Laplace demon

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The Laplace demon is a design by the mathematician Pierre-Simon Laplace.

The Laplace daemon is the illustration of the cognitive and scientific theory considers after it is possible within the meaning of the concept of a closed mathematical world system of equations, with the knowledge of all natural laws , and all initial conditions such as location, position and speed of all physical particles existing in the cosmos, at last and calculate and determine every future state. According to this statement, it would theoretically be possible to set up a world formula .

origin

The expression comes from the following statement by Pierre-Simon Laplace in the foreword of the Essai philosophique sur les probabilités from 1814:

“So we have to view the current state of the universe as the result of an earlier state and the cause of the state that comes after it. An intelligence which at a given moment knows all the powers with which the world is endowed and the present state of the structures which compose it and which, moreover, would be comprehensive enough to subject this knowledge to analysis, would in the same formula be Understand movements of the largest celestial bodies and those of the lightest atom. Nothing would be uncertain for them, future and past would be clear before their eyes. "

discussion

The basis of this idea is the determinism of law . According to the English chemist Robert Boyle in the 17th century, the universe is like clockwork; God created the universe with his laws in the way a watchmaker would build the perfect watch. Once created and brought into the correct initial state, let the universe run relentlessly according to the will of Divine Providence.

For Laplace, too, the world is completely determined by initial conditions and laws of motion, so that the task of natural philosophy , which is modeled on celestial mechanics , consists exclusively of the integration of differential equations. That would be the task of the “intelligence” that Laplace designs as a thought experiment. Arguments against the possibility of the existence of such an “intelligence” (the term “demon” was only established later) are the empirical inaccessibility of the small and the inaccessibility of very large masses in the cosmos.

Various objections can be raised against the possibility of a Laplace demon, which are based on principles recognized by Laplace's physics. Today, the Laplace demon only serves to illustrate a strictly deterministic worldview.

  1. The three-body problem (before 1888)
    Even before 1888 it was assumed, and since the corresponding work by Henri Poincaré and Heinrich Bruns , that differential equation systems that describe the motion of even three bodies can no longer be integrated in a closed manner and can therefore only be solved analytically in special cases. The demon is so for purely mathematical reasons not able "his knowledge of analysis to subject". At best, he can find approximate solutions that require more and more complex calculations or new measurements as time goes on. This applies to both calculating the future and the past. This objection is fundamentally mathematical.
  2. The theory of relativity (1905)
    According to the theory of relativity, it is not possible to grasp the entire cosmos, since information can be transported at the maximum speed of light. That is, a "horizon" is formed over which the demon could not look out. So he cannot capture all the states of the universe and consequently cannot predict them. This knowledge forbids the demon to exist.
  3. The uncertainty relation at the quantum level (around 1925)
    In quantum physics , no deterministic, exact predictions can be made, only probability statements are possible. According to the Copenhagen interpretation, this is not due to the ignorance of hidden variables , but reflects an absolute coincidence that exists at the quantum level. Hence, not only is the Laplace demon impossible (as after the two aforementioned objections), but determinism is inherently wrong. However, there are also deterministic interpretations of quantum mechanics, e.g. B. the De Broglie Bohm theory or the many worlds interpretation . If the measuring device is included, the measuring process can also be described without resorting to chance ( Von Neumann measuring process ) if the object is already in a state before the measurement in which the variable to be measured has a unique value (intrinsic state ). In all other cases, which also occur frequently, different measurement results are possible, for the frequency of which, for reasons of principle, only a probability can be calculated. Furthermore, the Schrödinger equation describes the state development of a system that develops undisturbed from the outside and can be described by a pure state . The time evolution operator can be formed from the Schrödinger equation , which is fundamentally unitary , i.e. H. describes a clear development (without chance) and is always mathematically reversible (i.e. the state can also be calculated back into the past). The Copenhagen interpretation expressly conforms to this for a pure state, only postulates future measurements from outside with a measurement operator that does not commute to this pure state as a coincidence. The restriction to a pure state is not a real restriction in this context - every system described by a mixed state can be interpreted as part of an overall system described by a pure state and mathematically supplemented. It can therefore not be decided empirically whether our reality is given by a pure state or a mixture of states. A Schrödinger equation encompassing the entire universe and all physical laws, effects and forces is, of course, very complex.
  4. Calculation Limits (1960s)
    The phenomena of chaos research also present the demon with an impossible task as long as he is part of the universe. Ultimately, the initial conditions clearly define the future, but the number of values ​​required for such a calculation grows exponentially. Therefore, it would take the demon a very long time to make predictions. Ultimately, so long that it usually needs at least as long to calculate the state of the universe as the universe needs to assume the state. His prediction, as a statement decoupled from the system, would come too late.

Since the demon is not supposed to represent an actual scientific goal, it does not have to be subject to a real condition, so the 1st, 2nd and 4th points are meaningless for the philosophical interpretation. Only the Copenhagen interpretation of quantum physics stands in the way of it, since it contains by definition unpredictable absolute coincidence. As far as point 3 is concerned, from an epistemological point of view, however, the entire world of science is built up inductively (i.e. it is fundamentally based on probability statements); deductive deductions can only be made in the formal systems (mathematics, logic).

See also

Individual evidence

  1. ^ O. Höfling: Physics. Volume II Part 1, Mechanics, Heat . 15th edition. Ferd. Dümmlers Verlag, Bonn 1994, ISBN 3-427-41145-1 .