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As far as I know, most of an atom is vacuum.

Therefore, in theory, would it be possible for me to throw a tiny stone through my window without breaking it because no matter actually collides?

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I will elaborate on @RedAct 's answer, to eliminate the coherence problem.

Let the stone be a crystal. A crystal can be described quantum mechanically with a state function and there is no coherence problem as the positions of the atoms are defined quantum mechanically.

Let the glass be of crystal too, again described by a single coherent wave function. This problem at the level of particle and barrier is given here.

barrier tunneling

Note that it is the height of the energy needed to penetrate the barrier that enters the calculations. In the quantum mechanical description the little crystal will have a probability of existing after the barrier at the same energy it had when thrown, with reduced probability.

The numbers that can give measurable probabilities of barrier penetration are the small masses of elementary particles. The exponential decay for high masses will give effectively zero probability for the incoming "stone" to continue through the barrier.

If the incoming little crystal has an energy much higher than the barrier energy, the probability might get higher but at the same time at high energies the individual nuclei with their strong forces will start to get in the game and then there will no longer be a coherent quantum mechanical wave function.

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The reason for a collision is not because the nucleus of the atoms in both the stone and the glass 'collide', it is because the 'empty space' is actually a manifestation of the coulomb force (because of the opposite charge of both the electron and proton). It is this force that you would need to overcome in order to throw a stone through a window without breaking it - at the atomic scale, the repellent nature of the protons and the electrons is responsible for making both the stone and the glass 'solid'.

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  • $\begingroup$ The author completely misses the role of Quantum Mechanics and particularly the Pauli exclusion principle. $\endgroup$
    – firtree
    Commented Aug 28, 2014 at 19:51
  • $\begingroup$ You're correct, I was giving perhaps an overly simplistic and incomplete picture... I would amend my answer, but you have done a good job of answering in more depth. $\endgroup$
    – Akoben
    Commented Aug 28, 2014 at 22:45
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Yes if you open it :-)

Joking aside...

The reason why solids interact when contacted is the Pauli exclusion principle. It says that two electrons cannot fill the same place if they are in the same state. That means their energy levels are same, or more technically, their wave functions are not orthogonal.

To make wave functions of the stone's electrons orthogonal to the ones of the window glass's electrons, we have to give them the momentum, at which they would have at least one wavelength on the length of the glass atom. (This is a rough estimate.) To calculate the lower bound, I'll take the length of the hydrogen atom, Bohr radius, and take it as the wavelength: $$a_0=\frac{\hbar}{m_e c\alpha}\approx\frac{\hbar}{m_e v},$$ which gives $v\approx c\alpha=c/137=2\,188\,\text{km/s}=1\,359\,\text{mi/s}$. Rather fast, huh? The actual limit would be higher by a factor of order unity.

This is not the end of the story. Though most of electrons will pass through the glass, some will collide, like they are hard balls of size called the scattering cross-section. This cross-section is calculated by some difficult formulas, and is speed-dependent. Speeding up stone (to some relativistic speed) we can make these collisions negligible, but there comes some other cross-section: nuclear. The cross-section of nucleus does not depend on speed, which means that nuclei really behave like balls or droplets. It is of order $\sigma=\pi r^2$, where $r$ is the radius of nucleus. The radius of nucleus is about $10^{-5}$ of the radius of atom, so if the thickness of the stone is more than $10^{10}$ atoms, then some nuclei will collide. But $10^{10}$ atoms is a macroscopic length - about 1 meter - so this bound does not bother us too much. EDIT: See below.

What if even some electrons or nuclei would collide? Is it a problem? Would the glass break? Not necessarily. The collisions would affect only individual particles. That would give the glass some energy, so it would heat up. Also the collisions give the glass some momentum, so it can be pushed forward even after the "stone" has passed through. Here the particle beam physics would give estimates which I cannot perform (I hope someone would contribute), but for me personally it seems not impossible that the stone (thin enough) could pass through the glass (thin enough) without giving enough energy to evaporate it, or enough momentum to puch and break it.

Generally speaking, when some object, for example a stone, moves with a high speed, it behaves at some speeds like liquid, then like gas, and at last - like the beam of radiation.

EDIT: Sorry, I found a major mistake in my estimate. When I was talking about stone being $10^{10}$ atoms thick, that implied that the glass is a monoatomic layer. To get the probability of collisions, we have to multiply thicknesses, so for the same thicknesses estimate becomes $\sqrt{10^{10}}=10^5$ atoms - only $\sim 10\,\mathrm{\mu m}$. That sounds more realistic though much less exciting :-) If the glass is 1 mm thick, then the "stone" should be only $10^{10}/10^7=10^3$ atoms thick, which is about 100 nm. Although, this bound can be somewhat weakened if we allow some collisions, keeping them few enough so that the total thermal and impact effect would be negligible. For example, if we allow 1 collision per 1000 atoms of glass, then the stone can be $10^{10}/10^3=10^7$ atoms thick, which is about 1 mm, though maybe 1 per 1000 is too much again.

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  • $\begingroup$ Okay, you dodged the Pauli exclusion principle, but what about electromagnetism? Did you hear about magnetic momenta of subatomic particles? And about Lorentz force? $\endgroup$ Commented Oct 25, 2014 at 18:29
  • $\begingroup$ That matter is covered in the paragraph about scattering and cross-sections. All the collisions electrons take part in are electromagnetic by nature. Also you can compare with the numbers in PDG paper Passage of particles through matter pdg.lbl.gov/2013/reviews/… $\endgroup$
    – firtree
    Commented Jan 24, 2015 at 17:27
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At least according to non-relativistic quantum mechanics, it's theoretically possible for the stone to pass through the glass without breaking it via quantum tunneling. However, the probability of that actually happening with a normal-sized pebble and sheet of glass is of course so extremely small that it's utterly negligible.

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    $\begingroup$ For this to be possible wouldn't the wavefunction of the stone need to remain coherent for a time at least as long as it takes to traverse the glass? For a macroscopic object like the stone the coherence time would be too small for it to travel far enough. $\endgroup$ Commented Aug 28, 2014 at 15:58
  • $\begingroup$ Even though the probability is extremely small, wouldn't that mean that sometime, somewhere, some man have put his fingertip on something and just "went through"? $\endgroup$
    – Roger
    Commented Aug 28, 2014 at 15:59
  • $\begingroup$ @Roger: No, to a confidence level of 0. followed by a lot of 9s. Something the mass of a "tiny stone" tunneling thru something the thickness of even the thinnest plausible window glass is so astronomically small as to be impossible with a certainty well beyond plenty of other things we consider "certain" without question. So basically "no". $\endgroup$ Commented Aug 28, 2014 at 22:02
  • $\begingroup$ @OlinLathrop If the entire observable universe was converted into tiny stones (and disembodied fingertips) on collision courses with thin, small sheets of glass, what then? $\endgroup$ Commented Aug 29, 2014 at 10:27
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I guess in some limited sense it is possible, if the material of the window can "self-heal". For example, you can push objects through a bubble without destroying it (http://www.hometrainingtools.com/a/bubbles-and-surface-tension-science-projects - at the end of the article; the object should be wet). On a different note, slow self-healing is possible in some situations (http://www.bbc.com/news/science-environment-27296365 ), so, technically, the material is broken, but the hole disappears with time.

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    $\begingroup$ Nice idea, since the glass is one of those "self-healing" materials, when heated :-) $\endgroup$
    – firtree
    Commented Aug 29, 2014 at 18:32
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When the stone gets really close to the window the electric field of the electrons in the stone's atoms will push against the electrons in the glass's atoms. That force will break the window, and there are no gaps in the field for it to slip through.

I am oversimplifying some. I am ignoring quantum effects such as the Pauli exclusion principle, but unless the stone becomes a piece of white dwarf matter it doesn't come into play.

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  • $\begingroup$ Actually ordinary solids are so hard due to exactly the same degenerate electron gas as in the white dwarfs (refer to the band theory of solids). Do not underestimate the Pauli principle :-) $\endgroup$
    – firtree
    Commented Aug 29, 2014 at 4:39
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I think no, for the glass needs to have be thin also so that the proton passes, for there are many sheets of atoms and eventually the proton would collide in on3 of them. Glass is amorphous so you can't have regular geometry sheets through which it might pass

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    $\begingroup$ Actually if you eliminated electromagnetic repulsion the stone would have no problem passing right through the glass. That's why a neutrino can pass straight through the Earth without hitting anything. $\endgroup$ Commented Sep 7, 2014 at 3:27
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I'm fairly sure that you could not throw a stone through glass without breaking it, but were you to have an incredibly accurate neutron gun, or something that shoots similar uncharged particles, you could aim between the atoms. In that case, you could have an uncharged particle pass through a window.

On the topic of particles not hitting stuff, check out this on neutrinos.

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