A Conversation for Wave-Particle Duality

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Post 1

Googolplex O'Shea

I am new to this system and perhaps in ignorance of how it works at a socio-political level would ask the following question, was the article written, 'tongue in cheek'?

The 'Double-Slit' experiment is perhaps the key issue/mystery that has spawned Quantum Theory. The Wave Particle Duality is NOT like tiny snooker balls travelling through space in an undulating fashion as intimated by the graphic associated with the article. Wave Particle Duality is the central mystery of the enigma that is Quantum Mechanics. Quantum Mechanics is the set of theories and principles associated with the very small and quantum effects only happen to particles that are smaller in mass terms than the Planck Constant. Its importance in Physics terms is paramount in the sense that Physicists know what happens within the experiment given certain circumstances however; they do not why it happens. Whilst Hawkings' 'Brief History Of Time' is a superb introduction to modern physics it is painfully clear that this subject is not fully explained with the due importance that it deserves and that perhaps even Hawkings himself was, at the time, as reluctant as Einstein always was, to believe that apparently 'God plays dice?'

There are a number of 'popular' theories that attempt to explain the behaviour of the Quantum world. Simplistically and in my own no doubt wholly inaccurate terms I see them as follows:

The Copenhagen Interpretation (Nils Bohr) suggests that a Probability Wave is present in what I will term sub-space (therefore not subject to E=MC^2) and it is observation that causes a collapse of that wave function to form reality from a particle that until that point exists in a super-position of states (like Schrodinger's famous cat). If we test or observe for waves then waves appear. If we then test for particles we see particles. It is the observer that causes the wave function to collapse. The wave function collapses in line with probability such that if we tested a particle for being an elephant it would not instantly transform into one just because we were looking for one. The theory taken to an extreme would ultimately suggest for the Universe to exist there must be something observing it from the outside and although a personal favourite of mine, it is 'probably' floored.

The Many Worlds Theory (David Everett) postulates that with each quantum change another Universe is spawned which runs parallel to the others with only the exception of that quantum difference. Clearly, Many Worlds Theory is suggesting a cosmological number of alternate Universes all running parallel to each other. There can be no physical contact with alternate versions of yourself in other worlds but in theory the principle could be utilised to build a device that could utilise the other world possibility to multiply it's effectiveness. Imagine a computer that could execute instructions simultaneously in several different worlds and correlate the results from each of the many world copies of itself! Theses Many Worlds would range from being minutely changed to almost completely changed, as differences would increase exponentially as particles interact in different ways over time. Is there a many world somewhere where Einstein was a Monk that sat on a pole on for 40 years and the Dalai Llama was a renowned physicist? Probably!

Whilst the mathematics would suggest that either of these two theories is 'possible' there is another more recent theory known, I think, as the Transaction Theory (John Cramer) that suggests particles radiate quanta that travel both forwards and backwards in time (possibly a tachyon!) to arrange the transaction with themselves in the past. There is an offer wave and an acceptance reply wave through the dimension of time setting up both the emitter and absorber particles for a net radiation of zero. The mathematics and indeed, the overall view of Transaction Theory is neat and tidy incorporating and in some ways explaining even obtuse questions regarding the direction of the arrow of time, the removal of the need for intelligent observers to form reality and the immense staggering numbers of many world copies that I still find somewhat difficult to accept. It also answers the mystery of the 'Double-Slit' as the transaction is formed in knowledge of the entire experimental set-up both in physical and time terms.

In summary physicists use the 'Quantum Cookbook' (do this and the result will be that but, don't ask us why!) to develop ever increasing technological developments and theories as to why the Universe is apparently the way it is however; the reality of modern physics is that they are all still scurrying around looking around for definitive answers and the irony is at the moment the more they look, the more they find to ask further questions about...

I would be very grateful for feedback to further assist my understanding!

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Post 2


Not sure I can help with understanding but I have a few thoughts.

It seems to me that wave/particle duality and quantum mechanics represents a failing in our mathematical methods rather than a deep metaphysical observation on the underlying nature of the universe.

My suspicion is that these problems arise from our use of a continuously variable number system and the mathematical constructs that this gives us. I don't have the education or wit to elucidate what a replacement system should be but I suspect that a system based on unitary integers would generate a very different mathematics.

The description of a wave like phenomena would be markedly different without continuously variable numbers as would the description of the properties of a particle - perhaps they would turn out to be the same thing!

Quantum mechanics, particularly quantum electrodynamics (QED), has been supremely powerful as a predictive tool, but it has been equally useless as an explanation of what is really going on.

An analogy I have heard relates to 2 people at the cinema:

One person asks the other to describe somebody sitting in front of them, 'they are in seat 12, row G of the stalls and wearing a brown hat'. 'What else can you say' asks the first, 'if they move forward one seat they will be in row F, if they move right they will be in seat 13 and if they swap hats with the person on their left they will be wearing a green hat'. 'But you've told me nothing about the person' presses the first, 'QED!' is the reply.

This is what I think quantum mechanics boils down to - a mechanism for juggling numbers to predict other numbers using a series of imperfect tools. If what I'm observing isn't explicable using a particle model then use a wave model as that seems to fit better. What we need is a mathematics that inherently expects waves to be lumpy!

Sorry if this is a bit random but I'd like to discuss further if you're interested.

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Post 3

Googolplex O'Shea

I am not entirely clear about the notion of changing the nature of mathematics. I would be terribly grateful for a more detailed account of your view.

For each element or theory of physics there is a mathematical description. The theories are not accepted as factual until the mathematics prove the theory. The areas could be viewed as mutually exclusive?

Bearing this in mind there are a number of theories that explain the basis of Wave-Particle Duality and each has an adequate mathematical proof. Whilst there have been a number of horrendous errors in mathematical proofs (von Neumann's proof of the non-existence of hidden variables) there has ultimately been a way of explaining each theory in mathematical terms. Indeed, Quantum Mechanics was named after using a little known and largely forgotten branch of mathematics, matrice mechanics.

Which came first? The theory or the mathematics?

Having said this you may be totally correct! Without the tools to accurately describe reality we can never know what the true description should look like. I am suspicious however that any notion can be explained mathematically using the tools currently available. The accuracy of QED in describing the quantised effects of electro-magnetic radiation were subject to re-normalisation (described by Feynman himself as a trick) to remove infinities for single electron activity. Hawkings and Penrose have used Imaginary Time (another mathematical trick to remove the infinities created by their early equations) as proof of their theories on the Big Bang.

Evidently, there is always a way but perhaps that is a classical view? Do explain your ideas, you maybe the new Maxwell or Dirac?

I can recommend QED (Feynman), The Ghost in The Atom (Davis & Brown) and by way of introduction, Schrodinger's Kittens (Gribben) as excellent further reading on the Wave/Particle Duality mystery.

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Post 4


Is this the same Googolplex O'Shea that also joined the thread relating to multiple observers and HUP?

In answer to your request for more detail - I'll try:

Our numbering system is old, from a time when technology couldn't dip very far beyond the limits of our senses. It very accurately describes what we can see and make sense of. As Technology improved it still held true and we became more sophisticated in how we used it.

Put simply, our number system allows us to always interpose a new value between any 2 existing values. Measure the length of a stick, cut it in half and measure it again, continue to cut and measure and you will always have a value of length for the stick. We escape from the recursion by allowing for infinity, in this case infinitely small.

However infinity can always have another 1 added. This is the first place where I think our number system falls over, ie. we have to allow for a construct called infinity but we cannot provide any logical definition for it. Many branches of mathematics rely upon infinity as a mechanism to tie up the loose ends, in reality we are saying that we don't know what happens this far out but the effect is very small and we can stop worrying about it.

In geometry we start from a euclidian view of a point, an object of zero extension in any direction. If we extend it orthogonally we get a line, extend that orthogonally and you get a plane etc etc. This gives me a real problem as I cannot see how a point of zero extension can ever be multiplied to give give a line of length n. There are an infinite number of points in a point of zero extent, if you double it you still have zero extent but twice as many points. Something has to happen to give a point a finite length.

The same applies to all the transformations, a line has a finite length but no breadth, how does it gain the first infinitesimal hint of breadth such that it can be multiplied up to become a plane?

These fundamental constructs in numbering and geometry are used to build a self consistent body of mathematics that in reality very closely defines exactly what we find in nature providing we don't get too close, ie. it works pretty well down to an atomic level and in certain respects at a subatomic level.

QED is very successful as a predictive tool because, in my view, it attempts to do no more than provide a number cruching mechanism. Maybe it's a bit like Log tables, feed the numbers in, follow the rules and an answer will pop out, for 'O' level maths (in my day) that's all you needed. The analogy falls over when you get a bit further and you can see why Log tables work, at the moment we don't know why QED works.

I think that our fundamental assumptions about numbers and geometry are wrong. There is no such thing as a dimensionless point, the fundamental unit of geometry is a line of finite (small) length and breadth (I like string theories as you might suspect). I also think that we should investigate a number system that actually has an upper limit (big), ie. infinity has an absolute value and thus, that we cannot subdivide beyond a certain level.

In the mathematics of physical systems we should not allow arbitrarily small intervals of time, length and mass. These should be quantised and we should deal in integer values of these units. As I mentioned in the earlier post I do not know how to start this but I suspect that such a change to the fundamental elements of mathematics would yield equations describing wave effects, and almost anything else, that are radically different from those we use today.

Is this all complete drivel, or does it make any kind of sense?

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Post 5

Googolplex O'Shea

No, this is not drivel at all! It does make sense and your examples are well taken.

It seems to me that in some ways physicists and mathematicians agree with your ideas and as previously stated although, I again failed to make it entirely clear, infinities indicate an incomplete proof and are rigorously removed using various mathematical tricks. Introducing theses tricks appears to be a slightly less radical suggestion than yours which, correct me if I am wrong, is to design a system which simply does not allow infinities, period.

I remain unconvinced by this approach and fear it may prove restrictive. The equation that throws out infinity is the one that often generates the most interest and consequently is solved using a new combination of existing methods (or a trick?).

I suspect we may be moving toward a philosophical discussion regarding the state of mathematics and how it is insufficient in describing an apparently random Universe from the simplest of sub-atomic particles to the vastness of cosmological entities? I err on the side of caution and see reasonable advances utilising existing methods even though I entirely agree they are by no means the ultimate in mathematical systems.

Whilst I have understood your posts fully I am by no means a mathematician but, and at the risk of going even further off the subject, have you read the Complexity Theory Guide Entry? Is it just me or can that opening line in the Entry be more totally and utterly wrong? What the opening line in the Entry describes is the concept of Chaos and it's associated theory area, non-linear dynamics. Complexity Theory is concerned with the same subject but from the diametric opposite end of affairs, namely, that complex systems tend to exhibit simple or emergent behaviour. Could Chaos offer a way to satisfy some of your ideas yet remain in the realms of conventional number systems that maintain incompleteness indicators such as infinities? Chaos paradoxically ascribes in some ways a probabilistic view of reality and that ties neatly in with the Copenhagen Interpretation, which clings, to idea of a probability wave collapsing wave functions to form reality in line with perception. Philosophically therefore, is the true nature of reality determined those observing it because the observer is actually a part of the same system?

Are we back to where we started and if so what are the chances of that?

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Post 6

Dad n Dave

A number of these thoughts I have expressed more fully in the sister thread to this on "Does matter exist and does it matter". I will try to paraphrase some here.

To me the underlying reality of what we perceive to be wave/particle duality seems to be one of energy transfer. Energy is being transferred from point A to point B, passing through whatever slits happen to be open at the time. At point B, if we run an experiment to detect a particle then what we do is detect the arrival of energy in a form that we perceive to be a particle. If we try to detect wavelike characteristics, then these too can be measured.

A water wave for example is a means by which energy from the wind (and therefore the sun) is transferred to the sea shore, dumping particles of water. While we perceive the sometimes forceful arrival of a water particle, the underlying reality is one of energy transfer.

I also think that there are some difficulties with our current mathematical system. I suspect that what we perceive to be matter is, in an underlying sense, continuous. This is hinted at, for example, by homeopathy in which infinitesimal concentrations seem able to have a measurable medical effect beyond that of a placebo. Also, particle accelerators seem to be able to find smaller and smaller fundamental particles with greater and greater energy input - would infinite energy locate infinitesimal (ie continuous) fundamental particles? Perhaps a fractal approach would provide a more fruitful mathematical route.

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Post 7

Googolplex O'Shea

Thanks for that input DnD! Most interesting!

I read your other contributions in the "Does matter exist and does it really matter?" thread (like the title!) and I am concerned that you are alluding to an "ether" type theory.

If you are not making this assumption then I apolgise but, if you are, then it's you or Einstein that is right! The Special Theory of Relativity (Einstein 1905) points to the speed of light as the Universal Constant or in other words photons will travel at a constant speed in a vacuum. The Lorentz Transformations complete the picture for establishing the relative motion of an observer in space-time which is not absolute and thus there is no requirement for an underlying "ether" when trying to understand the propagation of electromagnetic radiation. I will not bore you any further with Special Relativity.

I am however; interested in your idea of infinite particles getting smaller and smaller. Can you explain more? Is this String Theory? I have not the faintest idea about String Theory other than it is supposed to be tiny string-like structures all "jiggling" against each other...

I think the most interesting part of Double-Slit and Wave/Particle Duality is the observed behaviour in the sense that the interference pattern appears when the observer is not looking for particles but disappears the instant that he/she does look for particles. How does the wave/particle know it is being watched? Copenhagen comes right back into play I feel but, I definitely need to investigate String and Transaction Theory much more.

How can fractals help in this case? Fractals are part of non-linear dynamics or Chaos concept are they not?

In terms of QED I understand it has now been updated to Quantum Chromodynamics (QCD). I am not familiar with QCD but, whilst I agree to a large extent with JAOB in that QED explains results but not why the result is the way it is, I also believe that QED represents one of the most astonishing advances in human understanding to date. Is anyone aware of QCD and if so how does it improve on the original?

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Post 8


QED is an astonishingly accurate theory and represents a pinnacle of our ability to model physical systems. QCD is similarly powerful but substantially more complex. Both run out of steam pretty quickly when we try to describe a situation involving more than a very small number of particles.

I agree with DnD that the fundamental issue in the double slit experiment is that energy is transferred from point a to point b within the 3/4 dimensions we experience. I also feel that the conundrum the experiment generates is a product of our insistence on mathematical models that derive from our experiential viewpoint rather than from the physics they seek to describe.

I suspect that underlying our perceptions of the world, there is a continuous reality existing in several dimensions, to pick up from H2G2, a mouse is the 3 dimensional extension of a pan dimensional being. In my scenario mass, space, time etc are the 3/4 dimensional extensions of a pan dimensional continuum. String theories tend to view strings as isolated elements, my suspicion is that they are the lattice work of my multi dimensional continuum.

Visual models are great, the sheet of rubber with a ball in it immediately helps in comprehending Einsteins view of gravity. My mental picture is a 3 dimensional array of bedsprings, when you poke it the ripples spread out and interact with other ripples. The points of interaction and the modes of interaction translate, to us lower dimensional beings, as mass, spacetime etc.

Is this getting way off beam? Should we return to a more sober discussion?

Before we do, let me throw in another thought, we have much evidence to support the notion of an expanding universe. Is there any reason why we cannot stand the principle on it's head and suggest that the universe is not expanding but that we and all the 'things' within it are simply getting smaller? I prefer this as It suggests to me a decay back to a ground state of some sort. Think of the universe as an enclosed space with bright sparks within it that are slowly shrinking and fading away.

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Post 9


Many very interesting things have been mentioned in this thread. I find this a little bit surprising because I'm surrounded by people who don't question old theories, they simply use them (eg quantum mechanics).

For me, the most interesting question is whether GTR (Einstein) or QM will provide the next big step. I tend to GTR, mainly because nobody seems to understand QM, but also because QM is strictly linear and thus 'too simple' to explain this rather complex universe. Here your chaos theory comes in.

I could imagine a final theory where continuous space-time plays the unterlying role and all discrete QM effects are explained as an approximation for large scales and large times. So, particles would be waves (of space-time curvature) but rather different from QM waves. Basic properties would still remain however, to explain the effects that we see.

I'd love to see this return to classical cause--effect relations. Nobody understands this quantum jumping around, and more 'first class' physicists dislike it than most people think.

String theory seems to do something like that. However, I don't know much about it (it's supposed to be extremely complicated), and the string concept seems too simple to me. And equally strange. By the way, they don't manage to get something usable from it. For 15 years now.

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Post 10

Dad n Dave

In reference to comments by GO'Sh, I certainly wasn't intending to challenge Einstein. The reference I made to energy transfer through water waves was not intended to be related to the need for a transmission medium for electromagnetic radiation - it was more to do with the limits of perspective. What appears to a spot on a sea wall as the periodic appearance and disappearance of a particle of water is seen from a different perspective of being exactly that .... plus a whole lot more.

On the topic of smaller and smaller particles, I recall a Scientific American article in July 2001 that referred to slowing light to the point it was "frozen". A passing comment was made in this article to the effect that there is such a thing as a 1/400 of a photon. I am not sure of the context now, but it appears to challenge what I suspect is the classical view of a photon.

Regarding fractals, this is yet another one of an infinite number of things about which I know almost nothing. My understanding is that in two dimensions one can create a figure that has finite area but undefinable (perhaps infinite) perimeter. I recall that fractals sidestep some of the difficulties of infinte perimeters in finite areas by reference to a figure being neither 2 nor 3 dimensional, but, say, 2.4 dimensions. My intuition is simply that if we were to view particles and energy as fractals (the licks of a flame, for example, certainly appear to be fractal), then someone much cleverer than I might be able to have some meaningful insights.

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Post 11

Googolplex O'Shea

DnD, do please accept my apols for suspecting that it was an "ether" type scenario you were heading toward.

JAOB, Wow? I need to consider the multi-dimensional bedsprings further before I blunder into some more daft comments I suspect.

In terms of the energy transfer for the Double-Slit experiment can anyone explain the exact context? It seems to me that matter and energy are inextricably linked and to suggest that energy is moving from point a to point b could be entirely correct given a certain view point. What really intrigues me, and I am in danger of becoming boring at this point, is that the wave/particle changes it's behaviour depending on whether or not it is being observed. It would appear that moving toward a solution for this mystery would lead us closer to understanding the relationships of how apparently unique and isolated systems are all part of ever increasingly large systems.

Are humans simply tiny systems among many that are part of a large system, namely the Universe?

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Post 12

Dad n Dave

No need to apologise. Hey, who knows, Einstein might be wrong after all... Perhaps there really is an "ether" out there. Maybe it's dark matter, maybe it's neutrinos (from the perspective of which the earth, you and I practically don't exist).

Naturally I can't answer your query on wave/particles (or any other query for that matter), but I will offer the following thoughts in any case.

I don't think that the wave/particle does change its behaviour depending on whether or not it is observed in any way which requires it to "know" that it is being observed. If you fire a single photon or an electron, what are you actually doing? You are applying energy that radiates from the source. If, at any point along the way, you conduct an experiment that would detect that energy then you could choose an experiment that detects a particle characteristic or you could chose an experiment that detects wave characteristic. It has both.

So, I suspect for example that an electron that leaves a source would not be identifiably the same electron that is detected at a target. The act of detection measures the effect or impact of the energy that has radiated.

Humans as tiny systems? I recall once reading about a phenomenon that I think was termed a solitron - a wave that just kept going and going along a canal in England. Humans, and all matter for that matter, may be like such waves. Energy input into living matter, provided by burning oxygen for example, is enough to keep the wave intact; to grow. And if matter is indeed continuous in some manner, then perhaps we get to Dirk Gently's interconnectedness of all things.

It's a mystery!

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Post 13


Hi there GOSh and DnD - just got back to things. The double slit experiment shows that when electrons are fired through one slit a pattern emerges at the detector of random points bounded by the 'shadow' of the slit - classic particle behaviour. If a second slit is opened the pattern at the detector becomes the classical diffraction pattern one would expect from a wave, the wavelength representing the De Broglie wavelength of the incident electrons.

The conundrum occurs when the electrons are not fired en masse, but individually, they still form a diffraction pattern! How does a single electron 'know' as it passes through a (single) slit that there is another one close by and that it is required to interfere with the electrons that have gone before and maybe those still to come.

I think there are 2 things happening here.

Firstly, our concept of space and time is that things are separated both spatially and in time, this may not be the case when viewed from other dimensions. Consider a sheet of paper - make 2 dots. They are separated spatially, fold the paper so that they are coincident, they now have a spatial separation as small as you wish to make it. The transformation from 2 to 3 dimensions allows physical effects that the 2D flatlanders would consider very odd.

My view is that the 'electron' moves from A to B via another dimension (or 6), we simply see a low level manifestation of this. The transform affects our perception of both space and time, ie. our single electron is actually moving in concert with all the electrons that we perceive as being separated in time and/or space.

The second issue I have is the same as I waffled about earlier. We see a diffraction pattern and say - Aha - I have something that will do that, a wave will do that. When we see the single slit result we say, ah, a particle. Both of these are mathematical models that we have created and, as you know, I think there is a fatal flaw in the way we use numbers. I think we could arrive at a mathematical model that would allow a coherent description of the double slit experiment.

There is an analytical method used by structural engineers to model the performance of buildings, bridges etc. The name completely escapes me (finite cell analysis?) but the principle is to understand how a single cell behaves, elasticity, distortion under stress, strength etc and then aggregate this behaviour to understand how a complete structure will behave. I would be interested in what an impulse (particle) or an oscillation (wave) looks like in this kind of math.

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Post 14

Dad n Dave

JAOB - I think that we are barking up the same tree from slightly different sides.

Unfortunately the maths that I once knew has tended to desert me over the years, so I am unable to offer much assistance in that respect. However, I still feel that the idea of fractional dimensions and viewing energy transfer as a type of fractal phenomenon could be an interesting avenue to explore for those much more capabale than I.

By the way, you might recall my reference to a SciAm article on freezing light. In the letters page of the November issue, some further discussion on this indicates that a photon does not actually go through a material such as glass - the photon has an effect on the material which then causes a photon to be emitted from the opposite surface. At least this is my interpretation of the essence of the discussion. I wonder if this extends to other materials - such as air?

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Post 15

Googolplex O'Shea

Hello Chaps! Been somewhat busy lately but I have missed the ideas and discussion created within this forum.

I think JAOB's description of the Double Slit is spot on and from my perspective is representative of the Copenhagen Interpretation. The particle/wave travelling in a different dimension until a perceived effect is expected. The travelling therefore not subject to any rules (as well as our 3D mathematics presumably?) however; it still leaves the question, why does the particle/wave re-appear in our dimensions when we expect it to? Are we therefore forming reality at a sub-atomic level by simply being?

I am always amazed that the more science looks, the more it finds. For instance I was fascinated to read that a planet has been discovered with an atmosphere. The planet orbits a star over 150 light years away from the earth. It appears to me that anything we set out to find soon appears just as we predicted. Clearly, the advances in technology allow a more in depth explantion of what is around us but it just seems that sometimes the odds of discovering that which we postulate could exist are astonishingly high and yet, sooner or later we find exactly what we were searching for according to our projections of reality. The number of sub-atomic particles rises everyday as more are discovered. We go faster, further and longer with each passing moment but I think until such times as a serious attempt to break into alternate dimensions is made we can never harness the true potential of reality. We chip away in various directions and are rewarded like lab rats with tiny indicators of something far greater that remains hidden. Would a culture of bacteria ever realise that it is a lab experiment?

In terms of a fired particle not necessarily being the observed particle/wave the Double Slit works with the same results in a vacuum. However, again we see "quantum fluctuations" in vacuums whereby matter pops into existence and usually straight out again. There is a theory that the Universe is merely a quantum fluctuation that has lasted a bit longer than experimentally observed ones.


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Post 16


Hi GOSh,
Your latter point is an idea I have some sympathy with. This is why I wonder if we're all simply shrinking away rather than expanding, as a universe that is. The idea of us being a virtual particle in somebody elses universe attracts me a lot as well as the notion that all our particles are universes in their own right.

Hi DnD,
Fractals are fascinating constructs but they represent, to me anyway, almost the perfect expression of a number system that permits infinities as any fractal object has a non integer number of dimensions. In fact the exact dimensionality cannot be expressed as it is a recursive function. Like Pi, all you can do is set an upper and lower bound.

I think things come in absolute discrete lumps, space, time, mass etc etc and this includes dimensionality. For some really weird stuff you should try Roger Penrose and twistor mechanics, these operate in real space and 'imaginary' space and draw heavily upon the math associated with imaginary numbers.

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Post 17

Dad n Dave

Interesting what you say about time (and space etc) coming in discrete lumps. I recall at school reading a poem. Actually I read more than one but this was by a poet who had a thing about time. His name is Kenneth Slessor and the poem was, I think, "Five Bells". He presented different perspectives of time and if I am correct one was time as a continuity and the other he referred to as the "bumpkin calculus of time", which I took to refer to time as a collection of instants that tend to etch themselves into a mind. I think of time (and space) as a continuum but infinitely divisible in much the same way as expressed in calculus.

And then there is the connundrum that the brain sets us in terms of the perspective of time. For example, on hearing a noise in one's sleep, the brain can construct quite a lucid account of how it is that the noise came to arise - sort of projecting backward in time to make sense of the present.

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Post 18

Dad n Dave


Thanks for the reference. Maybe I will understand it some day.

In respect to fractals, I think that the underlying reality for matter is somewhat similar to that for, say, a biological cell.

When we look at cells, we see an integer number of cells. However, as a cell divides we know that there are lots of things happening inside that we can not see. And then the cell becomes two. The underlying reality is that a cell that has just divided is not the same as one that is just about to divide, even though ostensibly they are both one cell and practically indistinguishable to an outside observer. In some sense, it is one cell, then 1.0000000000001 ......1.99999999999 and then two cells. This is why I suspect that fractal mathematic techniques will be quite revealing if applied to physics.

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Post 19

Dad n Dave

Jaob - sorry I got the letters mixed up

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Post 20

Jaziniho ( Tom Green )

i was supposed to be revising for my Chemistry and Physics GCSEs today, instead i seem to have managed to spend most the time browsing through h2g2 reading articles on quantum mechanics and the like. So if i fail my exam i'm going to blame it on quantum mechanics, if quantum mechanics doesn't mind that is.

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