Ludwig Boltzmann Quotes

Every hypothesis must derive indubitable results from mechanically well-defined assumptions by mathematically correct methods. If the results agree with a large series of facts, we must be content, even if the true nature of facts is not revealed in every respect. No one hypothesis has hitherto attained this last end, the Theory of Gases not excepted.

If this theory were to hold good for all phenomena, we should be still a long way off what Faust's famous famulus [Wagner] hoped to attain, viz., to know everything. But the difficulty of enumerating all the material points of the universe, and of determining the law of mutual force for each pair, would be only a quantitative one; nature would be a difficult problem, but not a mystery for the human mind.

[I]t is our main purpose not to limit our discussion to thermal equilibrium, but to explore the relationship of this probabilistic formulation to the second theorem of the mechanical theory of heat.

When Lord Salisbury says that nature is a mystery, he means... that this simple conception of Boscovich is refuted almost in every branch of science, the Theory of Gases not excepted. The assumption that the molecules are aggregates of material points, in the sense of Boscovich, does not agree with the facts. But what else are they? And what is the ether through which they move? Let us again hear Lord Salisbury. He says<blockquote>"What the atom of each element is, whether it is a movement, or a thing, or a vortex, or a point having inertia, all these questions are surrounded by profound darkness. I dare not use any less pedantic word than entity to designate the ether, for it would be a great exaggeration of our knowledge if I were to speak of it as a body, or even as a substance."</blockquote>

These transverse vibrations are not produced (as in the older theories of light) by simple atomic vibrations, but their pitch depends on the shape of the hollow space which the molecule forms in the ether, just as Hertzian waves are not caused by vibrations of the ponderable matter of the brass balls, the form of which only determines the pitch.

Bring forward what is true, Write it so that it is clear, Defend it to your last breath!

It is clear that every single uniform state distribution which establishes itself after a certain time given a defined initial state is equally as probable as every single nonuniform state distribution, comparable to the situation in the game of Lotto where every single quintet is as improbable as the quintet 12345. The higher probability that the state distribution becomes uniform with time arises only because there are far more uniform than nonuniform state distributions... It is even possible to calculate the probabilities from the relationships of the number of different state distributions. This approach would perhaps lead to an interesting method for the calculation of the equilibrium of heat.

We want first to solve the problem... namely to calculate the probability of state distributions from the number of different distributions. We want first to treat as simple a case as possible, namely a gas of rigid absolutely elastic spherical molecules trapped in a container with absolutely elastic walls. Even in this case, the application of is not easy. The number of molecules is not infinite... yet the number of velocities each molecule is capable of is effectively infinite... to facilitate understanding, I will... consider a limiting case.

I take my stand before you as a reactionary, a survivor, who is still an enthusiast for the old and the classical as opposed to the modem.

It may be objected that the above is nothing more than a series of imperfectly proved hypotheses. But granting its improbability, it suffices that this explanation is not impossible. For then I have shown that the problem is not insoluble, and nature will have found a better solution than mine.

Mr. Culverwell says that my theorem cannot be true because if it were true every atom of the universe would have the same average , and all energy would be dissipated. I find, on the contrary, that this argument only lends to confirm my theorem, which requires only that in the course of time the universe must tend to a state where the average vis viva of every atom is the same and all energy is dissipated, and that is indeed the case.

The initial state in most cases is bound to be highly improbable and from it the system will always rapidly approach a more probable state until it finally reaches the most probable state, i.e., that of the heat equilibrium.

If this assumption were correct, our world would return more and more to ; but because the whole universe is so great, it might be probable that at some future time some other world might deviate as far from thermal equilibrium as our world does at present. Then the aforementioned H-curve would form a representation of what takes place in the universe. The summits of the curve would represent the worlds where visible motion and life exist.

Let us now tum to the second matter in dispute between us [about the rejection of philosophy in virtually all senses]. That the majority of students don't understand philosophy doesn't bother me. But can any two people understand philosophical [i.e. metaphysical] questions [and agree upon what it is that they understand]? Is there any sense at all in breaking one's head over such questions? Shouldn't the irresistible pressure [Drang] to philosophize be compared with the nausea caused by migraine headaches? As if something could still struggle its strangled way out, even though nothing is actually there at all? My opinion about the high, majestic task of philosophy is to make things clear, in order to finally heal mankind from these terrible migraine headaches. Now, I am one who hopes not to make you angry by my forthrightness, but the first duty of philosophy as love of wisdom is complete frankness. Through my study of Schopenhauer, I am learning Greek ways of thinking again, but piecemeal.

Let the molecules of certain es behave as rigid bodies. The molecules of the gas and of the enclosing vessel move through the ether without loss of energy as rigid bodies, or as Lord Kelvin's vortex rings move through a frictionless liquid in ordinary hydrodynamics. If we were to take a vessel filled with one gram of gas kept during an infinitely long time always at 0° C. and containing always the same portion of ether, every atom of ether and every atom of our gas molecules would reach the same average . If then we were to raise the temperature to 1° C and to wait till every ponderable and every ether atom was in , the total energy would be augmented by what we may call the ideal specific heat.