0811: "Starlight"

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Re: 0811: "Starlight"

Postby davidstarlingm » Wed Oct 27, 2010 8:00 pm UTC

jspenguin wrote:Interesting question: when a photon hits a mirror, does the original photon bounce or does it get absorbed, then a new photon is emitted? Is there, physically speaking, a difference?


Wow -- this is one of those times that the comic was great and the alt-text was cool, but the forum discussion made everything great. JSPenguin, great job with sparking a MASSIVE discussion with such a simple question....

I only recently figured out the neat fact that Randall references in the alt text. So, (obligatory) GOOMHR.

I'm a college senior finishing my B.S. in physics. My primary fields of research have been optics, astrophysics, and relativity, so I should be able to provide SOME decent answer to this.

atimholt wrote:Feynman's QED actually explains the reflection thing really well. It all has to do with the wave-like nature of light, and the reflecting surface not absorbing too much of it.


Most "sciencey" people are familiar with Einstein's two Postulates:

  • Postulate 1: The laws of Nature, the ways in which things behave, are the same in all inertial systems regardles of their speeds.
  • Postulate 2: The speed of light in a vaccum is completely independent of the motion of the source emitting it.

What is less well-known is that he had a third and fourth Postulate:

  • Postulate 3: Feynman will always be right.
  • Postulate 4: Whoever cites Feynman will automatically win.

So, yes. Feynman is right. However, in this case, citing Feynman gives an incomplete picture of the problem, because he was primarily discussing the issue based on semi-classical wave equations. The original question was "when a (singular) photon hits a mirror....", so we are dealing with individual photon behavior, not the wave nature of light. A beam of light is a wave with stream-of-particle characteristics; a photon of light is a particle with wave-like characteristics. Based on Randall's comic, it is the individual photon that we want to address (keeping in mind its wave-like properties).

The important thing to remember is that this is completely different from normal "absorption" that we would generally imagine happening. Spectral absorption takes place when a broad spectrum of light passes through a particular gas. Any photons whose wavelength gives them the specific energy of an electron excitation in that gas (for instance, one of the hydrogen excitations from n' = 2, given by the Balmer series, has an energy of 2.82 eV, which corresponds to a photon wavelength of 410 nm) is completely absorbed by one of the atoms in the gas, exciting that atom (this is why there an absorption line in the solar light spectrum at 410 nm). Note: this is one way we can determine precisely the degree of redshift in light from a distant star; it is not merely the overall spectrum that is redshifted, but the specific spectral line structures themselves.

When an individual photon strikes a mirror, however, a few things happen. A mirror is some metallic/reflective surface covered by a pane of glass. Since the refractive index of air is different from that of glass, the photon is slowed down as it enters the glass, and the wavelength is compressed so the energy of that photon stays constant. Assuming that the photon's path was not perfectly perpendicular to the mirror, this wavefront compression will translationally alter the path of the photon by some angle. Thus, the particle's direction changed because of a wave property interaction.

When the photon strikes the boundary between the glass and the reflective surface, the same kind of thing happens. As a wave, the photon is absorbed and re-radiated, so the particle itself bounces away from the surface. It is the same photon, but the wave that composes it has undergone a transformation that changed its direction.

So, the answer is this: the wave-like part of the photon is absorbed and re-emitted; the particle-like part of the photon simply bounces. At no point in time does the photon cease to exist. This is different from spectral absorption/emission, where the photon is completely absorbed and ceases to exist, then has its energy emitted as a new photon a few microseconds later.

A decrease in light intensity after reflection is not the result of anything that happens to the individual photon, but is rather a consequence of impurities in the mirror that cause a few photons to be completely absorbed (like spectral absorption) and not reflected at all. Usually, this absorption does not result in any subsequent emission; the energy is just spread out to the rest of the mirror as a tiny bit of heat.

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Re: 0811: "Starlight"

Postby Dark567 » Wed Oct 27, 2010 9:42 pm UTC

Berke wrote:Another favorite of mine. So deep and, well... deep.

Love the Alt-text too, I've always tried imaginining myself seeing things from the perspective of a photon.

Also,
littlelj wrote:Also,

Image

I heart this comic. Whimsy. Awesome.


Where is this comic from? I couldn't locate it... But I could LOVE it.


Its from the book Godel, Escher, Bach: An Eternal Golden Braid, by Douglas Hofstadter.
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Yakk wrote:The question the thought experiment I posted is aimed at answering: When falling in a black hole, do you see the entire universe's future history train-car into your ass, or not?

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Re: 0811: "Starlight"

Postby davidstarlingm » Wed Oct 27, 2010 11:24 pm UTC

DamnedHeathen wrote:I didn't get that that was a mirror at first. I thought it was a frame so that the character (who is wearing a beret and possibly implied to be an artist) could look at the sky as if it were a painting. The other possibility was that it was an HDTV frame, which would make this comic similar to a Calvin and Hobbes when he ponders his insignificance looking at the night sky, and then runs to the comfort of a warm house and television set.

As for wheather the same photon is reflected from a frame, I'd say that you reach a level of abstraction similar to wondering if when typing on a keyboard, you left-arrow over some text that you have typed and insert some other text, are the letters that got scootched over the *same* letters that you typed or merely copies of them? That is to say, is there anything distinguishing those letters from the letters that you would see if you deleted and retyped the text. Does the 'j' on your screen the *same* 'j' after you space it over to the right a bit?

Also, after you have lived long enough, and a lot of the individual molecules and cells in your body have been replaced, are you still the same person?


I, too, first thought it was a frame.

As far as your body parts being replaced....reminds me of http://xkcd.com/659.

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Re: 0811: "Starlight"

Postby Maximus_Light » Wed Oct 27, 2010 11:31 pm UTC

Awe. He's not bright but he's a good man.

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Re: 0811: "Starlight"

Postby Diadem » Wed Oct 27, 2010 11:39 pm UTC

lank wrote:
Diadem wrote:So what happens at the speed of light itself? Well, the length goes to zero. Everything in its direction of travel (forward and backwards!) is compressed to a point. What does that mean. It means that you lose a dimension. Light lives in a 2 dimensional universe. It can look to the sides in every direction, but it can't look forward or backwards. That dimension simply does not exist anymore for light.

light lives in a 4D universe (just like the rest of us) - it just lives on the null paths within it, because the metric is (ds)2 = c(dt)2 - (dx)2. there are no frames in this metric where any of the lengths is zero or a dimension "removed" - no matter how fast you're going in any direction relative to one frame, light is always moving at c in that direction in both frames. i.e. you can only approach the speed of light relative to another frame, and no lorentz boost can put you in the same frame as a photon - because that frame does not exist.

The frame must exist. Light lives in it.

We often say 'nothing can travel at the speed of light'. Indeed, neither we, nor any other object with mass, can travel at the speed of light. But light obviously can, so you must be careful with that statement. If you try to explain relativity to a highschool student you would say something like "The closer your speed gets to the speed of light, the more energy is required to accelerate further. As you approach c, the energy required goes to inifinity, so you can never reach c itself". A smart highschool student will notice that this explanation is not entirely satisfactory. It forbids reaching the speed of light, but not travelling at it. So you will have to explain about Lorentz transformations and stuff like that, and finally arrive at your statement "there is no inertial frame of reference that travels with the speed of light". A situation where you or I are travelling at the speed of light would be like having a square circle. It simply does not exist.

But the adjective is important. There is no inertial frame of reference that travels at the speed of light (relative to some other inertial frame). Absolutely true. But light doesn't care, it still happily travels at the speed of light. So obviously some sort of frame exists. The question "what does the universe look like from the point of view of a photon" is an entirely valid one. And you can't escape it by saying that travelling at the speed of light makes no physical sense, because light does.

The explanation I gave in my previous post is absolutely correct. A photon lives in a 2-dimensional universe. There is no forward direction for a photon. Nor is there time. This is intuitively clear if you realize that length and time go to zero if you approach the speed of light. That's not an entirely rigorous explanation, I admit, but if you want rigor you're going to have to do a lot of courses in theoretical physics.

But as an example let's look at the degrees of freedom of the photon. According to Maxwell the electromagnetic field has 2. So photons better have two as well. And indeed if you do the calculations it turns out they have only 2. But how can you have only 2 degrees of freedom in a 3-dimensional world? Simple, but not living in a 3-dimensional world at all :)
Last edited by Diadem on Wed Oct 27, 2010 11:41 pm UTC, edited 2 times in total.
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Re: 0811: "Starlight"

Postby davidstarlingm » Wed Oct 27, 2010 11:40 pm UTC

Eternal Density wrote:Yeah, the electron is going to fall back to the energy level it started from, thus the same colour of light. When looking at an 'infinite' reflection between parallel mirrors, it gets darker, not redder.

In other words, HighSchoolPhysicsTeacherFail.


Yes, very HighSchoolPhysicsTeacherFail. Individual photons have one parameter, and one parameter only: wavelength. Energy is dependent only on wavelength (alternately, frequency, if you want to be tricky). The "intensity" of an individual photon is meaningless; there is no way that one 410 nm photon can be any more or less intense than any other 410 nm photo.

Einstein got his Nobel Prize not for relativity, but for explaining the photoelectric effect: that light is a stream of particle-waves that can only be emitted or absorbed in discrete photon "chunks".

The individual photon is either completely reflected (bounced) off the mirror, or it is completely absorbed. It cannot be half-reflected. It cannot have its "intensity" decreased.

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Re: 0811: "Starlight"

Postby Wilhelm » Wed Oct 27, 2010 11:46 pm UTC

The beret guy was bringing a frame to appreciate the light from the stars fully as art, not just tiny dots.
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Re: 0811: "Starlight"

Postby davidstarlingm » Wed Oct 27, 2010 11:49 pm UTC

Meem1029 wrote:That's an interesting question. As a physics major I will eventually be able to say probably, but as a freshman I have no idea. I guess I have always thought of it as just bouncing with the same photon, but I'm not sure. As far as a difference, I think there is some sort of a difference because of the concept of quantum cryptography making it so listening can be detected, but I don't know. Of course thinking about it if the photon always moves at c it would have to have infinite acceleration to turn around completely and instantly. That or I just don't really understand what goes on at those levels (OK, I know I don't fully understand it, but I think I have a bit of a clue).


Remember, light really never travels at c. Except for brief spurts between galaxy clusters when it dodges hydrogen atoms, an individual photon will usually be slowed by air or interstellar gas or glass.

The wave-portion of the photon takes time to interact with the reflective surface, thus being accelerated over a non-zero period of time. This interaction, incidentally, imparts momentum to the mirror; this is how a stellar sail works.

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Re: 0811: "Starlight"

Postby furgle » Thu Oct 28, 2010 12:08 am UTC

This comic has done is made me think how weird and wonderful the universe is. and how little I understand

if light exist in no time, how does it travel? don't you need time to travel ?

Does white light contain the photons of all the colors of light, or are they separate photons?

And when light is in an interference pattern, what happens to the photons where the waves cancel each other out do they stop existing?

If light could love, would it be truly an infinite love?

If light could travel faster than the speed of itself, would we adjust time, or the speed of light?

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Re: 0811: "Starlight"

Postby Acilius » Thu Oct 28, 2010 12:22 am UTC

nahkaimurrao posted an interesting comment at 2:21 PM:

I had this revelation a few years ago, when you take this idea to its logical conclusion, that time does not pass for light and that there is no distance between two points in lights point of view then in one sense all things connected by light are concurrent, that the emitter and receiver of a photon are connected by zero time and zero distance from lights point of view.

This leads me to believe that ALL matter and energy in the universe is a single point (possibly a single photon) somehow expanded to exist in multiple locations.

Isn't that one of the reasons why there are theorists who want there to be a smallest unit of time? That if time is infinitely divisible, it would be hard to explain how any two events could occur simultaneously. If only one event occurs at a time in the universe, there would be no space, as there would be nothing for space to separate.

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Re: 0811: "Starlight"

Postby davidstarlingm » Thu Oct 28, 2010 12:39 am UTC

Mokurai wrote:All of the above is very accurately correct, but fundamentally wrong. The wave equation of quantum mechanics has been adapted for Special Relativity, but cannot be made to work in General Relativity. This is not a problem for photons, or whatever, which go along doing whatever it is they do with no need to have us understand what that is. There is, however, a problem for Young-Earth Creationists, who want to believe that we see stars by the light that they emit, and that they are really as far away as they seem. Creationism doesn't have time for this to happen, which means that God created the light close enough to us to get here on time as if it came from distant stars, or some other such humbug.


Diadem wrote:But the adjective is important. There is no inertial frame of reference that travels at the speed of light (relative to some other inertial frame). Absolutely true. But light doesn't care, it still happily travels at the speed of light. So obviously some sort of frame exists. The question "what does the universe look like from the point of view of a photon" is an entirely valid one. And you can't escape it by saying that travelling at the speed of light makes no physical sense, because light does.

The explanation I gave in my previous post is absolutely correct. A photon lives in a 2-dimensional universe. There is no forward direction for a photon. Nor is there time. This is intuitively clear if you realize that length and time go to zero if you approach the speed of light. That's not an entirely rigorous explanation, I admit, but if you want rigor you're going to have to do a lot of courses in theoretical physics.


Even more fun: we tend to think of c as something that is defined by light. But it is more accurate to say "light moves at c" than it is to say "c is the speed of light"; the concept of a maximum speed is much more important than the fact that photons happen to travel at this speed.

As Diadem pointed out, the reference frame being used makes all the difference. For a photon, both time and position collapse to a singularity. For the source of the photon and the recipient of the photon, different velocity reference frames give a different physical distance between the two points depending on where you are measuring from; this way each observer records the same value for c.

But things get even trickier if we use position to differentiate the reference frames instead of velocity. For the photon, this makes no difference, because at c, a velocity-dependent reference frame IS a position-dependent reference frame; only one possible position exists in a 2D universe. But for the light source and the recipient, it isn't nearly so simple. Using velocity to determine reference frames means they are separated by distance; using position to determine reference frames means they are separated by time. That's a consequence of a universe bounded by c.

Apply this to the nearest star: Alpha Centauri B, five light-years away. From a velocity-dependent reference frame separate from earth and ACB, it will take ten years for a photon to leave ACB, travel to earth, and be bounced back along its original path. But using earth as a positional reference frame, the photon travels through both time and space, thus reaching earth at the exact same moment it leaves ACB. From ACB's perspective, the photon takes ten years to reach earth, then returns home the instant that it strikes the mirror. Either way, the photon zips back and forth blissfully unaware that it has traversed time or space.

Relativity: it's special.

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Re: 0811: "Starlight"

Postby bfollinprm » Thu Oct 28, 2010 1:01 am UTC

For elections that are bound to individual atoms, that would be true (and it would be why non-reflective materials have colors instead of being all white or silver). However, the "electron sea" in metals is not bound to orbitals, and thus can absorb/release a much wider band of energies.

AFAIK the whole "reflects at the same angle" part is an example of the dual particle/wave nature of photons--it's a wavelike property.


Correct. The electrons in the mirror are free to move, and do so to directly oppose the magnetic field of the incoming photon (a moving charge creates a magnetic field). The electron reflects at the same angle because electromagnetic fields are (wave) vectors, and so things have to point in the opposite direction (exactly) to cancel out.

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Re: 0811: "Starlight"

Postby davidstarlingm » Thu Oct 28, 2010 2:33 am UTC

furgle wrote:If light exist in no time, how does it travel? don't you need time to travel ?


Light doesn't travel. At least, it doesn't realize that it is traveling. For a photon, distance (at least, along the direction the light is traveling), distance doesn't exist.

Does white light contain the photons of all the colors of light, or are they separate photons?


Individual photons can only have a single color/wavelength. White light is a wide spectrum of photons of every possible wavelength in the visible spectrum.

And when light is in an interference pattern, what happens to the photons where the waves cancel each other out do they stop existing?


A single photon can interfere with itself in a double-slit configuration. Where the waves cancel each other out are simply the places where it's impossible for the photon to end up.

If light could travel faster than the speed of itself, would we adjust time, or the speed of light?


Yes.

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Re: 0811: "Starlight"

Postby metafor » Thu Oct 28, 2010 2:51 am UTC

Meem1029 wrote:That's an interesting question. As a physics major I will eventually be able to say probably, but as a freshman I have no idea. I guess I have always thought of it as just bouncing with the same photon, but I'm not sure. As far as a difference, I think there is some sort of a difference because of the concept of quantum cryptography making it so listening can be detected, but I don't know. Of course thinking about it if the photon always moves at c it would have to have infinite acceleration to turn around completely and instantly. That or I just don't really understand what goes on at those levels (OK, I know I don't fully understand it, but I think I have a bit of a clue).


Light doesn't always move at c. Light moves at c through a vacuum. EM waves are affected by EM fields just like anything else. So if they move through an opaque matter, the EM fields of the individual atoms and their respective protons and electrons will affect the speed at which the photon travels.

If it helps you think of it abstractly, infinitely acceleration only requires infinite energy when accelerating a mass. And photons don't have mass :)

Edit: Reading through the alt-text again made me realize something I want to confirm. Because of relativity, wouldn't a photon technically only exist for an instant (or actually no time) in it's own reference frame? Or would it be forever? Asking random questions about relativity is so much more interesting than the lab I'm supposed to be doing.


Both actually. To an observer, it'd vanish instantaneously. To the photon, it'd exist indefinitely.

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Re: 0811: "Starlight"

Postby lank » Thu Oct 28, 2010 2:59 am UTC

Diadem wrote:
lank wrote:
Diadem wrote:So what happens at the speed of light itself? Well, the length goes to zero. Everything in its direction of travel (forward and backwards!) is compressed to a point. What does that mean. It means that you lose a dimension. Light lives in a 2 dimensional universe. It can look to the sides in every direction, but it can't look forward or backwards. That dimension simply does not exist anymore for light.

light lives in a 4D universe (just like the rest of us) - it just lives on the null paths within it, because the metric is (ds)2 = c(dt)2 - (dx)2. there are no frames in this metric where any of the lengths is zero or a dimension "removed" - no matter how fast you're going in any direction relative to one frame, light is always moving at c in that direction in both frames. i.e. you can only approach the speed of light relative to another frame, and no lorentz boost can put you in the same frame as a photon - because that frame does not exist.

The frame must exist. Light lives in it.


here's the thing: the paths through spacetime along which light propagates are not inertial frames. they are called "null geodesics" because the spacetime distance along them is zero. no massive particle can be "in" a null geodesic, and no massless particle can move outside a null geodesic (that is to say, no massless particle can not be in motion).

We often say 'nothing can travel at the speed of light'. Indeed, neither we, nor any other object with mass, can travel at the speed of light. But light obviously can, so you must be careful with that statement. If you try to explain relativity to a highschool student you would say something like "The closer your speed gets to the speed of light, the more energy is required to accelerate further. As you approach c, the energy required goes to inifinity, so you can never reach c itself". A smart highschool student will notice that this explanation is not entirely satisfactory. It forbids reaching the speed of light, but not travelling at it. So you will have to explain about Lorentz transformations and stuff like that, and finally arrive at your statement "there is no inertial frame of reference that travels with the speed of light". A situation where you or I are travelling at the speed of light would be like having a square circle. It simply does not exist.


i don't disagree with that.

But the adjective is important. There is no inertial frame of reference that travels at the speed of light (relative to some other inertial frame). Absolutely true. But light doesn't care, it still happily travels at the speed of light. So obviously some sort of frame exists.


what exists is a way to parameterise the null trajectory from P1 to P2. the parameter is physically meaningless, though - it is defined only up to an arbitrary constant factor.

The question "what does the universe look like from the point of view of a photon" is an entirely valid one. And you can't escape it by saying that travelling at the speed of light makes no physical sense, because light does.


it's a valid question until you analyse the maths and discover that "the point of view of a photon" is not a well defined concept. there is no frame in which the photon is at rest, and there's no way to draw a spacetime diagram where the light's propagation axis becomes the vertical axis.

The explanation I gave in my previous post is absolutely correct. A photon lives in a 2-dimensional universe. There is no forward direction for a photon. Nor is there time. This is intuitively clear if you realize that length and time go to zero if you approach the speed of light.


relative to which frame? if you are in an inertial frame, you are stationary relative to yourself. light is still travelling at c. the null geodesics still look the same, but the lengths of objects in other inertial frames are contracted (in the direction of motion) and their times dilated. intuition is not a good tool here.

That's not an entirely rigorous explanation, I admit, but if you want rigor you're going to have to do a lot of courses in theoretical physics.


agreed.

But as an example let's look at the degrees of freedom of the photon. According to Maxwell the electromagnetic field has 2. So photons better have two as well. And indeed if you do the calculations it turns out they have only 2. But how can you have only 2 degrees of freedom in a 3-dimensional world? Simple, but not living in a 3-dimensional world at all :)


maybe so, but does that make the photon's point of view a physically meaningful question, still?

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Re: 0811: "Starlight"

Postby Glass Fractal » Thu Oct 28, 2010 4:23 am UTC

davidstarlingm wrote:
Meem1029 wrote:That's an interesting question. As a physics major I will eventually be able to say probably, but as a freshman I have no idea. I guess I have always thought of it as just bouncing with the same photon, but I'm not sure. As far as a difference, I think there is some sort of a difference because of the concept of quantum cryptography making it so listening can be detected, but I don't know. Of course thinking about it if the photon always moves at c it would have to have infinite acceleration to turn around completely and instantly. That or I just don't really understand what goes on at those levels (OK, I know I don't fully understand it, but I think I have a bit of a clue).


Remember, light really never travels at c. Except for brief spurts between galaxy clusters when it dodges hydrogen atoms, an individual photon will usually be slowed by air or interstellar gas or glass.


I thought light did always move at c and that in a medium it seems to slow down because it constantly gets absorbed and emitted.

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Re: 0811: "Starlight"

Postby davidstarlingm » Thu Oct 28, 2010 5:04 am UTC

Glass Fractal wrote:I thought light did always move at c and that in a medium it seems to slow down because it constantly gets absorbed and emitted.


Not exactly. Light can travel through ordinary matter very easily; remember that 99% of the volume of an atom is empty space, and remember that a photon cannot interact with the nucleus via the strong nuclear force. Electrons are point particles, so the chance of a photon hitting an electron is literally zero. If the photon has the precise energy that the atom requires for an electron excitation, then it can be absorbed, but this is the only way that absorption is possible. Also, this kind of absorption is usually followed by emission of a new photon with equal energy, but in a completely different, random direction (unless, of course, the atom is surrounded by other atoms and can radiate the energy away as heat).

Passing through matter slows down photons in an entirely different fashion. A photon is a piece of an electromagnetic wave, and the speed of this wave is dependent on the electrical permittivity. In free space, this is the electrical constant, usually denoted as lowercase epsilon. However, in the presence of nearby electrons or protons (ie, in matter), the permittivity is changed, thus reducing the speed at which the electromagnetic wave can propagate.

Only in a universe completely free from matter would a photon be able to truly achieve c. However, being in a vacuum chamber on earth is pretty darn close. So is the intergalactic void, where the individual hydrogen atoms are scattered so thin that the entire volume of a 747 would only displace a few hundred atoms.

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Re: 0811: "Starlight"

Postby Diadem » Thu Oct 28, 2010 6:00 am UTC

furgle wrote:
If light could travel faster than the speed of itself, would we adjust time, or the speed of light?

Light must travel at the speed of light. Any particle that has no mass must. Anything else makes no physical sense.

I can explain this in a somewhat hand-waving kind of way like this. Remember Einstein's famous equation? E = mc^2. Well that is for particles at rest. For particles in motion you have to add the kinetic energy, and the equation becomes E = gamma * m * c^2, where gamma is a factor that depends on the velocity. To be precise y = 1 / Sqrt(1-v^2/c^2). As you can see gamma goes to infinity as v goes to c.

So a normal particle at v < c has finite gamma and thus finite non-zero energy. A normal particle travelling at c would have infinite energy, so this can't be. A massless particle at v < c has finite gamma but m = 0 => E = 0. It has no energy, so it doesn't exist. And a massless particle travelling at c? Well we now get E = 0 * Infinity, which is not well-defined. Clearly our math has broken down and we need to something else to calculate their energy. But anyway, massless particles like photons have to travel at the speed of light or they do not exist.

But can you change the speed of light? Well, the speed of light is a conversion factor between distance and time. Numerically it's not really a constant, measure something in feet instead of meters and you get a different numerical value for the speed of light. The speed of light and several other constants together make up the fine-structure constant. This constant is dimensionless, so it's always the same. This is the thing you would have to change to truly change the speed of light. But changing it will have far-reaching consequences for the entire universe. The speed of light doesn't merely dictate how fast photons go, it affects the strength of fundamental forces in our universe and stuff like that.
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Re: 0811: "Starlight"

Postby flamewise » Thu Oct 28, 2010 10:44 am UTC

Thanks for asking that question.

I liked speculating about the answer with my limited understanding, and then reading the more informed answers.

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Re: 0811: "Starlight"

Postby Yurgen » Thu Oct 28, 2010 12:52 pm UTC

It's pointless to consider whether it's the "same" photon or not. Particle physics is symmetric about particle exchange. Photons don't have tags on them that reveal their origins, they're indistinguishable from each other.

Eternal Density wrote:Yeah, the electron is going to fall back to the energy level it started from, thus the same colour of light. When looking at an 'infinite' reflection between parallel mirrors, it gets darker, not redder.
In other words, HighSchoolPhysicsTeacherFail.


The reflected photon is necessarily of lower energy, and so longer wavelenth than the incident one. This is because photons have nonzero momentum and the particle they're scattering off has finite mass, and so momentum (and energy) is transferred from the photon to the particle, which causes redshift. If reflection didn't transfer energy, solar sails wouldn't work.

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Re: 0811: "Starlight"

Postby gypkap » Thu Oct 28, 2010 4:10 pm UTC

On the mirror:
Dave Bowman said it best:
"Oh my God it's full of stars!"

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Re: 0811: "Starlight"

Postby tesseraktik » Thu Oct 28, 2010 6:08 pm UTC

First saw this comic on my iPhone, so I couldn't see the alt-text. Came here to write something like "What, no mention of the fact that in a lightlike observer's frame of reference, all distances along its own timeline are zero? Get into my head, Randall!", y'know, for the lulz and what-not.
Then I saw the alt-text.

...and so, I suppose I have no choice but to put:

GOOMHR!

...although I'd like to add: IGYNTMNT! ("I'll get you next time, Munroe; NEXT TIME!")

gypkap wrote:On the mirror:
Dave Bowman said it best:
"Oh my God it's full of stars!"
I laughed out loud in my mind.
ni'o mi nelci le zirpu sovmabrnornitorinku
Spoiler:
++$_ wrote:What's a "degree"?

EDIT: I looked it up on Wikipedia. Apparently it's some ancient Babylonian unit for angles :/

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Re: 0811: "Starlight"

Postby Diadem » Thu Oct 28, 2010 6:22 pm UTC

lank wrote:
Diadem wrote:
The question "what does the universe look like from the point of view of a photon" is an entirely valid one. And you can't escape it by saying that travelling at the speed of light makes no physical sense, because light does.

it's a valid question until you analyse the maths and discover that "the point of view of a photon" is not a well defined concept. there is no frame in which the photon is at rest, and there's no way to draw a spacetime diagram where the light's propagation axis becomes the vertical axis.

I reiterate: Photons exist. So the frame of reference of a photon must exist. If it didn't, photons wouldn't.

Relativity cannot describe a frame of reference like that. I entirely agree. This however is not a problem with photons, it's a problem of relativity. Indeed, you are applying the wrong theory to the problem. To describe photons you do not need relativity, you need field theory. With special relativity you can give the kind of hand-waving argument like I did, but if you want to be more formal you need field theory.

I don't know how I can explain it better. You remind me a bit of Mr. Bond. He insists that centrifugal forces do not exist. He can probably give long arguments based on Newtonian dynamics to back up his claim. The math no doubt all checks out. The centrifugal forces care about none of that though, they will still kill him.
It's one of those irregular verbs, isn't it? I have an independent mind, you are an eccentric, he is round the twist
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Re: 0811: "Starlight"

Postby SuperfluousFluteMusic » Thu Oct 28, 2010 7:25 pm UTC

Too bad Randall Munroe cannot appreciate the beauty of social systems. Then again, it might be like listening to earbuds on high volume for 10 years and then trying to hear the highs on actually good quality speakers.

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Re: 0811: "Starlight"

Postby Yurgen » Thu Oct 28, 2010 7:48 pm UTC

If the rest frame of a photon exists, you must be able to calculate the rest mass of the photon, which cannot be done. Or, more importantly, if the rest frame of a photon exists, you must be able to calculate the total amount of energy in the rest of the Universe from the photon's perspective. This is impossible because relativistic energy isn't well defined in this hypothetical photon frame (as velocity isn't well defined). Either you disallow Photon inertial frames on the grounds that they don't make any sense, or you throw out Conservation of Energy. I know which I'd choose.

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Re: 0811: "Starlight"

Postby Skip » Thu Oct 28, 2010 8:11 pm UTC

The comic has that awesome effect of those velvet posters you color in with markers. It's like an automatic bonus to photorealism and coolness.
Reginald Beaumont Berkes

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Re: 0811: "Starlight"

Postby Diadem » Thu Oct 28, 2010 8:23 pm UTC

Yurgen wrote:Either you disallow Photon inertial frames on the grounds that they don't make any sense, or you throw out Conservation of Energy. I know which I'd choose.

Or the photon frame of reference is not an inertial frame. Which indeed it isn't. I'm not sure if it's technically a frame of reference at all, I don't know if you can assign a coordinate system to it in a meaningful way. But for want of a better term I'll stick to 'frame of reference'.

Look. Photons exist. And they interact with the rest of the universe. So they must 'see' the rest of the universe. There is no escaping that logic. The universe exists from the point of view of a photon. So it must look like something. That's not even physics, it's pure logic. So what does it look like? That question is physics, and the answer is that the universe is 2-dimensional from the point of view of a photon.
It's one of those irregular verbs, isn't it? I have an independent mind, you are an eccentric, he is round the twist
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Re: 0811: "Starlight"

Postby StNowhere » Thu Oct 28, 2010 8:53 pm UTC

Diadem wrote:Look. Photons exist. And they interact with the rest of the universe. So they must 'see' the rest of the universe. There is no escaping that logic. The universe exists from the point of view of a photon. So it must look like something. That's not even physics, it's pure logic. So what does it look like? That question is physics, and the answer is that the universe is 2-dimensional from the point of view of a photon.


OK, this may either be a really stupid question, or a really pedantic one, but what is it to say a photon "exists"? In what manner does a photon exist? Can we argue about whether or not a radio wave "sees" the universe? And if so, how would it?

I'm not asking with a specific answer in mind. I'm honestly curious.

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Re: 0811: "Starlight"

Postby Yurgen » Thu Oct 28, 2010 9:07 pm UTC

Diadem wrote:Or the photon frame of reference is not an inertial frame. Which indeed it isn't.

Look. Photons exist. And they interact with the rest of the universe. So they must 'see' the rest of the universe. There is no escaping that logic. The universe exists from the point of view of a photon. So it must look like something.


Noninertial frames conserve energy too.

Okay, here's a system. Particle A, rest mass mA0 sees, from its reference frame (frame X), particle B, rest mass mB0, velocity vB and separation xB emit a photon P of energy EP directly towards it (necessarily with velocity vP -c x /|b|). The total energy of the system is ETOT = mA0 c2 + E + mB0 c2(1-v2/c2)-1/2 For your hypothesis to be correct, there must exist a transformation T from frame X to a frame X' such that vP' = 0, but ETOT' = ETOT. You claim field theory can solve this problem, so field theory must present this transformation. I myself am not up on field theory, so I'm not going looking for a transformation that I know cannot exist to do your legwork for you.

Alternatively: define "see". If the logic is as "inescapable" as you claim, this should be a well-defined concept for which you should easily be able to produce the definition.

FAKE EDIT: Nice backpedaling there with that edit. If you can't assign a coordinate system to it, it's not a space, you can't reconstruct the laws of physics in it, and it's not a valid frame. Also: The laws of physics require at least three dimensional space. Vector cross products don't exist in 2D space, and you can't have electromagnetic fields without doing cross products. This is problematic, as it means your photon reference frame can't have any electromagnetic fields, which means your photon reference frame can't actually have any photons in it.

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Re: 0811: "Starlight"

Postby Singulaire » Thu Oct 28, 2010 9:19 pm UTC

davidstarlingm wrote:
Eternal Density wrote:Yeah, the electron is going to fall back to the energy level it started from, thus the same colour of light. When looking at an 'infinite' reflection between parallel mirrors, it gets darker, not redder.

In other words, HighSchoolPhysicsTeacherFail.


Yes, very HighSchoolPhysicsTeacherFail. Individual photons have one parameter, and one parameter only: wavelength. Energy is dependent only on wavelength (alternately, frequency, if you want to be tricky). The "intensity" of an individual photon is meaningless; there is no way that one 410 nm photon can be any more or less intense than any other 410 nm photo.

Einstein got his Nobel Prize not for relativity, but for explaining the photoelectric effect: that light is a stream of particle-waves that can only be emitted or absorbed in discrete photon "chunks".

The individual photon is either completely reflected (bounced) off the mirror, or it is completely absorbed. It cannot be half-reflected. It cannot have its "intensity" decreased.


I believe I was refering to the energy of a photon, not its intensity. In fact, I complained that the response was centered around intensity whereas I was talking about single photons.
I fail to see how a teacher starting a discussion about whether thermodynamics apply at the sub-atmoic level or not can be considered a failure (Mind you, we were already done with the curriculum).
So far the only response that actually pertains to what I said was "The energy change is completely reversible because heat doesn't have anywhere to go", which is interesting, but I'd like to see the statement backed up somehow.

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Re: 0811: "Starlight"

Postby BioTube » Thu Oct 28, 2010 9:50 pm UTC

Yurgen wrote:FAKE EDIT: Nice backpedaling there with that edit. If you can't assign a coordinate system to it, it's not a space, you can't reconstruct the laws of physics in it, and it's not a valid frame. Also: The laws of physics require at least three dimensional space. Vector cross products don't exist in 2D space, and you can't have electromagnetic fields without doing cross products. This is problematic, as it means your photon reference frame can't have any electromagnetic fields, which means your photon reference frame can't actually have any photons in it.
Unless photons don't exist from their frame of reference, making them even more infuriating to describe than they already are.
Frédéric Bastiat wrote:Government is the great fiction through which everybody endeavors to live at the expense of everybody else.

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Re: 0811: "Starlight"

Postby Skip » Thu Oct 28, 2010 10:26 pm UTC

Skip wrote:The comic has that awesome effect of those velvet posters you color in with markers. It's like an automatic bonus to photorealism and coolness.


On that same note. Hello Yurgen! Holy shit that is a similarly-epic avatar you have. ...What's your phone number?
Image
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Re: 0811: "Starlight"

Postby davidstarlingm » Thu Oct 28, 2010 10:28 pm UTC

Yurgen wrote:It's pointless to consider whether it's the "same" photon or not. Particle physics is symmetric about particle exchange. Photons don't have tags on them that reveal their origins, they're indistinguishable from each other.
Eternal Density wrote:Yeah, the electron is going to fall back to the energy level it started from, thus the same colour of light. When looking at an 'infinite' reflection between parallel mirrors, it gets darker, not redder.

In other words, HighSchoolPhysicsTeacherFail.

The reflected photon is necessarily of lower energy, and so longer wavelenth than the incident one. This is because photons have nonzero momentum and the particle they're scattering off has finite mass, and so momentum (and energy) is transferred from the photon to the particle, which causes redshift. If reflection didn't transfer energy, solar sails wouldn't work.


Singulaire wrote:
davidstarlingm wrote:Yes, very HighSchoolPhysicsTeacherFail. Individual photons have one parameter, and one parameter only: wavelength. Energy is dependent only on wavelength (alternately, frequency, if you want to be tricky). The "intensity" of an individual photon is meaningless; there is no way that one 410 nm photon can be any more or less intense than any other 410 nm photo.

Einstein got his Nobel Prize not for relativity, but for explaining the photoelectric effect: that light is a stream of particle-waves that can only be emitted or absorbed in discrete photon "chunks".

The individual photon is either completely reflected (bounced) off the mirror, or it is completely absorbed. It cannot be half-reflected. It cannot have its "intensity" decreased.


I believe I was referring to the energy of a photon, not its intensity. In fact, I complained that the response was centered around intensity whereas I was talking about single photons.

I fail to see how a teacher starting a discussion about whether thermodynamics apply at the sub-atomic level or not can be considered a failure (Mind you, we were already done with the curriculum).

So far the only response that actually pertains to what I said was "The energy change is completely reversible because heat doesn't have anywhere to go", which is interesting, but I'd like to see the statement backed up somehow.


I stand (very much) corrected (both by Yurgen and Singulaire).

I spoke to one of the multi-doctorate theoretical physicists at my university (http://publish.aps.org/search/field/author/Dolmatov_V_K), and he cleared it all up.

Unless it is completely absorbed, the photon imparts no heat to the mirror. However, a scattered (reflected) photon imparts both momentum and kinetic energy to the surface it reflects off of. This is usually undetectable, though; the amount of kinetic energy given to the mirror is inversely proportional to the mass of the mirror.

If the mirror is a single, unattached electron, and the photon is a high-energy (20 MeV) gamma photon, then Compton scattering will take place. The photon will never touch the electron, but it will nonetheless lose energy, resulting in a barely measurable redshift. However, a single atom is more than 10,000 times the mass of a lone electron; scattering will still take place, but the slight energy transferred to the atom won't be detectable, and neither will the drop in photon energy.

For a physical mirror composed of quadrillions of atoms, the energy transfer will be unimaginably low, and therefore the reflected photon will pretty much have the exact same wavelength it started with.

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Re: 0811: "Starlight"

Postby Yurgen » Fri Oct 29, 2010 12:20 am UTC

For a physical mirror composed of quadrillions of atoms, the energy transfer will be unimaginably low, and therefore the reflected photon will pretty much have the exact same wavelength it started with.


This is largely correct, but I suspect (I'm not a solid state physicist, so I don't know for sure) that its safe to assume that individual photons are scattering off individual atoms (or small numbers of atoms), rather than off the bulk, because the waves don't penetrate very far into the material. The effect will still be barely detectible even in optimal conditions. Interferometers are pretty awesome at detecting even the smallest redshift, and you can design an experiment with a pair of parallel mirrors and a (very intense, to account for quantum losses) laser that's a few arcseconds off normal, so when the light comes out the other side it'll have scattered millions of times.

Skip wrote:On that same note. Hello Yurgen! Holy shit that is a similarly-epic avatar you have. ...What's your phone number?


Hello. Sadly, I can't claim any credit for my avatar, as it is the work of an artist called Ninomae, whose work could best be described as what Jhonen Vasquez would draw if he were Japanese, and loved rainbows. I'd link to his work, but all the convenient places that host it also host highly non-worksafe content, and I'm not sure of these fora's policies on that. He's not hard to google anyway.

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Re: 0811: "Starlight"

Postby cement » Fri Oct 29, 2010 12:48 am UTC

Wow, I just figured out that was supposed to be a mirror. :roll:

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Re: 0811: "Starlight"

Postby davidstarlingm » Fri Oct 29, 2010 2:32 am UTC

Yurgen wrote:
davidstarlingm wrote:For a physical mirror composed of quadrillions of atoms, the energy transfer will be unimaginably low, and therefore the reflected photon will pretty much have the exact same wavelength it started with.


This is largely correct, but I suspect (I'm not a solid state physicist, so I don't know for sure) that its safe to assume that individual photons are scattering off individual atoms (or small numbers of atoms), rather than off the bulk, because the waves don't penetrate very far into the material. The effect will still be barely detectible even in optimal conditions. Interferometers are pretty awesome at detecting even the smallest redshift, and you can design an experiment with a pair of parallel mirrors and a (very intense, to account for quantum losses) laser that's a few arcseconds off normal, so when the light comes out the other side it'll have scattered millions of times.


In the case of a mirror, the photons are scattered off of the "electron sea" of the metallic surface. That is specular reflection (where the angle of incidence is equal to the angle of reflection) happens; the electron sea allows for wave interference.

In the case of random scattering (for a matte surface), the individual photons are scattered off individual atoms, but those are still bonded to the material they are part of.

Either way, the momentum (and lost energy) is imparted to the entire object, not just to the individual atoms or electrons that the photon is scattered from.

Just for kicks, let's look at your example. According to this 2005 study, the most precise interferometers can measure wavelength differences with femtometer resolution.

If the mirrors have a mass of one kilogram each, then let's look at what happens to a photon after one bounce. This is the equation for wavelength shift under Compton scattering:

Image

where λ' is the new wavelength, λ is the original wavelength, me is the mass of the mirror, and θ is the scattering angle. You suggested a few arcseconds; let's say it is aimed one arcsecond off normal. That means that the scattering angle will be 179.9994 degrees. Plugging in all the values gives:

Δλ = 4.420e-42 meters

That's not much.

This means that the photon will need to bounce two hundred trillion trillion times before its wavelength will redshift by a femtometer. If the parallel mirrors are only a millimeter apart, trigonometry tells us that each bounce will move them 9.696 nanometers down the length of the mirror. That many bounces, though, adds up. The parallel mirrors will need to be 211 light years long before the redshift will be detectable by even the most precise of interferometers.

It's safe to say that's one experiment I won't be trying. At least, not in my lifetime.

Like I said, "the reflected photon will pretty much have the exact same wavelength it started with."

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Re: 0811: "Starlight"

Postby Yurgen » Fri Oct 29, 2010 2:56 am UTC

That's assuming momentum is instantly transferred to 1kg of mirror at the moment of reflection, which ignores the elasticity of the material. Rather than pushing the entire mirror back, you're only going to push back a small area under the beam down to a depth of a few atoms, because even in the electron sea, waves can only travel at an appreciable fraction of the speed of light. I don't know how "long" the photon remains in contact with the electron system, but at a guess I'd say the spatial extent is going to be of the order of the wavelength of incident light (this implies the process takes around a femtosecond, I'm not sure if this is okay or not). If momentum's only transferred to an eighth of a cubic micrometer of metal (i.e., a cube 500nm to a side), at 7*10^3kg/m^3 density of Generic Metal, you're only really dealing with 10^-15kg of material. Fifteen orders of magnitude off your 211 light years and you're only at a kilometer of mirror. Still silly, but not entirely impossible.

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Re: 0811: "Starlight"

Postby davidstarlingm » Fri Oct 29, 2010 5:56 am UTC

Yurgen wrote:That's assuming momentum is instantly transferred to 1kg of mirror at the moment of reflection, which ignores the elasticity of the material. Rather than pushing the entire mirror back, you're only going to push back a small area under the beam down to a depth of a few atoms, because even in the electron sea, waves can only travel at an appreciable fraction of the speed of light. I don't know how "long" the photon remains in contact with the electron system, but at a guess I'd say the spatial extent is going to be of the order of the wavelength of incident light (this implies the process takes around a femtosecond, I'm not sure if this is okay or not). If momentum's only transferred to an eighth of a cubic micrometer of metal (i.e., a cube 500nm to a side), at 7*10^3kg/m^3 density of Generic Metal, you're only really dealing with 10^-15kg of material. Fifteen orders of magnitude off your 211 light years and you're only at a kilometer of mirror. Still silly, but not entirely impossible.


Impressive.

But I left one factor out: the highest-reflectance mirrors (made of Generic Metal, that is) have a reflectance of 95-98%. Cutting down by 15 orders of magnitude as you calculated leaves us with just two hundred billion bounces. But with this reflectance, a mere 20,000 bounces alone will reduce the light to 1/(2e80) its original signal (this is where most calculators throw up their hands and call it quits). All the photons in the universe couldn't survive a million bounces, much less two hundred billion bounces.

The point is that whatever redshift occurs is truly negligible, no matter what else we are comparing it to. This isn't like saying "ignore air resistance"; this is like saying "ignore relativistic mass when calculating the kinetic energy of a snail." In fact, the relativistic mass of a snail is probably several orders of magnitude MORE significant than the redshift of a photon off a mirror.

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Re: 0811: "Starlight"

Postby Singulaire » Fri Oct 29, 2010 7:48 am UTC

That's about the conclusion we came to (although we used a different approach)- a photon loses very little energy when absorbed and re-emitted, definitely an amount that is negligibly small, but it's technically still there. Gee, I probably could've been more clear on that and saved a lot of back-and-forth. Then again, cool discussion.
If anyone's interested, the nail in the coffin, to us, was as follows:
If the photon is absorbed and re-emitted with the same energy, that means a conversion of energy has occurred that is completely reversible. Once we phrased it that way, no one really wanted to support that side of the argument. None too rigorous, I'm aware, but it WAS the end of the year and most people were begging the teacher to somehow confer upon them miraculous powers of test-passing, so I took what I could get.

Oh, and also- nice link, david. Between that and this thread I find myself wishing I had picked Physics rather than Computer Science when applying to college.

And just so we won't run out of things to argue about: Suppose a photon's energy is so small that it cannot excite the vast majority of particles. Would it still be reflected by a mirror? (Cue particle-or-wave shouting match :P).

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Re: 0811: "Starlight"

Postby davidstarlingm » Fri Oct 29, 2010 4:19 pm UTC

Singulaire wrote:That's about the conclusion we came to (although we used a different approach)- a photon loses very little energy when absorbed and re-emitted, definitely an amount that is negligibly small, but it's technically still there.

And just so we won't run out of things to argue about: Suppose a photon's energy is so small that it cannot excite the vast majority of particles. Would it still be reflected by a mirror? (Cue particle-or-wave shouting match :P).


Hooray for shouting matches! Okay, not really.

I still think there is a little disparity in answering the original question, because your second question depends on the first answer.

Jspenguin originally asked whether there is a physical difference between a "bounce" and absorption/emission. The answer is categorically yes; there definitely is a difference.

Absorption and emission happen when the photon is able to excite an electron within a particular atom to an excited state. The photon is absorbed and completely ceases to exist. When the electron relaxes a short while later, it emits a new photon in a random direction with precisely the same energy. Remember, thermodynamics doesn't operate in the same way at quantum levels.

Reflection is a completely different phenomenon. Whether something can be reflected has nothing to do with whether it can excite the electrons of a particular substance, because there is no excitation taking place during reflection. The photon is never absorbed, and no electrons reach any excited state. Instead, the photon is scattered off the surface (read this article for a primer on scattering) without ever touching it.

Even though the particle-part of the photon never touches the surface, the wave-part does interact with the wavelike properties of the surface. If the surface is a mirror, then the wave functions interact to produce specular reflection, bouncing the photon back such that it leaves at the opposite angle from whence it came.

So whether a given photon will reflect off a given surface has nothing to do with whether the photon can excite any atoms, because if excitation is happening, then no reflection is possible. Instead, it depends on the wavefunction properties of the substance compared to the wavefunction of the photon. If the photon's wavefunction is much larger than the surface wavefunction, the substance will be transparent to photons of that wavelength. If the two functions are close and form destructive interference, excitation will happen and the photon will be absorbed (but not re-emitted; the energy will simply be dispersed to adjoining atoms as heat), making the substance opaque to this wavelength. Finally, if the wavefunctions are close enough to form constructive interference, then the photon will be scattered under either specular reflection or diffuse reflection.

Finally, there is absorbance fluorescence. This happens when the wavefunctions form destructive interference over some range of wavelengths, absorbing a large spectrum of photons, then transfer all this energy to a particular element inside the substance. This element emits photons at a single wavelength that is lower than the absorbed light; the substance will appear to glow.

So, let's bring it all together.

When I look at my girlfriend's face while we are standing outside under a broad spectrum of photons:

  • Radio wavelengths and microwaves have much broader wavefunctions than the wavefunction of her skin, so those photons pass through her body unnoticed; she is radiotransparent. That's okay, though; my eyes can't see radio wavelengths.
  • Her skin forms destructive interference with the wavefunctions of most high-energy green and blue photons, absorbing it by electron excitation. This energy is diffused as heat, which is why she feels warmer by standing in the sun.
  • Her skin forms constructive interference with most other photons in the visible spectrum, scattering them under diffuse reflection. These photons reach my eyes; this is the color I see. She is flushed, and the blood rushing to her face absorbs a little bit of the yellow light that would otherwise be reflected, giving her a slightly more pink color in her cheeks.
  • A few of the green photons in the 525 nm range are absorbed (destructive interference and excitation) by the sodium atoms in her skin. These atoms build up the energy and release it as lower-wavelength photon (in the golden yellow wavelength range) fluorescence; this makes her skin appear to glow in the sunlight.
  • The thin coating of tears lubricating the surface of her eyes forms constructive interference with almost all photons in the visible spectrum; because of hydrogen bonding, the wavefunctions scatter light evenly under specular reflection, allowing me to see myself and the entire landscape behind me in her eyes.
  • Her skin is a little darker than mine, so the melanin in her skin forms constructive interference with ultraviolet photons, reflecting them away from her body diffusely. My skin will not fare so well; it forms destructive interference with ultraviolet light, absorbing it by excitation and heat transfer, and giving me a sunburn if I stay out in the sun all day.

Of course, I don't mention any of these things to her at the time, because when I look at her, I'm thinking about chemistry, not physics.

Thankfully, though, she's incredibly smart and curious, so she asks me to explain concepts in physics to her from time to time. "David, how does ionization work?"


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