When is an electron in a superposition?

[Ryan Bruch]

If the double-slit experiment is done using an electron, and wave function collapse occurs, is the electron originally in a superposition all along before the experiment starts? I need clarification.

 

[atyy]

An electron is always in a superposition. A state with a definite position is also a superposition of all possible momenta. Similarly, a state of definite momentum is a superposition of states of different positions.

If you start the experiment with the electron in a superposition of positions, then you measure its position, the state will collapse into a definite position. Although it is no longer in a superposition of position states, since it is in a state of definite position, it is in a superposition of momentum states.

 

[Simon Bridge]

That's a "yes and no" answer.

Particles are always in a superposition of some set of states. Which is to say that they have only one state, which may be described by a linear superposition of possible states. It only becomes important when some device tries to select from the possible states - then a particular superposition representation will become useful.

 

[bhobba]

Just to elaborate on what the two previous posters said all the principle of superposition means is the possible states (called pure for reasons no need to go into) form a vector space. Real numbers form a vector space. Pick any number say - 10. 10 is a superposition of 5 and 5 (5+5 = 10), 3 and 7 (3+7 =10) 8 and 2 etc etc.

Thanks
Bill

 

[Simon Bridge]

I suppose, we could push a metaphor and say that a cake to be cut into two exists in a superposition of possible 2-slice combinations.
The actual cutting of the cake "collapses" the wavefunction - by establishing which particular combination actually results.
I wonder what misconceptions I'd be inviting though...

 

[bhobba]

The actual cutting of the cake "collapses" the wavefunction - by establishing which particular combination actually results. I wonder what misconceptions I'd be inviting though...

That's not too bad.

Its the preferred basis problem from decoherence which basically has been solved with a few caveats eg the factorisation problem. What hasn't been solved is the so called problem of outcomes ie why do we get any outcomes at all. This is basically the issue, at a technical level, of how an improper mixed state becomes a proper one. Most interpretations simply shrug about that one, although in some like BM or MW its trivial.

Thanks
Bill

 

[Johan0001]

The actual cutting of the cake "collapses" the wavefunction - by establishing which particular combination actually results.
I wonder what misconceptions I'd be inviting though...

My question then , is the electron the cake ,or the cutting of the cake?

 

[bhobba]

My question then , is the electron the cake ,or the cutting of the cake?

The cutting of the cake is done by the electron interacting with the observational apparatus via the process of decoherence - which is a form of entanglement.
http://www.ipod.org.uk/reality/reality_decoherence.asp

Some issues do remain, but if after going through the link if you still have questions its probably best to start a new thread.

Thanks
Bill

 

[Johan0001]

The cutting of the cake is done by the electron interacting with the observational apparatus via the process of decoherence

But still ,we have described an electron only as a superposition of states , still not sure what this means.
If it has mass/energy , where is this mass before we measure it.

 

[bhobba]

But still ,we have described an electron only as a superposition of states , still not sure what this means.
If it has mass/energy , where is this mass before we measure it.

The mass is a property of the electron and is constant - its got nothing to do with the interference pattern.

No one here has described an electron as a superposition of states. Its meaningless - like 5+5 =10 and 7+3 =10.

If you want to see a correct explanation of the double slit here it is:
http://cds.cern.ch/record/1024152/files/0703126.pdf

What happens is each slit scatters the electron at an angle. The pattern is the superposition of that scattering - the physical set-up determines what supposition is relevant - in this case its the superposition of the scattering if there was only one slit instead of two.

Thanks
Bill

 

[Johan0001]

No one here has described an electron as a superposition of states

Point taken .To my knowledge an electron has properties such as mass and charge - which are constant , as you mentioned.
I guess my question is how are these constant properties (which we use to define an electron ) propagated from the electron source through the slits to the
detector/screen.
I mean at the point of entering the Slit(s), WHERE are these properties . Surely they must still exist, or else our definition of an electron at the slits
is meaningless .
IF the Charge goes along one path and the Mass another , then at that instance we do not have an electron , as the properties must coexist to be called an electron.

 

[bhobba]

I mean at the point of entering the Slit(s), WHERE are these properties . Surely they must still exist, or else our definition of an electron at the slits is meaningless .IF the Charge goes along one path and the Mass another , then at that instance we do not have an electron , as the properties must coexist to be called an electron.

QM is a theory about the probabilistic outcomes of observations. When not observed what's going on the theory is silent about . The only property it has is this thing called a state which encodes the probabilities of observational outcomes if you were to observe it.

The following may help in understanding what QM is really about:
http://www.scottaaronson.com/democritus/lec9.html

Thanks
Bill

 

[Johan0001]

QM is a theory about the probabilistic outcomes of observations. When not observed what's going on the theory is silent about

It is this silence that makes me question QM , as to what is really happening when we don't observe . We may be missing the boat.

Thanks for your input guys

 

[DennisN]

I suppose, we could push a metaphor and say that a cake to be cut into two exists in a superposition of possible 2-slice combinations.
The actual cutting of the cake "collapses" the wavefunction - by establishing which particular combination actually results.
I wonder what misconceptions I'd be inviting though...

"The Cake Interpretation of QM" .

It is this silence that makes me question QM , as to what is really happening when we don't observe . We may be missing the boat.

Thanks for your input guys

There have been suggestions of boats, but they have been traveling in different directions:
http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics#Comparison_of_interpretations

 

[bhobba]

It is this silence that makes me question QM , as to what is really happening when we don't observe . We may be missing the boat.

Many have tried - trouble is there is no way to experimentally test them.

Thanks
Bill

 

[Johan0001]

Personally I would much rather try to discover "smaller" detail .. than to be silent on the matter.

I did however read in DennisN 's link above that "A photon can only be observed ONCE" which is quite a profound statement in my view.
Obviously this implies that we only know that a photon is emitted once and detected ONCE when it is absorbed/destroyed. And nothing else.

Quite a sad end to a phenomenon of such great debate.

 

[bhobba]

Personally I would much rather try to discover "smaller" detail .. than to be silent on the matter.

Trouble is what people personally want to try has proven very unreliable - witness Einsteins personal beliefs when subjected to Bohrs scrutiny - Einstein admitted defeat.

I did however read in DennisN 's link above that "A photon can only be observed ONCE" which is quite a profound statement in my view.

Why you think that photons are generally destroyed when you detect them is profound I can't quite follow.

Quite a sad end to a phenomenon of such great debate.

I suspect Einstein thought so as well - but he did have one last joker up his sleeve - EPR. And it was experimentally testable - which lifted it into the realm of science rather than personal opinion.

Thanks
Bill

 

[naima]

a photon is emitted once and detected ONCE when it is absorbed/destroyed. And nothing else.

Quite a sad end to a phenomenon of such great debate.

Thanks to Buddha photons are not destroyed. Another life is waiting. :)

 

[Khashishi]

I think it's impossible to say when/where a quantum collapse occurs during an experiment. The collapse isn't an 'event' which can be pinpointed.

A simple example:
A photon passes through two polarizers angled 45 degrees to each other. Let's say the first polarizer is oriented vertically and the second one is diagonal. Before the first polarizer, the photon is polarized vertically, and after the second polarizer, it is polarized diagonally. What about the space between the polarizers? We can't say...

Reality isn't so simple as to allow a single state for each particle at each point in time. The total state involves the entire system at all times.

 

[bhobba]

I think it's impossible to say when/where a quantum collapse occurs during an experiment. The collapse isn't an 'event' which can be pinpointed.

That's true. Von Neumann showed the classical quantum cut could really be placed anywhere.

In the modern view based on decoherence its when the interference terms fall well below detectability which is to some extent arbitrary.

That said it does occur very very quickly.

Thanks
Bill

 

[JPBenowitz]

The electron wavefunction can always be expressed as a linear combination of its eigenfunctions. The superposition principle is a consequence of the fact that the wave function is an element of Hilbert Space, which itself is a linear space. The wave function is said to have collapsed once a measurement is made. A measurement in the mathematical sense is a specific linear hermitian operator that correspond to some physical observable which returns an particular eigenvalue (the eigenvalue being a physical observable itself such as energy).

 

[Simon Bridge]

Why you think that photons are generally destroyed when you detect them is profound I can't quite follow.

It's actually quite an important realization for many students - the usual picture people have is that a detector somehow "sees" a photon whizzing past like one may observe a passing car.