Why don't quantum fluctuations cause us to fall through the floor?

[BoxedCat]

I get the fact that a) electrons don't "like" each other so they force each other away and b) that this is why we don't fall through the floor. But my question is (since this is on the quantum mechanics section) since there is a probability that say the atom under your toe could pop up somewhere else in the Universe. Why would this not affect us humans or other living things on Earth if a few atoms were to take a vacation to another part of the Universe?

 

[phinds]

(1) Why would a single atom here or there matter to you?
(2) probability of it happening is small. Very small.

 

[BoxedCat]

What if I tripped? But excluding the small chance of it happening would anything bad happen like maybe a rip in your skin or would you just not feel it?

 

[atyy]

The reason you don't fall through the floor is the Pauli exclusion principle. Roughly, two electrons cannot be in the same place at the same time.

Technically, this says that fermion wave functions are antisymmetric. When writing down an anti-symmetric wave function for electrons in the floor, why don't we have to consider the electrons on the moon? In principle we must. But you can show (it's not obvious to me) that neglecting the electrons on the moon causes an error that is smaller than can be measured. It is discussed in Shankar's Principles of Quantum Mechanics, p273, in the section "When can we ignore symmetrization and antisymmetrization?"

 

[BoxedCat]

Alright. Well thanks for the help. I am now put at ease that no foreseeable accident could occur from the Universe (possibly) playing a great big trick on me.

 

[atyy]

Alright. Well thanks for the help. I am now put at ease that no foreseeable accident could occur from the Universe (possibly) playing a great big trick on me.

Well, I'm sure the electrons in the floor won't end up on the moon - but maybe you will

 

[Maui]

I get the fact that a) electrons don't "like" each other so they force each other away and b) that this is why we don't fall through the floor. But my question is (since this is on the quantum mechanics section) since there is a probability that say the atom under your toe could pop up somewhere else in the Universe. Why would this not affect us humans or other living things on Earth if a few atoms were to take a vacation to another part of the Universe?

At some point it's useful to remember that atoms are a model devised by people to draw a picture of the quantum world. In some respects it's able to provide a decent picture, in others it's quite lacking. The lower you go into scales, the more obvious it becomes that physics is just a model and the more lacking and inadeqate it becomes.

 

[BoxedCat]

Which is why we (not me, at least not yet) do what we do we can shore up the inadequacies which frankly will probably lead to more inadequacies but we do it anyways! But still, I like my atoms were they are, with me not traveling the Universe like it is some atomic scale version of Star Trek

 

[Double-Slit]

I get the fact that a) electrons don't "like" each other so they force each other away and b) that this is why we don't fall through the floor. But my question is (since this is on the quantum mechanics section) since there is a probability that say the atom under your toe could pop up somewhere else in the Universe. Why would this not affect us humans or other living things on Earth if a few atoms were to take a vacation to another part of the Universe?

a) Thats partially true they are the same charge of course but there are many factors that affect them for example protons still don't like each other yet they form helium,lithium,beryllium and so on; It's because of the strong interaction that clumps them together.Although with electrons it's different they are pulled to the nucleus yet there can be 2 electrons in the first orbital although their probability distribution intersect each other and they could be in the same place in the same time,but they only exist if their quantum state is different,in this case their spin so they don't violate the Pauli principle.

b)An atom can't pop somewhere else in the universe.The subatomic particles are confined in their probability distribution,in this case the electron to their orbit,and leave that position only if some energy is added.But even if the probability of that electron (with the rest of the atom) would be aligned to do this and move through the floor atom by atom that would be roughly 10^9 atoms in that section and they would all have to align themselves perfectly to allow the quantum tunneling of your entire body to fall into the floor.Thats highly unlikely ,probably more unlikely than winning the lottery 10000 times in a row.

 

[BoxedCat]

So I should not worry about falling through the floor and instead I should waste my money on winning the lottery? Is there anything I can do without wasting that much of my time that could guarantee the quantum tunneling of something?

 

[BoxedCat]

Is there anything I can do besides waste my time on the lottery to that degree to "activate" some sort of quantum tunneling? For say upon my cat(no pun intended) possibly?

 

[Double-Slit]

So I should not worry about falling through the floor and instead I should waste my money on winning the lottery? Is there anything I can do without wasting that much of my time that could guarantee the quantum tunneling of something?

You should not worry about it.Even if 1 atom does this which is also very rare since the atom is a collection of quarks and electrons the chances are still small,maybe time to time an atom from your shoe gets trapped in the floor,do you notice it ?

Is there anything I can do besides waste my time on the lottery to that degree to "activate" some sort of quantum tunneling? For say upon my cat(no pun intended) possibly?

There is nothing you can do.Nobody can manipulate this "randomizer function" of nature or atleast we don't know it how to do it yet if it's possible.This is automatic and works best in the quantum scale.It can be used for many useful things,like erasing PC harddisks and creating touch-screen phones,where electrons tunnel through a 2-3 nanometer thick barrier.Also there was an experiment where they put 2 plates of metal together of different compound and they leaved them very close to each other a year or so and when they separated them they found atoms of the other plate's compound in the other plate's surface,and even inside it,that was a clear proof of this tunneling.I don't know experiment's name but you can google it.

 

[ZapperZ]

This is a very good time for a lot of people, especially those who did not learn physics (or have not learned physics) formally, to make the realization that physics isn't just "What goes up, must come down". Physics is also "Where and when it comes down". This means that physics isn't just a qualitative description of something, it also contains a quantitative description of that something. There must be calculational numbers that come out that we can compare and verify with experiments.

So apply to this case. It isn't just sufficient to indicate that there's a possibility that tunneling of something is "possible". One must also calculate the probability of that occurring. This is where the magnitude of it happening makes a huge difference. If the probability is extremely small, so much so that the chances of it occurring is negligible within the age of the earth, or the universe, then call me crazy, but I'd say that it doesn't occur! So when dealing with something like this, one has to consider both parts: the phenomenon is valid, and the quantitative aspect of it.

I did my PhD work in tunneling spectroscopy in High-Tc superconductors. All I can say is that, throughout the 3 years of my experimental work, I WISHED it would occur as easily as people seem to make it! And I was doing tunneling by electrons, which is not a composite particle. In considering the tunneling of composite objects (objects made of more than one fundamental particle), there are extra complications that are not present when dealing with tunneling of fundamental particles. Let me explain.

In electron tunneling, for example, the electron itself can already be described via the straight-forward wavefunction. And all we care about is the probability of that single electron tunneling across the potential barrier. However, when you have a composite particle, say an H2 molecule, for that to tunneling across, the whole molecule must tunnel across together! Think about it for a second. The molecule consists of 2 protons and 2 electrons. Already, due to their different charges, they see different potential barriers. If you set up a potential barrier to the electrons, the protons see this as being a potential well! It is almost impossible to set up one barrier that is uniform and identical to both the electrons and protons. What this results in is that the probability of tunneling for the protons and electrons will be very different from each other! Different parts of the molecule have different tunneling probability and different chances of coming out on the other side of the barrier. Essentially, this makes it very difficult to imagine the whole entity making it through together! This extra factor is not present in tunneling of a fundamental particle.

Not only that, there is another issue at hand. When we try to detect quantum effects of larger objects, such as buckyball, etc., the most important characteristics that the system must have is that the entire entity (buckyball, 10^11 electrons, etc.) must be in a coherent state with each other. Having such phase coherence is one of the most fundamental aspect of a quantum property. This is why in experiments done on buckyball interference, the molecule had to be cooled down and isolated until all parts of the buckyball are in coherence with each other. It wasn't easy to detect quantum state at this scale, and one had to go through a lot of crazy gymnastics for that to occur. And this is to do something "simpler", i.e. 2-slit interference. Think of how much more difficult it is to make that buckyball tunnel through a potential barrier, consider the extra difficulty factor that I mentioned above.

This is why many of us in physics shake our heads when someone outside of physics only understands a phenomenon or a principle superficially, and then decides to extrapolate it into other areas. The Deepak Chopras of the world often like to justify and validate many of their pseudo-scientific beliefs by invoking the "mystical" consequences of quantum mechanics. They do this without any kind of a quantitative understanding of quantum mechanics, and thus, are completely clueless to the scale of such events, and whether such things are well-defined and likely to occur.

After that long-winded response, the answer to your original question is: NO. You will not tunnel through the ground. I can say that with utmost certainty.

Zz.

 

[Maui]

Not only that, there is another issue at hand. When we try to detect quantum effects of larger objects, such as buckyball, etc., the most important characteristics that the system must have is that the entire entity (buckyball, 10^11 electrons, etc.) must be in a coherent state with each other. Having such phase coherence is one of the most fundamental aspect of a quantum property. This is why in experiments done on buckyball interference, the molecule had to be cooled down and isolated until all parts of the buckyball are in coherence with each other.

According to Zeilinger, they didn't cool down the C60 molecules but heat them up:

"By using a suitable mirror assembly, the focus could be scanned with
micrometre resolution across the interference pattern. The
absorbed light then ionized the C60 fullerenes via heating and
subsequent thermal emission of electrons."
http://qudev.ethz.ch/content/courses/phys4/studentspresentations/waveparticle/arndt_c60molecules.pdfAs far as i know, the earliest types of double slit experiements didn't use radical cooling and the cooling technology necessary likely wasn't there at that time.In fact, in the paper Zeilinger states that decoherence does not occur because their setup did not allow which path information to be obtained. This is quite a radical notion and a big departure from "decoherence is caused by the interaction of the system with the environment or for short - the so called environment induced decoherence".

I am not arguing that molecules are in a coherent state all the time but wishing to clear this notion up for myself why cooling down is not always necessary for quantum effects to show up.

 

[ZapperZ]

Thanks for clearing it up. I thought they had to heat up the initial material to produce individual C60. I have to double check if it was the fullerenes that had the cooling issue in the double-slit experiment.

Zz.