July 02, 2007

GUEST BLOG: Philosophical Implications of Wave-Particle Duality: Part 2

A few days ago, I talked about the classical assumptions relevant to wave-particle duality, in part 1 of this series. I hope to build up to discussing the relevant philosophical questions, most of which probably won't come in until part 4. But first, here and in the next part, I'm going to briefly discuss the important experiments in the development of wave-particle duality, because however it's interpreted in the philosophical discussion, it can't run afoul of these. This post is mostly physics; however, there's no math whatsoever. As always, suggestions about how to improve the physics to philosophy ratio would be appreciated.

Part 2: Wave-Particle Duality of Light

Last time, we talked about some observations that, under the classical assumptions about waves and particles, would definitively establish a phenomena as a wave or particle phenomena. These were:
O1) Interference and/or diffraction phenomena (implies wave)
O2) Travels faster in matter of higher difference densities (implies wave)
O3) Interaction occurs only with discrete amounts of energy (implies particle)
O4) Highly localized interaction in space (implies particle)

Why Is Light A Wave?

Initially, light was thought to be a particle, but in the 1660’s that Robert Hooke suggested a wave theory. Experimental evidence came around the start of the 1800’s, when Thomas Young observed interference patterns of light in his famous double slit experiment. The wave nature of light was further confirmed when it was observed that light travels faster in glass than in air (glass being a denser medium). These two observations (corresponding to O1 and O2) convinced physicists that light was indeed a wave, and the theory to explain light as a wave wasn’t long in coming. Maxwell found his famous wave equations, which included light as a type of electromagnetic radiation. Experimentally this was supported when it was shown that radio waves (certainly a type of electromagnetic radiation) have similar properties to light waves. The disagreement seemed to be settled- light was definitively a wave, and furthermore, electromagnetic radiation.

Note, however, that both of these observations deal with how light travels- it interfering with other light waves while traveling, and how fast it travels. This will be relevant in future sections.

Why Is Light A Particle?

Before too long, though, it was discovered that there was a major problem in physics, in classical thermodynamics, which seems at first to be irrelevant to light, but is actually related. Thermodynamics is basically statistical mechanics with a heavy emphasis on temperature, and statistical mechanics is applying Newton’s Laws to a system through statistics. For example, if you had a box with 10,000,000 particles in it, you might just care about the average speed of the particles and its standard deviation, instead of wanting to know the speeds of all the individual particles.

In thermodynamics, a blackbody is an ideal system that absorbs all radiation that falls on it, and then radiates some energy back. Although it is an ideal system, it can be accurately approximated in laboratories. As a blackbody is heated, the amount of energy radiated increases and is concentrated in shorter wavelengths, according to classical thermodynamics (the Stefan-Boltzmann Law). There is a spectral distribution formula relating the power radiated from a blackbody to the wavelength (the Rayleigh-Jeans Law).

In theory, a graph of the power vs. the wavelength should look approach infinity at zero and approach zero at infinity. The experimental results agreed as it approached infinity extremely well, but as the wavelength became small, instead of approaching infinity, it crested an approached zero- a very different behavior than expected. Furthermore, the theory was founded on classical mechanics and statistics. Statistics, with its rigorous mathematical formulation and proofs, is certain- so that implies there is a problem in Newton’s Laws, the very foundation of physics. Since these experiments were done in the ultraviolet range, this was known as the ultraviolet catastrophe.

Then, Max Planck wrote down an equation that fit the experimental curve, which required the use of a constant (Planck’s constant- h). He then tried to find a way to “derive” this equation classically. Using similar techniques to what was used in thermodynamics, Planck broke the energy spectrum down into discrete amounts, parameterized by h, and then proceeded with the normal derivation. At the end of derivation of this type, one would take the limit as h approaches 0 to recover a continuous energy spectrum. (This is similar to integration, where one sums the area of rectangles of a finite width, and then takes the limit as the width of the rectangles approaches 0). However, if Planck didn’t do this last step and let energy spectrum remain discrete, it matched the fit equation. Furthermore, when h did approach 0, he recovered the classical equation. This shows that, for a given frequency f, energy comes in “packets” of size hf.

However, this is the same as O3 above, which implies particle behavior…however, some physicists suggested that the proper response was to say that localized energy wasn’t exclusively a particle phenomena, but perhaps under certain situations, waves could display it also. This is equivalent to changing the definition of a particle from P1 and P2 to just P1, where as in the last section, they are defined as:
P1) A particle is localized in space
P2) A particle exchanges energy at a point
However, another famous physicist, Albert Einstein, proved that waves also display O4, whose derivation (described in part 1), relies only on P1.

The photoelectric effect is that, when light is shines on metallic surfaces, electrons are emitted. Physicists have created an apparatus to do more experiments on this effect. Basically, light (or any type of electromagnetic radiation) shines on one metallic plate (the cathode) and a distance away from it is another metal plate, which can absorb electrons (the anode). Then wires, resistors, etc are added to create a voltage across these plates, and physicists run experiments to test the correlation between the current in the system (caused by the electrons emitted from the photoelectric effect) and the voltage. A positive voltage causes electrons to be attracted to the anode, but a negative voltage repels the electrons from the anode. When the voltage is negative, only the electrons that are emitted with enough initial kinetic energy to overcome the voltage difference make it to the anode.

Classically Newton’s Laws and our understand of the nature of atoms (as negatively charged electrons around a positive nucleus) combine to make certain predictions.
1) There should be a maximum voltage such that all the emitted electrons make it to the anode (since a positive voltage attracts the electrons). Increasing the voltage beyond this does not increase the current any further.
2) If one increases the intensity of the light hitting the cathode, corresponding to increasing the amount of energy hitting the cathode, while keeping the frequency of the light constant, this should increase the maximum kinetic energy of the electrons emitted, and thus electrons should be emitted with higher speeds. Hence, there should be no minimum voltage beyond which no electrons are emitted- at any voltage, if you increase the intensity of the light enough, there should eventually be an electron emitted with enough kinetic energy to make it to the anode.
3) Finally, one can calculate the length of time light of a given intensity needs to shine on the cathode before enough energy is gathered for an electron to be emitted. Lower intensities should have a longer delay than higher intensities, but eventually an electron should be emitted.

However, of the three predictions, only (1) was verified experimentally. Regarding (2), physicists noted that there was a minimum voltage beyond which no electrons were emitted (however long they waited). Even worse, for (3), physicists noted that either the electrons were emitted virtually instantaneously immediately or not at all (however long they waited); their predictions of several hours were completely rebutted by experimental evidence.

Einstein proposed taking Planck’s quanta of energy literally- that light was really packets localized in space that have discrete amounts of energy, which he called photons. Einstein proposed that instead of a wave uniformly and constantly hitting everything on the metallic surface, what really happened is that individual photons collide with individual electrons and transfer their energy to them. If they give the electrons enough energy, the electrons escape from their orbits and are emitted. For a given frequency of light, the extra energy a photon transfers to the electron (beyond escaping the orbit) is converted to a specific amount of kinetic energy. This means that there is a limit on the initial maximum kinetic energy an electron leaves with, and if that’s not enough to overcome voltage to get to the anode, then the electron won’t make it, ever. Thus, Newton’s Laws plus the quantized energy predicts that there will be a minimum voltage (remember negative voltages repel the electrons) beyond which no electrons will make it to the anode, as observed. For the timing- if the energy is great enough, as soon as the photon strikes the electron it will be emitted. This will happen with the first photon that hits an electron; they don’t need to accumulate over time. Thus, there is no measurable lag. However, if the energy of a photon isn’t enough to give the electron enough kinetic energy to escape, photons striking the electron won’t knock it out, no matter how long you wait. There will never be a situation where you will have a steady supply of electrons emitted after several hours because the energy doesn’t accumulate continuously until an electron is emitted (the energy dissipates between when one electron hits and the next).

Overall, this implies O4, that light is localized in space. If physicists rejected this from the definition of a particle, they’d have no definition left. Thus, they were forced to accept some sort of wave-particle duality, at least for light.

Before we discuss interpretations of wave-particle duality, and the issues of properties iit raises, we’re going to look at wave-particle duality with respect to matter next in part 3. This is because it gives us a clearer view of the nature of the waves involved, and also because we know from relativity that light is something special.

Note, for the future sections, that all of this particle behavior observations deal with light interacting with something, and not with how it travels.

Posted by lwozniak at July 2, 2007 08:57 AM
TrackBack URL for this entry: http://blog.kennypearce.net/admin/mt-tb.cgi/347
Post a comment
If you have never commented on this blog with your email address before, or if you choose not to enter an email address, please note that typing any links or URLs, including in the URL box below, will probably result in your comment being marked as spam. If, after posting, you see a page explaining the the spam filter didn't like your comment, please email kenny@kennypearce.net to ensure that your comment is approved. Thank you.

Remember personal info?

Return to blog.kennypearce.net
Philosophy Blogs - Blog Top Sites