Measurement and the creation/loss of information

In summary: I.e. there is no correct interpretation.)In summary, when measuring the polarisation of a photon, the collapse of its state along the eigenvector of the observable can be seen as both a loss and creation of information. However, this interpretation may not necessarily be accurate and is often not taken too seriously in practice. The postulates of quantum mechanics are mainly used as a starting point and the actual interpretation of the results is based on experience and experimentation.
  • #1
entropy1
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If we measure, say, the polarisation of a photon, the polarisation state of the photon collapses along the eigenvector of the observable corresponding to the measurement.

This may seem as a loss of information of the original polarisation (for it is now collapsed into another value). However, it can also be viewed as the creation of information (ie the measurement result).

What is the correct interpretation?
 
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  • #2
entropy1 said:
If we measure, say, the polarisation of a photon, the polarisation state of the photon collapses along the eigenvector of the observable corresponding to the measurement.

This may seem as a loss of information of the original polarisation (for it is now collapsed into another value). However, it can also be viewed as the creation of information (ie the measurement result).

What is the correct interpretation?

In this paper in section 5.4 you'll find a similar question discussed

Quantum mechanics: Myths and facts
Hrvoje Nikolic

http://arxiv.org/abs/quant-ph/0609163
 
  • #3
entropy1 said:
If we measure, say, the polarisation of a photon, the polarisation state of the photon collapses along the eigenvector of the observable corresponding to the measurement.

This may seem as a loss of information of the original polarisation (for it is now collapsed into another value). However, it can also be viewed as the creation of information (ie the measurement result).

What is the correct interpretation?
Neither.

The polarization of a beam of light changes upon passing the polarizer. Typically part of the light is absorbed and the intensity of the output beam is dimmed by a factor determined from Malus'[/PLAIN] law. Interpreted in terms of photons (as clicks of a hypothetical detector at the end of the ingoing or outgoing beam) the rate of photons is proportional to the intensity. One cannot say what happens to a single photon. The conventional way to talk about the reduced rate is to say that the photon emerges in the state determined by the polarizer with a probability given by Malus' law, and is absorbed otherwise.

But to interpret this in terms of the Copenhagen interpretation (where states can collapse) one needs to work in Fock space, representing input and output as a superposition of the dark (or vacuum) state ##|0\rangle## containing no photon and the 1-photon state ##|1,\psi\rangle##, where ##\psi## is the incoming polarizaion state, projecting it upon passing the polarizer to another such superposition. Measurable (in principle - though never done in practice) in this setting is the amount of energy left in the polarizer, nothing else. I never saw anyone actually doing that - people pay only lipservice to Born's rule, a probabilistic version of Malus' law (which refers to intensity) and the associated postulates and argue about the situation in a heuristic way. (What is measured in practice is the rate of clicks at a detector at the end of the outgoing beam, upon which the photon disappears, so that Born's rule is not applicable.)

Moral: Don't take the postulates of quantum mechanics too seriously. They exist only to introduce the subject and to motivate the formalism. Once one has digested the real thing one always resorts to shut-up-and-calculate, and imports from experience the little bits needed to interpret the results in terms of experiments as one sees fit.
 
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1. How is information created during measurement?

Information is created during measurement through the process of observation and data collection. When a scientist measures a physical quantity, they are gathering information about the properties and behavior of that quantity. This information is then recorded and used to gain a better understanding of the phenomenon being studied.

2. Can information be lost during measurement?

In most cases, information cannot be lost during measurement. However, there are certain factors that can affect the accuracy and precision of measurements, such as human error, equipment limitations, and external influences. These factors can result in the loss of some information, but it can often be corrected or minimized through proper measurement techniques.

3. How does the accuracy of a measurement impact the creation of information?

The accuracy of a measurement is closely related to the amount of information that can be created. A more accurate measurement will provide a more precise and detailed understanding of the quantity being measured, resulting in a larger amount of information being created. On the other hand, a less accurate measurement may result in a loss or distortion of information.

4. How does the type of measurement affect the creation/loss of information?

The type of measurement being conducted can greatly impact the creation or loss of information. For example, some measurements may involve direct observation of a phenomenon, while others may require the use of instruments or mathematical calculations. Each type of measurement has its own limitations and sources of error that can affect the amount of information that is created or lost.

5. Can information be created or lost during data analysis?

Yes, information can be created or lost during data analysis. After measurement, scientists analyze and interpret the data collected to draw conclusions and make discoveries. The accuracy and thoroughness of this analysis can greatly impact the amount of information that is created. Additionally, data analysis can also reveal errors or limitations in the original measurements, leading to the loss of some information.

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