Nondeterministic Universe, posible?

[gmalivuk]

Then they are no longer part of the same universe as us. If there is no way to get any information about them or have an interaction with them, then that means it doesn't exist. If the light from other galaxies ceased to reach us, then we would have no basis for conjecture about their existence other than their past interactions with us. Those galaxies would have vanished from our universe at that time, and they would inhabit a completely separate universe with a shared past. From the viewpoint of all of time, they are still part of the same universe, but to take any single reference time after we started separating beyond the speed of light, they are in separate universes.

So you're positing a huge violation of mass/energy conservation, whereby entire galaxies can cease to exist. Also, what about an object in between that can still observe both our galaxy and the distant one? It's a strange definition of "universe" that is intransitive. We are in the same universe as A, which is in the same universe as B, but we aren't in the same universe as B?

[Technical Ben]

Does that have any problematic implications in MWI too? I mean, if there is a small amount of interaction between "universes", is this not a whole can o-worms?!
If there is no interaction, then is it not an unprovable theory? So it seems like a problem to think along the lines of either version of MWI.

Oh, that seems off topic now I've typed it. What has the detectability of other parts of the universe got to do with deterministic systems again?

[gmalivuk]

Does that have any problematic implications in MWI too? I mean, if there is a small amount of interaction between "universes", is this not a whole can o-worms?!

No, it has nothing whatsoever to do with MWI, because worlds in MWI aren't the same things as universes in Danny Uncanny's formulation.

[Danny Uncanny7]

So you're positing a huge violation of mass/energy conservation, whereby entire galaxies can cease to exist. Also, what about an object in between that can still observe both our galaxy and the distant one? It's a strange definition of "universe" that is intransitive. We are in the same universe as A, which is in the same universe as B, but we aren't in the same universe as B?

I just defined the universe in a logical way. If a galaxy ceases to exist, it is the same calibre of problem regardless of the definition of the universe. If expansion will cause things to eventually expand faster than the speed of light, then that might give a mechanism for objects to cease to exist. It has all of the same implications.

And as for things inbetween universes, that is by definition impossible. First, in the abstract sense, because if we interact with something, and that something interacted with something else first, then we have indirectly interacted with that something else, which is the only premise that I put forward for the definition of existence in the universe. So that something else is in our universe by my definition. Secondly, for our specific case, the speed of light is the fastest that any information or interaction can travel. If we see an intermediate object, it cannot have been affected by anything that we cannot see (discounting occlusion) because that interaction would have arrived at the speed of light and we would have also received it at the same time or earlier than we saw its effect on the intermediate object.

[Technical Ben]

How does being far away == cease to exist? For example, from my point of view, I could conclude that quakes don't exist. I've never observed one right? So, just because the universe (parts of that is) are far away, why do they cease to exist?

Calling them separate or no longer detectable is one thing, but non-existent?

[Danny Uncanny7]

I don't think anyone suggested that far away things don't exist. I said that things with no effect on us (direct or indirect) don't exist. It defines things in a relative manner rather than an absolute manner, and I think it is clear that existence is relative. If you existed in an alternate reality, your measure of existence would be for that reality, not this one. If you are in the future or the past, your measure of existence is tied to that point in time. This is a pretty simple definition in my mind of the entire universe, because all of it affects every other bit of it. But apparently it's not very well received.

For the earth quake analogy. Even though you haven't observed earthquakes, you have been indirectly affected by them. You get news reports from the location. You may have indirect affects on your weather. You are affected by the graviational (and other forces) pull of every atom of matter that moved even though you might not consciously register it. And their are infinitely more pathways connecting that earthquake to you. That earthquake was most certainly a part of your universe. Now if there was an imaginary earthquake in an imaginary world that doesn't have any effect on you, then that earthquake would not exist.

[WarDaft]

And as for things inbetween universes, that is by definition impossible. First, in the abstract sense, because if we interact with something, and that something interacted with something else first, then we have indirectly interacted with that something else, which is the only premise that I put forward for the definition of existence in the universe. So that something else is in our universe by my definition. Secondly, for our specific case, the speed of light is the fastest that any information or interaction can travel. If we see an intermediate object, it cannot have been affected by anything that we cannot see (discounting occlusion) because that interaction would have arrived at the speed of light and we would have also received it at the same time or earlier than we saw its effect on the intermediate object.

Except by your definition of universe, it most definitely is possible. Consider a universe where space doubles in size over a year. Then arrange 1000 objects evenly spaced on a line 3 lightyears long. Each object is then a mere light day from the next, and it will 8 or so years before they are outside each other's horizons, each can clearly interact with those to either side of it fairly quite easily in the first few years. But one end of the chain, by your definition, is in a different universe from the other. So exactly which of these objects exist? Actually we can make things even worse for your definition. Arrange a ring of 10,000 objects 1/10th of a lightyear across. At the start, any object can clearly interact with any other, as space expands however objects on the far side drop outside our horizon, but nearby objects remain in our zone of interaction. Now there is no privileged 'end' of the chain, every item in our ring is equally valid - under your definition - of claiming that the rest of the ring no longer exists because it is outside 'the universe'.

And yes, space tends to expand expontially, or close to it - the rate of expansion is proportional to the distance, so if an object is X distant at time T, there is a time T+K where it is 2X distant, T+2k where it is 4X distant, T+3K where it is 8X distant, and so on (roughly, the Hubble constant is slowly decreasing I think? So it's slightly longer each time, but still close enough to exponential). In this model, once an object is far enough away so that the distance between you is increasing at greater than c, the distance between you and the photons it emits will only continue to increase. The photon travels 1 LY towards you, but the whole system is 3 LY further away, and since it's further away it moves away even faster and the next LY the photon travels, the whole system moves even further away it did for the first LY.

[gmalivuk]

I just defined the universe in a logical way. If a galaxy ceases to exist, it is the same calibre of problem regardless of the definition of the universe.

But that's my point: under any reasonable definition, the matter in a galaxy *can't* cease to exist in a given universe, while under yours, it can.

And as for things inbetween universes, that is by definition impossible. First, in the abstract sense, because if we interact with something, and that something interacted with something else first, then we have indirectly interacted with that something else, which is the only premise that I put forward for the definition of existence in the universe.

No, you're talking about events now, while I'm talking about objects as they persist through time. There are things whose light has already reached the Andromeda galaxy, but won't reach us for a couple million years yet. Are those things in our universe, even though they have never interacted with us directly or indirectly?

[Danny Uncanny7]

You guys are all thinking of time as some fixed absolute. You are trying to fit the universe into an objective reference frame of knowledge while still keeping all of the relative aspects of time and space. Time is relative to the observer. If you want to consider a reference throughout all of time (or without time), then all those things which have interacted with us in the past and will interact with us in the future are a part of our universe. I said this right at the start. But if you want a time dependent reference, then you must consider that time and space are linked by the speed of light. Objects and events are linked. Right now would you say that the future exists? Say that defying all known laws of physics, a new planet pops into our solar system tomorrow. Does that planet exist today? No, it exists tomorrow. Say that the sun disappeared yesterday. It vanished from the sky and ceased to have any interaction or effect on us. Does the sun still exist? We all agree that it DID exist, but does it exist today?

For WarDafts scenario, assuming that at some point all of these objects sprang into existence from nothing, and space was expanding. What would happen is that at time zero, you see nothing, because there was nothing there before you existed. And then every day, you see a new object pop into existence as its light reaches you. And because space is expanding somehow, distances are growing larger and everything is accelerating away from you until it is receding faster than the speed of light. But that means that the light in transit also got stretched out. You see that object slow down more and more until it recedes at the speed of light and time freezes and the light gets red shifted off the bottom of the spectrum (approaching infinite wavelength). The future of that object is now outside of the universe it can't affect you. The object hasn't actually left, because it will always be there frozen in time, but you will never find out what happens to it. WarDafts suggests that future object can affect your nearest neighbour which is still receding below the speed of light and that neighbour interacts with you, apparently a contradiction.

But the nearest neighbour is also moving away. So you are seeing its time slow down also. If the expansion rate is constant, it will also appear to freeze in time before you see any of its interaction with the far object beyond the time that that far object disappeared. If the furthest object had shot a laser death ray at your neighbour after it stopped interacting with you, you would never see the effects of that death ray, because your neighbour would appear to freeze in time before it got hit. If your neighbour stopped moving away from you, then it would never get hit by the laser because the distance between it and the laser would be growing at faster than the speed of light.

But that's my point: under any reasonable definition, the matter in a galaxy *can't* cease to exist in a given universe, while under yours, it can.

All of the scenarios described which caused the galaxy to disappear under my definition would have the EXACT same result under any other definition. It is the scenarios which are physically impossible, not the definition.

No, you're talking about events now, while I'm talking about objects as they persist through time. There are things whose light has already reached the Andromeda galaxy, but won't reach us for a couple million years yet. Are those things in our universe, even though they have never interacted with us directly or indirectly?

You are confusing absolute and relative time again. How can some light emitting object produce light which has reached the Andromeda galaxy but never reached us before? For that to happen, that object must have spontaneously appeared at a very far distance from us and begun emitting light. That means that object is defined by an event, its own spontaneous appearance. We will not see its spontaneous appearance until after the Andromeda sees it appear. So it will not be a part of our universe until we see it appear. Similarly, we will not observe the moment that the Andromeda galaxy sees it until sometime after we see it ourselves. So no, it is not a part of our universe while it is not interacting with us. It hasn't yet popped into existence, just like the planet that will magically pop into existence right beside us tomorrow is not yet a part of our universe.

The problem you are seeing isn't the definition of the universe, it's your own scenarios of things popping into existence out of nothing or receding at faster than the speed of light.

[gmalivuk]

All of the scenarios described which caused the galaxy to disappear under my definition would have the EXACT same result under any other definition. It is the scenarios which are physically impossible, not the definition.

No, a galaxy really truly could recede outside of our light cone, if expansion is accelerating as it seems to be. It is most definitely *not* physically impossible. The difference is that, according to real physics, "the universe" still includes that galaxy, even if the observable universe doesn't, so no actually mass-energy has been created or destroyed. The problem is that according to your definition, the galaxy really truly does leave our universe, which means matter is not conserved in our universe, which means you can't count on physical laws staying the same through time.

The problem you are seeing isn't the definition of the universe, it's your own scenarios of things popping into existence out of nothing or receding at faster than the speed of light.

We don't need anything popping into existence out of nothing. We only need things that have always been far apart, and expanding space. And it just so happens that both of these things are actually the case, therefore we get things far enough away that no light from them has reached us yet, and we get things receding faster than light. And with less pathological definitions of "universe", neither of these things causes any problems.

[Danny Uncanny7]

No, a galaxy really truly could recede outside of our light cone, if expansion is accelerating as it seems to be. It is most definitely *not* physically impossible. The difference is that, according to real physics, "the universe" still includes that galaxy, even if the observable universe doesn't, so no actually mass-energy has been created or destroyed. The problem is that according to your definition, the galaxy really truly does leave our universe, which means matter is not conserved in our universe, which means you can't count on physical laws staying the same through time.

The future galaxy leaves our universe, what you would see is the galaxy slow down and then freeze in time, redshifting off the spectrum as it moves away at the the speed of light. Again, it's not the definition, it's the scenario. The definition of what something is doesn't change the physics of what happens.

We don't need anything popping into existence out of nothing. We only need things that have always been far apart, and expanding space. And it just so happens that both of these things are actually the case, therefore we get things far enough away that no light from them has reached us yet, and we get things receding faster than light. And with less pathological definitions of "universe", neither of these things causes any problems.

What does it mean for two things to "have always been far apart" That means that they began existence far apart. That means two separate objects spontaneously came into existence. You have no problem with objects spontaneously popping into existence in your definition of the universe, but it is not allowed for something to spontaneously pop into existence in my definition? Why is that?

You seem to think that I'm trying to rewrite physics. I'm not. I'm just giving you a definition of what the universe is. My definition is independent of any physical phenomenon and doesn't change the results of any experiments or change depending on the results of any experiments. It is useful because it clearly defines what is and is not part of the universe. This is useful if you want to start thinking about other universes or theoretical universes. A blanket statement like "all of mass and energy" simply leads to the problem of how do you know what all the mass and energy is? It's not a clear cut definition. My definition gives a simple litmus test as to whether an entity is part of the universe or not. Does it affect you in any way no matter how insignificant? If the answer is yes, then it exists.

[gmalivuk]

The future galaxy leaves our universe, what you would see is the galaxy slow down and then freeze in time, redshifting off the spectrum as it moves away at the the speed of light. Again, it's not the definition, it's the scenario. The definition of what something is doesn't change the physics of what happens.

Except, we can see things which are moving away faster than light. Because it's space that's expanding, rather than anything moving through space.

What does it mean for two things to "have always been far apart" That means that they began existence far apart.

Yes, at the time of the big bang.

I'm just giving you a definition of what the universe is. My definition is independent of any physical phenomenon and doesn't change the results of any experiments or change depending on the results of any experiments. It is useful because it clearly defines what is and is not part of the universe.

And it is useless because what is part of it can change over time, and "is in the same universe as" is not a transitive relation.

[Danny Uncanny7]

Except, we can see things which are moving away faster than light. Because it's space that's expanding, rather than anything moving through space.

No we aren't getting light from any object moving faster than light. Consider what the wavelength would be.

And it is useless because what is part of it can change over time, and "is in the same universe as" is not a transitive relation.

So if the sun disappeared right now, regardless of any laws of physics, just vanished poof! According to your definition of existence it would still exist tomorrow even though we can't see it or have any interaction with it. And you say your definition makes more sense.

[Argency]

And it is useless because what is part of it can change over time, and "is in the same universe as" is not a transitive relation.

So if the sun disappeared right now, regardless of any laws of physics, just vanished poof! According to your definition of existence it would still exist tomorrow even though we can't see it or have any interaction with it. And you say your definition makes more sense.

I think that's an unrealistic example. It's not really fair to Gmal's model to say that it doesn't work anymore if we throw the laws of physics out the window.

[PM 2Ring]

Except, we can see things which are moving away faster than light. Because it's space that's expanding, rather than anything moving through space.

No we aren't getting light from any object moving faster than light. Consider what the wavelength would be.

Well, we can't receive photons from objects that were moving away from us at c or faster when those photons were emitted, but we certainly can see objects that are "now" moving away from us at c or faster because they were moving away from us at a sufficiently subluminal velocity when the photons were emitted. I put "now" in quotes, since the notion of a universal now is somewhat problematic, but for convenience we can use the CMB rest frame.

Also see
http://en.wikipedia.org/wiki/Relativity_of_simultaneity
http://en.wikipedia.org/wiki/Comoving_distance

[eSOANEM]

So you're positing a huge violation of mass/energy conservation, whereby entire galaxies can cease to exist. Also, what about an object in between that can still observe both our galaxy and the distant one? It's a strange definition of "universe" that is intransitive. We are in the same universe as A, which is in the same universe as B, but we aren't in the same universe as B?

I just defined the universe in a logical way. If a galaxy ceases to exist, it is the same calibre of problem regardless of the definition of the universe. If expansion will cause things to eventually expand faster than the speed of light, then that might give a mechanism for objects to cease to exist. It has all of the same implications.

And as for things inbetween universes, that is by definition impossible. First, in the abstract sense, because if we interact with something, and that something interacted with something else first, then we have indirectly interacted with that something else, which is the only premise that I put forward for the definition of existence in the universe. So that something else is in our universe by my definition. Secondly, for our specific case, the speed of light is the fastest that any information or interaction can travel. If we see an intermediate object, it cannot have been affected by anything that we cannot see (discounting occlusion) because that interaction would have arrived at the speed of light and we would have also received it at the same time or earlier than we saw its effect on the intermediate object.

And those implications are that the laws of physics are not the same everywhen (and by simple extension) everywhere. This is a big problem because, if this is the case we do not necessarily have any real ability to make accurate predictions whatsoever.

The problem with your argument in the second paragraph is that, a galaxy less than c/H0 away from us may still be within c/H0 of another galaxy so it will still be able to see that galaxy even if we can't. This is just simple geometry.

How does being far away == cease to exist? For example, from my point of view, I could conclude that quakes don't exist. I've never observed one right? So, just because the universe (parts of that is) are far away, why do they cease to exist?

Calling them separate or no longer detectable is one thing, but non-existent?

We're working in Danny Uncanny's definition of a universe whereby only objects within our past lightcone can be said to exist.

Objects and events are linked.

But they are not the same thing. An object has a worldline representing it's reference frame as co-ordinate time evolves. An event is a point in spacetime.

For WarDafts scenario, assuming that at some point all of these objects sprang into existence from nothing, and space was expanding. What would happen is that at time zero, you see nothing, because there was nothing there before you existed. And then every day, you see a new object pop into existence as its light reaches you. And because space is expanding somehow, distances are growing larger and everything is accelerating away from you until it is receding faster than the speed of light. But that means that the light in transit also got stretched out. You see that object slow down more and more until it recedes at the speed of light and time freezes and the light gets red shifted off the bottom of the spectrum (approaching infinite wavelength). The future of that object is now outside of the universe it can't affect you. The object hasn't actually left, because it will always be there frozen in time, but you will never find out what happens to it. WarDafts suggests that future object can affect your nearest neighbour which is still receding below the speed of light and that neighbour interacts with you, apparently a contradiction.

You say that we need to consider that space is relative yet here you make declarations about the absolute state of the universe based solely on the observations of one reference frame (that that galaxy is frozen in time).

Consider an alien sitting on a planet in that galaxy, to him everything is normal and we're frozen in time.

Clearly, if we are to take SR into account, neither galaxy is actually frozen in time at all, the only way we can reconcile these facts is if all that is happening is that the two objects are approaching a distance c/H0 between them. Just because SR prohibits absolute reference frames does not mean there is no fundamental reality.

But that's my point: under any reasonable definition, the matter in a galaxy *can't* cease to exist in a given universe, while under yours, it can.

All of the scenarios described which caused the galaxy to disappear under my definition would have the EXACT same result under any other definition. It is the scenarios which are physically impossible, not the definition.

No they don't because most universes used in modern cosmology are infinite and don't declare that everything that exists is observable. For this reason, that situation simply cannot arise in those universes.

No, you're talking about events now, while I'm talking about objects as they persist through time. There are things whose light has already reached the Andromeda galaxy, but won't reach us for a couple million years yet. Are those things in our universe, even though they have never interacted with us directly or indirectly?

You are confusing absolute and relative time again. How can some light emitting object produce light which has reached the Andromeda galaxy but never reached us before? For that to happen, that object must have spontaneously appeared at a very far distance from us and begun emitting light. That means that object is defined by an event, its own spontaneous appearance. We will not see its spontaneous appearance until after the Andromeda sees it appear. So it will not be a part of our universe until we see it appear. Similarly, we will not observe the moment that the Andromeda galaxy sees it until sometime after we see it ourselves. So no, it is not a part of our universe while it is not interacting with us. It hasn't yet popped into existence, just like the planet that will magically pop into existence right beside us tomorrow is not yet a part of our universe.

The problem you are seeing isn't the definition of the universe, it's your own scenarios of things popping into existence out of nothing or receding at faster than the speed of light.

No, the distinction between objects and events does not rely on any sort of absolute time, only that all reference frames have time. This is morally true so therefore it should be obvious that there must be a distinction between objects and events (with an even simply being a point in spacetime but an object being a piece of matter with its own worldline traced out in spacetime which includes all the events that object takes part in).

We don't need anything popping into existence out of nothing. We only need things that have always been far apart, and expanding space. And it just so happens that both of these things are actually the case, therefore we get things far enough away that no light from them has reached us yet, and we get things receding faster than light. And with less pathological definitions of "universe", neither of these things causes any problems.

What does it mean for two things to "have always been far apart" That means that they began existence far apart. That means two separate objects spontaneously came into existence. You have no problem with objects spontaneously popping into existence in your definition of the universe, but it is not allowed for something to spontaneously pop into existence in my definition? Why is that?

Surely you accept that the big bang happened? If you do, by "always far apart" we simply mean that, at the big bang, they were far apart. If you're going to try arguing that the big bang was one infinitely small point then I'm afraid that isn't the case. That's a pop science tv-show description because talking about an infinitely dense point everywhere is a might counterintuitive however this is the real truth of what the big bang theory says. The big bang happened everywhere, it is meaningful to talk about points having been far away at the big bang.

You seem to think that I'm trying to rewrite physics. I'm not. I'm just giving you a definition of what the universe is. My definition is independent of any physical phenomenon and doesn't change the results of any experiments or change depending on the results of any experiments. It is useful because it clearly defines what is and is not part of the universe. This is useful if you want to start thinking about other universes or theoretical universes. A blanket statement like "all of mass and energy" simply leads to the problem of how do you know what all the mass and energy is? It's not a clear cut definition. My definition gives a simple litmus test as to whether an entity is part of the universe or not. Does it affect you in any way no matter how insignificant? If the answer is yes, then it exists.

Except your definition allows for energy to leave the universe and therefore, by Noether's theorem, implies the laws of physics vary with time. This is a very big problem.

And it is useless because what is part of it can change over time, and "is in the same universe as" is not a transitive relation.

So if the sun disappeared right now, regardless of any laws of physics, just vanished poof! According to your definition of existence it would still exist tomorrow even though we can't see it or have any interaction with it. And you say your definition makes more sense.

The sun disappearing is a very different beast from what we're suggesting. We're suggesting that, in your definition, all sufficiently far objects can cease to exist. The sun ceasing to exist, but not any other objects between it and the edge of the observable universe would be a completely different problem.

[Danny Uncanny7]

So your definition of the universe depends on the laws of physics within that universe. In your universe, If something flies off beyond any possible interaction and has no further effect whatsoever on anything else within the universe, it continues to exist, but if it were to magically disappear and have no further effect on anything else it doesn't exist. What if it instantly altered its velocity to beyond the speed of light? Would it exist then? The last two situations have the same result for any observer. Things can pop into existence at arbitrary locations at the time of the big bang but they can't pop into existence at any other time because those are the laws of the physics in the universe as you've defined it. But what if that happened? Apparently you just say it can't and that's good enough. You want to define a universe as though you have absolute knowledge of it, even without absolute knowledge.

See the problem? Your definition is narrow and inflexible and cannot describe any theoretical alternate universe or any universe that functions differently than you imagine in your head. You're defining the universe through the pathway of observation defines theory and theory defines universe. Your universe can't accommodate any future observations that might refute the theory its built upon. My definition is simple and flexible and accommodates any reference at any time in any situation. My definition of a universe could apply to a computer simulation of bits or a thought experiment about simplified physics and spherical chickens. Your definition describes the universe from the reference point of absolute knowledge about infinite space as though you have that absolute knowledge. With only partial knowledge. For all you know, the edge of our solar system could be a giant holographic screen projecting radiation. Your definition involves describing everything, even though you don't know for sure what that everything is. So how do you know what the universe is? Your definition of the universe is an undefined entity because you don't know everything. It has no succinct description.

You are the only human on the world. You have no memory. What is the universe you are in? Can you define it in a meaningful way? Do you need to know about the big bang and the cosmos? Do you need to know the laws of physics? Do you have to redefine the universe every time you learn something new about it? But I thought the universe didn't change.

[Technical Ben]

Thanks eSOANEM, that is what I was asking Danny.

Danny Uncanny7, can you clear up something you said?
You complained that others were looking at a "universal reference frame (or timeline)" and that we should not do that. However, they all used relativity (which does not have a universal reference frame!) to show how things like a ring of galaxies could prove your definition wrong. Then you said that from "our own light cone" your definition is correct. However, your "light cone" is a preferred reference frame! Is that not a contradiction?

Again, do we use our evidence, tests and experiences to define things? We cannot use our "theory" or thoughts to define things. The real world (our experimental evidence) trumps our own ideas every time.
So, why do you suggest your definition, which is taken on it's own merits, to have any relation to the real world? As the real world is not described by our own ideas, but by the realities observed.

For example, if I choose to define 2+2=5 I have a problem if I've defined 5/2=2.5 as well. Your current definition of a Universe only works in one part, but contradicts it's self in others.

[WarDaft]

For WarDafts scenario, assuming that at some point all of these objects sprang into existence from nothing, and space was expanding. What would happen is that at time zero, you see nothing, because there was nothing there before you existed. And then every day, you see a new object pop into existence as its light reaches you. And because space is expanding somehow, distances are growing larger and everything is accelerating away from you until it is receding faster than the speed of light. But that means that the light in transit also got stretched out. You see that object slow down more and more until it recedes at the speed of light and time freezes and the light gets red shifted off the bottom of the spectrum (approaching infinite wavelength). The future of that object is now outside of the universe it can't affect you. The object hasn't actually left, because it will always be there frozen in time, but you will never find out what happens to it. WarDafts suggests that future object can affect your nearest neighbour which is still receding below the speed of light and that neighbour interacts with you, apparently a contradiction.

Good job on completely and totally missing the point of my example. No, an object on the opposite side of the ring outside your horizon cannot affect you, but what you cannot do is pick an object, define the horizon around it to be a universe, and then declare that nothing in this universe can ever interact with things outside that universe. Early on, A can interact with B, and B with C, and C with D, all the way round the ring back to A, but it is entirely reasonable that no interaction can pass from D all the way through the chain to A. So by your definition, A and D are in different universes, but there's a chain of objects interacting from A to D, so how can you possibly claim that A has any sort of privileged claim to defining the universe? Even more-so because it is a ring, and every object can be totally identical. There's no way to pick one and say "that's the universe, yep!"

And "expanding somehow" ? Really? Space IS expanding. Out there. Right now. It's an extraordinarily well documented phenomenon, and it's doing it roughly exponentially, just like my case scenario.

You are the only human on the world. You have no memory. What is the universe you are in? Can you define it in a meaningful way? Do you need to know about the big bang and the cosmos? Do you need to know the laws of physics? Do you have to redefine the universe every time you learn something new about it? But I thought the universe didn't change.

"Can you define the universe in any meaningful way without knowing anything about the universe?" No, of course not, don't be ridiculous. The universe is what it is, and it could not care less how we define the term. Our definition is either accurate or not, and if we learn something new about the universe, yes we had darn well better change our definition if its necessary. The universe, from a timeless view, does not change. The observable universe? Sure, it can do just about whatever it wants. ΔE = 0 for the universe as a whole, but the observable universe can go either way just fine.

And so far as I know, you still haven't covered how objects spontaneously ceasing to exist is not a massive flaw in your definition of universe. These aren't just nit-picks, these are huge glaring flaws.

[Danny Uncanny7]

Good job on completely and totally missing the point of my example. No, an object on the opposite side of the ring outside your horizon cannot affect you, but what you cannot do is pick an object, define the horizon around it to be a universe, and then declare that nothing in this universe can ever interact with things outside that universe. Early on, A can interact with B, and B with C, and C with D, all the way round the ring back to A, but it is entirely reasonable that no interaction can pass from D all the way through the chain to A. So by your definition, A and D are in different universes, but there's a chain of objects interacting from A to D, so how can you possibly claim that A has any sort of privileged claim to defining the universe? Even more-so because it is a ring, and every object can be totally identical. There's no way to pick one and say "that's the universe, yep!"

My point is that the universe is relative to your reference. There is no absolute universe, it is a relative concept. That's what I've been saying from the start. If A is your reference, after D hits light speed, it is gone from A's universe. It has disappeared from the universe. Not physically flown out of it, but disappeared in the exact same manner that the future does not exist in todays universe. Get it? Time is relative, existence is relative to time and time is relative to space. So existence is relative. If you say that New York in the year 2013 exists right now, most people would say you're wrong. It's the future. It doesn't yet exist. It has had no effect on us. It's not a part of our universe from today's point of view. It hasn't affected us In that exact same fashion that D does not exist after it achieves the speed of light relative to A. D is in the future relative to A and further more, unless it slows down, it will always be in the future of A for eternity.

"Can you define the universe in any meaningful way without knowing anything about the universe?" No, of course not, don't be ridiculous. The universe is what it is, and it could not care less how we define the term. Our definition is either accurate or not, and if we learn something new about the universe, yes we had darn well better change our definition if its necessary. The universe, from a timeless view, does not change. The observable universe? Sure, it can do just about whatever it wants. ΔE = 0 for the universe as a whole, but the observable universe can go either way just fine.

Well I gave you a meaningful definition regardless of your knowledge and you spit on it. ΔE = 0 is a theory based on observation of the universe. You're putting the chicken before the egg. You want to define a universe with exact knowledge that you build from observation of said universe. You criticize a functional definition that can have things leaving the universe. But you have no problem with a definition that has no concrete shape or form and can change with every observation. Basically a non-definition.

And so far as I know, you still haven't covered how objects spontaneously ceasing to exist is not a massive flaw in your definition of universe. These aren't just nit-picks, these are huge glaring flaws.

I don't see how an object ceasing to exist is a flaw in the definition in the universe. Why can't something cease to exist? We haven't seen it happen but that doesn't mean it can't happen. I don't think the definition of the universe should contain the laws of physics which operate within it. If it happened, what would be the implications for your definition of the universe? If you observed the the sun disappear?

For that matter. Take two future scenarios. In one instance, the the distance between galaxies accelerated and they all went beyond the speed of light so that we cannot observe them. In the other, the distance between galaxies accelerate and they all went beyond the speed of light, and then the galaxies blinked out of existence. Their mass disappeared. If you were to show up in either future and saw the dark sky how would you tell the difference between the two? Why is something vanishing a problem, but an event with the exact same result as things vanishing but a different name not a problem?

[gmalivuk]

My point is that the universe is relative to your reference. There is no absolute universe, it is a relative concept. That's what I've been saying from the start. If A is your reference, after D hits light speed, it is gone from A's universe. It has disappeared from the universe.

And what we're saying is that this is a useless definition, because it's not transitive. B is in A's universe, and A and C are both in B's universe, but C is not in A's universe. How is that useful? How is that somehow better than just having *two* concepts, one called "universe" and the other called "observable universe", where the latter has all the properties you want, and the former has the useful property of being a transitive relation.

Well I gave you a meaningful definition regardless of your knowledge and you spit on it. ΔE = 0 is a theory based on observation of the universe.

No, it's a mathematical result of the laws being time-invariant.

But you have no problem with a definition that has no concrete shape or form and can change with every observation. Basically a non-definition.

Which definition do you think changes with every observation? Sure, that is what the observable universe does, but is that surprising? It's right there in the name. The advantage of the conventional nomenclature is that we can distinguish between the observable universe and the universe as a whole. Which incidentally *can* be defined rigorously so that each point in the universe has some other point in the universe in its own observable universe. Patch all the observable universes together, in other words.

Why can't something cease to exist? We haven't seen it happen but that doesn't mean it can't happen.

It can't happen if the fundamental laws of physics don't change depending on when/where you are. If they can, then science is out the window because we can't make predictions in any case.

I don't think the definition of the universe should contain the laws of physics which operate within it. If it happened, what would be the implications for your definition of the universe? If you observed the the sun disappear?

If the sun disappeared and was no longer part of the observable universe of any other point we agree is in our universe, or a chain of such points connected transitively, then yes, the sun would have disappeared from our universe. The problem with your definition is that even "normal" everyday things that *don't* violate everything we know about reality would cease to exist in your universe. Things only cease to exist in a conventionally defined universe if they actually cease to exist from all lightcones within that universe.

In the other, the distance between galaxies accelerate and they all went beyond the speed of light, and then the galaxies blinked out of existence. Their mass disappeared. If you were to show up in either future and saw the dark sky how would you tell the difference between the two? Why is something vanishing a problem, but an event with the exact same result as things vanishing but a different name not a problem?

All of them blinking out of existence is *also* a problem, it's just that it's equally a problem for any formulation of physics with time-invariant laws. Meanwhile it's only your weird definition that also has problems with normal everyday events like the expansion of space.

[Danny Uncanny7]

Which definition do you think changes with every observation? Sure, that is what the observable universe does, but is that surprising? It's right there in the name. The advantage of the conventional nomenclature is that we can distinguish between the observable universe and the universe as a whole. Which incidentally *can* be defined rigorously so that each point in the universe has some other point in the universe in its own observable universe. Patch all the observable universes together, in other words.

gahhh, I've said this like a hundred times, you can't have a "whole view" of the universe where time means anything. This whole argument is about a definition that defines things around present time and past and future. You can't have any of those times with a "whole universe" view. Because all of those times are relative to a specific point in space. You can't talk about the future, unless you also have a location. There is no absolute time, so if you want a universe that is dependent on time, where the future doesn't exist alongside the present, then you need to have a location. You can't say what the future or past is without a reference. And if things can exist where nothing existed in the past, like say the big bang, or any of the theoretical ABCD objects, then time is a very important part of defining what exists.

How can you have a universe with no relative observer or point. What defines it? Why should the universe where the Boltzman constant is what it is be THE universe, and not a universe where it is slightly different. You need something to peg reality, otherwise an imaginary universe is not different from our universe. I suggested that we be that reference.

So like I said the universe is everything that interacts with a relative entity that is known to be in that universe. If you want to forget about time, the universe is everything that has an will interact with an entity in that universe. Either way, I am the only one who has actually put up a real definition and I have yet to see a flaw in it.

Lastly, why why why are you defining the universe by the laws of physics within the universe. Remember that stemmed from a conversation on multiverses. How can you define the term universe and apply it to other theoretical universes when you pigeonhole that the laws of physics have to be a certain way in the universe. The universe should not be subject to the contents of the universe. It's an encompassing definition. If mass is conserved or not, or space is filled with fluffy pink elephants, it should not affect the definition of the term universe. Whatever the rules are, they are the rules within the universe, they don't define what a universe is. Like you said, if you have new observations, you have to change your definition. Doesn't that suggest that maybe you don't have a clear definition of what a universe is? You are trying to define the term universe by what the contents of our universe are. But you don't have a clear definition of what the contents are. The contents are just what are inside the universe, so you are going around in circular logic, defining the universe by what it contains.

[gmalivuk]

How can you have a universe with no relative observer or point. What defines it?

Events A and B are in an observable universe together if either can observe the other or there is a past event that could have affected both or a potential future event that can be affected by both. Events A and B are in the same (whole) universe if they are in the same observable universe or if there is a sequence of events starting at A and ending at B where each is in an observable universe with its predecessor and is in an observable universe (possibly different) with its successor.

There, I've just defined "universe". I have done it relative to specific points, but in a way that allows events to be in the same universe even if neither actually observes the other. We can then define *our* universe as the collection of points in the same (whole) universe we are in.

I am the only one who has actually put up a real definition and I have yet to see a flaw in it.

This is not the first time I've defined a universe as above, and flaws in your definition have been brought up since you first defined it.

[eSOANEM]

In your universe, If something flies off beyond any possible interaction and has no further effect whatsoever on anything else within the universe, it continues to exist, but if it were to magically disappear and have no further effect on anything else it doesn't exist. What if it instantly altered its velocity to beyond the speed of light? Would it exist then? The last two situations have the same result for any observer.

No, if it instantaneously jumped to c it could still interact with objects. If it instantaneously jumped to >c it can still interact. Sketch the diagrams if you're not sure.

Your definition describes the universe from the reference point of absolute knowledge about infinite space as though you have that absolute knowledge. With only partial knowledge. For all you know, the edge of our solar system could be a giant holographic screen projecting radiation. Your definition involves describing everything, even though you don't know for sure what that everything is. So how do you know what the universe is? Your definition of the universe is an undefined entity because you don't know everything. It has no succinct description.

No. The definition I am using (which is as close as I can get to how I believe it is usually used in cosmological discussions) merely requires that such information exists. Yours assumes that we alone in the universe produce valid observations which implies privileged reference frames and violation of SR.

If we have an observation which refutes SR the definition used for the universe may well change however it certainly does not make sense to use a definition contrary to what is a very well tested theory.

You are the only human on the world. You have no memory. What is the universe you are in? Can you define it in a meaningful way? Do you need to know about the big bang and the cosmos? Do you need to know the laws of physics? Do you have to redefine the universe every time you learn something new about it? But I thought the universe didn't change.

The universe is the n-dimensional manifold containing everything which can/could/will be able to be observed and everything that everything which can/could/will be able to be observed can/could/will be able to observe and so on. It is this daisy-chain-ing which is necessary in order to produce consistent reasonable results. Now, I wouldn't actually use this definition because it is far too general to be useful and doesn't give any good understanding of what's going on), in practice, depending on the context of the discussion (be it classical, relativistic, quantum etc.) I would use something more specific so that my definition was precise and could actually be used to do things. As War Daft said, the cosmos does not have some intrinsic name and doesn't care how we define "universe", "cosmos" or "world" or any similar term, those words are merely conveniences for ease of communication.

This definition holds for an ancient view of the universe (by which I mean earth is a flat(ish) plane covered by a semispherical dome with everything evolving in time), a classical one, a relativistic one and a quantum one even if the exact specifics vary.

The exact specifics:

In the ancient view, the manifold's co-ordinates lie in R³xR¹ and some form of hyper-cyclindrical co-ordinates (whereby the co-ordinates in R³ are spherical) seem most appropriate, the manifold is flat and may be closed, open or infinite. In the hyper-cylindrical co-ordinates we take our first angle to be the bearing and the second to be the attitude.

In the classical view, we've realised the earth is round and so what was the universe in the ancient picture is now rolled into a ball and embedded in a new R³xR¹ space. The manifold is flat and infinite.

In the relativistic view, the manifold is now in a more complicated space arguably either C⁴ or R³xI¹, it is no longer necessarily flat but is infinite.

In the big bang picture, the universe is not infinite in its extent back in time.

In MWI, you could say that the collection of all worlds is the universe. In other interpretations you might use a slightly different interpretation.

Good job on completely and totally missing the point of my example. No, an object on the opposite side of the ring outside your horizon cannot affect you, but what you cannot do is pick an object, define the horizon around it to be a universe, and then declare that nothing in this universe can ever interact with things outside that universe. Early on, A can interact with B, and B with C, and C with D, all the way round the ring back to A, but it is entirely reasonable that no interaction can pass from D all the way through the chain to A. So by your definition, A and D are in different universes, but there's a chain of objects interacting from A to D, so how can you possibly claim that A has any sort of privileged claim to defining the universe? Even more-so because it is a ring, and every object can be totally identical. There's no way to pick one and say "that's the universe, yep!"

My point is that the universe is relative to your reference. There is no absolute universe, it is a relative concept. That's what I've been saying from the start. If A is your reference, after D hits light speed, it is gone from A's universe. It has disappeared from the universe. Not physically flown out of it, but disappeared in the exact same manner that the future does not exist in todays universe. Get it? Time is relative, existence is relative to time and time is relative to space. So existence is relative. If you say that New York in the year 2013 exists right now, most people would say you're wrong. It's the future. It doesn't yet exist. It has had no effect on us. It's not a part of our universe from today's point of view. It hasn't affected us In that exact same fashion that D does not exist after it achieves the speed of light relative to A. D is in the future relative to A and further more, unless it slows down, it will always be in the future of A for eternity.

This is claiming that our frame is privileged. It is the exact opposite of using a relative concept. If you want that, you need to find some objective reality which can explain all observers' observations otherwise you end up with each observer claiming, as you are, privileged information contrary to each other and you end up proving the inconsistency of your system.

And so far as I know, you still haven't covered how objects spontaneously ceasing to exist is not a massive flaw in your definition of universe. These aren't just nit-picks, these are huge glaring flaws.

I don't see how an object ceasing to exist is a flaw in the definition in the universe. Why can't something cease to exist? We haven't seen it happen but that doesn't mean it can't happen. I don't think the definition of the universe should contain the laws of physics which operate within it. If it happened, what would be the implications for your definition of the universe? If you observed the the sun disappear?

For that matter. Take two future scenarios. In one instance, the the distance between galaxies accelerated and they all went beyond the speed of light so that we cannot observe them. In the other, the distance between galaxies accelerate and they all went beyond the speed of light, and then the galaxies blinked out of existence. Their mass disappeared. If you were to show up in either future and saw the dark sky how would you tell the difference between the two? Why is something vanishing a problem, but an event with the exact same result as things vanishing but a different name not a problem?

To the first paragraph:

It is a flaw because if things can cease to exist, energy (and momentum) are not conserved. If they are not conserved, that implies that the laws of physics are not constant in time (or space). Not only does this not seem to be the case (note, variation in "constants" like c is not variation in the laws of physics because the fundamental laws are the same, it's just the values they spit out which changes) but it would mean that we could not actually predict anything because the laws of physics could change at random (and indeed, would have to, otherwise the changes in the laws would be governed by laws which would be constant in time and energy would be conserved).

To the second:

Because in one it is no longer observable but still exists, in the other, it no longer exists. The first (that I listed) requires only that not all the universe is observable (this should be intuitive, for one thing, objects can block line of sight) and maintains constancy of the laws of physics. The second, doesn't require anything but means it is impossible to make accurate predictions.

Look up Noether's theorem if you don't believe us about what violation of conservation of energy would imply.

Which definition do you think changes with every observation? Sure, that is what the observable universe does, but is that surprising? It's right there in the name. The advantage of the conventional nomenclature is that we can distinguish between the observable universe and the universe as a whole. Which incidentally *can* be defined rigorously so that each point in the universe has some other point in the universe in its own observable universe. Patch all the observable universes together, in other words.

gahhh, I've said this like a hundred times, you can't have a "whole view" of the universe where time means anything. This whole argument is about a definition that defines things around present time and past and future. You can't have any of those times with a "whole universe" view. Because all of those times are relative to a specific point in space. You can't talk about the future, unless you also have a location. There is no absolute time, so if you want a universe that is dependent on time, where the future doesn't exist alongside the present, then you need to have a location. You can't say what the future or past is without a reference. And if things can exist where nothing existed in the past, like say the big bang, or any of the theoretical ABCD objects, then time is a very important part of defining what exists.

What makes you say that you can't have a holistic view of the universe?

This is the only way to reconcile contradictory observations, you need some way of mapping observations between reference frames. Without an absolute universe which is just viewed differently by different observers, you end up with contradictory observations and no way to reconcile them. This is a bad thing.

As I understand your view of the universe, you have no way of resolving these contradictions, you simply ignore them.

As an example, without an absolute universe how do you reconcile the simple prediction of SR that two trains passing moving away from a station in opposite directions will each see the other's clock ticking slower than theirs?

How can you have a universe with no relative observer or point. What defines it? Why should the universe where the Boltzman constant is what it is be THE universe, and not a universe where it is slightly different. You need something to peg reality, otherwise an imaginary universe is not different from our universe. I suggested that we be that reference.

Observation is what we tie reality to. Where we get conflicting observations, we must use some theory to resolve. In the case of SR, the easiest way to do this is to draw the Minkowski diagram.

Wrt your Boltzmann constant example, we know it is what it is because it has been observed to have one value.

If we were to get different values in reference frames, we would find the value when all the equipment is in the rest frame of all the rest of it and then we would also find the way to transform the value from one reference frame to another (in the case of SR this will be the Lorentz transformation).

So like I said the universe is everything that interacts with a relative entity that is known to be in that universe. If you want to forget about time, the universe is everything that has an will interact with an entity in that universe. Either way, I am the only one who has actually put up a real definition and I have yet to see a flaw in it.

The flaw is that it requires that the laws of physics are not constant in time or space.

If this is the case, science is a completely futile enterprise because no predictions can be made.

Lastly, why why why are you defining the universe by the laws of physics within the universe. Remember that stemmed from a conversation on multiverses. How can you define the term universe and apply it to other theoretical universes when you pigeonhole that the laws of physics have to be a certain way in the universe. The universe should not be subject to the contents of the universe. It's an encompassing definition. If mass is conserved or not, or space is filled with fluffy pink elephants, it should not affect the definition of the term universe. Whatever the rules are, they are the rules within the universe, they don't define what a universe is. Like you said, if you have new observations, you have to change your definition. Doesn't that suggest that maybe you don't have a clear definition of what a universe is? You are trying to define the term universe by what the contents of our universe are. But you don't have a clear definition of what the contents are. The contents are just what are inside the universe, so you are going around in circular logic, defining the universe by what it contains.

Because without the relevant theory we cannot do anything with our definition and, as I discussed above, with the most general definition, we cannot really do anything. In order to be able to use our definition, we must use that theory to describe "reality" as a thing as best we can. This is almost certainly not the actual description of reality (as I've stated before, I am of the opinion that "the" fundamental theory will never be known) however reality doesn't care what we call it or what things we its "name" for.

The reason we're kicking up a fuss about conservation of mass-energy is that, without that, physics (and indeed, all sciences except mathematics) cannot exist because no predictions can be made.

As for defining the universe by what it contains, what else are we to do? Define it by what it doesn't? Define it by embedding it in some other space? The former of these would be ridiculous for obvious reasons and the latter is not necessary due to the theorema egregium.

[WarDaft]

Well I gave you a meaningful definition regardless of your knowledge and you spit on it. ΔE = 0 is a theory based on observation of the universe. You're putting the chicken before the egg. You want to define a universe with exact knowledge that you build from observation of said universe. You criticize a functional definition that can have things leaving the universe. But you have no problem with a definition that has no concrete shape or form and can change with every observation. Basically a non-definition.

I just want to add one more re-enforcement of how important ΔE = 0 is.

Noether's theorem says (basically) that any action which is continuous and symmetric, conserves what it acts on. This is a mathematical theorem. It has been proven true. The result is that if we throw out ΔE = 0, then we throw out continuous symmetric actions that affect an objects energy, and so the momentums are out too. But is that really such a big deal? How many things can possibly be "continuous symmetric actions?" Well, it means for example, that things can no longer spin. This bears repeating. THINGS CAN NO LONGER SPIN. The fan that's spinning to keep your CPU from overheating as you read this webpage? Yeah, that's impossible. Swivel chairs? Impossible!

In short, without ΔE = 0, there is absolutely no particular reason why your computer will not burst into flames five seconds after you read this, and then start changing colours, then turn into Godzilla. In fact, it should do something even more unexpected and even faster. Really, it's a marvel it hasn't happened already.

[starslayer]

Eh, that's not quite true. GR, for example, does not respect global energy conservation if the cosmological constant exists (we do not know yet if dark energy is a cosmological constant). Since its energy density is constant, as space expands, more of it comes into existence. Where from? Who the hell knows.

Assuming I understand Noether's Theorem correctly, it is also not true that if energy is not conserved, the laws of physics must change randomly with time. This is because energy conservation comes out of the time symmetry of the Lagrangian/Hamiltonian. If it were to turn out that those were not time-symmetric, there could still be some underlying, non-random manner in which they changed with time, but energy conservation would be lost. It is also not true that energy conservation violation implies momentum conservation violation, because they are related to two different symmetries. If rotational symmetry of the Lagrangian holds, for example, but time symmetry does not, angular momentum is still conserved, and things can still spin the same way they always have.

[eSOANEM]

Assuming I understand Noether's Theorem correctly, it is also not true that if energy is not conserved, the laws of physics must change randomly with time. This is because energy conservation comes out of the time symmetry of the Lagrangian/Hamiltonian. If it were to turn out that those were not time-symmetric, there could still be some underlying, non-random manner in which they changed with time, but energy conservation would be lost. It is also not true that energy conservation violation implies momentum conservation violation, because they are related to two different symmetries. If rotational symmetry of the Lagrangian holds, for example, but time symmetry does not, angular momentum is still conserved, and things can still spin the same way they always have.

I may have been overstating the case wrt requiring random change (I wasn't sure at the time of posting but wanted to see what other people thought) however, because of SR, conservation of energy is the same law as conservation of momentum (conservation of 4-momentum), and the corresponding translation symmetry is a general one in 4-space.

[WarDaft]

Eh, that's not quite true. GR, for example, does not respect global energy conservation if the cosmological constant exists (we do not know yet if dark energy is a cosmological constant). Since its energy density is constant, as space expands, more of it comes into existence. Where from? Who the hell knows.

Assuming I understand Noether's Theorem correctly, it is also not true that if energy is not conserved, the laws of physics must change randomly with time. This is because energy conservation comes out of the time symmetry of the Lagrangian/Hamiltonian. If it were to turn out that those were not time-symmetric, there could still be some underlying, non-random manner in which they changed with time, but energy conservation would be lost. It is also not true that energy conservation violation implies momentum conservation violation, because they are related to two different symmetries. If rotational symmetry of the Lagrangian holds, for example, but time symmetry does not, angular momentum is still conserved, and things can still spin the same way they always have.

Energy has mass, and mass has momentum, how can violation of conservation of energy not violate conservation of momentum? I suppose that's not really derivable from the math (at least not the same math), and I should have put them further apart conceptually at least. Actually, regardless of that, his definition of the universe implies violation of conservation of momentum and angular momentum every bit as much as it does conservation of energy - when an object leaves the universe, unless it is perfectly balanced by another object leaving the universe at the opposite side "simultaneously" (so obviously it's not possible), we have violation of conservation of momentum.

And how can we have rotation anything like what we know today without time symmetry? In the absence of friction and gravitation, an object will spin forever. Spin it in the other direction, and it's indistinguishable from the first case time reversed.

[starslayer]

Wardaft, set an object spinning, then heat it up. The angular momentum won't change, but there is now more energy in the system. In other words, kinetic energy is not the only form of energy. To break energy conservation, all we need to suppose is that the object magically heats itself or cools itself off as it spins. To more directly connect it with the Lagrangian, if the potential is changing somehow, the angular momentum of an object may not be affected by it, even though the energy of the system changes.

eSOANEM, I'll have to think about it more. My intuition says that while breaking energy conservation does break four-momentum conservation, it should not necessarily break three-momentum conservation. I'll see if I can work through the math, but if you can point me at a source/textbook which does, I'd be grateful.

[eSOANEM]

eSOANEM, I'll have to think about it more. My intuition says that while breaking energy conservation does break four-momentum conservation, it should not necessarily break three-momentum conservation. I'll see if I can work through the math, but if you can point me at a source/textbook which does, I'd be grateful.

I'm not working from any textbook however, because boosts will map some of the energy component of 4-momentum onto the momentum and the momentum onto the energy component when transforming between reference frames, violation of conservation of energy in one frame must be seen as a violation of conservation of momentum in others. In order to reconcile these we say there is one conservation law and one symmetry (just as we wouldn't say that momentum in the x,y plane was conserved just because we observed that it wasn't in the z axis).

[doogly]

Conservation of Energy a la intro physics is no longer the thing you want to be talking about by the time you have moved on up in the world to consider GR and QFT. You want

\nabla_\mu T^{\mu\nu}=0

That is, the divergence of the stress tensor is zero.

The cosmological constant satisfies the above quite delightfully.