**Please write so it\'s possible to read, had problems in the past with a good a
ID: 1770628 • Letter: #
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**Please write so it's possible to read, had problems in the past with a good answer that wasn't legible at all Appreciate it
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4. Virtual particles are fluctuations in the zero point energy of a vacuum, where the energy of these particles and the time these particles exist are dictated by the uncertainty principle AAt > They can be described as particle anti-particle pairs coming in and out of existence in short time intervals. These fluctuation can lead to real forces as in the example of the Casimir force between two uncharged plates. Consider two uncharged parallel plates placed a short distance (L) apart in a vacuum. Exper- iments show that these plates will move together. (a) Using the concept of zero-point energy introduced in class explain how virtual particles can cause the plates to move together. Hint: Consider the energies allowed for particles inside and outside the plates. (b) If the two plates are 1 nm apart, find the longest time that a virtual electron-positron pair could exist inside the plates (assume that the mass of a virtual electron is the same as an electron mass).Explanation / Answer
The following explanation is on the basis of the virtual particles:
(a) Since the virtual particles are the fluctuations in the zero point energy of a vaccum, which means in a medium like vaccum at the lowest energy level, the fluctuations produced are due to the virtual particles which are in the constant state of fluctuations according to the quantum theory, so how would be able to move together the uncharged plates, for this let's look at the information which is given in the question, that is the fluctuations which leads to the rise to the real forces like the casimir effect, so to move these plates together there is a force which is associated with it and also the energy which is required make that force work. Now with respect to the casimir effect, between the plates, there are virtual photons( photons which are the quanta of the particle and in vaccum they are virtual photons), whose allowable wavelengths, which are fitted wavelengths between the energy density of the two plates,are those wavelengths which are being considered when the vaccum energy is being calculated. There is a small force which is driving the two plates together and towards each other, which is the attractive casimir force defined as
F = (pi x h x c/ 480 L4 ) x A, where h is the planck's constant, c is the speed of light, A is the area of the two plates and L is the distance between them.
So, in the level of zero-point energy, since the particles are in the state of continuous fluctuations, these fluctuations give rise to the attractive casimir force which leads to movement of plates and drawing them closer to each other.
(b) Since th plates are 1 nm apart, the time will be calculated as, since L is 1 nm, according to the formula of casimir attractive force which is F = (pi x h x c/ 480(1)4) x A, since virtual electron positron pair is in a constant state of fluctuations, there will be a frequency associated to them, which is v = 1/T, where T is the longest time of vibration, so we know that v = c/lambda, and c = v x lambda, so putting in the formula we get
F = pi x v x lambda x 0.01379 x 10-34 x A (6.62/480 = 0.01379)
F = pi x 1/T x lambda x 0.01379 x 10-34 x A
T = (pi x lambda x 0.01379 x 10-34 x A) / F, which is the required expression of the longest time of virtual electron positron pair.
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