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When a photon from a distant star hits the earth, a superposition of a plethora of observers is created, which detect the photon at a specific place for each one of them.
Ash Small wrote:
I would dispute this.
I'd argue that only one observer 'sees' each photon, and that the energy from that photonis 'recieved' by the eye of that observer.
You're right. I didn't say, what I meant to. What I mean is, that in one particular world of the many worlds interpretation, the observer will see the photon in his telescope. In another world, the photon will hit a leaf of grass somewhere, where it very likely goes unnoticed by the observer.
Say you completely fill the earth's surface seamlessly with telescopes. Then the observer will find the photon in exactly one of them. From the point of view of the MWI, the wave function of the universe will split into a superposition of states. In every state there will be exactly one photon detected and it will be a different telescope for each one of the states.
Registered Member #3414
Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245
Yep, that is pretty much what I said in my initial posts in this thread, between being emitted and recieved, the photon is 'everywhere', or, at least, 'on all possible trajectories', ie, it is emitted, or radiated from one point, then collapses about another.
The time between these two events is proportional to the distance between the point of emission and the point of absorbtion.
A photon is just a transfer of 'a packet of energy' (quantum) from one particle to another, at diffefrent locations, which are connected by a 'line of sight'. The 'many worlds' or 'parallel universe' theory can be used to predict 'all possible outcomes'. (until we understand more about the mechanisms involved)
EDIT; if you cover the Earth seamlessly with telesopes, you 'may' detect the photon you mention above in exactly one of them, as there are other possible outcomes as well.
Yep, that is pretty much what I said in my initial posts in this thread, between being emitted and recieved, the photon is 'everywhere', or, at least, 'on all possible trajectories', ie, it is emitted, or radiated from one point, then collapses about another.
The problem of collapse is the one I addressed. It is a non local process and the issue that the OP was puzzling about. The point of the MWI is, that it avoids the assumption of collapse. In the MWI the observer is linked with the result of his observation, so that the other possible outcomes of his experiment are not observable to him. That does not mean that the universal wave function does not contain amplitudes of observers, who see the photon hitting somewhere else.
This may seem a dubious trick but it is conventional quantum theory applied to the experiment _and_ the observer.
Registered Member #3414
Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245
Uspring wrote ...
This may seem a dubious trick but it is conventional quantum theory applied to the experiment _and_ the observer.
Well, yes.
The probability that one (and only one) of the 'possible' observers' will 'see' the photon is equal to one.
Ths seems to be the limit of 'conventional quantum theory'.
It can only predict 'probable outcomes'. Heisenberg implies that we actually no nothing about the actual mechanism of energy transfer, other than that beween emission and aborbtion the energy is 'everywhere' (all possible trajectories).
Registered Member #89
Joined: Thu Feb 09 2006, 02:40PM
Location: Zadar, Croatia
Posts: 3145
Hi Steve
Well, I'm not sure if the concept of physical size applies to photons any more than it applies to electrons or whatever other point-like particle.
I also have very hard time contemplating your concept of "photon monochromaticity". All life I've been taught that photon is a discrete packet of energy, which is exactly related to a single discrete frequency. The photon only manifests when it imparts energy, and this energy can be measured!
So putting a single photon through a telescope would modify the shape of it's wavefunction, but the photon would still end up interacting with a sole electron somewhere once it collapses.
On the other hand, my knowledge on concepts of coherence and wavefunction collapse is still very poor, they didn't explain it at all on our QM classes!
The time independent Schrodinger equation deals with wavefunctions that are stationary in time (much like AC network analysis); particles to be analyzed by it have to be specially prepared, by having perfect coherence. Their wavefunction will then represent a perfect timeless sinusoid with an exact frequency.
I'm not sure what in real world could cause a wavefunction to approach such situation; perhaps a photon travelling an infinite distance before hitting our detector would be suitable candidate.
Such equations in one dimension turn into very simple differential equation that is easily solvable by students, but I'm not sure how much it tells about real world.
On the other hand, the time dependent Schrodinger accounts for time evolution of the wavefunction. Take an example where a very short pulse of light is emitted by laser; it can be even a single photon.
In this case of a more realistic wavefunction, the probability amplitude would be a short wave packet instead of a timeless sinusoid. This is where mindfuck starts: if we do fourier analysis of the nonperiodic wave packet, it would have a continuous spectrum consisting of infinitely many frequencies.
I assume this led you to the concept of "polychromatic photon"; or, we could assume that the wave packet consists of infinitely many superposed photons with dE energy. I think both ideas are apsurd: the concept of photon only makes sense once it interacts with matter (in this case, the energy of whole wavepacket would be exactly the energy of one photon).
The true mindfuck, though, is the following: what made these two wavefunctions so different from start? What physical proceses impart uncertainty into wavefunction and cause it to vary in coherence, despite we're looking at a single photon in bot cases?
Once a particle is measured, the size of it's wave packet will shrink; this process is called "wavefunction collapse" or whatever; but what physical processes decide to what extent will this shrinkage happen, after interaction with other wavefunctions or particles?
..And even more importantly, once the coherence is lost, what physical processes can bring it back? I have a gut feeling it has to somehow arise spontaneously over time/space - the wavefunction of our single photon laser pulse would surely spread out much and approach the state of the one that has already travelled infinite distance...?
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Posts: 6706
The many worlds interpretation might get round the non-locality of wave function collapse, but it does this at the cost of introducing even more far-fetched notions. The idea of infinitely multiplying universes doesn't sit well (for me at least) with thermodynamics and the principle of least action. But then zero-point energy is an accepted fact even though I don't much like it either.
I'd be happy with this for a compromise: Wavefunction collapse happens, the photon is detected in just one of the hypothetical telescopes. The non-locality of this process is allowed because no information can be transmitted faster than light by it.
Maybe it could be seen in terms of quantum entanglement, all the possible paths of the photon are entangled because they are the same photon. By being detected in one place, it can instantly tell itself not to be detected in any of the others, in the same way that doing something to one particle of an EPR pair instantly affects the other.
Registered Member #3414
Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245
The idea of multiple universes doesn't sit well with me either, Steve. I prefer to think of multiple 'possible outcomes' (Shroedinger).
But if we accept the idea of multiple dimensions (aka string theory), and that all events affect the whole universe, I think it becomes a bit easier to understand.
My point is that, between being emitted and detected, the photon is 'everywere and nowhere'.
The time independent Schrodinger equation deals with wavefunctions that are stationary in time (much like AC network analysis); particles to be analyzed by it have to be specially prepared, by having perfect coherence. Their wavefunction will then represent a perfect timeless sinusoid with an exact frequency.
I'm not sure what in real world could cause a wavefunction to approach such situation; perhaps a photon travelling an infinite distance before hitting our detector would be suitable candidate.
A photon travelling in free space would, as you say, be infinitely long to have a definite energy, i.e. be an energy eigenstate. You can also have these states if you put a photon in a high Q resonator, e.g. a superconducting metal box.
I assume this led you to the concept of "polychromatic photon"; or, we could assume that the wave packet consists of infinitely many superposed photons with dE energy. I think both ideas are apsurd: the concept of photon only makes sense once it interacts with matter (in this case, the energy of whole wavepacket would be exactly the energy of one photon).
It is certainly strange, that whenever you measure the photons energy you only get a certain value and at the same time the claim stands, that it has many values at once. But this is not absurd. An analogous situation arises in the double slit experiment. When you measure the position of the particle directly behind the slit, you will either measure it left or right. But if you don't measure the position there but much further behind, you'll see an interference pattern from a wave going through both slits, i.e. a superposition of left and right. My analogy replaces multiple energies by multiple positions. Interference patterns can only arise from multiple positions. And you can't explain all the properties of a photon without assuming multiple energies.
The true mindfuck, though, is the following: what made these two wavefunctions so different from start? What physical proceses impart uncertainty into wavefunction and cause it to vary in coherence, despite we're looking at a single photon in bot cases?
If, e.g. an excited atom emits the photon, the lifetime of the excited state determines the energy spread of the photon. A short lifetime will emit a short photon with a large energy spread.
Steve Conner wrote:
The many worlds interpretation might get round the non-locality of wave function collapse, but it does this at the cost of introducing even more far-fetched notions. The idea of infinitely multiplying universes doesn't sit well (for me at least) with thermodynamics and the principle of least action.
Each of the worlds behave conventionally. Where's the problem? A nice thing about the MWI is, that some of the rules of quantum mechanics, like the collapse, can be derived instead of being "axiomatic". Also it is more universal, because it views the observer not being something distinct from the observed. It is epistemologically simpler.
Maybe it could be seen in terms of quantum entanglement, all the possible paths of the photon are entangled because they are the same photon. By being detected in one place, it can instantly tell itself not to be detected in any of the others, in the same way that doing something to one particle of an EPR pair instantly affects the other.
That is very close In the MWI every observer is entangled with his observation. Thus he can see only the world he is entangled with. Formally it is much like the EPR pair.
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A quantum head scratcher
