This isn't always obvious-- even some things that are fundamentally quantum, like black-body radiation , appear to involve continuous distributions. But there's always a kind of granularity to the underlying reality if you dig into the mathematics, and that's a large part of what leads to the weirdness of the theory. One of the most surprising and historically, at least controversial aspects of quantum physics is that it's impossible to predict with certainty the outcome of a single experiment on a quantum system.

When physicists predict the outcome of some experiment, the prediction always takes the form of a probability for finding each of the particular possible outcomes, and comparisons between theory and experiment always involve inferring probability distributions from many repeated experiments. There's a lot of debate about what, exactly, this wavefunction represents, breaking down into two main camps: those who think of the wavefunction as a real physical thing the jargon term for these is "ontic" theories, leading some witty person to dub their proponents "psi-ontologists" and those who think of the wavefunction as merely an expression of our knowledge or lack thereof regarding the underlying state of a particular quantum object "epistemic" theories.

In either class of foundational model, the probability of finding an outcome is not given directly by the wavefunction, but by the square of the wavefunction loosely speaking, anyway; the wavefunction is a complex mathematical object meaning it involves imaginary numbers like the square root of negative one , and the operation to get probability is slightly more involved, but "square of the wavefunction" is enough to get the basic idea.

This is known as the "Born Rule" after German physicist Max Born who first suggested this in a footnote to a paper in , and strikes some people as an ugly ad hoc addition. There's an active effort in some parts of the quantum foundations community to find a way to derive the Born rule from a more fundamental principle; to date, none of these have been fully successful, but it generates a lot of interesting science.

This is also the aspect of the theory that leads to things like particles being in multiple states at the same time. All we can predict is probability, and prior to a measurement that determines a particular outcome, the system being measured is in an indeterminate state that mathematically maps to a superposition of all possibilities with different probabilities.

Whether you consider this as the system really being in all of the states at once, or just being in one unknown state depends largely on your feelings about ontic versus epistemic models, though these are both subject to constraints from the next item on the list:. A quantum teleportation experiment in action.

## Quantum chemistry on quantum computers | Feature | Chemistry World

The last great contribution Einstein made to physics was not widely recognized as such, mostly because he was wrong. In a paper with his younger colleagues Boris Podolsky and Nathan Rosen the "EPR paper" , Einstein provided a clear mathematical statement of something that had been bothering him for some time, an idea that we now call "entanglement. The EPR paper argued that quantum physics allowed the existence of systems where measurements made at widely separated locations could be correlated in ways that suggested the outcome of one was determined by the other.

They argued that this meant the measurement outcomes must be determined in advance, by some common factor, because the alternative would require transmitting the result of one measurement to the location of the other at speeds faster than the speed of light. Thus, quantum mechanics must be incomplete, a mere approximation to some deeper theory a "local hidden variable" theory, one where the results of a particular measurement do not depend on anything farther away from the measurement location than a signal could travel at the speed of light "local" , but are determined by some factor common to both systems in an entangled pair the "hidden variable".

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This was regarded as an odd footnote for about thirty years, as there seemed to be no way to test it, but in the mid's the Irish physicist John Bell worked out the consequences of the EPR paper in greater detail. Bell showed that you can find circumstances in which quantum mechanics predicts correlations between distant measurements that are stronger than any possible theory of the type preferred by E, P, and R.

This was tested experimentally in the mid's by John Clauser, and a series of experiments by Alain Aspect in the early 's is widely considered to have definitively shown that these entangled systems cannot possibly be explained by any local hidden variable theory. The most common approach to understanding this result is to say that quantum mechanics is non-local: that the results of measurements made at a particular location can depend on the properties of distant objects in a way that can't be explained using signals moving at the speed of light.

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This does not, however, permit the sending of information at speeds exceeding the speed of light, though there have been any number of attempts to find a way to use quantum non-locality to do that. Refuting these has turned out to be a surprisingly productive enterprise-- check out David Kaiser's How the Hippies Saved Physics for more details. You could decide to put the jar on the counter-top, or on one of the shelves above it. It just means they come in levels. In the quantum world, everything is split into levels.

But the quantum world is weird.

Give an electron a kick of energy and it will jump instantly from one level to another. Somewhere between the scale of the atom and the billiard ball there is a crossover point in the laws of physics — a bit like a jurisdictional handover between state and federal police. Stick enough atoms together and weird quantum effects fade away, the behaviour becomes classical.

This is called the correspondence principle.

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Some things in quantum physics are literally unknowable. One way to understand this is through the related observer effect — how making a measurement can change the result. For example, to find out where an electron is, you need to detect it with something for example a photon of light but this probing, however gentle, will knock the electron off its original course.

The electron tells you where it is, but forgets where it was going. But the uncertainty principle goes much deeper than the observer effect alone. It says there is an innate fuzziness to nature. The electron is not a point particle, but a smear of electron-ness spread out in space.

Quantum objects like photons and electrons have split personalities — sometimes they behave like waves, and sometimes like particles.

### Rule breakers

Crucially, quantum wave-functions can have many possible solutions — each with a distinct probability of being true. Amazingly, the different possible answers seem to interact with one another in a sort of limbo of states called superposition — as if conspiring together to give us the reality of our universe see "two-slits" below. Imagine a cat in a box along with a vial of cyanide. There is a hammer held by a string above the vial. The hammer is designed to fall when tripped by a random quantum event for example, the decay of an atom of uranium.

The atomic decay follows quantum laws, and so its wave-function has two solutions: decayed or not decayed. According to quantum theory, until you make a measurement these two possibilities are equally valid. Or get the original from my archive.

## Mathematical Concepts of Quantum Mechanics

Giunta operates a website where one can get brief copies of Langmuir's, Kossel's, and others' classical papers, and he is Co-Editor of Foundations of Chemistry. He also gives good links to other sites, the link-title being : Other web sites on mainly the History of Chemistry, History of Science, and Scientific Biography. Some interesting connections to the early classics of the chemical bond. Eric R. Scerri, Faculty page, Scerri's publication list may also be found there. Obituary : DFT - Peter M.

Gill is Prof. He may be found under his Faculty Page at Nottingham University. History in another mode of presentation - educating and entertaining. Some DFT'ists might object, yet, as Daudel once answered to this website: "It's published, you know". Short-time expositions [due to limited web space] :. Gadamer was THE famous philosophy teacher of the recent period.

### Description

Here for a limited period untill I need the space otherwise a short clipping of a lecture 7 min concerning philosophy and modern natural sciences. The language is synchronized Italian, very clear, so it should be understandable to all romanic language speaking people. Origin: RAI-edu-cultura. Compressed in MPEG4, no streaming, needs e.

Karl Popper remember?