OK… so I was reading up on Einstien, learnin about relativity and all, when the whole idea of matter not being able to exceed light speed started making sense.
I began going over the concept of matter increasing in density as it approaches light speed, and wonderred what the state of infinite density would be. I came upon two possibilities:
Imagine 2 circles each representing an atom. Now imagine those circles progressively overlapping eachother until they become one circle. Same matter occupying same space. Would this be infinite density?
Imagine one circle representing an atom. Now imagine it being compressed further and further, becoming an oval, becoming a straight line, and then becoming entirely 2 dimensional, occupying no space. Is this infinite density?
It seems to me the second is correct. I dunno why, just intuition. Matter at infinite density could only exsist at the speed of light… it makes me wonder if matter occupying no space might not have measurable mass (how do you calculate mass of a two dimensional object?) or a gravitational field. How would it react to gravitational fields of matter in 3 dimensional space at non-infinite densities?
Maybe someone can make some sense of all of this? Am I completely off?
jon, you might consider asking a Mod to move this to General Questions since it’s much more than Mindless and Pointless and it’s a perfectly valid Question, not Sharing. You’ll probably find more of the readership there that can provide you with the answers you’re looking for.
Interesting question, but you’re not taking into account that what you’re postulating isn’t possible. One of the big physics guys a while ago (Dirac, I think) proved that it is impossible for two particles to share the same quantum state; in other words, no two pieces of matter can occupy the same space.
Also, atoms can’t really overlap; there are two states somewhat resembling that, though:
Covalent bond: the two atoms share an electron, and so you could say that the outer shell of one atom intersects that of the other.
Plasma: the component pieces of the two atoms would be disassociated and intermingle; they would be occupying similar and very close space, but they wouldn’t be in the same space, and they wouldn’t really be atoms anymore.
If you could actually squeeze an atom into occupying no space, I’d be inclined to agree with you. However, you keep doing weird stuff with your models and trying to translate your alterations to reality. Matter is essentially the curvature of space, and I’ve got a gut feeling that space can only curve so much.
However, if this were possible, and if it were done, what effect would that have on the surrounding space?
Yeah, I think this will enjoy a better participation if I move it over to GQ where the physics wonks congregate. They’re nearly at infinite density over there on some days.
The concept of “infinite density” is really just a convenient fiction as far as most physics is concerned; but as far as that convenient fiction goes, Idea #2 in the OP is correct. Essentially when we say “infinite density”, we mean exactly that we take some object of finite density and take its spatial extent to zero while holding its mass constant.
I think you’re thinking of the Pauli exclusion principle, but that only holds for certain types of particles called fermions. Another class of particles, called bosons, can have an arbitrary number of particles in the same state. However, any particle that you or I might think of as “matter” is a fermion (i.e. electrons, neutrinos, protons, neutrons, quarks, etc.) The best-known boson is the photon, but there are also mesons and gluons that you might have heard of too.
Well… this is a matter of much debate in physics today. As far as Einstein’s theory of General Relativity (“classical” relativity) goes, it predicts infinite curvature at the centre of a black hole — or, more precisely, it predicts that the curvature gets arbitrarily large the closer we get to the centre. (The centre, also called the singularity, isn’t technically part of the solution.) However, most physicists working in the field expect that we’re getting this oddball result because we don’t know everything that happens at such high curvatures (after all, we don’t have any experimental evidence to guide us), and that there’s some other theory out there that agrees with classical relativity up to a very high degree of precision, but gives us more sensible results when we ask it what happens at the centre of a black hole.
Notwithstanding the answers about infinite density–as matter approaches the speed of light, it doesn’t increase in density, it increases in mass. Well, on second thought, maybe it does increase in density due to Lorentz contraction, but the way your question was worded invites the clarification.
I’ve come across this contradiction in speaking with several people, some saying that matter approaching the speed of light increases in density and some saying it increases in mass (and therefore density).
I don’t understand how mass can just increase arbitrarily. I’m not a scholar of physics. Its just a passing fancy for me, so alot of my approach to it is intuitive and sophomoric. I believe I am familiar with Lorentz contraction, but I’m not sure that the contraction is uniform. Seems to me the contraction should only exsist on on dimension, that being linearly parallel to the direction in which the object is moving. Then again, I might not be familiar enough with it to know that it already states it that way.
Again, this is all supposition and intuition, I could be way off.
This isn’t actually correct, given the definitions currently used in physics. In relativity, “mass” is usually defined as the norm of the 4-momentum, which makes it an invarient quantity. In other words, when a physicist says “mass”, he means what’s sometimes called “rest mass”, not what’s referred to as “relativistic mass”. What used to be called “relativistic mass” is now just called energy.
Now, then, about density. Usually, we’re interested in the energy density, which increases for two reasons. First, there’s more energy there, and second, due to Lorentz contraction, it’s in a smaller space. But even if we’re interested in mass density (which I don’t think is ever particularly relevant, but one could define it anyway), the density would still increase due to the Lorentz contraction.
Getting back to the original question, if either scenario in the OP were possible, then the second would be infinite density, but the first would only be twice the density of a normal atom.
IIRC, if you cool He-4 down to temperatures of a few Kelvin, then He-4 forms what’s known as a Bose-Einstein condensate, and the individual He-4 atoms act as bosons.
Yes, atoms which are themselves made up of elemenatry particles which are fermions which have integer values of S (the vector sum of the spin quantum numbers (s) of the constituent particles) are bosons. Also you can get a fermionic condensate from fermonic atoms (that is atoms with odd half-integer values of S) which ‘pair-up’ with other identical fermonic atoms to form weird de-localized bosons (as the vector sum of S for any two fermions will always be an integer value) at very low temps.
You mean that the atoms have integer values of S, as obviously they must as bosons? Because fermions always have half integer values of S. Sorry - the sentance is a little confusing.
Yes, it is was a poorly constructed sentence, I mean that atoms with integer values of S are bosons, despite being made up of elemnatry particles which are fermions (which as you say have half integer values of s).
