By Don Lincoln, Fermilab
Second Quantization refers to the more modern advances that were devised in the late 1940s and 1950s. These newer ideas are often not included in books about quantum mechanics and they are collectively called the second quantum revolution.
How Do They Differ?
How do traditional quantum mechanics and second quantization differ? Well, traditional quantum mechanics governs questions about whether electrons and photons are waves or particles, with the answer that they are both and neither. It’s more accurate to say that subatomic particles are another type of matter that has both wave and particle properties. In the old days, they were often called “wavicles”, but that term has fallen into disuse.
The key difference between traditional quantum mechanics and second quantization can be most simply illustrated by how the two theories model atoms. In both theories, electrons, which is to say matter particles, are quantized. They come in distinct lumps. However, the force that binds them to the atom—which is, of course, the electric field—is not.
In traditional quantum mechanics, the electric fields are treated as continuous. It’s a huge stretch, but maybe you can imagine electrons in electric fields, as being much like ping-pong balls in water.
Second quantization takes the principles of quantum mechanics to their logical extreme. Instead of electrical fields being continuous, second quantization treats them as quantum objects, with distinct chunks of electric field. Using the water analogy, if a classical electric field is water, in second quantization, you cannot ignore individual water molecules.
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Virtual Photons of Second Quantization
The quantum particle of electric fields is the photon. We already have some familiarity with photons. They are the particles of light. They are massless. They are the fastest things in the universe and travel at 186,000 miles per second. They have infinite range and are the familiar photons.
However, the photons of second quantization don’t have to adhere to such strict parameters. They don’t have to have zero mass. They don’t have to travel at the speed of light. They certainly don’t have infinite range. These second quantization photons are quite different from any photons for which you have any sort of intuition.
The name for these peculiar photons is virtual photons. They are ephemeral and they break the familiar laws of physics. Their odd behavior arises basically from the Heisenberg uncertainty principle of traditional quantum mechanics.
How Heisenberg Principle Comes Into Play
In classical physics, energy is always conserved, which means that it never changes. No matter what you do, energy is constant. But that’s not true even in classical quantum mechanics.
The Heisenberg uncertainty principle says that energy doesn’t have to be conserved, as long as the amount of time it’s not conserved is very short. The more that energy isn’t conserved, the shorter amount of time that situation is allowed.
It’s this non-conservation of energy that is the origin of virtual photons. In any particular location in space, the average energy is zero, or at least unchanging.
But, according to Heisenberg, there can briefly be a change in energy. The energy can temporarily be a smidge higher than is possible in classical physics. And, if the energy is higher, then a virtual photon can appear out of nothingness.
Now, it can’t exist for long. Heisenberg forbids that. So, the photon disappears, and the energy returns to zero. This process occurs over and over again, with these virtual and temporary photons appearing and disappearing.
Non-zero Energy of Second Quantization
For the amount of time that the virtual photon is in existence, with its non-zero energy, that’s the new normal. Heisenberg still applies, and there could be an additional fluctuation in energy. This time, what appears is not another photon, but the photon can temporarily convert into a pair of particles, one matter and one antimatter.
Remember that Heisenberg says that small energy fluctuations are more common and persist for longer periods of time. That means that the most common matter/antimatter particles are the lightest ones, as they have the least energy. Thus, electron matter/antimatter pairs are the most common. But they’re not alone.
More rarely, the pairs could be quarks and antimatter quarks. Just to add to the confusion, these matter and antimatter particles can each create a virtual photon of their own, which can exist only for a short period of time before getting reabsorbed and disappearing into nothingness.
Thus, because of Heisenberg, empty space consists of appearing and disappearing photons and pairs of matter and antimatter particles. And the tumult is constant. Empty space is a constant and writhing mess of photons, particles, antiparticles, more photons, more particles and antiparticles, appearing and disappearing.
The situation is even more chaotic in the proximity of known subatomic particles, where the creation of virtual particles is even more vigorous. But the bottom line is the subatomic world is a hustling and bustling place.
Common Questions about How Traditional Quantum Mechanics Is Different from Second Quantization
The Second Quantization refers to the more modern advances that were devised in the late 1940s and 1950s. These newer ideas are often not included in books about quantum mechanics and they are collectively called the second quantum revolution.
The photons of the second quantization do not have to adhere to the strict parameters of traditional quantum mechanics. They don’t have to have zero mass. They don’t have to travel at the speed of light. They certainly don’t have infinite range. These second quantization photons are quite different from any photons for which you have any sort of intuition. The name for these peculiar photons is virtual photons. They are ephemeral and they break the familiar laws of physics.
The Heisenberg uncertainty principle says that energy doesn’t have to be conserved, as long as the amount of time it’s not conserved is very short. The more that energy isn’t conserved, the shorter amount of time that situation is allowed.
