What is your interpretation of quantum mechanics?

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Offline David Cooper

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Re: What is your interpretation of quantum mechanics?
« Reply #50 on: 21/05/2013 19:33:38 »
I would like to throw a thought into the ring to see if it is in any way new. To many, the idea of a cat being both alive and dead at the same time until it's observed by someone is a step too far, and this is because if a human observer is able to force a collapse of the wavefunction, a cat should really be able to do likewise. But what is it about us (and cats) that could drive this collapse? 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.

It may really be that when we look out into the universe through a telescope, we can potentially force whole uninhabited galaxies to throw off most of their possible states so that they can appear to us in a particular, specific form rather than a fuzzy mess of multiple possibilities. This would not result in any causality travelling back billions of years through time though, because it would only force that galaxy to take up a specific form now, while it's entire past history up to that point would remain fuzzy. The first complex observer to look at it would force a collapse, and that collapse would be transmitted throughout the universe in an instant such that no other observer could force an incompatible collapse of the wavefunction of the same object.

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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #51 on: 21/05/2013 21:57:45 »
Quote from: David
The first complex observer to look at it would force a collapse, and that collapse would be transmitted throughout the universe in an instant.....

That's going to need some serious thought. 

The first thing that comes to mind is that you have linked the two parts of this thread.  Your instantaneous transmission could happen only if every part of the Universe were in contact with every other part.

Come back Bohm, all is forgiven!   :)   
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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #52 on: 22/05/2013 09:10:48 »
...  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.
This sounds like an Objective Collapse interpretation, using complexity as the trigger. The problem I have with these interpretations is their arbitrariness. At one extreme, it reduces to Wigner's interpretation, i.e. only the complexity of a human consciousness will collapse it, and at the other extreme, it reduces to interaction collapse, i.e. any particle interaction is sufficiently complex to collapse it.

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?   


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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #53 on: 22/05/2013 09:40:09 »
... Your instantaneous transmission could happen only if every part of the Universe were in contact with every other part.
That would be OK if it was a case of primordial entanglement (e.g. originating at the big bang). The problem I have with it is that it smells of special pleading for consciousness. I'm wondering quite how it would work in practice; would the first creature of sufficient information processing capability cause collapse as soon as the first photon from a distant galaxy hit its retina, or would there be a delay until the resulting signal had been through the visual cortex? Would it take multiple photons? how many, how much processing? would some early hominin look up at the sky at night, see a distant galaxy as a barely visible dot and collapse its wavefunction without even knowing what it was? And why, in David's example, if the universe was superposed this way, would only the one galaxy wavefunction collapse, wouldn't it be entangled with the rest of the universe? and what about intelligent life elsewhere in the universe - had the first arrivals already collapsed the universal wavefunction millions of years before we arrived on the scene?

It just doesn't smell right to me.

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Offline lightarrow

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Re: What is your interpretation of quantum mechanics?
« Reply #54 on: 22/05/2013 13:10:44 »
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).

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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #55 on: 22/05/2013 17:36:49 »
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).
Well yes, but that's just restating wavefunction collapse. Loss of coherence == decoherence. Decoherence is what the observer sees as wavefunction collapse.

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Offline David Cooper

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Re: What is your interpretation of quantum mechanics?
« Reply #56 on: 22/05/2013 18:46:38 »
Well, I wasn't really suggesting that a galaxy could maintain a form that never simplifies through any collapses of wavefunctions until an intelligence finally gets round to looking at it after several billion years, but 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. The galaxy will therefore repeatedly simplify itself as it becomes too hard to maintain all the superpositions, but every time it does so it will immediately start to generate new superpositions again which will in turn collapse when they become too complicated to maintain. Having a complex data system analyse the situation would merely hasten a point of collapse by increasing the complexity of the system as a whole.

It's easy enough for a single bit of data to be both a zero and a one at the same time, but to try to maintain that for billions of bits and with a program which must simultaneously run along trillions of different paths to process tham is not going to be at all easy. 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.

This means that when we send a photon through a double slit, the photon starts out as a single leg of a spider and immediately multiplies into many legs as the wave spreads out. Some of the legs go through one slit, while some go through the other, and a lot of waves hit the gap in between or the surrounds. Those that continue on through keep multiplying and radiate out from the slits, interfering with each other and ending up hitting the screen in an interference pattern, but for a photon to land on the screen, all the energy has to be sent to a single point. The spider determines which leg the full energy of the photon will be transferred to and the rest of the legs simply let go of the web. Alternatively, several of the legs remain attached to the web and each of them transfers the photon provisionally so that a superposition of different possible realities is to be maintained until some later complexity forces a further simplification.

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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #57 on: 22/05/2013 23:23:45 »
Now that the two themes in this thread seem to have come together, I shall have to go back and do some re-reading, but first; a bit more of the ongoing saga.

The Infinite Cosmos  Part 4

 John Wheeler said that “Time is nature's way to keep everything from happening all at once”. This may sound like a flippant comment, but it is in fact quite a profound observation.  We might say that eternity is the absence of time, and that in eternity everything must happen at once.  However, even that statement is misleading: in order for something to happen there must be some passage of time.  In eternity, everything just is.

  Whatever one can do with mathematical infinities, it seems inescapable that any physical infinity must be immutable.  The corollary of this is so important it is worth repeating.  An infinite cosmos cannot be multiplied nor divided.  It can have nothing added to it, because there is nothing outside it that could be added.  It can have nothing taken away, because to take something away would either make it less than infinite, or it would mean that there was something other than the all-embracing infinity, which would constitute a contradiction in terms.

Even Cantor recognised that the absolutely infinite differed from his other "infinities".  He is said to have equated the it with God. 

  The observable Universe, as we have seen, appears to have started its existence at a specific point, and must therefore be finite.  It is important not to think of the Big Bang as having happened at a particular point in time, or at a particular location in space.  Many cosmologists assure us that time and space were created with the Universe.  However, the Big Bang has to be seen as a pivotal point in the history of the Universe.  Given that there can never have been a time when there was nothing, it follows that there must be more to our Universe than meets the eye.  For convenience we will call this extra something the “cosmos”, and will, at this point, not be diverted into considering whether that might be a “multiverse” or simply some sort of vacuum energy state from which the Universe appeared in accordance with the “rules” of quantum uncertainty. 

  If we were able to divide infinity, for example, by two, what would we be left with?  One possibility seems to be that we would have two halves of infinity.  Each half would be less than infinite, thus it would be measurable.  Measure this quantity and multiply it by two and we have a measure of infinity, which is nonsense.  The second possibility must be that each “half” somehow becomes infinite.  Mathematically this seems reasonable; after all we can multiply or divide zero by any number we choose, and the outcome will be zero.  Perhaps we also could do this, mathematically, with infinity.  Consider Cantor's infinities: the whole numbers constitute an infinite series, so do the even numbers and the odd numbers.  Thus, Cantor demonstrated that, not only were there numerous infinities, but they were not all the same size.  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?  There seem to be at least two reasons why this cannot be the case.  The first is that 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.  The other is that, practically there is the complication that 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.

Wikipedia says:  " In mathematics, "infinity" is often treated as if it were a number (i.e., it counts or measures things: "an infinite number of terms") but it is not the same sort of number as the real numbers. In number systems incorporating infinitesimals, the reciprocal of an infinitesimal is an infinite number, i.e., a number greater than any real number. Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes (called cardinalities).[2] For example, the set of integers is countably infinite, while the set of real numbers is uncountably infinite."

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".

Wikipedia says:  "Transfinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite."

Perhaps "transfinite" would be a less confusing term to use for mathematical infinities; then "infinite" could be reserved for what Cantor referred to as "absolutely infinite".  This latter term has about it no less an air of tautology than does, for example, "absolutely perfect".

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Offline yor_on

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Re: What is your interpretation of quantum mechanics?
« Reply #58 on: 23/05/2013 00:37:20 »
Well, define it as all observe all :)
Then use 'c' to define the 'speed' by which we see action and reaction, in between 'observers' normally.

And leave quantum logic to the scale where it belongs. You might use decoherence for defining where it 'disappear' possibly? Doing so you get 'two' universes as I think, or two descriptions of one theoretical, co-existing. And what differ them is the scale you use. It's not too hard describing two planets macroscopically, or the earth and the moon orbiting. But try to do the same quantum mechanically, taking into account all possible interactions.
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Offline yor_on

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Re: What is your interpretation of quantum mechanics?
« Reply #59 on: 23/05/2013 12:10:01 »
Or we are walking on the edge of infinity, scale-wise :)
=

I'm starting to look at it as a projection from infinity, and there we have scales, pointing us home. And that is where the men in white coats will smile..
« Last Edit: 23/05/2013 12:46:28 by yor_on »
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Offline lightarrow

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Re: What is your interpretation of quantum mechanics?
« Reply #60 on: 23/05/2013 13:01:04 »
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).
Well yes, but that's just restating wavefunction collapse.
In my opinion, not, because it would provide a (generic) model for the collapse.

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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #61 on: 23/05/2013 18:28:29 »
...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.
OK; that sounds like an Objective Collapse model, which is fine as far as it goes, but for me, it needs some meat on its bones to reduce its arbitrariness.

Quote
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.
The problem here is that we only become aware of wavefunction collapse when we measure/observe the system, and increasing complexity means more interactions, which makes the complexity collapse model increasingly indistinguishable from the interaction collapse model.

Quote
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.
Yes, I've thought about entangled particles being locally connected in a higher spatial dimension, which is fundamentally not so different from your spider, but I don't know whether this would be covered by locality in a dimensionally extended version of relativity, and I don't have the maths to find out. It's the kind of thing a physicist would think of, and I've not heard it proposed as a solution, so I'm guessing that either it is covered by locality, in which case Bell theorem invalidates it, or it just doesn't work.
« Last Edit: 23/05/2013 18:41:24 by dlorde »

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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #62 on: 23/05/2013 18:39:44 »
Well yes, but that's just restating wavefunction collapse.
In 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?

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Offline David Cooper

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Re: What is your interpretation of quantum mechanics?
« Reply #63 on: 23/05/2013 19:35:37 »
What we really need to do is find experiments that allow us to push QM to the limits of how far it can sustain superpositions. I've found one that might fit the bill: http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser. The path to D0 can be kept very short while the other path to the D1, D2, D3, D4 cluster can be lengthened without limit, and the key point here is that it's what happens at this far end that dictates what "happened" a moment earlier at the D0 end. If the longer path can be stretched out to a year, you can appear to have backwards causation in time going back for a year. You can also bend the long path back on itself such that both ends are physically located right next to each other in the same lab.

Clearly it would be hard to stretch the path out to a year as the light would need to travel a whole lightyear to cover that distance, but a minute would probably be more than adequate, and a second might suffice. Even so, that's still going to be a long path. It may also be possible to slow down the light - I've read of materials in which it can be slowed down by 90% plus and even halted, so this could maybe enable very long time delays in a small space, hopefully without destroying the entanglements.

So, we have a setup in which there is a long delay between a future cause and its past effect, but I don't think there's really any backwards-in-time causation: what will actually happen is that the data received at D0 will be maintained in an state of superposition after it's been measured, and when the measurements are made later on at the far end, those states of the data can then simplify to remove the superpositions. However, if we take the data immediately after it's been taken generated at D0 and use it in complex calculations, we could maybe do something sufficiently complex with it to force it to lose its superpositions early, with the result that no interference patterns would be observed at the far end.

Addition to this post:-

To clarify a key feature of the experiment which I linked to, if you remove the beam splitter BSc, the interference patterns disappear at both ends of the experiment, so you can sit in a lab with the long path doubled back on itself (let's say a hour long) such that you can remove BSc and put it back in again and thereby dictate what happened at D0 an hour earlier.
« Last Edit: 23/05/2013 19:45:36 by David Cooper »

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Offline lightarrow

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Re: What is your interpretation of quantum mechanics?
« Reply #64 on: 23/05/2013 21:15:47 »
In 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?
I added the concept of irreversibility, which is certainly far from being clarified in qm, but which is not simply decoherence.
But I admit I was quite criptic about it.

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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #65 on: 23/05/2013 23:02:52 »
I 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?

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Offline cheryl j

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Re: What is your interpretation of quantum mechanics?
« Reply #66 on: 24/05/2013 00:01:09 »
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.

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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #67 on: 24/05/2013 00:27:20 »
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.
I don't quite follow you; whether you get particle or wave behaviour does depend on your measurement setup. The object itself has the properties of both a particle and a wave in some strange way (sometimes called a 'wavicle').

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Offline lightarrow

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Re: What is your interpretation of quantum mechanics?
« Reply #68 on: 24/05/2013 11:49:13 »
I 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?
Making a measure means making a macroscopic registration of an event. 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.

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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #69 on: 24/05/2013 13:18:03 »
... 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. That sounds to me like statistical thermodynamics; all the underlying interactions are reversible, but entropy increases because disordered states are more likely than ordered states, hence the arrow of time, and macro irreversibility...

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Offline yor_on

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Re: What is your interpretation of quantum mechanics?
« Reply #70 on: 24/05/2013 20:28:25 »
You're perfectly correct Cheryl, although dlorde is too :) (a born diplomat, that's me)
As long as you add yourself as a part of the experiment, your observation of the setup defining the outcome, I hope we can agree on it. Remember that question if a tree falls in the wood, did it? If no one is there to see it? We are the ones observing outcomes, and our observations is what define them. You can use a lot of intricate logic and that way question a lot of outcomes. But in the end I expect it to come down to if a universe can be expected to 'work' without us, or not? I think it can, and in that way you should be right in that circumstances define outcomes.
=

either my spelling, or my fingers, sux :)
Corrected though.
« Last Edit: 24/05/2013 20:51:38 by yor_on »
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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #71 on: 28/05/2013 23:08:38 »
Quote from: dlorde
OK, go for it :)

Some people just don't know when to run for the hills. :)

Actually, this thread has given me the impetus to pull together some of the scattered notes I have made over a few years, so I guess it's done me some good.
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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #72 on: 29/05/2013 02:23:41 »
The Infinite Cosmos      Part 5

  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?  If it is not, and if our Universe is “part” of this infinite cosmos, then we seem to have a problem.  However, the problem may not be as difficult to solve as it at first appears.  Consider the following possibility.  The cosmos is infinite; therefore every part of the cosmos is the cosmos.  Everything, including our apparently finite Universe, is infinite.  The birth of the Universe and perhaps its ultimate death exist together in infinity, along with all the things that “happen” between those two points.  It is all there, in eternity, in an all-embracing now.  We perceive spatial differences, and the passage of time, because our minds need to make sense of the partial image to which we are restricted.  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.  Without time "to keep everything from happening all at once", our familiar concept of causality needs some re-thinking. We cannot hope to stretch our finite understanding around infinity and eternity.  Only if and when we realise the full potential of our oneness with everything in the cosmos could we hope to do that.  In the meantime, we can reason that the finiteness and change that we perceive occur only in our finite frames of reference, beyond which there is no change, and therefore no passage of, or through, time because everything just “is”. 

Julian Barbour writes of a realm – “Platonia” – in which movement and the apparent passage of time are illusions resulting from the way in which our minds interpret what he describes as a series of “snapshots” of a static, timeless cosmos.  It is a short step, if indeed it is a step at all, from Platonia to an infinite cosmos.  However, it would have to be acknowledged that in a truly infinite cosmos, the process of interpreting the snapshots, and the sequence of those snapshots, would also be illusions.  In a truly infinite realm every snapshot is every other snapshot; they exist together with no semblance of order or chronology.  We cannot move from one to another because there is no sequence and no passage of time in which to move.  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.  In no way am I denying the reality of our Universe.  I am simply saying that our reality may not be "absolute" reality.

  What is, perhaps, even harder to comprehend is that, because no “part” of infinity can be distinct from any other “part”, then, any distinction which we, as individuals, perceive between ourselves and other individuals – past or present, living or dead – must also be an illusion, as must be the apparent distinction between ourselves and other creatures and objects.  Our individuality, our personality, that which we recognise as “I”, can be no more than an illusion created so that we may make sense of the limited perception which we have of “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.  In fact, this is the way in which we have to look at the things I have just referred to as illusions.  It cannot be denied that they are real in our frames of reference, but reality is relative.

 In an infinite cosmos existence is infinite; everything that exists shares that same existence.  Each thing is everything.  There are no divisions or distinctions, only an all-pervading oneness.  Michael Talbot says this of the work of physicist David Bohm: “As he looked more carefully into the meaning of the quantum potential he discovered it had a number of features that implied an even more radical departure from orthodox thinking.  One was the importance of wholeness.  Classical science had always viewed the state of a system as a whole as merely the result of the interaction of its parts.  However, quantum potential stood this view on its ear and indicated that the behavior of the parts was actually organized by the whole.  This not only took Bohr’s assertion that subatomic particles are not independent ‘things’, but are part of an indivisible system one step further, but even suggested that wholeness was in some ways the more primary reality.”  This fits well with the idea that infinity is the primary reality, and that our seemingly finite existence is a mere shadow of that reality

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.  Talbot (1996) again refers to Bohm: “…he believes that dividing the universe up into living and nonliving things also has no meaning.  Animate and inanimate matter are inseparably interwoven, and life, too, is enfolded throughout the totality of the universe.  Even a rock is in some sense alive, says Bohm, for life and intelligence are present not only in all of matter, but in ‘energy,’ ‘space,’ ‘time,’ ‘the fabric of the entire universe,’ and everything else we abstract out of the holomovement and mistakenly view as separate things”.

 If all this is right, it might be tempting to say: “We are the cosmos”.  However, the term “we” implies distinction, therefore it would be more correct to say: “I am the cosmos”, recognising, of course, that every “I” in the cosmos can rightly make the same claim.  Talbot brings together two quotes from Whitman’s “Mystical Life” when he talks of “…feeling that ‘everything is everything’ and ‘I am that’.”             

Can we talk about dimensions in infinity?  Apparently some scientists feel that we can.  Some of the current cosmological theories relating to dimensions suggest that our Universe has more than four dimensions, but that we are able to detect only three of space and one of time.  Among the explanations offered for the fact that we are not aware of these other spatial dimensions is that they might be rolled up so tightly that our instruments cannot detect them.  It is even claimed that these dimensions might be rolled so tightly as to be infinitely small.  I have yet to find a definition of infinitely small that is able to distinguish it from non-existent.  However, that is another matter.  An alternative concept – the one that lets in the idea of dimensions of infinity – is that ours is a four dimensional Universe embedded in a higher dimensional cosmos, and that this cosmos might have infinite (sometimes stated as an infinite number of) dimensions.

 Any attempt to calculate the dimensions of infinity must be a matter of conjecture.  The most logical assumptions would seem to be that it might have infinite dimensions; or, perhaps, one infinite dimension.  The latter possibility seems the more likely; because, if infinity had more than one dimension, each of the dimensions would have to be all of the others, and one has to wonder how this would differ from having just one dimension.  The possibility must also be considered that dimensions are features of finite, temporal realms, and cannot be applied to infinity.  Thus, infinity would be timeless and dimensionless.  Those who have read Edwin Abbott’s “flatland” will undoubtedly notice a similarity between this interpretation of infinity and “Pointland”; although, it would have to be said that the occupant of “Pointland” was heard to be talking, which would indicate that “Pointland” must not have been timeless. 
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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #73 on: 29/05/2013 12:34:48 »
I'm afraid I found that post confused, confusing, and somewhat incoherent. Confusion between a subjective and an objective view, unsubstantiated assertions, and leaps to unjustified conclusions...

For example:

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?
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.

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

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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.
These are two sides of the same coin in a 4D Parminidean block universe. Part of the future is dependent on the 'choices' we make now, but those choices are deterministic events like all others, from the 4D viewpoint. That we see them subjectively as free choices is a reflection of our ignorance of all the deterministic influences involved, including the processes in our own brains (and, of course, we can't see the future). Even in a deterministic universe we will act as if we have free will - we have no choice  ;D

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In a truly infinite realm every snapshot is every other snapshot; they exist together with no semblance of order or chronology.
Chronology is temporal order. But I don't see how it follows that infinity must be disordered. Consider the integers - a truly infinite extent of numbers in the plus and minus directions, and definitively ordered. All the evidence suggests that there is an ordering to time, at least at a macro scale; causality, statistical thermodynamics. There may be uncertainties at the quantum scale (see what I did there?), but they generally don't affect our subjective experience of chronology. The logical implication of your suggestion is that if we have chronology in this universe (which we appear to), it can't be infinite... I'm not averse to it being finite, but it ought to be for some coherent reason.

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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.
So what are you saying? It isn't an illusion?  And surely saying 'if something exists in our reality, it is real for us' is tautologous - what does it mean? what is 'our reality' but what is real for us?

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no “part” of infinity can be distinct from any other “part”
Why? what makes you think so?

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In no way am I denying the reality of our Universe.  I am simply saying that our reality may not be "absolute" reality.
If reality is what is real to us, what is 'absolute reality'? what do you mean by it?

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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.
Relativity is totally pervasive. Time and space are different for every observer. You could even say that from the 'point of view' of a particle travelling at light speed, there is no time or space (though how useful that would be isn't clear to me  ;) ).

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What happens if we apply this reasoning to life, as, of course, we must?
Why?
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If life is infinite, then it must be possessed by every “aspect” of the cosmos, whether or not we perceive it as being alive.
What does 'if life is infinite' mean? and why does it imply that it must be a property of every aspect of the cosmos? Two different things can be infinite without one necessarily being an attribute of the other.

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if infinity had more than one dimension, each of the dimensions would have to be all of the others...
Why?
« Last Edit: 29/05/2013 18:18:45 by dlorde »

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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #74 on: 29/05/2013 18:11:49 »
Dlorde, thanks for your response.  One of the great things about being able to share ideas is that others usually think of things in a different way and add new perspectives.

Sorry you found the last post "confused and confusing".  I've just had a look back through it, and I agree on both counts, although much less so if it is taken in conjunction with preceding posts. 

As I mentioned, these posts are pulled together from scattered notes.  It would undoubtedly have been better if I had spent more time organising them, but time is a bit short.  There should be one more "Part" to come, which may touch on some of your questions, but I will address each of them separately, anyway.   
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Offline Pmb

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Re: What is your interpretation of quantum mechanics?
« Reply #75 on: 29/05/2013 18:58:27 »
I was wondering if anyone here has read The Philosophy of Quantum Mechanics: The Interpretations of Quantum Mechanics in Historical Perspective by Max Jammer (Dec 3, 1974)? I was told my a physics historian friend of mine that it's an excellant book on the philosophy of quantum mechanics. If you're really interested in this subject then this is a must read on your list of books to consider buying and reading.

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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #76 on: 29/05/2013 19:06:23 »
Looks interesting; the question is how to find a copy...

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Re: What is your interpretation of quantum mechanics?
« Reply #77 on: 29/05/2013 21:35:12 »
There's one on Amazon UK at a little over £790! I think I might try the local Library.
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Re: What is your interpretation of quantum mechanics?
« Reply #78 on: 29/05/2013 22:49:37 »
The Infinite Cosmos      Part 6        (Final Part)

What happens in infinity?  Popular science books often point out that, in eternity, everything that can happen, must happen.  Few, if any, take this to its logical conclusion.  Because there can be no succession of events in eternity, everything that can happen, and must happen, must be now.  Even the assertion that it must be happening now is misleading, because, to say that something is happening implies that it is undergoing a process of occurring, which requires a passage of time.

  Consider events A, B and C.  In linear time these might occur, one after the other, in that order.  In eternity, though, they would all be present together.  There could not have been a point in eternity when, for example, A had happened, but not B or C.  The whole of eternity must contain A, B and C, in their entirety, for all eternity.

If the past - the period up to now - is infinite, then A, for example, has already happened, an infinite number of times, as have B and C.  What sense does it make to claim that, because they occur in the sequence: A- B- C, there must have been a point at which A had happened more times than B or C? 

If that were the case, it must be that if we had selected a point in the past as our "now", there would have been a chance that we opted for a point at which A had happened more times than B or C.  This would mean that they had not happened an infinite number of times.  Manifestly, this is not possible if the past is infinite, and if in infinity everything that can happen must happen an infinite number of times.

  It is not possible to envisage a “part” of eternity that does not contain everything that is contained in eternity.  I have been using the term “eternity” rather than “infinity” in order to stress the “everlasting” aspect, but we must not lose sight of the fact that it is only our time- and space-bound perception that persuades us that we should distinguish between space-like and time-like infinities.  What applies to eternity applies equally to infinity.               
 
We started by trying to apply rational thought to the origin of the cosmos and the position that our Universe might occupy within that cosmos.  We are still left with one fundamental question:  Is there any way in which we can work out whether our Universe was created, or whether it is simply part of an eternal cosmos?  First, we have to ask if the cosmos was created, or if it is eternal.

If the cosmos was created, it must form part of the infinite realm of the creator.  As discussed above, this implies that it has always been part of that realm; it, too, is eternal.

If the cosmos is eternal, and the Universe forms part of the cosmos, it follows that the Universe has always been part of the cosmos; the Universe is also eternal. 

We seem to have reached a juncture at which we are saying that arguing about whether or not the Universe was created is totally pointless.  If there can never have been a time when there was nothing, something must be eternal, and therefore infinite.  Our Universe must be part of that infinite something, and therefore, according to the above reasoning, must be infinite. 

Now I seem to be arguing that the Universe is finite, and infinite, at the same time.  The logical way round this must, surely, be to assume that the Universe, and the whole cosmos, are infinite, and that our perception of differentiation of space, the “passage” of time and of any change is simply an illusion resulting from our very restricted viewpoint. 

We should look briefly at the idea of the holographic universe.  What is the holographic universe?  Does it imply that the Universe is a hologram?  I shall assume sufficient knowledge of holograms to make a description unnecessary.

When scientists, such as David Bohm, and authors, such as Michael Taylor describe the Universe as a hologram I very much doubt that they are suggesting that some other-worldly being is projecting laser images with an incredibly gigantic projector to produce what we experience as the Universe.  I suspect that it would be more appropriate to say that the three-dimensional images we can produce with laser technology are as near as we can come to producing an effect that, to some extent, mimics the way in which our Universe works. 

The kind of holographic image with which most people are familiar is that which is viewed by reflected light and produces a very limited three-dimensional image when observed directly.  However, the kind of holographic image that is of interest in terms of the holographic universe model is that which is not directly observable simply by looking at the plate on which it is captured.  Viewed by reflected light the plate seems to contain only vague, swirling the marks of interference.  The true image can be seen only when the plate is illuminated by transmitted light.  The image then stands out from the plate, forming a three-dimensional image that can be viewed from any angle.  The object may appear real, but any attempt to touch it will reveal that it is not there, it is simply a product of the ability of our brains to interpret electromagnetic frequencies.  One remarkable thing about these holographic plates is that if you cut one in half, each half will produce the same, complete, image.  In fact, how ever many times you divide the plate, each fragment will produce the whole image.  Only the quality of the reproduction will deteriorate as the fragments get smaller.  The best explanation for this must be that the entire image is contained in every part of the plate.  It is this quality of the holographic image that makes it particularly significant in the context of a possibly infinite universe.  If our Universe is actually infinite, then the entire Universe is contained in every atom of what we perceive as a collection of divisible entities.  William Blake’s “….World in a Grain of Sand” is no longer just poetic imagery; it is a small step towards seeing things as they really are. 

When we talk of the holographic Universe we are suggesting two things.  The first is that, as with the holographic images produced by lasers, it is our brains that interpret the “frequencies” of the Universe to produce the images we see and the reality we perceive around us.  The second point is that every part of the Universe is, in a very real sense, the whole Universe, “….and I am that”.     

Sighs of relief all round - it's over!   Later I'll try to tackle some of the questions.   


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Offline Pmb

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Re: What is your interpretation of quantum mechanics?
« Reply #79 on: 30/05/2013 05:50:42 »
There's one on Amazon UK at a little over £790! I think I might try the local Library.
If they don't have it ask them about an inter-library loan.

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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #80 on: 30/05/2013 13:46:46 »
Popular science books often point out that, in eternity, everything that can happen, must happen.
It's not quite as simple as that; it depends precisely what you mean by 'can happen'. There may well be possible states for a system (e.g. the universe) to be in that cannot be reached by any stepwise change or progression because there is a dependence on priors (see Does Everything Possible Have To Happen?).

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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #81 on: 30/05/2013 23:39:20 »
Quote
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 seems that, in Part 4, I didn't cover the reasoning behind the opening statement of Part 5.   My bad!

" 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.  However, let's stick with it for the time.

" You can paint a line across it and divide it into two infinite lengths,"

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?

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Re: What is your interpretation of quantum mechanics?
« Reply #82 on: 31/05/2013 02:07:46 »
Quote
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.

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. 
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Re: What is your interpretation of quantum mechanics?
« Reply #83 on: 31/05/2013 02:33:33 »
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?
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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #84 on: 31/05/2013 10:56:38 »
" 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.
Well of course. All discussion about infinity is either mathematical or thought experiment. 

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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.
That's a semantic straw man. An infinite extent can start wherever you like. Consider the integers, or the real numbers; consider Hilbert's Hotel.

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It was not my intention to get into etymological discussion, but you rather invite it in your comment about time.  :)
I don't follow you - which comment and how is it relevant?

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"..... 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?
I didn't say you will reach infinity, simply that you can repeat the operation an infinite number of times in either direction. Consider the integers as an analogy for the road. You can move in the positive and negative directions, 'marking' every 5th integer to infinity in either direction. You'll get an infinite number of finite sequences of 5 integers. You might also consider that between every pair of integers there is an infinite number of real numbers. The integers are countably infinite, the reals are uncountable; the positive integers make the smallest ordinal infinity, the uncountably infinite real numbers are a bigger ordinal infinity. It's fascinating stuff.
« Last Edit: 31/05/2013 11:14:53 by dlorde »

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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #85 on: 31/05/2013 11:04:06 »
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.
What's wrong with 'timeless state', or '4D block'? I sometimes use 'Parminidean block universe', because it's a reminder that these ideas are ancient, but it's a bit clumsy and can sound pompous. When you stand outside time in this way, you need to look at time as just another dimensional axis; 'now' and 'then' and 'future' and 'past' are points and directions relative to observers on that axis.
« Last Edit: 31/05/2013 11:13:40 by dlorde »

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Re: What is your interpretation of quantum mechanics?
« Reply #86 on: 31/05/2013 11:11:09 »
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".
Not really. It's main point is that not all possible states of a system will necessarily occur even given an infinite time. That's why I linked it.

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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?
It just took a particular example that used gravity to illustrate the point; in that hypothetical universe familiar laws applied (surely it would only confuse matters to try and illustrate a point with totally unfamiliar physical laws?).
Is there any reason to suppose that the physical laws familiar to us would not operate in a universe of infinite extent? As far as I know, we still have no definitive evidence that our own universe isn't infinite in extent beyond the observable horizon.
« Last Edit: 31/05/2013 11:12:54 by dlorde »

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Re: What is your interpretation of quantum mechanics?
« Reply #87 on: 01/06/2013 02:24:24 »
Quote from: dlorde
Well 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.

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That's a semantic straw man.

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.

I recall that a few years ago I wrote some notes about the Hilbert hotel.  Unfortunately I can't find them at the moment.  However, my recollection is that it is a clever mathematical illusion. 

Time has caught up with me again, but I'll try to pick up the thread tomorrow.  Sorry that responses are rather bitty, but that's how things are at the moment.
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Re: What is your interpretation of quantum mechanics?
« Reply #88 on: 01/06/2013 14:36:03 »
Quote from: dlorde
Well 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.
By pointing out that it's either mathematical or thought experiment, I was emphasising the point that they are abstractions and not (necessarily) real-world considerations. But, whatever.

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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. Coincidentally, I'm currently on a short course at the University of Cambridge, on 'Philosophical Paradoxes', and we've just had a session on paradoxes of infinity. In particular, talking about Kant's paradox that there are compelling arguments both that the universe must be infinite in time of existence (the requirement for 'sufficient reason' for starting at some point), and that it cannot be infinite in time (this would make the present the end of an infinite series of events, and an infinite series cannot be completed). Much of the discussion of the second argument involved the choice of starting point for infinite sequences, in time (events), spatial extent, and in numbers (e.g. the positive integers start at 1 (or 0) and extend to infinity in unit increments; there is a lower bound, but no upper bound). We had no problem with starting points for an infinite series, sequences, or extents. Nobody suggested that they necessarily corresponded to any real-world contexts, these were all metaphysical abstractions, thought experiments.
« Last Edit: 01/06/2013 18:42:08 by dlorde »

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Re: What is your interpretation of quantum mechanics?
« Reply #89 on: 01/06/2013 17:26:14 »
sounds fun dlorde. And on a totally unrelated question made by Pete. Try to search on < 'jammer.pdf' Max Jammer > for a taste. Not that I would advice anything more than a search naturally, but I did find something from that book in the middle of the search.
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Re: What is your interpretation of quantum mechanics?
« Reply #90 on: 02/06/2013 04:02:18 »
Quote from: dlorde
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

I couldn't have put it better myself. :)

Unfortunately, it is quite common to see the surface of a sphere referred to as infinite.

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

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

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

In maths and philosophy reality can be ignored.

"Gradually mathematicians lighted upon a new concept of existence.  Mathematical ‘existence’ meant only logical self-consistency and this neither required nor needed physical existence to complete it.  If a mathematician could write down a set of non-contradictory axioms and rules for deducing true statements from them, then those statements would be said to ‘exist’."    John D Barrow.
 
Enjoy your course.
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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #91 on: 02/06/2013 08:56:23 »
Since directionality is subjective, what sense does it make to talk of being able to start an infinite series?
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); likewise the negative integers are an infinite series starting at 0 (or -1). Why should starting an infinite series be a problem?

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Enjoy your course.
Thanks, it's been good so far...

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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #92 on: 02/06/2013 23:06:00 »
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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?


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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #93 on: 03/06/2013 16:44:42 »
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.
As I said, it's the start of an infinite series. Just as 3.1415... is the start of the infinite series of digits that is the decimal representation of pi.

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There are two problems here:

1.  There is no such thing as an infinite series.

2.  There is no such thing as infinite time.
I wouldn't mention 1. to a mathematician, they use infinite sequences and series all the time. Archimedes had a method for summing a decreasing infinite series before 212 BC; that task is now done with calculus. Perhaps you're taking the Aristotlean/Intuitionist view that infinities are potential rather than actual? 

Statement 2. is debatable - that's what Kant's paradox is about - he argued that logically, time both must be and could not be infinite. But he used separate arguments to do so.

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

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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 don't see it; how?
« Last Edit: 03/06/2013 16:58:22 by dlorde »

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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #94 on: 04/06/2013 21:57:47 »
Quote from: dlorde
I wouldn't mention 1. to a mathematician

Too late!  as far back as the late 1960s, when I worked in a residential school, I had several discussions with the maths teacher about infinite series.  Eventually he conceded that although the infinite series was a valid mathematical concept, with which I have no problem, the concept was not valid in the real world.
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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #95 on: 04/06/2013 22:46:22 »
One of the problems with long posts, especially multiples of long posts, is that people are inclined to skim over them, or even lose patience and not read them.  I am ashamed to confess, I sometimes do that myself when time is very short. 

We may have to be more selective in our points, and work towards added clarity, if we are ever to get anywhere with this.

Perhaps we could start with an opinion from any interested poster on the following:

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?
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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #96 on: 04/06/2013 22:53:37 »
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?
As I understand it, yes.

However I would much prefer that you outline your arguments to support statements 1 and 2 than go through some Socratic dialogue; perhaps the dialogue could follow the arguments so we know what we're debating.

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Offline Bill S

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Re: What is your interpretation of quantum mechanics?
« Reply #97 on: 04/06/2013 23:46:20 »
Quote from: dlorde
Do you have any argument to support assertions 1. or 2. ?

Let's start with an extract from "Part 5". If you can't find what you want we can progress from there:

"
Consider Cantor's infinities: the whole numbers constitute an infinite series, so do the even numbers and the odd numbers.  Thus, Cantor demonstrated that, not only were there numerous infinities, but they were not all the same size.  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?  There seem to be at least two reasons why this cannot be the case.  The first is that 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.  The other is that, practically there is the complication that 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.

Wikipedia says:  " In mathematics, "infinity" is often treated as if it were a number (i.e., it counts or measures things: "an infinite number of terms") but it is not the same sort of number as the real numbers. In number systems incorporating infinitesimals, the reciprocal of an infinitesimal is an infinite number, i.e., a number greater than any real number. Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes (called cardinalities).[2] For example, the set of integers is countably infinite, while the set of real numbers is uncountably infinite."

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"."
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Offline dlorde

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Re: What is your interpretation of quantum mechanics?
« Reply #98 on: 05/06/2013 11:09:24 »
... It is evident that the infinity containing the even, or odd, numbers must be half the size of the infinity containing the whole numbers.
You may think it's evident, but what is intuitive isn't necessarily correct. The definition of an infinite set is that any proper subset has the same size as the whole set. The elements of the subset can be mapped one-to-one with the members of the whole set.

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

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... 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.
I don't know whether Cantor used the set of all infinite sets in his calculations (do you have a source for this?), but there are an infinite number of infinite sets, so it must be a mathematical infinity. What is your argument that it is not?

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...anything that is truly infinite must contain everything; there cannot be two infinities, because each would have to contain the other.
What precisely does the truly in 'truly infinite' mean? It is generally accepted that there are multiple infinite sets; e.g. the real numbers are infinite, the whole numbers are infinite, neither set contains the other. If you introduce your own concept of 'truly infinite' that way, you're not talking about the same thing; and I don't see how it has any coherent meaning - can you explain? 

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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.
That simplistic version of the Reflection principle is clearly self-contradictory for all classes of universal sets, and so is useless in that form. A description of a non-contradictory formulation is given here: Motivation for reflection principles.

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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".
Another custom infinity... so what does the qualifier 'absolute' mean in this context?

Infinity is a particular kind of unboundedness, it doesn't require 'more' than that.

Cantor himself defined an Absolute Infinite as that which transcended the transfinites (all other infinities). He said:

"The actual infinite arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the Absolute Infinite or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type".
 
For him it was a kind of mathematical deity, possessing a reflection principle that every property of the Absolute Infinite is also held by some smaller object. Personally, I think this is a step beyond the coherent, but I'm no set theorist.

Was that what you had in mind? if not, what? and is your 'absolute' infinity different from what you call 'truly' infinite? if not, why use two names for it?
« Last Edit: 05/06/2013 11:12:45 by dlorde »

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Offline lightarrow

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Re: What is your interpretation of quantum mechanics?
« Reply #99 on: 05/06/2013 22:37:17 »
It should take infinite time to reach the end of an infinite series. 
I can do it in a finite time, and I can even prove it.