Quantum

“ This is perhaps a particularly favorable epoch in the history of physics to urge the essential complexity of nature, because all our new quantum phenomena indicate a vast wealth of hitherto unsuspected relations on the very edge of the attainable. There is one aspect of quantum relations, as also of our ideas of the nature of the structure of the nucleus of the atom, which is particularly significant in this respect, namely, that we have to describe phenomena by statistical methods. ”

“ In the discussion of these questions, it must be kept in mind that, according to the view taken above, radiation in free space as well as isolated material particles are abstractions, their properties on the quantum theory being definable and observable only through their interaction with other systems. ”

“ The postulates of the quantum theory. The quantum theory in the form in which it has been applied to the problems of atomic structure rests upon two postulates which have a direct bearing on the difficulties mentioned above. According to the first postulate there are certain states in which the atom can exist without emitting radiation, although the particles are supposed to have an accelerated motion relative to one another. ”

“ The unexpected phenomenon is that instead of each atom absorbing one-millionth of a quantum, one atom out of every million absorbs a whole quantum. That whole quanta are absorbed is shown by the photoelectric experiments already described, since each of the issuing electrons has managed to secure the energy of a whole quantum. ”

“ While quantum mechanics was busy overthrowing other pillars of classical physics, it seemed to only reinforce this one: the whole is nothing more than the sum of its parts. While the behavior of that sum may be difficult (or even impossible) to predict sometimes just by looking at the parts, there’s nothing fundamentally new to be learned by looking at systems; any higher-level scientific laws are just special cases, course-grainings, or simplifications of the story that fundamental physics has to tell. ”

“ Experiment has isolated what are believed to be units of action, which at least in many phenomena behave as indivisible atoms called quanta; but the theory, as at present developed, does not permit us to represent the quantum of action by the number 1. The quantum is a very minute fraction of the absolute unit. ”

“ As far as we now know, quantum phenomena are always associated with atoms. We make for the atom a mental model with all the properties of the mechanisms of the ordinary scale of magnitude and with a few impressed properties in addition which represent the new quantum relations. As we now think of it, the atom has a massive core about which electrons revolve under an inverse square law, the connection between the mass of the electron, its acceleration, and the force acting on it being that usual in Newtonian mechanics. ”

“ For example, many quantum phenomena are made to involve the emission of energy when an electron jumps from one orbit to another. But always the elements to which reduction is made are themselves quantum phenomena, and these are still so new and unfamiliar that we feel an instinctive need for explanation in other terms. We seek to understand why the electron emits when it jumps. ”

“ In the quantum theory we meet this difficulty at once in the question of the inevitability of the feature of irrationality characterising the quantum postulate. I hope, however, that the idea of complementarity is suited to characterise the situation, which bears a deep-going analogy to the general difficulty in the formation of human ideas, inherent in the distinction between subject and object. ”

“ The other paths which the quantum-theory permits are occupied, until we get to a considerable distance from the nucleus, whereas in hydrogen they are vacant. Paths that have large [Pg 107] quantum numbers, though possible in theory, cannot occur in practice, at any rate in the laboratory, because they are so large that they would cause the electron to get into the region of other atoms. In certain nebulæ, where matter is almost inconceivably tenuous, the spectrum shows that electrons can travel round hydrogen nuclei in orbits whose total quantum number is as large as 30. ”

“ Now we know how the electrons and light behave. But what can I call it? If I say they behave like particles I give the wrong impression; also if I say they behave like waves. They behave in their own inimitable way, which technically could be called a quantum mechanical way. They behave in a way that is like nothing that you have ever seen before. Your experience with things that you have seen before is incomplete. The behaviour of things on a very tiny scale is simply different. An atom does not behave like a weight hanging on a spring and oscillating. ”

“ The very nature of the quantum theory thus forces us to regard the space-time co-ordination and the claim of causality, the union of which characterises the classical theories, as complementary but exclusive features of the description, symbolising the idealisation of observation and definition respectively. ”

“ To Quantum (as to Essence or Substance) there exists no contrary.47 There is nothing contrary to a length of three cubits or an area of four square feet. Great, little, long, short, are more properly terms of Relation than terms of Quantity; thus belonging to another Category. Nor is Quantum ever more or less Quantum; it does not admit of degree. The Quantum a yard is neither more nor less Quantum than that called a foot. That which is peculiar to Quanta is to be equal or unequal:48 the relations of equality and inequality are not properly affirmed of anything else except of Quanta. ”

“ In the second the atom uses the small fraction of a quantum offered to it to buy a ticket in a sweepstake in which the prizes are whole quanta; some of the atoms will win whole quanta which they can absorb, and it is these winning atoms in our retina which tell us of the existence of Sirius.
The collection-box explanation is not tenable. As Jeans once said, not only does the quantum theory forbid us to kill two birds with one stone; it will not even let us kill one bird with two stones. ”

“ FIG. 3. Quantum dots in a planar optical microcavity form the basis of the QuDOS hardware platform. (a) The quantum dots are arranged 1 �m apart in a two-dimensional square array. The quantum dots trap single electrons, whose spins will be used for quantum information processing. (b) Side view. The electron spins are manipulated with laser pulses sent into the optical cavity from above, and two neighboring quantum dots can be coupled by a laser optical field that overlaps them. The purple and green layers are AlGaAs and GaAs, grown by molecular-beam epitaxy. ”

“ Because it is a thought, it does not belong to perception: but it is a thought which is characterised by the externality of perception.—Not only therefore may the quantum be increased or diminished without end: the very notion of quantum is thus to push out and out beyond itself. The infinite quantitative progression is only the meaningless repetition of one and the same contradiction, which attaches to the quantum, both generally and, when explicitly invested with its special character, as degree. ”

“ This realization that symbols and experience do not follow the same rules has been brought to the science of physics by the formidable quantum logic. The possibility that separate parts of the universe like you or any other thing are connected in ways which both our common experience and laws of physics belie has forced its way into physics under Bell's theorem.
Laser fusion research and the hunt for quarks are paradigms of physics. A paradigm is an established thought, a framework. Quantum logic calls us back from the realm of symbols to the realm of experience. ”

“ Hitherto we have only regarded certain general features of the quantum problem. The situation implies, however, that the main stress has to be laid on the formulation of the laws governing the interaction between the objects which we symbolise by the abstractions of isolated particles and radiation. ”

“ There is a familiar table parallel to the scientific table, but there is no familiar electron, quantum or potential parallel to the scientific electron, quantum or potential. We do not even desire to manufacture a familiar counterpart to these things or, as we should commonly say, to “explain” the electron. After the physicist has quite finished his world-building a linkage or identification is allowed; but premature attempts at linkage have been found to be entirely mischievous.
Science aims at constructing a world which shall be symbolic of the world of commonplace experience. ”

“ From the expression for the atom of energy or quantum , where is a constant and is the frequency of the radiation, it is obvious that there exist as many different types of quanta of energy as there exist different frequencies of radiation. There is no one unique type of quantum of energy in nature. That which is universal is not the quantum of energy , but the constant . It can be shown that Planck’s constant is not a mere number; it represents some definite abstract mathematical entity, and that entity is action. ”

“ The fact that the symbolical quantum theory methods ascribe a particular phase to each stationary state the value of which depends upon the previous history of the atom, would for the first moment seem to contradict the very idea of stationary states. As soon as we are really concerned with a time problem, however, the consideration of a strictly closed system is excluded. ”

“ Each of these two determinations is at the same time identical with the other; discretion cannot be conceived without continuity, nor continuity without discretion. The existence of quantity, or the limited quantity, is the quantum. The quantum has also manifoldness and unity in itself; it is the enumeration of the unities, i. e. number. Corresponding to the quantum or the extensive greatness, is the intensive greatness or the degree. With the conception of degree, so far as degree is simple determinateness, quantity approaches quality again. The unity of quantity and quality is the measure. ”

“ Ultimately, we can write
where the factor C is the same in both cases. We do not have to deal with it because it is sufficient to determine the ratio of X to Y.
Now we obtain the Planck formula - which can be regarded as an expression of reality - if we make on the function ω the following hypothesis, which is consistent with quantum theory.
Let ε be the magnitude of the quantum of energy which is specific to the resonators considered, and denote by δ an infinitely small quantity [2] . ”

“ Thus, in quantum theory, there is no reason why we should not be willing to accept as an [Pg 47] ultimate the fundamental fact that when an electron jumps radiation is emitted, provided always that we can give independent meaning in terms of operations to the jumping of an electron. If there is no experiment suggesting other and intermediate phenomena, we ought to be able to rest intellectually satisfied with this. ”

“ In the realm of quantum phenomena it is of course the merest commonplace that our old ideas of mechanics and electrodynamics have failed, so that it is a matter of the greatest concern to find how many, or indeed whether any, elements of the old situations can be carried over into the new. ”

“ By radiation absorption and scattering energy is shuffled among the different receptacles in matter and aether, but only a whole quantum passes at each step. It was in fact this definiteness of thermodynamical equilibrium which first put Prof. Max Planck on the track of the quantum; and the magnitude of was first calculated by analysis of the observed composition of the radiation in the final state of randomness. Progress of the theory in its adolescent stage was largely due to Einstein so far as concerns the general principles and to Bohr as regards its connection with atomic structure. ”

“ Indeed, the proper vibrations of the Schrödinger wave equation have been found to furnish a representation of the stationary states of an atom meeting all requirements. The energy of each state is connected with the corresponding period of vibration according to the general quantum relation (1) . Furthermore, the number of nodes in the various characteristic vibrations gives a simple interpretation to the concept of quantum number which was already known from the older methods, but at first did not seem to appear in the matrix formulation. ”

“ Now the quantum postulate implies that any observation of atomic phenomena will involve an interaction with the agency of observation not to be neglected. Accordingly, an independent reality in the ordinary physical sense can neither be ascribed to the phenomena nor to the agencies of observation. After all, the concept of observation is in so far arbitrary as it depends upon which objects are included in the system to be observed. Ultimately every observation can of course be reduced to our sense perceptions. ”

“ If now the number of operationally independent concepts on the quantum level turns out to be the same as on the level of ordinary experience, and if there is also the possibility of continuous transition from the operations of the quantum domain to those of ordinary experience, then it seems to me that we should say that our usual concepts of space and time still apply in the quantum domain. But if the number of operationally independent concepts is either greater or less than on the ordinary level, then I believe we must say that the ordinary concepts of space and time cannot apply. ”