Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: neilep on 17/08/2012 00:36:40
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Ok......I know I am not really going to comprehend your answers but I am going to ask anyway.
The Pauli Exclusion Principles states that no two electrons anywhere in the entire universe can have the the same energy state right ?.....so....If I change the state of an electron somewhere in the universe an electron MUST change it's state to accommodate the change. Doesn't matter if the electron is in the next room or right at the other end of the universe !!!
Is it possible to provide (in simplistic terms- if you're able to) how two electrons at opposite ends of the universe are communicating ?
I thought nothing can travel faster than the speed of light !
....also...this may task ewe even further....but any chance on a plain English explanation of what The Pauli Exclusion Principle is ?
Ta !!
Neil
xxxx
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Let me reassure you -- your understanding of the Pauli Exclusion Principle is not quite correct. Two electrons at opposite ends of the solar system are quite free to have the same energy. The Pauli Exclusion Principle applies only to stationary states of electrons, or to electrons bound within the same atom, molecule, or neighbourhood. What the Pauli Exclusion Principle is REALLY saying, in practical terms, is that you can only have a maximum of 2 electrons in the same place at the same time, and those two must have opposite spin. Electrons are in the family of particles known as fermions, which obey a set of rules known as Fermi-Dirac Statistics.
The Pauli Exclusion Principle is usually applied in the context of atomic structure or chemical bonding in molecules, and solutions to the Time-Independent Schrödinger Equation. In the context of atomic structure it helps to explain the capacity of the various electron shells and sub-shells. An electron in an atom, in the single-electron wavefunction approximation, is assigned a set of 4 quantum numbers:
n which is the main contributor to the energy of the electron in an atom, and to its average distance from the nucleus. It is a positive integer.
l which determines the shape of a wavefunction. It is also an integer, and may range from 0 (spherical) to n-1, and can also affect the energy of a multiple electron atom.
ml determines the orientation of the wavefunction. It takes integer values between –l and +l .It does not affect the energy.
ms takes a value of either –1/2 or +1/2.
So, to take an example, if we think of a sodium atom which has 11 electrons, each of those electrons in the atom has to have a different set of quantum numbers.
The first two go to the lowest energy shell: with quantum number sets (1,0,0,–) and (1,0,0,+). There are no other possibilities for the lowest energy shell. The next two go to a higher energy subshell with quantum number sets (2,0,0,–) and (2,0,0,+), and then six more can be accommodated in a slightly higher energy subshell (2,1,–1,–), (2,1,–1,+), (2,1,0,–), (2,1,0,+), (2,1,1,–), and (2,1,1,+). In an isolated atom these six all have the same energy. Finally, the 11th electron has no more possibilities with n=2, so it must go to the higher energy shell with n=3, where it sits all alone with the quantum number set (3,0,0,–). That is why sodium loses an electron so readily, and why the chemistry of sodium is dominated by the positive sodium ion with only 10 electrons.
There is a problem, an unresolved one, relating to quantum particles and faster-than-light communication. It comes under the umbrella of "quantum entanglement", and there is a wikipedia article that will provide a reasonable introduction if you want to follow that up.
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Damocles ..Thank you !
It's still a tad tricky for me to grasp but you have explained it in a way that I feel I have digested a good portion. Certainly, it has motivated me to delve deeper.
I really do appreciate the time and effort you have taken to respond and thanks to you I will move slightly from the shallow end towards the deeper end of the pool ! Hopefully I will have more questions as a result.
Thank You
Let me reassure you -- your understanding of the Pauli Exclusion Principle is not quite correct. Two electrons at opposite ends of the solar system are quite free to have the same energy. The Pauli Exclusion Principle applies only to stationary states of electrons, or to electrons bound within the same atom, molecule, or neighbourhood. What the Pauli Exclusion Principle is REALLY saying, in practical terms, is that you can only have a maximum of 2 electrons in the same place at the same time, and those two must have opposite spin. Electrons are in the family of particles known as fermions, which obey a set of rules known as Fermi-Dirac Statistics.
The Pauli Exclusion Principle is usually applied in the context of atomic structure or chemical bonding in molecules, and solutions to the Time-Independent Schrödinger Equation. In the context of atomic structure it helps to explain the capacity of the various electron shells and sub-shells. An electron in an atom, in the single-electron wavefunction approximation, is assigned a set of 4 quantum numbers:
n which is the main contributor to the energy of the electron in an atom, and to its average distance from the nucleus. It is a positive integer.
l which determines the shape of a wavefunction. It is also an integer, and may range from 0 (spherical) to n-1, and can also affect the energy of a multiple electron atom.
ml determines the orientation of the wavefunction. It takes integer values between –l and +l .It does not affect the energy.
ms takes a value of either –1/2 or +1/2.
So, to take an example, if we think of a sodium atom which has 11 electrons, each of those electrons in the atom has to have a different set of quantum numbers.
The first two go to the lowest energy shell: with quantum number sets (1,0,0,–) and (1,0,0,+). There are no other possibilities for the lowest energy shell. The next two go to a higher energy subshell with quantum number sets (2,0,0,–) and (2,0,0,+), and then six more can be accommodated in a slightly higher energy subshell (2,1,–1,–), (2,1,–1,+), (2,1,0,–), (2,1,0,+), (2,1,1,–), and (2,1,1,+). In an isolated atom these six all have the same energy. Finally, the 11th electron has no more possibilities with n=2, so it must go to the higher energy shell with n=3, where it sits all alone with the quantum number set (3,0,0,–). That is why sodium loses an electron so readily, and why the chemistry of sodium is dominated by the positive sodium ion with only 10 electrons.
There is a problem, an unresolved one, relating to quantum particles and faster-than-light communication. It comes under the umbrella of "quantum entanglement", and there is a wikipedia article that will provide a reasonable introduction if you want to follow that up.
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Nice explanation, maybe we should have some 'stickies' on the ones we find easiest to digest? We've had some really nice ones under the years, and often when I try to find that really good one that I felt understood, made maybe just some months or year ago, I have to search for eons :)
Because when you are wondering about some particular thing such a one really helps you out, and help you see if you're assuming, or just presuming :)
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A great reply damocles but you need to add a short extension that clarifies the picture. What neilep says is actually true as is what you say. it is just that the further apart the electrons are the less this difference has to be you can see this in the way that electrons behave in different materials. Let me explain.
What Damocles says is perfectly true for isolated atoms for example atoms in low pressure gases. however as the atoms get closer together in high pressure gases liquids and solids the individual electron levels start to get distorted and spread out. so the spectrum of the energy levels can be seen to change.
The first is pressure broadening in gases. the spectrum lines in high pressure gas become gradually less sharp as the pressure rises. This can be seen very well in the spectra of white dwarf stars which exhibit almost no spectrum lines because their atmospheres have a very high pressure where they radiate light into space.
When you get to liquids and solids the energy levels can get very distorted so that some electrons are actually freed from their atoms but confined to the solid. This results in electrical conduction through the materials. Atoms that hold on totheir electrons very strongly are insulators and of course we find semiconductors somewhere in between.
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Yes SS, that is a fair enough point, although for electrons at even centimetres of separation the interaction is completely ridiculously small. But it can certainly be observed in materials in condensed phases, and even in gases at fairly high pressure.
However, Neil in his original question asked about "energy states", and only bound electrons have energy states, and even for them, different electrons can have the same energy if their other quantum numbers are not identical -- especially if they have different non-interacting symmetries. The phenomenon you are really talking about is 'mixing of wavefunctions', and in a totally accurate quantum mechanics we would have to include every electron in the (hypothetical, non-relativistic) universe, and incorporate them into a packaged single antisymmetric multi-electron wave function. Not a task I would look forward to, although it has been done for simple ideal infinite and semi-infinite lattices.
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I recall that in some work I did with a very high resolution UV spectrum of benzene vapour at a few thousandths of an atmosphere (with J Callomon and J Parkin at UCL in the early 70s) the pressure broadening of individual lines was quite a noticeable quantity. If I recall correctly, though, we used to treat it in terms of the time-energy uncertainty principle, and average collision times in a low pressure gas.
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Again ..thank you very much Soul Surfer and Damocles I am grateful for your continued contributions here (great suggest yor-on).
Can I just ask for your opinion of this short 3 minute video by Brian Cox ?
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I totally agree with his statement. Although the changes are incredibly tiny and not ever observable. however this fact applies to all fermions not just electrons that is every quark in every particle in avery nucleus of every atom as well.
it also implies that the universe is simultaneously very large and very small
Furthermore if supersymmetry is valid it would apply to the supersymmetric fermionic particles related to our familiar bosons the photon and the graviton the photino and the gravitino.
The effect would be that these particles would also avoid each other. There is no reason why some of the dark matter particles are not fermionic and effectively pushing each other apart to create space and dark energy.
No one seems to mention this when they talk about dark matter. except when they talk about a sterile neutrino which is in fact a fermion like an ordinary neutrino because these are particles with spin but no net charge.
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Interesting SoulSurfer :)
And then we get to 'especially if they have different non-interacting symmetries.' Damocles ::))
Symmetries are weird phenomena.
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No I don't agree with Prof Brian Cox (although I think he is great and the best thing in Physics for years - enrolments at school levels are up in physics courses!!!).
Brian Cox's physics for celebrities (which was inspiring) did cause a fairly large wave of discontent in the academic community - the upshot was a lot of arguing between Brian (and Jeff Forshaw) versus large swathes of the academic and research community. Sean Carroll admirably summed up the initial sparring (after Tom Swanson (http://blogs.scienceforums.net/swansont/archives/11081) has started everything rolling)
http://blogs.discovermagazine.com/cosmicvariance/2012/02/23/everything-is-connected/
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In my opinion Brian Cox is right because all elementary particles are entangled and there is a maximum value for a change in the spins without any energy exchange, still, you need an energy signal to measure it. But it's not the standard model, SM is not causal!
Is there a response from Brian Cox? The standard model has just no answer to that question...
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Interesting SoulSurfer :)
And then we get to 'especially if they have different non-interacting symmetries.' Damocles ::))
Symmetries are weird phenomena.
Yor-on I am not a high powered quantum physicist. I am a theoretical chemist who mostly works with simplistic models and approximations -- essentially a caricaturist.
The sort of thing I had in mind when I referred to symmetry runs something like this:
Usually two electrons that appear to have identical energy at an approximation level of single-electron wavefunctions will interact to produce two slightly separated energy levels if they make combinations (psi1 + psi2) and (psi1 – psi2).
This cannot happen, though, in a situation like an isolated oxygen atom, where the two unpaired p- electrons, which we might assign as (2,1,+1,–) and (2,1,0,–) physics style or (2,1,x,–) and (2,1,z,–) chemistry style, have different symmetry species in the spherical symmetry environment, and interaction between them is therefore necessarily zero at all levels of approximation.
I usually have to struggle with understanding the way that physicists look at these issues -- I hope that they will have less trouble in absorbing the way that a chemist looks at them.
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Approximations of chemical interactions? As for symmetries I don't think we have anyone here really able to express it any better :) Do you find a lot of difference between the way physics describe it and chemistry?
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I really like Stanford university. http://plato.stanford.edu/entries/symmetry-breaking/
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Approximations of chemical interactions? As for symmetries I don't think we have anyone here really able to express it any better :) Do you find a lot of difference between the way physics describe it and chemistry?
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I really like Stanford university. http://plato.stanford.edu/entries/symmetry-breaking/
Yes, yor-on, chemists and physicists do approach things, and especially issues like symmetry, from totally different perspectives. If a chemist and a physicist are trying to address the same problem, their starting point and the first part of the pathway will look completely different; when they get to the later stages they may well converge.
I will illustrate this in two different ways: first a weblink to an Oxford University set of lecture notes for undergraduate students. It introduces a typical chemistry approach to symmetry (for advanced and highly motivated students) and makes an interesting comparison with your Stanford notes.
http://vallance.chem.ox.ac.uk/pdfs/SymmetryLectureNotes2009.pdf (http://vallance.chem.ox.ac.uk/pdfs/SymmetryLectureNotes2009.pdf)
I will follow that with an allegory (hopefully I will manage to keep it short) that is a metaphor for molecular structure:
Once upon a time, in a parallel universe, the Nyankis family took advantage of the latest genetic engineering techniques to produce a clone of a dozen children who were very athletically gifted. When they went to school, they took up baseball, and were remarkably successful. In early adulthood they formed their own Nyankis baseball team, which won the World Series 5 years in a row.
When they took the field they had some unusual features about the way they would play. The commentators were unable to distinguish the individual family members, and as they were all equally talented in all roles, they liked to frequently change places around the field -- several times in an inning! (This was partly to escape boredom and partly to confuse the opposition).
Some physicists and some chemists were called upon to analyse the play style and the singular success of this team. The physicists' first approach to this problem was to consider the family as a whole and the interactions within it, and to analyse the symmetries of their peculiar style of play. The chemists, on the other hand, wanted to start from issues like how the pitcher, the short stop, and the first baseman used to co-operate to frequently make double-plays (regardless of who was temporarily occupying those field positions).
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It's interesting Damocles. Don't know what to make of it yet, but I definitely will look at the pdf you linked to see what I can learn from it.