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Quantum Theory / Mechanics: Albert Einstein: The development during the present century is characterized by two theoretical systems essentially independent of each other: the theory of relativity and the quantum theory. The two systems do not directly contradict each other; but they seem little adapted to fusion into one unified theory.(Albert Einstein, 1940) "In the year nineteen hundred, in the course of purely theoretical (mathematical) investigation, Max Planck made a very remarkable discovery: the law of radiation of bodies as a function of temperature could not be derived solely from the Laws of Maxwellian electrodynamics. To arrive at results consistent with the relevant experiments, radiation of a given frequency f had to be treated as though it consisted of energy atoms (photons) of the individual energy hf, where h is Planck's universal constant. During the years following, it was shown that light was everywhere produced and absorbed in such energy quanta. In particular, Niels Bohr was able to largely understand the structure of the atom, on the assumption that the atoms can only have discrete energy values, and that the discontinuous transitions between them are connected with the emission or absorption of energy quantum. This threw some light on the fact that in their gaseous state elements and their compounds radiate and absorb only light of certain sharply defined frequencies." (Albert Einstein, 1940)

Quantum Theory: Albert Einstein

Albert Einstein on Plank's Discovery of Quantum Properties of Light

In 1900 Max Planck made a profound discovery. He showed (from purely formal/mathematical foundations) that light energy must be emitted and absorbed in discrete amounts if it was to correctly describe observed phenomena (i.e. Blackbody radiation).
Prior to then light had been considered as a continuous electromagnetic wave, thus the discrete nature of light was completely unexpected, as Albert Einstein explains;

About fifteen years ago [1899] nobody had yet doubted that a correct account of the electrical, optical, and thermal properties of matter was possible on the basis of Galileo-Newtonian mechanics applied to molecular motion and of Maxwell's theory of the electromagnetic field. (Albert Einstein, 1915)
Then Planck showed that in order to establish a law of heat radiation (Infra red light waves) consonant with experience, it was necessary to employ a method of calculation whose incompatibility with the principles of classical physics became clearer and clearer. For with this method of calculation, Planck introduced into physics the quantum hypothesis, which has since received brilliant confirmation. (Albert Einstein, 1914)

Albert Einstein (1905) used Planck's relationship to explain the results of the photoelectric effect which showed that the energy E of ejected electrons was wholly dependent upon the frequency f of incident light as described in the equation E=hf. It is ironic that in 1921 Albert Einstein was awarded the Nobel Prize for this discovery, though he never believed in particles and acknowledged that he did not know the cause of the discrete energy transfers (photons) which were contradictory to his continuous field theory of matter.
In 1954 Albert Einstein wrote to his friend Michael Besso expressing his frustration;

All these fifty years of conscious brooding have brought me no nearer to the answer to the question, 'What are light quanta?' Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken. (Albert Einstein, 1954)

Most importantly, Albert Einstein also suspected that Matter could not be described by a continuous spherical force field;

I consider it quite possible that physics cannot be based on the field concept, i.e., on continuous structures. In that case, nothing remains of my entire castle in the air, gravitation theory included, [and of] the rest of modern physics. (Albert Einstein, 1954)

Albert Einstein's suspicions were well justified, for he had spent a lifetime trying (and failing) to create a unified field theory of matter that explained both Quantum Theory / Light and Relativity / Gravity.
However, his work on the photoelectric effect confirmed that light energy was emitted and absorbed by electrons in discrete amounts or quanta. This quanta of light energy soon became known as the 'photon' (i.e. discrete like a particle) and led to the paradox that light behaved both as a continuous e-m wave (Maxwell, Albert Einstein) as well as a discrete particle/photon (Planck, Albert Einstein). So we see that Albert Einstein was partly responsible for the discovery of the particle/photon concept of light, though he completely rejected the notion of discrete particles. He writes;

Since the theory of general relativity implies the representation of physical reality by a continuous field, the concept of particles or material points cannot play a fundamental part, nor can the concept of motion. (Albert Einstein)

I wished to show that space time is not necessarily something to which one can ascribe to a separate existence, independently of the actual objects of physical reality. Physical objects are not in space, but these objects are spatially extended. In this way the concept empty space loses its meaning. (Albert Einstein)

Quantum Theory: Louis de Broglie

de Broglie's Discovery of the Wave Properties of Electron Interactions (1927)

The next step was taken by de Broglie. He asked himself how the discrete states could be understood by the aid of current concepts, and hit on a parallel with stationary (standing) waves, as for instance in the case of proper frequencies of organ pipes and strings in acoustics. Albert Einstein, 1954)

de Broglie's realisation that standing waves exist at discrete frequencies and thus energies is obviously true and important, yet he also continued with the particle concept and thus imagined particles moving in a wavelike manner. These predicted wave properties of matter were shortly thereafter confirmed from experiments (Davisson and Germer, 1927) on the scattering of electrons through crystals (which act as diffraction slits). As Albert Einstein confirms;

Experiments on interference made with particle rays have given brilliant proof that the wave character of the phenomena of motion as assumed by the theory does, really, correspond to the facts. (Albert Einstein, 1954))

In 1913, Niels Bohr had developed a simple (though only partly correct) model for the hydrogen atom that assumed;
i) That the electron particle moves in circular orbits about the proton particle.
ii) Only certain orbits are stable / allowed.
iii) Light is emitted and absorbed by the atom when the electron 'jumps' from one allowed orbital state to a another.

This early atomic model had some limited success because it was obviously created to explain the discrete energy states of light emitted and absorbed by bound electrons in atoms or molecules, as discovered by Planck in 1900.
de Broglie was aware of Bohr's model for the atom and he cleverly found a way of explaining why only certain orbits were 'allowed' for the electron. As Albert Einstein explains;

de Broglie conceived an electron revolving about the atomic nucleus as being connected with a hypothetical wave train, and made intelligible to some extent the discrete character of Bohr's 'permitted' paths by the stationary (standing) character of the corresponding waves. (Albert Einstein, 1940))

de Broglie Wave Electron Orbits

Fig: 1. The allowed discrete orbits of the electron as imagined by de Broglie.

de Broglie assumed that because light had both particle and wave properties, that this may also be true for matter. Thus he was not actually looking for a wave structure of matter. Instead, as matter was already assumed to be a particle, he was looking for wave properties of matter to complement the known particle properties. As a consequence of this particle/wave duality, de Broglie imagined the standing waves to be related to discrete wavelengths and standing waves for certain orbits of the electron particle about the proton. (Rather than considering an actual standing wave structure for the electron itself.)
From de Broglie's perspective, and from modern physics at that time, this solution had a certain charm. It maintained the particle - wave duality for BOTH light and matter, and at the same time explained why only certain orbits of the electron (which relate to whole numbers of standing waves) were allowed, which fitted beautifully with Niels Bohr model of the atom. de Broglie further explains his reasoning for the particle/wave duality of matter in his 1929 Nobel Prize acceptance speech;

On the one hand the quantum theory of light cannot be considered satisfactory since it defines the energy of a light particle (photon) by the equation E=hf containing the frequency f. Now a purely particle theory contains nothing that enables us to define a frequency; for this reason alone, therefore, we are compelled, in the case of light, to introduce the idea of a particle and that of frequency simultaneously. On the other hand, determination of the stable motion of electrons in the atom introduces integers, and up to this point the only phenomena involving integers in physics were those of interference and of normal modes of vibration. This fact suggested to me the idea that electrons too could not be considered simply as particles, but that frequency (wave properties) must be assigned to them also. (de Broglie, 1929)

Quantum Theory: Erwin Schrodinger

Schrodinger Wave Equations (1928)

Quantum theory is essentially founded on the experimental observations of frequency and wavelength for both light and matter.
1. Planck's discovery that energy is related to frequency in the equation E=hf
2. The Equivalence of Energy, Frequency and Mass E=hf=mc2, which deduces the Compton Wavelength Y=h/mc
3. The de Broglie wavelength y=h/mv

It was Erwin Schrodinger who discovered that when frequency f and de Broglie wavelength y were substituted into general wave equations it becomes possible to express energy E and momentum mv (from the above equations) as wave functions - thus a confined particle (e.g. an electron in an atom / molecule) with known energy and momentum functions could be described with a certain wave function. From this it was further found that only certain frequency wave functions, like frequencies on musical strings, were allowed to exist. These allowed functions and their frequencies depended on the confining structure (atom or molecule) that the electron was bound to (analogous to how strings are bound to a violin, and only then can they resonate at certain frequencies). Significantly, these allowed frequencies corresponded to the observed discrete frequencies of light emitted and absorbed by electrons bound in atoms/molecules. This further confirmed the standing wave properties of matter, and thus that only certain standing wave frequencies could exist which corresponded to certain energy states. The agreement of observed frequencies and Schrodinger's Wave Equations further established the fundamental importance of Quantum Theory and thus the Wave properties of both light and matter. As Albert Einstein explains;

How can one assign a discrete succession of energy values E to a system specified in the sense of classical mechanics (the energy function is a given function of the co-ordinates x and the corresponding momenta mv)? Planck's constant h relates the frequency f =E/h to the energy values E. It is therefore sufficient to assign to the system a succession of discrete frequency f values. This reminds us of the fact that in acoustics a series of discrete frequency values is coordinated to a linear partial differential equation (for given boundary conditions) namely the sinusoidal periodic solutions. In corresponding manner, Schrodinger set himself the task of coordinating a partial differential equation for a scalar wave function to the given energy function E (x, mv), where the position x and time t are independent variables. (Albert Einstein, 1936)

It should also be noted that Schrodinger's wave equations describe scalar waves rather than vector electromagnetic waves. This is a most important difference. Electromagnetic waves are vector waves - at each point in Space the wave equations yield a vector quantity which describes both a direction and an amplitude (size of force) of the wave, and this relates to the original construction of the e-m field by Faraday which described both a force and a direction of how this force acted on other matter particles.
Scalar wave equations yield a single quantity for each point in space which simply describes the wave amplitude (there is no directional component). For example, sound waves are scalar waves where the wave amplitude describes the Motion (or compression) of the wave medium (air).

With de Broglie's introduction of the concept of standing waves to explain the discrete energy states of atoms and molecules, and the introduction of scalar waves by Schrodinger, they had intuitively grasped important truths of nature as Albert Einstein confirms;

Experiments on interference made with particle rays have given brilliant proof that the wave character of the phenomena of motion as assumed by the theory does, really, correspond to the facts.

The de Broglie-Schrodinger method, which has in a certain sense the character of a field theory, does indeed deduce the existence of only discrete states, in surprising agreement with empirical facts. It does so on the basis of differential equations applying a kind of resonance argument. (Albert Einstein, 1927)

Quantum Theory: Heisenberg Born Probability Interpretation

Heisenberg's Uncertainty Principle & Born's 'Probability Waves' Interpretation of Quantum Theory (1928)

At the same time that the wave properties of matter were discovered, two further discoveries were made that also profoundly influenced (and confused) the future evolution of modern physics.
Firstly, Werner Heisenberg developed the uncertainty principle which tells us that we (the observer) can never exactly know both the position and momentum of a particle. As every observation requires an energy exchange (photon) to create the observed 'data', some energy (wave) state of the observed object has to be altered. Thus the observation has a discrete effect on what we measure. i.e. We change the experiment by observing it!
Further, because both the observed position and momentum of the particle can never be exactly known, theorists were left trying to determine the probability of where, for example, the 'particle' would be observed.

Born (1928) was the first to discover (by chance and with no theoretical foundation) that the square of the quantum wave equations (which is actually the Wave-Density) could be used to predict the probability of where the particle would be found. Since it was impossible for both the waves and the particles to be real entities, it became customary to regard the waves as unreal probability waves and to maintain the belief in the 'real' particle. This maintained the belief in the particle/wave duality, though in a new form where the 'quantum' scalar standing waves had become 'probability waves' for finding the 'real' particle.

Albert Einstein agreed in part with this probability wave interpretation of Quantum Theory, as he believed in continuous force fields (not in waves or particles) thus to him it was sensible that the waves were not real, and were mere descriptions of probabilities. He writes;

On the basis of quantum theory there was obtained a surprisingly good representation of an immense variety of facts which otherwise appeared entirely incomprehensible. But on one point, curiously enough, there was failure: it proved impossible to associate with these Schrodinger waves definite motions of the mass points - and that, after all, had been the original purpose of the whole construction. The difficulty appeared insurmountable until it was overcome by Born in a way as simple as it was unexpected. The de Broglie-Schrodinger wave fields were not to be interpreted as a mathematical description of how an event actually takes place in time and space, though, of course, they have reference to such an event. Rather they are a mathematical description of what we can actually know about the system. They serve only to make statistical statements and predictions of the results of all measurements which we can carry out upon the system. (Albert Einstein, 1940)

It seems to be clear, therefore, that Born's statistical interpretation of quantum theory is the only possible one. The wave function does not in any way describe a state which could be that of a single system; it relates rather to many systems, to an 'ensemble of systems' in the sense of statistical mechanics. (Albert Einstein, 1936)

Albert Einstein refers to the now well established fact that matter interacts with other matter throughout the universe. He realised that because matter is somehow spherically spatially extended we must give up the idea of complete localization and knowledge of the 'particle' in a theoretical model. Einstein believed it was this lack of knowledge of the system as a whole that is the ultimate cause of the uncertainty and resultant probability inherent in Quantum Theory.

Thus the last and most successful creation of theoretical physics, namely quantum mechanics (QM), differs fundamentally from both Newton's mechanics, and Maxwell's e-m field. For the quantities which figure in QM's laws make no claim to describe physical reality itself, but only probabilities of the occurrence of a physical reality that we have in view. (Albert Einstein, 1931)

I cannot but confess that I attach only a transitory importance to this interpretation. I still believe in the possibility of a model of reality - that is to say, of a theory which represents things themselves and not merely the probability of their occurrence. On the other hand, it seems to me certain that we must give up the idea of complete localization of the particle in a theoretical model. This seems to me the permanent upshot of Heisenberg's principle of uncertainty. (Albert Einstein, 1934))

Albert Einstein believed that Reality could be represented by continuous spherical force fields, that reality was not founded on chance (as Bohr and Heisenberg argued) but on necessary connections between things (thus his comment 'God does not play dice'!).

Quantum Theory: Famous Quotes

The more success the quantum theory has, the sillier it looks. (Albert Einstein to Heinrich Zangger, May 20, 1912)

God does not play dice with the cosmos. (Albert Einstein)

I think that a 'particle' must have a separate reality independent of the measurements. That is an electron has spin, location and so forth even when it is not being measured. I like to think that the moon is there even if I am not looking at it. (Albert Einstein)

Einstein, don't tell God what to do. (Niels Bohr in response to Einstein)

Those who are not shocked when they first come across quantum mechanics cannot possibly have understood it. (Niels Bohr on Physics)

When it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images.
It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we say about Nature. (Niels Bohr, 1885-1962)

Niels Bohr brainwashed a whole generation of physicists into believing that the problem (of the interpretation of quantum mechanics) had been solved fifty years ago. ( Murray Gell-Mann, Noble Prize acceptance speech, 1976)

This statistical interpretation is now universally accepted as the best possible interpretation for quantum mechanics, even though many people are unhappy with it. People had got used to the determinism of the last century, where the present determines the future completely, and they now have to get used to a different situation in which the present only gives one information of a statistical nature about the future. A good many people find this unpleasant; Einstein has always objected to it. The way he expressed it was: "The good God does not play with dice". Schroedinger also did not like the statistical interpretation and tried for many years to find an interpretation involving determinism for his waves. But it was not successful as a general method. I must say that I also do not like indeterminism. I have to accept it because it is certainly the best that we can do with our present knowledge. One can always hope that there will be future developments which will lead to a drastically different theory from the present quantum mechanics and for which there may be a partial return of determinism. However, so long as one keeps to the present formalism, one has to have this indeterminism.
(P.A.M. Dirac, "The Development Of Quantum Mechanics" Conferenza Tenuta il 14 Aprile 1972, in Roma, Accademia Nazionale dei Lincei, 1974)

Both matter and radiation possess a remarkable duality of character, as they sometimes exhibit the properties of waves, at other times those of particles. Now it is obvious that a thing cannot be a form of wave motion and composed of particles at the same time - the two concepts are too different. (Heisenberg, 1930)

The solution of the difficulty is that the two mental pictures which experiment lead us to form - the one of the particles, the other of the waves - are both incomplete and have only the validity of analogies which are accurate only in limiting cases. (Heisenberg, 1930)

Light and matter are both single entities, and the apparent duality arises in the limitations of our language.
It is not surprising that our language should be incapable of describing the processes occurring within the atoms, for, as has been remarked, it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. Furthermore, it is very difficult to modify our language so that it will be able to describe these atomic processes, for words can only describe things of which we can form mental pictures, and this ability, too, is a result of daily experience. Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme - the quantum theory - which seems entirely adequate for the treatment of atomic processes; for visualisation, however, we must content ourselves with two incomplete analogies - the wave picture and the corpuscular picture. (Heisenberg, 1930)

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. (Erwin Schrodinger)

Let me say at the outset, that in this discourse, I am opposing not a few special statements of quantum mechanics 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.(Schrödinger E, The Interpretation of Quantum Mechanics. Ox Bow Press, Woodbridge, CN, 1995).I don't like it, and I'm sorry I ever had anything to do with it. (Erwin Schrodinger talking about quantum mechanics)

I think it is safe to say that no one understands quantum mechanics. (Richard Feynman on Physics)

The next question was - what makes planets go around the sun? At the time of Kepler some people answered this problem by saying that there were angels behind them beating their wings and pushing the planets around an orbit. As you will see, the answer is not very far from the truth. The only difference is that the angels sit in a different direction and their wings push inward. (Richard Feynman, Character Of Physical Law)

One does not, by knowing all the physical laws as we know them today, immediately obtain an understanding of anything much. (Richard Feynman, 1918-1988)
I love only nature, and I hate mathematicians. (Richard Feynman 1918-1988)

... the more you see how strangely Nature behaves, the harder it is to make a model that explains how even the simplest phenomena actually work. So theoretical physics has given up on that. (Richard Feynman 1918-1988)

What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school... It is my task to convince you not to turn away because you don't understand it. You see my physics students don't understand it. ... That is because I don't understand it. Nobody does.
(Feynman, Richard P. Nobel Lecture, 1966, 1918-1988, QED, The Strange Theory of Light and Matter)

Editor: Haselhurst