[Herra Tohtori]

I'm not sure if I understood what's the problem then.

However, tracing photons from the emitter to the shader loses some part of light on the slit. The setup is not a true reverse system if you don't include those lost on the slit itself (at exact phase, location, direction, time and polarization) when going through it backwards.

Could you explain why a delta spike as a wave function disproves the whole reverse thing?

Okay, let's analyze a situation where one photon passes through the slit in real time.

It goes through it (this is established in the premise).

It arrives at the shader somewhere, probability of the location predicted by the wave function.


In reverse, the photon emerges from the shader, goes to the double slit and passes through it.

Then what?

Does quantum mechanics in reverse time handle a double slit as a convergent rather than divergent (interference-inducing) element? If so, can it really predict from one single photon's reversed trajectory that it will hit the original emitter, and even the original electron that happened to emit the photon?

A delta spike wavefunction, even with fairly high "spikyness" (narrow arrival area within reasonable probability) the photon technically could end up anywhere in the wave function's area (which by definition should be in range of negative to positive infinity).

In short, the problem I have is that statistical approach doesn't work with something that has already happened. You get one shot at predicting what will happen - giving a wave function that gives you some approximate where the photon probably came from is a cop-out and provides an infinite amount of incorrect answers, situations which clearly didn't happen (as we observed them).


To be time-symmetric, you should be able to run an experiment and record it; then run it in simulation both forward and backward, starting from start and end states respectively, and you should be able to start from observed end values and end up in start values.


Of course, I'll concede that this is only a problem if we consider the past unchangeable (which, for practical purposes of retaining one's sanity is preferable).

If we view the past just as much unpredictable as the future in QM, then we get into an interesting variant of many-worlds situation where infinite amounts of pasts converge into observed present from infinite amount of different states, and diverge into infinite amounts of futures.

I am unsure if this would have any hope of working with Copenhagen interpretation, but I suppose technically a many-worlds interpretation with multiple pasts and futures could satisfy the insufficient predictive powers of QM when run in reverse time.


The philosophical implications are, however, somewhat disturbing.

[Mika]

An interesting thought experiment you put up there. Let's see where this leads us.

The thing that I'm thinking is that once the location of the photon is known on the shader, its path might be fixed to a quite a large degree. Could it be so that when passing the slit, it is crucial to have all the surrounding atoms and their electrons to behave exactly the same way as earlier in order to get the photon go opposite in the reversed direction?

I wouldn't worry about the resulting delta yet, we can't know exactly where the photon started to begin with (Heisenberg). Then it goes to the scale of the delta.

Just a couple of thoughts for tonight.

[redsniper]

infinite amounts of pasts converge into observed present from infinite amount of different states, and diverge into infinite amounts of futures.

[watsisname]

The thing that I'm thinking is that once the location of the photon is known on the shader, its path might be fixed to a quite a large degree. Could it be so that when passing the slit, it is crucial to have all the surrounding atoms and their electrons to behave exactly the same way as earlier in order to get the photon go opposite in the reversed direction?

I believe that could be, but quantum mechanics does not deal with this possibility because it cannot.  To remove the probabilistic nature of quantum mechanics would be to completely throw out the theory in exchange for a more complete one, which as of yet does not exist.

By their very nature, the exact position/momentum of the electrons are unknowable without making a measurement that would change them.

[Astronomiya]

I think there's some misunderstanding of what T-symmetry really means in this thread.  Basically, if you set up a new variable t' = -t, insert it into the equation in place of t, and it comes back the same, the equation has T-symmetry.  The Schrodinger equation, for example, does not have T-symmetry by this measure.  A particle's position in classical mechanics does:

Let x = v(t)*t.  Now insert t'=-t; i.e., reverse time.  x does not change sign, but t does, as does velocity, since v = dx/dt, and v' = dx/dt' = dx/(-dt) = -dx/dt = -v.  So, x = v(t')*t' = -v(t)*-t = v(t)*t.  Therefore, a particle's trajectory has T-symmetry in classical mechanics.

Now let's look at electromagnetism.  First, we need Maxwell's Equations.  Gauss's Law (for both electricity and magnetism) is obviously time-symmetric.  If this is not clear, consider what produces electric fields:  charges, which are constant in time.  Faraday's and Ampere's Laws are also time-symmetric, though it might not seem this way at first.  The dt's change sign, as does the current term in Ampere's Law.  That leaves B, the magnetic field.  Because B is generated by currents, when the current changes direction, it changes sign as well.  Therefore, the signs cancel and Maxwell's equations (and, by extension, EM) are T-symmetric.  This extends to quantum EM as well.

Since Herra's thought experiment must incorporate both the QED Lagrangian and quantum dynamics, it will of course not be time-symmetric.  Another way of thinking about this is to realize that reversing time is not like watching a movie backwards; you are fully reversing the direction of time, so that the past is now the future, and the future is now in the past.  When time reverses, you don't "go back in time," you reverse the whole direction of its propagation!

[Herra Tohtori]

Since Herra's thought experiment must incorporate both the QED Lagrangian and quantum dynamics, it will of course not be time-symmetric.  Another way of thinking about this is to realize that reversing time is not like watching a movie backwards; you are fully reversing the direction of time, so that the past is now the future, and the future is now in the past.  When time reverses, you don't "go back in time," you reverse the whole direction of its propagation!

Exactly! This is precisely why I think quantum mechanics can't be truly time symmetric. It doesn't give discrete predictions when going forwards in time, so how could it possibly do so when going backwards? It's impossible to run the model backwards from a certain state and make sure the progression stays on the path of what actually happened, when the model isn't confined to a single timeline of future in the first place.

I can understand how classical electrodynamic equations can be time-symmetric, as they don't take into account the small quantum differences... but even classical physics gets into serious trouble with certain things as far as time-symmetry goes - mainly, thermodynamics.


Like the example I used before, it would be impossible for classical thermodynamics to be run in reverse and see Zoidberg's ink converge back into Zoidberg's ink pouch, because the information of the ink's original location has been lost. Similar things happen if you have two sections of cold and warm water, separated by a wall... you remove the wall, and water mixes and temperature evens out - but when you run the model backwards, there is no possibility to know that the water wasn't an even temperature block to begin with, and even less hope of deriving the original temperature distributions. You'd see an even temperature body of water stay where it is, and then a wall being lowered into the middle of the pool for no apparent reason.

Similarly, I could accept that the photon experiment I described could be valid - if there was a way to retain each photon's wave function. I'm sure there would be way to run the wave function through the slit and reverse the slit's effect on the photon stream based on that, and that way you would be able to pinpoint the photons' original emitter location - but this is impossible; you don't know the wave function that causes the interference pattern just by observing individual photons emerging from the shader when you reverse the time. You just know that this photon emerged from the shader and is traveling towards the double slit...

[Astronomiya]

I never said quantum mechanics was time-symmetric.  In fact, it is explicitly not so as you noted (neither the Dirac equation nor the Schrodinger equation are time-symmetric).  QED, however, as a subset of it, is.  Go test it out on the QED Lagrangian if you want.  Not a single term changes sign in the end.

[Mika]

Another way of thinking about this is to realize that reversing time is not like watching a movie backwards; you are fully reversing the direction of time, so that the past is now the future, and the future is now in the past.  When time reverses, you don't "go back in time," you reverse the whole direction of its propagation!
 

This is an excellent comment.

Regarding Herra Tohtori's thought experiment with a single photon and a dual slit, the following might be relevant to it or not. Suppose a diffraction grating optimized for splitting power between zeroth order and the first order, these diffraction orders are separated by some angle. Now when laser sources are placed in the direction of those orders and both of them fire beams back towards the grating, the beams indeed recombine into one beam and travel towards the original source. This is called a grating beam combiner, though there are better methods of doing the same - I could find only one paper related to researching this. But notice that thin slits are diffraction gratings too.

Now if I think the situation from the classical EM perspective, my answer is that at least when you have the same wavefront starting from the shader directed towards the slit, it will recombine into a direct beam back towards the laser source. Should the slit be a more complex grating, the above thing happens. But I find it difficult to think this in terms of probability functions, and after a slight thinking, Schrödinger equation itself doesn't actually work with photons - and as a personal comment, the thought never crossed my mind earlier (or maybe it's just such a long time since I last read it).

Also, if the nature of the photon travel is probabilistic (electron might emit the photon to any direction), I find it difficult to explain to myself how does a mirror or a lens work as well as it does. QED might give the explanation for that, the answer should be applicable on photons passing the dual slit too. Guess I need to check QED stuff again from the optics perspective, but that'll be tomorrow.

[Astronomiya]

Also, if the nature of the photon travel is probabilistic (electron might emit the photon to any direction), I find it difficult to explain to myself how does a mirror or a lens work as well as it does. QED might give the explanation for that, the answer should be applicable on photons passing the dual slit too. Guess I need to check QED stuff again from the optics perspective, but that'll be tomorrow.

The QED explanation is actually rather similar to the semi-classical one.  The first part of the key is the differing path lengths that photons take from emitter to absorber.  For a mirror, they have a basically equal probability of being scattered in any direction by the atom they strike.  However, if we consider a source S bouncing light off a mirror to a point P, and then draw out all the paths light could take from S to P, it becomes immediately obvious that there is a minimum path length that can be taken, and that the path length varies from path to path.  If we assume that the center of the mirror is point for which a_i=a_r, the optical path length (OPL) is shortest there, and longest at the edges.  The phase of each photon also constantly changes as it flies, so photons following different paths will have different phases when they arrive at P.  This is the second part of the key.  At any given point in time, the probability that you receive a photon from the center of the mirror is higher than of getting one from the edge, due to the differences in travel time.  So, if you draw a phasor diagram of the photons coming off the mirror headed for P, the phasors at the center of the mirror are larger than those at the edges.  In addition, since larger OPL differences correspond to larger phase differences between photons, the photons coming from the center of the mirror are in phase with each other, while those only a little ways out from it are out of phase with their counterparts on the opposite side of the center.  Thus, an observer at P sees an image of S only in the center of the mirror, since the contributions from the other portions of the mirror cancel each other out.

[Herra Tohtori]

Also, if the nature of the photon travel is probabilistic (electron might emit the photon to any direction), I find it difficult to explain to myself how does a mirror or a lens work as well as it does. QED might give the explanation for that, the answer should be applicable on photons passing the dual slit too. Guess I need to check QED stuff again from the optics perspective, but that'll be tomorrow.

It's probabilistic but that really only affects things in quantum scale.

Macroscopic optics is all about wavefronts, which are combined effect of insane amounts of photons traveling in a statistically sufficiently similar way. On individual photons, quantum deviations appear, but on large scale, the wavefront formed by the photons appears united, which is why reflections and refractions work in the first place.

In all optics, there is loss of photons from the wavefront, depending on optical qualities of the mediums and reflective surfaces - scattered or non-uniformly reflected photons are not useful in optics, and avoiding them is the key to observing as much of the photons that arrive into the instrument. Statistically, though, we are unlikely to observe the quantum inaccuracies in each individual photon's arrival location. In terms of physically describing what happens is that the delta spike in the photons' probability functions is narrow enough that without very very small scale instruments, we won't notice any difference whether the photon arrives two picometres this direction or that - it'll still hit the same observation instrument with all likelihood: a pixel, or perhaps a cell in your retina.

Or, the expectation value is almost always very close to where the photon will actually end up.

Quantum inaccuracies really only start to become visible when you look at things in a scale that is at least as small as the deBroglie wavelength of the particle. If you're unable to measure things smaller than this, then you'll likely see the particle's behaviour approximate with classical physics - except in situations where it doesn't, such as the double slit interference experiment, which is perhaps the simplest demonstration of wave-particle duality. In this experiment we FORCE the photons to encounter a formation in the scale of their wavelength, and as a result the photons form up in a typical interference pattern.

In refraction and reflection, individual photons don't typically end up in situations where they would go through something like a double slit - although some statistically predictable amount of photons will scatter into statistically more or less predictable directions - predictability of photon scattering angles depending on whether the optical matter is of regular crystalline quality, or something less regular like gas, liquid, particulate suspension or the like. This is used in x-ray crystallography, where the x-ray photons' scattering angles depend on the qualities of the crystal. But I digress.

If you look at a reflection or refraction in quantum terms you'll notice that even if you handle each photon individually, the statistical prediction of how the wavefront will look after reflection or passing through the lens, it'll be largely intact - sufficiently so that we can recognize it as the original image, if projected on a surface. Remember that wavefronts staying intact depends on the quality of surface they are reflected from, and from the quality of the optical border between mediums that they travel through (as well as the transparency of the mediums, how much scattering occurs etc.). Individual photons don't see any difference between different kind of surfaces - say, glass or paper. When photons are reflected from paper, they are diffused into lots of different directions depending on what part of the paper they hit. But when multiple photons are reflected similarly, then their wavefront remains recognizeable, and our optics can work.



After all, photons never interfere with each other - the interference patterns like the one in double slit experiment, or Newton's rings, results from their own wave characteristic interfering with itself, so a wavefront traveling through a medium is safe from collapsing by photons in it interfering each other into oblivion.

Schrödinger equation itself doesn't actually work with photons

It's true that Schrödinger equation isn't ideally suited for photons (you need to jump through some hoops to use it) but in context of the thought experiment, this argument is irrelevant as the photons can be substituted by an electron beam or individual electrons, and the fundamental result is the same...

[Mika]

I'm aware of QED explanation being quite close to Fermat's principle, though the question I actually have about that is that the photon should then see all the possible paths towards any detector, and somehow it explores all the possible routes simultaneously and chooses the shortest one in space time. But never mind, I'm perfectly happy that the Fermat's principle exists, it makes my work considerably easier. But after having relied on it for several years one though starts to think where does this thing actually stem from. This is similar to one of the memorable quotes I heard in a lecture was from a professor in Electrical Engineering, who stated that after 20 years he now starts to understand the deeper meaning of the Ohm's law... A photon is a time like particle, and it would be interesting think the microscopic situation from its perspective. How does it see the microscopic world when it travels through a medium.

The interesting thing here is that superficially macroscopic tests allow for a time reversal. But once somebody evaluates the situation in microscopic level and counts individual photons, that isn't possible anymore. But, it is unclear to me what is the effect of the electrons in the structure of the slit in a double slit experiment.