### When energy isn’t conserved – a physics conundrum

#### It’s two years this week since my Mum passed away. She was hugely interested in the why of the universe and usually asked me if she wanted something about it explained. It’s a while since I’ve done a science post, so I thought I’d run one this week. It’s about why our law of energy conservation doesn’t work out there in the big black of the universe.

To us on everyday Earth it’s pretty much axiomatic. If you heat up a pot of water to boiling on a stove top, then turn off the heat and wait a while, it’ll cool down. But has the energy the water contained been lost? Of course not. It’s simply been transferred to the atmosphere, slightly raising the temperature of your kitchen.

That’s why restaurant kitchens usually don’t need heating in the winter.

It demonstrates one of the fundamental axioms of physics – which is that energy can’t be destroyed, merely transferred from one form to another. Thanks to the Second Law of Thermodynamics, we also know that the default end-game is that the energy is diffused among increasing numbers of particles, which end up moving more and more slowly – but the total net energy of the system remains the same.

The key thing here is that it’s a time thing. The total quantity of energy doesn’t change over time. The form of that energy may change, but the quantity doesn’t.

Another fundamental axiom of physics is that things are always going to work the same, always and everywhere – the principle of invariance.

Now let’s scale that up to the universe. The reason we know the universe is expanding is due to ‘cosmological red-shift’. What this means is that wavelengths of light arriving from distant parts of the universe are stretched out – made longer – which moves them towards the lower (red) end of the spectrum.

We also know that wavelength determines the amount of energy contained in that light. So, by stretching the electromagnetic wavelengths out – reddening them – energy is being lost.

And here’s the kicker. Conservation of energy says we can’t actually lose energy. It has to go somewhere. So where does it go at this scale? The answer is – nowhere. It simply vanishes.

This discovery came pretty much at the same time as the discovery of red-shift at cosmological scale. Cosmological red-shift was identified in work done between 1912 and the early 1920s by Vesto Slipher and Edwin Hubble, among others. The implication of it was clear in Einstein’s theory of General Relativity of 1915, which made clear that red-shift was due to an expanding universe. What that implied in energy terms came out of the work of Emmy Noether, a mathematician working in the same period on problems of time symmetry.

The upshot is that yes, energy is conserved – providing it is within the same inertial reference frame. Einstein showed that this frame is defined by space-time and by observer position. Because your kitchen and you are essentially the one frame, it’s conserved. And that’s true of every real-world experience. (Yah – no perpetual motion machines for us…damn…)

But take that out into the universe, and you have a different picture. Einstein made clear that space and time are aspects of the one thing – a four-dimensional ‘fabric’ of reality; and they’re not fixed. He showed how mass/energy can distort space-time, and how gravity is a second-order product of that distortion. And over distances that span our expanding universe, space-time itself is stretching. That provokes other issues – in this case, the absolute loss of energy as radiation propagates across cosmological distances, as seen from any given reference frame. (That said, we can’t talk about the net energy of the universe – that is meaningless, because it’s all relative, among other things).

I’ve been explaining all of this in the deterministic terms of Einstein, but the principle has also been shown to work in quantum terms, so it’s definitely a thing.

Needless to say, if the universe were contracting, everything would be cosmologically blue-shifted, which means energy would get added, apparently out of nowhere. Yup – something for nothing, sort of. In a cosmic sense. This is NOT quantum vacuum-energy, but a consequence of Einstein’s determinist theory.

Don’t forget to check out my book Explaining Our Weird Universe – which looks at Einstein, quantum physics and more – available right now on Kindle.