Gas is a phase of matter which has no fixed shape or volume. Its constituent particles (either atoms or molecules) keep on moving in random directions until they collide either with other particles or with the walls of the container to reflect back. In the field of Physics the subject “Kinetic theory of gases” studies the macroscopic properties of the gas in detail [1]. To study these properties, three assumptions are to be made. They are 1) Each individual particle of gas is considered to occupy negligible space, 2) All collisions it undergoes are considered to be perfectly elastic and 3) There is no force acting between the particles. Most of the gases like Nitrogen, Oxygen, and Nobel gases behave in this accordance at standard conditions (i.e at room temperatures and low pressures) within permissible error. Although these assumptions are not always true, they allow us to study the fundamental properties of gas in the simplest possible way. The gas following these properties is called an “Ideal gas“.

When we think about dilute Ideal gas confined within a volume or a cylinder, we always picture it as tiny particles jiggling around at different speeds and different directions. See Fig.1(a). The speeds of the particles define the average temperature ‘T’ of the gas. More the temperature of the gas, faster the particles move. If there is no external potential acting on the gas particles, the average kinetic energy along each degree of freedom is equal and measures to be ‘ Kb*T/2’. Where “Kb” is the Boltzmann constant. If this was not true, the gaseous particles would move along a certain degree of freedom more than others. These particles while colliding with each other and with the walls of the cylinder exchange energy. They also exert pressure on the walls of the cylinder which can push the piston.

Fig.1 (a) Gas particles moving in random directions at room temperature. The arrows represent the direction of the gas particles. De-Broglie wavelengths λdB of particles are very small and the wave nature of particles is not prominent here. (b) At lower temperatures (~0.001 Kelvin) the particles behave as a wave. (c) At the lowest temperature, all the individual waves overlap to become one massive wave and the phase is called Bose-Einstein Condensate.

To each of these moving particles, a wave nature is associated with it according to the de-Broglie hypothesis. Each particle of a gas has a wavelength λdB=1/SQRT(3*Kb*m*T)  where ‘m’ is the mass of the gas-particle and ‘h=6.64×10-34Js‘ is the Plank’s constant. When the temperature of the gas is of the order of room temperature (i.e around 300 Kelvin), the wavelength associated with each particle is very small compared to the average interparticle separation. So the wave nature of these particles is never important here. To make the wave nature of particles prominent the temperature of the gas has to be reduced. The simplest way to reduce the temperature of the gas is the “Adiabatic expansion“. In this process volume of the container is increased. While expanding, external heat should not be allowed to enter the container.

To reduce the temperature of the gas (or the average speed of the gaseous particles) further, a sophisticated cooling technique called  “Laser cooling” is used [2]. In this method particles moving along certain directions are slowed down using the “Doppler effect”. The lowest temperatures reached using this method are around 0.001 Kelvin. The gas is called as ‘Ultra-Cold’ gas here. Here the de-Broglie wavelengths of gas particles become comparable to their interparticle separation, and it results in touching of the individual waves to the neighboring ones. See Figure 1 (b). At this point, the distinguishability of these particles starts to cease and we cannot keep a track of a particle as an individual. The particles interact with each other via the overlap of waves and we call it a ‘Quantum Critical Region’.

In this Quantum Critical Region, depending upon the physical structure of the particles, they start distributing the energy or velocity states available among themselves accord to either ‘Bose-Einstein’ statistics or ‘Fermi-Dirac’ statistics. The particles which obey Bose-Einstein statistics are called ‘Bosons’ and particles obeying Fermi-Dirac statistics are called ‘Fermions’. We will focus on Bosons as they have a peculiarity that more than one Bosonic particle can share the same energy or velocity state.

The speeds of the Bosonic gaseous particles are further reduced or temperature can be further lowered by using a process called ‘Evaporative cooling‘ [3]. This process lets high-velocity gaseous particles escape out of the system. See Fig.2. The temperatures achieved by using Evaporative Cooling after Adiabatic expansion and Laser cooling are around 0.000000001 Kelvin (or called as Nano-Kelvin) which are the lowest temperatures possible in the entire universe. Here the individual de-Broglie wavelengths of particles are large and they overlap on each other to form a giant single macroscopic wave. See Figure 1(c). This phase is called ‘Bose-Einstein Condensate’ (BEC). Here all the Bosonic particles condense to the most fundamental and lowest energy or velocity state possible. It was theoretically predicted in 1925 by Albert Einstein extending the work of our own Satyendranath Bose. Experimentally this phase was first time realized in the laboratory [4] in 1995 using laser and evaporative cooling. It took 70 hard evolutionary years of experimenting to obtain this phase after its first theoretical prediction. This work was flagged with Nobel Prize in 2001.  See Fig.3.

Fig.2 Hot water molecules escaping cup of Black Coffee, resulting into cooling of Coffee. This is an everyday example of Evaporative Cooling.

At BEC even though the temperature tends to zero Kelvin, the particles don’t freeze! Due to “Heisenberg’s Uncertainty Principle” the gas flows without any friction or viscosity. This fluid is called the “Super-Fluid”. No open container can hold it as the fluid starts crawling out of the container walls due to its non-viscous nature.

Fig.3 Velocity distribution of Rubidium-87 atoms at three different temperatures (Nano-Kelvins) near BEC transition. The left panel is ‘before’, the middle panel is ‘at’, and the right panel is ‘after’ reaching  BEC. Colors correspond to the number of atoms at each velocity: Red for atoms having the highest velocity to White for atoms having the lowest possible velocity. The first panel represents that atoms have a spread in velocities. As the temperature is lowered (middle panel) a large number of atoms fall into lower velocity states resulting in a peak. With further lowering of temperature  (right panel) almost all the atoms fall into a single smallest velocity state possible.

It is completely stupid, illogical but interesting to make an analogy between these dilute gaseous particles with the thoughts or the ideas which come into our mind. If we sit still and close our eyes, we realize that the thoughts in our mind start jiggling, colliding, exchanging momentum with one another within the container of our imagination. They take shape of our imagination just as gas takes of its container. The Temperature like quantity of these thoughts would be a parameter which increases the speed of random thoughts or the disorder or chaos in our mind. In other words, Temperature here would be a quantity which reduces the control over the thoughts.

By paying attention to these thoughts we find that all these thoughts are different than one another or they are completely distinguishable. By paying more attention to them can follow which thought has led to the next one and we can completely trace them just as the gaseous particles at room temperature. More the temperature more will the chaos or speeding of disturbing thoughts. This can give rise to feelings of anxiety or anger and can exert pressure on our mind to take different actions.

To reduce the chaos of these thoughts we can use a similar technique like Adiabatic-Expansion. This will be to allow our imagination to expand, accept things, and be open to all the possibilities around us without any external influence. Or to be more tolerant towards himself/herself and other things. This will make the person more peaceful. This would be just as cooling of gas by expanding its volume and restricting the influence of heat in the system.

Further, the chaos is mind or the temperature of the thoughts can be reduced greatly by using a method much alike to Laser cooling of the gas. That will be slowing down the flow of thoughts along certain directions which makes us disturbed. With much practice and patience of this, the chaos in mind will be reduced and we can enter a Quantum critical region of thoughts. Here all the peaceful ideas in mind will be intertwined with others and distinguishability between them will cease. Pundits and Saints may call this as a process of Meditation.

With more patience and hard work, we can further reduce the disturbance in our thoughts by a technique similar to that of Evaporative-cooling of gaseous particles. This would be to forget the highly disturbing thoughts in our mind or allow them to escape or let go out of our mind. At the lowest temperatures of thoughts possible, all the thoughts will condense into a single, simplest, purest, and fundamental state which will be similar to the “Bose-Einstein Condensate” of gas. Here this one single macroscopic thought will flow without any restriction and can crawl out of the trapping walls of our imagination to explore new areas or dimensions. Such type of thought would make a person extremely peaceful, complete, and focused. This phase of the oneness with an idea or Bose-Einstein Condensate of thoughts may be what is realized by the Saints or Spiritually-Enlightened minds.

The section regarding the comparison of thoughts with gaseous particles is an imagination of the author. But, the reader has full freedom and right to explore, prove, disprove, or improve this idea. You can comment here or share your comments or suggestions on my email

References :

[1]G. Venkatraman, Vignettes in Physics Universities Press 1993, ISBN: 8173710104.

[2] William D. Phillips, Rev. Mod. Phys.70,(1998) 721-741.

[3] W. Ketterle and N.J. Van Druten; Adv. At. Mol .Opt. Phys, 37, 1996 (181-236).

 [4] M.H Anderson,; Science 269, 1995, (198-201).

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