Would it then be theoretically possible to create a perpetual motion machine that used energy derived from the expansion?
This is a very interesting question. AFAIK, there is no deep theoretical principle that forbids it. The fact is that in GR there is no such thing as global energy conservation. Full stop. Anything goes. As an example, suppose you were to attach a string to a distant galaxy. As the galaxy moves away from you on earth, it pulls on the string. You can let the string drive a piston, extracting energy indefinitely. There is one catch in this example: you would need an infinitely long string. I figure this is just a detail, but who knows, it is possible all such ideas are plagued by some seemingly trivial detail.
There are also some other interesting limitations to consider. As two objects move away from each other, they eventually become causally disconnected – any information or light coming from one object can never reach the other. A simple way of saying this is that two distant galaxies can easily be moving away from one another faster than the speed of light (if you only ever learned SR this may sound wrong, but it is not, it is standard GR). In our above example, this would imply that the string would break.
Another issue: the fact that light coming from distant galaxies is red shifted. This is an example of where even though more energy is technically being added to the universe, it is becoming less useful. This is related to the last point. Another way of saying this is that when (as per above) galaxies become causally disconnected, they are effectively their own separate universes, since they cannot exchange information with any other. So on a practical level, the amount of useful energy available to someone locally may in fact be decreasing.
It isn’t actually too difficult to understand why energy conserved is only conserved locally in general relativity.
In special relativity as in Newtonian kinematics energy is only conserved in inertial frames. There is no real sense in which it can said to be conserved in non-inertial frames. But that’s fine because global inertial frames always exist and what’s more they’re usually easy to work with so they’re given primacy over non-inertial frames.
In general relativity a local inertial frame will always exist, but in general global ones will not. It’s hard enough to even define energy over a spatially extended area in general relativity let alone define it so that it is conserved. sometimes properties specific to certain spacetiumes such as staticity and asympotic flatness can be taken advanatge of in order to get a nice defintion of energy that is conserved. In general though there is no meaningful way that energy is conserved in general relativity beyond the local. I’ll point out local in this sense doesn’t mean an area of any size, it means an area of vanishing volume.
No way is known of doing it. If you look at your long string example in detail, you’ll end up finding that the gravitational field of the tension in the string eventually throws everything off. If there is a way, it’s probably some weird quantum mechanical process which extracts energy directly from whatever it is that makes up the dark energy. But even if we had any clue how to do that, I wouldn’t recommend trying it, since it could run the risk of knocking the vacuum out of a local minimum and creating a chain reaction that could destroy the Universe as we know it.
Thanks for all the answers everybody. I wasn’t aware that the energy in the universe was increasing so that’s probably a sign for me to do some more reading on cosmology. My erroneous ideas on the subject come for senior high school, but I guess our teacher didn’t want to confuse us too much with all that relativity meant, better to just explain a closed system since it’s serviceable in most situations. So, I guess that the energy transfer would balance out possibly disastruously so that is that.
As a continuation, I don’t know if it is a silly question, but what I tried to blather about energy’s or matter’s uniqueness is something like this.
Let’s think that there is a closed system(just to keep things simple, tell me if it matters in this contexts). In this closed space we find ten quarks and nothing else(also to keep single, these quarks are just specks of energy and are at the moment separate from any hadrons or othe bigger partcles). These Quarks are named Q0 to Q9. Now, at point X in time all the quarks are in positions around in the space described and with time they change places, but do not change in other respects. Then it happens that a wormhole inexplicably appears at pont Y in time and Q0 is transferred back to point X in time and Q9 comes to Y, keeping the energy constant. Now, does it mean anything or matter at all that there are arguably two Q0s at point X and two Q9s at point? Are the Quarks the same or does everything change merely with the passage of time and locations in space? Or would this sort of time-twin cause problems not associated with conservation of energy?
I’m sorry it’s drifting from the original question, but I thought that the conservation thingy law was relevant? I’m sorry if it seems like a silly question, I’m just interested whether theoretical physics considers this relevant in any way.
Zamander – your example isn’t very realistic, but that’s OK, I won’t nitpick the details.
Your question ultimately seems to be, is it OK for this to happen:
{q0,q1,q2,q3,q4,q5,q6,q7,q8,q9} --> {q0,q0,q1,q2,q3,q4,q5,q6,q7,q8}
The answer is yes, as long as the energy remains the same, and as long as other conserved quantities remain the same (the overall electric charge, momentum, etc). The number of quarks is not even necessarily conserved. Depending on what you start with, this may be possible:
{q0,q1,q2,q3,q4,q5,q6,q7,q8,q9} --> {q0,q1,photons}
Another aspect of your question: yes, if you have multiple copies of any type of particle, they are completely indistinguishable. So if, in your above example, the type of quark q0 is the same as q9, then the set of quarks you started with is the same set you ended with, even though you added a q0 and removed a q9.
Wait, you mean there’s a project so awesome it could conceivably destroy the universe and we’re not working on it, because?
Awesome aside, assuming some theoretical way, isn’t space full of things more energetic and intense than we could ever hope to do?
I won’t pretend to be an expert in vacuum states, but if there is a lower energy state than things like baryonic matter, wouldn’t there likely been natural events to push it over the cliff?
I remember when they were gonna activate the LHC a bunch of people went nuts over “a non-zero chance of micro-singularities”. Despite the fact earth gets pummeled by particles much more energetic than the LHC could ever produce. The earth has been around for billions of years so baring extremely good luck…
I guess it’s pointless to speculate on hypothetical undiscovered physics.