neutrons, and atoms.  For large macroscopic objects that contain a huge number of atoms, most quantum effects are negligible. <...snip...>  Even the smallest 1-celled animal, too small to be seen without a microscope, is considered "very large" by the standards of quantum physics.
      One way to evaluate a theory is the correspondence principle:  If a new theory is to be judged satisfactory it must be able to correctly account for the experimentally verified results of older theories.  Do you see why special relativity and quantum physics pass this test?  <...snip...>
      When it is acceptable — for most everyday events, which involve objects that are relatively slow and large — it is usually easier (and more intuitive) to use classical physics than the more complex methods of relativity or quantum physics.

      Energy Quantization and the Existence of Life
      When you first study quantum physics ideas (proposing that an atom is mostly empty space, and all matter has wave-properties) it might seem that matter is not very substantial or reliable.  But the strange wave-nature of electrons is what causes energy quantization, and this in turn produces things that we consider normal, that allow life.  In the following passage, from page 101 of The History of Quantum Mechanics, Victor Guillemin describes what would happen if Planck's constant was zero, which would mean that energy was not quantized:
    The deterministic laws of classical mechanics would be universally valid, a highly desirable state of affairs, so it would seem.  However, if Planck's constant were zero, there would have been no Planck, and indeed no rational beings, or any forms of life, for it is quantization that accounts for the existence of stability and organization in the atomic substratum of the universe.  Because the energy content of atoms is restricted to certain discrete values (page 57), an assault of considerable energy is needed to jolt them out of their normal state, and afterward they return quickly and precisely to normal.  Without quantization there could be no definite normal state.  Any electronic configuration whatsoever would be possible, and the slightest disturbance could alter this configuration permanently.  Atoms would have no stable and specific properties.  There would be no well-defined organization of atoms into molecules or of molecules into large structures.  The universe would be a formless and meaningless blob without history, plan or purpose.  In our present earthly environment quantization alone makes atoms act — to use Newton's words — like the "solid, massy, hard, impenetrable particles" formed by God in the beginning, "that nature may be lasting."
      This is a good description of why quantization is necessary for life.  But to make a non-quantum universe seem even less desirable, think about what would happen to protons (with positive electric charge) and electrons (with negative charge) if there was no wave-particle duality and quantization:  they would attract each other until they came into contact and formed +- clumps that would be useless as building blocks for life.

      17.4  The Uncertainty Principle

      To find the speed of a tennis ball in a dark room we could take two flashbulb photographs, measure the distance the ball travels between the photos, the time between them, and calculate "distance/time = speed".  When we take a photograph, some flashbulb photons hit the ball (which reflects them back to the camera film) and a tiny amount of photon momentum is transferred to the ball.  But the ball's mass is so large that this momentum doesn't have a significant effect on the ball's motion.  <...snip...>

      But if we use this method to measure the speed of an electron, interaction between a photon and the tiny electron will change the electron's motion in a significant and unpredictable way... so we cannot predict with certainty what it will do next.

      During any act of observation there is unavoidable interaction between the observing-instrument and thing-being-observed (a photon and electron, respectively, in the example above).  Wave-particle duality produces energy quantization, so the changes that occur during an observation-interaction cannot be reduced below a certain level.  This causes a natural limitation on the precision of measurements, a limitation that is called the uncertainty principle.  <...snip...>

      These limitations are imposed by nature, not by a lack of technology or cleverness.  No matter how carefully we make measuring instruments and plan experiments, we cannot make measurements that are more precise than is allowed by the uncertainty principle.  <...snip...>

      17.5  Quantum Physics and Critical Thinking

      The introduction to Chapter 17 states that to understand quantum physics you must be freely imaginative without being silly.  Later, the end of Section 17.2 encourages you to drop preconceived ideas about the way nature "should be" and use your imagination to understand the way it "really is."
      Now it's time to establish boundaries, to avoid being silly.  Yes, wave-particle duality is strange, and so is the quantum physics used to describe it, but there are limits to the strangeness.  Some popular books about quantum physics, with titles that include mystical-sounding words like "Tao" or "Wu Li", have gone far beyond the boundaries of scientific validity.  In the following discussion these books, and their claims, are referred to as mystical physics (MP).  Let's compare some claims of MP with valid scientific theory.
      MP books contain many logical errors, including...

      This section, radically revised and expanded, is in a new page,
Quantum Physics — Science, New Age Religion, and Schrodinger's Cat

This website for Whole-Person Education has TWO KINDS OF LINKS:
an ITALICIZED LINK keeps you inside a page, moving you to another part of it, and
 a NON-ITALICIZED LINK opens another page.  Both keep everything inside this window, 
so your browser's BACK-button will always take you back to where you were.
Here are some related pages:

 New Age Speculations about Quantum Physics (by various authors)

 Quantum Physics: Science versus New Age Speculation (by Craig Rusbult) 

The Joy of Science (illustrated in the History of Quantum Mechanics)

WORLDVIEWS — Knowledge and Evaluation

This page is

Copyright © 2002 by Craig Rusbult
all rights reserved