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Running head: WAVE-PARTICLE DUALITY OF MATTER

Wave-Particle Duality of Matter

University of Alabama

WAVE-PARTICLE DUALITY OF MATTER

Wave-Particle Duality of Matter

There seems to be an inherent contradiction in the statement

“x is both a wave and a particle.” Yet, experiments have shown

that matter, contrary to intuition, displays characteristics of

both a wave and a particle (Feynman, 1963). This short paper will

address several issues. They are: How light, commonly viewed as

displaying wave-like behavior, in certain instances, displays the

characteristics of a particle; how electrons, likewise, generally

thought of as particles, in certain instances, display wave-like

behavior; a prominent interpretation of this wave-particle

duality of matter, the Copenhagen interpretation; as well as a

discussion of the metaphysical implications of the wave-particle

duality of matter.

Double-Slit Experiment

The double-slit experiment can be used to illustrate the

particle-like behavior of light “waves.” In the double-slit

experiment, we set up a device, say, a laser beam that can send a

beam of light towards a detection screen, which is placed at the

opposite side of the experiment. In between the laser and the

detection screen is a thin wall that has two parallel slits in

it, slit 1 and slit 2. The laser is turned on, and the light

travels from the laser through the double-slit wall and is

detected at the detection screen. The pattern that shows up on

the detection screen is one that would result if waves traveled

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through the slits, interfered with one another, and then arrived

at the detection screen. When I say that the waves interfere with

one another, what I am saying is that when the crests, or

troughs, of two waves meet, this causes constructive

interference, and the amplitude of the wave is intensified. When

a crest and a trough meet each other, this causes deconstructive

interference, and the amplitude of the wave is mitigated. To

visualize the interference pattern that develops, you can think

of the pattern that would result if water waves were propagating

through the experiment. Hence, light acts as a wave. However, the

light shows up on the detection screen in “lumps,” or discrete

pieces of matter (Leclair, 2012). To further display the

particle-like behavior of light, one only needs to place

detectors at each slit. This would allow the observer to know

which slit, 1 or 2, the light actually traveled through on its

way to the detection screen. When detectors are place at the

slits, the interference disappears and a particle-like pattern is

detected (Brukner & Zeilinger, 2002). The pattern that results is

the same as if the laser were actually a gun, randomly shooting

discrete bullets though the slits towards the detection screen.

Therefore, the double-slit experiment provides evidence that

light does, in fact, behave like a particle. The double-slit

experiment is not simply limited to experiments involving light,

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however. The experiment can also show the wave-particle duality

of electrons.

The conception that many of us non-physics students have of

electrons is that of a tiny discrete piece of matter orbiting

around the nucleus of an atom. Yet, the double-slit experiment

yields results that show that electrons exhibit wave-like

behavior (Feynman, 1963). To understand this, we simply need to

replace our laser with an electron gun. The electron gun fires

randomly, so we do not know if the electron will travel though

slit 1 or slit 2 on its way to the detector. Now, if the

electrons are like particles, we should see a pattern on the

detection screen as if we watched a gun randomly fire discrete

bullets. When we start the electron gun, though, this is not what

we see. We do see the electrons arrive at the detection screen in

discrete lumps, but, after a while, we see an interference

pattern develop on the screen (Feynman, 1963). Even if the

electron gun’s rate of fire is reduced so as to fire a single

electron at a time, the interference, like that observed in water

waves, still exists. So, is the electron a particle or a wave?

This also leads to the intuitive question, which slit did the

electron travel through, 1 or 2? There are various

interpretations of what the double-slit experiment is actually

telling us, the most popular, perhaps, being the Copenhagen

interpretation. I will now give a brief discussion of the

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Copenhagen interpretation as well as discuss the metaphysical

implications of the Copenhagen interpretation.

Copenhagen Interpretation

From my limited understanding of the Copenhagen

interpretation, it holds that we cannot, actually, know where a

electron is located between the slit and the detector; we can

only give the probability of its being in a certain place. That

is, there is no fact of the matter whether the electron is in

region a, or region b, at a certain time between the wall and the

detector. The most that can be said is that there is a “so and

so” percent chance that the electron is in region a. The

Copenhagen interpretation is therefore, probabilistic in nature.

The electron is, in a sense, in all of the places until it is

measured. Once it is measured, the electron collapses on itself

at a certain point (Leclair, 2012). The collapse is known as the

wave function collapse. Professor Leclair describes the wave

function of a particle (or electron) as the amplitude of the

particle at a certain location and time (2012). The probability

of finding the particle at a certain location, a, at a time t, is

|φ (x, t)|2. Were φ is simply the wave function. It seems that

what is actually real, according to the Copenhagen

interpretation, is probability. So, is the electron a particle or

a wave? The Copenhagen interpretation would say that the electron

has wave-like properties (Leclair, 2012). Which slit did the

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electron go through 1 or 2? If we observe the electron as it is

traveling from the gun to the detector, it will choose one of the

slits, but the interference will disappear. If we do not observe

the electron, we cannot say which slit the electron took. There

seems to be a sense that the Copenhagen interpretation does not

care which slit the electron took, only if the probabilities can

lead to testable results, which, as I understand the Copenhagen

interpretation, it does.

Metaphysical Implications

If the Copenhagen interpretation is correct, it is not a

meaningful question, physics-wise, to ask which slit the electron

took. However, for the metaphysician, she will certainly not be

content with “it doesn’t matter.” I, with my major in philosophy,

intuitively want to say that the electron took either slit 1, or

slit 2. Einstein contended that there were missing variables

that, if accounted for, could provide for a complete theory

(Leclair 2012). If Einstein had not been proven incorrect, I

would likely side with him. There seems that there is an

objective reality, which we are only observing, not bringing into

being by observing it.

A possible remedy for this problem, I contend, may lie with

what Professor Leclair stated in a lecture for PHL 480 in the Sp.

’12 semester. We have gotten the question backwards. We are

trying to assign everyday behavior to material that exists at the

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quantum level. We want to label an electron as either a wave or a

particle, but it is neither. It is an electron. The real question

is how everything that exists arises from something that, at its

deepest level, is only probabilistic.

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References

Brukner C, Zeilinger A (2002). "Young’s experiment and the

finiteness of information". Philos.Trans. R. Soc. Lond. 360:

1061-1069.

Feynman, R., Leighton, R., & Sands, M. (1963). The Feynman

Lectures on Physics: Volume 1 (2nd Edition ed., Vol. 1).

Boston: Addison-Wesley.

Leclair, P. PHL 480 Class Handout. (2012, Spring). PHL 480:

Physics and Metaphysics. University of Alabama, Department

of Physics: Dr. Patrick Leclair.

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