ask a physicist

[Landifarne]

That is an interesting thought. I'm not aware of anything that really just deals with the nodes, though there are a lot of different approaches in quantum chemistry, so it's possible I just don't know of one. But I'm not terribly sure it would be useful, either. You really need the whole wavefunction in some kind of approximation to get the energy levels. Measurement-wise, knowing where the nodes are might help, but I don't know of a way to make that measurement in analogy to diffraction, either.

The big issue is the approximation that you can just use hydrogen-like orbitals filled up one at a time without interaction. That generally doesn't work very well at all quantitatively. It gives some rough guidelines for qualitative chemical behavior (hence the periodic table), but the numbers don't come out well.

Yeah, it was interesting. Neat to think that we could characterize/fingerprint a particular atom by the nodal surfaces and the surfaces' intersections. I hadn't heard anyone ever speak of such a thing and was wondering if the resulting geometries/topologies had any significance, relation or analogy to higher level stuff.

 

[CaptainGemini]

Something that has me curious...

Conservation of mass and conservation of energy... Is it possible those two laws of conservation prevent all forms of time travel? That you cannot travel through time because, from the laws of physics, it would be destroying mass and energy in one time and creating them in another?

 

[AbdulAlhazred]

Something that has me curious...

Conservation of mass and conservation of energy... Is it possible those two laws of conservation prevent all forms of time travel? That you cannot travel through time because, from the laws of physics, it would be destroying mass and energy in one time and creating them in another?

Modern notions of time travel all involve the construction of some sort of 'closed time-like curve', that is some sort of 'wormhole' into the past. So you would literally pass through. The question then is at what point would you say something had been created or destroyed?

Truthfully there are vastly many things that would be broken by time travel, including every single known conservation law I believe, at least from some observer's perspective. This is why physicists are mostly pretty down on the whole concept, it seems most likely to be something that "just can't happen". Again Noether's Theorum raises its head here, if these conservation laws are broken, then their dual symmetries are also broken.

There is an 'out' here though. As best we can interpret the evidence the Universe is truly vast, and the part we can see, and ever be causally connected to, is only a tiny fraction (something on the order of one part in 10^120th power parts) of all that there is. If the Universe is really so extensive, then almost every conceivable configuration of matter must exist somewhere within it. That would include, say, a planet exactly like Earth except just like Earth was 3 weeks ago. If you could go there, would that be time travel? Opening up a wormhole to such a place and stepping through, would that violate any conserved property of the Universe? It would seem not.

So, perhaps, we could go any place outside of the portion of the Universe causally connected to Earth. We could go there regardless of any limitations imposed by the speed of light or any other consideration of causality. You just have to find a way to build such a 'wormhole'. Of course there likely simply is no such way, but we really don't know enough to rule it out.

 

[Umbran]

Modern notions of time travel all involve the construction of some sort of 'closed time-like curve', that is some sort of 'wormhole' into the past.

Well, wormholes are the most popularized, but there are other solutions that have closed time-like curves that don't involve wormholes. In these, you'd just be flying along, and when you finished flying, you'd find you landed before you took off.

And, conversely, not all use of wormholes end up with closed time-like curves.

There is an 'out' here though. As best we can interpret the evidence the Universe is truly vast, and the part we can see, and ever be causally connected to, is only a tiny fraction (something on the order of one part in 10^120th power parts) of all that there is. If the Universe is really so extensive, then almost every conceivable configuration of matter must exist somewhere within it. That would include, say, a planet exactly like Earth except just like Earth was 3 weeks ago. If you could go there, would that be time travel? Opening up a wormhole to such a place and stepping through, would that violate any conserved property of the Universe?

"Travel to a place that is a lot like what my world 3 weeks ago," doesn't really violate anything. In and of itself, it is just going to another planet. However, if you go there *faster than light could get there*, then we have the same problems as any other travel faster than light. The nature of the destination isn't the issue, it's how fast you get there that matters.

So, perhaps, we could go any place outside of the portion of the Universe causally connected to Earth.

Note that, as soon as you go to a place, that place is causally connected to Earth. You came from Earth, and you can now cause events there.

 

[AbdulAlhazred]

Well, wormholes are the most popularized, but there are other solutions that have closed time-like curves that don't involve wormholes. In these, you'd just be flying along, and when you finished flying, you'd find you landed before you took off.

And, conversely, not all use of wormholes end up with closed time-like curves.

I didn't mean to imply that wormholes MUST have 'time-like' world lines. I'm not sure about 'other solutions', there are a LOT of different formulations of GR, including rotating space time that could produce various results. Wormholes are at least the one that I know of that is localized. In any case they are probably impossible.

"Travel to a place that is a lot like what my world 3 weeks ago," doesn't really violate anything. In and of itself, it is just going to another planet. However, if you go there *faster than light could get there*, then we have the same problems as any other travel faster than light. The nature of the destination isn't the issue, it's how fast you get there that matters.

I'm not so sure about that. Remember, we're talking about a part of the Universe which has never been in communication with the part we inhabit since the start of inflation, no photons have ever been exchanged, and none ever could be. So, if you took some action somewhere in that space time which would violate causality, etc in OUR space time's past, no observer would ever be able to tell, because they inherently cannot compare the events in the two places, there isn't any light cone anywhere that overlaps both.

I think you would have to have some inertial frame of reference in which an actual observer could exist who would observe some violation of causality or some conservation law in order for a 'problem' to exist. Because the two areas of space time don't interact with each other or any other reference frame that interacts with either one of them, a sort of loophole is created. Such areas of the Universe, because they cannot exchange information with us, don't really exist in some formal sense as far as we're concerned. At least one COULD look at it that way. Obviously we don't know what is or isn't possible, and we haven't even a clue how one would open up a 'pathway' of some sort to such a remote location. Its just as likely such considerations are moot because it simply isn't possible.

Note that, as soon as you go to a place, that place is causally connected to Earth. You came from Earth, and you can now cause events there.

As to how they would become connected going forward, sure they would, but so what? There's no 'paradox' there. If you kill 'alternate grandfather' it will surely mean that 'alternate you' won't come into existence (or whatever) but 'prime you' still has a grandfather, prime grandfather. I would at least vote for their being no violations of conservation laws either, because, as you say, the two areas of space time ARE now connected. Still, for your own purposes, if you wished to 'go back in time and kill your grandfather' you can now fully enjoy the benefits of having done so, as long as you aren't concerned about y

 

[Landifarne]

...
If the Universe is really so extensive, then almost every conceivable configuration of matter must exist somewhere within it. That would include, say, a planet exactly like Earth except just like Earth was 3 weeks ago.
...

I'm sorry, but I don't find this argument at all convincing.

You're suggesting that an infinite number of "Similar Earths" exist out there, and that an infinite number of branches have continuously broken away from them every fraction of a second for nearly 5 billion years (or, perhaps ~14 billion years). Correct me if I'm wrong, but that's infinity to an infinite number of infinite powers...which is a tad larger than 10^120 * ("the known universe.")

 

[AbdulAlhazred]

I'm sorry, but I don't find this argument at all convincing.

You're suggesting that an infinite number of "Similar Earths" exist out there, and that an infinite number of branches have continuously broken away from them every fraction of a second for nearly 5 billion years (or, perhaps ~14 billion years). Correct me if I'm wrong, but that's infinity to an infinite number of infinite powers...which is a tad larger than 10^120 * ("the known universe.")

No, you're talking about a 'many worlds' interpretation of quantum mechanics. I'm talking about the sheer brute physical size of the single Universe we inhabit. If our ideas of its scale are correct, then it is SO VAST that almost every conceivable configuration of matter which could possibly exist under the laws of physics must be actualized somewhere.

Its NOT an infinite number however. There is some huge percentage of the Universe that is outside our light cone and thus causally disconnected from us (we cannot even in principle know what exactly is happening there, and as long as the Universe continues to exist no information will ever be exchanged with those locations). 10^120th power is a truly unimaginably vast number BTW. I'm not sure exactly where that number was derived from, like many such numbers it is probably some guesstimate or other, so I wouldn't put too much emphasis on it, except in the sense of being 'really really huge'.

I seem to recall a Sci-Am that had some authors discussing different sorts of 'Multiverse'. The terminology considered this the simplest form, physically disconnected areas of a single space-time, though you could quibble that it isn't really 'outside our Universe' in some sense. Level 2 in that scheme is IIRC your 'many worlds' or other similar concepts, then we have string theory concepts of the 'bulk', and finally one could imagine 'Universes' where the rules of logic we think by simply don't apply or apply differently, which would be well beyond string-theoretical concepts of differing fundamental constants.

 

[Umbran]

I seem to recall a Sci-Am that had some authors discussing different sorts of 'Multiverse'.

Yep. By Max Tegmark, in SciAm May 2003, if no other time....

http://space.mit.edu/home/tegmark/PDF/multiverse_sciam.pdf

Other references...

https://www.youtube.com/watch?v=w3TDO1AA1Sw

http://physics.about.com/od/astronomy/f/ParallelUniverseTypes.htm

http://www.space.com/18811-multiple-universes-5-theories.html

http://space.mit.edu/home/tegmark/crazy.html

 

[tomBitonti]

No, you're talking about a 'many worlds' interpretation of quantum mechanics. I'm talking about the sheer brute physical size of the single Universe we inhabit. If our ideas of its scale are correct, then it is SO VAST that almost every conceivable configuration of matter which could possibly exist under the laws of physics must be actualized somewhere.

Its NOT an infinite number however. There is some huge percentage of the Universe that is outside our light cone and thus causally disconnected from us (we cannot even in principle know what exactly is happening there, and as long as the Universe continues to exist no information will ever be exchanged with those locations). 10^120th power is a truly unimaginably vast number BTW. I'm not sure exactly where that number was derived from, like many such numbers it is probably some guesstimate or other, so I wouldn't put too much emphasis on it, except in the sense of being 'really really huge'.

I seem to recall a Sci-Am that had some authors discussing different sorts of 'Multiverse'. The terminology considered this the simplest form, physically disconnected areas of a single space-time, though you could quibble that it isn't really 'outside our Universe' in some sense. Level 2 in that scheme is IIRC your 'many worlds' or other similar concepts, then we have string theory concepts of the 'bulk', and finally one could imagine 'Universes' where the rules of logic we think by simply don't apply or apply differently, which would be well beyond string-theoretical concepts of differing fundamental constants.

Whoa there Nelly. I didn't think that the proposed scales (120b ly?) are anywhere near big enough to provide room for "almost every conceivable configuration of matter". I don't even think that 10^120 comes close to being big enough for that, even. How many plank units are there in a 20b ly radius? What is 2^that number?

I do think there start to be philosophic problems, of whether it is proper to consider stuff outside of our range of interaction to be "in our universe". That stuff would be implied because we have an easier time of mentally picturing the state of the universe as a whole, which is a psychological need more-so than a testable physical one.

As a slight tangent, something that doesn't ever seem to arise in the many-universes interpretation is whether to consider different regions which are identical as actually the same (issue number 1), and how the whole ensemble is connected (it seems multiply connected) (issue number 2), and how vastly big such an ensemble would be (as every point would be simultaneously branching to every possible outcome) (issue number 3). Just beginning to imagine the topology of the ensemble is difficult, let alone getting a clear description of the whole.

Thx!
TomB

 

[freyar]

Without getting into all of it, a truly infinite space/universe in the sense of infinite size geometry poses a lot of questions about how to think of probabilities (since everything is copied over somewhere). There are people who think about that. It's a tough problem, though.

To TomB: the many-world interpretation isn't about different regions of space. It's about the quantum state of the universe becoming more and more complicated. So geometric notions of "connected" and "topology" don't apply at least in the usual sense. The state is just some vector in an infinite-dimensional space, and it continuously moves in a direction that looks complex from the point of view of separate parts of the universe. I'm sure I'm not explaining that very well, but I didn't sleep well last night and am at something of a loss to do better right at the moment. There are some geometrical concepts that can be adapted to entanglement, but my understanding is that they're pretty far from what you would normally think of. But it's unquestionably not about almost-duplicates of the universe in different regions of space.