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The Nature of Measurement
Contents:
  1. uncertainty principle | Definition & Equation | nyarefwheatgmenti.ml
  2. Was Heisenberg wrong?
  3. Common Interpretation of Heisenberg's Uncertainty Principle Is Proved False
  4. Heisenberg's Uncertainty Principle

At least at the subatomic level. To measure the properties of a particle such as an electron, one needs to use a measuring device, usually light or radiation.

uncertainty principle | Definition & Equation | nyarefwheatgmenti.ml

But the energy in this radiation affects the particle being observed. If you adjust the light beam to accurately measure position, you need a short-wavelength, high-energy beam. It would tell you position, but its energy would throw off the momentum of the particle. Then, if you adjust the beam to a longer wavelength and lower energy, you could more closely measure momentum, but position would be inaccurate. This principle punctured the centuries-old, firmly held belief that the universe and everything in it operates like clockwork.

To predict the workings of the "clock," one needs to measure its qualities and parts at a specific point in time. Classical physics assumed that the precision of measuring is theoretically unlimited. But Heisenberg stated that since you could never with great certainty measure more than one property of a particle, you could only work with probability and mathematical formulations. The uncertainty principle was hard even for scientists to accept at first.

After struggling with it, however, Bohr developed complementarity theory. This stated that there was a dual nature to things -- an electron was a wave and a particle, for example -- but we could only perceive one side of that dual nature.


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A sphere, for instance, has a convex and concave aspect. We can sense the convex from outside the sphere, but from inside it appears completely concave.

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This theory would affect much more than physics, but other fields of science, as well as art and philosophy. Heisenberg and Bohr's theories were compatible and became known together as the Copenhagen interpretation and accepted as the foundation for quantum theory. Fully mathematical physicists listened to his brief exposition of a conception which will make it necessary to modify belief in what we are pleased to call "common sense" and "reality. This then leads to the following picture.

First we measure the momentum of the electron very accurately. At this instant, the position of the particle becomes well-defined and, again, one can regard this as a physically real attribute of the particle. The meaning and validity of this claim can be verified by a subsequent momentum measurement. The question is then what status we shall assign to the momentum of the electron just before its final measurement.


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  • Is it real? According to Heisenberg it is not. Before the final measurement, the best we can attribute to the electron is some unsharp, or fuzzy momentum.

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    These terms are meant here in an ontological sense, characterizing a real attribute of the electron. The interpretation of these relations has often been debated. Or else, are they restrictions of an ontological nature, i. The difference between these interpretations is partly reflected in the various names by which the relations are known, e.

    The debate between these views has been addressed by many authors, but it has never been settled completely. Let it suffice here to make only two general observations. However, ontological questions seemed to be of somewhat less interest to him. For example, there is a passage Heisenberg , where he discusses the idea that, behind our observational data, there might still exist a hidden reality in which quantum systems have definite values for position and momentum, unaffected by the uncertainty relations.

    He emphatically dismisses this conception as an unfruitful and meaningless speculation, because, as he says, the aim of physics is only to describe observable data. Similarly, in the Chicago Lectures, he warns against the fact that the human language permits the utterance of statements which have no empirical content, but nevertheless produce a picture in our imagination. He notes,. So, Heisenberg also endorsed an interpretation of his relations as rejecting a reality in which particles have simultaneous definite values for position and momentum.

    Was Heisenberg wrong?

    The second observation is that although for Heisenberg experimental, informational, epistemological and ontological formulations of his relations were, so to say, just different sides of the same coin, this is not so for those who do not share his operational principles or his view on the task of physics. Alternative points of view, in which e. The statement, often found in the literature of the thirties, that Heisenberg had proved the impossibility of associating a definite position and momentum to a particle is certainly wrong.

    And because no agreement has been reached on this latter issue, one cannot expect agreement on the meaning of the uncertainty relations either. In the English literature the name uncertainty principle became most common. But this can well be read as his yielding to common practice rather than his own preference. But does the relation 2 qualify as a principle of quantum mechanics?

    Several authors, foremost Karl Popper , have contested this view. Popper argued that the uncertainty relations cannot be granted the status of a principle on the grounds that they are derivable from the theory, whereas one cannot obtain the theory from the uncertainty relations. There are many statements in physical theories which are called principles even though they are in fact derivable from other statements in the theory in question. Einstein proposed this famous classification in Einstein Constructive theories are theories which postulate the existence of simple entities behind the phenomena.

    Common Interpretation of Heisenberg's Uncertainty Principle Is Proved False

    They endeavour to reconstruct the phenomena by framing hypotheses about these entities. Principle theories, on the other hand, start from empirical principles, i. The purpose is to build up the theory from such principles. That is, one aims to show how these empirical principles provide sufficient conditions for the introduction of further theoretical concepts and structure.

    The prime example of a theory of principle is thermodynamics. Here the role of the empirical principles is played by the statements of the impossibility of various kinds of perpetual motion machines. These are regarded as expressions of brute empirical fact, providing the appropriate conditions for the introduction of the concepts of energy and entropy and their properties.

    There is a lot to be said about the tenability of this view, but that is not our topic here. Now obviously, once the formal thermodynamic theory is built, one can also derive the impossibility of the various kinds of perpetual motion. They would violate the laws of energy conservation and entropy increase. But this derivation should not misguide one into thinking that they were no principles of the theory after all. The point is just that empirical principles are statements that do not rely on the theoretical concepts in this case entropy and energy for their meaning.

    Heisenberg's Uncertainty Principle

    They are interpretable independently of these concepts and, further, their validity on the empirical level still provides the physical content of the theory. A similar example is provided by special relativity, another theory of principle, which Einstein deliberately designed after the ideal of thermodynamics.

    Here, the empirical principles are the light postulate and the relativity principle. Again, once we have built up the modern theoretical formalism of the theory Minkowski space-time , it is straightforward to prove the validity of these principles. But again this does not count as an argument for claiming that they were no principles after all.

    So, it must have seemed obvious to his readers that he intended to claim that the uncertainty relation was a fundamental principle, forced upon us as an empirical law of nature, rather than a result derived from the formalism of the theory. Similarly, in a paper of , he described the content of his relations as:. It has turned out that it is in principle impossible to know, to measure the position and velocity of a piece of matter with arbitrary accuracy.

    Heisenberg 26, [emphasis added]. So, although Heisenberg did not originate the tradition of calling his relations a principle, it is not implausible to attribute the view to him that the uncertainty relations represent an empirical principle that could serve as a foundation of quantum mechanics.