You’re right. I was looking for a mechanical/local answer. (I have been since high school physics when I completely rejected the way magnetism was explained, only to find that was the way it is always explained).
If I found such an answer here—and I wouldn’t be totally surprised if I did—I would use that answer about light to try and maybe finally understand electromagnetism better.
What do you mean “mechanical/local”? Maxwell’s equation’s (in what I consider their most fundamental form) describe how the electric and magnetic fields change at any point based on derivatives of those fields, the charge, and the movement of charges at that point. That is certainly local. And, together with the laws describing the forces experienced by charges in the fields (also local), they mechanically describe how a system will evolve.
OK, I’ll update again that it is just me that doesn’t understand the light wave mechanically. (I didn’t mean this facetiously—I know light is really strange for everyone, I just meant that I can’t seem to possibly understand it.)
Do you mean that you do not understand Maxwell’s equations? That you don’t understand how the wave mechanics are derived from Maxwell’s equations? Or that some part of this is not “mechanical”?
I’m beginning to suspect that my insistence on understanding things a certain way is peculiar and possibly overly narrow.
But suppose that I look outside my window and see a light wobbling across the horizon. I think that I don’t understand the trajectory of the light. Then someone finds the equation that describes the motion of the light: it turns out to be perfectly regular and periodic. I still feel I don’t understand it. For me, the path of the light isn’t understood until you discover that the light is a reflector attached to the wheel of a car, and the trajectory you see is a combination of the car’s linear movement and wheel’s rotation. This is what I mean by a mechanical understanding.
I could study Maxwell’s equations, but I know they wouldn’t help. Do we have a ‘mechanical’ understanding of the motion of light, or just the equation description?
Are you saying you want to understand light as being made out of components that behave like the macroscopic objects you are used to interacting with? That isn’t going to happen, because light does not work that way.
I don’t mind if light behaves in different ways than I’m used to, but I still expect that these ways are causally dependent upon other things. Especially with a spatial pattern, I expect that any pattern produced by certain geometric rules can be reproduced by a model of those rules.
Even at the macroscopic scale—if a model is possible (physically realizable) at that scale. If it is not possible, I would have to spend a lot of mental energy modeling those rules mentally, but that would still lead to mechanical understanding. My problem is that I haven’t heard (or don’t believe I’ve heard) exactly what rules should be modeled.
Um. I’m having one of those I-can’t-believe-I’ve-been-this-stupid-over-the-last-ten-years moments.
I went back and reread what you wrote and the part I missed before was this:
The wave described is light.
So it isn’t that light “happens to follow” this wave equation. That wave equation IS light—that is, that specific interaction between the electric and magnetic fields is light.
Honestly, I’d never thought of it that way before. I can go back to that chapter in electromagnetism and see if I understand things differently now.
I look at the light bulb on my desk and I wouldn’t even call it ‘light’ anymore. It is electromagnetic interaction.
I photographically recall the poster over an exhibit at a science museum, “Light Is Electromagnetic Radiation’. I thought that meant that light was radiation (obviously, it radiates) that was associated in some way with electromagnetic theory and I remember thinking it was a decidedly unpleasant verbal construction.
You know, this really calls for a cartoon-y cliche “light bulb turning on” appearing over byrnema’s head.
It’s interesting the little connections that are so hard to make but seem simple in retrospect. I give it a day or so before you start having trouble remembering what it was like to not see that idea, and a week or so until it seems like the most obvious, natural concept in the world (which you’ll be unable to explain clearly to anyone who doesn’t get it, of course).
(which you’ll be unable to explain clearly to anyone who doesn’t get it, of course)
Seriously. Apparently, I wrote the key insight she needed (not knowing that it was the missing insight), but she didn’t click on it the first time, and then, as I am asking questions to try to narrow down what the confusion is, something I said, as a side effect, prompted her to read that insight again and she got it. Now, how can one systematically replicate a win like that?
I remember you and I also discussed what it means to understand something, and I definitely sympathize and largely agree with your standard for what counts as “understanding”. (I’ll find the link to that discussion when I get a chance.)
My standard is that you understand something if and to the extent that:
1) You have a mathematical model that generates the observations with good success. (Not necessary here what labels you use—this part can be “Chinese room”-ish.)
2) That model is deeply connected (via the entities it shares, quantities it uses, mutual interaction, etc.) to your model for everything else, and thus connected, ultimately, to your intuitive (raw, qualia-laden) model of the world.
Correct me if I’m wrong, but I think this is where you are: for light, you understand it in the sense of meeting 1), but don’t meet it with respect to 2). Would you say that is accurate?
I am not certain if this is going to be helpful, but I’m going to try re-expressing what the equations describe, in non-mathy words. It seems to me that the local understanding you are looking for actually is contained in Maxwell’s equations, and that you are blocking on something in that description. Of course I could be quite mistaken in this; it’s hard to understand a multi-year confusion based on a few forum posts. So if I’m not helpful here, sorry!
Let me start with an antenna; that is, a straight, electricity-conducting piece of metal. I run an electric current through it, or more accurately, I start running a current. As I’m doing this, the electric field within the antenna is changing; electrons are moving around, spitting out photons, and generally changing their state, heading towards the steady movement they’ll have when the current is fully established. Before they can get there, however, I perversely and maliciously reverse the current’s direction, and the electrons scramble to attain a completely different steady state! In fact, at no time in the following is the antenna going to be in an equilibrium state; I, the experimenter, am constantly changing its condition and keeping the electrons hopping.
Now, when I change the electric field in this manner, that change causes a magnetic field to arise. It seems possible to me that this step is the cause of your confusion, so I’ll digress a bit: Why does a changing electric field cause a magnetic field? Maxwell’s equations do not say anything about the causation; they merely quantify the observed fact. Studying Maxwell does not give you any greater understanding of the causation than you would have from the good old 1830s experiment of running a current through a wire and seeing a nearby compass needle deflected; all it does is to allow you to calculate how much deflection to expect. I often see this sort of confusion in the way basic physics is taught; because the equations are the full description of what’s going on, people expect them also to contain the full understanding at the causal level. So there is confusion about Maxwell, and also about special relativity; people ask “What does it mean that the time-direction’s sign is reversed in the inner product?”, and the answer is that it describes the way matter behaves, but the causality is much deeper. It may be a mistake to teach Newton before anything else in physics, just because F=ma is so intuitively clear; we all see that this is just a formalisation of the way rocks behave. Throw the rock harder and it hits the other monkey faster, causing more damage: Our brains are well adapted to this piece of physics! But it does us a disservice in studying other equations, because we expect them to be similarly clear and contain a similar causal-level explanation, and they just don’t.
At any rate, then, the crucial point is that when I move the electrons, they cause a magnetic field to exist. If you look deeply enough into QED, you can find an explanation of this in the way the force-carrier photons are moving, but personally I am quite unable to visualise this; all I can do is go through the math that shows Maxwell’s equations coming out as the classical limit of QED. (Well, anyway, I could do it for an exam some years ago.) However, it may be helpful to visualise it like so: When I accelerate the electrons, the virtual photons that they spat out a few nanoseconds ago (messengers for their electric field) are ‘unable to return home’ (home having moved) and must find something else to do; the something else is to interact with other particles, which we measure as a magnetic field.
Now, because I’m varying the acceleration of the electrons, the size of the magnetic field caused by their acceleration is also changing. And a varying magnetic field… causes an electric field. It is inaccurate, but possibly helpful, to view this as being caused by the aforementioned no-longer-so-virtual photons interacting with electrons in the quantum foam and moving them around, creating a momentary polarisation of space.
So now there is a changing electric field not just at the antenna where I’m doing my thing with the electric current, but also some distance away where the resulting magnetic field is causing a reflection of that process. Rinse and repeat: This electric field’s changing causes a magnetic field over here, which causes… You will get a chain of electric/magnetic fields running across the entire universe. This is what is meant by a ‘light wave’.
Maxwell allows us to describe in numbers what I just described in words, but the causal understanding is all in the observed fact that a changing (not a steady) electric current causes a compass needle to deflect. You can take this as unadorned, experimental observation, “We don’t know why that happens”, or you can try to visualise it in terms of messenger photons as I outlined above. I hope that helps.
Thank you for this explanation, it includes exactly the sort of mechanical explanations I was looking for. Not necessarily simple or easy to understand, but about entities with certain properties interacting in certain ways.
When I accelerate the electrons, the virtual photons that they spat out a few nanoseconds ago (messengers for their electric field) are ‘unable to return home’ (home having moved) and must find something else to do; the something else is to interact with other particles, which we measure as a magnetic field.
For example, this is a mechanical explanation. It’s probably somewhat inaccurate due to being expressed verbally, but a person can then turn to the equations to get the detailed, accurate picture.
I often see this sort of confusion in the way basic physics is taught; because the equations are the full description of what’s going on, people expect them also to contain the full understanding at the causal level.
I think I would have done so much better in physics if they had explained the causality with the equations. For me, now, understanding that light is the interaction of the electric and magnetic fields has been a wonderful paradigm shift in way I view things. I had already assimilated that most things I experience are electrostatic—that a table is non-compressible and the chair supports me because of electrons and their interactions. And now my idea of light has changed—I no longer see it as an independent substance reaching me, but as information about the change in an electric field propagating towards me at a fixed speed from whatever sources are emitting or reflecting the light.
My ideas are topsy-turvy at the moment, it will take some time and reading for them to settle in any accurate way. But I’ll share some of my first-day thoughts . For example: A room full of light is ‘bright’ because the light contains so much information. And: it seems amazing that visible light is so faithful (non-noisy) when you think of it as a wave propagating in all directions; only a particle at the moment of observation.
A room full of light is ‘bright’ because the light contains so much information. And: it seems amazing that visible light is so faithful (non-noisy) when you think of it as a wave propagating in all directions; only a particle at the moment of observation.
I find that your bright room-observation and an analogy with low-light photography almost helps me grasp how come the world seems classical despite its quantum “underwear”:
Think of a (digital) photograph taken in very low light. Something like this.
Think of being in a pitch black room, and imagine your eyes are perfectly sensitive. You have a flashlight pointed away from you.
Now imagine the flashlight is very dim: it only sends one photon every few seconds, by moving one of its electrons; the electric field propagates at c as a spherical wavefront to “notify the universe” of the change. Whenever this front passes through another electron (say, of the wall before you), it may be absorbed. If it’s not absorbed, the electron does nothing (in a way, it doesn’t care that the first electron changed position). However, if it is absorbed (the two electrons exchanged a photon), then the absorbing electron now changes position to conform to the new information; doing so starts another wave-front communicating this information. Note that this second wave-front is not just going back, it’s still a spherical front starting from the wall electron. Again it starts propagating through space until it hits another electron. Suppose this last electron is used by your eye as a detector. Then you just noticed a tiny “flash” of light somewhere in your vision field.
Note that the two absorptions happen (until now) randomly. If you use just that flashlight you’ll only see random flashes in the room. More precisely, in the many-worlds interpretations, from a single train of emission-absorption-reemission-detection “events”, each you in every world will see the tiny flash in random parts of their vision field. This is both because different wall electrons would have done the absorption-reemission, and because of different electrons in your eyes would do the detection. You can extend this metaphor a bit more: in worlds where the re-emitted photon didn’t hit your eye, but (say) another electron deeper in the wall, that world’s version of you won’t notice anything. (The absorption-reemission chain will just bounce electrons and nuclei randomly throughout the wall, which just means heat.)
OK, here’s the “brightness” part: even though the absorption-reemission electron is randomly chosen by each world, not all of them are equally likely to be chosen. The wave-functions of the particles, and the interactions of those wave-functions as given by QM equations, cause the distribution of “picks” to have a certain “shape”.
Imagine that you take your flash-light and you increase its brightness; say it sends 10, then 100, then a million photons at the same time. You’ll start seeing several flashes, from random positions in your field of vision. (Each of you in the many-worlds will see the flashes coming from different places.) But the wave-function says how likely it is that you’ll see flashes from different places: even if each version of you sees different flashes, each of them will see more flashes coming from bright (white) objects than from dark (black) objects. As a result, you’ll see a grainy image of room in all worlds, even though a different one (that is, with the grain positioned differently) in each. The more photons your flashlight sends, the more “smooth” your image will be, converging on the “shape” of the wave-function. The image above shows a noisy image obtained in low light (although for normal cameras the source of noise is different).
Imagine you take several consecutive photos in those conditions; each image will be very grainy and dim, and the position of grain will vary among your many-world alternates. However, if you combine your successive photos in one, you’ll accumulate a brighter, clearer image (the more so as you add more photos). Each many-world version of you will get a different one, but they’ll converge to the same: the shape of the world’s wave-function. (Of course, the different worlds will eventually diverge in shape, too.)
You can stretch this analogy to visualize all sorts of interactions. For bright objects the re-emission is more likely to occur “towards” the outside of the object (or, inversely, electrons within bright objects tend to not communicate between themselves the news about outside). For dark objects it’s the other way around: photons are more likely to be passed among the object’s electrons rather than towards you.
Or take diffraction: A photon is emitted, passes through a screen with two holes (thus, it’s not absorbed by its electrons), and hits a wall. Even if you send photons one-by-one, they’ll still form a diffraction pattern on the wall. You can imagine it this way: the initial emission (the wave-front carrying the message) is spherical; when it hits the screen, either it’s absorbed (the message was passed to the screen), and you see nothing), or not: the message passed through both holes. But from each hole the message continues to propagate in a sphere centered on that hole. When the “message” hits the detector area, it is both these spheres that hit; depending on the difference in distance of the two paths, in some areas the two “copies” of the message can contradict each other or agree; you’ll have successful detection (a movement of an electron in the detector wall) only where the two copies agree, thus forming the interference pattern—but, for a single photon, exactly what point of the interference pattern will be hit is random.
You’re right. I was looking for a mechanical/local answer. (I have been since high school physics when I completely rejected the way magnetism was explained, only to find that was the way it is always explained).
If I found such an answer here—and I wouldn’t be totally surprised if I did—I would use that answer about light to try and maybe finally understand electromagnetism better.
What do you mean “mechanical/local”? Maxwell’s equation’s (in what I consider their most fundamental form) describe how the electric and magnetic fields change at any point based on derivatives of those fields, the charge, and the movement of charges at that point. That is certainly local. And, together with the laws describing the forces experienced by charges in the fields (also local), they mechanically describe how a system will evolve.
OK, I’ll update again that it is just me that doesn’t understand the light wave mechanically. (I didn’t mean this facetiously—I know light is really strange for everyone, I just meant that I can’t seem to possibly understand it.)
Do you mean that you do not understand Maxwell’s equations? That you don’t understand how the wave mechanics are derived from Maxwell’s equations? Or that some part of this is not “mechanical”?
I’m beginning to suspect that my insistence on understanding things a certain way is peculiar and possibly overly narrow.
But suppose that I look outside my window and see a light wobbling across the horizon. I think that I don’t understand the trajectory of the light. Then someone finds the equation that describes the motion of the light: it turns out to be perfectly regular and periodic. I still feel I don’t understand it. For me, the path of the light isn’t understood until you discover that the light is a reflector attached to the wheel of a car, and the trajectory you see is a combination of the car’s linear movement and wheel’s rotation. This is what I mean by a mechanical understanding.
I could study Maxwell’s equations, but I know they wouldn’t help. Do we have a ‘mechanical’ understanding of the motion of light, or just the equation description?
Are you saying you want to understand light as being made out of components that behave like the macroscopic objects you are used to interacting with? That isn’t going to happen, because light does not work that way.
I don’t mind if light behaves in different ways than I’m used to, but I still expect that these ways are causally dependent upon other things. Especially with a spatial pattern, I expect that any pattern produced by certain geometric rules can be reproduced by a model of those rules.
Even at the macroscopic scale—if a model is possible (physically realizable) at that scale. If it is not possible, I would have to spend a lot of mental energy modeling those rules mentally, but that would still lead to mechanical understanding. My problem is that I haven’t heard (or don’t believe I’ve heard) exactly what rules should be modeled.
Earlier I said (emphasis added):
Would it make more sense if I said:
Um. I’m having one of those I-can’t-believe-I’ve-been-this-stupid-over-the-last-ten-years moments.
I went back and reread what you wrote and the part I missed before was this:
So it isn’t that light “happens to follow” this wave equation. That wave equation IS light—that is, that specific interaction between the electric and magnetic fields is light.
Honestly, I’d never thought of it that way before. I can go back to that chapter in electromagnetism and see if I understand things differently now.
I look at the light bulb on my desk and I wouldn’t even call it ‘light’ anymore. It is electromagnetic interaction.
I photographically recall the poster over an exhibit at a science museum, “Light Is Electromagnetic Radiation’. I thought that meant that light was radiation (obviously, it radiates) that was associated in some way with electromagnetic theory and I remember thinking it was a decidedly unpleasant verbal construction.
I’m thankful, and sorry...
You know, this really calls for a cartoon-y cliche “light bulb turning on” appearing over byrnema’s head.
It’s interesting the little connections that are so hard to make but seem simple in retrospect. I give it a day or so before you start having trouble remembering what it was like to not see that idea, and a week or so until it seems like the most obvious, natural concept in the world (which you’ll be unable to explain clearly to anyone who doesn’t get it, of course).
Seriously. Apparently, I wrote the key insight she needed (not knowing that it was the missing insight), but she didn’t click on it the first time, and then, as I am asking questions to try to narrow down what the confusion is, something I said, as a side effect, prompted her to read that insight again and she got it. Now, how can one systematically replicate a win like that?
Be polite and patient when people are confused?
Well, that is important. But that is more part of not automatically failing, than actually making progress towards dispelling the confusion.
Lacking understanding, that’s the best advice I can give.
I remember you and I also discussed what it means to understand something, and I definitely sympathize and largely agree with your standard for what counts as “understanding”. (I’ll find the link to that discussion when I get a chance.)
My standard is that you understand something if and to the extent that:
1) You have a mathematical model that generates the observations with good success. (Not necessary here what labels you use—this part can be “Chinese room”-ish.)
2) That model is deeply connected (via the entities it shares, quantities it uses, mutual interaction, etc.) to your model for everything else, and thus connected, ultimately, to your intuitive (raw, qualia-laden) model of the world.
Correct me if I’m wrong, but I think this is where you are: for light, you understand it in the sense of meeting 1), but don’t meet it with respect to 2). Would you say that is accurate?
I am not certain if this is going to be helpful, but I’m going to try re-expressing what the equations describe, in non-mathy words. It seems to me that the local understanding you are looking for actually is contained in Maxwell’s equations, and that you are blocking on something in that description. Of course I could be quite mistaken in this; it’s hard to understand a multi-year confusion based on a few forum posts. So if I’m not helpful here, sorry!
Let me start with an antenna; that is, a straight, electricity-conducting piece of metal. I run an electric current through it, or more accurately, I start running a current. As I’m doing this, the electric field within the antenna is changing; electrons are moving around, spitting out photons, and generally changing their state, heading towards the steady movement they’ll have when the current is fully established. Before they can get there, however, I perversely and maliciously reverse the current’s direction, and the electrons scramble to attain a completely different steady state! In fact, at no time in the following is the antenna going to be in an equilibrium state; I, the experimenter, am constantly changing its condition and keeping the electrons hopping.
Now, when I change the electric field in this manner, that change causes a magnetic field to arise. It seems possible to me that this step is the cause of your confusion, so I’ll digress a bit: Why does a changing electric field cause a magnetic field? Maxwell’s equations do not say anything about the causation; they merely quantify the observed fact. Studying Maxwell does not give you any greater understanding of the causation than you would have from the good old 1830s experiment of running a current through a wire and seeing a nearby compass needle deflected; all it does is to allow you to calculate how much deflection to expect. I often see this sort of confusion in the way basic physics is taught; because the equations are the full description of what’s going on, people expect them also to contain the full understanding at the causal level. So there is confusion about Maxwell, and also about special relativity; people ask “What does it mean that the time-direction’s sign is reversed in the inner product?”, and the answer is that it describes the way matter behaves, but the causality is much deeper. It may be a mistake to teach Newton before anything else in physics, just because F=ma is so intuitively clear; we all see that this is just a formalisation of the way rocks behave. Throw the rock harder and it hits the other monkey faster, causing more damage: Our brains are well adapted to this piece of physics! But it does us a disservice in studying other equations, because we expect them to be similarly clear and contain a similar causal-level explanation, and they just don’t.
At any rate, then, the crucial point is that when I move the electrons, they cause a magnetic field to exist. If you look deeply enough into QED, you can find an explanation of this in the way the force-carrier photons are moving, but personally I am quite unable to visualise this; all I can do is go through the math that shows Maxwell’s equations coming out as the classical limit of QED. (Well, anyway, I could do it for an exam some years ago.) However, it may be helpful to visualise it like so: When I accelerate the electrons, the virtual photons that they spat out a few nanoseconds ago (messengers for their electric field) are ‘unable to return home’ (home having moved) and must find something else to do; the something else is to interact with other particles, which we measure as a magnetic field.
Now, because I’m varying the acceleration of the electrons, the size of the magnetic field caused by their acceleration is also changing. And a varying magnetic field… causes an electric field. It is inaccurate, but possibly helpful, to view this as being caused by the aforementioned no-longer-so-virtual photons interacting with electrons in the quantum foam and moving them around, creating a momentary polarisation of space.
So now there is a changing electric field not just at the antenna where I’m doing my thing with the electric current, but also some distance away where the resulting magnetic field is causing a reflection of that process. Rinse and repeat: This electric field’s changing causes a magnetic field over here, which causes… You will get a chain of electric/magnetic fields running across the entire universe. This is what is meant by a ‘light wave’.
Maxwell allows us to describe in numbers what I just described in words, but the causal understanding is all in the observed fact that a changing (not a steady) electric current causes a compass needle to deflect. You can take this as unadorned, experimental observation, “We don’t know why that happens”, or you can try to visualise it in terms of messenger photons as I outlined above. I hope that helps.
Thank you for this explanation, it includes exactly the sort of mechanical explanations I was looking for. Not necessarily simple or easy to understand, but about entities with certain properties interacting in certain ways.
For example, this is a mechanical explanation. It’s probably somewhat inaccurate due to being expressed verbally, but a person can then turn to the equations to get the detailed, accurate picture.
I think I would have done so much better in physics if they had explained the causality with the equations. For me, now, understanding that light is the interaction of the electric and magnetic fields has been a wonderful paradigm shift in way I view things. I had already assimilated that most things I experience are electrostatic—that a table is non-compressible and the chair supports me because of electrons and their interactions. And now my idea of light has changed—I no longer see it as an independent substance reaching me, but as information about the change in an electric field propagating towards me at a fixed speed from whatever sources are emitting or reflecting the light.
My ideas are topsy-turvy at the moment, it will take some time and reading for them to settle in any accurate way. But I’ll share some of my first-day thoughts . For example: A room full of light is ‘bright’ because the light contains so much information. And: it seems amazing that visible light is so faithful (non-noisy) when you think of it as a wave propagating in all directions; only a particle at the moment of observation.
I find that your bright room-observation and an analogy with low-light photography almost helps me grasp how come the world seems classical despite its quantum “underwear”:
Think of a (digital) photograph taken in very low light. Something like this.
Think of being in a pitch black room, and imagine your eyes are perfectly sensitive. You have a flashlight pointed away from you.
Now imagine the flashlight is very dim: it only sends one photon every few seconds, by moving one of its electrons; the electric field propagates at c as a spherical wavefront to “notify the universe” of the change. Whenever this front passes through another electron (say, of the wall before you), it may be absorbed. If it’s not absorbed, the electron does nothing (in a way, it doesn’t care that the first electron changed position). However, if it is absorbed (the two electrons exchanged a photon), then the absorbing electron now changes position to conform to the new information; doing so starts another wave-front communicating this information. Note that this second wave-front is not just going back, it’s still a spherical front starting from the wall electron. Again it starts propagating through space until it hits another electron. Suppose this last electron is used by your eye as a detector. Then you just noticed a tiny “flash” of light somewhere in your vision field.
Note that the two absorptions happen (until now) randomly. If you use just that flashlight you’ll only see random flashes in the room. More precisely, in the many-worlds interpretations, from a single train of emission-absorption-reemission-detection “events”, each you in every world will see the tiny flash in random parts of their vision field. This is both because different wall electrons would have done the absorption-reemission, and because of different electrons in your eyes would do the detection. You can extend this metaphor a bit more: in worlds where the re-emitted photon didn’t hit your eye, but (say) another electron deeper in the wall, that world’s version of you won’t notice anything. (The absorption-reemission chain will just bounce electrons and nuclei randomly throughout the wall, which just means heat.)
OK, here’s the “brightness” part: even though the absorption-reemission electron is randomly chosen by each world, not all of them are equally likely to be chosen. The wave-functions of the particles, and the interactions of those wave-functions as given by QM equations, cause the distribution of “picks” to have a certain “shape”.
Imagine that you take your flash-light and you increase its brightness; say it sends 10, then 100, then a million photons at the same time. You’ll start seeing several flashes, from random positions in your field of vision. (Each of you in the many-worlds will see the flashes coming from different places.) But the wave-function says how likely it is that you’ll see flashes from different places: even if each version of you sees different flashes, each of them will see more flashes coming from bright (white) objects than from dark (black) objects. As a result, you’ll see a grainy image of room in all worlds, even though a different one (that is, with the grain positioned differently) in each. The more photons your flashlight sends, the more “smooth” your image will be, converging on the “shape” of the wave-function. The image above shows a noisy image obtained in low light (although for normal cameras the source of noise is different).
Imagine you take several consecutive photos in those conditions; each image will be very grainy and dim, and the position of grain will vary among your many-world alternates. However, if you combine your successive photos in one, you’ll accumulate a brighter, clearer image (the more so as you add more photos). Each many-world version of you will get a different one, but they’ll converge to the same: the shape of the world’s wave-function. (Of course, the different worlds will eventually diverge in shape, too.)
You can stretch this analogy to visualize all sorts of interactions. For bright objects the re-emission is more likely to occur “towards” the outside of the object (or, inversely, electrons within bright objects tend to not communicate between themselves the news about outside). For dark objects it’s the other way around: photons are more likely to be passed among the object’s electrons rather than towards you.
Or take diffraction: A photon is emitted, passes through a screen with two holes (thus, it’s not absorbed by its electrons), and hits a wall. Even if you send photons one-by-one, they’ll still form a diffraction pattern on the wall. You can imagine it this way: the initial emission (the wave-front carrying the message) is spherical; when it hits the screen, either it’s absorbed (the message was passed to the screen), and you see nothing), or not: the message passed through both holes. But from each hole the message continues to propagate in a sphere centered on that hole. When the “message” hits the detector area, it is both these spheres that hit; depending on the difference in distance of the two paths, in some areas the two “copies” of the message can contradict each other or agree; you’ll have successful detection (a movement of an electron in the detector wall) only where the two copies agree, thus forming the interference pattern—but, for a single photon, exactly what point of the interference pattern will be hit is random.
Nitpick: s/similar causal-level explanation/similar intuitive appearance of a causal-level explanation/