LIMIT OF LOW TEMPERATURE,FREEZE DECAY
Jitendra Kumar Barthakur
10 Feb 2005
The old seventeenth century gas laws presumed that at "absolute zero temperature" (0 K) the gaseousness of the gases ended. The concept had been carried forward, erroneously, to a surmise that 0 K was the lowest limit of temperature; and the entropy acquired a zero value at 0 K.
These presumptions are not tenable because of two other well-established concepts: "Zero-point" energy and the principle of "indeterminacy" for electrons in quantum theory. Also the principles of "critical points" of phases of fluids and solids, behavoiur of the "clusters", "mismatch" of electronic energy and superconductivity, etc., indicated that 0 K could not be the lowest limit of temperature. The existing black hole literature helped to understand that at a critical temperature, which was lower than 0 K, the molecule, atom and neutron had to let the electron, other particles and sub-particles constituting an atom or neutron, leave the atom or neutron and dissipate into "space".
At very low temperature, which is much below 0 K, matter turns to dissolute particles just like it does at very high temperature and pressure.
Black hole limit of temperature
The concept of black hole raises the question whether the lower limit of temperature is 0 K. In the existing literature on black hole, if a neutron star collapses with the increasing gravitational force, the temperature of the star drops and eventually reaches the level of absolute zero at the mathematical singularity of black hole. There are difficulties in accepting this hypothesis.
At 0 K the molecules retain their internal energy, the zero-point energy. If the zero point energy is not kept hold of, then the atoms and electrons inside the molecule would allow their positions be determined precisely. That would be against Werner Heisenberg's uncertainty principle of 1927, the principle of indeterminacy. Uncertainty principle is based on quantum theory - which remains unaffected by the general theory of time. There is another predicament. If the molecule has a zero-point energy, the kinetic energy of atoms carries a positive value at 0 K. That provides the potential energy to the molecule by virtue of its known position at 0 K. Or, the singularity of black hole cannot be at 0 K; it has to be at a lower temperature - below 0 K. Neither the kinetic energy of the atoms nor the potential energy of the molecule can be conceived without associating time with them. Consequently, time cannot die out at 0 K as is required in the black hole literature. It is obvious that 0 K should not be the lowest limit of temperature.
It is not.
Absolute zero of temperature is the product of study of gases in physical chemistry; and they are the requirements of Boyle's Law (1662) and Charles's Law (1787) fortified later by Avogrado's Law (1811). All gases ought to liquefy or even solidify at 0 K, which is 273 K below the triple point of pure water; and the pure water boils and turns to vapour at 373 K, which indicates how the scale of K is graduated. These are the fundamentals of measurement in cryogenics that started with liquid oxygen at 90 K in 1877. The air could be liquefied at 40 K and separated into its major components in 1895. Helium was liquefied in 1908 at 4.2 K. It is obvious that the cryogenic temperature has been studied more extensively for gas rather than liquid and solid. Gas loses gaseousness at 0 K; so, there is an expectation of "no gas" state at 0 K. The gas laws work principally for this reason. Logically, therefore, a "no liquid" state below 0 K should be there, where all liquids, including liquid helium, would solidify.
In the study of the property of superconductivity of the solids, unwittingly, almost all equations assume that 0 K is the limit of temperature where entropy is zero. There is hardly an attempt made for the verification of these assumptions. Till 1997, when temperature as close to one millionth part of a centimetre away from 0 K could be reached, there was an obvious complacency that superconductivity of the conductors and non-conductors was to be investigated within the limit of 0 K at which entropy acquired the zero value.
Background of cryogenics
Johannes Diederik van der Waals (1837- 1923) of Holland won Nobel Prize for Physics in 1910 for his research on gaseous and liquid states of matter. One of his major contributions is what he had proposed in 1873 and come down to be known as the "van der Waals force" that says that the neutral molecules of gas, liquid and solids attract one another with a weak electric force, which is proportional to the inverse of the seventh power of the distance between the centres of the atoms or molecules. There are three ways these forces are generated. First is that the distribution of electric charge is sometimes distorted in "permanent electric dipoles", one side of the molecule being a bit positive and the other negative. A net force of mutual attraction of molecules results from it. Secondly, when such molecules with electric dipole stay alongside other molecules that are electrically neutral, they "induce" forces to turn the neutral molecules become "temporary electric dipoles" that pull each other. Thirdly, at sufficiently low temperature when gases condense to liquid, their molecules attract each other just because the phase of gas changes to the phase of liquid. Half a century later, in 1930, Fritz Wolfgang London, a German who was born in Polland and later became an American citizen, (1900-1954), showed that there was a constant disorientation of electric balance of a molecule: It is unlikely that at a given instant of time the centre of negative charge of the electrons and the centre of the positive charge of the nucleus would coincide. So the molecules attract each other because they carry this property of "time-varying dipole", adding attractive forces even for the molecules that are permanent electric dipoles all the time.
Atoms and molecules exist under the normal conditions of nature and they are the building blocks of matter that the human beings know about. The basic feature of the binding forces of atoms and molecules arise out of the uncertainty of quantum fluctuations in the distribution of the electrons that changes constantly as the electrons move "around" the nucleus of the atom, as aforesaid, a process that is internal to atom and "unseen" by the human beings with ordinary means. In gases, the molecules are independent entities. There is a low probability that the molecules of gas meet one another or collide against the wall of the container, especially at a low temperature; their mutual attractions do not depend upon, or arise erroneously from, the random meeting of the molecules.
The liquids are different. The volume of a given weight of gas is 1,600 times greater than the volume of an equal weight of liquid. When the temperature is kept above the "critical temperature", then the compression of a gas from 1,600 units of volume to 1 unit of volume does not affect the phase of gaseousness - gas remains compressed gas. On the other hand, if the temperature is lowered below the critical temperature, the gas turns abruptly liquid when compressed; thence the pressure remains unaltered till the whole of the gas turns liquid. Why this happens remains an unsolved problem of statistics and physics. In other words, at the critical volume or density, critical temperature and critical pressure, or at or above the "critical point" of fluid, liquid and its vaporous gas are the same; and below it they exist unfathomably.
Soon after, the search for similar critical points spread out, especially to the spheres of magnetism and electronics; and for mathematics the critical point remained stated thus: If a function is defined for n dimensional manifold, its behaviour may be studied by introducing n coordinates in which the function becomes just a function of the same coordinates. Such point or set of points is a critical point if its partial derivatives are zeros. The idea has application in finite calculus and study of arcs; however it is doubtful if logic allows this mathematical concept of critical point be applied to physics. On the other hand, the critical points obviously have the non-mathematical potential of replication for the change of state from liquid to solid at lower temperature, as had been suggested before in this essay, although such a change is not yet established for the simple reason that it involves the concept of temperature below 0 K - which is not yet acceptable, but should be.
The sameness of gas and liquid is only partly carried over to the solid phase of matter. When the assembled molecules carry no net charge, "dipole moments", the van der Waals force provides the crystal binding. An example is provided by the diatomic molecule of hydrogen that is gas in room temperature, liquid at 41 K and solid at 20 K. The molecular structure of hydrogen remains the same for its gaseous, liquid and solid phases and van der Waals forces provide the crystal binding. Covalently bound hydrogen acts like a "bigger" and electrically insulated molecule that are kept together by van der Waals forces in all phases. One may take a clue from it and pass on to the concept of "clusters" or the aggregates of atoms, molecules or ions that remain as tiny parcels, often for short periods. Clusters show effects on melting points of solid and electrical conductivity - like a cluster of a few atoms of mercury are insulators while the individual atoms of mercury conduct electricity. Importantly, it is not yet known why the properties of clusters differ with the size of the clusters.
The properties of solids found at normal temperature on the surface of earth are studied for their mechanical properties of "stress" and "deformation". When melted, as in metallurgy, the study of the aspects of "transformation" and "strength", etc., becomes important. [The iron of the ships sailing the waters of Antarctica turned brittle at sub-zero temperatures as per the news dispensators.] There is a cut off point of temperature below which the "frozen" metals show the properties of superconductivity. At temperatures below the transition temperature wherefrom the logarithm of the electronic specific heats tend to decrease inversely as the superconductivity moves to a higher state, the distribution of energy levels available to the electrons in the superconductor mismatch for all conductors, and even for those that are non-conductors at normal temperature. When the temperature is (1) further lowered and reaches closer to 0 K, (2) the matter is specific, like copper oxide - cuprate, and (3) the pressure is inconsequential, a second transition temperature is reached when the superconductivity of "no resistance" class sets in. The reason is assigned to "pairing of electron", Cooper pairs. The question naturally arises as to whether this is the last of the transition temperatures that had been studied. The mismatch of electronic excitation with thermal or other types of energy levels at 0 K should be unending, considering that (1) there must be a zero point energy, (2) molecular movements are theoretically eliminated, and (3) the electrons stay excited at least inside the molecule; there would be (4) a left out of free, or paired, or grouped electrons that retained energy at 0 K, because (5) it is not logical to assume that the process of super-superconductivity would terminate suddenly. It is possible that the electrons would assemble and (6) self-generation of power, failing in which a nova-like burst of energy, would result at another critical point of temperature! Thence, at another critical point of lower temperature (7) matter would dissipate into particles and neutrons into sub-particles, just like gases liquefy, and the particles and sub-particles would escape into the surrounding physicality of space.
Conscious time would accompany the particles and sub-particles; and also the sub-sub-particles when they are discovered.
Entropy is not "zero" at 0 K. The construction of the third law of thermodynamics is statistical and there can be doubts like (1) why a system should be at the ground state at 0 K with a logarithmic function of degeneracy, (2) when the hypothesis of zero-state of energy, which has the support of the quantum theory, has not been counteracted.
[Suggestion for research: The 1997 Nobel Prize for Physics was given to three scientists who had used laser beamed from several sides to slow down gas particles to create a pea sized cloud containing about one million chilled atoms. That process allowed reaching temperature that was about one millionth part of a centimeter above 0 K; and opened a new path of research. There are multifarious uses of laser in science and industry. So, it is expected that good research facilities and data are already available.
The optically pumped liquid state lasers may work in steps, laser in each step being cooler than the previous, (like liquid CO2, liquid oxygen, liquid helium providing three liquid laser steps), to examine if it is possible to cross the limit of 0 K by reducing the excitement of the electrons inside the atoms constituting the molecules kept close to 0 K. The difficulty is anticipated in a possible resonant behaviour of the electrons since their diameter is same as the wave length of light; but that may even help to reach the aim of the experiment, namely, temperature exists below 0 K.]
Use of black hole literature
Black hole is an image in Riemannian space and its associates are imagination time and idealistic space. These had been discussed in this web site and the references given be-low. The yearly reports on NASA sighting black hole, as for example in March 2004 and January 2005, are not convincing. The general theory of time rejects the use of relativity in space-time continuum for 'past' and 'present'; the black hole is not an event in the past that can now be seen through a telescope. The black hole should not exist; yet its literature is not devoid of value - it can be used, as for example, to understand the "low temperature".
A number of 'presumptions' are needed to uphold the concept of black hole and practically all of them need be questioned. One of them notably is the usability of the concept of "absolute zero temperature" producing "zero-entropy" in the mathematical singularity in-side the event horizon.
One may rename 0 K as the 'absolute-zero temperature for gas' and devise another term called 'absolute-zero temperature for liquid' allowing some liquid, like liquid helium that ostensibly survive the 'absolute-zero temperature for gas' and stay liquid, to follow the normal laws of change from liquid to solid phase at a critical point below 0 K. For the solid phase, there can be a term called 'absolute-zero temperature for solid' where solids are no longer molecules or atoms but become groups of electrons, like in a class of stars called white dwarf, or groups of neutrons, like in a neutron star. White dwarf is hot because the electrons do not stay inert on account of the uncertainty principle discussed before. The neutron stars are cold and get colder because they emit energy.
A digression is necessary. The force that keeps sub-particles together in a particle is stronger than the force that keeps particles together. The force that keeps particles together in an atom is stronger than the force that keeps atoms in an element together. The force that keeps atoms in an element together is stronger than the force that keeps element in a molecule together. This 'stronger than thou' of forces goes on and stops at gravity that is the weak force of cosmos. If atom or heavier build-ups are called 'solid', then the temperature at which atom loses energy to let the particles go, may be called the 'absolute-zero temperature for solid'.
In black hole, the force of gravity increases and expected to reach the level of 'infinite' force. As gravity goes on increasing, matter is literally hard-pressed and their composition gets compromised due to extreme compression. Then, the composite solidity of matter may give way to create more room to let matter-structures survive. If the composite breaks half and half 'at an earlier stage', and rounded, the split twoness of the composite becomes about one-fourth of the original oneness of the rounded composite volume. If mass of each of the twoness of the composite is yet larger than the critical mass required for forming black hole, then gravity would press on to let two black holes happen. If one is larger than the critical mass while other is not, then one of the two is pressed on to become black hole while the other one stays on as dense star. Should the split be at one to nine ratios, the rounded splits retain three-fifth of the original rounded compositeness. Therefore, there is a good possibility that chipping away of the bits of the black hole material is more likely than an outright split of half and half or in other proportions. The process would start, evidently, much before 'absolute temperature for solid' is reached. It is possible that that happens thus: The temperature of black hole has to reach the level where entropy would acquire zero-value to let time die out. On its way, and before the death of time, gravity certainly reaches the level of force to counteract the force that keeps the particles and sub-particles together in the 'cool state for atom' at 'absolute-zero temperature for solid', which is not cool enough for particles and sub-particles; and that enhanced force of gravity let the particles and sub-particles dance away to places outside the confine of the atomic structure! This may be called the "freeze decay".
It can be said in short that the general theory of time reveals a new and fascinating as-pect of temperature and gravity. There are different and special absolute zero temperatures for gas, liquid and solid. When 'absolute zero temperature of solid' is nearly reached and the internal 'binding' energy of matter is dissipated below a critical limit, there are conditions that the force of gravity may be higher than the force that keeps the particles and the sub-particles of solid together. At that stage a 'freeze decay' of matter may start.
At very low temperature matter turns to dissolute particles just like it does at very high temperature and pressure in laboratory, or in relativistic imaginations like "before" big bang.
Matter, as we know it, exists between two critical points of temperature, just like life does.
The lowest limit of temperature would be lower than 0 K.
It is unlikely that entropy can attain a zero value at 0 K.
There is a critical point at a very low temperature where the molecules, atoms and even neutrons lose energy to such an extent that they cannot keep the constituent electrons and other particles together, and decay; and whence the electrons, other particles and sub-particles that compose the molecules, atoms and neutrons dance away into the space surrounding the molecules, atoms and neutrons, [may be after a burst of energy that we, the human beings, will be able to harness some time in the future].
Or, the molecules, atoms and neutrons become non-existent below a critical point of temperature, which is much below 0 K.
That may account for the mismatch of the estimate of matter and energy in the cosmos than what is observed.
Or, a theory of "black matter" and "black energy" may not be necessary.
- Barthakur, Jitendra Kumar; Time; Kumud Books, C-8806 Vasant Kunj, New Delhi - 110070, India; 1999
- Barthakur, Jitendra Kumar; General Theory of Time; Kumud Books, C-8806 Vasant Kunj, New Delhi - 110070, India; 2004