# What causes solidity of objects?

• B
Jimmy87
Hi,

Please could someone give me an accurate description of why, for example, a table is solid? What I mean is that if you calculate the amount of empty space in an atom, it is 99.999% empty space so why can't your hand go through the table (like a ghost)? I have looked on lots of, what I think, are reliable sources that say conflicting things. The ideas I have come across are:

1) Matter is almost entirely empty space. The reason you can't put your hand through a solid object is because of electrostatic repulsion of the electrons.

2) Matter is not empty space but according to QM it is filled with wavefunctions so thinking of this hand through the table idea wouldn't be suitable to address since matter is not empty at all. The problem with this is that lots of sources say the wavefunction is not a physical object but just a mathematical model to find the probability of certain quantum events like the position of a particle so how can it be full of wavefunctions if a wavefunction is not a physical entity?

3) The Pauli Exclusion Principle is the reason your hand doesn't go through the table. No two fermions can occupy the same quantum state so, although matter is mostly empty space, the PEP prevents this from happening.

4) I have found a fourth source saying source 3 is wrong because the PEP only applies to isolated atoms and not for multiple atomic system coming together and that the solidity illusion is caused by electrostatic repulsion like in explanation 1.

5) I found a physics stackexchange thread that seems to get 200 likes! This seems to be mainly aimed at explanation 2 (https://physics.stackexchange.com/q...-other-matter-if-atoms-are-99-999-empty-space).

So please could someone kindly tell me which explanation is the most accurate and modern way of looking at solidity. Is it good to think of solidity as an illusion? Is it wrong to think of the atom as empty space? Lots of university lecturers talk about the atom being mostly empty space but then other talk about it being full of wavefunctions whilst other say a wavefunction is not a physical thing! Some guidance would be very much appreciated,

Thanks!

Delta2

Homework Helper
Gold Member
Basically option 5) says it all and I believe its the correct answer. In this forum also there were many threads with hot debates regarding which of the PEP or the electrostatic repulsion is the dominant cause, at the moment let's suppose that it is a combination of both.

I want to say something about 2) (it is already being said in that link for 5) I just want to clarify it here), matter is not exactly filled by wavefunctions (since according to Copenhagen interpretation the wave function is not something real), it is rather filled by electron clouds. Electrons are not sharply localized when they are orbiting an atomic nucleus , which means we cannot consider them as point particles but rather as electron clouds that cover the atomic nucleus (though when electrons are not orbiting a nucleus and are in a free state we can consider them as point particles). The density of the electron cloud in a point of space near the nucleus is proportional to the squared amplitude of the wave function (of the electron) , at that specific point.

Jimmy87
Jimmy87
Basically option 5) says it all and I believe its the correct answer. In this forum also there were many threads with hot debates regarding which of the PEP or the electrostatic repulsion is the dominant cause, at the moment let's suppose that it is a combination of both.

I want to say something about 2) (it is already being said in that link for 5) I just want to clarify it here), matter is not exactly filled by wavefunctions (since according to Copenhagen interpretation the wave function is not something real), it is rather filled by electron clouds. Electrons are not sharply localized when they are orbiting an atomic nucleus , which means we cannot consider them as point particles but rather as electron clouds that cover the atomic nucleus (though when electrons are not orbiting a nucleus and are in a free state we can consider them as point particles). The density of the electron cloud in a point of space near the nucleus is proportional to the squared amplitude of the wave function (of the electron) , at that specific point.

Thanks for the detailed answer. So if both PEP and electrostatic repulsion play a role is it therefore fairly accurate to say solidity is an illusion? When your walking on the pavement are you really walking on empty space and it feels solid because of the electostatic repulsion?

Homework Helper
Gold Member
Thanks for the detailed answer. So if both PEP and electrostatic repulsion play a role is it therefore fairly accurate to say solidity is an illusion? When your walking on the pavement are you really walking on empty space and it feels solid because of the electostatic repulsion?

No it is not exactly empty space, it is filled by the atomic nucleuses as well as the electron clouds around them. The electron clouds of our feet can't overlap with the electron clouds of the pavement ( due to PEP and/or electrostatic repulsion) hence we feel solidity but you are kind of right that it is not as solid as our intuition tell us, but it is neither as empty space as you thought.

Jimmy87
Jimmy87
No it is not exactly empty space, it is filled by the atomic nucleuses as well as the electron clouds around them. The electron clouds of our feet can't overlap with the electron clouds of the pavement ( due to PEP and/or electrostatic repulsion) hence we feel solidity but you are kind of right that it is not as solid as our intuition tell us, but it is neither as empty space as you thought.

Thanks. I get what your saying that it isn’t fully empty due to the nuclei but if you do mass/volume of an atom you get 99.999% empty space (mass being neutrons + protons + electrons mass). This 99.999% idea I always see being thrown around, is it not quite accurate? I would that thought that even though the electron is spread out like a cloud as its position is uncertain it still has its normal mass and therefore the density of the atom should be the same regardless of whether you use the classical approach or quantum electron cloud approach?

Homework Helper
Gold Member
Thanks. I get what your saying that it isn’t fully empty due to the nuclei but if you do mass/volume of an atom you get 99.999% empty space (mass being neutrons + protons + electrons mass). This 99.999% idea I always see being thrown around, is it not quite accurate? I would that thought that even though the electron is spread out like a cloud as its position is uncertain it still has its normal mass and therefore the density of the atom should be the same regardless of whether you use the classical approach or quantum electron cloud approach?
I spent some time reading about the calculations that claim that atom is 99.999% empty space. What they do is that they consider the space around the atom in which the electron cloud extends as empty space, but that's the whole point, it is not exactly empty space, it has the electron cloud!

Of course an atom is not as solid as the continuum mass hypothesis of classical physics would assume, but it is not exactly 99.999% empty space, let's better say its volume consists 99.999% of electron clouds.

nasu
Gold Member
Please could someone give me an accurate description of why, for example, a table is solid?
Jimmy, I have bad news for you, an accurate description of a solid requires the knowledge of quantum mechanics. It explains how exactly solids are formed and allows for calculating their properties. Short of QM, only parables are available that can give you a hint of the physics behind it.
The first statement was that atoms are 99.999% empty space. Is it true? Well, yes and no at the same time. It depends on what you use to look at atoms.
What do atoms look like? Nobody knows, you can't image something that small with light of wavelength 1000 times bigger. But the picture is as follows:
Atoms are about 1 angstrom size (1 angstrom = 10-10m or about 1 billion times smaller than the smallest thing you can see with your eyes).
Atoms consist of a nucleus, whose size is about 1000 time smaller, surrounded by a cloud of one (hydrogen) or more electrons. The nucleus is made of neutrons and protons.
Another piece of information is the Pauli's exclusion principle. It applies to Fermions (elementary particles of fractional spin) and it says that two same particle cannot occupy the same quantum state. It means that no two electrons can be in the same quantum state but an electron and, for example, a neutron can happily coexist in the same state because even though both are fermions, they are different fermions.
So is a solid 99.999% empty space? it depends. If you want to probe it with electrons, you find out that it is 100 % filled with electrons and any additional one has to go to a much higher energy state.
But neutrons can pass right through any solids because nuclei (containing among other neutrons) occupy only a small fraction of the volume. In his ground-breaking experiment, Rutherford bombarded a thin gold foil with alpha particles and most of the went just straight through the foil. Only a small fraction got deflected due to electrostatic repulsion between the positively charged alpha particles and nuclei of the gold.
So yes, for electrons, any solid is 100 % filled. but for other particles, its 99.999 % empty. For neutrinos (another Fermion particles0 the matter is so empty that out of a millions of neutrinos generated by the Sun and striking our planet, only a small fraction is scattered.
That explains one part of your question, which is why we can't compress the matter into a point but not why a table is a solid.
How do solids come into existence? individual atoms occupy space but do not have any particular shape. To condense atoms into solids you need some kind of attractive interaction between atoms, in other words, bonding.
Bonding between the atoms cannot be understand in classical physics terms as it is entirely a quantum effect. The simplest way to explain bond forming is that sharing electronic states lowers energy. There are three types of bonds relying on sharing electronic states: metallic bond, covalent bond and ionic bond.
Metallic bond is applicable to simple metals such as alkali (lithium, sodium, potassium, etc.). In this bond, all the atoms contribute one electron each to the common pool. After that, the atoms are arranged to minimize the electrostatic energy.
At another end is an ionic bond applicable to things like common salt (sodium chloride). Here we don't really have sharing of electrons. Instead, halogen elements (chlorine, fluorine, iodine, bromide) like to accept an extra electron. Bring close an alkali metal, which easily gives away an electron and we have a system of positively charged alkali ions and negatively charged halogen ions forming a lattice. The net result is lowering overall energy due to electrostatic attraction between the positive and negative charges. But add a bit of water (high dielectric constant, lowers the electrostatic forces) and the salt breaks down and dissolves.
At the third corner there is the covalent bond. A typical case is a carbon atom with four valence electrons. These valence electrons form highly directional quantum states and as result if a very rigid structure (diamond is the hardest mineral in existence).

aaroman, nasu and Delta2
Gold Member
2022 Award
Please could someone give me an accurate description of why, for example, a table is solid?
I think the root cause of you puzzlement is that you are using an English language word, "solid", which has a lot of meanings, some of them shaded, to try to describe something in physics that can only be truly described by the math of quantum mechanics (as henryk pointed out).

Sticking with something like "why don't we fall through the chair we're sitting on" then for a really good first cut at an answer, electrostatic repulsion is good enough.

Staff Emeritus
This is a very confusing thread. The OP doesn't appear to understand his/her own question.

A "solid" means that there is a relatively fixed position of atoms and molecules making up that substance. A liquid and a gas are not solids, because the atoms and molecules making up those substance move about relative to one another. So asking "What causes solidity of objects" means asking why don't these atoms and molecules move about freely in a solid. The simple answer is relatively straightforward: the inter-atomic or inter-molecule bonding fix these atoms and molecules relative to one another.

However, what the OP has been asking, and what becomes confusing, appears to be the question on why we feel solid objects. This is no different than the numerous threads that we have in the General Physics and Quantum Physics forums about objects "touching" one another and why things can't penetrate through other things. This is now a different issue than objects being a "solid" as opposed to liquid or gas.

I suggest looking up those threads that have already addressed such issue, because I do not see anything new can be added to those.

Zz.

Gold Member
Sticking with something like "why don't we fall through the chair we're sitting on" then for a really good first cut at an answer, electrostatic repulsion is good enough
No it isn't. an atom is electrically neutral and there is no net electrostatic force between them, definitely not a repulsive force.
The reason that atoms can't penetrate each other is the Pauli exclusion principle: you can't just have electrons of different atoms at the same place and still in the same quantum state.
There is, however, something called virtual dipole-dipole interaction or van der Waals force. It works as follows: an atom is neutral on average but it is a dynamic entity and at any given instance, there could be a non-uniform distribution of charge (electron density) producing a dipole moment and a dipole-type electric field. Bring another atom close enough and it would become polarized due to that instantaneous of the first atom and the interaction between the two dipoles would result in an attractive force between the two atoms.
This does happen to noble gases at sufficiently low temperatures. However, the resultant force is very weak, the weakest of all the known forces between atoms.

Klystron and Delta2
Homework Helper
Gold Member
No it isn't. an atom is electrically neutral and there is no net electrostatic force between them, definitely not a repulsive force.
The reason that atoms can't penetrate each other is the Pauli exclusion principle: you can't just have electrons of different atoms at the same place and still in the same quantum state.
There is, however, something called virtual dipole-dipole interaction or van der Waals force. It works as follows: an atom is neutral on average but it is a dynamic entity and at any given instance, there could be a non-uniform distribution of charge (electron density) producing a dipole moment and a dipole-type electric field. Bring another atom close enough and it would become polarized due to that instantaneous of the first atom and the interaction between the two dipoles would result in an attractive force between the two atoms.
This does happen to noble gases at sufficiently low temperatures. However, the resultant force is very weak, the weakest of all the known forces between atoms.
This seems like a very nice explanation, however let's assume this example:

I strike my hand at a table with force. It is a well know fact that the table exerts on my hand an equal and opposite force. What is the nature of this force? according to mainstream physics it can be one of the four known forces (gravitational, electromagnetic, weak-nuclear, strong-nuclear). There is no force classified as PEP force at least not according to mainstream physics..

In my opinion the explanation of why we can't pass through solid objects is a combined explanation of PEP and electrostatic repulsion between the electron clouds. It is not the same as the van der Waals force between atoms of gases because here we press each solid towards each other, so there is something that can make the electrostatic repulsion quite stronger than the van der Waals force (a table made of steel can exert up to thousands of Newtons of force on my hand, if my hand could strike with a force of such magnitude).

DrClaude