What happens in a universe with only two electrons? Do they stay as waves or do they collapse into particles?
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asked Apr 24, 2015 at 15:19
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5$\begingroup$ I have no idea what you mean. Things don't "collapse in particles" and they do not "stay as waves", even with more stuff around. $\endgroup$– ACuriousMind ♦Commented Apr 24, 2015 at 15:21
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$\begingroup$ Can you describe a universe with single electron ? Is it a little ball standing in the middle of noware ? $\endgroup$– Sharon SalmonCommented Apr 24, 2015 at 15:32
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$\begingroup$ Just solve Schrödinger's equation with the proper boundary (in your case, "no boundary"), and then interpret the solution. $\endgroup$– Physicist137Commented Apr 24, 2015 at 16:25
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$\begingroup$ I don't know how to solve the equation.that is why I ask the question.What I know is that the electron is potentially existing in many places in certain probabilty and when it is being measured it becomes actual rather than potential.so my question about single electron is does it become actual if there is no one to measure it or does it stay only with potential existance ? $\endgroup$– Sharon SalmonCommented Apr 24, 2015 at 16:52
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$\begingroup$ The electron exists in actuality whether you measure it or not... Measuring it only tells you its position or momentum, it doesn't change it from a "potential" electron to an "actual" electron. $\endgroup$– AsherCommented Apr 24, 2015 at 21:07
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1 Answer
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The question doesn't have an answer because electrons aren't waves and they aren't particles. This is a common source of confusion, and has led to the endless debates about wave particle duality. Quantum systems are described by a wavefunction that can behave as a wave in some circumstances and behave like a particle in others.However it is vital to understand that the description of an electron as a wave or as a particle is an approximation that works in some circumstance but not in others.
To describe two electrons alone in the universe simply requires us to calculate the wavefunction that describes them. If we assume energies are low enough not to require a relativistic treatment we calculate the wavefunction by solving the Schrodinger equation.
The trouble is that the Schrodinger equation is a partial differential equation, and like all (most?) partial differential equations it doesn't have a unique solution. Instead there are an infinite family of functions that are solutions to the Schrodinger equation, and to find the solution that describes our system we have to use the initial conditions i.e. the state of the system at time zero.
You specify your system is two electrons isolated from anything else, but what is the state of the system at time zero? Suppose we start with both electrons having a well defined momentum, in which case the uncertainty principle tells us they don't have a well defined position. In this case the wavefunction will be wave-like, by which I mean describing the electrons as waves is a good description.
Then suppose we start with both elections having a well defined position, in which case the uncertainty principle tells us they don't have a well defined momentum. This initial state is particle-like, by which I mean describing the electrons as particles is a good description. However the uncertainty in momentum means the particle spreads out with time and becomes more and more wave-like as time goes on.
The point of all this waffle is that we can't answer your question because you've left out something very important i.e. the initial conditions.
answered Apr 24, 2015 at 16:53
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$\begingroup$ In the double slit experiment do you know the initial conditions ? Does the initial conditions effect the fact that the single electon go through both slits ? Lets assume the initial conditions are exactly like when it goes through the slits. $\endgroup$ Commented Apr 24, 2015 at 17:23
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$\begingroup$ @SharonSalmon In the double slit expt the momentum is well defined and the position is almost entirely unknown, so the electron is well approximated as an infinite plane wave. That's why it can go through both slits. If we set up your xpt like that the two electrons would start as plane waves and continue forever as plane waves - all pretty boring really. $\endgroup$ Commented Apr 24, 2015 at 18:51
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$\begingroup$ I know it is boring but I am not here to amuse. What if instead of 2 electrons there are billion of particals that start as plane waves or even more ? Is it still that boring plane waves ? $\endgroup$ Commented Apr 24, 2015 at 19:03
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$\begingroup$ @SharonSalmon: The is really a different question, because now you're asking about the mechanism by which superpositions collapse i.e. how is a delocalised particle localised. There are lots of views on this but my favourite is a process called decoherence. This requires a complex system for the particle to interact with, so shove enough particles into your universe and you can start getting decoherence. In the slits the electron is localised when it interacts with the photographic plate and decoheres. $\endgroup$ Commented Apr 24, 2015 at 19:11
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$\begingroup$ The trouble is that the maths for this quickly gets super hard. Follow the link in my comment to give yourself an idea of what decoherence is. $\endgroup$ Commented Apr 24, 2015 at 19:12