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Author Topic: How can a definitive theory of Fermi Energy exist?  (Read 5785 times)

Offline QuantumClue

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''The Fermi energy is a concept in quantum mechanics usually referring to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature''

http://en.wikipedia.org/wiki/Fermi_energy

Ok, big queerie coming along. How does a fermi energy exist then? Absolute zero is like one of those mythical fairytales your grandma reads you at night. It doesn't exist.


In our very early understanding of quantum mechanics, motion of particles contributed a temperature to a system. In theory if you could slow down all the particles to a zero momentum, we would have an outdated, archaic definition of the zero-point energy field.

But objects cannot be slowed down to these speed because of the uncertainty principle, so no matter how much energy you pump into your cooling machine, the objects experimented on will never reach an absolute rest, there is still movement and energy left over. As for negative energy, particles existing in the potential of our vacuum do have negative energies. This is a consequence of the Dirac Equation.

Negative energies can correspond to antiparticles, or they may directly correspond to virtual particles in the vacuum. The virtual particles in the vacuum can be said to be authenticated by the existence of the Casimir Effect, which is believed to be directly responsible for small energetic bursts of energy between two seperated plates. The energy between the plates is also increasingly negative.

But zero point is unnattainable, so therefore, how can it justify the passage that the fermi energy level maintains the highest occupied energy states for electrons at zero point temperatures...? If it does not exist, neither can the Fermi energy!!

http://courses.washington.edu/overney/FermiEnergy.pdf


 

Offline JP

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How can a definitive theory of Fermi Energy exist?
« Reply #1 on: 01/02/2011 01:37:26 »
There's a couple of things going on here.  Absolute zero does exist theoretically.  In a quantum system, you can describe a system in it's lowest energy state and that's absolute zero.  Whether you can reach that in an experiment or not is another question.

The Fermi energy is just the energy of the highest quantum state in lowest-energy configuration of some system.  Fermions can't occupy the same states, so if you have 100 energy levels of increasing energy and 50 Fermions, the lowest energy state will have levels 1-50 occupied, and the Fermi energy will be given by the 50th energy level.
 

Offline Geezer

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How can a definitive theory of Fermi Energy exist?
« Reply #2 on: 01/02/2011 01:53:01 »
170nK (nanokelvin) is pretty close to 0K (no, not OK, 0K, OK?)
 

Offline QuantumClue

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How can a definitive theory of Fermi Energy exist?
« Reply #3 on: 01/02/2011 09:26:27 »
There's a couple of things going on here.  Absolute zero does exist theoretically.  In a quantum system, you can describe a system in it's lowest energy state and that's absolute zero.  Whether you can reach that in an experiment or not is another question.

The Fermi energy is just the energy of the highest quantum state in lowest-energy configuration of some system.  Fermions can't occupy the same states, so if you have 100 energy levels of increasing energy and 50 Fermions, the lowest energy state will have levels 1-50 occupied, and the Fermi energy will be given by the 50th energy level.

We disagree with your first sentance.

I do beleieve you are wrong. Zero-point is when all motion ceases, and you have successfully frozen your system to zero temperature. Zero-point energy does not exist, because no matter how much you cool your system, it will never completely loose motion. So not being able to achieve zero-point is a big thing when considering a fermi energy, which relies soley on the fact that zero-point energy is achievable somehow.

Also, a lowest energy state is not a zero-point. An electron can fall to it's lowest energy state and this would be called it's ground state. It's not a zero-point state however, because that is a contradiction. Because again, we cannot reach the zero-point state of a  system.
 

Offline JP

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How can a definitive theory of Fermi Energy exist?
« Reply #4 on: 01/02/2011 12:37:40 »
I think you're confused on what zero-point energy is.  From wikipedia, "Zero-point energy is the lowest possible energy that a quantum mechanical physical system may have; it is the energy of its ground state."   It does exist and agrees with what I said above about the Fermi energy.  I'm not sure where this idea of all motion ceasing comes from.  Zero-point energy states can definitely have non-zero momentum.  Not to tout my credentials too much, but I have studied Fermi-Dirac statistics and the Fermi energy in graduate level physics coursework, so I'm quite sure what I'm saying about them is correct.  I think this was the book we used, if that helps. 
 

Offline QuantumClue

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How can a definitive theory of Fermi Energy exist?
« Reply #5 on: 01/02/2011 12:39:55 »
I think you're confused on what zero-point energy is.  From wikipedia, "Zero-point energy is the lowest possible energy that a quantum mechanical physical system may have; it is the energy of its ground state."   It does exist and agrees with what I said above about the Fermi energy.  I'm not sure where this idea of all motion ceasing comes from.  Zero-point energy states can definitely have non-zero momentum.  Not to tout my credentials too much, but I have studied Fermi-Dirac statistics and the Fermi energy in graduate level physics coursework, so I'm quite sure what I'm saying about them is correct.  I think this was the book we used, if that helps. 

I am not confused at all. Our archaic definition of zero-point systems is when you cool them down and find no movement at all. However, according to the equation provided by wiki, you find there is still half the energy left in the system. The name zero-point energy caught on, saying that absolute cooling of systems was impossible. If by lowest energy, that is simply a ground state of the system, but the zero in zero-point, is never achieved.
 

Offline QuantumClue

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How can a definitive theory of Fermi Energy exist?
« Reply #6 on: 01/02/2011 12:42:34 »
Think about what the ''zero'' in zero-point means. Go back to when we believed you could cool the system to absolute temperatures. We cannot cool our system to an absolute freezing temperature. We can only get so close, and then it evades us. There is always thermodynamics in a system. I can settle with ''ground state'' this is very true. I don't settle with the terminology that we can make soemthing reach a zero-point temperature. That is false.
 

Offline QuantumClue

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How can a definitive theory of Fermi Energy exist?
« Reply #7 on: 01/02/2011 12:51:42 »
''The Absolute Zero of temperature is thought of as an unattainable goal.''

http://www.chronon.org/articles/absolute_zero.html

And that was a very quick search.
 

Offline Geezer

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How can a definitive theory of Fermi Energy exist?
« Reply #8 on: 01/02/2011 18:43:55 »
So, how far from 0K do you think 170nK is?
 

Offline QuantumClue

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How can a definitive theory of Fermi Energy exist?
« Reply #9 on: 01/02/2011 19:45:59 »
So, how far from 0K do you think 170nK is?

You seem to be arguing there is not much difference. If you want to pedantic, then of course, normal spacetime is very close to zero-point energy - that is, a vacuum never reaches zero temperatures. If you take your attention to the wiki article however, the Fermi energy requires the idea of a zero temperature, which is incorrect through terminology and experimentation.
 

Offline Geezer

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How can a definitive theory of Fermi Energy exist?
« Reply #10 on: 01/02/2011 20:37:59 »
Actually, I'm referring to temperatures that have been created by scientists in labs.

EDIT: I was merely pointing out that, despite your assertion -

"Absolute zero is like one of those mythical fairytales your grandma reads you at night. It doesn't exist."

While I agree we will probably never get all the way there, we have created temperatures that come remarkably close to 0K, so I would not exactly describe it as a fairytale. As we reached 0.00000017K about fifteen years ago, it's perhaps being pedantic to say 0K does not exist.

At what temperature do you think we might declare victory?
 
« Last Edit: 02/02/2011 06:07:40 by Geezer »
 

Offline JP

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How can a definitive theory of Fermi Energy exist?
« Reply #11 on: 02/02/2011 01:45:31 »
Think about what the ''zero'' in zero-point means. Go back to when we believed you could cool the system to absolute temperatures. We cannot cool our system to an absolute freezing temperature. We can only get so close, and then it evades us. There is always thermodynamics in a system. I can settle with ''ground state'' this is very true. I don't settle with the terminology that we can make soemthing reach a zero-point temperature. That is false.

Having a personal dislike for the terminology is different than having a legitimate beef with the science.  Your personal opinion is unlikely to change scientific consensus on the terminology:
1) Zero-point energy means essentially the quantum ground state, which is not necessarily zero-energy.
2) Absolute zero is taken to be the case of a system in it's lowest energy state, which is not zero-momentum (which is classically zero movement).
3) The Fermi energy is the energy of the highest quantum particle when a system is at absolute zero.  This doesn't have to be physically achievable, but it is a theoretical and physical limit on the system.

All these are perfectly well defined and are theoretical as well as physical limits, regardless of whether you can obtain them in a lab--no matter how much you cool something you can get as close as you want to absolute zero without passing it, the same with the Fermi energy.
 

Offline QuantumClue

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How can a definitive theory of Fermi Energy exist?
« Reply #12 on: 02/02/2011 12:51:09 »
Actually, I'm referring to temperatures that have been created by scientists in labs.

EDIT: I was merely pointing out that, despite your assertion -

"Absolute zero is like one of those mythical fairytales your grandma reads you at night. It doesn't exist."

While I agree we will probably never get all the way there, we have created temperatures that come remarkably close to 0K, so I would not exactly describe it as a fairytale. As we reached 0.00000017K about fifteen years ago, it's perhaps being pedantic to say 0K does not exist.

At what temperature do you think we might declare victory?
 

This depends on how much energy you are willing to pump into your cooling system, and also the magnitude of energy you began with. It's not easy to ask how low we can actually go. It's safer to state that we will never reach the condition T=0.
 

Offline QuantumClue

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How can a definitive theory of Fermi Energy exist?
« Reply #13 on: 03/02/2011 11:18:01 »
Think about what the ''zero'' in zero-point means. Go back to when we believed you could cool the system to absolute temperatures. We cannot cool our system to an absolute freezing temperature. We can only get so close, and then it evades us. There is always thermodynamics in a system. I can settle with ''ground state'' this is very true. I don't settle with the terminology that we can make soemthing reach a zero-point temperature. That is false.

Having a personal dislike for the terminology is different than having a legitimate beef with the science.  Your personal opinion is unlikely to change scientific consensus on the terminology:
1) Zero-point energy means essentially the quantum ground state, which is not necessarily zero-energy.
2) Absolute zero is taken to be the case of a system in it's lowest energy state, which is not zero-momentum (which is classically zero movement).
3) The Fermi energy is the energy of the highest quantum particle when a system is at absolute zero.  This doesn't have to be physically achievable, but it is a theoretical and physical limit on the system.

All these are perfectly well defined and are theoretical as well as physical limits, regardless of whether you can obtain them in a lab--no matter how much you cool something you can get as close as you want to absolute zero without passing it, the same with the Fermi energy.

Oh I don't know about that: for me, having a beef with the terminology requires an understanding of what you are arguing about in the science of things. Saying Fermi energy requires an electron at absolute zero temperatures is incorrect! Since we can never reach zero temperatures, it may not be fair to even state a real Fermi energy exists if it depends on this crucial feature.
 

Offline JP

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How can a definitive theory of Fermi Energy exist?
« Reply #14 on: 03/02/2011 12:22:40 »
You do realize it exists as a limit, which is perfectly well defined?
 

Offline QuantumClue

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How can a definitive theory of Fermi Energy exist?
« Reply #15 on: 03/02/2011 12:49:30 »
You do realize it exists as a limit, which is perfectly well defined?

There are limits in mathematics. The term ''limit'' however can be decieving. For instance, you could have a limit on an equation, where something tends towards zero, while another limit tends towards infinity. The infinity could be anything, but because infinity hardly exists in any practical terms for us, the limit can be meaningless in the sense it is unnatainable. It just so happens we try an draw other meanings from these limits, and a good example would perhaps be Einsteins equations of motion mr = m0 /sqrt(1 - v2/c2) where relativistic mass increases proportional to an increase with velocity and energy reaches infinity as the object reaches lightspeed.

But it would not make sense to say we have an infinite amount of energy when we finally make a peice of matter reach lightspeed. Just like the zero-Point temperatures, it does not matter how much energy you put into your machine to make that particle accelerate towards lightspeed. It will reach the very boundary of this limit, and then always fail to ever get to that speed. We don't say that the particle will reach lightspeed, that doesn't happen and will never happen, a true matter of experimentation. If we did state that, that then would be analogous to stating that a particle can experience zero temperatures, which the wiki article seems to be hinting at from word go.
 

Offline QuantumClue

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How can a definitive theory of Fermi Energy exist?
« Reply #16 on: 03/02/2011 12:58:50 »
In my eyes this is how wiki should have written the first line in the article:

The Fermi energy is a concept in quantum mechanics which refers to the energy of the highest occupied quantum state in a system of fermions which exist near absolute zero temperatures

That would be much more correct than saying:

''The Fermi energy is a concept in quantum mechanics usually referring to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature''
 

Offline yor_on

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How can a definitive theory of Fermi Energy exist?
« Reply #17 on: 03/02/2011 20:35:41 »
QC, life can be a **

Don't take it personally when physics already have made their definitions clear. It's part of life, and to know a field, and be seen as knowing it, you must have the proper terminology. JP is perfectly correct in his descriptions, it's just that every day use is less 'precise' in their definitions.

Sometimes it can go overboard though, acronyms can drive me mad at times.
 

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How can a definitive theory of Fermi Energy exist?
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