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If gravity is a fundamental force which bends spacetime and dark energy is energy which stretches spacetime, what is the difference between the terms force and energy?

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This is all just terminology.

'Force' is a term from Classical mechanics really.

'Fundamental Force' is a term for any one of the set of four theories, gravity, and the three Standard Model interactions, Strong nuclear, weak nuclear and electromagnetic.

The strong nuclear interactions (plural) for example could be said to be eight 'forces'. It's just that they're all quite the same!

So usually when we move to Quantum Field Theory we drop this word for 'interaction', since this gives less confusion (or the sort that you are suffering!). Then three of those fundamental forces are collections of interactions that share lots of properties (namely, the gauge group of the force/ interaction).

Then as for gravitation, there will be some debate about this.

From a mathematical point of view, in my humble opinion (and the opinion of many others) it is not correct to call it a force, once you realise the Einstein gravity of general relativity.

Rather, the motion of bodies in spacetime, orbits etc., is a consequence of the fact that given general covariance we must move along geodesics which are curved (since we live on a Lorentzian manifold). I'm afraid this is hard to give a convincing argument in non-technical terms, without going on for pages...

Then, as regards the dark energy, some people indeed think that it is an interaction (force), and they have a theory called Quintessence. This theory postulates some extra scalar field $\phi$ which causes extra interactions between the matter fields of our universe. This extra interaction could be called a force, just as the electromagnetic interaction is. Note that Quintessence is just one of many competing theories of Dark Energy.

We usually call in Dark Energy (or Cosmological Constant, $\Lambda$) since that is the way that we have infered it's existance. Namely, that there must be some extra term in the Einstein equations which are causing the accelerting cosmic expansion that we measure from far away galaxy clusters.

As a finally possibly techincal definition, you should think of energy as the canonically conjugate generalised momentum to the zero component of a generalised coordinate four-vector.

That is, $\vec{p}$ to $\vec{x}$ as $E$ is to $t$, sort of...

Does this help?

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  • $\begingroup$ yes this is helpful. I don't think that gravity qualifies as a force that much, it is quite dissimilar from the other 3 fundamental forces. $\endgroup$ – stanley dodds Apr 11 '14 at 16:52
  • $\begingroup$ @Stanletdoods I just found a similar question and thought of your question. Here Marek talks a little about the use of the word 'force' for gravity, and the dark energy. $\endgroup$ – Flint72 Apr 13 '14 at 22:29

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