Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: John Burnap on 27/03/2011 06:30:02
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John Burnap asked the Naked Scientists:
Chris,
Firstly, thank you very much for answering my question last week.
This one is really theoretical. In the Young Double-Slit experiment, light interferes with itself. Most intriguingly, shooting only one photon at a time will also create an interference pattern. According to Feynman the explanation involves the photon traversing multiple universes (dimensions) to get to the sensor. How can a photon interfere with itself while in a parallel universe?
John Burnap
What do you think?
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"How can a photon interfere with itself"
It's about how you look at the idea defining a photon. The idea of a photon is a superposition, meaning that photon have all states possible, simultaneously. Also people mix the idea of waves and photons in this intermediary 'state' which in a way is acceptable, as long as you haven't observed a 'interaction'.
It's like the Greeks, not the photon per se, but the 'idea' of a photon that can interfere with itself. The expression of that interference will then be what defines what you look at in the double slit experiment. A photon, or a wave.
And in Feynman's reasoning it's also so that all paths are taken, simultaneously, but get 'rolled up' by the photon interference, equaling themselves out, only leaving the most 'probable' path to be seen for us.
Or you can do as I do. Decide that it will be the surroundings that defines the outcome. Then you don't really need to care about how it does it, just look at the way you set it up and from there draw your conclusions.
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Thank you very much!
I like the idea of simplifying the question to "how can a photon interfere with itself?". So there seems to be some kind of probability matrix to define the likelihood of an interaction with a particular area on the detector. Is this matrix defined by the environment, the photon, or a combination of both? It almost seems like the probability matrix is always there, defining the probable paths through the slits, and the photon rides that wave. Also, is there any way to accurately predict where the photon will strike the detector, or is it painfully random?
[:o]
John
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There is always a probability that sort it out. Turn it around and look at your chair, it's there now right? And you expect it to be there tomorrow too :) That's probability for you, it seems there always will be some ways of behavior more probable than others. The question is how to find the parameters for that probability, when looking at it from a quantum level.
Feynman defined this way.
"Assume that a particle can travel between two points a and b by a - possibly infinite - number of different paths. Each one of these paths will have a certain probability associated with it. In quantum mechanical terms, these probabilities are encoded in the wavefunction that describes the particle, which assigns to each possible path a different probability amplitude; the square modulus of this amplitude gives the corresponding probability.
The crucial point is that these different amplitudes have a wavelike nature, and as they spread through space they interfere with each other, their respective wave patterns either reinforcing or canceling each other out at various points. And if you sum over all the amplitudes of all the different paths, i.e. you sum-over-histories, then the different amplitudes will reinforce or cancel each other in such a way that the only path that survives this interference process is the one that the particle actually follows.
Feynman's sum-over-histories approach is nowadays given the name of the (Feynman) path-integral formalism of quantum field theory, which is based upon the calculus of variations and the principle of least action. This is now the standard mathematical formalism used by most physicists working in quantum field theories, because it is extremely powerful, highly visual, and will often yield answers far more quickly and simply than other formalisms."
That contrasts against the Copenhagen quantum definition in where The Heisenberg uncertainty principle (HUP) was seen as the principle defining the possibility/probability.
"An unobserved system, according to the Copenhagen interpretation of quantum theory, evolves in a deterministic way determined by a wave equation. An observed system changes in a random fashion, at the moment of observation, instantaneously, with the probability of any particular outcome given by the Born formula. This is known as the "collapse" or "reduction" of the wavefunction. The problems with this approach are:
(1) The collapse is an instantaneous process across an extended region ("non-local") which is non-relativistic.
(2) The idea of an observer having an effect on microphysics is repugnant to reductionism and smacks of a return to pre-scientific notions of vitalism. Copenhagenism is a return to the old vitalist notions that life is somehow different from other matter, operating by different laws from inanimate matter. The collapse is triggered by an observer, yet no definition of what an "observer" is available, in terms of an atomic scale description, even in principle.
For these reasons the view has generally been adopted that the wavefunction associated with an object is not a real "thing", but merely represents our knowledge of the object. This approach was developed by Bohr and others, mainly at Copenhagen in the late 1920s. When we perform an measurement or observation of an object we acquire new information and so adjust the wavefunction as we would boundary conditions in classical physics to reflect this new information. This stance means that we can't answer questions about what's actually happening, all we can answer is what will be the probability of a particular result if we perform a measurement. This makes a lot of people very unhappy since it provides no model for the object."
In the Copenhagen Interpretation, the wave and particle pictures of the atom are "complementary" to each other. That is, they are mutually exclusive, so in a final interaction there can only be one (as in Highlander:) of them, but for describing the 'wave function' before that final interaction you will need both.
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Where The Copenhagen definition discuss the uncertainty or 'superposition' of that wave function , being both wave and particle simultaneously, before that interaction defines it, Feynman used 'sum over paths' instead. Defining it as if every path was taken for that wave function, simultaneously. All of them needed for the final outcome/interaction as they acted like waves do, in some cases reinforcing each other, in other quenching each other. the summation of all those probabilities for that wave function lead you to the same answer as you got by the older Copenhagen definition, but no longer involving 'uncertainty' as it is assumed that this always will give you the correct outcome.
But you might notice that instead of HUP:s uncertainty you now have a wavefunction that 'must' take all paths for the solution to make sense. And choosing between two ah, uncommon? Approaches to reality? I don't know, both seems to work and both describes 'reality'. Neither one is wrong. But Feynman's solution question time in a different way than HUP does it seems to me? I do like HUP myself, and Shrödinger, as they both describes a universe where we can't know it all. Feynman by questioning time present his solution as more 'probable' as we then just have to redefine 'times arrow' to something new, maybe some entropic quality? But as I trust that there actually is a 'arrow of time' same for us all, as observed where we are? I don't know?
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Why not suggest that "A photon" is many things? Just because something is always found in one place when it is measured doesn't make it one thing. Lightning strikes in one place, we wouldn't call lightning one thing. And drops out of a leaky faucet all strike with the same amount of energy and in the same place, we don't consider water drops one thing. Why not suggest that part of a photon travels through one slit while the other part travels through the other? That way it makes sense to picture "one" thing interacting with itself. There are tons of examples of matter not acting like particles. quantized sizes don't prove something is indivisible. It's impossible to prove something is indivisible. Yet everybody assumes it as so. I think the reason nobody can shed this mindset is because the first things we are ever taught about matter is that things are made up of individual particles.
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Thank you!
I need an analogy, no matter how convoluted. How about a short trip to the market. So, when I go shopping for groceries, there are several markets nearby that I can choose from. But there are variables such as traffic and construction, which must be considered to choose the ideal market and route. Unfortunately, the only way to know the ideal market and route is to drive to all possible markets using all possible routes, all at once. So, lets just say I do that by temporarily cloning myself into virtual copies. During my parallel drive, one of my clones will arrive at a market, at which point all the other clones disappear.
Now lets say a street vendor flags down any one of my clones and happens to have everything I need from the market. The search ends and my clones disappear. In the interest of competition, the vendor wants to know which route I was going to take and to which market. But I cannot know the route I would have taken or the market I would have arrived at due to his interference. Also, as a clone I have a bad memory and I don't know the path I had taken prior to encountering the vendor. He would only know that his location was on the path my virtual self was taking at the time he flagged me down. Consequently, because I am trying all possible routes, he will find me on any route he chooses - so long as he catches me before I arrive at a market.
Lastly, lets say one of my clones arrives at a market and all the other clones disappear. The clerk wants to know what route I had taken, but because of my bad memory, I do not have that information. All the clerk knows is that his market happened to be the one I arrived at.
I know this sounds ridiculous, even crazy, but is this at all a fair analogy?
John
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I liked it :)
I don't know how to see it either :)
It depends on how you look at it and from where. It's like a wrench, they come in all sizes and all of them fits something. But they are tools, we use them because they fit. The same goes for this, we expect certain things to be true, like 'propagation' and we have good reasons for expecting it experimenting. Then we look at interactions and find that depending on how we set up a experiment light behaves differently, either as a particle like a bowling ball hitting something using its kinetic energy to move what it hits. In the photons case it's as far as I know a electrostatic energy but? I'm not sure there either, in any way it moves what it 'hits'. Or we find it to be a wave when it 'hits' acting in a whole new manner. Feynman build his reasoning, even though not stated, on waves as I see it. The original Copenhagen definition carefully avoid stating what it is moving before the interaction as I understands it. If you like the Feynman description then 'clones' seems as good as any, rather fun actually, with some sort of unspoken entanglement involved, possibly? Maybe :)
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And yes Brain, myself I'm only reasoning from interactions nowadays. And I'm not even sure if light is propagating at all. So I'm probably weirder than them :) or at least just as weird. What physics is doing, as I see it, is prodding 'reality'. The place where we are born and die and even though it can't, and won't, discuss the philosophical aspect of reality we are free to do so, not actually involved in preparing papers for peer reviews.
But we have to be careful too, ideas that goes totally against experiments is very difficult to support. And using QM to describe SpaceTime do not work, yet at least. If 'Gravity' is found to be 'quanta/particles' a quantum description may work? And if we go past the QM level we find guys like Smolin and 'string theory'. They do not discuss quanta as I see it, instead they discuss 'discrete events' that to its very nature do not fit anything we know from QM. The question there is if those 'discrete events' is what creates 'SpaceTime' or if they are happening on a 'background'. Einsteins 'SpaceTime' is background independent as I see it. It has four properties from a main stream perspective. Length, width, height and time/times arrow. Those interact and adapt to each other seamlessly, creating effects like Lorentz contraction and Time dilation. So if you want your theory to fit in with Einsteins, you probably need to make it background independent.
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it's weird :)
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http://people.ccmr.cornell.edu/~muchomas/8.04/Lecs/lec_FeynmanDiagrams/node3.html
And this one discuss what principles Feynman built on
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The statement that was made early in the history of quantum theory, that the photon interferes with itself is generally consider false by most quantum physicists. However, it is so pervasive in common culture that David Ellerman at the University of California felt compelled to publish a paper titled "A Very Common Fallacy in Quantum Mechanics" to dispel the absurdity: arXiv.org/pdf/1112.4522.pdf .
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The statement that was made early in the history of quantum theory, that the photon interferes with itself is generally consider false by most quantum physicists. However, it is so pervasive in common culture that David Ellerman at the University of California felt compelled to publish a paper titled "A Very Common Fallacy in Quantum Mechanics" to dispel the absurdity: arXiv.org/pdf/1112.4522.pdf .
It is pretty dominant in physics as well as common culture. Frankly you need to be a philosopher to be as dogmatic about the underlying reality of quantum mechanics as David Ellerman - and it turns out that he is! There are many interpretations of the results we obtain from experiments in quantum mechanics - to claim that one is better than others is pretty standard and pretty unimportant; the maths and predictability is the important part. I have not been through the details of his argument so it could be correct or it might be steaming bovine waste - but at first glance it seems unrevolutionary (and a little catty and snarky) and the fact that it is unpublished is testament to this fact.
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My post was consistent with the most widely accepted interpretation of quantum physics. In the Bohr interpretation no photon actually travels any path and there is not any photon interference.
If you go to my two post in the tread "Light Wave - Particle Duality" you will see a more detailed explanation.
You will also learn that I personally do not accept this interpretation as I am aware of an experiment that demonstrates photon interference and also have a different experiment of my own that I think proves it for correlated in-phase photons.
Before you can demonstrate challenges to a prevailing interpretation your audience needs to understand it.
"If you are not trouble by quantum theory then you probably do not fully understand it ", Neils Bohr.