Energy Conservation: Does Violating it explain Dark Energy? (Patreon)

 [This is a transcript with links to references.]

I got quite a few questions about a paper that supposedly revolutionizes our understanding of the universe by throwing out energy conservation.  The questions came in two varieties. Can you do that, isn’t energy always conserved? And isn’t energy conservation violated anyway? I thought it would be interesting to clear this up because I think the idea isn’t remotely as crazy as it sounds. Let’s have a look.

 Astrophysicists have invented two types of mysterious stuff: dark energy and dark matter.  It’s not just because they like the word “dark”, though maybe there’s that.   It’s because they need the dark stuff to make the predictions of their theory fit with observations. But just what dark energy and dark matter is made of or where it comes from has remained a mystery.

 They need dark energy  ​to make the expansion of the universe speed up and ​they need dark matter to make galaxies rotate fast​er, because that's what observations require. ​The idea that this happens because energy ​just isn’t conserved ​and comes out of nowhere is ​quite appealing. ​If you have extra energy, it sounds plausible enough that you can make the universe blow up or speed up galaxies. The question is, how can this be compatible with Einstein’s theory of general relativity?​Albert is really worried about that part.

Before we can talk about General Relativity, we need to sort out what physicists mean by energy.  It’s not what we mean by energy in every day life. Usually we talk about energy as something we need to do things. Your phone  needs energy to work, your car needs energy  to run, you need energy to follow  what Sabine is saying, and so on.

Well in physics this is more specifically called “free energy”,  that’s the useful part of energy, so to speak, the energy that we can do something with. However, like most YouTube Comments, most energy is not of the useful type. Take for example the air molecules around you.  They have kinetic energy because they’re moving. But you can’t do anything with that. Your phone won’t just magically charge if you hold it into the air. When physicists talk about energy conservation, they mean all that energy,  the useful and the useless one. This total energy is conserved in daily life, to good approximation. Which means, actually, strictly speaking, it’s not conserved.

Yes, sorry, energy really isn’t conserved. Energy can increase or decrease whenever space itself changes in time.

The easiest way to see this is to imagine you have a part of space in which you have quanta of light, those are the photons.  Photons have a wavelength, that tells you the colour of light, and the wavelength also tells you the energy. The longer the wavelength, the lower the energy. The total energy in those photons is their number times their energy.

Now imagine that the box expands.  You still have the same number of photons but now their wavelength is longer, so their energy is lower. So the total energy has gone down. Where did it go?  It didn’t go anywhere, it just isn’t conserved.  This isn’t merely theory, it matches observations. The lack of energy conservation in the expanding universe is why the cosmic microwave background is so cold.

So energy really isn’t conserved if space can stretch and shrink, which is what happens in Einstein’s theory of general relativity.  However, in his theory we have a more complicated type of energy conservation.  In essence it says that if energy isn’t conserved that’s because space changes in time. The change in energy needs to match to the change in space. It’s called the covariant conservation law of the stress energy tensor, in case you want to impress your neighbor. But for the rest of the video, I’ll just call it the generalized energy conservation.

This then brings us back to the opening question,  can we fiddle with this generalized energy conservation to explain dark matter and dark energy. The brief answer is no. But that’s for an interesting reason. It’s because in Einstein’s theory, this generalized energy conservation is automatically fulfilled.  It’s a mathematical identity. It’s always true, so long as you use his theory at all.

What this means in practice is that any attempt to throw out generalized energy conservation  has the consequence that a new contribution appears in the equations that makes up for the mismatch.  And that new contribution, guess what, that can look like dark energy and that can look like dark matter, but it’s nothing new. It’s mathematically the same thing, you just interpret it differently.

And that’s what this new paper is about. Now this is a single authored paper in a so-so journal, so one doesn’t expect much, but it’s actually a fairly reasonable paper for the state of the art in that area.

Look. I’m really trying to be nice okay. Don’t make it harder than it is.

 The author uses this energy non-conservation approach to arrive at specific predictions he says that this leaves some small features in the cosmic microwave background which is what people usually “predict” in this area. The issue is that even if that prediction would turn out to be correct, there are like a hundred  or so other models giving the same prediction.

 Personally I think that one shouldn’t dismiss this idea too quickly, because, you see, the problem with dark matter and dark energy is that we know too little about it. If it came about in a particular way,  for example by violating this generalized energy conservation, then that makes it more specific, so it reduces the ambiguity. This isn’t to say that I think it’s correct, but to me it makes more sense than just cooking up a few hundreds of particle physics models.

Though I’m afraid we still won’t be able to charge our phones from dark energy.