CASIMIR EFFECT AND HAWKING RADIATION

CASIMIR EFFECT AND HAWKING RADIATION

What is the Casimir Effect?

In 1948, a Dutch Physicist Hendrick Casimir came up with a method to detect a tiny force caused by zero-point energy or also known as vacuum energy exerted by virtual particles. To understand this phenomenon, imagine a rigid reinforced crate with a vacuum inside of it, so that you would expect for there to completely nothing within the crate. Now add 2 parallel mirrors about 100 atoms apart from each other into the crate. The result of this experiment is that the two mirrors miraculously end up moving towards each other, clearing the gap that was previously put between them. This strange behaviour completely questions our understanding of vacuums and whether vacuums are quiet and empty.

What is causing this strange behavior?

In order to explain this phenomenon, we must look carefully at Werner Heisenberg’s uncertainty principle, which states that you may not know both the position and momentum or the energy and duration of a subatomic particle to great accuracy (Δx Δp ≤ ℏ/2, ΔE Δt ≤ ℏ/2). So as our values for these variables tend towards zero the uncertainty also tends toward zero and hence according to the uncertainty principle particles cannot have both zero energy and zero duration, leading to the fact that particles which do not exist have a great chance of coming into existence for a short period of time from quantum vacuum fluctuation.

 These “virtual” particles occur in annihilation pairs (antimatter and matter particle pair) and very quickly eliminate each other or if you think of them as waves, they destructively interfere, cancelling each other’s amplitudes out, which has been proved by Einstein’s equation E=mc^2 and Planck’s constant, which lead to showing that particles can be modelled as waves with wavelengths by De Broglie . Due to the fact that waves can have an infinite amount of wavelengths, we know that there can be an infinite amount of different waves in open space but in our crate, they must be a form of a standing wave and harmonics of that a standing wave (which is still infinite) in order to exist between our mirrors.

There is a greater probability of having more particles on the outside of the mirrors than in between the two mirrors and these particles can collide with the mirrors exerting a force on the mirrors. As there is a greater net force pushing the mirrors together than the force pushing them apart, they come together.

However, when attempting to calculate the mass and energy of these particles, a lot of infinities were calculated so mathematicians had to result in renormalization, which pretends that these infinities do not exist. This effect is extremely useful in explaining Hawking radiation.

What is Hawking radiation?

After it has been detected that black holes emit radiation and shine, Steven Hawking attempted to prove that black holes do not shine and instead proved the opposite, by combining laws of quantum mechanics and general relativity and found out that stuff can escape near the event horizon of a black hole and that black holes do shine.

If an antimatter and matter particle pair is formed close to the event horizon, there is a chance of one of the particles getting sucked in by the black hole and the other one escaping so that they can no longer annihilate each other. This escape particle has an energy that we can detect as Hawking radiation. You would think that this violates conservation of energy but as from our point of view, this escape particle has positive energy meaning that the black hole must have gained negative energy, which is the same as the black hole losing mass, which is equal to losing energy, so that ultimately energy is conserved and the energy of the escaping particle is interestingly due to the black hole losing mass.

Black Hole Explosion

This phenomenon can lead to black holes being drained and decreasing in size. Hawking proved that as black holes evaporate by gaining negative energy, they increase in temperature so that the smallest black holes are the hottest ones. As the black hole’s mass decreases to zero, a powerful explosion of gamma rays will occur, which subsequently causes the most powerful eruption to ever be detected. This knowledge of black holes is due to the proof of vacuum energy by Hendrick Casimir and the Casimir Effect.