Zero Point Energy

HydrodynamicaThe kinetic theory of heat was first proposed by the Swiss scientist Daniel Bernoulli in 1738 in a publication entitled Hydrodynamica. In it he proposed that gasses were composed of molecules all moving in different directions and that pressure is felt as a result of collisions between these molecules and the container walls.  Phenomena associated with heat, temperature for example, is the result of the kinetic energy of these particles.  The theory was not widely accepted at first but later work by others, including Maxwell and Boltzmann and Einstein’s 1905 paper on Brownian motion consolidated the theory which was then able to make useful predictions.

As the gas is heated the molecules become more agitated, their average velocity increases and hence their energy increases and so does the temperature.  Conversely when a gas is cooled the motion of the molecules is less, their energy is less and hence the temperature is less.  The motion of the molecules ceases altogether when the temperature reaches absolute zero.

Although all molecular motion ceases at a temperature of absolute zero, there is however a residual amount of energy possessed by the molecules.  In a paper published in 1913 by Albert Einstein and Otto Stern they suggested that the level of this residual energy for the hydrogen atom is hv/2 where h is Planck’s constant and v the frequency of the residual oscillation of the atom.  This can be rewritten in terms of ħ and ω as:

 ZPE Equation 1

Equation 1

The question is where this energy comes from? And what is its nature if the atom has ceased to move at this temperature?

In Sampling the Hydrogen Atom I proposed a model for the hydrogen atom in which the orbiting electron does so at speeds very close to that of light.  In the model the orbital velocity varies from 99.9973% c for the base energy state to 100% c for the theoretical maximum energy state.  The radius of the electron orbit remains constant for all energy states and is constrained by the effects of Planck’s constant to have a value of

 ZPE Equation 2

Equation 2

From which

 ZPE Equation 3

Equation 3

Since the electron is orbiting at very close to light speed, R can also be expressed in terms of the angular velocity ω and the speed of light.

Hence

 ZPE Equation 4

Equation 4

Substituting for Energy in Equation 1 gives

 ZPE Equation 5

Equation 5

Which is the kinetic energy of an electron moving at (very close to) the speed of light.  This gives us a simple mechanical interpretation of the nature of Zero Point Energy for hydrogen.  Zero Point Energy is the kinetic energy of the orbiting electron after all motion of the atom as a whole has ceased.  The electron continues to orbit the atom at close to the speed of light.  If it did not, the atom would be unstable and the electron would fly off at a tangent.

One comment

  1. Each orbital space can be considered similar to a resonant cavity whose resonant frequency is that of the electron and whose position and shape is determined by the protons in the nucleus and to a lesser degree the neutrons. In the case of the innermost orbital there is room for two electrons if they have opposite spins. The wave aspect of the electron dominates but if you want to regard the electron’s particle aspect it can also be thought of as the electromagnetic analog of a geodesic where the electron “thinks” it is traveling in a straight line thus eliminating energy loss due to EM radiation.

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