Is electron a quantum observer?

Question

An electron can receive information and can modify internal state according to it. Is electron itself a quantum observer or it's applicable to classic objects only?

Answer 1

The difference between classical and quantum should be a continuum. As the number/complexity of a system increases, it should take "more classical" behaviors. It's common sense.

So we could say that an electron is an observer, just a really really poor one, on one edge of the spectrum (a detector screen being on the other edge, a great observer).

But, according to the postulates of QM, this is not true. This is not up to interpretation, it is a fact of QM.*

There's a fundamental incompatibility between both regimes that cannot be crossed. A quantum system can never even approach classical behaviors. Classical physics is not an extreme limit of QM. It is a whole, fully separate, utterly incompatible model.**

So no, an electron cannot be an observer. Even a detector screen, or an entire human being, cannot be an observer, if modeled within QM.

Only by modeling them as "the external classical thing" can they be observers. But such model for a single electron is ridiculously inaccurate to the point of uselessness.

*(It's specified in the postulate that says how QM states (mere pure math) can be converted to actual experimental results, often called the Born rule)

**(This is often called "the measurement problem")

Answer 2

In the Copenhagen interpretation of quantum mechanics there is the concept of Heisenberg cut, which separates the observer or measuring device (the "observer" does not have to be conscious in the Copenhagen interpretation) and the quantum system that is being observed or measured. The distinction is that the observer/measuring device must behave classically. Since a single electron is an intrinsically quantum system and does not have a purely classical description, it cannot be an "observer" in the Copenhagen interpretation.

A single electron can become entangled with another quantum system, but some other measuring device (that behaves classically) is then required to trigger the wavefunction collapse of this larger quantum system and to record the result of this collapse.

Answer 3

An "observer", referred to a given observable, is nothing but a physical system, an instrument, that is able to associate a (relatively) definite value for that observable for a quantum system that interacts with it.

I will henceforth use the term instrument in place of observer, as the latter may lead to some methaphisical implcations (e.g. consciousness), which make even more complicated an already difficult discussion.

The interaction with the instrument also changes the state of the measured quantum system and one speaks of post measurement state.

The measurement instrument satisfies properties similar to classical ones. In particular, it can be handled as a classical object. For instance, there is an output that is classically described (e.g., a display etc.)

However, there are several possible descriptions of the intrinsic nature of that instrument, and also a quantum nature is permitted a priori.

As a matter of fact, there are at least two Copenhagen interpretations. One due to Bohr, where instruments are of classical nature. The other, due to von Neumann, where instruments are of quantum nature, though they appear as classical objects at least regarding the description of outcomes of measurements. Here the interaction responsible for the measurement is a quantum process of a quantum system made of the measured system and the instrument. Nowadays, this latter interpretation is mostly used in quantum information when dealing with the so called mesurement schemes. There are however several open issues within this approach, issues somehow related to the notion of decoherence. Also the interpretation of the quantum formalism enters the game: if quantum theory is a theory of single systems or it always refers to an ensemble of identical systems

It is evident that an electron cannot be considered a measurement instrument according to the above discussion. At most, it can be used as a probe which is a part of an instrument.

Answer 4

Some people advocate the Copenhagen interpretation, which claims that observers are fundamental for some unexplained reason. But the equations of motion of quantum systems say nothing about observers, so if we take those equations without modification, then observers play no fundamental role in quantum theory, claims to the contrary notwithstanding.

When a quantum system interacts with another quantum system in an interaction that produces information that can be copied that suppresses interference - this is called decoherence. When decoherence takes place, observables evolve the way that the relevant quantity would evolve in classical physics to a good approximation. However, the world is not actually classical and decoherent systems can and do carry quantum information and neglecting this has led to false claims that quantum physics is non-local.

An interaction with an electron can cause decoherence since it can copy information about another system. But an electron doesn't necessarily spread that information widely so the laws of physics wouldn't forbid undoing the interaction, which would reverse the decoherence.

Answer 5

An electron can receive information and can modify internal state according to it.

Do not confuse the description of the state of an electron (via a wave function or density matrix) with an electron.

An electron can not "receive information."

An electron does not have any "internal state," unless you would like to consider the spin direction part of its "internal state." (Though this can be misleading, since there is no sense in which the electron is an extended body that is "spinning.")

There are no hidden mechanisms inside an electron. There is no internal mechanism for storage inside an electron.

Is electron itself a quantum observer or it's applicable to classic objects only?

No, an electron is not an observer.

An observer can perform a measurement of an Observable (Hermitian operator with complete set of states) and the result is a real value (the measured value).

An "observer" should be thought of as a measurement apparatus.

One simple example of a measurement apparatus is the Stern-Gerlach apparatus. This machine takes a particle beam as input and separates the beam into its fixed-spin components. For example, a Stern-Gerlach apparatus can split an electron beam into spin-up and spin-down components, thereby enabling the measurement of spin.

After passing through the spin-up output of a Stern-Gerlach apparatus, the beam will not be split again if it is subjected to another Stern-Gerlach apparatus with Stern-Gerlach field in the same direction. Thus the wave function can be said to have "collapsed." Please note that this "collapse" has absolutely nothing to do with any physical "implosion." All we mean is that the subsequent description of the system (via a wave function of density matrix) has changed drastically since we only need to consider the part of the wave function projected out by the Stern-Gerlach apparatus.

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Let me give you one more example, from the field of quantum computing.

A measurement of an N-qubit quantum state can only ever result in an N-bit string (string of N classical bits). In this case you can think of the measurement apparatus as a bunch of Stern-Gerlach apparatuses, or just as some abstract display panel that you look at to see a readout of N bits.

Suppose the state of a 2-qubit system is described by the (entangled, but who cares) wave function: $$ |\Psi_0\rangle = \frac{1}{\sqrt{2}}\left(|00\rangle + |11\rangle\right) $$

When I perform a measurement on 2 qubits there are four different results in general, but only two results with non-zero probability of being measured in the case we are considering.

When I measure, half the time I find that the result is: $$ 00 $$ after which the wave function is: $$ |\Psi_1\rangle = |00\rangle $$

When I measure, half the time I find that the result is: $$ 11 $$ after which the wave function is: $$ |\Psi_2\rangle =|11\rangle\;. $$

No information has been "sent" or "received" by either electron in this experiment.

Answer 6

The free electron produced by the absorption of a photon in a photoelectric detector is surely an observer of the photon in the Copenhagen sense. The interaction is, in practice, irreversible. That practical irreversibility is what distinguishes observation from coherent interaction.

Answer 7

The answer to your question isn't as simple as yes or no. You must bear in mind that quantum mechanics is a way to model reality, and you can build quantum mechanical models with different degrees of complexity. If you take a double slit experiment, for example, a typical way of modelling what is happening is to assume the inbound electron has a wave function in the form of a plane wave, and the detecting screen is a classical object which 'collapses' the wave function. In reality that is a gross simplification. What really happens is the electron moves from a region in which it can be modelled to a reasonable degree as a plane wave into a region near the detector in which it is increasingly affected by the presence of the countless electrons and ions that form the surface layers of the detector, and its wave function is perturbed accordingly until it is absorbed by the detector screen or reacts with it in some other way that can be registered by a human or a machine. Either way, the electron in the environment of the detector has a completely different Hamiltonian from the Hamiltonian that was assumed (implicitly or explicitly) when you had the electron coasting through a vacuum towards the slits, and it is that which determines the wave-function of the electron during and post detection.

Given that, I would say that by 'observer' in QM, what we mean is some system which can interact with the object being observed in a way that causes the object's wave function to change into an eigenfunction of the property being measured. If you can design an experimental set-up that allows a single electron to play that role, then yes it can be an observer for that particular set-up, but if you can't it can't.