I’m not so sure, for instance, according to the Wikipedia article on typing monkeys, the probability of a monkey typing Hamlet is around 1 in 10^360,000. Or essentially 0, in terms of any numbers that exist in reality in the universe. However, the last item on linked chart refers to “10^(10^(10^(10^(10^(1.1))))) years”, a number so unfathomly greater than 10^360,000, I think in that circumstance, it should be deemed a certainty.
I really like that last 1.1 in there.
I seriously doubt the calculation could be that precise given some of the assumptions that have to made to do the calculation.
Oh, and the poster that was wondering where energy “goes”. Take a finite volume of space. It obviously has a finite amount of energy in it. Now, assume the universe is expanding. That space will expand with the universe. If the universe can expand infinitely, you are going to have a finite amount of energy spread over an ever increasing volume. Finite over Infinite is basically zero. Even finite over very damn large results in pretty damn small.
Oh, and this whole topic depresses the hell out of me.
No, it’s worse than that. Your expanding volume of space will contain the same number of photons on average at any given time, but the photons at later times will be more redshifted. So you actually have less energy in that volume.
Yep, but I wanted to keep it simple.
Now, YOUR post does bring up again the question of where does the energy go?
To which I can only reiterate that conservation of energy is a local quantity. If you look at a box of fixed size, you don’t have any problem: You see that the energy in the box is decreasing, and you can see where it’s going-- It’s going outside the box through the walls. If the Universe were a constant finite size, then this would imply that the energy content of the Universe as a whole is conserved. But it’s not, so it doesn’t.
Hm, I’m trying to visualize this “Local but not global” conservation of energy, and having difficulty grasping what’s being pointed out. Could you give a simple mathematical example of this phenomenon in action?
Okay.
Lets take one photon in one finite but expanding box.
The box expands. The photon gets red shifted and is now less energetic.
Where did the energy go?
Analogous situation that might help: Consider a box with actual physical walls, and with something outside (a piston, say). As the piston expands, the contents cool off, and lose energy. Here, you can answer the question of “where the energy goes” by looking at the boundary, and seeing that the piston did work on something outside. But the Universe as a whole has no boundary and no outside.
I have heard it posited that the total amount of energy in the Universe is precisely 0.
All we are observing is the local differentials.
I bet that Chronos or some other big-domed person will know if I heard incorrectly.
Okay I can see that if inside the box has a higher pressure and is allowed to expand, work has been done outside the box and thats where the energy went. But is the same true when you expand the piston on purpose even though the pressure inside doesnt “want” to? Its been forever since I’ve cracked a thermo book.
But that implies the “photon” pressure inside the box is doing work on the “outside”. That appears to me to be a bit different than space expanding for whatever reason it does and redshifting the photon in the process.
I’m still having trouble seeing a counterexample to “Local conservation implies global conservation”. Then again, I don’t know anything. But suppose, for example, I wanted to give a short history of the universe by describing, for each moment of time, how much energy is in each region, and how that energy flows around. Could a simple example along this line be given illustrating a change in the global amount of energy while maintaining the property of local conservation of energy?
Hm, I suppose it’s not so hard, although I don’t really know how anything is being formalized. But if energy were distributed throughout all of space with constant non-zero density and zero flux, while the open universe was expanding in volume, then I suppose that would have local conservation of energy but not global conservation of energy. So I guess the former really doesn’t entail the latter.
Not that I think that’s the example under discussion, but that’s the sort of thing I was stuck on.
“This is the way the world ends.
This is the way the world ends.
This is the way the world ends,
Not with a bang but a whimper.”
– T.S. Eliot
Sure, that just means that there are other things doing work on your piston, too. But expanding a cylinder full of gas is easier than expanding an evacuated cylinder, because the gas inside is helping you.
Are your regions fixed in size, or are they expanding proportionately to the universe?
You tell me; I don’t know how to properly interpret the term “local conservation”, but you do. When one says the energy in a region can only change in response to flux across its boundary, does one mean a region which stays fixed in size or one which expands proportionately to the universe? (I imagine if they stay fixed in size, you can have local conservation without global conservation along the lines of my last post, and if they don’t, you can’t (since you can just rescale everything as if nothing ever changes size, and then apply the divergence theorem as usual), is that right?)
The question, “Where does the energy go?” is a red herring. The energy of the “Big Bang” echoes through the ages and gets more diffuse as the universe expands, but it is all still here. The “Heat Death” of the universe comes about when all matter is at the same temperature! Useful work can only be done when there is a potential difference (voltage, height in a gravitational field, thermal gradient, and so on…)
When all energy has been absorbed and re-emitted ad infinitum, the universe will have reached maximum entropy, and there will be no differences to exploit for useful work. The temperature could be in the millions of degrees F (but more likely near absolute zero), yet, for practical purposes, it may not perform any work.
No, DHMO, while you are correct about work, you are not right about the red herring. Picture an expanding universe with one photon. As the universe expands, the photon redshifts. The energy of a photon is proportional to its frequency, so there is less energy in that universe. Yeah, the energy density has dropped due to the increased volume of the universe, but Chronos is entirely correct that the universe is losing energy as it expands. It doesn’t go anywhere, because there is nowhere for it to go to.
That’s correct, local conservation assumes regions of constant size. If the regions are allowed to change in size, then you could just call the Universe as a whole one region.
Heh, good point. Thanks, that clears it up for me.
The best I can offer for the difference between local energy and global energy is to consider a universe consisting of a nonspinning black hole, and lots of empty space. There is no global definition of time in this universe, for reasons akin to the difficulties of mapping a globe onto a plane. (I almost said mapping onto a map!) Far from the black hole, there is a coordinate that you can call time, and a coordinate that you call the radius. When you cross the event horizon, the “time” coordinate becomes like a radius, and the “radial” coordinate becomes like a time coordinate.
What does time have to do with energy? Both QM and relativity say everything. A relativistic four momentum has a time component, which is the energy, and 3 spatial components, which are position. To compute the total energy of the system, you have to integrate over the time component of something. (In reality, there is a tensor relationship in there.) Without a global time there is no way to integrate over the whole universe. In effect, you can’t compute a bunch of local energies and add them all together to get a global energy, because there is no global surface to add them over.
You can define an “energy at infinity”, in this case, though. IIRC, this is conserved - at infinity. Whether or not our universe is infinite, you can’t get infinitely far from matter and energy, so we don’t even have that.