The Nature of Energy

This posting is a little more advanced than usual. Read on at your own discretion...

I was reading a number of articles on general relativity recently, and I started thinking about exactly what energy is and perhaps more important - how is it actually defined?

The definition I have tended to favour is that energy is the variation in the action due to changes in the g_00 component of the spacetime metric. This definition works very well in almost every situation. It also means that the Einstein equations of general relativity are actually a statement that the total energy (and momentum) - at any point in spacetime- must vanish.

But then I started reading this papers about the energy localization hypothesis, in which it is claimed that gravity does NOT carry energy! And they have several published examples supporting the hypothesis. But that means that my definition cannot be accurate, because it includes gravitational energy through the Einstein tensor.

And suppose that you have two pendulae in space, one swinging and one at rest. The swinging one has energy, but it is also applying a gravitational force on the second one. The second one will start swinging along with the first, and so energy has been transported by the gravity.

So now I am wondering if the energy referred to in these papers in really energy, or is this hypothesis actually stating that gravitational energy cannot curve spacetime any further. Does it actually mean that the energy-momentum tensor in Einstein's equations does not include gravitational energy, but that gravity still has energy?. If anyone knows the answer to this, please post a rely below...

Free Will?

This posting, which is the result of a class discussion on free will, is philosophical with influences from modern physics. Those readers who prefer pure science are advised to skip this posting.

Does free will exist? It is a very important question that is overlooked in the serious sciences. Biologists and chemists tend to avoid the question, but the underlying principles of those sciences - as well as classical physics - suggest the answer is no. If an observer were able to measure the exact location of every neuron and every cell, then the known scientific theories could be used to predict every future thought by the observed individual. That means there can be no free will!

The theory of relativity appears to make the situation even worse. Since time is nothing more than an additional dimension, the entire future of every person - including every thought - already exists and we simply haven't experienced it yet. That means that your course is pre-determined, and you can never change it! Another strike against free will!

That leaves only one chance - quantum mechanics. The theory that every physicist uses but no one truly understands. Quantum mechanics contradicts relativity and classical physics, with the correct answers requiring that the future is random, and a full prediction of a complicated system's future is impossible. So how can both relativity and quantum mechanics be correct? The answer is not completely known - the best that can be done is to rely on a hybrid of the two, which doesn't necessarily properly include the principles of either.

Perhaps free will is a large-scale manifestation of countless quantum fluctuations, which together produce the random thought patterns that the brain reshapes into free will. Quantum mechanics already introduces the idea of consciousness, with the famous claim of a cat who is both alive and dead until someone looks at it. (Which leads to another unresolved question - can't the cat observe himself? He knows if he is alive or dead. And if the observer is sealed in a windowless lab, does the life-or-death decision occur when the observer looks at the cat or when her boss opens the lab door to observe which outcome the observer observed?).

Can quantum mechanics exist without free will, or does it simply require a complex mind but not necessarily a free will? Is free will merely a result of quantum fluctuations? Does free will exist, or is it an illusion created by our inability to view the time-dimension?

If you have read this far without going insane, we invite you to leave your own thoughts (predetermined or not)...