Question

What is the 2d equivalent of mass? Say I had a 2d circle in 2d space with a density (area density) of 10 and an area of 2, what units would the mass equivalent quantity (density x volume) be in?

Answer 1

in 3D space density is defined as mass per unit volume. so I /guess/ in 2D space density would be defined as mass per unit area. so in 2D space mass would be density x area. but then we have just moved the question to what are the units of density in 2D space?

as I understand it, mass is defined as the amount of matter an object has. one of the qualities of mass is that it has inertia.

to complicate matters even more - according to the theory of relativity and according to observations, adding movement to any massive object makes it more massive. some portion of the massiveness of any moving object must therefore be due only to movement.

also, the elusive search is still on for Higgs Boson. the Higgs field is supposed to be responsible for mass.

hmmm - I'm not sure if I have helped at all in your question? :-(

Answer 2

Mass is mass. It is the units of density that change. Linear density (kg/m), areal density (kg/m^2) and traditional volumetric density (kg/m^3).

Answer 3

For your 2-d circle (really a disc, right?), the density (here an areal density) would be measured in units like kg/m^2. The area of your disc (which would take the place of volume) would be measured in units like m^2, and so as usual , we get mass in kilograms.

Answer 4

well i was thinking more of a circle - a 2d object - rather than an very thin object in 3d. in this case, of course, mass can't exist because mass requires some extension. area density doesn't describe the same thing because it's referring to a 3d world. i'm wondering if there's some notion which has been devised of a 2d equivalent of mass which exists in that flat 2d world. this interests me because it would enlighten me as to a possible relationship between mass in 3d and higher spatial dimensions. if you extend an object with mass, for example, into a 4th spatial dimension, it will have a mass of infinite kg, but that doesn't mean there isn't a 4d equivalent of mass that will give a more sensible answer.

Answer 5

A circle is not a 2-D object, it's a 1-D object. It is a 1-D object that occupies 2-D space.

Answer 6

Mass does not a priori require some extension, either. As far as physics is concerned at the moment (resp. string theory), the elementary particles (quarks and leptons) are all point particles, so they are zero-dimensional. They occupy no spatial volume, if you disregard the quantum mechanical fuzziness associated with them. In this sense, the density of an elementary particle is not a well-defined quantity. Since everything in the universe is composed of these particles, when we refer to the density of an object we really in a sense refer to the "number density" of these zero-dimensional elementary particles, e.g. how many quarks per cubic meter.

Answer 7

I think you are mistaking the dimensionality of an object with the dimensionality of the space that it occupies. Just as a circle is a one dimensional object that lives in two dimensional space, the sphere is a two dimensional object that lives in three dimensional space. So the questions of mass or density have nothing to do with the space that an object occupies, you see? And when you consider things from an elementary particle point of view, density is not well-defined, so mass-density, which is what we commonly refer to as density, is really the mass of the elementary particles times the number density of elementary particles, where this number density is calculated with respect to the generalized volume that the particles occupy (by generalized volume, I mean that the "volume" of a 1-D object is its length, the "volume" of a 2-D object is its area, etc).

Answer 8

Sorry, I meant 'disk', not 'circle'. So essentially what you're saying is you can't go from the idea of moment of inertia in 2d to in 3d by, say, integrating and taking the disk as being an infinitesimally small element of a 3d cylinder, as you'll have to count the actual number of particles in the circle an infinite number of times, giving an infinite mass?

Answer 9

That's what I thought you meant. I didn't say that, and in fact you can do that. All I'm trying to say is that mass (rest mass if you're gonna be picky) is a fundamental property of elementary particles that is independent of the geometrical configurations in which those particles find themselves.

Answer 10

If you're saying that we can define a 2d mass density by counting the number of particles in a particular area, I don't see how you can take something with mass in a 2d universe, and turn it into mass in a 3d universe by integrating it - essentially adding it an infinite number of times. Surely it would have to be some concept analogous to mass but not mass as we understand it.

Answer 11

if I happen to have a bunch of oranges and I arrange them in a line (3 oranges per meter) and then I arrange them in a rectangular array flat on the floor (9 oranges per square meter) and then I put them in crates and stack them on top of each other to make a cube (27 oranges per cubic meter) then neither the number of oranges nor the total mass of my system changes in the slightest.