Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: chris on 16/09/2014 23:08:14
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Would someone please explain the phenomenon of quantum tunnelling to me... Thanks!
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Ahem, let me start by saying, Ouch :)
It's about probabilities of somethings existence. Classically I do not know any counterpart to it? For something to 'tunnel' you first need a barrier of some sort, then a way for the particle to pass it. It's about whatever probability that particle has, described through its 'wave function', of being able to exist past the barrier. That it can't 'stop' inside the barrier should then be definable to the Pauli exclusion principle that explicitly forbid it to materialize there, as all possible 'places/states' already should be taken, for simplicity assuming they are. The idea, described as waves, seems to be that this/those wave(s) does not find themselves cut of by the barrier, instead having a (low) probability of extending further through and past it. It's a weird one.
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Would someone please explain the phenomenon of quantum tunnelling to me... Thanks!
Quantum tunneling refers to a particle which is able to travel between regions of space even though it didn't have enough energy to move through a region of space where the potential energy was greater than the total energy. That region where the potential is too high is referred to as a barrier. See http://en.wikipedia.org/wiki/Quantum_tunnelling
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According to "Classical" physics (as recognisable by Isaac Newton), certain events cannot occur because a particle does not have enough energy.
In "Quantum" physics, all particles have some wave-like nature, which means that you are never totally sure of where a particle is, and what momentum it has (Heisenberg's uncertainty principle (http://en.wikipedia.org/wiki/Heisenberg_uncertainty_principle)). So there is a finite probability that a particle which you believed was on the left-hand side of a wall could be found on the right-hand side of a wall: it's as if the particle has tunelled through the wall.
This effect only becomes noticeable on very small sizes and very short timescales, impacting things like radioactive decay of a nucleus, operation of some semiconductor devices, and possibly some mutations in DNA.
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Tunneling is also fairly important in some chemical reactions. Lighter particles have a greater aptitude for tunneling, so it is usually an electron or proton (H+ ion) that tunnels. Usually the "barrier" is space...
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Tunneling is also fairly important in some chemical reactions. Lighter particles have a greater aptitude for tunneling, so it is usually an electron or proton (H+ ion) that tunnels. Usually the "barrier" is space...
In quantum mechanics the barrier is always space.
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In quantum mechanics the barrier is always space.
Sometimes the barrier has additional components which represent an energy barrier, such as:
- a change in reistivity in a Josephson junction
- a voltage in semiconductor devices
- strong nuclear force in nuclear fission
- an electrostatic potential in nuclear fusion (and if you are very patient)
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So the Pauli exclusion principle doesn't count for tunneling?
then? What is a barrier? Free space (perfect vacuum) is presumably 'empty', so how do I define that as a 'barrier' for the probability of a particle materializing?
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Would it be so that the particle to materialize need something more than a vacuum? Because that's the only thing I can come up with for now? If it just was a question of a probability density then I don't know why it couldn't be placed in that vacuum?
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If I look at charge.
"Corvidae said.. 'Apropos electrons and charge'..
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Maybe a mammalian analogy would be more enlightening. Think of a conductor as a long field of gopher holes. Every hole is an atom with it's own set of gophers. There is exactly enough room in each gopher hole for 29 gophers (copper gopher holes). And every gopher hole needs 29 gophers to keep itself maintained.
Along comes farmer Battery and he shoots a gopher on one end of the field and releases one gopher on the other end of the field. The gophers in the hole where one was shot, now need an extra gopher. However the new gopher is WAY on the other end of the field. It's much easier to steal a gopher from a nearby hole. So the gophers charge (Yup, the mystical charge) over to the other hole (atom), and steal a gopher (electron). Now that gopher hole needs a new gopher and does the same thing to another hole that's closer to the new gopher.
Rinse and repeat until you get greasy grimy...no wait wrong analogy..Until you reach the far end of the field, and the new gopher gets pulled into the nearest hole that's missing a gopher.
In the end, the new electrons (gophers) don't actually move very far, since there is always a nearby atom needing a negative charge. For an electron to actually move all the way down the field, it'd take a whole lot of gopher killing.
If you want to get really confused about it. Try figuring out the actual electron flow involved in receiving an FM radio signal. "
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bm1957 writes...
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Corvidae's analogy covers one of the points I was going to make. Electrons have negative charge and protons have positive charge, but it's only the electrons which move. When one electron moves from where it was, it leaves a 'virtual' positive charge there. This is referred to as a 'hole'. The movement of negative electrons in one direction is entirely equivalent to the movement of positive holes in the other direction. Protons very rarely move in an electrical circuit (except maybe when ions are conducting, off point though.).
The transfer of energy (according to currently accepted theory) is entirely through the transfer of photons between electrons; an electron receiving a photon becomes excited and jumps to a higher energy level. When it falls back down to its original energy level, it releases a photon. This is the proposed mechanism for the electromagnetic force. Photons can easily transfer across a junction between the socket in the wall and the plug which is inserted into it, as can electrons flow both ways (equivalent to positive holes moving in opposite directions to the electrons) across the junction. This is also true if it was your finger which went into the socket and completed the circuit to ground.
Back to AC. The electrons are still moving, but the net flow rate is zero. They go backwards and forwards on the spot, about 20 times a second (at 50Hz). The distance they go backwards and forwards depends on the voltage. The average DC current being transferred is zero. If you somehow tweak your 'receiver' to flip every cycle (as motors and electronic circuits can), then you extract the energy of the 'positive DC electrons' then flip, and extract the energy of the 'negative DC electrons'. Since you flip in between, the energies add together because they were 180deg out of phase before the flip, and are now exactly in phase. The wiki rectifier link should clarify this.
Hopefully this is all following logically??? "
and a tunneling microscope uses a charge, passing a tiny barrier of vacuum.
"An STM works by measuring the tunneling current as electrons tunnel between a scanning tip and the surface. Now, according to classical physics there shouldn't be any current flowing since the tip and surface are separated by a vacuum which creates a large barrier and blocks the current regardless of the applied voltage*. However, the tunneling probability through this barrier is high enough to allow for a relatively large current which can quite easily be measured. The neat thing is that the magnitude of this current (which is proportional to the tunneling probability) depends upon the properties of the surface; you can also to some extent choose which energy scale you want to study by varying the voltage applied between the tip and the surface. Hence, an STM will give you more than just the topology the surface; you also get the density of states for "free"." by f95toli.
So yes, it's about charge here. And charge transfers through photons
"The transfer of energy (according to currently accepted theory) is entirely through the transfer of photons between electrons; an electron receiving a photon becomes excited and jumps to a higher energy level. When it falls back down to its original energy level, it releases a photon."
That should move us to tunneling.
This is what JP writes on the possibilities of light (waves/photons).
It's lifted out of its context, which was a discussion about electrons, but I think i can use it here.
"Quantum mechanical wavepackets have a variety of conjugate variables, such as position/momentum. If you know one well, you know the other poorly, which is a basic statement of the uncertainty principle. Now, let's take position, x, and momentum, p, for example. The uncertainty principle tells us that
ΔpΔx≥h/2,
where Δx is a measure of the width of the wavefunction expressed as a function of position, and Δp is a measure of the width of the wavefunction expressed as a function of momentum. Some states (they're Gaussian wavepackets) are minimum uncertainty states. In other words, they are at the lower bound of the uncertainty relation:
ΔpΔx=h/2.
Now, for these Gaussian wavepackets, it turns out that they have a Gaussian shape in both x and in p, and the uncertainty relation basically says that the wider they are in x, the narrower they are in p. If you "squeeze" the state to be narrower (better-defined) in position, it gets wider in momentum. If you "squeeze" it narrower in momentum, it gets wider in position.
It turns out that when dealing with light, the natural variables are the field quadratures, amplitude (Q) and phase (P), rather than position and momentum. I spent a while trying to come up with a nice explanation, but this page does it much better than I could, and it has nice pictures, too:" http://gerdbreitenbach.de/gallery/
As I get it this how tunneling works, quantum mechanically.
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But what about a particle tunneling?
Eh, that should mean restmass..
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What I probably should ask is in what way (assuming that it is electrons, not only 'photons' tunneling) a vacuum barrier forbid this electron from materializing in it? Alternatively it is force carriers that tunnel here, meaning 'photons' in which case the question still stands about 'rest mass'. As a photons 'path' experimentally only exist in its sources 'recoil' and subsequent sink(measurement of it) that one meets no problems with me. A wave function makes a lot of sense there.
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Physics is weird, but interesting. Here's another thread in where we find tunneling mentioned, as a example. http://www.thenakedscientists.com/forum/index.php?topic=31047.msg306712#msg306712
"For evanescent waves in total internal reflection, the analogy with tunneling is pretty good. You expect all the wave's energy to be reflected, and therefore the tiny bit that gets into the reflecting material is evanescent and dies off quickly. If you had a very thin layer of reflecting material, some of that energy would "tunnel" through just as in QM, so that you'd get a little bit of light coming out the other side with most of it reflected. Near an antenna or anything else that's emitting radiation, the evanescent waves are a little more tricky. They have the same mathematical form, but they're associated with the fact that the antenna is emitting all kinds of waves, including these evanescent ones."
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But what about a particle tunneling?
Eh, that should mean restmass..
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What I probably should ask is in what way (assuming that it is electrons, not only 'photons' tunneling) a vacuum barrier forbid this electron from materializing in it? Alternatively it is force carriers that tunnel here, meaning 'photons' in which case the question still stands about 'rest mass'. As a photons 'path' experimentally only exist in its sources 'recoil' and subsequent sink(measurement of it) that one meets no problems with me. A wave function makes a lot of sense there.
The "barrier" that needs to be tunneled through is just a region of space where the potential is much higher--this could be related to the pauli exclusion principle if there are occupied low energy states, requiring that a higher energy state be occupied--but there could also be no low-energy state in a particular region (vacuum is higher energy than near the positively charged nucleus of an atom). I think of tunneling as leakage of the wavefunction of an electron (or other particle) through a region that only allows for significantly higher energy states than the two regions it is between in which the particle is likely to be found. The particle does not have to be observable in the barrier region, for the particle to be observable (interactable) on both sides.
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I get stuck on '(vacuum is higher energy than near the positively charged nucleus of an atom)' Chiral, how do you mean there? Using PEP is okay to me :) Actually that seems quite reasonable in most other cases, but how do I define a vacuum as having all 'states' occupied?
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If we are considering an electron as the particle that is tunneling, we can map out the electrostatic potential within a given space around the electron, based on other electrons and nuclei in the vicinity. If the electron is tunneling from one molecule to another through space, it is going from an occupied energy orbital in one molecule to an unoccupied orbital in the other molecule. If it were actually moving in a continuous fashion, it would first have to go away from all of the nuclei in the first molecule, which, unless this first molecule has a large excess of electrons, would mean an increase in electrostatic potential as it leaves, followed by decreasing potential as it approaches the second molecule. However, since such classical trajectories are not very useful descriptions, we can just think of the electron as instantaneously appearing in the second molecule as it disappears in the first, with some probability that is determined by the difference in energy between the two orbitals, the distance between the molecules, any external field that may be present, and several other variables...
I agree that it makes no sense to have occupied states in a vacuum--this appears to be wrong by definition. But an electron can also tunnel from one point in a molecule to another point in the same molecule (or from one molecule to another with matter between them), in which case the electronic structure of the intervening portion of the molecule (or molecules) is very important--there are occupied and unoccupied orbitals in between the starting and ending positions, whose energy, and symmetry can dramatically effect the tunneling barrier.
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What is synaptic quantum tunnelling ?
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Is protons delocalization in biological systems possible?
Why is classical neuropsychology require quantum biology theory to postulate the existence of synaptic quantum tunnelling in brain activity?
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What is synaptic quantum tunnelling ?
I would have to say it is a wild hypothesis at this stage.
To demonstrate tunneling, you have to show that there is a potential barrier of some form (necessarily very thin), and that there is some quantum particle which appears on the other side of the barrier without any classical mechanism for getting there.
The synapses of a cell do have a barrier: The cell wall, a dual lipid layer (http://www.cerebromente.org.br/n07/fundamentos/neuron/parts_i.htm#membrane).
- It's fairly thick - thicker than you would expect for quantum tunneling.
- But it also has a classical mechanism for transmission of ions - the ion channel (http://en.wikipedia.org/wiki/Ion_channel), which passes through the cell wall.
Is protons delocalization in biological systems possible?
Proton delocalization is much more difficult than electron delocalization, due to their much greater mass/shorter wavelength. For the same reason, delocalization and quantum tunneling of Na+ and Ca2+ ions is even less likely than for protons.
In the physics lab, such quantum states are very fragile, and are best seen under carefully controlled cryogenic conditions (eg with liquid helium cooling). Liquid helium is not compatible with water-soluble organic systems like us.
Why is classical neuropsychology require quantum biology theory to postulate the existence of synaptic quantum tunnelling in brain activity?
It doesn't.
At the atomic scale, all physical, chemical and biological processes depend on quantum effects. Mainstream quantum biology focuses on possible quantum effects at the scale of large molecules (eg chlorophyl) and cellular structures (eg microtubules and muscle movement). Some philosophers have wondered if quantum effects are foundational for consciousness - but at this stage this is pure speculation.
If there are ways to achieve biologically useful functions with organic chemicals more effectively using quantum effects than with classical effects (at body temperature), it would not surprise me if biological systems used them. But at this time, I haven't seen evidence for them in synapses.
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What is synaptic quantum tunnelling ?
I would have to say it is a wild hypothesis at this stage.
To demonstrate tunneling, you have to show that there is a potential barrier of some form (necessarily very thin), and that there is some quantum particle which appears on the other side of the barrier without any classical mechanism for getting there.
Thank you for the reply. First I believe exocytosis is essential for synaptic quantum tunnelling.
https://en.wikipedia.org/wiki/Exocytosis
The synapses of a cell do have a barrier: The cell wall, a dual lipid layer (http://www.cerebromente.org.br/n07/fundamentos/neuron/parts_i.htm#membrane).
- It's fairly thick - thicker than you would expect for quantum tunneling.
- But it also has a classical mechanism for transmission of ions - the ion channel (http://en.wikipedia.org/wiki/Ion_channel), which passes through the cell wall.
The release of neurotransmitter molecules (synaptic exocytosis) occurs across the presynaptic membrane "with probabilities much smaller than one per each impulses reaching the synapses."
Experimental analysis of transmitter release by spine synapses of hippocampal pyramidal
cells has revealed a remarkably low exocytosis probability per excitatory impulse.
Exocytosis as a whole certainly involves macromolecular dynamics (Fig. 5). We propose, however, that it is initiated by a quantum trigger mechanism: An incoming nerve impulse excites some electronic configuration to a metastable level, separated energetically by a potential barrier V(q ) from an unstable state which leads in a
unidirectional process to exocytosis.
Does the superpermittive properties of water activity inside neurons generates an incoming nerve impulse? If so, one can assert that intracellular water activity is implicated in synaptic quantum tunnelling.
Why is classical neuropsychology require quantum biology theory to postulate the existence of synaptic quantum tunnelling in brain activity?
It doesn't.
At the atomic scale, all physical, chemical and biological processes depend on quantum effects. Mainstream quantum biology focuses on possible quantum effects at the scale of large molecules (eg chlorophyl) and cellular structures (eg microtubules and muscle movement). Some philosophers have wondered if quantum effects are foundational for consciousness - but at this stage this is pure speculation.
If there are ways to achieve biologically useful functions with organic chemicals more effectively using quantum effects than with classical effects (at body temperature), it would not surprise me if biological systems used them. But at this time, I haven't seen evidence for them in synapses.
I believe neuronal hypercomputation is a function of synaptic quantum tunnelling: The biological processing and integration of conscious activity and memories into a coherent quantum state may arise from the electronic configuration of consciousness. Thus, is exocytosis influenced by the vibrational spectrum of water in brain activity?