Ludwig Boltzmann Quotes

Which is more remarkable fact about America: that millionaires are idealists or idealists become millionaires.

[W]e will consider the , rather than the velocity of the molecules. Each molecule can have only a finite number of values for its kinetic energy. As a further simplification, we assume that the kinetic energies of each molecule form an ...<math>0,\epsilon,2\epsilon,2\epsilon,...p\epsilon</math>We call <math>P</math> the largest possible value of the kinetic energy, <math>p\epsilon</math>. ...after the collision, each molecule still has one of the above values of kinetic energy.

I am conscious of being only an individual struggling weakly against the stream of time. But it still remains in my power to contribute in such a way that, when the theory of gases is again revived, not too much will have to be rediscovered.

The possibility of the transference of energy being so gradual cannot be denied, if we also attribute to the ether so little friction that the Earth is not sensibly retarded by moving through it for many hundreds of years.

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.

[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.

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.

But if we ask why this state is not yet reached, we again come to a "Salisburian mystery."
I will conclude this paper with an idea of my old assistant, Dr. Schuetz.
We assume that the whole universe is, and rests for ever, in thermal equilibrium. The probability that one (only one) part of the universe is in a certain state, is the smaller the further this state is from thermal equilibrium; but this probability is greater, the greater is the universe itself. If we assume the universe great enough, we can make the probability of one relatively small part being in any given state (however far from the state of thermal equilibrium), as great as we please. We can also make the probability great that, though the whole universe is in thermal equilibrium, our world is in its present slate. It may be said that the world is so far from thermal equilibrium that we cannot imagine the improbability of such a state. But can we imagine, on the other side, how small a part of the whole universe this world is? Assuming the universe great enough, the probability that such a small part of it as our world should be in its present state, is no longer small.

O! immodest mortal! Your destiny is the joy of watching the evershifting battle!

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 be so—and hardly any physicist will contradict this—then neither the Theory of Gases nor any other physical theory can be quite a congruent account of facts, and I cannot hope with Mr. Burbury, that Mr. Bryan will be able to deduce all the phenomena of spectroscopy from the electromagnetic theory of light. Certainly, therefore, Hertz is right when he says: "The rigour of science requires, that we distinguish well the undraped figure of nature itself from the gay-coloured vesture with which we clothe it at our pleasure." But I think the predilection for nudity would be carried too far if we were to forego every hypothesis. Only we must not demand too much from hypotheses.

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>

We assume initially, each molecule is only capable of assuming a finite number of velocities...<math>0, \frac{1}{q},\frac{2}{q},\frac{3}{q},...\frac{p}{q}</math>where <math>p</math> and <math>q</math> are arbitrary finite numbers. ...but after the collision both molecules still have one of the above velocities ...the actual problem to be solved is re-established by letting p and q go to infinity.

[I]t is possible to calculate the state of the equilibrium of heat by finding the probability of the different possible states of the system.

The first question I answer in the affirmative, but the second belongs not so much to ordinary physics (let us call it orthophysics) as to... metaphysics.