Ludwig Boltzmann Quotes

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

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

It is curious to see that in Germany, where till lately the theory of was much more cultivated than in Newton’s native land itself, where Maxwell’s theory of electricity was not accepted, because it does not start from quite a precise hypothesis, at present every special theory is old-fashioned, while in England interest in the Theory of Gases is still active; vide, ...the excellent papers of Mr. Tait, of whose ingenious results I cannot speak too highly, though I have been forced to oppose them in certain points.

The system of particles always changes from an improbable to a probable state.

It can never be proved from the alone, that the minimum function H must always decrease. It can only be deduced from the laws of probability, that if the initial state is not specially arranged for a certain purpose, but haphazard governs freely, the probability that H decreases is always greater than that it increases. It is well known that the theory of probability is as exact as any other mathematical theory, if properly understood. If we make 6000 throws with dice, we cannot prove that we shall throw any particular number exactly 1000 times; but we can prove that the ratio of the number of throws in which that number turns up to the whole number of throws, approaches the more to 1/6 the oftener we throw.

[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.

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.

But this theory agrees in so many respects with the facts, that we can hardly doubt that in es certain entities, the number and size of which can roughly be determined, fly about pell-mell. Can it be seriously expected that they will behave exactly as aggregates of Newtonian centres of force, or as the rigid bodies of our Mechanics? And how awkward is the human mind in divining the nature of things, when forsaken by the analogy of what we see and touch directly?

The following assumptions, while not professing to explain the mysteries... nevertheless show that it is possible to explain the spectra of gases while ascribing 5 degrees of freedom to the molecules, and without departing from Boscovich's standpoint.

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.

[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.

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.

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.

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. Thus in this book [this Part] I will now include the parts that are the most difficult and most subject to misunderstanding, and give (at least in outline) the most easily understood exposition of them.

Wie ohnmächtig der Einzelne gegen Zeitströmungen bleibt, ist mir bewusst. Um aber doch, was in meinen Kräften steht, dazu beizutragen, dass, wenn man wieder zur Gastheorie zurückgreift, nicht allzuviel noch einmal entdeckt werden muss, nahm ich in das vorliegende Buch nun auch die schwierigsten, dem Missverständnisse am meisten ausgesetzten Theile der Gastheorie auf und versuchte davon wenigstens in den Grundlinien eine möglichst leicht verständliche Darstellung zu geben.