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As with Gödel's proofs, proving that it is impossible to come up with an experimentally verifiable demonstration that the multiverse theory is correct would be

by yborg 12y ago

As with Gödel's proofs, proving that it is impossible to come up with an experimentally verifiable demonstration that the multiverse theory is correct would be a major achievement. And Gödel didn't end mathematics with his theorems. It simply moved on, as would physics.

ccvannorman 12y ago
Along similar lines, I've wondered if it's possible to prove "any observing entity (e.g. a human) cannot possibly fully understand the system within which it is contained" .. any complete knowledge of a system should necessitate a larger system.
- Xcelerate 12y ago
  I've always wondered this as well. Consider a finite collection of atoms consisting of a human and an environment. For simplicity, assume these atoms move classically. The human is a subsystem, and since the entire system involves deterministically, there is only a limited number of configurations that the human subsystem can realize within the environment. If a "human" is what is necessary to comprehend reality, then there are aspects of the system that cannot be realized by the subsystem, since there are far more states available to the total system. Then again, I could just be rambling.
  - danbruc 12y ago
    I would argue it depends on the nature of the system. If the system follows (simple) rules then you can likely compress the description of the system into something that fits into a (small) subsystem. If the system and its behavior is a uncompressible mess this will not work out. Up to now, I would say, our universe with all its relatively simple laws of physics looks pretty structured and easily compressible.
  - hasenj 12y ago
    I don't think this works. You don't have to encompass everything about the universe in your mind. You can just comprehend a formula that allows you in principle to calculate any part of it that you need. Think of a fractal. http://en.wikipedia.org/wiki/Mandelbrot_set http://en.wikipedia.org/wiki/Mandelbrot_set
- evanb 12y ago
  There's some relevant discussion on this old thread: https://news.ycombinator.com/item?id=7244476 https://news.ycombinator.com/item?id=7244476
- rndn 12y ago
  It’s easy to prove "we don’t know that" since maybe it is possible to introspect our universe. For example, suppose someone interacts with some quantum system and it unexpectedly outputs a binary string. It turns out that this string can be interpreted as a command-line interface where one can access the states of individual particles and inspect the running process. Given the program code of our universe is reasonably short, we could possibly fully understand the system from within.
vorg 12y ago
> Gödel didn't end mathematics with his theorems. It simply moved on That's another way of saying Godel's theorems didn't end Mathematics, mathematicians just redefined what Mathematics was, presumably so they could keep their jobs.
kazinator 12y ago
The negation of the multiverse hypothesis can be taken to be, "no, there aren't multiple universes, let alone an infinity of them; there is only this one". This negation is just as hard to prove as the multiverse hypothesis. Lack of evidence of the existence of other universes doesn't prove their non-existence, nor does it rule out their existence. However, note that the multiverse hypothesis is simpler in its content. The statement that this universe exists, while all the other ones do not, goes one step beyond the statement that they all exist. Is there no evidence that there are no other universes? Mathematics shows us that there are: it shows us that entities exist which are not located anywhere in this universe. For instance, the number pi. We accept pi as real, but where in this universe is it? It is not computable, so that even if we use all the particles in this universe as the beads of an abacus, it will not represent pi. If this universe is all there is, then there is no pi; we must stop talking in terms such as "there exists a real number that gives the ratio of the circumference to the diameter of a circle". (Of course, the existence of this one is shared between the multiverse hypothesis and its negation.)
- hasenj 12y ago
  PI is a concenpt. Of course it doesn't exist physically* in the universe. * Well, various "physical" representations/encodings of this concept must exist in different people's brains.
  - kazinator 12y ago
    Whether the existence of pi is different from the existence of a given stone is a philosophical question! Maybe you and I exist exactly in the same sense that pi exists: no more, no less. Concepts can be reshaped. If pi is merely a concept, why can't we conceive it to be something else, like 4.0?
    - TheOtherHobbes 12y ago
      In a curved spacetime Pi could easily be 4.0. Pi is an idealised approximation of a certain kind of curvature in a certain kind of spacetime. Pi appears to have infinite precision only if you assume the curvature and the spacetime are perfectly smooth and have infinite resolution. Given there's a Planck limit, it's unlikely the universe really is perfectly smooth. So Pi in the real universe is not very likely to have infinite precision. That's where the concept of Pi as a Platonic example of mathematical perfection trips over the reality of physics as a messy thing where traditional math structures can only ever provide approximate descriptions. Beyond a certain level of detail Other Stuff is happening, and you can't assume smoothness or infinite precision. We don't know a whole lot about the Other Stuff yet. One reason is that math was built to work with smooth functions with infinite precision, and there's no equivalent math that describes the lumps of whatever spacetime is made of, or the relationships between the lumps.
kazinator 12y ago
The multiverse hypothesis by definition asserts that such a thing is impossible. The universes are separate. Any entanglement between universes means they are in fact just constituents of a larger universe. I think that the hypothesis will be quasi-proven when science hits the ultimate limit beyond which there is no explanation. This will show that the world just proceeds by arbitrary rules that are traceable to axioms. Once you have that, you have shown that it's indistinguishable from any other such a formal system. That is to say, that it exists in the same way: the world is no more or less real than, say, the plane of the complex numbers. After that, although you still don't have empirical evidence of other worlds, there is no short supply of imaginable worlds (such as in mathematics) which are just as real. In other words, once it becomes obvious that the world is just "math all the way down", it will be as foolish to deny other existences as to deny the square root of -1.

by yborg 12y ago

ccvannorman 12y ago

Along similar lines, I've wondered if it's possible to prove "any observing entity (e.g. a human) cannot possibly fully understand the system within which it is contained" .. any complete knowledge of a system should necessitate a larger system.

Xcelerate 12y ago
I've always wondered this as well. Consider a finite collection of atoms consisting of a human and an environment. For simplicity, assume these atoms move classically. The human is a subsystem, and since the entire system involves deterministically, there is only a limited number of configurations that the human subsystem can realize within the environment. If a "human" is what is necessary to comprehend reality, then there are aspects of the system that cannot be realized by the subsystem, since there are far more states available to the total system. Then again, I could just be rambling.
- danbruc 12y ago
  I would argue it depends on the nature of the system. If the system follows (simple) rules then you can likely compress the description of the system into something that fits into a (small) subsystem. If the system and its behavior is a uncompressible mess this will not work out. Up to now, I would say, our universe with all its relatively simple laws of physics looks pretty structured and easily compressible.
- hasenj 12y ago
  I don't think this works. You don't have to encompass everything about the universe in your mind. You can just comprehend a formula that allows you in principle to calculate any part of it that you need. Think of a fractal. http://en.wikipedia.org/wiki/Mandelbrot_set http://en.wikipedia.org/wiki/Mandelbrot_set
evanb 12y ago
There's some relevant discussion on this old thread: https://news.ycombinator.com/item?id=7244476 https://news.ycombinator.com/item?id=7244476
rndn 12y ago
It’s easy to prove "we don’t know that" since maybe it is possible to introspect our universe. For example, suppose someone interacts with some quantum system and it unexpectedly outputs a binary string. It turns out that this string can be interpreted as a command-line interface where one can access the states of individual particles and inspect the running process. Given the program code of our universe is reasonably short, we could possibly fully understand the system from within.

vorg 12y ago

> Gödel didn't end mathematics with his theorems. It simply moved on That's another way of saying Godel's theorems didn't end Mathematics, mathematicians just redefined what Mathematics was, presumably so they could keep their jobs.

kazinator 12y ago

The negation of the multiverse hypothesis can be taken to be, "no, there aren't multiple universes, let alone an infinity of them; there is only this one". This negation is just as hard to prove as the multiverse hypothesis. Lack of evidence of the existence of other universes doesn't prove their non-existence, nor does it rule out their existence. However, note that the multiverse hypothesis is simpler in its content. The statement that this universe exists, while all the other ones do not, goes one step beyond the statement that they all exist. Is there no evidence that there are no other universes? Mathematics shows us that there are: it shows us that entities exist which are not located anywhere in this universe. For instance, the number pi. We accept pi as real, but where in this universe is it? It is not computable, so that even if we use all the particles in this universe as the beads of an abacus, it will not represent pi. If this universe is all there is, then there is no pi; we must stop talking in terms such as "there exists a real number that gives the ratio of the circumference to the diameter of a circle". (Of course, the existence of this one is shared between the multiverse hypothesis and its negation.)

hasenj 12y ago
PI is a concenpt. Of course it doesn't exist physically* in the universe. * Well, various "physical" representations/encodings of this concept must exist in different people's brains.
- kazinator 12y ago
  Whether the existence of pi is different from the existence of a given stone is a philosophical question! Maybe you and I exist exactly in the same sense that pi exists: no more, no less. Concepts can be reshaped. If pi is merely a concept, why can't we conceive it to be something else, like 4.0?
  - TheOtherHobbes 12y ago
    In a curved spacetime Pi could easily be 4.0. Pi is an idealised approximation of a certain kind of curvature in a certain kind of spacetime. Pi appears to have infinite precision only if you assume the curvature and the spacetime are perfectly smooth and have infinite resolution. Given there's a Planck limit, it's unlikely the universe really is perfectly smooth. So Pi in the real universe is not very likely to have infinite precision. That's where the concept of Pi as a Platonic example of mathematical perfection trips over the reality of physics as a messy thing where traditional math structures can only ever provide approximate descriptions. Beyond a certain level of detail Other Stuff is happening, and you can't assume smoothness or infinite precision. We don't know a whole lot about the Other Stuff yet. One reason is that math was built to work with smooth functions with infinite precision, and there's no equivalent math that describes the lumps of whatever spacetime is made of, or the relationships between the lumps.

kazinator 12y ago

The multiverse hypothesis by definition asserts that such a thing is impossible. The universes are separate. Any entanglement between universes means they are in fact just constituents of a larger universe. I think that the hypothesis will be quasi-proven when science hits the ultimate limit beyond which there is no explanation. This will show that the world just proceeds by arbitrary rules that are traceable to axioms. Once you have that, you have shown that it's indistinguishable from any other such a formal system. That is to say, that it exists in the same way: the world is no more or less real than, say, the plane of the complex numbers. After that, although you still don't have empirical evidence of other worlds, there is no short supply of imaginable worlds (such as in mathematics) which are just as real. In other words, once it becomes obvious that the world is just "math all the way down", it will be as foolish to deny other existences as to deny the square root of -1.