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Towards the phenomenon of quantum entanglement



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A. Zeilinger, Dance of the Photons, Farrar, Straus and Giroux (2010)


Taken partly from the delightful book "Dance of the Photons" by Anton Zeilinger marked with quotes. Science and humor are not contradictions, sometimes violating Bell's inequality. Key formulas be added over time if necessary.

Bell’s inequality

"A mathematical expression derived by John Bell. It expresses the fact that correlations between two classical systems are limited in strength. Quantum mechanical measurements on entangled states are able to violate Bell’s inequality."

Bell states

"The concept that the polarizations of two photons can be entangled in four different ways with each other. These are the four maximally entangled Bell states."

Double-slit experiment

"An experiment where light, or any other particle, passes a diaphragm with two slit openings. The resulting particle distribution pattern on an observation screen depends on which kind of information exists about the path taken by the particles." Feynman: We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery [Fey62].


"The concept in quantum physics that two or more particles can be connected in a much stronger way with each other than in classical physics. Measurement on one can instantly, over an arbitrary distance, influence the quantum state of the other one. Albert Einstein called entanglement 'spooky'."

Heisenberg’s uncertainty principle

"The idea that quantum particles cannot be at a well-defined position and have a well-defined momentum (that is, speed) at the same time. If one is more certain, the other becomes more uncertain."

Imaginary Time

Hawking describing the Carter-Penrose diagram: There is another asymptotically flat region on the left that seems to correspond to another universe that is connected to ours only through a wormhole. However, as we shall see, it is connected to our region through imaginary time [Haw94].


"A particle is well localized in a single position and moves along a well-defined trajectory through space."


Photons have each a definite energy and momentum, depending on the frequency of the light. A fraction of a photon is never observed [Dir30].


"Initially, each atomic or subatomic particle. Today, every system that shows quantum behavior such as superposition and entanglement."

Quantum complementarity

"The feature that two or more observables of a quantum system—for example, the path taken by a particle in a double-slit experiment and the interference pattern—cannot be well-defined at the same time."

Quantum mechanics

"As opposed to classical mechanics, the realm of physics that describes, originally, very small particles, but now, increasingly, larger objects. It is governed by notions like quantum uncertainty and entanglement." Feynman: “Quantum mechanics” is the description of the behavior of matter and light in all its details and, in particular, of the happenings on an atomic scale. Things on a very small scale behave like nothing that you have any direct experience about. They do not behave like waves, they do not behave like particles, they do not behave like clouds, or billiard balls, or weights on springs, or like anything that you have ever seen [Fey62].

Quantum nonlocality

"The viewpoint of most physicists is that the violation of Bell’s inequality shows us that quantum mechanics is nonlocal. This nonlocality is exactly what Albert Einstein called 'spooky'; it seems that the act of measuring one particle could instantly influence the other one."

Quantum superposition

"The feature that a quantum system can be in two states at the same time, for example, two different spin states."

Quantum teleportation

"The transfer of a quantum state -that is, certain properties of a system- over to another system, which may be in principle arbitrarily far away. Quantum teleportation uses entanglement as the means of transmitting that information."


Form of the physical reality (Form der körperlichen Wirklichkeit) [Wey19].


There is no need to introduce the idea of an ether, whose presence anyway cannot be detected, as the Michelson–Morley experiment showed. The theory of relativity does, however, force us to change fundamentally our ideas of space and time. We must accept that time is not completely separate from and independent of space, but is combined with it to form an object called spacetime [Haw94].


Form of stream of consciousness (Form des Bewußtseinstromes) [Wey19].


For discussion: The collapse of space [thus time] is a necessary criterion for quantum nonlocality and entanglement.


- Scientific statements on quantum entanglement to be published from 2024 on -

"I would recommend not to use the term 'criterion'. In quantum mechanics, it is particularly important not to think of quanta as mass points. Nonlocality and entanglement are simply not compatible with the classical concepts of space and time. We can ask: where do these classical concepts come from? Should we modify (generalise) them or should we accept their incompatibility? We have to think about time together. Time does not collapse. This is only special if you are familiar with Kant's 'a priori' and believe that the 'a priori' must be there before any cognition and cannot be changed by the act of cognition."

Prof. Dr. Siegmar Roth, formerly Max Planck Institute for Solid State Research, dpt. Prof. Dr. Klaus v. Klitzing