How much mass has the universe lost as energy since First Light?
Energy is the by-product of nuclear fusion. This is usually expressed as photons. Other nuclear reactions produce other massless products like neutrinos. The end result is the same: mass is lost and energy produced. But some photons are absorbed. Neutrinos famously go through virtually everything, but some interact. So how much mass has the universe lost to energy?
None of it. Mass is conserved in these reactions.
That’s what E = mc[SUP]2[/SUP] means. It’s not a chemical reaction where one thing changes into another. It’s an equivalence. Whenever there is mass, there is some amount of energy, and whenever there is energy, there is some amount of mass, and the equation explains how much.
That said, stars do convert matter into other forms of matter, and this conversion releases energy (and with it mass, as I’ve explained above).
What happens in the sun is that 700 million metric tons of hydrogen are fused into 695 million metric tons of helium every second. This leaves 5 million tons of mass (or energy) that gets released eventually into rest of the universe. Given that there are about 7 × 10[SUP]22[/SUP] stars in the universe—and given that the sun is an average star—this makes about 3.5 × 10[SUP]29[/SUP] tons of energy being released every second.
The energy density of radiation is not that significant in the present era of the Universe and much less than the energy density of matter (both visible and dark). Compared to the total energy density there isn’t a significant amount of the energy density of matter being converted into radiation energy density either.
Mass is not conserved. Total energy counting mass as E=mc[/sup]2[sup] is conserved, but mass itself is not. However, I think the answer depends very strongly as to when you start counting. Theory now has it that pairs of particles and anti-particles were created (out of energy). This increased mass. Most of these annihilated converting mass back to energy. Inside of stars some mass is also turned to energy in the fusion process.
There is much more mass than energy now (not counting dark energy), but originally I believe there was none. so the answer is negative if you go back far enough.
Not quite. Both energy and mass are conserved in these reactions. Moreover, for a given amount of mass, there is always the same amount of energy. Now in nuclear reactions, some of that mass “flies away,” but it doesn’t disappear. If you could fit a star in a box so solid that nothing, not even heat, could escape from it, the mass of the box would not change over time.
IANAP, But I don’t think this is correct. Mass is a form of energy. It’s a bit confusing to say mass has energy; it’s more correct (and less confusing) to say mass is energy. Since mass is a form of energy, it can be converted to other forms. Other forms of energy can be converted to mass.
Mass and energy always go hand in hand. You cannot get the mass to go away through any sort of chemical or nuclear reaction, and you cannot get the energy to go away either. The mass is always there. The energy is always there. All you can do is change around the form that they take on.
If you have a nuclear reaction that starts with 1.0 grams of matter and ends up with 0.8 grams of matter, that “missing” 0.2 grams of mass is not actually missing. It is there somewhere. However, that mass is just not taking the form of matter anymore. There is no law of conservation of matter. There is a law of conservation of mass.
In special relativity, mass energy and momentum are all rolled into the 4-momentum vector. Energy, which is not invariant under the change of frame, is one component of this vector.
The correct/most useful definition of mass in special relativity was at one time a little controversial and due to E = mc[sup]2[/sup], sometimes ‘mass’ is used as a synonym for ‘energy’, however these days ‘mass’ usually means ‘rest mass’ which is the norm (the length, if you like) of the 4-momentum vector and is invariant under a change of frame.
The 4-momentum of a system is the sum of the 4-momenta of its constituent parts and conservation of 4-momentum means that the 4-momentum vector of a closed system doesn’t change with time.
As the 4-momentum doesn’t change with time neither does its components (if you don’t change frame), so this implies conservation of total energy. Also as you when you sum vectors in a given basis, the nth component of the sum is just the total of the nth components, the total energy of the system in a frame is the sum of the energies of its constituent parts.
For rest mass, the conservation of 4-momentum also implies the total rest mass of a closed system doesn’t change. However the length of the sum of a set of vectors is not necessarily equal to the sum of the lengths of those vectors the total rest mass of a system is not necessarily equal to the sum of the masses if its constituent parts (as a result of the slightly quirky nature of spacetime geometry the total rest mass is greater than or equal to the sum of the rest masses).
In other words conservation of mass in special relativity only works if you use mass as a synonym for energy or if you define total mass in terms of the total 4-momentum rather than summing masses.
As we’re talking about the Universe though we’re in the realm of general relativity. In general relativity 4-momentum is rolled into a tensor called the stress-energy tensor. Because in general relativity the stress-energy tensor is coupled to the geometry of spacetime, global conservation of energy and mass become very slippery concepts, which should not be taken to always apply.
You should not therefore expect to find a useful global conservation law for energy and/or mass in all general relativistic cosmological models. However thanks to the assumption that the Universe is very ‘regular’ on large scales, the cosmological stress-energy tensor is comparatively very simple. At any given time the stress-energy of the Universe can be described simple by its mass density and pressure. ’
Matter’, which is any particles whose mean speed (weighted by energy) is small compared to c (e.g. atoms, electrons, protons, most particles with mass) has a pressure that is very close to zero. ‘Radiation’, which is any particle whose mean speed is c or close to c (e.g. photons and high-energy neutrinos) has a pressure that is close to one third their energy density. Due to Hubble red-shift in an expanding Universe, the energy density of radiation falls off much quicker than the energy density of matter. The result being in the current era the energy density of matter is several orders of magnitude larger than the energy density of radiation.
There are also thermodynamic considerations, however outside of the early Universe matter converting to radiation and radiation converting to matter does not make a significant difference to the energy density of matter.
The OP’s question then doesn’t have an easy answer as transfer of energy density between matter and radiation is not the only thing (or even the most significant thing) that alters the ratio of the two energy densities.
Obviously, things have changed since I majored in physics years ago, can you explain simply how when an electron and positron annihilate to photons rest mass is conserved? Wasn’t it positive originally and zero now? The only think I can see is that somehow while a photon has zero rest mass, two photons traveling in opposite directions have a non-zero total rest mass. Stranger things happen in Quantum Mechanics so I wouldn’t be too surprised.
You’re thoughts are absolutely correct, except for you don’t need to delve into QM, just special relativity.
If for simplicity’s sake let’s say we use natural units where c=1 so we can ignore that constant (and also to slightly simplify the calculations below, where the rest mass of an electron is also unity), 4-momentum has the components (E,p[sub]x[/sub], p[sub]y[/sub], p[sub]z[/sub]), where E is energy and p[sub]x[/sub], is the component of momentum along the x-axis, etc.
The rest mass, m, can be calculated from: m[sup]2[/sup] = E[sup]2[/sup] - p[sub]x[/sub][sup]2[/sup] - p[sub]y[/sub][sup]2[/sup] - p[sub]z[/sub][sup]2[/sup]
Let’s say electron has 4-momentum (2,sqrt(3),0,0) and annihilates with a positron with 4-momentum (2,-sqrt(3),0,0). The rest mass of each particle is 1 and the total 4-momentum is (4,0,0,0), meaning the total rest mass of the system is 4.
Now lets say two photons are produced, one with 4-momentum (2,2,0,0) and the other with 4-momentum (2,-2,0,0). The total 4-momentum is still (4,0,0,0) so 4-momentum (and therefore energy and momentum) is conserved and the total rest mass of the system is also still 4. However the rest mass of the two photons are both zero.
NB in the above example I deliberately chose the rest frame of the system. In the rest frame of the system total rest mass = total energy, but this is not so for other frames.
Or to make it clearer, the mass of a system is not equal to the sum of the masses of the system’s components.
Nitpick: neutrinos aren’t massless. We know this because neutrinos oscillate between flavors. Measurements from solar neutrino emissions were lower than expected; the solution was that the neutrinos changed type somewhere between emission and detection on Earth. This implies that they have mass because massless particles move at c and don’t experience time; for a particle to oscillate it must experience time, and therefore doesn’t move at (exactly) c.
Asympotically fat explanation: TL;DR 
Keeping it simple, energy is conserved, mass is not necessarily conserved. Only for stationary particles is there a fixed mass / energy equivalence.
Keeping it just as simple but also correct, energy is conserved, and mass is also conserved. There are no exceptions to either.
The mass of the system is conserved. The sum of the masses of the objects in the system is not conserved.
Keeping it simple, but not too simple. Energy is conserved. Mass is conserved too as long as you’re thinking about it the way a physicist thinks about it, but otherwise YMMV.
I guess what I’m asking is the following. Does the statement mass is conserved mean anything above and beyond the statement “Energy and linear momentum are both conserved”?
Forgetting angular momentum and the energy associated with rotation for the moment, are there three conservation laws: energy, mass, momentum (as there are in a classical Newtonian system I think) or are there only two conservation laws.
I found this article on mass and energy by a theoretical physicist very helpful.
I guess I actually mean four conservation laws since momentum is a vector and each component is conserved separately so that the four components of the energy-momentum four vector are separately conserved but there is no separate (from that) conservation of mass.