Background to Special Relativity:

The Wave Theory of Light ca. 1900

Newton’s “New Theory of Light and Colours” stated that white light is a mixture of heterogeneous rays, separated by refraction (e.g. by a prism) according to their degrees of refrangibility, with the degrees of refrangibility corresponding to the spectral colours.

In the wave theory, a ray of light of a given degree of refrangibility, corresponding to a given colour, is produced by a wave of a given wavelength.

Light is just one kind of electromagnetic radiation, corresponding to one small part of a spectrum of possible wavelengths, which includes waves shorter than those of "violet" light ("ultraviolet" light) and longer than those of "red" light ("infrared" light).

Wavelike behavior of light:

Interference: waves of differing wavelengths combining to produce a wave with different characteristics

Diffraction: Bending of light around edges of objects

The Ether: If light is a wave, it is natural to assume that it is a wave propagating in some medium; the waves must be the vibrations of something.

Since electromagnetic radiation appears to be everywhere, and can even pass through solid bodies, this medium must fill all of space, including the interstitial spaces of the fundamental parts of matter.

This medium became known as the "luminiferous" (light-bearing) ether. Measurements of the velocity of light showed that it travels at a constant velocity (c), which was assumed to be a velocity relative to the ether.

The Galilei-Newtonian theory of relativity: The laws of physics make no distiction between uniform motion and rest. Mechanical effects depend only on the acceleration, not on the velocity, of the system. Given a system in which the Newtonian relation between force, mass, and velocity holds, any system in uniform motion relative to this system is dynamically indistinguishable from it.

Maxwell-Lorentz electrodynamics: Electrodynamical effects depend on the propagation of waves in the ether, and therefore they depend on the velocity of the system relative to the ether.

The velocity of light relative to the ether is a measureable constant.

Are these two principles incompatible?

No!

The velocity of light is not an absolute velocity in space, but a velocity relative to the ether. It is, in principle, no more a difficulty than the existence of a determinate velocity of sound relative to air.

The velocity of light as measured by any observer should depend on that observer’s own velocity relative to the ether.

In other words, the velocity of light should obey the Newtonian principle of the addition of velocities: Newtonian relativity implies that any velocity depends on the velocity of the system in which it is measured.

A sufficiently sensitive measurement should reveal the dependence of the velocity of light on the motion of the earth through the ether (the “ether wind”).

A light beam from A goes to a half-silvered mirror at B: the reflected part goes to D, and the transmitted part goes to E; the paths BD and BE have the same length (L). The parted beams are reflected at D and E and then rejoin. If the apparatus is at rest, times of the two trips BE and BD are equal, and the rejoined waves will be in phase.

If the apparatus is moving through the ether at velocity v, with the direction BE parallel to the direction of motion, the times of light travel along the two arms will not be equal. The time from B to D and back should be shorter than the time from B + E and back.

But the result of the experiment is null!

How to interpret this?

To accept that motion relative to the ether really makes no physical difference, we would have to accept the notion that there is actually a velocity (the velocity of light) that has the same value for observers in different states of uniform motion-i.e. a velocity that appears the same to observers with different velocities. This seems absurd.

The Lorentz contraction: The light did not travel at the same speed in both directions; rather, the times were the same because the path BE contracted. In other words, the speed of light appears to be the same because the measuring apparatus contracted in the direction of motion. All objects moving through the ether contract in the dimension parallel to their motion through the ether, and this explains why motion through the ether cannot be detected.

Einstein on simultaneity (1917):

We encounter the same difficulty with all physical statements in which the conception " simultaneous " plays a part. The concept does not exist for the physicist until he has the possibility of discovering whether or not it is fulfilled in an actual case. We thus require a definition of simultaneity such that this definition supplies us with the method by means of which, in the present case, he can decide by experiment whether or not both the lightning strokes occurred simultaneously. As long as this requirement is not satisfied, I allow myself to be deceived as a physicist (and of course the same applies if I am not a physicist), when I imagine that I am able to attach a meaning to the statement of simultaneity.

The present (“now”)

time

space

The future

The past

Events that can still be influenced by what you do now, but that cannot influence what is happening now

Events that can influence what happens now, but that cannot be influenced by anything you do now

here and now

The “causal structure” of spacetime

time

space

Events that can still be influenced by what you do now, but that cannot influence what is happening now: the “future light cone” of p

Events that can influence what happens now, but that cannot be influenced by anything you do now: the “past light cone” of p

p

What if you couldn’t travel faster than light?

Causally inaccessible to p

Causally inaccessible to p

time

space

p

If you can’t travel faster than light, then what’s happening “now” can only influence you later.

“now”

What is simultaneous for a bat?

time

space

The bat in spacetime

Visual simultaneity

time

space

Visual perception in spacetime

If light propagation is isotropic, then light from the explosion goes equal distances in equal times, and reaches equidistant points at the same time.

The same thing, in space-time

time

space

Einstein on the train

(Dramatization)

€

x'= x − vt

y'= y

z '= z

t'= t

Galilean transformations Lorentz transformations

€

x'=x − vt

1− v 2 c 2

y'= y

z'= z

t'=t − vx c 2

1− v 2 c 2

t2

t1

F1F2

t-

t+

Einstein:• The invariance of the

velocity of light is real.• Simultaneity is relative:

whether two events occur at the same time depends on the frame of reference.

• Therefore the Lorentz contraction and time-dilatation are mere frame-dependent appearances.

Lorentz:• The contraction and

dilatation are real.• Simultaneity is absolute:

it is an objective fact whether two events occur at the same time.

• Therefore the invariance of the velocity of light must be mere appearance.

Two views of the electrodynamics of moving bodies:

Mach’s Principle

Einstein: Two spheres S1 and S2, rotate relative to one another, and S2 bulges at its equator; how do we explain this difference?

No answer can be admitted as epistemologically satisfactory, unless the reason given is an observable fact of experience....Newtonian mechanics does not give a satisfactory answer to this question. It pronounces as follows: The laws of mechanics apply to the space R1, in respect to which the body S1 is at rest, but not to the space R2, in respect to which the body S2 is at rest. But the privileged space R1... is a merely factitious cause, and not a thing that can be observed.

Einstein, 1916

What does Nature care about our coordinate systems?

Einstein, 1922

What makes the situation appear particularly unpleasant is the fact that there should be infinitely many inertial systems, moving uniformly and without rotation with respect to one another, that are distinguished from all other rigid systems.

Einstein 1949

Bending of light-rays as they pass the Sun

The gravitational lens effect

F1 F2

equator

polegeodesics of the earth’s surface

space-time geodesics

p1 p2

Particles p1 and p2 fall in the earth’s gravitational field; how is this fact to be interpreted?

g1g2

p1p2

Newton: The particles would follow space-time geodesics g1 and g2, but are forced into curved space-time trajectories

g1 g2

p1p2

Einstein: The free-fall trajectories g1 and g2 are geodesics of space-time, and their convergence measures the curvature of space-time.

Newton’s equation: The strength of the gravitational field, as measured by the relative acceleration of falling particles, depends on the distribution of mass.

Einstein’s equation: The curvature of space-time, as measured by the relative acceleration of geodesics, depends on the distribution of mass-energy.

Gab = 8πTab

{x,y}

P

M

p1p2

c1c2

Coordinates in flat and curved spaces

Black hole’s effect on the light-cone structure

time

space

Space at time t

“Laplacian determinism” in the classical world: if you knew the positions and momenta of all particles at a given time t, you could deduce their trajectories for the entire future or past.

Specific assumptions of the classical viewpoint:

Theoretical magnitudes can take on a continuous range of values.

Any particle has a definite trajectory in space-time, and a definite position and momentum at any time.

The future position and momentum of any particle can be predicted with certainty from its position and momentum at any given time.

Electromagnetic radiation is wave propagation in a continuous field.

Black body radiation:

Assumption: Intensity of black body radiation should take on a continuous range of values. This will be proportional to the frequency.

Fact: This assumption only agrees with the phenomena at very low frequencies.

At higher frequencies, according to the assumption, the intensity heads toward the “ultraviolet catastrophe”.

Planck: The correct values result when radiation is assumed to be distributed in multiples of a constant (“Planck’s constant”).

The photo-electric effect:

Light incident on a thin metal foil causes the release of electrons. You might expect:

--that the energy of the electrons is proportional to the intensity of the incident light.

Instead it is proportional to the frequency. “Red” light doesn’t cause electrons to be released, no matter how intense it is. Violet light, no matter how weak, will release electrons of the same kinetic energy.

--that there would be some time-lag between the first incidence and first ejection.

Instead, it begins when incidence begins.

The photoelectric effect

Einstein’s explanation:

Light is distributed in clumps with energy E = h,

i.e. energy is proportional to frequency.

The wave theory of light

Polarization:

Linear polarization

Circular polarization

Elliptic polarization

The wave theory of light: destructive interference

Constructive interference

Interference of waves in two-slit experiment

The atomic nature of electricity: the electron

1897: J.J. Thomson discovers that cathode rays consist of streams of negatively-charged particles, “electrons”. The ratio of charge to mass of the particle could be measured by its deflection in a magnetic field.

The old atomic “theory”: Atoms are small, homogeneous objects. (cf. Newton: “Solid, massy, impenetrable particles”)

J.J. Thomson’s model:

E. Rutherford, 1911:

Atom consists of a positively-charged nucleus surrounded by negatively-charged electrons.

But the Rutherford model is inherently unstable:

Bohr’s model:

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Principles of the Bohr model of the atom:1) Electrons assume only certain orbits around the nucleus. These orbits are stable and called "stationary" orbits.2) Each orbit has an energy associated with it. For example the orbit closest to the nucleus has an energy E1, the next closest E2 and so on.3) Light is emitted when an electron jumps from a higher orbit to a lower orbit and absorbed when it jumps from a lower to higher orbit.4) The energy and frequency of light emitted or absorbed is given by the difference between the two orbit energies:

E(light) = Ef - Ei, n = E(light)/h

h= Planck's constant = 6.627x10-34 Js "f" and "i” = final and initial orbits.

De Broglie’s wave interpretation of the Bohr atom

* t represents time, * r represents displacement, * m is the mass of the particle, * i is the square root of minus one and * h is Planck's Constant.

The Schroedinger equation:

What does the Schrödinger equation mean?

Schrödinger’s view: The wavelike variation of physical properties of a system in space and time.

Quantum-mechanical view: A “probability wave,” i.e. the probability of finding a particle in a particular state

The Solvay Council, 1927

The more I think about the physical portion of Schrödinger's theory, the more repulsive I find it...What Schrödinger writes about the visualizability of his theory 'is probably not quite right,' in other words it's crap.

--Werner Heisenberg, writing to Wolfgang Pauli, 1926

We believe we have gained “anschaulich” (“intuitive,” or “visualizable”) understanding of a physical theory, if in all simple cases, we can grasp the experimental consequences qualitatively and see that the theory does not lead to any contradictions.

Heisenberg, 1927, On the Intuitive Content [anschaulich Inhalt] of the Uncertainty Relation )

Heisenberg’s Uncertainty Principle (a.k.a. “Indeterminacy Principle”): The “wave-particle duality” reflects a fundamental limitation on the determinateness of the properties of a physical system.

It should at least in principle be possible to observe the electron in its orbit. One should simply look at the atom through a microscope of a very high revolving power….Such a high revolving power could to be sure not be obtained by a microscope using ordinary light, since the inaccuracy of the measurement of the position can never be smaller than the wave length of the light. But a microscope using -rays with a wave length smaller than the size of the atom would do.

Heisenberg’s Gamma-Ray Microscope: The apparatus used to measure a particle inevitably disturbs it.

The position of the electron will be known with an accuracy given by the wave length of the -ray. The electron may have been practically at rest before the observation. But in the act of observation at least one light quantum of the -ray must have passed the microscope and must first have been deflected by the electron. Therefore, the electron has been pushed by the light quantum, it has changed its momentum and its velocity, and one can show that the uncertainty of this change is just big enough to guarantee the validity of the uncertainty relations.

At the same time one can easily see that there is no way of observing the orbit of the electron around the nucleus. … the first light quantum will have knocked the electron out from the atom. The momentum of light quantum of the -ray is much bigger than the original momentum of the electron if the wave length of the -ray is much smaller than the size of the atom. Therefore, the first light quantum is sufficient to knock the electron out of the atom and one can never observe more than one point in the orbit of the electron; therefore, there is no orbit in the ordinary sense.

HV

HV

HV

HV

Photons polarized horizontally or vertically always keep their polarization when measured by subsequent HV polarizers.

HV

±45º

±45º

45º

But if a polarization measurement is followed by a measurement in a different orientation, the initial polarization is lost.

45º polarized photons, after passing through an HV polarizer, subsequently emerge at random through a second ±45º filter.

HV

HV±45º

45º 45º

45º

45º

On the wave model, it is easy to see how polarized waves can be recombined to the original polarization state. But how does this happen with polarized photons?

Niels Bohr and Werner Heisenberg

It would in particular not be out of place in this connection to warn against a misunderstanding likely to arise when one tries to express the content of Heisenberg's well-known indeterminacy relation by such a statement as ‘the position and momentum of a particle cannot simultaneously be measured with arbitrary accuracy’. According to such a formulation it would appear as though we had to do with some arbitrary renunciation of the measurement of either the one or the other of two well-defined attributes of the object, which would not preclude the possibility of a future theory taking both attributes into account on the lines of the classical physics. (Bohr 1937, p. 292)

“According to relativity theory, the word “simultaneous” admits of a definition in no other way than through experiments in which the velocity of light propagation enters essentially. If there were a “sharper” definition of simultaneity, for example by signals that propagate infinitely fast, relativity theory would be impossible….The case is similar with the definition of the concepts, “position of the electron,” “velocity,” in quantum theory. All the experiments that we can perform toward the definition of these words necessarily contain an uncertainty…. If there were experiments that made possible a sharper determination of p and q than that corresponding to [the uncertainty relations], quantum mechanics would be impossible.”

Heisenberg, 1927

The Uncertainty Relation: two interpretations

1. The disturbance theory: the uncertainty relations concern the inevitable influence of the measurement apparatus on the state of the system to be measured.

2. The “Copenhagen interpretation”: The state of a (quantum) physical system cannot be meaningfully specified independently of its interaction with particular (classical) measuring devices. The definitions of concepts such as “position” and “momentum” must make reference to the means of measuring them.

Is it possible to decide between these views on the basis of experiment?

“Can the Quantum-Mechanical Description of Physical Reality Be Considered Complete?” (Einstein, Podolsky, and Rosen, 1935)

Criterion of Completeness: “Whatever the meaning assigned to the term complete, the following requirement for a complete theory seems to be a necessary one: every element of the physical reality must have a counterpart in the physical theory.”

Criterion of Reality: “If, without in any way disturbing a system, we can predict with certainty the value of a physical quantity, then there exists an element of reality corresponding to this quantity.”

The EPR argument:

Given two physical systems I and II that have interacted, they are described by a common quantum-mechanical state ψ.

(Assume that they are sufficiently separated in space to make interaction impossible.)

In the case of two particles, ψ assigns to their positions a negligible probability of being found within some large (macroscopic) area.

By measuring an observable A on system I, we can predict with certainty the result of a measurement of observable P on system II.

By measuring some different observable B on system I, we can predict with certainty the result of a measurement of observable Q on system II.

But observables P and Q are non-commuting, i.e. they cannot have definite values, according to the Uncertainty Principle. (E.g. P is position, Q is momentum.)

Since the measurements on I are made without disturbing II (recall that the two are two far apart to interact), we can conclude that the values of P and Q are both elements of reality.

But the quantum mechanical state ψ does not assign definite values to P and Q.

Therefore ψ does not give a complete description of physical reality.

“One could object to this conclusion on the grounds that our criterion of reality is not sufficiently restrictive. Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted.

On this point of view, since either one or the other, but not both simultaneously, of the quantities P and Q can be predicted, they are not simultaneously real. This makes the reality of P and Q depend upon the process of measurement carried out on the first system in any way. No reasonable definition of reality could be expected to permit this.”

Niels Bohr, 1935: “Can the Quantum-Mechanical Description of Physical Reality Be Considered Complete?”

EPR argument does not affect the soundness of quantum mechanics, “which is based on a coherent mathematical formalism covering automatically any procedure of measurement like that indicated. The apparent contradiction in fact only discloses an essential inadequacy of the customary viewpoint of natural philosophy for a rational account of physical phenomena of the type with which we are concerned in quantum mechanics.”

“A criterion like that proposed by EPR contains...an essential ambiguity when it is applied to the actual problems with which we are here concerned. The ambiguity regards the meaning of the expression, ‘without in any way disturbing the system.’”

The question is not the mechanical disturbance of one system by the measurement of the other. It is, instead, “an influence on the very conditions which define the possible types of predictions regarding the future behaviour of the system.”

It must here be remembered that even in the indeterminacy relation [Δq Δp ≈ h] we are dealing with an implication of the formalism which defies unambiguous expression in words suited to describe classical pictures. Thus a sentence like "we cannot know both the momentum and the position of an atomic object" raises at once questions as to the physical reality of two such attributes of the object, which can be answered only by referring to the conditions for an unambiguous use of space-time concepts, on the one hand, and dynamical conservation laws on the other hand.

Bohr’s reply to Einstein:

From our point of new we now see that the wording of the above-mentioned criterion of physical reality proposed by Einstein, Podolsky, and Rosen contains an ambiguity as regards the meaning of the expression ' without in any way disturbing a system.' Of course there is in a case like that just considered no question of a mechanical disturbance of the system under investigation during the last critical stage of the measuring procedure. But even at this stage there is essentially the question of an influence on the very conditions which define the possible types of predictions regarding the future behaviour of the system.

Since these conditions constitute an inherent element of the description of any phenomenon to which the term "physical reality" can be properly attached, we see that the argumentation of the mentioned authors does not justify their conclusion that quantum-mechanical description is essentially incomplete. On the contrary, this description, as appears from the preceding discussion, may be characterised as a rational utilisation of all possibilities of unambiguous interpretation of measurements, compatible with the finite and uncontrollable interaction between the objects and the measuring instruments in the field of quantum theory.

(Bohr’s reply)

In fact, it is only the mutual exclusion of any two experimental procedures, permitting the unambiguous definition of complementary physical quantities, which provides room for new physical laws, the coexistence of which might at first sight appear irreconcilable with the basic principles of science. It is just this entirely new situation as regards the description of physical phenomena that the notion of complementarity aims at characterising.

(Bohr’s reply)

The spin of a particle: for a given spatial axis, the particle has an “intrinsic angular momentum,” its tendency to be deflected up or down.

A schematic “EPR” experiment:

The quantum mechanical state ψ for a system of two particles, created at a single source and therefore initially in causal interaction, implies certain correlations between their respective behaviors afterwards.

In a symmetrical Stern-Gerlach experiment, there is a statistical correlation between spins of particles on each side.

But the correlation, apparently does not depend on characteristics of the particular particles, or the orientation of the pair of magnets through which any particle passes.

Rather, it depends on the relative orientation of the two pairs of magnets.

How does each particle know what to do when it reaches its magnet? How does it know how its magnet is oriented with respect to the other one?

By signals?

The correlation is, in principle, completely independent of the distance between the two pairs of magnets. The experiment can be arranged to rule out any possibility of communication at the speed of light or less.

Source

Past light cone of the measurement event

Past light cone of the measurement event

Space-time diagram of a correlation experiment with Stern-Gerlach magnets: no possibility of causal signaling

Hidden variables: the “reality” of which quantum mechanics gives an “incomplete” picture?

Is it possible that the particles “know what to do” by “previous arrangement”?

Does their behavior when measured depend on their own internal states, as determined in their common causal past?

Could there be “instruction sets” laid down at the source, that result in the correlations observed at the magnets?

“Bell’s theorem” (John S. Bell)

Is it possible to express these questions mathematically, and thereby to answer them by experiment?

Is it possible to set minimal conditions on correlations that may result from previously established “hidden states”?

That is, is it possible to “instruct” pairs of particles in advance so that when they are measured-- later-- the outcomes are correlated as required by quantum mechanics?

Bell’s Inequality: the minimal correlation between pairs of outcomes, given that the outcomes depend only on the “hidden variables.”

According to quantum mechanics, the experiment described yields anti-correlations for spin values.

The probability that the two particles will have opposite values of spin (up vs. down) depends on the angle θ between the two magnet-pair orientations:

probability = ½cos2(θ/2)

When θ= 0 (when both pairs have the same orientation), the particles will have opposite spin values with probability =1.

When the angle between the orientations =+120º,

probability of opposite spins = 1/4

(Recall that the detectors can be sufficiently separated to preclude any causal influence.)

How could we prepare the particles to produce these results?

Consider three possible orientations: vertical, + 120o from vertical, and -120o. In the case of the constant anticorrelation (when both detectors have the same orientation), the initial states of the particles could contain instructions that produce opposite spins:

Particle L: “spin up when the detector is vertical, down if +120o, and down if -120o”.

Particle R: “down if vertical, up if +120o, up if -120o”

But these instructions work only on the assumption of identical orientations.

When θ0, however, there are six possible pairs of orientations:

12, 21, 13, 31, 23, 32

If the particles have the instructions described above, which were rigged to yield opposite spins when θ=0 i.e. up-down-down and down-up-up -then clearly in two of the six possible orientation pairs, namely 23 and 32, the two particles will have opposite spins.

Moreover, since there could also be pairs with instructions: up-up-up and down-down-down, which would always show opposite spins, two out of six is only the minimum value for the probability of opposite spin values.

Bell's theorem: if the eventual spin measurements of particle pairs are determined by hidden initial states, then in all cases where the detectors have different orientations, spin values will be opposite with a probability of at least 1/3.

Prediction of quantum mechanics: 1/4.

Which is wrong?

1.Locality: Systems that are spacelike separated do not influence on another. Causal influence is transmitted through space at the speed of light, or slower.

2.Separability: The complete description of the state of any system does not include any information about systems that are spacelike separated from it.

3.The predictions of quantum mechanics.

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Which of our classical assumptions does quantum mechanics compel us to abandon?

Pierre Duhem (1861-1916) W.V.O. Quine (1908-2000)

The Duhem-Quine thesis: No scientific principle can be tested in isolation.

The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience. A conflict with experience at the periphery occasions readjustments in the interior of the field. Truth values have to be redistributed over some of our statements. Re-evaluation of some statements entails re-evaluation of others, because of their logical interconnections -- the logical laws being in turn simply certain further statements of the system, certain further elements of the field. (W.V.O. Quine, 1951)

If this view is right, it is misleading to speak of the empirical content of an individual statement -- especially if it be a statement at all remote from the experiential periphery of the field. Furthermore it becomes folly to seek a boundary between synthetic statements, which hold contingently on experience, and analytic statements which hold come what may. Any statement can be held true come what may, if we make drastic enough adjustments elsewhere in the system.

Even a statement very close to the periphery can be held true in the face of recalcitrant experience by pleading hallucination or by amending certain statements of the kind called logical laws. Conversely, by the same token, no statement is immune to revision. Revision even of the logical law of the excluded middle has been proposed as a means of simplifying quantum mechanics; and what difference is there in principle between such a shift and the shift whereby Kepler superseded Ptolemy, or Einstein Newton, or Darwin Aristotle?

Even a statement very close to the periphery can be held true in the face of recalcitrant experience by pleading hallucination or by amending certain statements of the kind called logical laws. Conversely, by the same token, no statement is immune to revision. Revision even of the logical law of the excluded middle has been proposed as a means of simplifying quantum mechanics; and what difference is there in principle between such a shift and the shift whereby Kepler superseded Ptolemy, or Einstein Newton, or Darwin Aristotle?

Hilary Putnam: “Is logic empirical?” (1968)

Quantum mechanical experiments can be reconciled with realism if we accept a revision in our logic.

Distributive law:

A and (B or C) (A and B) or (A and C)

e.g. “The electron reached the screen and

(passed through slit B or passed through slit C)” implies:

“The electron reached the screen and passed through slit B”

OR,

“The electron reached the screen and passed through slit C”

The measurement problem:

How does a superposition of different possibilities resolve itself into some particular observation?

John Von Neumann (1903-1957)

Process 1: Determination of the state of a system by a measurement process

Process 2: Deterministic evolution according to the Schrodinger equation

Schrodinger’s “Cat paradox”

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following diabolical device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small that perhaps in the course of one hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. The Psi function for the entire system would express this by having in it the living and the dead cat (pardon the expression) mixed or smeared out in equal parts.

It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a “blurred model” for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.

(Schrodinger, 1935)

The “ensemble interpretation”:

Quantum mechanics has nothing to say about the properties of individual particles or systems.

Its essential subject matter is the statistical correlations exhibited by large collections, or “ensembles,” of objects.

The “Many Worlds” Interpretation

Einstein: EPR correlations, in conjunction with special relativity, imply the existence of local hidden variables not described by quantum mechanics.

Bell’s theorem: Empirical correctness of quantum mechanics implies the impossibility of local hidden variables.

David Bohm (1917-1992): The conjunction of Bell’s theorem with the empirical success of quantum mechanics implies that a non-local reality lies beneath the quantum statistics.

Bohmian mechanics: Particles move deterministically in a Galilean-- pre-relativistic-- background spacetime. Their motions are guided by “pilot waves,” which are responsible for their wave-like behavior.

“Is it not clear from the smallness of the scintillation on the screen that we have to do with a particle? And is it not clear, from the diffraction and interference patterns, that the motion of the particle is directed by a wave? De Broglie showed in detail how the motion of a particle, passing through just one of two holes in screen, could be influenced by waves propagating through both holes. And so influenced that the particle does not go where the waves cancel out, but is attracted to where they cooperate. This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored.” (Bell 1986)

Pilot waves in the double slit experiment