| History 2: Young, Helmholtz, Riemann, Maxwell, Weyl, Schrödinger, Heisenberg, Dirac, Einstein | ||||||
![]() Thomas Young 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."
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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. ![]() Young's double-slit experiment |
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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 S1 is transferred unchanged to the other S2. 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 |
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![]() Hermann von Hemhholtz 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.
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![]() Bernhard Riemann |
[...]so few and far between are the occasions for forming notions whose specialisations make up a continuous manifoldness, that the only simple notions whose specialisations form a multiply extended manifoldness are the positions of perceived objects and colours. More frequent occasions for the creation and development of these notions occur first in the higher mathematic. Definite portions of a manifoldness, distinguished by a mark or a boundary, are called Quanta [...]
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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. ![]() |
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![]() James Clerk Maxwell |
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![]() Hermann Weyl 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.
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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. ![]() |
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What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just schaumkommen (appearances). ... The world is given to me only once, not one existing and one perceived. Subject and object are only one. The barrier between them cannot be said to have broken down as a result of recent experience in the physical sciences, for this barrier does not exist. ... The scientist only imposes two things, namely truth and sincerity, imposes them upon himself and upon other scientists.
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![]() Erwin 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.
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![]() Werner Heisenberg ![]() |
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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. |
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| 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 | ![]() PAM 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. ![]() | |||||
![]() 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. ![]() |
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. |
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| History 3: Russell, Whitehead, Pauli, Bohm, Bell, Feynman, Lockwood, Churchland | ||||||