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Einstein showed that energy is matter; for something to exist in a physical sense it must be incarnated as matter. So on the face of it - it seems that the answer should be no.

However what about empty space - it certainly exists. Then there is no matter and hence no energy, and since also there is no matter space cannot be curved so energy can't be stored in the curvature of space.

edit

It’s perhaps worth pointing out that Einstein’s equation with the Cosmological constant shows that empty space has an associated energy.

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    There are a few problems. Most importantly, the first sentence, "Einstein showed that energy is matter," is just plain wrong. Einstein showed that energy has inertia, whereas previously it was thought that only matter has inertia. – David H May 28 '13 at 21:21
  • @DavidH: Whats the difference between matter & inertia? Correct me if I'm wrong here. But it was noticed I think before Einstein that there were two different notions of mass when thought of operationally - inertial & gravitational mass. One is a term in Newton second law, and the other in his law of gravitation. These were experimentally seen to be equivalent. This is what lead Einstein to discover the geometrical theory of gravity via his equivalence principle. In other words it really doesn't matter (pun intended) if one refers to mass as matter or as inertia. – Mozibur Ullah May 28 '13 at 22:01
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    Matter can basically be thought of as "what stuff is made of"; generally it has both mass and volume, and usually it's comprised of atoms. Inertia is the resistance of physical systems to changes in its state of motion. – David H May 28 '13 at 22:06
  • Quantum mechanics presents a problem though. In a process like pair-production/annihilation, matter is not conserved (e.g., #electrons-before =/= #electrons-after). However, energy and momentum will be conserved, and so the system as a whole will have the same inertia afterwards as it did before. – David H May 28 '13 at 22:16
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    Yes, empty spacetime itself does have energy because of the cosmological constant – David H May 28 '13 at 22:47
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You need to explain what you mean by exists and without energy.

There are many cases where the presence of energy is incidental to the existence of "something": take a DVD for example, where your movie "exists" as a series of little holes in the recording layer of the DVD. If you compare the total rest energy of this thing with the rest energy of a blank DVD, you'll find that the difference could go in any direction, including down, depending on the details of the pit-forming process. (So you very easily can have less energy and your movie; existence doesn't take any extra energy in comparison to the default configuration.)

On the other hand, there is thought to be zero point energy even in "empty" space. So as long as you have space to have something, you also have energy (or at least fluctuations therein, which is enough, since energy is always relative).

So, yes or no, depending on how you prefer to look at it.

  • I think the debate with DavidH has settled it. The cosmological constant measure the enrgy density of empty space. Current observations make it positive but small; and planck-scale quantum fluctuations as in virtual particles and possibly topological change go into zero-point energy and so on contribute to the cosmological constant I was thinking physical existance. I can't see how you can imprint a movie at a cost of negative energy!? – Mozibur Ullah May 28 '13 at 22:56
  • @MoziburUllah - We are so awash in energy because we have matter that anything that reduces the amount of matter even a tiny bit is a net win in energy. So if you design a DVD such that e.g. a tiny bit of gas escapes after the hole is burned, your burned DVD has lower energy than your unburned one. Of course, we can't actually take that tiny bit of gas and use it in a fusion reactor to power the whole system, but in principle we could. (Matter has a stupid amount of energy in it. Two ounces is equivalent to over a 1 megaton bomb, enough to obliterate a large city.) – Rex Kerr May 28 '13 at 23:42
  • @Kerr: Ok, I see. Interesting point of view. – Mozibur Ullah May 28 '13 at 23:56
  • @RexKerr, your claim "existence doesn't take any extra energy in comparison to the default configuration" with the DVD example is probably wrong. To be able to say that a "movie" exists, it should be distinguisable from "random" holes (noise), an "orderly" arrangement of holes, some information you load on the system, which must cost "extra energy"! This is a law of termodynamics. It should be compliant with E=mc2 equivalance of small gass as well. Situation resembles Maxwell's demon. I think your example needs revision taking into account information theory and law of thermodynamics as well. – mami May 29 '13 at 0:54
  • @mami - The burned DVD, we are supposing necessarily has less mass--that's how the burning process works. (You can imagine physically burning holes if you want.) You're almost certainly increasing entropy also at the molecular level (decreasing energy). Even if the burned pattern has lower entropy, the tiniest bit of matter loss utterly overwhelms that. Of course burning the DVD adds entropy to the universe, but that goes back to the question of what you mean by "exists". – Rex Kerr May 29 '13 at 1:12
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However what about empty space - it certainly exists. Then there is no matter and hence no energy, and since also there is no matter space cannot be curved so energy can't be stored in the curvature of space.

I think this is wrong, I am not expert but I'm pretty sure "empty space" does have energy.

The Casimir Effect. http://en.wikipedia.org/wiki/Casimir_effect

Although the Casimir effect can be expressed in terms of virtual particles interacting with the objects, it is best described and more easily calculated in terms of the zero-point energy of a quantized field in the intervening space between the objects.

As the other other answer says

Zero-Point Energy. http://en.wikipedia.org/wiki/Zero-point_energy

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From a scientific standpoint the answer is clearly no. But there are caveats. The whole universe would still exist if it contained only a single electron. But it may not exist (as we know it), if it contained only photons, since photons don't interact with time.

There is the question of memes. What is an idea? Does it require energy to exist? If I write down a recipe for Pizza, and you find the recipe ten years later, what is it that passes from the page into your oven?

Personally I think that even with memes, which are potentially massless, they require energy. Since a meme requires an 'agent' (a consciousness). Just as virus's require a host body.

Again, this is only from a realist, scientific perspective.

  • Do large undiscovered prime numbers exist? – elliot svensson Jan 22 at 17:07
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    @elliotsvensson not without an 'agent' no. If you point out somewhere outside of human consciousness that anything is "numerated" I'll reconsider my answer. – Richard Jan 22 at 17:11
  • Funny... that's where mathematical realism and scientific realism diverge, I guess. – elliot svensson Jan 22 at 17:45
  • Apparently data does have mass, and the internet weighs about as much as an egg. shop.coolmaterial.com/products/the-scale-of-things-book – christo183 Jan 24 at 5:38
  • @christo183 I wonder if this notion that information has mass, has ever been proven experimentally? – Richard Jan 24 at 10:11

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