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Question

I have heard that humans have a wavelength. Is this true?
Asked by: Brendan Playford

Answer

In 1932, a French scientist named Louis de Broglie suggested that the wave-particle duality applied to not only light, but also to matter. That is to say, he proposed that all matter possessed wave-like characteristics. To understand how he arrived to this conclusion, we must explain how light can possess both wave and particle properties.

Until the eighteenth century, light was thought of purely as a wave, like sound. There were several problems associated with this theory, however, one of the foremost being the lack of medium in space. Waves require a medium through which to travel, and without such substance, the wave cannot exist - - this is why sound cannot travel through a vacuum. In space, however, there did not appear to be any medium that would allow light to travel, yet light obviously traveled through space to reach the Earth. In order to explain this, scientists visualized a material that existed everywhere and through which light could propagate. This material came to be called the 'luminiferous ether'. The wave theory was further promoted when, in 1803, a scientist named Thomas Young demonstrated the interference of light in the famous 'double slit experiment'. This experiment could only be explained by the wave-nature of light.

So, how does the particle theory enter the picture? The wave nature of light does not explain everything, particularly the fact that light diffraction was not as readily observed as was other wave diffraction, such as sound or water waves. Things were further complicated with the photoelectric effect, a phenomenon where light striking metals produced an emission of 'photoelectrons', that is, an electric current. The empirical data of the photoelectric effect could only be explained by the corpuscular (particle) theory of light.

In the meanwhile, Clerk Maxwell synthesized everything that was then known about electricity and magnetism in what are known as Maxwell's equations. These equations described visible light as a portion of the electromagnetic spectrum, and said that the luminiferous ether was not necessary for electromagnetic waves to propagate through space. He proposed an experiment through which the absence of ether could be demonstrated, but believed that the precise measurements required for the experiment were not possible. Albert Michelson and Edward Morley proved him wrong in July of 1887. The famous Michelson-Morley experiment sent light in two orthogonal (perpendicular) directions and used an 'interferometer' (invented by Michelson) to detect the shift in the wavelengths of the light beams. This shift was supposed to be caused by the speed of the Earth moving through the luminiferous ether, but no such shift occurred. Thus the speed of light was shown to be the same, regardless of the relative motion of the frames. So, is light a wave or a particle? It is perhaps best to say that light is a complicated phenomenon that is neither a wave nor a particle. The wave and particle theories are simplified models of light, and in certain situations, one or the other of these 'models' offers a more convenient explanation.

Now, enter Prince Louis de Broglie. Max Planck and Einstein had related energy to the frequency of waves, and by Einstein's famous equation E=mc2, mass was related to energy. Thus de Broglie supposed that matter might also be related to the frequency of waves. The elementary particle of light, the photon, had been shown to exhibit wave-properties; de Broglie wanted to extend this fact to all matter.

The momentum of a photon, p, was given by the ratio between Plank's constant and the photon's wavelength. De Broglie applied this relationship to all matter. Since Plank's constant is on the order of 10-34, the de Broglie wavelength is virtually undetectable for large amounts of matter.

There is much evidence of matter possessing such a de Broglie wavelength. The double slit experiment demonstrates interference effects in photons, electrons, and neutrons, the last of which being very significant, considering that the neutron is perhaps the densest mass on Earth.

What about humans? Well, theoretically, since all matter possess wave-like properties, so do humans, and cats, and whatever you please. We could hypothetically demonstrate this fact by performing the double slit experiment with these 'particles'. So here we go, firing cats haphazardly at two slits, trying to get cats to interfere with each other. Will it work? Well. . . kinda. There are a lot of little technicalities, so you'll have to be careful not to aim at the slits (i.e., you must fire randomly to create a incoherent cat-beam), and you'll have to space out the firings. You fire one cat, you wait for a while, then you fire the other cat. Eventually, you'll form the familiar interference pattern on the other side of the slits. Unfortunately, that waiting period between firings is about the age of the universe when you're using cats.

Finally! What IS the wavelength of a human being? Assuming he/she weighs 70 kg, and is being fired at 25 m/s, it's about 3.79 x 10-37 meters.
Answered by: Aman Ahuja, Physics student, WPI, Mass.


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(1879-1955)


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