Q&C




History 2: Young, Helmholtz, Riemann, Maxwell, Weyl, Schrödinger, Heisenberg, Dirac, Einstein                                                       1, 3, 4












Young



















Feynman


Thomas Young
Young


Much as I venerate the name of Newton, I am not obliged to believe that he was infallible. I see ... with regret that he was liable to err, and that his authority has, perhaps, sometimes even retarded the progress of science.


The course of nature is the art of God.


Repeated time and again with unimaginably more sophisticated and sensitive apparatus than Young's, the double-slit experiment encapsulates, said the physicist Richard Feynman, the "heart of quantum mechanics," its "only mystery."


§

Polymaths have always posed a problem in academia. How do they relate to specialization and interdisciplinarity, genius and dilettantism, inspiration and perspiration? Robert Hooke, Benjamin Franklin and Alexander von Humboldt were among those who were too academically wide-ranging for posterity to cope with, and their scientific reputations suffered as a consequence. Individual curiosity is the driving force of science, but when insatiable, can it hamper the intellectual? The life and work of the polymath Thomas Young (1773-1829) illuminates the issue perhaps more acutely than that of any other scientist. Today, views of Young span the spectrum from near-universal genius to dabbling dilettante. Those who appreciate him
especially physicists, physiologists and Egyptologists admire his range, his intuition and his far-sightedness. Those who do not, depreciate these same aspects of his life and work as sloppiness and opportunism.

 Robinson


What we see is the solution to a computational problem; our brains compute the most likely causes from the photon absorptions within our eyes.


The physiology of the senses is a border land in which the two great divisions of human knowledge, natural and mental science, encroach on one another’s domains; in which problems arise which are important for both, and which only the combined labor of both can solve.

§

Similar light produces, under like conditions, a like sensation of color.

Helmholtz



Hamiltonian

Hamiltonian


Mathematics has introduced the name isomorphic representation for the relation which according to Helmholtz exists between objects and their signs. I should like to carry out the precise explanation of this notion between the points of the projective plane and the color qualities [...] the projective plane and the color continuum are isomorphic with one another. Every theorem which is correct in the one system Σ1 is transferred unchanged to the other Σ2. A science can never determine its subject matter except up to an isomorphic representation. The idea of isomorphism indicates the self-understood, insurmountable barrier of knowledge. It follows that toward the "nature" of its objects science maintains complete indifference. This for example what distinguishes the colors from the points of the projective plane one can only know in immediate alive intuition.

Weyl
 
  



Young made a pioneering contribution to the understanding of light by demonstrating interference patterns, known as "Young's fringes", around 1800, which led to the Young-Fresnel undulatory theory. He also formulated an important measure of elasticity, called "Young's modulus." He was the first to explain the accommodation of the eye; he discovered the phenomenon of astigmatism; and he proposed the three-color theory of vision.

Robinson


Thomas Young recognized that if light behaved like a wave it would be possible to create patterns of constructive and destructive interference using light. In 1801 he devised an experiment that would force two beams of light to travel different distances before interfering with each other when they reached a screen.

Stites



Young's interference

Young's double-slit experiment


In 1931, Einstein paid tribute to him in a brief foreword to Newton's Opticks; he referred to Newton's observations of the colors of thin films "as the origin of the next great theoretical advance, which had to await, over a hundred years, the coming of Thomas Young."


The term energy may be applied, with great propriety, to the product of mass or weight of a body, into the square of the number expressing its velocity. Thus, if the weight of one ounce moves with a velocity of a foot in a second, we call its energy 1; if a second body of two ounces has a velocity of three feet in a second, its energy will be twice the square of three, or 18.

§

Supposing the light of any given colour to consist of undulations, of a given breadth, or of a given frequency, it follows that these undulations must be liable to those effects which we have already examined in the case of the waves of water, and the pulses of sound. It has been shown that two equal series of waves, proceeding from centres near each other, may be seen to destroy each other's effects at certain points, and at other points to redouble them; and the beating of two sounds has been explained from a similar interference. We are now to apply the same principles to the alternate union and extinction of colors.

Young



Helmholtz
Hemhholtz


Whoever, in the pursuit of science, seeks after immediate practical utility, may generally rest assured that he will seek in vain.

The most startling result of Faraday's Law is perhaps this. If we accept the hypothesis that the elementary substances are composed of atoms, we cannot avoid concluding that electricity also, positive as well as negative, is divided into definite elementary portions, which behave like atoms of electricity.

I have been able to solve a few problems of mathematical physics on which the greatest mathematicians since Euler have struggled in vain ... But the pride I might have held in my conclusions was perceptibly lessened by the fact that I knew that the solution of these problems had almost always come to me as the gradual generalization of favorable examples, by a series of fortunate conjectures, after many errors. I am fain to compare myself with a wanderer on the mountains who, not knowing the path, climbs slowly and painfully upwards and often has to retrace his steps because he can go no further—then, whether by taking thought or from luck, discovers a new track that leads him on a little till at length when he reaches the summit he finds to his shame that there is a royal road by which he might have ascended, had he only the wits to find the right approach to it. In my works, I naturally said nothing about my mistake to the reader, but only described the made track by which he may now reach the same heights without difficulty.




Riemannian geometry


[So] few and far between are the occasions for forming notions whose specialisations make up a continuous manifold, that the only simple notions whose specialisations form a multiply extended manifold are the positions of perceived objects and colors. More frequent occasions for the creation and development of these notions occur first in the higher mathematic.

Definite portions of a manifold, distinguished by a mark or a boundary, are called Quanta [...]

Riemann










Helmholtz
Main menu
Riemann  

Riemann
Riemann

Therefore, either the reality on which our space is based must form a discrete manifold or else the reason for the metric relationships must be sought for, externally, in the binding forces acting on it.

What remains to be resovled is the question of knowing to what extent and up to what point these hypotheses are found to be confirmed by experience.


      manifold
Maxwell

When a beam of light falls on the human eye, certain sensations are produced, from which the possessor of that organ judges of the color and luminance of the light. Now, though everyone experiences these sensations and though they are the foundation of all the phenomena of sight, yet, on account of their absolute simplicity, they are incapable of analysis, and can never become in themselves objects of thought. If we attempt to discover them, we must do so by artificial means and our reasonings on them must be guided by some theory.
Maxwell


Main menu JC Maxwell
Maxwell



Weyl
Hermann Weyl
Weyl


God exists since mathematics is consistent, and the devil exists since its consistency cannot be proved.

In our time, the angel of topology and the devil of abstract algebra are fighting for every mathematical domain.

Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.

Symmetry, as wide or narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty, and perfection.


symmetry



Main menu
Epistemologically it is not without interest that in addition to ordinary space there exists quite another domain of intuitively given entities, namely the colors, which forms a continuum capable of geometric treatment.

§

The characteristic of an n-dimensional manifold is that each of the elements composing it (in our examples, single points, conditions of a gas, colors, tones) may be specified by the giving of n quantities, the "co-ordinates," which are continuous functions within the manifold.

§

Thus the colors with their various qualities and intensities fulfill the axioms of vector geometry if addition is interpreted as mixing; consequently, projective geometry applies to the color qualities.

§

The processes on the retina produce excitations which are conducted to the brain in the optic nerves, maybe in the form of electric currents. Even here we are still in the real sphere. But between the physical processes which are released in the terminal organ of the nervous conductors in the central brain and the image which thereupon appears to the perceiving subject, there gapes a hiatus, an abyss which no realistic conception of the world can span. It is the transition from the world of being to the world of appearing image or of consciousness.

Weyl
 

continuum













 projective
Schrödinger  
What this something is cannot be said; by calling it matter or field or whatnot, we just give it a name. The relevant point is that it is not supposed to have any other properties but geometrical configuration, changing in time according to certain "laws of nature." It is not in itself yellow or green, sweet or cold. If parts of it appear to us so, there is no hard, indubitable fact to make this judgment true or false.

This view is strongly supported by our analysis of actual experimental procedure, and it is attractively simple. It carries us comfortably a long way, indeed so long, that we may have forgotten its artificiality, when we meet the obstacles that it renders unsurmountable. So it is better to ask the naive but very pertinent question right away: how do red and yellow, sweet and hot come in at all? Once we have removed them from our "objective reality," we are at a desperate loss to restore them. We cannot remove them entirely, because they are there, we cannot argue them away. So we have to give them a living space, and we invent a new realm for them, the mind, saying that this is where they are, and forgetting the earlier part of the storyall that we have been talking about till nowis also in the mind and nowhere else. But deeming it to be something elseobjective realitywe run against the unanswerable question: how does matter act on mind, to produce in it the sensory qualitiesand also how does mind act on matter, to move it at will? These questions cannot, so I believe, be answered in this form, and they owe their embarrassing form precisely to our having posited an objective reality which is a pure geometrical scheme of thought and deprived of everything real given by experience.

Schrödinger




Erwin Schrödinger
Schrödinger


Let me say at the outset, that in this discourse, I am opposing not a few special statements of quantum physics held today (1950s), I am opposing as it were the whole of it, I am opposing its basic views that have been shaped 25 years ago, when Max Born put forward his probability interpretation, which was accepted by almost everybody.



wave equation




Heisenberg

Werner Heisenberg
Heisenberg


matrix mechanics


Main menu


Therefore, the transition from the 'possible' to the 'actual' takes place during the act of observation. If we want to describe what happens in an atomic event, we have to realize that the word 'happens' can apply only to the observation, not to the state of affairs between two observations. It applies to the physical, not the psychical act of observation, and we may say that the transition from the 'possible' to the 'actual' takes place as soon as the interaction of the object with the measuring device, and thereby the rest of the world, has come into play; it is not connected with the act of registration of the result by the mind of the observer. The discontinuous change in the probability function, however, takes place with the act of registration, because it is the discontinuous change of our knowledge in the instant of registration that has its image in the discontinuous change of the probability function.

Heisenberg


particles
matrix









Dirac
When a state is formed by the superposition of two other states, it will have properties that are in some vague way intermediate between those of the original states and that approach more or less closely to those of either of them according to the greater or less 'weight' attached to this state in the superposition process. The new state is completely defined by the two original states when their relative weights in the superposition process are known, together with a certain phase difference, the exact meaning of weights and phases being provided in the general case by the mathematical theory. When a state is formed by the superposition of two other states, it will have properties that are in some vague way intermediate between those of the original states and that approach more or less closely to those of either of them according to the greater or less 'weight' attached to this state in the superposition process. The new state is completely defined by the two original states when their relative weights in the superposition process are known, together with a certain phase difference, the exact meaning of weights and phases being provided in the general case by the mathematical theory.

Dirac
Albert Einstein
Einstein


By his clear critique Hume did not only advance philosophy in a decisive way but also - though through no fault of his - created a danger for philosophy in that, following his critique, a fateful 'fear of metaphysics' arose which has come to be a malady of contemporary empiricist philosophising; this malady is the counterpart to that earlier philosophising in the clouds, which thought it could neglect and dispense with what was given by the senses. ... It finally turns out that one can, after all, not get along without metaphysics.

§

Physics constitutes a logical system of thought which is in a state of evolution, whose basis (principles) cannot be distilled, as it were, from experience by an inductive method, but can only be arrived at by free invention. The justification (truth content) of the system rests in the verification of the derived propositions (a priori/logical truths) by sense experiences (a posteriori/empirical truths). ... Evolution is proceeding in the direction of increasing simplicity of the logical basis (principles) ... We must always be ready to change these notions
that is to say, the axiomatic basis of physics  in order to do justice to perceived facts in the most perfect way logically.

Einstein


symmetry



Dirac
Dirac

It seems clear that the present quantum mechanics is not in its final form [...] I think it very likely, or at any rate quite possible, that in the long run Einstein will turn out to be correct.











 superposition



















Einstein


Russell


Hume

The more aristocratic illusion concerning the unlimited penetrative power of thought has as its counterpart the more plebeian illusion of naive realism, according to which things 'are' as they are perceived by us through our senses. This illusion dominates the daily life of men and of animals; it is also the point of departure in all of the sciences, especially of the natural sciences.

As Russell wrote:

'We all start from naive realism, i.e., the doctrine that things are what they seem. We think that grass is green, that stones are hard, and that snow is cold. But physics assures us that the greenness of grass, the hardness of stones, and the coldness of snow are not the greenness, hardness, and coldness that we know in our own experience, but something very different. The observer, when he seems to himself to be observing a stone, is really, if physics is to be believed, observing the effects of the stone upon himself.'


Gradually the conviction gained recognition that all
knowledge about things is exclusively a working-over of the raw material furnished by the senses. Galileo and Hume first upheld this principle with full clarity and decisiveness. Hume saw that concepts which we must regard as essential, such as, for example, causal connection, cannot be gained from material given to us by the senses.

§


As soon as one is at home in Hume's critique one is easily led to believe that all those concepts and propositions which cannot be deduced from the sensory raw material are, on account of their 'metaphysical' character, to be removed from thinking. For all thought acquires material content only through its relationship with that sensory material. This latter proposition I take to be entirely true; but I hold the prescription for thinking which is grounded on this proposition to be false. For this claim 
if only carried through consistently  absolutely excludes thinking of any kind as 'metaphysical.' In order that thinking might not degenerate into 'metaphysics,' or into empty talk, it is only necessary that enough propositions of the conceptual system be firmly enough connected with sensory experiences and that the conceptual system, in view of its task of ordering and surveying sense experience, should show as much unity and parsimony as possible.

Einstein





     
History 3: Russell, Whitehead, Pauli, Bohm, Bell, Feynman, Lockwood, Churchland




powered by FreeFind