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I admit, it's been a few years since I've studied physics, but the following question came to me when I was listening to a talk by Lawrence Krauss.

Is there any knowledge of from where matter that exists today originated? I recall that the law of conservation of mass asserts that matter cannot be created nor destroyed, but surely the matter we see today had to be created at some point? Perhaps I am applying this law in the wrong fashion.

The reason I ask, is because Krauss mentioned that the elements of organic matter where created in stars, not at the beginning of time (whenever that may have been), but I ask, where did the building blocks for these elements arise? Were they too created in stars? If so, from where did their constituent building blocks come?

Please forgive me if this off topic, it is my first post on this particular stackexchange site. Thank you.

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The law of conservation of mass is only valid in the classical limit. More in general, the combination of mass and energy is conserved, as they can be exchanged under certain conditions $E=mc^2$.

In very simplified terms, it is currently understood that, initially, possibly only energy was present. Then this energy started to partially change into mass, forming first quarks and electrons (mostly). Then heavier particles. Finally, once the universe cooled down a bit more, the first atoms started to form through the aggregation of the particles. It is calculated that atoms would be split between hydrogen and helium with a 3:1 ratio - these are the two lightest atoms.

This was enough to create the first generation of stars, which with fusion and with their dying blast generated the heavier elements that build life.

This explains the currently understood principle of nucleogenesis - if you are instead more interested in how and why energy is changed into mass, and what is the nature of mass, then space_cadet's answer gives you a quick overlook of the hypotheses that are being studied.

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This is correct but you fail to mention the difficult corollary problem: given that pair creation processes are symmetric in Baryon and Lepton numbers, why is the observed universe almost entirely devoid of anti-matter? (To which there are no final answers as yet. CP violation may play a part.) – dmckee Jan 4 '11 at 4:31
"only energy was present" -> um, this part is horribly wrong. Initially (and always) there were some particles. The closer to Big Bang the higher the temperature and more massive particles you'll get. In particular, there was certainly quark-gluon plasma and a soup of heavier particles (most of which we probably don't know yet). One also needs to take into account the restoration of electroweak symmetry and perhaps grand unification. There were also lots of micro-BH and going even further probably other amusing objects of quantum gravity. – Marek Jan 4 '11 at 9:00
@dmckee: I left out that part purposefully. It's irrelevant to the question. – Sklivvz Jan 4 '11 at 10:08
This hints at the right physics, but the details are muddled. It doesn't make sense to talk about "only energy" being present; rather, there was a hot plasma of photons, electrons, quarks, gluons, and other particles. At the earliest times we have good evidence and understanding of, these were a plasma with a temperature on the order of 10 MeV. As it cooled, the plasma wasn't hot enough to split nuclei into free quarks and gluons. Nucleons formed then, as you mention. But before that, there was plenty of matter around, with more baryons than antibaryons (for unknown reasons). – Matt Reece Jan 5 '11 at 2:58
There is no such thing as "pure energy" whatever that means. Might as well call it "pure ectoplasm" while you're at it. In the context of modern cosmology you have to mention CP violation and the other two Sakharov conditions if you going to speak of the "origin of matter". Nucleogenesis itself doesn't tell you anything about the origin of electrons, protons or neutrinos. Those are the inputs for nucleogenesis. But where did these "inputs" arise from? Is there a simple, self-consistent explanation for their presence? – user346 Jan 5 '11 at 3:05

the conservation of energy is violated in cosmology - in all situations described by general relativity in which the time-translational symmetry of the "background" is broken. That's clearly the case of the Big Bang, too.

Again: By Noether's theorem, the conservation of energy is linked to the time-translational symmetry (the properties of the Universe don't depend on time) which is broken in an expanding Universe.

So one can see that the total energy/mass of the Universe is not conserved in time. In particular, the "dust" with zero pressure has a conserved total energy/mass. However, the energy carried by radiation - such as photons - decreases as $1/a$ - inverse linear size of the Universe - because the wavelength gets larger as well, which decreases the energy of each quantum.

On the contrary, the energy/mass carried by the dark energy is increasing with the volume because the energy density is constant - that's why dark energy is the normal realization is known as the cosmological constant. The density is constant but the volume of space is growing: the total energy is growing, too.

It is very likely that the huge mass of the Universe around us was created by inflation. During inflation, there was also a nonzero "dark energy" - energy density of the vacuum - which was constant while the volume of space was exponentially growing. This created lots of energy, and at the very end, a big part of the energy (kinetic energy of the inflaton which is proportional to the total energy etc.) was converted to ordinary particles that eventually gave rise to the galaxies etc.

So the exponentially large mass of the Universe is a large, unnatural number, but this unnatural number is actually explained by inflation. As Alan Guth, the main father of inflation, said, the Universe is the ultimate free lunch.

Best wishes Lubos

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@ Luboš Motl. This is by far the best answer out of the three, not sure why it does not have more votes :( – stringpheno Feb 25 '11 at 5:59
@stringpheno: Possibly because the difficulty of contents are far beyond the level of the original question. It may be correct, but it's not clear to me that the original question asker will have gained anything from it. (Not that I am claiming that I could do half as well.) – Beska May 27 '11 at 14:27

The origin of matter is a major problem in modern physics. Sure we have a description in terms of the Standard Model of particle interactions, but that is simply an empirical framework built upon observation. There is no compelling reason, for instance, why the gauge group of the SM should be $ SU(3)\times SU(2) \times U(1) $ and not any other. Grand Unified Theories (GUT) attempt to provide an answer which seemingly complicates the issue further by suggesting bigger groups $SO(5), SO(10), \ldots$ which can contain all three families of particles.

Certain streams of contemporary research appear to favor an alternative and perhaps simpler approach, one that was favored by Einstein and Wheeler among others - that matter is simply another aspect of geometry. The paper of Einstein and Rosen which is commonly cited as the source of the notion of wormholes, was in fact an attempt to provide an explanation for particles as topological defects in the vacuum.

Anyhow, all of this sounds pretty technical. To simplify the notion greatly the viewpoint favored by approaches such as Non-Commutative Geometry, LQG and (IMHO) String Theory is that particles are topological defects in a background geometry. If you think of geometry as a sheet then these defects can be thought of as punctures in this sheet. How such punctures can join up and interact should be governed by simple rules and one would hope these rules will yield the S.M. in a suitable coarse-grained approximation.

Edit: Changing some wording in 2nd para to something a little less absolute in response to comments by @matt and others.

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Sure they do. I have nothing against them. They just defeat the purposes of discussion. – user346 Jan 4 '11 at 5:16
Regarding string theory: various particles are just excitations of the strings so your statement amounts to saying that strings are topological defects. Even if this view could somehow be made correct (e.g. by interpreting open string attached to a brane as topological torus) I don't believe anyone holds such a view or that it is in any way useful. – Marek Jan 4 '11 at 9:09
I don't know what you mean by saying that bigger groups "contain all three families" of particles. The groups contain only gauge bosons; each generation of particles we know fits into some representation of these groups, but the generations are not unified. Also, I absolutely do not agree that research is "abandoning" field-theoretic ideas, which if nothing else are valid descriptions of low-energy physics. It's not at all clear to me in what sense either string theory or noncommutative geometry imply that matter is topological defects. – Matt Reece Jan 5 '11 at 4:17
Your statement was about what GUTs attempt to do. They don't attempt to unify families. The fact that Garrett Lisi does is neither here nor there; I'm not going to argue about the definition of "crackpot," but his theory made little sense and rather than try to understand the obvious criticisms he seems to keep writing papers on the same thing. At any rate, I think this site should have answers involving accepted physics, of which GUTs are an example and whatever Lisi is doing isn't. – Matt Reece Jan 5 '11 at 6:06
I was not referring to E8 which I could not care less about, just to your original answer. When a non-expert comes and ask a question, I'll let him know what is known with near certainty (the answer to this question has probably to do with reheating). I also like the idea of matter from geometry, and Wheeler's geons and all the rest, but the fact is that this idea currently plays no role in accepted mainstream theories, and in most research directions to extend them. That may change in the future, at which point it would be legitimate to include it in an answer. – user566 Jan 5 '11 at 15:44

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