[lightarrow]

But if the light beam is made of single photons, a photon's wavefunction doesn't collapse after having passed through the glass prism, so that "interaction" is not a "measure" of the quantum state of the photon (in particular, of its frequency).

If you read Feynman (QED pp.101 & 107), you'll see he explicitly describes the scattering interaction as the photon being absorbed by an electron and a new photon being emitted. If you prefer the wavefunction collapse interpretations, the absorbed photon's wavefunction clearly must collapse. There is a probability amplitude for photons to pass through the glass without interacting, but for the observed refraction, the scattered photons are also required.

As already mentioned, the frequency of the light doesn't change, but its phase velocity does (depending on frequency). The use of 'measure' in physics generally refers to an observation (collapsing the wavefunction if you like), but in QM, any interaction has this effect, so 'measure' is the subset of interaction that involves observation. That's all I was saying.

I don't have Feynmann's QED available in this moment, so don't know what he means, but let me contest your interpretation. If that were a qm measure, why you can't say which is the photon's energy after coming out of the prism?
(As you know, infact, the photon's wavefunction is still in the same superposition of frequencies which had the photon before entering the prism).

--
lightarrow

[lightarrow]

Yes Lightarrow To me it's a question of what 'reality' should be seen as. The first thing I would like to measure is if the photon would differ for passing that glass. If it won't, then that need a explanation, as I would from my first definition expect anything meeting another object to interact, especially if passing through it.

The photons which enters the prism is not the same as the one who comes out, but in a very subtle way; the photon which comes out has now frequency entangled with its direction: if the detector detects the photon at a specific angle, then its energy is specific (larger angles = larger frequencies) but *you can't say the photon's energy before detecting the angle of arrival of the photon*, so its wavefunction hasn't collapsed after coming out of the prism.

[CD13]

Bill S,

Thanks for the arguments. It seems that until we can understand infinity (and I mean understand, not describe), we'll always be like ants thinking that our bit of the nest is everything,

As a scientist myself, I can understand the frustration this may bring. At the age of eight, the annoyance of being told by schoolmates that the highest number in the world can be beaten by the highest number plus one is still a vivid memory. Cantor's work was impressive but it reminds me of the school playground again.

[CD13]

Bill S,

Oh, and another thing.

If the cosmos or multiverses are infinite, surely there must be a infinite amount of information/knowledge. So our partial knowledge will always be zero. Yes, I know you can't divide by infinity but you know what I mean. So I know as much now as I did when I was eight.

[Bill S]

So our partial knowledge will always be zero.

Mathematically our partial knowledge would be zero, but there must be another way to look at it, because if you apply the same reasoning to matter in an infinite cosmos, then our "share" of that matter must be zero - yet we are here.

My protracted ramblings should - I hope - reach that alternative, I just hope others have the patience to stay with the animadversions of an old codger long enough. 

[dlorde]

Want to expand on that one dlorde?

Sure, you can read it in Feynman's own words HERE (page 107). If you need to get up to speed on his summing of probability amplitude arrows approach, start from the beginning of Chapter 3, 'Electrons and their Interactions' (p.87). He explains it more clearly and precisely than I ever could.

[dlorde]

If that were a qm measure, why you can't say which is the photon's energy after coming out of the prism?

If it was a measurement, you could know. Like I said, measurements are the subset of interactions where an observer is involved. All measurements are interactions, but not vice-versa. If an interaction occurs unobserved, you're not going to know the energy. If you arranged things so that you captured the scattered photons, you could measure their energy.

As you know, infact, the photon's wavefunction is still in the same superposition of frequencies which had the photon before entering the prism).

The way I read it, the wavefunction describes the quantum state of a particle. Feynman explicitly says (with italicised emphasis) that the scattered photon is  a new photon, which means a new particle wavefunction (with the same frequency probability amplitudes as the incoming photon, but different in some other respects). From the point of view of the system of including incoming photon, electron and scattered photon, it's all part of the same evolving complex wavefunction that describes that system. Whether the wavefunction of a particle that persists through the interaction, e.g. the electron, collapses at the interaction would depend on your interpretation - go with Wigner and it doesn't collapse until a conscious observer (e.g. 'Wigner's Friend') 'observes' it; go with Objective Collapse interpretations, and it collapses when the system superpositions reach a certain complexity or size, etc.; go with Many Worlds and it never collapses, it just looks that way to an observer.

It's worth noting that Feynman doesn't mention the collapse of the wavefunction in his discussion of refraction, he deals only with the probability amplitudes of various actions. He'd probably say the interpretation doesn't matter if you can work out what happens without it (and you can).

I'm happy to take corrections and adjustments to my description if they correspond to my understanding of Feynman's description, or explain where my understanding of Feynman's description falls short.

[Pmb]

If it was a measurement, you could know. Like I said, measurements are the subset of interactions where an observer is involved.

I have some problems with the notion of an observer being involved. One has to define "observer" and I'm sure that we can all agree that the universe existed before observers where here and that life existed before it knew how to make an observation.

[yor_on]

I had the same problems Pete, in the end I found the best way to be to think of it as relations, and define them as 'observing' each other. That way you can add whatever you like to it, as long as it introduce something new, be it a measurable change or just something changing the relations I thought I knew before finding it. And a consciousness it just one more relation as I think, slightly differing in that it discuss 'free will', so becoming 'indeterministic' to me. Although that one is discuss-able depending on how you define chaos, probabilities, and randomness.

As well as what we find to be statistics naturally. Without statistics existing, and provable, to give us the logic, binding a past to a present, enabling us to predict a future, I wouldn't expect us to find a logic order (causality) to anything. Although maybe there is some other way to define it? But I still expect statistics to be the ground for defining it otherwise. What I mean is that we might not have thought about it this way in Newtonian society, as that was a 'clock work' universe presumed to be 'finite', but behind that we now find statistics, as I think

But everything is parameters, and it will be you that define them, depending on what you find yourself knowing at that time.

[dlorde]

I have some problems with the notion of an observer being involved. One has to define "observer" and I'm sure that we can all agree that the universe existed before observers where here and that life existed before it knew how to make an observation.

That's my point; interactions happen regardless of the existence of observers (which usually refers to consciousness, even if there is an intermediary device). There's no reason for special pleading for consciousness. So a measurement is just an interaction that has meaning for an observer. If interactions collapse the wavefunction, then a measurement will do so; if interactions don't collapse the wavefunction, then neither will a measurement. Or so it seems to me.

All assuming 'measurement' doesn't have some other meaning I'm unaware of.

[David Cooper]

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.

[Bill S]

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!      

[dlorde]

...  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?   

[dlorde]

... 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.

[lightarrow]

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).

[dlorde]

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.

[David Cooper]

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.

[Bill S]

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".

[yor_on]

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.

[yor_on]

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..