Sanford

Okay, then entropy is an intermediate quantity, like the wave function.

Newtonian gravitation is a valid theory of physics. The mathematical basis is clear and consistent. There is agreement with observations. Special relativity is also a valid theory. SR agrees with observations more than Newtonian, such as the Mercury orbit. Stat mech and entropy is not a valid theory. We cannot speak about the number of possible arrangements of molecules in a gas as we cannot observe this. Second law of thermo prohibits adding energy to a gas and extracting the same energy. However, this imaginary processes is behind imagining possible arrangements of the molecules. We must not discuss impossible things. An example is that even God does not know the positions of the atoms of superfluid helium except to say they are in the container.

Let us not confuse physics with a physics theory.

Summary of my position: A mathematical system starts with arbitrary consistent statements, and concludes with the logical conclusions. A physical theory is a mathematical system along with empirical verifications. All quantities must start with observable quantities or the conclusions from observable quantities. Do you disagree with any of this?

The point is that light is defined from Maxwell's equations. What are you saying? Sorry, but you lost me. Talk to me in physics. I mentioned several points about entropy. Where do you disagree?

Right. But A. Einstein wrote in his paper that constant light speed is a postulate.

We physicists must be careful to insure that theories begin with correct principles. One basic principle is that all quantities must be capable of being observed or measured. If a theory uses a quantity that cannot be observed, then it is not a physics theory, but a hypothesis or a phenomenological explanation. These are important logical explanations, and possibly quite useful for proper applications, but not a proper theory. We must continue our efforts to find a proper theory. An example of a theory that does not begin from basic principles is special relativity as originally expressed by Einstein. He postulated the speed of light is constant in all inertial frames. His mistake is that light is not fundamental, but a consequence of Maxwell's Equations, ME. The correct way to develop this theory is to postulate that ME is valid in all inertial frames. Entropy is phenomenological, not a basic concept of physics, at the current state of physics. In statistical mechanics, SM, entropy is defined as the log of the number of possible arrangements of the molecules. This cannot be measured, and so current ideas about entropy are not part of a physics theory. The idea is that we can move a molecule of a gas to a higher energy state, and simultaneously move a molecule at this higher energy state to a lower state, so that the total energy is constant. We can imagine performing this experiment using lasers. There are two issues. One is that there is no observable difference between these two states, and so to discuss the number of such states is not meaningful physics. Second, we cannot imagine performing this experiment. A principle of thermodynamics is that we cannot add energy to a system and remove the same energy. Let us illustrate this with superfluid helium. The entropy is zero. We cannot picture this as individual helium atoms each having position and momentum, the way we picture helium gas, except to say the atoms are in the container. Since there is no possible way to rearrange the atoms, the entropy is zero. The concepts of position and momentum are not valid for the atoms of superfluid helium. By the way, this is a beautiful example of quantum mechanics on the macroscopic level. Just as we cannot picture the position and momentum of an atom of superfluid helium, we cannot picture the rearrangement, at constant system energy, of atoms of helium gas. If we cannot picture this and cannot measure it, it cannot be a fundamental principle. Entropy is a very useful concept in thermodynamics. In SM, we can define the probability of particles, p(i) with energy E(i). This is because in QM there are discrete numbers of energy levels. We can define the temperature of a system by measuring heat flow. The Boltzmann assumption is a meaningful statement as it involves meaningful quantities. We can define the partition function and energy U. We would like to continue and derive the thermodynamics potentials, such as A and S (entropy). If we succeed in this derivation, we can then say entropy is a meaningful concept. We need to search for a derivation of entropy that starts with SM and not with the unphysical idea that entropy is the log of the possible rearrangements. Once we correctly derived entropy, we can then show, as a result of the theory's postulates, things like Gibbs' expression for entropy and say that this shows that entropy is the log of all possible rearrangements. This would be fine; it is not fine to start with this as the first step. Here is a paper that started my thinking. Entropy.pdf

The statement, “A black hole is a region of spacetime whose gravitational field is so strong that nothing which enters it, not even light, can escape”, taken from Wald, Robert M., General Relativity (1984) is dated. 21st publications clearly show this statement to be false. This is discussed by Aranoff in “Basic Assumptions and Black Holes”, Physics Essays 22, 559 (2009), and by Aranoff in Teaching and Helping Students Think and Do Better (2007). It is also discussed by Hynecek, “The Galileo effect and the general relativity theory”, Physics Essays 22, 4 (2009). This paper makes the following statement, “The Schwarzschild metric, which is the vacuum solution of Einstein field equations, is clearly a nonphysical metric and predicts the existence of such absurdities as black holes.” It is surprising that people still accept old incorrect ideas! The reasoning is simple. Due to time dilation, it takes forever to reach the black hole, and so it is meaningless to speak about the “inside”. The puzzle is that why then do so many discuss the inside. There is another solution of the equations for the viewpoint of an observer falling down the black hole. According to this solution, he enters the black hole in a finite time. However, this solution is not valid, as mathematicians have proven that at the center of the black hole there is a singularity, that is, the solution is not valid.

Prof. Hawking said the world is like a goldfish bowl. Just as the fish knows only the bowl, we only know what we see. Hawking simply does not understand what science is, for him to make such a statement! A science theory is based upon mathematics, which is a collection of arbitrary fully consistent statements. The theory must also agree somewhat with observations and experiments. The fish does not understand mathematics, as mathematics is a human creation, and so the fish does not have a scientific understanding of the world. General Relativity is a valid theory, as the mathematics is consistent, and many observations (not all) agree with the theory. Quantum mechanics is also a valid theory. However, these conflict, as the mathematical assumptions are different. We can live with this conflict, as relativity deals with large objects like planets, and quantum mechanics deals with small objects like atoms. Currently, it is impossible to measure the gravitational force between two atoms, and so we cannot make an experiment to determine which theory is correct. Hawking speaks a lot about the nature of the universe. Here he is out of his league. There is currently no theory of cosmology, that is, there is no consistent mathematical framework that agrees with observations. The reason is that current theories, general relativity and quantum mechanics conflict with each other, and both are needed for a correct explanation of cosmology. All discussions of cosmology, such as the Big Bang idea, are hypotheses, that is, guesses, not rigorous scientific theories. We must be careful not to confuse theories, which are rigorous explanations, with hypotheses, which are guesses hopefully paving the way to a theory.

Enough with this theoretical nonsense, like medieval scholars debating the number of angels on a pin. Please clarify the basic assumptions of GR, and how we can devise experiments to verify this. I do not mean experiments that verify various conclusions, such as the orbit or Mercury, but experiments that verify the two initial assumptions as Weinberg presented it in his 1972 book.

Someone emailed me the following statement that does not make sense to me. "The Einstein theory is an example of a non-linear theory in which the stress energy tensor vanishes in a mass zero zone." Is there any evidence of nonlinearity? How can the tress energy tensor vanish near a mass when the field does not vanish?

Wrong. True only in a mass free zone. Otherwise, mass does contribute to T.