In quantum information science, groups of two or more quantum objects can have energetic states that are entangled. These states can have properties unlike anything in classical physics. In classical information science, a familiar example is a string of bits, encoded via real physical objects, like the spin of an atomic nucleus or the polarization of a photon of light, but abstractly by zeros (down-state) or ones (up-state). A qubit, the quantum version of a bit, has many more possible states than just these two. The quantum version reveals that each of these two states is split into a multiplicity of states so that the final outcome can be weighted in many, many different ways.(1)
Entanglement, as explained by Aczel(2) is an application of the superposition principle to a system comprised of two or more subsystems. In his case, he lets each of the subsystems be a single particle and asks “What does it mean to say that the two particles are entangled?” He postulates that Particle 1 has equal probability of being in states A or C, which represent different physical locations. Particle 2, on the other hand, has equal probability of being in states B or D which have two additional, different locations. When the overall system of these two particles has fully reacted with each other and is in the product state, AB, Particle 1 is known to be in State A while Particle 2 is known to be in State B. Similarly, the other possible product state CD has Particles 1 and 2 in States C and D, respectively. The implicit assumption, here, is that non-local states are connected somehow.
Since the mathematical aspects of the superposition principle also allows the system to be in a combination of product states, the state AB + CD is also an allowed state and thus, for the entire system, this is called an entangled state. This entangled state says that there are now Particle 1 and 2 possibilities that are strongly correlated. Thus, if an experimental measurement finds Particle 1 in State A, then Particle 2 “must” be in State B and cannot be in State C or D. This means that, when Particles 1 and 2 are entangled, there is no way to characterize either one of them by itself, as if it were isolated from the other. In the superposition state the two are strongly linked and do not have independence of action!
Erwin Schröedinger, Nobel Prize Winner in the 1930’s for his mathematical formulation of the probability wave function equation for quantum mechanics, was the very first to predict the existence of quantum entanglement for fundamental particles and photons. Einstein labeled this “spooky action at a distance”.
In 2003, Ghosh(3) and his collaborators at the University of Chicago analyzed ten year old experimental data on some very low temperature (~1o Kelvin) magnetic susceptibility and heat capacity of a small magnetic salt crystal containing holmium atoms and compared them to quantum theory. Above ~1oK, classical mechanics theory gave a good match to the experimental data. However, quantum mechanical entanglement contributions had to be added in order to give a good match with his experimental data below 1oK.
This is typical of many, many experiments carried out to distinguish classical vs. quantum type of behavior as a function of system temperature and system size. It has been generally found that (1) as the temperature increases from very low values, a few degrees, and (2) the system size increases from ~two photons or fundamental particles to a very small crystal, the boundary between quantum-like behavior and classical-like behavior becomes very fuzzy. Well-developed classical-like behavior sets in far below room temperature and system sizes well below 1 cubic centimeter.
The effect validated by Ghosh et al(3) was first predicted by Vedral(4) two years earlier. If the theoretical idea of Reznik(5) is true, that all of empty space (the physical vacuum) is filled with entangled particles, then quantum-like behavior might be retained up to almost room temperature. Continuing along this line of thought, Brukner, Vedral and others(6) showed theoretically that time can become entangled too. This latter information puts space and time on an equal footing in quantum mechanics which is an absolute “no-no” for our “present-day” formulation of quantum mechanics.
M. A. Nielsen, “Rules for a complex quantum world?, Scientific American, 287 (5) (2002) 67.).
D. Aczel, Entanglement (A Plume Book, Penguin Group, London, 2003).
S. Ghosh, Nature 425 (2003) 48.
M. C. Arnesen, S. Bose and V. Vedral, “Thermal Entanglement in 1D Heisenberg Model”, Phys. Rev. Lett. 87, 017901 (2001).
B. Reznik, “Entanglement from the Vacuum”, Foundations of Physics, 33 (1) 167-176, January 2003.
W. A. Tiller, White Paper III, Why CAM and Orthodox Medicine Have Some Very Different Science Foundations, www.tillerfoundation.org