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The first complex observer to look at it would force a collapse, and that collapse would be transmitted throughout the universe in an instant.....

... what is it about us (and cats) that could drive this collapse?[/quote I reckon the answer is that both contain information systems, and trying to maintain highly complex information in multiple states may be more difficult than maintaining mountains of material in multiple states, so if the model in the brain is forced to simplify and take up a specific form, that would force the external reality to simplify too to remain compatible with the data. So, it isn't measurement that forces a collapse, but the integration of the resulting data into an information system which will then apply complex processing to it.

... Your instantaneous transmission could happen only if every part of the Universe were in contact with every other part.

What's missing is some explanation of why (information) complexity is relevant (why not mass, or particle count, or number of interactions, ...?), and why it becomes critical at some arbitrary level. Could a mouse collapse it? a pidgeon? frog? ant? amoeba? and what about a non-biological information processing system, a PC?, IBMs 'Watson'? the internet? Where do you draw the line, and why?

Maybe, as I wrote, it's not exactly a matter of "complexity" but of irreversibility / loss of coherence (which is related to complexity but not the same thing).

Quote from: lightarrow on 22/05/2013 13:10:44Maybe, as I wrote, it's not exactly a matter of "complexity" but of irreversibility / loss of coherence (which is related to complexity but not the same thing).Well yes, but that's just restating wavefunction collapse.

...what I actually have in mind is that things can maybe maintain a certain amount of superpositions until it reaches a point where it's too hard to maintain them all, at which point some kind of simplification must occur.

What we'd need to test this idea though is a way to measure the total amount of complexity involved in order to see if there is some consistent level where a collapse of the wavefunction becomes more likely than not.

I envisage real material as being outside the universe and merely contacting with it at a multiplicity of points, a bit like a spider with many legs hanging onto a web. Outside of the universe where the spiders reside there is no speed limit of c, but the movement of all the points of contact with the web are limited by c. Each leg continually multiplies into many new legs, following the waves in the web and maintaining an external, instant communication system between all these points. When the wavefunction has to collapse due to complexity, the spider simply lets go of the web with many of its legs and absorbs them back into itself.

Quote from: dlorde on 22/05/2013 17:36:49Well yes, but that's just restating wavefunction collapse. In my opinion, not, because it would provide a (generic) model for the collapse.

Well yes, but that's just restating wavefunction collapse.

Quote from: lightarrow on 23/05/2013 13:01:04In my opinion, not, because it would provide a (generic) model for the collapse.But since wavefunction collapse is decoherence observed, saying that wavefunction collapse may be a matter of decoherence is not a particularly useful generic model. Perhaps I've missed something - can you clarify?

In my opinion, not, because it would provide a (generic) model for the collapse.

I added the concept of irreversibility, which is certainly far from being clarified in qm, but which is not simply decoherence.

What I've never understood is why the particle or wave question is linked to the actual act of choosing to observe or not observe and isn't a result of the system of measurement used to observe.

Quote from: lightarrow on 23/05/2013 21:15:47I added the concept of irreversibility, which is certainly far from being clarified in qm, but which is not simply decoherence.Ah, OK... so in what sense might the collapse of the wavefunction be a matter of irreversibility? irreversibility of what?

... Imagine a single photon hitting a fotomultiplier: something happens inside the macroscopic bulk of photo-sensitive metal, which then releases an electron, which then hits another electrode which releases 2 electrons and so on until a macroscopic current can be detected. I don't know what happens exactly, but certainly all the process is irreversible. If, instead, a single photon hits a single atom and excites it, this proces is reversible. Maybe from the microscopic --> macroscopic some process becomes irreversible.

OK, go for it

The apparently intrinsic indivisibility of infinity leads one to wonder if any “part” of infinity can be distinct from any other “part”. Is it in any way meaningful to talk of parts of infinity?

It is all there, in eternity, in an all-embracing now.

This sounds like a recipe for predestination, but I am not suggesting that we should abdicate all responsibility for our actions; far from it. In eternity, things are as they are, permanently. However, we cannot entirely rule out the possibility that they are as they are, to some extent, because of the choices we seem to be making now.

In a truly infinite realm every snapshot is every other snapshot; they exist together with no semblance of order or chronology.

If we live in an infinite cosmos, then every change we perceive, every movement we detect and every second that “ticks past” on our clocks must be an illusion. Illusion is perhaps not the best word to use because if something exists in our reality, it is real for us.

no “part” of infinity can be distinct from any other “part”

In no way am I denying the reality of our Universe. I am simply saying that our reality may not be "absolute" reality.

Perhaps relativity is a more all pervading concept than we might imagine. It has to be possible that, not only are time and space relative within our perception, but also that time and space exist only in our current frame of reference. They are “real” within that frame of reference, but may be completely different, even non-existent, in another.

What happens if we apply this reasoning to life, as, of course, we must?

If life is infinite, then it must be possessed by every “aspect” of the cosmos, whether or not we perceive it as being alive.

if infinity had more than one dimension, each of the dimensions would have to be all of the others...

There's one on Amazon UK at a little over Ł790! I think I might try the local Library.

Popular science books often point out that, in eternity, everything that can happen, must happen.

Why does it seem apparently intrinsically indivisible to you? It seems to me that infinity is divisible into any number of parts, including an infinite number of parts. In any division, there will be at least two infinite parts. Consider a road that stretches away from you to infinity in either direction. You can paint a line across it and divide it into two infinite lengths, then paint another line across, making two infinite lengths and one finite length. You can do this an infinite number of times in either direction.

It's not an 'all embracing now', because you're outside of time in that perspective; 'now' is a subjective experience of observers traversing the time dimension.

(see Does Everything Possible Have To Happen?).

" Consider a road that stretches away from you to infinity in either direction."Mathematically, this may be an acceptable thing to ask, but in reality, you are asking the impossible.How could you possibly know that the road went to infinity? There is certainly no way to prove that it does.OK, you could argue that this is only a thought experiment, but it pertains to something that, almost certainly, cannot exist.

Literally, "infinite" means "without end". When you paint your line you mark an end to the first part of your quasi-infinite road. Beginning and end are dependent on subjective viewpoint, so all you need to do is turn round and your line marks an end to the other half of your road.

It was not my intention to get into etymological discussion, but you rather invite it in your comment about time.

"..... then paint another line across, making two infinite lengths and one finite length. You can do this an infinite number of times in either direction."No, you can't. As you rightly point out; one length is finite, so however many times you repeat the action, you will never reach infinity, in fact, you will always be infinitely far from it. How could something finite become infinite?

One of the difficulties involved in talking about infinity is that our terminology is rooted in linear time. Suggest a better term for a timeless state and that will be a big step in the right direction.

Quote from: dlorde(see Does Everything Possible Have To Happen?).That's an interesting link, but most of what it says amounts to "everything that can happen, will happen, but not is it can't happen for some reason".

Also, it seems to assume that the same laws (e.g. gravity) that apply in our seemingly finite Universe would automatically in infinity. Can that be justified?

Well of course. All discussion about infinity is either mathematical or thought experiment.

That's a semantic straw man.

Quote from: dlordeWell of course. All discussion about infinity is either mathematical or thought experiment.True, but this misses the salient point that infinite roads, infinite divisions and all other forms of the infinite series exist only in the (presumably finite) minds of those who think about these things.

No. something that may be considered to have no end in one direction, but be clearly limited in the other may be said to be unbounded in one direction, but not infinite. It is possible to argue reasonably and logically that something is unbounded, but to describe any physical thing, in our 4D reality, as infinite, without stipulating that you are talking about a mathematical, or pseudo, infinity is presumptuous and usually inaccurate.

There is a difference between unboundedness and infinity; infinity has the property of unboundedness in some respect (e.g. along some particular vector), but not all unboundedness is infinite, e.g. the surface of a sphere is unbounded but not infinite

this would make the present the end of an infinite series of events, and an infinite series cannot be completed

Nobody suggested that they necessarily corresponded to any real-world contexts, these were all metaphysical abstractions, thought experiments.

Since directionality is subjective, what sense does it make to talk of being able to start an infinite series?

Enjoy your course.

I don't see what direction has to do with it - e.g. the positive integers are an infinite series starting at 0 (or 1)

Consider your positive integers; move from 0 to 100. Now turn round and go back the other way. When you reach 0, you have come to the end of an infinite series. It should take infinite time to reach the end of an infinite series.

There are two problems here:1. There is no such thing as an infinite series.2. There is no such thing as infinite time.

Quote from: dlorde It's not an 'all embracing now', because you're outside of time in that perspective; 'now' is a subjective experience of observers traversing the time dimension.Does that not support statement 2?

I wouldn't mention 1. to a mathematician

Do the positive integers 1,2,3...., the negative integers -1,-2,-3..... and the real numbers (eg) between 0 and 1 constitute three infinite series?

Do you have any argument to support assertions 1. or 2. ?

... It is evident that the infinity containing the even, or odd, numbers must be half the size of the infinity containing the whole numbers.

Could it be that question is answered, that we can divide infinity and that any parts into which we divide it will be infinite?

... even Cantor does not seem to have performed mathematical calculations with the infinite set of all infinities; this appears to be the only one of his infinities that is not actually a mathematical infinity.

...anything that is truly infinite must contain everything; there cannot be two infinities, because each would have to contain the other.

Applying the Reflection Principle to the infinite set of all infinities would lead to the following contradiction: The reflection principle holds that within a universal set, containing all sets, it must be possible to find a set that contains any property found in the universal set. The obvious contradiction is that the universal set contains all other sets (that is one of its properties), but this property cannot be found in any of the other sets.

Cantor defined a countable infinity to be one that can be put into one-to-one correspondence with the list of natural numbers, whereas an uncountable infinity cannot. Useful as these concepts may be to the mathematician, none is an "absolute" infinity, and cannot therefore be considered as more than "unbounded".

It should take infinite time to reach the end of an infinite series.