The Light of Creation

How did the Universe create matter and radiation, seemingly in blatant violation of the law pertaining to conservation of energy? How can mass and energy emerge from empty vacuum? What precisely does the conservation law have to say on the matter?

To answer that last question, we need to know whence the conservation law comes. Why does energy obey a conservation law? The answer to that question is a rather straightforward deduction that begins with conservation of linear momentum.

Conservation of linear momentum is easy to deduce. We note that nothing exists outside the Universe (even "outside" does not exist), so the Universe as a whole cannot have any motion. That fact necessitates that all of the motions inside the Universe always and forever add up to a perfect net zero. If the linear momentum of some body changes, then the linear momentum of another body must, at the same time and the same place, change by the same amount in the opposite direction: the two changes cancel each other out. That’s the conservation law, which we also recognize as Newton’s third law of motion.

Deducing conservation of energy is a little trickier. We
know that mass and energy are different forms of the same thing, related to each
other through Einstein’s famous equation, E=mc^{2}. So let’s imagine
bringing a quantity of energy into existence as a particle carrying a certain
mass. The particle comes into existence motionless in our laboratory, so we
believe that we have not created any linear momentum in violation of the
conservation law. Creation of energy from nothing would seem to be a
straightforward matter of calling the particles into existence.

But an observer in a different inertial frame, one in which our laboratory is moving, would disagree. In that observer’s experience our particle has appeared out of nothing bearing an amount of linear momentum equal to its mass multiplied by the velocity at which our laboratory moves through that observer’s frame of reference. That linear momentum has come into being without the requisite equal and oppositely-directed reaction, so the appearance of the particle does actually violate the conservation law. Thus the particle cannot just appear out of nothing. We must infer, then in consequence, that energy can be neither created nor destroyed – it must be conserved.

Suppose, though, that we could bring into existence a quantity of energy manifested in something that has zero linear momentum in all inertial frames. Could we thus bypass the conservation law? It seems reasonable to assert that we could, but what phenomenon will give us zero linear momentum in all inertial frames?

An isotropic burst of light consists of a set of photons all flying away from a point in straight lines. If for each and every photon the burst contains a photon of the same frequency moving in the opposite direction, then the linear momenta of the photons will all cancel out and the burst will have zero net linear momentum in the inertial frame occupied by the object that emitted the burst. We also want the burst to have zero net linear momentum in all other inertial frames, too. A burst of radiation with that property must consist of a photon distribution that appears to be unaffected by the Doppler shift between any two inertial frames.

Every photon has a frequency associated with it: we say that the photon occupies a certain frequency state. When we go from one inertial frame to another, the relative velocity between the frames brings the Doppler shift into play. Photons comprising the light that we saw in the first frame get shifted out of their frequency states and into new frequency states, making the light appear bluer or redder, depending on whether in our second frame we move toward or away from the light’s source. To have a burst of light that appears unchanged by the Doppler shift we must have the photons so distributed among the frequency states that when one photon gets shifted out of a given state another photon gets shifted into that state.

A photon distribution that satisfies that criterion consists of photons evenly distributed among frequency states that form a continuous infinite set, one analogous to the set of the real numbers. In that distribution photons have frequencies from zero to infinity. Such a distribution, if it occurs, can only occur once in the history of the Universe. It comes into existence at or near the boundary of space at or near the instant of creation, it flashes across the Universe, and it ends up on the opposite side of space with its photons in hot pursuit of the boundary.

As the photons cross space, the hottest of them, with extremely small to infinitesimal wavelengths, pass through anything in their paths: they’re just too small to hit anything. The mid-wavelength photons, carrying energies of millions to billions of electron-volts, realize virtual particles out of the quantum vacuum in matter-antimatter pairs. And the softest photons, carrying energies less than one million electron-volts, get caught and trapped in the emerging matter-antimatter plasma, further heating it.

Once that initial burst of radiation passed through any given region of space, the disturbed space began to evolve into the Universe we see today. Matter and antimatter underwent mutual annihilation, throwing more photons into the ever-hotter plasma. For a reason we don’t yet know, the particles of matter outnumbered the particles of antimatter by one billionth of the total, so when the annihilation went to completion there was matter left over, in the form of a hot plasma. Expansion of space thinned the plasma and eventually the trapped light was able to escape, removing radiation pressure from within the plasma, thereby allowing the plasma to manifest the notorious instability of those ionized gases. The plasma gathered itself into vast filaments, like those we see in supernova remnants, such as the Crab Nebula. The matter in those filaments became galaxies, with their collections of stars and other bodies. Thus we got the Universe that we see today.

Meanwhile the infinite light, minus a finite amount of its original energy, continues its flight, flashing across expanding space in endless pursuit of the boundary. As seen from any point in space, it would appear as a thin, isotropic, spherical shell. Because the Universe that we observe lies inside that shell, the light of creation exerts no gravitational effect upon light or matter. Further, for each small part of that shell there exists an equal part moving in the opposite direction, regardless of how any observers are moving, so the light of creation does not generate a gravitonic field that would give matter extra inertia (see "Newton’s Bucket and Einstein’s Ellipsoid" for a description of how a gravitonic field creates inertia). The initial burst of light, having created the Universe, moves on.

In this essay I have tacitly assumed that the initial burst of radiation that created the Universe consisted entirely of photons. It might also have contained neutrinos, which also fly at the speed of light. We won’t know its actual composition until we can deduce how and why it came into being. That’s a topic for another essay.

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