The Casimir Effect

By Sparsh Gupta

The mysterious, attractive force between two mirrors suspended in a vacuum helped develop many theoretical ideas such as Hawking Radiation and even Zero-point (or Vacuum) Energy!
In 1948, Dutch physicists Hendrik Casimir and Dirk Polder predicted that when two mirrors are placed in front of each other extremely close (just about 100 atoms apart!) in an absolute vacuum, they attract each other and slowly move closer. This seems counterintuitive at first glance; how can nothingness lead to a force? Although this force indeed exists and was also detected in 1997 by S. Lamoreaux.Β 
To understand how this force comes into existence, we will first understand Heisenberg’s uncertainty principle. Heisenberg stated that it is impossible to accurately measure both; the velocity and position of a particle at a given instant. A corollary1 can easily be shown that the energy and duration of the existence of a particle cannot also be measured together.
If we find the energy of particles, then the amount of time they exist (in β€˜our’ sight or in our frame of reference) decreases and hence they disappear quickly. But when we go to empty space or vacuum, it creates a paradox, since there are no particles in a vacuum whatsoever, the duration of the existence of one particle is zero! But if the particle didn’t exist for any time, then it must not possess any energy either; hence we know its energy, i.e., zero. This violates the Heisenberg uncertainty principle; we cannot know both the energy and duration of a particle even though both are zero.Β 
The solution to the above paradox leads to a fascinating and absurd image of a β€œvacuum” that says empty space is not really β€˜empty’. In a vacuum, particles emerge as pairs of matter and anti-matter particles out of nothing, energy is spontaneously created in a vacuum! But this energy is quickly destroyed when this matter and anti-matter pair collide and annihilate into nothingness again. The Uncertainty principle leads to the idea that a vacuum is indeed a sea of particles and antiparticles getting created and annihilating into nothingness. These particles are called Virtual Particles, particles that don’t actually β€˜exist’.
The last step to understanding the Casimir Force will require us to dwell in Quantum Field Theory. According to QFT, all particles and antiparticles are nothing but vibrations/waves on a β€œfield” spread out all over space and time. An analogy to this can be the vibration of a string on a guitar; each string creates a different sound when pulled by a certain amount. Similarly, every particle has a specific vibration associated with its respective field.Β 
We can imagine the fields in a vacuum-like the ocean, where every wave in the ocean represents a particle. Like the ocean, there will be many waves everywhere in a vacuum that represent our virtual particles coming into existence, interfering with each other and then annihilating. Hence vacuum is full of fluctuating waves (specifically Electromagnetic waves), just like the ocean.Β 
Now when the two mirrors are placed in a vacuum, they create constraints for the number of virtual particles that can be made between the mirrors. This is because the two mirrors act as a box for the waves of the particles, which means only those particles can exist whose wavelengths are an integral multiple of a given wavelength. This wavelength is determined by the properties and the distance between the mirrors. Consequently, the average number of virtual particles between the mirrors is less than the average number of virtual particles outside the space between the mirrors.
Since every particle has some momentum and energy and can collide with the mirrors, we observe a net inward force. This is because more virtual particles collide with the mirror outside when compared to the space between the mirrors. This net inward force is called the Casimir Force.Β 
This is how Casimir and Polder showed how dynamic nothingness can actually be!Β Β 
1: Corollary: A proposition that follows from one already provedΒ 
An interesting demonstration of the Casimir Effect:
https://www.youtube.com/watch?v=H-GnwnEnLCA
References –Β 
https://www.scientificamerican.com/article/what-is-the-casimir-effec/
https://physicsworld.com/a/the-casimir-effect-a-force-from-nothing/
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