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Atoms are 'nothing but' space versus 'mostly' space

  1. Aug 26, 2011 #1
    It is common to see this line: "atoms are mostly empty space". That line appears inadequate and misleading.

    Atoms are ultimately made up of electrons and quarks. Electrons and quarks are by definition 'point particles', meaning they have no spatial extent. So there is nothing there that takes up space.

    Wouldn't it be more accurate to state something like 'atoms have mass and electrical fields but there is nothing there that takes up space', or, in the spirit of the 'mostly empty space' line to say 'atoms are nothing but empty space'. That is a bit extreme because of presence of fields but there is nothing there that actually takes up space since we are dealing with point particles.

    Any ideas on this?
  2. jcsd
  3. Aug 26, 2011 #2


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    It really depends on how you want to define "empty space". Atoms are full of electromagnetic fields and the particles that produce them. These particles can only get a certain distance from each other before the Pauli Exclusion Principle kicks in. Not to mention the repulsion of like charged particles. If you consider everything to be made of point particles and those being "nothing", then it still doesn't make any sense, as then nothing makes up everything!

    So, it really just depends on your definition of empty space.
  4. Aug 27, 2011 #3
    Thank you Drakkith for your kind reply.

    It appears to be the standard thing to say that 'atoms are mostly empty space'. This implies that the constituents of the atom, the electrons and nucleus (quarks at the most fundamental level) are something other than empty space, like little bits of matter, that they take up space. But as point particles, they do not take up space. Thus the particles that comprise an atom actually do not take up ANY space, at all.

    There is clearly a difference between the space within the atom and the space outside the atom. We have point particles bound together, forming electric fields. But nothing within the atom actually takes up space. Points don't take up space. The extent or size of the atom is determined by the extent of the electric fields. If fields are viewed as taking up space, the atom is not 'mostly empty space', but 'completely full space'. That is a very different statement from 'the atom is mostly empty space'. In either case, the 'mostly empty space' comment is wrong and worse, it is misleading.

    I just wanted to bounce my thoughts on this topic off real physicists.
  5. Aug 27, 2011 #4


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    I have never liked the description of fundamental particles as point particles because it conjures up the idea of classical point particles and exactly this kind of misunderstanding. The fundamental particles are not classical point particles so classical ideas such as assigning them a volume of zero are also incorrect. When we say they are point particles all we mean is that using the shortest wavelength photons we have they scatter photons like point particles in Rutherford scattering experiments. We do not mean that they are classical little balls of infinite density and so forth.

    The fundamental bosons follow Bose Einstein statistics and obey the Pauli exclusion principle. So two of them may not be positioned infinitely close together. I would define their size based on that. As Drakkith states, the idea that an atom is mostly empty space is flat wrong and is based on classical thinking. The atom is filled with fields of all kinds.
  6. Aug 27, 2011 #5


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    I think the element of truth to 'common wisdom' is simply that apparent atomic radius defined by the electrons is so much larger than the apparent radius of the nucleus, so 99.9+% of the mass is contained in 'almost none' of the volume. It isn't really accurate to go from these statements to statements about 'empty space'. I guess one more thing to say is the probability of an electron being closer to the nucleus than some radius (defined by the inner shell) is small; probabilistically, there is a region of near zero charge density between the nucleus and inner electron shell radius.
  7. Aug 28, 2011 #6
    Atoms can experience a variety of forces, which implies they are not empty. Something must be there to experience the forces.

    Imagine a large empty building with one person inside. Although the building is mostly "empty space", a large variety of random things can happen. Further imagine trillions upon trillions of such buildings, each containing one person. The people inside the buildings can communicate with people in other buildings. An observer, quite some distance away, might complain about the fact that the community is totally empty space, yet marvel at the eerie productivity. (The observer can not see inside the buildings, yet can infer that they must be very nearly empty.)
  8. Aug 28, 2011 #7
    Thank you DaleSpam. PAllen and Jodo Kast. I appreciate you sharing your thoughts.

    From the Quantum Mechanics section of the Wikipedia on Point Particles, http://en.wikipedia.org/wiki/Point_particle

    "It is in this sense that physicists can discuss the intrinsic "size" of a particle: The size of its internal structure, not the size of its wavepacket. The "size" of an elementary particle, in this sense, is exactly zero."

    We are all aware of the presence of electical forces and such within the atom. My focus is on the statement "atoms are mostly empty space" that we see all the time and even ourselves would use to describe the atom. And for the sake of introduction, I am very aware of uncertainty, exclusion and QED. I posted because I don't have anyone in my circle that can talk to about such things and this particular topic jumped out at me recently.

    If the wiki article reflects a QM view that point particles really do not take up space, then there is nothing in the atom that takes up space. Of course, the point is there and if it exists, it must take up space. But according to definitions, it does not. Thus we have an issue.

    It appears much more accurate to use some other sentence. The 'mostly empty space' wording implies, to me at least, that there is something in there, the matter of the atom, so to speak. But it really appears that there is nothing there except forces and that which the forces center upon, namely the point particles.
  9. Aug 29, 2011 #8
    I would argue that the phrase "atoms consist of mostly empty space" in textbooks is put there by authors who either do not understand quantum physics or are afraid to present beginners with the truth. Atoms are crammed full with the quantum wavefunctions of the bound electrons. An every day atomic object, such as a non-ionized iron atom, has 26 bound electrons spread out in quantum waves, most of them overlapping spatially. Try to plot the spatial nature of all 26 bound electron wavefunctions an iron atom at once on the same diagram and you will get a feel for how packed atoms are. The wavefunction state of an electron is very real.
  10. Aug 29, 2011 #9
    ... is refering to a classical representation of the matter and to the strange and puzzling fact that we cannot say where the masses (inner, proper energies) of the elementary particles really are. So small, bad localized and allways moving... and developping a volume which is quite biggest than the one we could give to that points (approx. 4. pi. 10-15m3)!!!
  11. Aug 29, 2011 #10


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    Yes, I mentioned this as well in my reference to scattering experiments.

    I just don't know how you can consider a region filled with all sorts of fields to be empty space? In what way is it empty? There are fields filling it. It is not empty.

    If you read the whole article I think that no such view is reflected.
  12. Aug 29, 2011 #11


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    I agree with the last few posts: the phrases in question are usually used in the context of old quantum theory and not in quantum mechanics.

    However, it is a matter of interpretation: in Bohmian mechanics (BM), the particles have well-defined positions. The orbitals represent only our incomplete knowledge about this position and are therefore not physical. Wether the space between the particles should be regarded as empty or not, is a matter of taste then.
  13. Aug 29, 2011 #12
    It is not a matter of taste if words having meaning and meaning has consequences. "Empty" is defined in the dictionary to mean "holding or containing nothing". Some being empty has the consequence that it could be filled. An neutral atom does not contain space in between its electrons where we can cram more electrons, therefore there is nothing empty about it.
  14. Aug 29, 2011 #13
    In the commonly stated sentence "The atom is mostly empty space.", (Google that exact phrase, with quotes, and you get about 300,000 hits) the focus is on the matter, not the fields. I am sure that everyone who makes that statement agrees the atom's space is filled with fields. That is not the focus of the sentence. The focus is on the matter or mass of the atom.

    What PAllen said, "99.9+% of the mass is contained in 'almost none' of the volume" is very accurate and does not involve the 'fields' issue. So it is a clean and accurate statement.

    And for DaleSpam and the rest... I agree about the volume being filled with fields. My statement of "the atom is nothing but space" was focused on the matter concept. I see that my statement is misleading as well. Input on that thought was the goal of posting. So in the larger sense, my statement also needs to be dropped. Maybe "the atom is point particles and fields."

    Let's look at the point particle again. Using the Wiki page, orders of magnitude, http://en.wikipedia.org/wiki/Orders_of_magnitude_(volume [Broken])

    Let's take that data and assign a volume of 10^-46 meters^3 for the classical volume of the electron. Also from that atrticle, the volume of the hydrogen atom is about 10^-33 m^3.

    Dividing gives us about 10^-13 meters^3. More like 5.75 x 10^-12 cubic meters for four point particles. That is a really small number. We could take PAllen's statement and adjust to it something like "99.9+% of the mass is contained in 5.75 x 10^-10 percent of the volume". (to state this excessively).

    However, that begs another question. Just how much energy is in the fields of a hydrogen atom? That would give us a way of saying how much of the mass is actually in that 5.75 x 10^-10 percent of the volume.

    Plus, this could be adjusted for a quantum mechanical electron volume, versus the classical one I used. I bet you guys can get that faster than I can. In any case, I got what I came for. So thanks everyone!
    Last edited by a moderator: May 5, 2017
  15. Aug 30, 2011 #14


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    In my mind, talking meaningfully about 'seemingly empty' requires discussion of interactions. In this sense, degree of emptiness depends on what probes you use, and amounts to a discussion of distribution of interaction cross section.

    The extreme case probe would be the neutrino. One might say from this point of view, there is really almost nothing in an atom: the ratio of interaction cross section to atomic volume is (if I recall right) << 1 in 10^50. Even the nucleus appears 'mostly empty' to a neutrino.

    However, to any other particle, the nucleus can crudely be said to be solid - it has high interaction cross section with anything else. Historically, it is this fact that is behind the 'mostly empty space' statement. One is simply talking about the ratio of effective atomic radius (defined by electron distribution) with effective nuclear radius measured with any probe other than a neutrino; also noting the nucleus is 99.9+% of the mass.

    Any attempt to give more meaning than this leads to misconception.

    One thing I said earlier was wrong. If you use electron probes to measure the 'likelihood' of electrons very near the nucleus, you would find non vanishing probability very close to the nucleus. Thus charge distribution and mass distribution (both probabilistic) due to electrons would appear fill the space of the atom, with the exact shape of the distribution dependent on the atom and its excitation state.
  16. Aug 30, 2011 #15


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    Matter is fields too. In particular, the electron is matter and its field is the field that takes up most of the volume of an atom. Again, this distinction between matter and fields is a classical distinction, it doesn't exist in modern QM. There are boson fields and fermion fields, but it is all fields.

    In fact, most of the mass of the atom is contained in the nucleus, and most of the mass in the nucleus is in the strong force bosons, not the quark fermions. So if you neglect fields you get rid of all of the mass of the atom or even if you neglect only boson fields then you get rid of most of the mass of the nucleus. It just doesn't make sense to draw this distinction.
    Last edited: Aug 30, 2011
  17. Aug 30, 2011 #16


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    :redface: Oops. That should be "The fundamental fermions follow Dirac Fermi statistics and obey the Pauli exclusion principle." :redface:
  18. Aug 30, 2011 #17


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    Again, this is interpretation dependent. Restrictions like the pauli principle apply to wavefunctions/states. In realistic interpretations -where a particle has a well-defined position at all times- these restrictions are only statements about average values and not about individual particles.

    Maybe this was a poor choice of words on my side. What I wanted to emphasize is that it's a matter of taste because choosing an interpretation is a matter of taste and not because one can define "empty" the way one likes.
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