Location (physics)

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In physics, locality is the property of a theory that processes only have direct effects on their immediate spatial environment. Non-locality also makes it possible to predict long-range effects .

In the case of non-locality and locality , the main question is whether or under what conditions an event can influence another event. In physics, an event is understood to be any physical process that takes place at a specific time at a specific location. The answer to that question is different in each of the physical theories detailed below.

Locality in Newtonian physics

In classical physics or Newtonian mechanics , the question of when which events can influence each other is not explicitly investigated, but as a direct consequence of Newton's basic assumptions ( absolute time , absolute space , etc.) it emerges that in principle every event influences every other can. In other words, any remote action is possible.

A typical example is the (outdated) classical Newtonian concept of gravity , according to which it acts remotely and instantaneously.

Locality in the special theory of relativity

In Einstein's special theory of relativity , the Newtonian terms of space and time were modified so that a new answer to the above question became interesting. It has been shown that there are events that in principle cannot influence one another. These are z. B. Pairs of events that cannot be connected by the world line of a ray of light, because in the special theory of relativity the speed of light is regarded as the uppermost limit speed.

Example: An event A, here and now on Earth , and an event B that takes place a year later on Alpha Centauri cannot be connected by a ray of light because Alpha Centauri is four light years away and the ray of light is Alpha Centauri after a year has not yet reached. Since an influence - of whatever kind - cannot be faster than light, A and B cannot influence each other. Physicists speak of a space-like separation of events A and B. It is also said that event B is non-local for event A (see also light cone ).

It is a fundamental statement of the (special) theory of relativity that causality , i.e. the strict sequence of cause and effect, is only preserved if events A and B cannot influence each other. Since you don't want to give up causality, you tend to accept the presence of events that cannot influence each other. The principle of locality is therefore formulated in the special theory of relativity : Only local events can influence a physical process. In this sense, the principle also applies in relativistic quantum field theories .

Non-locality of quantum theory

In the initially dominant Copenhagen interpretation of quantum mechanics , the situation looks different. The quantum theory was formulated a few years after the relativity theory in the first third of the 20th century. It was built entirely from non-relativistic principles; Questions of the locality initially played no role.

In principle, quantum mechanics states that only probabilities can be specified for the distribution of the results of a measurement of certain physical quantities (“ measured values ”). A typical example is the distribution of the probability of an electron being in the atomic orbital . It is nowhere zero, neither very close to the atomic nucleus , nor at a distance of light years (although there very low or almost zero). This residence probability distribution is described by the square of the magnitude of the amplitude of the wave function . At the moment of a real measurement (“Where is the electron now?”) The probability at the found location of the electron becomes one, everywhere else zero. This transition is known as the collapse of the wave function .

The question to which quantum mechanics only gives an implicit answer is whether the collapse of the wave function occurs instantaneously or "only" propagates at the speed of light. In other words, if an electron is measured on Earth, how quickly does the wave function change its value to zero on Alpha Centauri? Immediately or in four years? The implicit answer of quantum theory is: The collapse of the wave function takes place instantaneously, so it is non-local (therefore implies remote effects). It is precisely this fact that is called quantum non-locality. An important thought experiment looking at this issue is the Einstein-Podolsky-Rosen paradox .

However, these theoretical explanations can already be practically simulated with entangled quantum pairs, where a quantum mechanical measurement at one location results in a collapse of the wave function at another location. It turns out that although the collapse of the wave function occurs instantaneously, no real information can be transmitted, so that the Einstein causality is still preserved. These results correspond to the Copenhagen interpretation of quantum mechanics, which ascribes no direct physical reality to the wave function, but only to the measurement results . The "collapse" of the wave function is therefore not a measurable phenomenon; H. not a physical phenomenon that would have to be "transmitted" at the speed of light. Our knowledge of the realized possibility of the measurement process on one part of the entangled pair only excludes certain measurement results on the other part. However, you only know which measurement results are excluded if you know the first measurement result. This information must be transmitted classically, i.e. taking locality into account.

However, this quantum teleportation offers the possibility of particularly secure encryption : If the sender and recipient each have part of an entangled pair, they can send each other encrypted messages that, in principle, could not be eavesdropped by third parties unnoticed ( quantum cryptography ). However, this only applies in the event that the “eavesdropper” uses a classic measurement process to determine the quantum state of an intercepted particle . In November 2006, a group of US scientists from the Massachusetts Institute of Technology succeeded in listening to up to 40% of the transmission unnoticed in a message encrypted using the BB84 protocol - albeit in a simulation and under laboratory conditions .

Web links

literature

  • Tim Maudlin: Quantum non-locality and relativity - metaphysical intimations of modern physics. Blackwell, Malden 2002, ISBN 0-631-23220-6 .
  • Peter G. Bergmann: Classical and quantum nonlocality. World Scientific, Singapore 2000, ISBN 981-02-4296-4 .
  • Andrej A. Grib et al: Nonlocality in quantum physics. Kluwer, New York 1999, ISBN 978-0306461828 .
  • William M. Dickson: Quantum chance and non-locality - probability and non-locality in the interpretations of quantum mechanics. Cambridge University Press, Cambridge 1998, ISBN 0-521-58127-3 .
  • Michael Redhead: Incompleteness, nonlocality and realism - a prolegomenon to the philosophy of quantum mechanics. Clarendon Press, Oxford 1987, ISBN 0-19-824937-3 .
  • John S. Bell : Indeterminism and Nonlocality. In: Natural science and worldview - mathematics and quantum physics in our thought and value system. Hölder-Pichler-Tempsky, Vienna 1992, ISBN 3-209-01466-3 , pp. 85-98.

Individual evidence

  1. It is now assumed that the effect of gravity also spreads with the speed of light.
  2. Taehyun Kim, Ingo Stork called Wersborg, Franco NC Wong, Jeffrey H. Shapiro: Complete physical simulation of the entangling-probe attack on the BB84 protocol. Phys. Rev. A 75, 042327 (2007). (PDF; 180 kB).