Compton Wavelength

Discussion in 'Physics & Math' started by Harmony, Jan 10, 2012.

  1. AlphaNumeric Fully ionized Registered Senior Member

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    Except that isn't actually answering his question, you've just come up with some concept which allows you to count in whole numbers.

    Besides, your method doesn't gel with the required behaviour. For example, fermionic spin is half integer spin, ie 1/2 or 3/2. Bosonic spins are 0, 1 or 2. Your method cannot build spins higher than 1, since you define it as 1/N if the number of twists are N. You can build spins of say 1/5, except no such spin exists.

    You can view the spin as how the wavefunction changes, ie \(|psi\rangle \to e^{2\pi i s}|\psi \rangle\) if \(|\psi\rangle\) has spin s properties. If s is an integer than it doesn't change. If s is half integer it picks up a factor of -1. Anyons let s be anything except, as I said, they only arise in 2+1 dimensional space-time. You cannot have a Mobius strip in 2+1 dimensional space-time in the manner you describe so you cannot view them in such a manner.

    Now there are topological things related to particles which can be viewed in terms of tori, Mobius strips, spheres and plenty more weird and wonderful spaces. However, the specific connection to these things is constructed formally. Many of them cannot be viewed geometrically because they are say 6 or 10 or 50 dimensional structures with multidimensional loops and handles and twists and other shapes we don't even have names for. Simply thinking "I need something which counts integers. Oh, a Mobius strip!" doesn't cut it. Personally if someone asked me to think of a space which counts integers I'd think a torus, since that's what its fundamental group measures. Twice!

    For example, the reason you only get \(\pm 1\) transformations in space-times with more than 2 spatial directions is to do with the first homotopy group of the space-time's metric symmetry group, which is \(\mathbb{Z}_{2}\), which the group ( * , {1,-1} ) forms a representation of. If d=2 then you get \(\mathbb{Z}\) and all sorts of problems arise. But if you didn't know any group theory and algebraic topology this would not be known. And this isn't mathematical navel gazing, 2+1 dimensional gauge theories are finding serious applications in the development of graphene based materials and condensed matter.

    I can understand why you would find a simple geometric point of view palatable but you have absolutely no way of demonstrating such a point of view is actually any reflection of the behaviour of the system. The mathematical constructs in mainstream physics are derived from physically motivated premises and they allow specific predictions to be made and then tested. Approaches like Farsight's obsession with giving some simple geometric point of view are not going to be of any use if they are just plucked from nowhere. Given a specific property of a system it's easy to come up with another simple system which has a similar property. But if you have to give a different analogy for each property it's of no use because the analogies don't allow you to reason about anything else in the system. Unless there's some actual derivation/justification beyond the construction of a simple point of view there's absolutely no reason to think it's worth putting any trust in.

    The application of mathematics to physics is precisely because we can trust the end result to be as sound as the premises. Unfortunately too many hacks try to delude themselves they can accomplish great things in developing physics models without actually formalising any models. When asked "What happens to a ball when it is thrown into the air" the answer "It comes down" is true but an answer which tells you where, when and how fast is the better one, no matter how palatable the justification for "It comes down" might seem.
     
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  3. RJBeery Natural Philosopher Valued Senior Member

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    Well, I'm flattered that you seem to be critiquing my comment as an actual proposal; I was just pointing out a geometric method for generating half numbers from whole ones. Also, since you mentioned it, I'd point out that you aren't quite thinking about it correctly. If we consider the bosonic spin to be the "number of twists per orbit" then we can easily envision a complete twist plus one-half per orbit, resulting in a 3/2-spin fermion. We can do this with 5/2, 7/2, etc. It's geometrically sound in that regard.
     
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  5. przyk squishy Valued Senior Member

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    As AlphaNumeric explained you're not really answering my question. You've just got a scheme with integers and rational numbers in it. Integer and half-integer spin states are defined by certain theoretical as well as as measurable properties, and it doesn't make sense to call something a "spin" state unless you can recover those properties.

    Also, I was asking how you could build half-integer spin states out of integer spin states, not just have both. Although you haven't answered this I don't see too much point in dwelling on this anyway. This building fermions out of bosons stuff is only necessarily an issue if you're sticking close to mainstream physics and you're actually trying to build electrons out of photons, as opposed to, say, imagining both are built out of some common substance. I originally included those comments because Farsight has at some times in the past claimed he wasn't modifying QED but just "explaining" it, although it's clear he's actually describing something very different from QED.

    That said, any serious model is going to have to account for spin. You've indicated the model you've described above isn't a "serious" proposal, but I still feel I should point out a couple of other obvious issues with it (in addition to what I said above):
    • In nature we only see integer and half-integer spins. Your scheme seems to allow any rational number "spin" (and one could wonder why it's even restricted to rational numbers) and gives no indication why only integer and half-integer spin states exist in nature (current theory behind spin does explain this).
    • A spin k system can exist in 2k + 1 distinguishable states (eg. spin up and spin down for spin 1/2). Your scheme gives no indication where this multiplicity comes from (again, current theory does).
    • Spin states transform in very specific ways under rotations. For example for spin 1/2 states, the spin "up" state pointing in the \((\theta,\,\varphi)\) direction in spherical coordinates is the superposition
      \(| {\uparrow}_{\theta,\varphi} \rangle \,=\, \cos(\theta/2) | {\uparrow}_{z} \rangle \,+\, \sin(\theta/2) e^{i \varphi} | {\downarrow}_{z} \rangle \,.\)​
      Your scheme gives no indication how transformation properties such as this arise. In current theories, these transformation properties are practically the definition of spin states. It doesn't even make sense to call what you have "spin" unless you can incorporate or recover them.
     
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  7. RJBeery Natural Philosopher Valued Senior Member

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    Przyk, it is unfair to try giving credibility to your own objection by referring to AlphaNumeric's objection, when he simply misunderstood my explanation. It's also a bit silly to point out that my horribly superficial geometric mental exercise would allow for spin 11/3, for example, because while this may be true I can come up with two reasons off the top of my head why this is not necessarily a death knell: 1) perhaps the "soliton boson" math, which provides an additional constraint on the system, doesn't allow for it or 2) perhaps the theory would actually predict new types of matter which we have not observed. I've said more than once that this isn't a serious proposal, but I have to admit that I'm finding it entertaining "defending" it against your protestations.

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    That's interesting. As long as I'm just pulling suppositions out of my arse we could change the scheme a bit and say that the soliton-boson can only make a 1/2 twist per orbit. That means that the boson would orbit 6 times in a spin 3/2 fermion. Then we could claim that each double-orbit has a geometric feature which is macroscopically observable. This change would also resolve your "arbitrary, rational spin state" objection.
    No indication? Jesus man, it's one thing to object to fundamental impossibilities but it's quite another to object with "not enough flesh on the bones". If we're going to stick with a geometric framework we could say that spin state measurement literally rotates the soliton.
     
  8. przyk squishy Valued Senior Member

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    Er, you really didn't answer my question, regardless of what AlphaNumeric said. But as I explained that doesn't even necessarily matter anyway. My comments about making integer spin states out of half-integer spin states had a narrow focus, and I've explained a couple of times why I made them. But specifically, I was talking about electrons being made out of photons, and you sound like you're trying to imagine electrons and photons both being different configurations of the same (classical) field, which isn't quite the same thing. That doesn't mean there might not be other obstacles to that idea, but my comments about spin and bosons/fermions don't directly apply to it.

    It's silly because you indicated you weren't making a serious proposal anyway. I read that as an acknowledgement that you're aware it's lacking important details that a serious model would need to fill in. So don't read my comments as a definitive rough rebuttal or rejection.

    That said, there's no harm throwing a few factoids about spin your way, is there? I'm telling you some of the details a serious proposal would need to fill in.
     
  9. RJBeery Natural Philosopher Valued Senior Member

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    I was rather enjoying this. Perhaps you could expand on what you mean by "isn't quite the same thing"?

    Also, just out of curiosity, what is your personal assessment of what the concept of spin is in general?
     
  10. przyk squishy Valued Senior Member

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    I'm just talking about the difference between electrons being made of photons, and both being made of some common object. The rules of spin addition apply if you're trying to imagine the electron is really a bound state of two or more photons, very similar to the way an atom is a bound state of electrons and a nucleus. What you're describing sounds more like you want to imagine the electron is a certain configuration of the electromagnetic field, and the photon is some different configuration of the electromagnetic field.

    Depends on what kind of answer you're looking for. The most "physical" one is that a particle's spin is an internal degree of freedom that you can think of as intrinsic angular momentum, both because it has the same algebraic characteristics as quantum angular momentum and because it contributes to the angular momentum conservation law.

    But there's also a more abstract point of view that doesn't care much about electrons or Stern-Gerlach experiments or even all that much about quantum mechanics, and is just based on rotational symmetry. To understand the motivation, imagine you're a theoretical physicist in the business of putting together physical models, and you've noticed that nature has rotational symmetry. Suppose you decide you're interested in understanding what sorts of mathematical tools and objects would be useful for putting together rotationally symmetric theories in general, without necessarily being focused on any specific area of physics. You already know about two sorts of physical quantity - the scalar and the vector - that are affected in a well defined way by rotations. Specifically, scalars don't change, and vectors have their components multiplied by the rotation matrix. Well it turns out you can "derive" more general types of geometrical objects, which you can think of as "generalised" vectors that have more general transformation rules under rotations (called "representations" of the rotation group). You end up deriving exactly the mathematical description of quantum mechanical spin states in this way.
     
  11. Farsight

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    I think it's better to imagine the effect of electromagnetic four-potential as a configuration of space, pryzk. Curved space, for want of a better word. Think of the photon action over one wavelength as a bulge in space propagating linearly at c. As it passes you by, space starts to curve, then flattens at the middle of the bulge, then curves again the other way, then flattens again as the bulge passes totally by. Then think of the electron as the same action travelling entirely through itself in a double-loop configuration where its own space-curve keeps it in a closed "moebius" chiral path. Yes it's a different configuration, and now we have a standing field rather than a field-variation passing at c. But we still have a dynamical entity which moves linearly when you put it down in "curved space", and rotationally too when you throw it. Think roton, think vorticial attraction and repulsion. Think vector-vector, but don't think cross-product. Think rotation. This ↑ and this → doesn't give you this ↗ it gives you this ↗↘ then this →↓ and so on. Like a rocket with an orthogonal rocket on its nose.
     
  12. przyk squishy Valued Senior Member

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    Can you make any numerical predictions with any of this?
     
  13. RJBeery Natural Philosopher Valued Senior Member

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    I predict at least two others will jump on Farsight's ass for posting it.

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    Say what you will, but reading Farsight's descriptions has had some value for me. The post on the Infinite Wall is an indirect product of it -- if we think of gravity surrounding mass as being analogous to gelatin in a pool...which allowed me to make the connection to gradient-index optics as I mentioned earlier...then I wanted to explore that relationship even further. Since it's only the gradient of the refractive index that causes a pathing change for light (i.e. light moves straight through a uniformly-indexed medium) then I wondered if gravity would be absent in a uniform gravity field. There are three such fields that I could come up with: absolute vacuum, interior of a Newton's Shell, and eventually the Infinite Wall. In the first two it's clear that gravity is absent. I'm still learning about the third case, and regardless of the outcome I find it to be a wonderful learning opportunity...
     
  14. Farsight

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    Not that I know of. You can retrofit to known values and explain the proton-electron mass ratio, but that's postdiction rather than prediction. Maybe somebody like Andrew Worsley or John Williamson or Martin van der Mark or Qiu Hong Hu will come up with something. Or somebody else. We'll have to see.

    The main point to absorb is that the electron and proton don't accelerate towards one another because they're exchanging little flashes of light, or because of some magical mysterious action-at-a-distance. But because they're dynamical. They might not look dynamical at first glance, just as you don't see the dynamical aspect of a standing wave in a box. But open the box, and whoosh, now you see it. You see it in electron-positron annihilation too, that's like using two boxes to open each other, whereafter you've got no boxes left. Mull it over. Look to gravitomagnetism for clues. You'll get there in the end. Then maybe you'll be able to make some numerical predictions.
     
  15. AlphaNumeric Fully ionized Registered Senior Member

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    You make it sound like you're passing little nuggets of knowledge down to us from your 'intellectual table' but really you have nothing but analogies and vagary. Without any mathematical formalism, concrete predictions or logical derivation you really have nothing and saying "You'll get there in the end" is like a person of Religion A saying to person of Religion B "Read my holy book and you'll get there in the end". You have the same amount of scientific validity and methodology as a religion.

    Why don't you hold your own claims to standards you attempt to hold the mainstream to? Why is it okay for you to have absolutely nothing of any substance, especially quantitative testable models, yet you complain string theory has nothing like that (which is false)?

    This isn't a rhetorical question Farsight. If you're going to come here into the main physics/maths forum and spout what is little more than your uninformed opinion about things you have no experience or knowledge of then you're going to have to give some justification beyond "Because I say so". If you are unwilling to answer these questions then in future all discussion pertaining to any of your claims will be moved to the alternative theories or pseudoscience forum. If you don't take the hint then official warnings would follow because just like we don't allow Pincho or wlminex or Sylwester to post their nonsense here, there's no reason to make an exception for you. Of course if you can provide what I've been asking you for (for years), namely a quantitative testable model of some, any, real world phenomenon along with its derivation from your claims then that'll be fine.

    Otherwise consider this the last thread in this subforum where you're allowed to talk at any length about your claims.
     
  16. Farsight

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    Doubtless, RJ. Sadly it seems that some people here don't like people talking physics, and seek to close down physics discussions.

    It's certainly worth kicking around. But remember that any concentration of energy causes gravity, not just mass. A massive body only causes gravity because it's a concentration of energy. A photon has no mass, but it's a concentration of energy so it causes gravity, so we say that it has "gravitational mass". Because of this IMHO it's better to think as space as the gelatin. When you put energy in at some location it's like injecting "more space" with a hypodermic needle at that location. You then create curvature in the surrounding space. If you then move along a little and inject some more, and repeat until you've got a line of injection points, then repeat the lines to make a horizontal sheet of injection points, the curvature tends to flatten out, and then you're left with a pressure gradient above and below. If you then make one further injection above the sheet, and animate it so that it's moving horizontally like a pulse, the pressure gradient caused by the sheet makes it veer downwards. We talk of this curved motion as curved spacetime.

    Good stuff, RJ. That's what makes physics so enjoyable. What I'd say you need to look into here is the distinction between potential and field. Potential is more fundamental than field. If say you have a region of space where the gravitational potential is the same throughout, there is no gravitational acceleration in that region, so there is no gravitational field there. It's similar with electromagnetism. If you've got a vacuum tube with an cathode and an anode, and both are at a million volts, electrons don't accelerate down the tube. Take a look at Aharonov-Bohm effect on wikipedia for this, and note this bit The Aharonov–Bohm effect shows that the local E and B fields do not contain full information about the electromagnetic field, and the electromagnetic four-potential, A, must be used instead. All a field is, is a map of how the potential changes, something like a contour map. And if your terrain is all at the same height, then regardless of its altitude, your map is blank.
     
  17. przyk squishy Valued Senior Member

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    Postdiction is fine here, and I'm not even asking about anything as ambitious as the proton-electron mass ratio. I'm asking about all the routine applications of electrodynamics, some of which even kids learn about in highschool, like what path a charge will follow in a certain electromagnetic field or what field an oscillating dipole will produce. Can you or any of the people you named numerically predict any of the usual, routine predictions of electromagnetism, and from your/their own ideas rather than just copying the way the textbooks do it?
     
  18. przyk squishy Valued Senior Member

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    If by "uniform" you mean "the same everywhere" as in "no point in space is distinguishable from any other" then there's an obvious counter-example: imagine all the space in the universe is a 3-sphere. It has constant, but non-zero curvature, and is thus a uniform but non-zero gravitational field.
     
  19. RJBeery Natural Philosopher Valued Senior Member

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    Fair enough, I will look into it. My thought process, though, is that the potential isn't the cause, but a measurement of the effect (doesn't that make more sense anyway? If the potential energy actually physically existed in the clock as we raised it, as you contend, then why does it not contribute to the "gravitational mass" of the clock causing it to tick more slowly?). Perhaps we can model all gravitational potential in terms of gradient coordinate time dilation. An observer on the inside of a Newton's Sphere would tick more slowly than an infinite observer, even though neither have any gravitational potential because there is no gradient. Using that logic, we must first show the differential in time dilation of clocks above the infinite wall to show gravitational potential, not the other way around. If they pass time at the same rate, under this (imaginative) scheme, then the gravitational potential is zero.
     
  20. Farsight

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    Noooo! This is one of the juiciest things about physics, seeing where things are back to front. Light doesn't curve because a gravitational field is there, it curves because the space down there isn't the same as the space up here. The potential is just a cipher for the state of space.

    It does contribute to the gravitational mass of the clock. Think about a system consisting of two bodies that are initially stationary some distance apart. They fall towards each other. They impact spectacularly, and their kinetic energy gets radiated away into space. Conservation of energy tells you that what's left has less mass, you've now got a mass defect. To pull them apart takes work, you have to put energy in, and the two separated bodies now have more mass and more gravitational mass than they had when they were bound.

    No, the extra gravitational mass doesn't make it tick more slowly. Best to look at a light clock for this, and GPS. That uses atomic clocks, which use microwaves, so they're a form of light clock. And they tick faster at a higher altitude.

    No, really, the potential is more fundamental than the field.

    True.

    False. There's no discernible local gradient for either of them, but there is a gradient between the two. The observer inside a Newton sphere is at a lower gravitational potential than the infinite observer. It's like he's on a plate which is flat where he is, but which slopes up from the outer surface of the Newton sphere. The "infinite" observer is so far away that he can't discern the slope.

    Sorry RJ, but if they tick at the same rate, the gravitational field is zero. If they don't tick at all, the gravitational potential is zero. Clocks can't tick any slower than that.
     
  21. Tach Banned Banned

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    ...and just like this, this forum reaches an all time low.

    ...and the records for BS keep getting toppled.
     
  22. Farsight

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    Yes. But don't think the textbook mathematics is wrong. It's a different interpretation. For example E tells you how a dynamical frame-dragging roton moves linearly with respect to another rather being a some magic field that makes some static point-particle thing move in a mysterious way. It's like, you take curl at face value, space is curved in more than one dimension, this diminishes with distance, and it isn't like that for nothing. Play with paper strips, gyroscopes, Falaco solitons, hairballs, and look at gravitomagnetism. Then you'll see it.

    Sheesh, look at the time. I'm off to bed.
     
  23. przyk squishy Valued Senior Member

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    So where is all this done? You realise you can't just take any math and say it should be interpreted a certain way, right? You've got to be able to show that you can recover that math from your interpretation of it. It's not like electromagnetism is trivially equivalent to anything you've said. I know the mathematics of electromagnetism, and I know the mathematics of curved spaces, and they're not the same. So where do you or any of the people you've named make the connection? What are the models behind the buzzwords you're using, and how do you derive or recover the mathematics of electrodynamics from those models?

    Er, no, curl is just the name of an operator in vector calculus, and we'll say a vector field \(\bar{F}\) has curl if \(\bar{\nabla} \times \bar{F} \neq 0\). The reason the operator is called "curl" isn't random of course, but it's got nothing to do with space being curved or twisted or anthing like that. Water stirred in a glass has curl (or more correctly, it's local velocity does) by the vector calculus definition, for example.
     

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