# Casimir Effect

We have heard that the force of attraction exists between two objects. According to Newton’s law of gravitation, every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In this session, let us study a small attractive force that acts between two close parallel uncharged conducting plates known as the Casimir effect.

## What is Casimir Effect?

” The attractive force between two surfaces in a vacuum – first predicted by Hendrik Casimir over 50 years ago – could affect everything from micromachines to unified theories of nature.”

The Casimir effect is a small attractive force that acts between two close parallel uncharged conducting plates. The force arises due to the quantum fluctuation of the electromagnetic field.

The attractive force between two plates of area A separated by a distance L can be calculated as:

$$\begin{array}{l}F=\frac{\pi hc}{480L^4}A\end{array}$$

where h is Planck’s constant and c is the speed of light.

## History of Casimir Effect

Dutch physicists Hendrik Casimir and Dirk Polder proposed a force between two polarizable atoms and called it the Casimir–Polder force. After a discussion with Niels Bohr, who suggested it had something to do with zero-point energy, Casimir alone formulated the theory predicting a force between neutral conducting plates in 1948, which is called the Casimir effect in the narrow sense.

## Understanding The Casimir Effect

The Casimir Effect can be understood with a typical example of a vacuum in space. According to modern physics, the vacuum consists of varying electromagnetic waves, and it can never be eliminated. It can be compared to a vast ocean of waves that consistently shows its existence, unstoppable. These waves always possess a package of viable wavelengths. Thus implying that an empty space consists of a minimum amount of energy. The energy that we can never feel, in spite of presence.

Now consider two mirrors that are placed in a vacuum facing each other. As a result, some waves will occupy the space between the mirrors bouncing backwards and forward. Once the mirrors are moved closer to each other the longer waves which are present, due to lack of space may no longer fit in. As a result, the total amount of energy that is present between the plates will be a bit less compared to the energy that is present elsewhere in the vacuum.
The two mirrors attract each other just as two objects are held together by a stretched spring. Until the energy stored in the spring decreases, there exists a movement of two mirrors. Due to this effect, the two mirrors will be attracted to each other, and this effect is termed the Casimir Effect.

### Coupled Ground State Energy:

It is one of the suggested possible causes in understanding the Casimir Effect that is based on canonical macroscopic quantum electrodynamics. There may exist a vacuum of a coupled system that detects the properties of an electromagnetic field that will give rise to force. Casimir force is characterized by a property of a coupled system wherein the synergy between the two plates is mediated by the zero-point fields.

### Measuring the Casimir Effect

Marcus Sparnaay, in 1958, conducted one of the first experimental tests in a delicate and challenging experiment with parallel plates, obtaining results not in contradiction with the Casimir theory but with significant experimental errors. A more accurate measurement of the Casimir effect was conducted by Steve K. Lamoreaux of Los Alamos National Laboratory and Umar Mohideen and Anushree Roy of California, Riverside. In practice, we use one flat plate and another plate that is a part of a sphere with a large radius to measure the Casimir effect because using two parallel plates would require accurate alignment to ensure they are parallel. Finally, in 2001, using microresonators, a group at the University of Padua succeeded in measuring the Casimir force between parallel plates.

## Applications of Casimir Forces

• Casimir Forces have their broad application in nanotechnology, especially silicon integrated technology-based on Casimir oscillators, nano-electromechanical, and Microsystems.
• A few examples state that the repulsive force that arises between two uncharged objects is due to the Casimir effect. This has created interests in the development of applications regarding the advancement of levitating devices.

## Frequently Asked Questions – FAQs

Q1

### What is the Casimir effect?

The Casimir effect is a small attractive force that acts between two close parallel uncharged conducting plates. The force arises due to the quantum fluctuation of the electromagnetic field.
Q2

### How does the Casimir Effect work?

The Casimir effect can be understood by two mirrors that are placed in a vacuum facing each other. Some waves in the vacuum will occupy the space between the mirrors bouncing backwards and forward. Once the mirrors are moved closer to each other the longer waves due to lack of space may no longer fit in. As a result, the total amount of energy that is present between the plates will less compared to the energy that is present elsewhere in the vacuum. The two mirrors attract each other just as two objects are held together by a stretched spring. Until the energy stored in the spring decreases, there exists a movement of two mirrors. Due to this effect, the two mirrors will be attracted to each other, and this effect is termed the Casimir Effect.

Q3

### How strong is the Casimir Effect?

Although this force might appear small, at distances below a micrometre the Casimir force becomes the strongest force between two neutral objects.

Q4

### What causes Casimir Effect?

The Casimir effect is caused due to the quantum fluctuation of the electromagnetic field.
Q5

### The Casimir effect is named after which Physicist?

The Casimir effect is named after Hendrik Casimir

Hope you have learned in detail about the Casimir effect. Stay tuned to BYJU’S to learn concepts of physics with the help of interactive video lessons.