I understand that the density of the oceans on Earth in on average constant regardless of the depth. It is 1020 kg/m^3 at the surface and 1050 kg/m^3 at deep waters.

I understand too that this is not the case with the atmosphere. The density of the atmosphere decreases with height.

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Though, I could not find any description in QM, that would describe the difference between the two media, and how they react differently to gravity, and the distance from the center of mass does or does not change their density.


  1. Is there an explanation why the density of the oceans is (mostly) independent of depth, but the atmospheric density changes with height (is this just because of one is liquid and one is gas)?

  2. Is there a QM explanation to this (different material) or is this just because of the distance from the center of mass (GR)?

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    $\begingroup$ Why do you think QM and GR have anything to do with this? Water is incompressible, air is compressible, and this is a basic fact in classical physics about states of matter. $\endgroup$ – ACuriousMind Jul 20 '18 at 18:21
  • $\begingroup$ I wanted to find out if there is a QM explanation for their compressibility level. $\endgroup$ – Árpád Szendrei Jul 20 '18 at 18:23
  • $\begingroup$ And since atmospheric density decreases with distance from the center of mass, I thought that gravity would explain this (the decrease's direction). Am I wrong with these? $\endgroup$ – Árpád Szendrei Jul 20 '18 at 18:25
  • $\begingroup$ Yes gravity does affect the density but it is overkill to invoke GR for it. $\endgroup$ – Triatticus Jul 20 '18 at 18:32
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    $\begingroup$ Water molecules are not mutually in a covalent bond. This discussion should be moved to chat or new questions should be asked, such as why is water in the ocean a liquid? Why is the air in the atmosphere a gas ? $\endgroup$ – my2cts Jul 20 '18 at 20:06

What I do not understand is, why is air not one single average density, why does density decrease?

Here is a simple analogy that may help understand why the density and pressure at the bottom of the atmosphere is greater than at the top.

Imagine a million of compression springs stacked on top of each other.

The spring at the bottom will be compressed a lot, because it'll have to counter the weight of the rest of the springs pressing on it from the top. The spring in the middle will be compressed half way, since it'll have to counter the weight of half of the springs. The spring on the top won't be compressed at all.

So we can see that even if the gravity does not change with altitude and all springs weigh the same, the compression of the springs (and their effective density), will be increasing linearly from the top to the bottom.

Of course, the degree (coefficient) of the compression will depend on the ratio between the spring weight and the spring constant: the greater the ratio, the greater the compression.

A similar thing happens with the water in the oceans and the air in the atmosphere, i.e., we can view a column of water or air as many water or air cubes stacked on top of each other, the degree of their compression (pressure and density) being a function of the ratio of their weight and effective "spring constant".

  • $\begingroup$ thank you. I think I understand. And water is just less compressible. So this effect has less dominance on water because water molecules are already closer, and density will just slightly increase as the weight of the top layer pushes down. $\endgroup$ – Árpád Szendrei Jul 21 '18 at 1:02
  • $\begingroup$ @ÁrpádSzendrei You've got it. $\endgroup$ – V.F. Jul 21 '18 at 1:16

The incompressibility of liquids is due to the fact that they are made of atoms or molecules of finite radius. The atoms in a liquid are constantly in contact with their neighbors, and increasing the density would require that atoms or molecules overlap, which they typically don't do very readily. as such, liquids have an essentially fixed density.

In a gas, the atoms/molecules are not in contact with their neighbors, so the density can vary widely as the distance between one atom/molecule and its neighbors increases or decreases.

No QM or GR is required here.

  • $\begingroup$ Thank you. Can you please tell me why air density decreases with height, and away from the center of mass? Does that direction not involve stress energy and bending of spacetime? $\endgroup$ – Árpád Szendrei Jul 20 '18 at 18:34
  • $\begingroup$ @ÁrpádSzendrei As ACuriousMind pointed out, the density of the air decreasing with height only requires classical gravity. For gas to be at equilibrium, any external forces must be balanced by an on-average force provided by a pressure gradient. Gravity is an external force, so there must also be a pressure gradient to oppose it, so that individual constituents of the gas feel no force on average (gravity pulling them down is balanced, on average, by the increased pressure below them). Higher pressure in a gas means higher density, so the density increases as you go down. $\endgroup$ – probably_someone Jul 20 '18 at 18:39
  • $\begingroup$ Thank you I think now I understand why air is not equally dense. You are saying that the pressure gives a balancing force against gravity and lower there is more pressure so it can balance more gravity (stronger stress energy as you go closer to center of mass). Higher, there is less gravity and less pressure can balance it. $\endgroup$ – Árpád Szendrei Jul 20 '18 at 18:46
  • $\begingroup$ Not quite. There doesn't necessarily have to be "more gravity" at the bottom, whatever that's supposed to mean. Even if gravity were just a constant downward-pointing force (as it is usually approximated near the surface of the earth), you would still get this behavior. In fact, since the atmosphere is quite thin compared to the Earth's radius, gravity is basically constant across its whole length (it only varies by 2% over 150 km). $\endgroup$ – probably_someone Jul 20 '18 at 18:50
  • $\begingroup$ Can you please explain then why the direction of more density is downwards if more bending of spacetime (closer to cernter of mass) is not involved? I understand that water molecules are held togethet by EM forces, so water molecules are constantly in a covalent bond. Air molecules are not in a covalent bond with each other. So air molecules are moving more freely randomly and trying to fill all space they have. Now the only thing is gravity that is keeping them from flying away. $\endgroup$ – Árpád Szendrei Jul 20 '18 at 18:58

The barometric formula predicting the density curve of the atmosphere is a prediction of classical Newtonian gravity and fluid dynamics, no general relativity required.

The (in)compressibility of gases and fluids is related to the average distance between the molecules in gases compared to fluids, and the distance in fluids is so small that the repulsion of molecules as you try to compress them further is rather strong, while it is rather weak for the "large" distance in gases. This is related to the shape of the Lennart-Jones potential, as John Rennie explains in a bit more detail here.

  • $\begingroup$ Thank you. Do you have an explanation for this: "Why are all the air molecules not pulled towards the center until they are not any more compressible? - " $\endgroup$ – Árpád Szendrei Jul 20 '18 at 19:02
  • $\begingroup$ @ÁrpádSzendrei Because they have kinetic energy and angular momentum, both of which are conserved in an ideal gas (in which all collisions are elastic). $\endgroup$ – probably_someone Jul 20 '18 at 19:09
  • $\begingroup$ @ÁrpádSzendrei They are pulled towards the center (that's why the air is denser at lower elevations!). Gravity makes no exceptions for anything. $\endgroup$ – ACuriousMind Jul 20 '18 at 19:10
  • $\begingroup$ OK so the reason that they are gradually denser towards the center of mass is that spacetime is bent gradually towards the center of mass. the more bent spacetime is, the more denser air is. $\endgroup$ – Árpád Szendrei Jul 20 '18 at 19:17
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    $\begingroup$ @ÁrpádSzendrei No, spacetime being "bent more" doesn't even mean anything. This isn't about spacetime. This is plain, old Newtonian gravity: The closer you are to the mass, the stronger the gravitational force is. It already explains the phenomenon perfectly, there is no need to involve GR when it's Newtonian approximation perfectly suffices. Beware the dangers of reductionism: Just because everything is ultimately QM and GR, that does not mean the most insightful explanations are produced by QM and GR. $\endgroup$ – ACuriousMind Jul 20 '18 at 19:24

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