Where does matter come from?

Question

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.

Answer 1

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

Answer 2

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.

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

Answer 3

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.