Let "Their" be Light

[Amy]

Whoa, whoa. The universe may be more than we comprehend; it may even be more than we *can* comprehend. But more than we can ever *hope* to comprehend? I think not. Hoping to comprehend the universe is what science is for. Whether it's possible to succeed or not, as Tom Stoppard would say, "It's wanting to know that makes us matter." (Hm, so what makes us matter is energy? )

[kitakaze]

Jennifer,

That's kind of the way I see it too. I don't think light has a wave/particle duality, but we can see wave attributes when we try to measure wave attributes (the double slit experiment) and we can see particle attributes when we try to measure particle attributes (the Compton Effect, Black Box radiation and Pair production for example).

Incidently, those nutty physicists (I have a degree in physics and specialised in particle physics, and I still don't believe or understand a lot of the 'standard model.'

Incidently, Flameboy, the cat in the box, in simple to understand english: put a cat in a box with a random number generator. When a specific condition is met by the number generator, a cyanide gas is released killing the cat.

So, looking at the box, is the cat dead or alive? Quite frankly, you don't know. All you know is the probability of whether the cat is alive or dead. Particle physics says that the cat is 40% alive and 60% dead (as an example), which is why it is difficult to comprehend for us mere mortals.

So with the photon, probability mechanics would assign a percentage chance of the photon appearing in one of the slits, so every photon that is released will hit one band, after the dice are rolled.

Einstein didn't like this answer. He felt the universe was deterministic: if you knew enough of the variables, you could predict the outcome. Probability mechanics and quantum physics says that you can't predict the outcome, and that the outcome isn't even determined until it is observed.

Getting back to the cat. The cat is neither alive nor dead until the box is opened.

I hope that confuses everyone as much as it confuses me. I love this stuff, but it makes my head spin.

For more info on the particle nature of light experiments, see http://www.tri-c.cc.oh.us/metro/faculty/gram/web/quantum.htm

Oh, the answer to this puzzle is, that it is the nature of the experiment, that determines the outcome. It is meaningless to talk about the 'particle nature of light' when you are measuring the wave nature. The light doesn't know you are observing it. It behaves as it should.

So when talking about the double slit experiment, we can't talk meaningfully about photons.

[Ghost Post]

I would like to comment on this just because!

To try and grasp questions (and answers) like these is definately stimulating. However, I find it hard to believe that some of the participants in the discussion actually understands what they are trying to make us (non-physicists) understand. The concept of light existing as some sort of fluid in another dimension (4th or 5th depending on if time is a dimension or not) and only sometimes becoming visible to us existing in the other dimensions, is fine in quantum physics - but isn't it strange, that we never see any traces of this next dimension (or the need for it) in all the rest of reality. Isn't it a foundation in science not to state a fact until it's proven? Isn't the leap to think that there is another dimension to great to make already, when we have so little evidence (if any) of it yet? Isn't it just a remote theory and not the standing point of the majortiy of physicists as someone claimed above?

[Amy]

Well, in the first place, I don't think anyone here stated it as a "fact." It's just a conjecture--a very intriguing one that's worth examining. After all, you have to make conjectures and examine them in order to "prove" anything. And in the second place, the reason I put "prove" in quotation marks is because nothing in science is ever absolutely proven. Even theories we apply every day without questioning them, like universal gravitation, are open to amendment in the face of new evidence. So no, you don't have to prove a "fact" before stating it.

[Ghost Post]

Martin_A.

In a previous incarnation did you also pronounce the world flat?
Before ships the only evidence we had that indicated the world might be round was also light (the Sun and stars in the sky).

-Jen

[Ghost Post]

Martin_A.

In a previous incarnation did you also pronounce the world flat?
Before ships the only evidence we had that indicated the world might be round was also light (the Sun and stars in the sky).

-Jen

[kitakaze]

Martin A does raise a good point, though.

While the theories and models used by science are supposed to be dynamic (that is, change, and evolve as new evidence discounts old theories), often they are taken as immutable (especially by old guard scientists).

It took a long time for the Bohr Model of the atom to replace the old 'raisons in a bun' model.

It took 5 years after the wright brothers flew before most governments and scientific establishments accepted that heavier than air flight was real, and then it took 20 years longer before Scientific American formally acknowledged it.

But, enough rambling. This is off topic for a 'puzzle' board. Though this behaviour is puzzling, since science is supposed to be objective.

[Ghost Post]

Science = Truth?

Newtons Laws of motion are known to be incorrect, yet they are still in common use.

Why?

Because they provide a reasonably good approximation of observed motion, and unless you are sending rockets into space, the errors incurred, due to ignoring relativity effects, are negligible.

The purpose of science is to provide us with models which we can use to predict effects. The models are not the "truth" but are instead human constructions. The models are only valid when they can be used to make correct predictions.

In this way, the dimensions X, Y and Z don't actually exist. They are just mathematical constructions. It would be just as valid to use dimensions A, B and C that are not perpendicular to each other but are instead arranged at some arbitrary angle. Though this would make for more difficult maths.

So you see, light doesn't "really" exist in several dimensions, instead our model of light can be described in our model of the universe to exist in dimensions we created. In this way, we can make predictions that match what we observe in the "real world". It is therefore perfectly valid to add dimensions to our model if it means that the results of the experiment (i.e. photons behaving like waves) can be anticipated.

[Ghost Post]

I think that by the way that the beam is positioned between slits A & B the photons will split up and go off at different angles, bouncing back into separate bars because since they went off at different angles instead of having a beam of light with two gaps in it you get many gaps

[Ghost Post]

Re: insane -- I know that in ethics, at least, I can hold contradictory beliefs simultaneously. Specifically, I do this with what you might call elitism and egalitarianism. I remember just after I learned this trick, reading Auden's "September 1, 1939" (did I get the year right?) and holding both reactions to the egalitarian passage "...the error bred in the bone/of each woman and each man/craves what it cannot have/not universal love/but to be loved alone." This is a terrifying thing to do consciously. Don't try it at home.

[Ghost Post]

To JenniferMarwhit

Yes, I probably would have thought the world flat, and I think so would you have. Back then someone had to gather enough proof to really convince the rest of the scientists that the world really was round. Until then, the common "truth" in the world (!) of science was that it was flat. What I'm surprised to hear is that the majority of the physicists already believe in another dimension (not just as a construction Sean, but real - just like time and physical distance - just not perceptible to us other than in some tiny quantum experiments).

I sense some philosphical tendencies toward the standing point that "we can never know the truth, - because there is none". This is not my view of the world - and I think, not the one of any good puzzler (Not that I therefore is a good puzzler...)

[Ghost Post]

Re: light vs water waves

I think light waves can be explained analogously to water waves. In water waves, we have a fluid which moves around according to the equations of hydrodynamics. Similarly, in light waves we also have a fluid: energy. The entire universe is filled with a soup of quantum vacuum energy. A photon wave is can be explained as an excitation of this fluid. You can create a wave in water by sticking an oar in it and moving it around. Similarly, you can create a light wave by sticking an electric charge in the energy fluid and moving it around. This quantum vacuum is the basis for quantum field theory, a theory pioneered by Feynman and others. In fact, just this year, t'Hooft and Veldtmann received the Nobel Prize for rigorously establishing the mathematical foundations for this theory. Check out www.nobelprizes.com. (I'm computer illiterate so you'll have to type it yourself!)

Interestingly enough, QFT also explains the process of nuclear decay using a fluid of energy. Imagine if you took a glass of water and put it upside down on a table using the ole' dish sliding trick. The glass is inhibiting the 'decay' of this rather peculiar and otherwise unstable arrangement of water molecules. If you lift the glass, the water will of course splash everywhere. Similarly, if you took a nice bundle of energy, say a piece of uranium 235, and stick it in the universe, the energy would eventually be scattered all over the place in various forms of radiation, each type being a different kind of energy wave in the quantum fluid. It takes a longer time, but the energy dissipates nonetheless.

[Amy]

Martin_A: I consider myself a reasonably good puzzler, and I hold to some extent to the relativistic view of "truth." I do not claim that "we can never know the truth because there is none," but rather that we can never know the truth *absolutely* because no truth is absolute. That does *not* mean that nothing is true; it means, rather, that the truth of anything depends on our frame of reference.

Frankly, I see no problem with this. It doesn't mean we can never state anything as a fact; it's just that our facts must be stated with an implied degree of certainty that is less than 100%. 99.9%, in my opinion, is still plenty good enough to call them "facts," but we have to acknowledge that there is a nonzero chance these "facts" will be contradicted by later evidence.

[Steve]

I'm facinated by all this and being a complete physic noviceI see some possible explanation in the concept that a wave has to have a medium. Maybe the photon contains it's own finite medium which transports the wave. If receptors (measuring device, cat .. whatever) actually measure the medium and not the wave then it could explain a lot.

Maybe receptors absorb the medium and if the receptor at the slits absorbs the medium before it is completely split then the wave part of the photon in the second slit is lost as it no longer has a medium.

I don't know if this idea has merit or even sense in terms of quantam physics.

Also has nayone conducted the experiment with the slits opening into separate chambers - and if so what were the results?

[hank]

Okay guys, but I can't resist my explanation for the observed properties of light. I'm no scientist but I was never comfortable with wave-particle duality and in particular, the notion that a photon knows and can anticipate how it is being observed. I remember that Einstein was not comfortable with quantum mechanics and neither am I. I will use his famous equation E=mc2 as the basis of my theory for the model of my photon. Unfortunately I can't prove it, but you may either find some merit to this theory or completely trash it. Please feel free.

A photon is really an undulating blob of energy with undetectable mass. This blob is larger than the distance between the slits so that one photon will transit both slits.The photon recombines behind the slits before completely being separated by the slits. This is important to the theory, because I don't think we want to split the photon(I would anticipate a big bang). All that forward energy, mostly velocity, will take the easiest path. However, when a photon hits a solid object such as a detector in one of the slits, velocity is transformed to mass and the blob contracts. This is when the detector registers a hit. The photon must stay together and the initial impact point of developing mass attracts the remainder of the blob so that no portion of the photon can transit the second slit. The photon can then rebound, turning mass into energy again(The Little Bang Theory).

Now lets look at the recombined photon that has passed the two slits.(Remember this photon has never completely split). Because the photon is its own undulating medium it will exhibit the properties of a wave in an interference pattern. Although distinct dark bands show up on the screen, continuity of the blob is maintained as the blob is 3 dimensional. The first point at which the undulating blob strikes the screen will once again develop mass and draw in the remainder of the photon. Photon strikes on the screen will eventually assemble into lines as the photons arrives in a broad front and the leading point can vary with each photon.
See any problems with this theory?

[AcidFast]

I think that this problem has gotten people to start using their brains in ways we are not used to, and that is what puzzling is all about. If we're ("we" being humans, not Labyrinthians) ever going to solve this problem, it will have to be with thought processes such as these. I feel all warm and fuzzy when I think about it.....or maybe that's the beer.....

Steve: As a matter of fact, there is a school of thought in quantum physics that holds to the theory that the photon carries its medium with it. This is a very interesting idea, but there is probably a school of thought regarding almost every conceivable explanation for this phenomenon. i still don't buy any of them.

Hank: I like your train of thought, hank, but I have a problem with your theory. It sounds to me like you are explaining how a photon (call him "Hal"), can behave as a wave in motion and a particle when measured yadda-yadda, but I think what we are talking about is the fact that Hal can behave like a particle all he wants, and like a wave all he wants, but it doesn't make sense for Hal to be able to predict how we will measure him and then adjust himself accordingly. Or, for that matter, for Hal and his identical twin, Sal, to be able to leave one spot absolutely identical, then become inherently different when we measure them two different ways. In other words, if we measure them differently, they were never identical twins to begin with, but if we measure them the same, they have always been identical.

I think that the most convincing argument I have heard to explain this phenomenon is the light-being-more-then-three-dimensional-and-we-being-three-dimensional-beings-can't-see-it-for-what-it-really-is type explanation. It might sound strange to some, but compared to some of the explanations that the physics world uses today, it is pretty reasonable. I think that Einstein would approve. I would like to explore that one some more.

[hank]

I've re-read your response Acidfast, and I'm not sure what your problem is with my theory.

In any event , I said earlier that I couldn't prove" the little bang theory". Has anyone heard of the double slit experiment with a divider behind the slits? (I don't know if anyone ever performed it that way). If the depth of this divider beyond the slits is increased in incremental stages, I would imagine that recombination of the photon may no longer be possible behind the slits at a certain depth, and the photon can then only transit one of the slits showing no evidence of an interference pattern on the screen. Of course, a significant depth of open space should still exist between the divider and the screen to set up the interference pattern if it is at all possible. If we find a change in the pattern on the screen from interference pattern to a single band at a certain depth of divider, then we have supported the theory, and have a quantitative method to measure the size of the photon in flight. No change, however might indicate that a photon (in flight) could be very large indeed with no clearly defined boundary but diminishing energy towards the extremities. In that case we have proved nothing, and this theory might just as well be bovine excrement.

[kitakaze]

Hank,
The biggest problem I have with the photon blob idea, is that, for it to work, you are suggesting the blob is bigger than the distance between the slits. So, what if we move the slits apart to 1cm, 10cm, 1km, etc. The interference pattern still occurs. How big is the blob. IT would have to be infinitely large, or at least as large as the universe, otherwise, at some point, the double slit experiment would no longer work.

I read an interesting theory once, about the medium or 'ether' is a sea of stationary photons. When a photon is released, it just bumps all the other ones, creating a 'movement' of ripple.

Of course, it's just a theory, but the authors convincingly described the wave/particle duality using this theory.

Kaze

[Wonko the Sane]

Alright, I'm not even going to attempt to make an utter fool out of myself by raising many points. Someone mentioned how when you measure/change a subatomic particle, the effects of that instantaniously reach across all of space. That may be true, but the only time that really matters is in electron pairs where if we could get rid of the photons that are giving us this riddle, we could use for communication, but the photons always smack the electrons around and break the connections so they "rebond". I'll stop rambling now. Anyway, here's the point.

How does a photon know that somebody is looking at it?
Obviously it isn't intelligent, however it seems to have a lot to do with Shrodinger waveforms, doesn't it? You fire the particle through one of two slits (apparently randomly) and it's a wave if it makes it to the surface and a point if you measure it. Now assume you fire it in to the infinite reaches of space and that there are no other photons in the universe to disturb it, then according to Shrodinger it is neither wave nor particle. Uncertainty fits in just as someone mentioned it earlier. When you measure it, you lose the wave. If you have two probability waveforms though, measuring it (either by using an orbiting panal to measure location or a surface to reflect the wave pattern), then the other waveform colapses and it becomes either particle or waveform. As a particle, it goes through one slit and if you could measure it without stopping it, likely, as someone said, you'd get lines parallel to the slits, otherwise you'd get the wave pattern that's confusing everyone. Feel free to tear this apart, because I definately suffer no illusions to the fact that a lot of it may be wrong.

~Wonko

[Wonko the Sane]

Please don't tlel me that someone already said that. I was so proud of myself too and I figured I'd just post that, and suddenly I see a message with the whole specifics of the Shrodinger's Cat experiment. Someone humor me and tell me I added something new or I'll feel really stupid.

[Ghost Post]

To Kaze (and Hank)

I must say I like Hank's theory! Kaze you say we can have an infinite distance between the slits, and still get a wave pattern. I haven't heard of any experiment showing that (How could one be set up?). Isn't that just a conclusion made "in reverse", when one already have accepted the "other dimension"-theory?

And, the fact that the photon shows up as a wave in some expriments and as a photon in some - is that really a problem to Hanks theory? I can't see how it could be - that's exactly what would be expected according to his "little bang theory"!

And by the way...isn't the wave measureing tool different from the particle measureing tool? Or is there a tool that can get both results - because if that's the case I've misunderstood the whole setup...

[AcidFast]

The measuring tool is simply a wall or something. The act of measuring it is simply looking at the pattern of light on the wall. Of course, all quantum particles behave in this strange way, yet electrons, for example, are almost just as easy to measure. You are doing it now, as you observe the patterns on your monitor and when you watch TV.

[AcidFast]

Hank: Maybe its because I have read about many more experiments than this one, and perhaps some not mentioned, but I will try again.

You have suggested a blob that will behave as a wave in some instances, and a particle in others. In fact, in other experiments that have been performed, in order to (logically) explain how quanta behave, they would have to have been EITHER a particle (or at least behaving like one) OR a wave from THE beginning of the action being measured to the end. This is the way that I understand it, anyway. Do you understand what I meant now?

[Rachel]

The fundamental issues in the '2-slit' experiment were well expressed in parts 1 and 2 of "Let there be Light". My solution, so far developed only at the mathematical level*, can be summarised as follows. This experiment, when carefully analysed, illustrates two important aspects of quantum mechanics. The first is that all predictions are conditional - what happens and what the theory allows us to predict, depends on initial conditions. The second is that in this example distinct conditions are inappropriately assumed to be the same.

Recall that this case involves a 'double-slit' barrier between a light source and detector, and the difficulty of reconciling what happens when just one slit, A or B is open, with what happens when both A and B are open. In either of the first cases there is no interference pattern on the detector, while in the second, with both slits open, an interference pattern appears even when the photons travel one-by-one past the barrier.

We must be careful here in analysing the different conditions, corresponding to different configurations of the barrier, and must especially be careful in identifying different conditions as equivalent. That is, we should not assume that a photon arriving on the detector having passed through the double-slit-open barrier, meets the same condition as a photon passing through one of two other configurations mentioned, i.e. through either the slit-A-only-open barrier or the slit-B-only-open barrier.

It helps to remember the physical scale of the microscopic world, and the fact that the distance between the slits must be of the same order of magnitude as the slits themselves. While we assume for billiard balls, that travelling through a double-slit-open barrier is equivalent to travelling through just one of the single-open slits, this is not a logical truth, nor is it self-evident in the microscopic case. We cannot reject out of hand the possibility that "…a single photon passes through both slits at the same time, like a wave would". [Part 1] even though, as the author says "Any time we try to detect photons, they reliably seem to be in one place". Microsystems perhaps can behave like this, and anyway there are other possibilities. One can conceive for example that at this scale movement of a particle through one slit with two open allows other influences to arise on this motion, i.e. perhaps the "wave like" influence is a local distortion of space, not the "splitting" of what moves.

At any rate we cannot assume that movement through the double slit barrier is equivalent, logically or physically, to movement through either of a single open slit. When we recognise that the conditions of the experiment with two slits open cannot be reduced to equivalent single-slit experiments, we should not be surprised that the outcomes are not the same.

To go back to the Martians. One part of the solution is clear. Given a properly constituted microscopic double slit experiment, and Martians in the appropriate line of sight, the Martians would see an interference pattern when both slits are open, no matter what else they saw. Quantum mechanics tells us, and various experimentation now confirms, that the interference pattern will arise in the situation when both slits are open.

Some people will want to argue that we know more than this, that in addition to seeing the interference pattern, the Martians appropriately placed will certainly not see any photons "blip" at the slits in the barrier prior to landing on the interference pattern. I however do not agree.

An argument for the Martians seeing no "blip" might go like this: Let quantum state C correspond to the arrival of a particular photon at point C on the detector's interference pattern. Then state C cannot be reconciled with a state A, say, describing the photon at slit A prior to arrival at C, nor can it be reconciled with A' describing the photon at the other slit B. For quantum state C assigns certainty to neither A-magnitude. Furthermore as we know, quantum mechanics properly predicts the interference pattern - which is to say that the probability according to quantum mechanics of the photon arriving at C given that it passed through A, or its probability of arriving at C given that it passed through B, differs from the probability that it arrived simply passing through D, i.e. through the open double slits on the barrier. Thus it might be argued we can conclude with certainty that neither state A nor A' describes the photon in state C, and so there can have been no "blip" at either slit, prior to its arrival.

In rejecting this argument we must carefully recognise the condition-dependence of quantum states. Firstly we should point out there are difficulties anyway arising the fact that state C and states A, A' refer to different times. For arrival at the barrier is prior to arrival at the detector. For this reason state C tells us nothing about state A or A'. But even ignoring this issue, and supposing A, A' can be re-expressed in terms of the time of arrival at C, we still have to conclude that these states have different initial conditions to C. State A for example corresponds to passage of the photon exclusively through slit A, and its complement A' corresponds to exclusive passage through A'. But state C corresponds to arrival at C given initial condition state D, i.e. having passed through the double slit open barrier. As noted above it is not self-evident that the two conditions A, A' are equivalent to D. (Although vectors A, A' span a Hilbert Space, this is not the space over which vector C is defined.) It follows that the "blip" which might be seen by the Martians at slit A prior to the arrival of a photon on the detector screen at C, is not properly described by state A nor is a "blip" at B described by state A'. It follows that seeing a "blip" at either slit does not necessarily conflict with the quantum state C, and so quantum theory does not rule it out.

The second part of the Martian question is thus answered by saying that quantum mechanics cannot tell us what they see prior to noting the interference pattern on the detector when the 2-slit experiment is performed. Quantum theory predicts the interference pattern in the double slit configuration, but cannot provide information about the photon position on the barrier.

We can understand this as a limitation of quantum mechanics, expressed by the Uncertainty Principle. Accurate information about all the magnitudes of a quantum system cannot all be combined in a single state-description, as it can in classical mechanics, and instead we are left with various conditional descriptions which can never answer all our questions about a micro-system.

To some extent how we view this limitation is a matter of philosophical attitude. Bohr maintained that our brains restrict us to the Uncertainty Principle, that we must accept there are things we can never exactly describe. I prefer to think that if we were suddenly to see like these Martians, to gain some extra knowledge of micro systems by direct observation, then we would quickly devise a new and better analysis of what occurs. More science is what we need to discover what the Martians see, more investigation that will ultimately lead us to an even better theory of microphysics.

* Garden, Rachel Wallace, Modern Logic and Quantum Mechanics, Adam Hilger Ltd, Bristol, 1984
Garden, Rachel Wallace, Logic, States and Quantum Probabilities in International Journal of Theoretical Physics, Vol 35, No 5, 1996

[Raye]

Can somebody revert all this to a level which a 12-year-old can understand, please?

[AcidFast]

Hey, Raye, here's a suggestion:
If you are really interested in understanding this stuff, go to your local library and look up Quantum Physics or Mechanics. There are always plenty of books designed for beginners to help them understand this stuff. That is how I learned to understand some of it. I have probably read about 20 books on the topic, in increasing levels of technicality, but I know that I have still not even scratched the surface. I still have trouble with the math, but I'm getting the hang of many of the concepts.

[firemeboy]

Not to bring a dead horse back to life, only to beat it to death again...

But... I am curently reading a book by Michael Crichton called Timeline, I am sure most of you have heard about it. He deals with this very issue a little bit in his book. He comes up with an interesting theory. Rather than me try and explain it, I will just tell you what page number it is on. Starting on page 108 and going through 114 will get you the meat of the theory. He continues for the next 30-40 pages to give you additions here and there. It is pretty interesting. Anyway. I have said my peace.

[Calfaile]

Oooh! I read that! Loved it, definately better than sphere! Chriton is such an interesting writer!

[Griffin]

Sphere is my favorite Michael Crichton book. As for Timeline, I've only read the first few chapters, but the introduction blew me away. Did you realize that quantum teleportation has already been demostrated, and may soon be use for the teleportation of solid objects. It's cool.

[Amy]

Firemeboy--what edition of the book are those page # references from? (Publisher, year, hardcover or soft? Sorry, but I have to ask these things...)

[firemeboy]

Sorry Amy, I have been out of town and couldn't answer your question. On top of that, I don't have the book with me to actually answer the questions. On thp of THAT, it is now back at the library. It was a hardback book, and I am assuming it was the first print. It is crichton's latest book so I think there is just one printing of it.

[Daniel]

Sorry for reviving this apparently quite old topic. Just don't reply to it again if you want it to sink... ;-)

I only just found this site and browsed through the interesting riddles...

I saw that there was a lot of interest for the topic at discussion here, and seeing as I am actually a physics undergraduate student at university, and about to take some exams on Quantum Mechanics in a few weeks' time, there's a number of questions which you guys raised which I do (I hope, for my grades' sake) know the answers to... As it happens, I am actually a fairly decent writer (as well as a physicist! you gotta be lying!) so I should be able to explain stuff in a less cryptic way than what you'd find in a university book about quantum mechanics (which would involve lots of mathematics).

Seeing as you guys seemed to want to know about the stuff, which is extremely interesting stuff (that's why I chose to study physics) and since I should be able to clear up some of your questions at least, I thought I'd just let you know that if you gather up the questions which you'd like answered (about this experiment - not "what's the purpose of life?") and email them to me, I'll take some time to write out reasonably clear answers, and even answer questions about the answers, if you have some (which you probably will).

I am probably not going to get any answer since this is a fairly old topic, but I thought I'd give it a chance, just in case there is someone who'd like to know more about this.

I'll give you my hotmail email address, just in case some spam-bot picks it up, so that my proper email doesn't get infested with junk mail, but don't worry! It's still legitimate .

So... gather up the... say 20 questions you'd most like to have answered out of the big lot here, and I'll write out some answers that can be (hopefully) understood by people who have NOT been studying hardcore mathematical physics for the last 3 years...

My email:

TDan000@hotmail.com

Again, sorry for bringing the topic back from the dead - I'm just trying to be helpful...

Daniel

Note: Don't bother replying to me in this forum, it is very unlikely that I should check it again ever in my whole life!... Reply to me by email if you have any questions. You can even flame me if you feel like it, as I won't particularly care.