Does the conservation law prove that energy is eternal?

kote

Of course there is a strong basis for the assumption, which I mentioned. I don't agree that laws can be tested for truth or that they can be verified. Those ideas fly in the face of Popper's generally accepted notion of falsifiability. In science we do falsification, not verification. It seems that you just said that though, so I'm not sure there's any real disagreement.

Chalnoth

Er, what? One of the major goals of modern high-energy experimental physics is to show that certain symmetries (from which conservation laws can be derived) are only approximations to the true behavior. That the left-right symmetry is broken was one of the major discoveries that lead to the nature of the weak nuclear force, for instance.

kote

It's still assumed that there is some better, underlying, symmetric explanation. E=mc^2 didn't break symmetry, it expanded it. We are always assuming an underlying symmetry - we can't describe causation (natural law) without it.

Chalnoth

That's only because symmetries have proven an exceedingly useful way of thinking about the behavior of the universe. If, in time, some other way of thinking about the universe turns out to be a more useful way of interpreting the evidence, then we will drop all this talk about symmetries and move onto that instead.

Just because we don't yet know how to describe the behavior of the universe without symmetries doesn't mean that we assume them by fiat. It just means that we haven't yet discovered a better theory of the behavior of the universe without them.

Now, given the incredible usefulness of symmetries, it is my suspicion that there exist some very fundamental symmetries to our universe. But there's no reason for me to hold fast to that belief against evidence, were evidence to start to appear in some other direction.

kote

The thing is, we define objective reality through symmetries. You wouldn't know evidence for asymmetrical laws of nature if you saw it... from Wigner, “if the correlations between events changed from day to day, and would be different for different points of space, it would be impossible to discover them.” Also:

It is widely agreed that there is a close connection between symmetry and objectivity, the starting point once again being provided by spacetime symmetries: the laws by means of which we describe the evolution of physical systems have an objective validity because they are the same for all observers. The old and natural idea that what is objective should not depend upon the particular perspective under which it is taken into consideration is thus reformulated in the following group-theoretical terms: what is objective is what is invariant with respect to the transformation group of reference frames, or, quoting Hermann Weyl (1952, p. 132), “objectivity means invariance with respect to the group of automorphisms [of space-time]”.[22] Debs and Redhead (2007) label as “invariantism” the view that “invariance under a specified group of automorphisms is both a necessary and sufficient condition for objectivity” (p. 60). They point out (p. 73, and see also p. 66) that there is a natural connection between “invariantism” and structural realism.

http://plato.stanford.edu/entries/symmetry-breaking/#5

If physics is in the business of describing objective reality, then it must assume causal symmetry. There's no other option.

apeiron

Agreed that symmetry should be taken as the most basic concept - though locality and atomism have also been taken as the "fundamental" guiding image in earlier physics.

But then you have to ask what is "perfect symmetry"? Or the most generalised possible notion of symmetry? A rotation or a translation or a gauge symmetry are all just local examples of a more universal something.

Even "closed" symmetries are a particular family of symmetries.

Chalnoth

That doesn't strike me so much as an assumption as it is just a statement that it's always going to be possible to describe the world in terms of some symmetries. One can show, for instance, that it is possible to take purely random, time-variant laws of nature, and show that due to the ambiguity of the time coordinate, there exists a time-invariant way of describing the system:

http://arxiv.org/abs/0708.2743

I tend to expect that in a sense, then, the existence of some symmetries is an inevitability, just based upon how we approach understanding the world.

That said, physical theories don't just rest at the most basic of symmetries like time invariance. Hypothetical high-energy laws of physics typically consider all of physical law as stemming from some fundamental construct (particles, strings, what have you) that obey some very specific symmetries.

I don't think the most basic of symmetries are really an assumption so much as order we impose on the world by the way in which we describe it.

apeiron

Again, it is hard to talk about symmetries and asymmetries unless you have really thought through the most general possible definitions.

For example, Chalnoth mentioned chiral symmetry-breaking. That would be an "asymmetry" across a single scale. Left and right, positive and negative - each direction is the same size still, even if only one route is taken.

But a more general asymmetry would be a breaking of symmetry over all scales. A fractal or scalefree breaking.

The causality of the universe, for example, is broken in this asymmetric fashion - the causal light cone story. And it is why time on the global scale looks to have just a single progressive direction, but on a local scale - that of individual events - appears to be symmetrically bi-directional.

apeiron

Or alternatively, symmetry-breaking - the thermodynamic-like gradient from max symmetry to max asymmetry - could be actually the way worlds emerge via self-organisation.

The human brain does indeed dichotomise to impose order on experience. It's neural architecture is set up to break the chaos of impressions into figure and ground, focus and fringe, event and context, what and where, etc.

But this would be no coincidence. Brains have to employ self-organisation too. The same dynamics are at work for any "system", whether it be cosmological or neurological. So symmetry, symmetry-breaking, and asymmetry are deep concepts because they get at the deep causality of SO systems.