Principle of locality

Locality is in physics the property of a theory that operations affect only their direct spatial environment. Nonlocality also allows to predict effects with long-term effects.

Basics

In non-locality and locality it is in principle to the question of whether or under what conditions an event can influence another event. ( Sub- event is understood in physics any physical process that takes place at a certain time in a certain place. ) The answer to this question falls within the running down of physical theories vary.

Locality in Newtonian physics

In classical physics or Newtonian mechanics this question (namely, when and what events can influence ) does not explicitly investigated, however, arises as a direct consequence of Newton's basic assumptions ( absolute time, absolute space, etc.) that in principle any event any other can influence. In other words, there are any long-term effects possible.

A typical example is the classical Newtonian concept of gravity, which seems arbitrary remote and instantaneous.

Locality in special relativity

In the special theory of relativity Einstein the Newtonian concepts of space and time have been modified so that a Neubeantwortung the above question was interesting. It has been shown that there are events that could not in principle be influenced. These are, for example, pairs of events that can not be connected by a beam of light, as in the special theory of relativity the speed of light is regarded as the top speed limit.

Example: An event A, here and now on earth, and an event B, which takes place a year later on Alpha Centauri, can not be connected by a light beam, as Alpha Centauri four light-years away and all of the light beam after a year of Alpha Centauri has not been reached. Since an influence - of any kind - can be as light is not faster, A and B can not influence each other as well. Physicists call this from a space-like separation of the events A and B. It is also said that the event B for the event A is non- local.

It is a fundamental statement of the ( special ) theory of relativity, that the causality, ie the strict sequence of cause and effect, only be maintained if the events A and B can influence each other. Since you do not want to give up causality, one accepts the existence of more that will not uncontrollable events. We therefore formulated in the special theory of relativity the principle of locality: Only local events can affect a physical process.

Non-locality in quantum theory

In the Copenhagen interpretation of quantum mechanics, the situation looks different. Since the development of quantum theory (although later developed ), the theory of relativity was not observed ( but the quantum theory was constructed entirely of non-relativistic principles ), it is not surprising that the principle of locality does not apply here.

In principle postulates of quantum mechanics, that the distribution of the results of a measurement of certain physical quantities ( " readings " ) probabilities can be specified only. A typical example is the probability distribution of the electron in the atom (atomic orbital). It is ( almost ) never zero, near the nucleus not, but not on Alpha Centauri (although very low, almost zero). This location probability distribution is described by the magnitude square of the amplitude of the wave function. At the moment, a real measurement (" where the electron is now " ) collapses the wave function: At the site of the electron becomes one, zero everywhere else. The question to which the quantum mechanics only implicitly gives an answer is whether this collapse of the wave function instantaneously ( at the moment ) occurs or is "only " propagates with the speed of light. In other words, if a measurement of the location of an electron on earth is done, how fast the wave function changes its value to zero on Alpha Centauri? Immediately or in four years? The implicit answer of quantum theory means that the collapse of the wave function occurs instantaneously, so it is non-local (hence implies action at a distance ). Exactly this fact is known as quantum non-locality.

This highly theoretical models can, however, re-enact practically already with so-called entangled pairs, where a quantum mechanical measurement attracts a place a collapse of the wave function at a different location to be. This shows that although the collapse of the wave function occurs instantaneously, but no real information can be transmitted, so that the Einstein causality remains. These results correspond to the Copenhagen interpretation of quantum mechanics, the attributes of the wave function is no immediate physical reality, but only the measurement results. The " collapse" of the wave function is therefore not a physical phenomenon that would have to be " transferred " the speed of light. Our knowledge of the realized possibility of the measurement process to a part of the folded pair excludes only certain other measurement results to the other part. What measurement results are excluded, but you just know when you know also the first measurement result. This information must be transmitted classical.

However, this so-called quantum teleportation allows a particularly secure encryption: If the sender and receiver each have a part of an entangled pair, so they can send encrypted messages that could not be intercepted by third unnoticed principle ( quantum cryptography ). However, this applies only in the event that the " eavesdropper " a classical measurement process in determining the quantum state of a trapped particle used. A group of U.S. scientists from the Massachusetts Institute of Technology succeeded under the leadership of Kim Taehyun in November 2006 unnoticed listen to up to 40 % of the transmission in an encrypted according to the BB84 protocol message - but in a simulation and in laboratory conditions. The results of the experiment were published on 25 April 2007 in the journal Physical Review.