Can any one explain to me what the crests and troughs are for in a light wave? I understand the nodes are points of interaction.

1) Are they a mathematical tool used to describe a particles motion along a straight line. ie. spacing?
2) Does the particle transverse the crest and trough?

The wave view of light is distinct from the particle view.

When you run an experiment which shows wave properties, no particle properties are observed and vice versa.

It is well known that we cannot visualize quantum level processes. Do not expect an explanation that makes sense.

so when you say wave i'm just suppose to imagine a physical wave or an analogical wave?

the light wave can be viewed as a composition of 2 things. 1. electric field 2. magnetic field.

each of these oscillate in space and time and are orthogonal to each other. their cross product gives the direction of the light wave propagation.

what does this oscillation mean though that a physical tranversed wave or an analogy of some sort?
And yes I know that dir'n is ortho(E and B) but that still doesn't answer my question what is this wave. I think in sound waves is teh compression/expansion of system of particles moving.

btw i've taken QM, AP, CompPHys, Mathphys, relativity all at the senior level of university with flying colours in everything but QM.

I never really asked teh question of what exactly is a wave in light. I know how sound waves are.

light is fundamentally different than sound though. it has no medium to travel through. actually the very question you're asking is exactly what everyone wants to know. sound needs a medium to propagate its energy through, some kind of matter. light can propagate in a vacuum and as you probably know, it can behave like a particle or a wave. and that's all i can really say about it. if you want know more, the part of physics you should read up on is optics.

so its not necessarily that the particle element tranverses along the wave element?

cuz my friend says the particle is the wave like its coming outta a textbook
and that means to me that inside a little region called the particle is a wave.

so its not necessarily that the particle element tranverses along the wave element?

cuz my friend says the particle is the wave like its coming outta a textbook
and that means to me that inside a little region called the particle is a wave.

The best way to think of any quantum entity, in my opinion, is as of something non-local, i.e. a field that is spread out to space. When you interact with that field, e.g. measure the light, then this can only happen through an energy quantum h-bar ω.

The wave aspect is the non-locality, the "particle" aspect is that when you actually look, the interaction is quantised into photons (the energy packets h-bar ω).

Light is not a particle with waves inside; like any quantum object, it is both at the same time (welcome to the quantum world).

and that means to me that inside a little region called the particle is a wave.

To me it seems as though you are not sure whether light (electromagnetic radiation) should be treated as a particle or as a wave. You mentioned the wave theory in your first post, and now you are talking about a particle consisting of a wave.

Well this is almost true in my opinion. Of course, whether something is percieved as a particle or a wave depends on the "operating dimension" of the tool used to measure it. You are in doubt familiar with the wave function and that even you and I exist as a continuum of sine waves. If you measure something whose wavelength is much, much smaller than the apparatus' dimension then we are convinced that it is a particle and vice versa.

This should be all too familiar since you have taken a senior year course in QM.

Now once you start talking about light as a particle (photon) then it gets interesting and maybe not so intuitive. If 'light' (I would use this term loosely as it implies the 'visible' part of the spectrum) is said to be a particle as you mentioned, then does or some of it oscillate? Your question is it not?

Well, a photon must have a wavelength if it is to obey Quantum Mechanics. Wavelength equals Planck's Constant divided by its momentum. Momentum is a classical notion and applies to matter. Hence matter can have a wavelength.

If matter (indeed a photon) is to be described as a wave then it is described by Schrodinger's Equation. And from Heisenburg's Postulate, if something (say our photon) has a wave nature then it is theoretically impossible to know precisely the position and its momentum simultaneously.

But notice that /\p/\x >= h-bar/2 has an equal to inequality! This means that there is some particular wave which yields the minmum uncertainty! This wave form is called the Gaussian and (in free space) is also the predicted shape of the photon.

Have you ever seen the Gaussian wave form? It is unique in that it is close to being a particle, yet it is a wave. Quite remarkable. This means that as its wave form is as close to being a particle as possible, it still is a wave.

Now if we treat the photon as a moving object, i.e. as a travelling wave. Whoa, object and wave in the same sentence!? This is important. We concluded above that the photon represents a Gaussian wave form, that is, it is a 'pulse' and that its corresponding particle is 'most likely' to be found in the region where the pulse is largest.

and that means to me that inside a little region called the particle is a wave.

So you where almost right. In fact you where back-to-front. The wave has a region where it can be interpreted as a particle. This region in the wave (the Gaussian) moves at the same speed as the particle would.

Now for some mathematics.

The Gaussian wave form is

phi(x) = A[e^-(x/2E)^2][e^(ikx)]

The [e^-(x/2E)^2] bit is the Gaussian bit.

The [e^(ikx)] bit gives the wave function its oscillatory nature.

Hence the photon is oscillatory and is a particle in the region where the Gaussian is largest.

You can integrate this wave function using Gaussian Integrals. Which arise from considering the waveform as a sum of many waves.

I hope this has helped. In fact, It better because this took about 20 minutes to respond!

Cheers.

HAHA no it didn't

OXYMORON: so the wave is a physical thing and not just a mathematical tool.
My particle post was in response to one of the above post.
SO the "particle" regions moves along teh wave?
so what do the crest and troughs of the wave represent?

CRISP: PLZ EXPLAIN: "The best way to think of any quantum entity, in my opinion, is as of something non-local, i.e. a field that is spread out to space. When you interact with that field, e.g. measure the light, then this can only happen through an energy quantum h-bar ω.
The wave aspect is the non-locality????"

Neurocomp2003: You are asking (hoping) for a model of light (more properly electromagnetic radiation) that you can visualize.

That is a forlorn hope. Quantum level entities and processes cannot be visualized by human minds. Over several million years, our minds evolved the skills required to survive quite well as hunter/gatherers in a world which is modeled very well by classical physics.

The quantum world is fundamentally different from the classical world. It is so different that our minds cannot visualize any model which accurately describes that world.

We can measure properties of light which we call wave length and frequency. Such properties are analogous to sound waves and also to waves caused by dropping a marble into a still pond of water. Sound waves are not really like water waves, although both have properties called frequency and wave length. Both types of waves can be modeled by plotting the sine function.

We can measure properties of light called frequency and wave length, but light is not like sound nor is it like water waves.

We can also measure particle-like properties of electromagnetic radiation (light), but no particle we can visualize is a good model for light.

You need to realize that you will never have a model of quantum phenomena which makes sense to your classical mind. The best you can hope for is an understanding of the mathematics, a knowledge of the measurements resulting from various experiments, and an understanding of the effects of devices like lasers.

When viewed as particles, quantum entities seem capricious, with discontinuous trajectories. This makes any particle model foreign to the human mind. Wave models of classical phenomena are a bit mysterious to our intuitive notions of what is happening, and wave models of quantum phenomena are even worse. Note that without analysis and experimentation, our intuitive notions are incorrect for visualizing what is really happening when a small pebble is dropped into a still pond. I remember being very skeptical when I was first told that water waves were caused by molecules moving vertically, not horizontally.

Men with great minds are expressing serious ideas in a humorous fashion when they make statement like the following (paraphrases, not exact quotes). Neils Bohr: If you are not confused by Quantum Theory, you do not understand it.


Feynman: Do not ask me how it can be like that. Nobody knows how Quantum phenomena can be like that.It helped me when I read a story about Neils Bohr and a conversation he had with a student. It was something like the following (not a quote)Before I answer your question, let me tell you about a very well known illusion. It is possible to make a drawing which looks like a black vase if you focus on the central part of the drawing. If you focus on the white area left and right of the center, the drawing looks like the profiles of two people facing each other.

You can easily see either the vase or the profiles, but you cannot see both simultaneously.

If you ask me what is really there, I will reply there is neither a vase nor two profiles: What is really there is black ink on white paper.

If you ask what is really there referring to light, I will reply that light is neither waves nor particles. Unfortunately, I cannot tell you what is really there. Nobody can visualize what is really there at the quantum level.

The best way to think of any quantum entity, in my opinion, is as of something non-local, i.e. a field that is spread out to space. When you interact with that field, e.g. measure the light, then this can only happen through an energy quantum h-bar ω.

The wave aspect is the non-locality, the "particle" aspect is that when you actually look, the interaction is quantised into photons (the energy packets h-bar ω).

Light is not a particle with waves inside; like any quantum object, it is both at the same time (welcome to the quantum world).

I love it when people do this and express their own way of thinking about things. OK Crisp, are u saying that there is a probability (wave aspect) that the photon could be anywhere in space and that when u 'collapse' this wavefunction (by observing it) then it is quantised at a particular place (which is generally a region of high probability)?

Neurocomp2003.

Okay, I think I know what you mean now: Why do we use waves to represent all this quantum stuff anyway? Is it because they actually are waves or because that is all we can do mathematically.

The answer is quite simple, but I have to go so I will post later on... however, now that I've read dinosaur's post that accounts for the reason why it is needed.

PS. I'm sorry it didn't help. Well actually, it helped me - once taught twice learnt.

Cheers.

Hehe...yeah thats really what I wanna know is it physical reality or mathematical....

it seems to me that physicist don't like CAs or alot of them don't study dynamical systems(i know there are quite a few who do esp in classical mechanics...but the problem always comes down to not enough computational power).

and when your taking the course you don't think of these things all you care about is getting by(unless of course your doing lab work) and my math bkgd was good enough to get me by. I remmeber during exam day though i didn't fare well the majority of the class was in the library copying down past years exam solutions onto cribsheets...me being the moral idiot decided not to copy thinking all the prof and his text book is all you need to do. My friend told me he envied my moral strength but man i shoulda copied those things!!!

If you're thinking about light as a wave, forget the particle picture. There are no light particles in a light wave.

Also, a light wave doesn't have crests and troughs like a water wave, so throw away that image too. What a light wave has is regions of high electric and magnetic field magnitude, interspersed with regions of zero electric and magnetic field magnitude. If you plot the amplitude of the electric field or the magnetic field against time or distance, it is only then that you see the maxima and minima as peaks and troughs.

Hope this helps.

It is well known that we cannot visualize quantum level processes. Do not expect an explanation that makes sense.
Maybe it's just me, but I always thought that sounded like a cop-out reply.

I love it when people do this and express their own way of thinking about things. OK Crisp, are u saying that there is a probability (wave aspect) that the photon could be anywhere in space and that when u 'collapse' this wavefunction (by observing it) then it is quantised at a particular place (which is generally a region of high probability)?

Well, not really, I was trying to put it in simple words, and surely trying to avoid measurement issues ;) ...

From a non-relativistic quantum point of view, the photon is the quantum of energy that is exchanged between the field (e.g. particle in harmonic potential) and the observer (or other system, or whatever the field is interacting with). The photon as such has no wavefunction in this picture.

If you model the electromagnetic field interaction as a harmonic potential, then you have the field aspect on one side (or the "wave" aspect if you like) which is in the background, and you can exchange photons with that field (which is then your particle, or "localised" aspect).

This only partially answers the question, since I am not talking about the propagation of the EM-wave, which is more or less assumed to happen in classical way here. I do not want to drag in QFT or QED ;)

Bye!

Crisp

Surely the photon has a probability of being anywhere in the universe at any time though (within limits imposed by c) and this probability can be mapped by a 3D wavefunction which we can call the 'probability wave'. What is the difference between this wave/field and an EM field?! Are they the same?

One Raven: Referring to my statement that you cannot visualize quantum level phenomena, you said.Maybe it's just me, but I always thought that sounded like a cop-out reply.If geniuses like Bohr & Feynman claim that they cannot visualize what is happening at the quantum level, I do not feel dumb for admitting that I cannot do it.

There are some limits to what the mind can do. I once spent 2-3 hours per week over a periods of 5-6 years trying to develop the ability to visualize 4D objects. A friend of mine who is a genius (much brighter than I) also spent about half that much time on the project. He gave up sooner: Perhaps because he is smarter than I; Perhaps because he is not as stubborn.

It was not time wasted. We both learned a lot about the mathematics and properties of 4D objects. It is never a waste of time to learn something interesting, even if it is not useful. It is not a waste of time to try to visualize quantum phenomena. You can learn a lot while pursuing an unreachable goal.

The original planetary model of the atom is easy to visualize. Bohr used it to develop some insight into the nature of the atom. While it is not a valid model, it was useful to Bohr and other early quantum physicists.

Perhaps your (or somebody else’s) quest for a model that can be visualized might result in further insight into the nature of quantum phenomena.

Somebody once said that if you could visualize quantum phenomena with a classically evolved mind, you could build scaled up working models of quantum entities.

BTW: There are some very simple concepts that are difficult to visualize. Did you know that on a torus, seven colors are required to avoid having two adjacent regions with the same color? I can easily visualize a configuration on a sphere which requires 4 colors. I have diagramed a torus showing that 7 colors are required. I cannot visualize the configuration without making the diagram. I do not think this is an impossible visualization task, only difficult. It is an easier task than trying to visualize some quantum phenomena.

"BTW: There are some very simple concepts that are difficult to visualize. Did you know that on a torus, seven colors are required to avoid having two adjacent regions with the same color? I can easily visualize a configuration on a sphere which requires 4 colors. I have diagramed a torus showing that 7 colors are required. I cannot visualize the configuration without making the diagram. I do not think this is an impossible visualization task, only difficult. It is an easier task than trying to visualize some quantum phenomena." and what are these regions we speak of? isometric regions? non-closed regions?

Surely the photon has a probability of being anywhere in the universe at any time though (within limits imposed by c) and this probability can be mapped by a 3D wavefunction which we can call the 'probability wave'.

Not in non-relativistic quantum mechanics. A photon there on itself is only used to label a quantum of energy which is connected to (typically) harmonic potentials.

Where would the speed of light suddenly come from in non-relativistic quantum mechanics ?

Bye!

Crisp

Neurocomp2003: I was referring to the classical map problem proven about 5-10 years ago by a man named Wiley (I think that is his name). I thought everybody was familiar with that age old problem.

Think of making drawing a map on a plane or a sphere. You ignore countries with two or more separated regions like the USA, with Hawaii & Alaska not connected to the rest of the states. You also ignore countries that only touch at a point. Now how many colors do you need if no two adjacent countries are allowed to be the same color?

For centuries, it was known that three colors were not enough. Everybody believed that four were sufficient, but nobody was able to prove that four would suffice. Without drawing every one of an infinite number of possible maps, how could you be certain that no map would require 5 colors?

About 5-10 years ago, it was proven that 4 colors were sufficient.

If you draw maps on the surface of a torus, 7 colors are required. This was proven a long time ago, perhaps 100-150 years ago. In some respects, a torus is easier to deal with than a sphere or a plane. The plane presents problems because it must be viewed as infinite or else as having infinitely many abrupt terminations of otherwise continuous curves. The sphere has a problem with any coordinate system. Latitude, for example, has no meaning at the Poles. A torus does not have such problems. It is finite and there are no anomalus points where the coordinate system breaks down.

As noted in my previous post, it is difficult to visualize a map on the surface of a torus which requires 7 colors. It is easy to diagram such a map. You can model a torus with a rectangle if you do not want to work with a 3D model of a torus. Merely imagine the sides as being the same line and the ends as being the same line. Then draw your diagram on that rectangle.

Yes I know of these problems but the way you worded it was unfamiliar or rather undescriptive...btw: they are called color-graph problems(or chromatic) and there's another term for them but i can't remember(this term comes from comp.geometry)....and the solution depends on the largest Kn-graph in the connectivity in which case your sphere problem it is K=4.

But how would you draw an atlas map on a torus? where would the poles be? On the inside of the torus opposite each other?

Neurocomp2003: When told about the 4-color map problem, some mathematician thought about the same problem on a torus instead of a sphere. I guess he was an early SciFi fan and dreamed up an intelligent species somewhere in the universe living on a planet shaped like a doughnut. If here was a Jewish mathematician, he would think bagel.

I once did a lot of thinking about a torus. The geodesics are interesting, but that is too far removed from this thread to discuss.

The poles of a torus are circles at latitudes +90 and -90 degrees. Imagine two equal circles of radius r with their centers separated by distance R. They can represent the cross section of a torus. As R grows without bound, the torus becomes more and more like a cylinder. As R approaches zero, the torus becomes more and more like a sphere. The Polar circles approach the North & South Poles of the sphere.

Latitude and Longitude can be used as co-ordinates on a torus. For a sphere, Latitude ranges from -90 to + 90 degrees. On a torus, it ranges from -180 to +180 degrees. A torus has an outer and an inner equator, while the sphere has only one equator corresponding to the outer equator of a torus. An entire sphere would only map to part of the torus. It would be a bit like a Mercator projection, with the poles mapping to circles.

...you can also solve the utility problem on a torus! You cannot on a sphere.

Not in non-relativistic quantum mechanics. A photon there on itself is only used to label a quantum of energy which is connected to (typically) harmonic potentials.

Where would the speed of light suddenly come from in non-relativistic quantum mechanics ?
Bye!
Crisp

OK but lets talk relativistic QM. We might as well use the two theories if we wanna talk about a model which fits 'reality' best. In relativistic QM is this how u see it?

OK but lets talk relativistic QM. We might as well use the two theories if we wanna talk about a model which fits 'reality' best. In relativistic QM is this how u see it?

I do not have enough experience in relativistic qm / qed to talk enough sense about that. But since you have been dying to tell us for three days already, go ahead how you think of it.

I would not have enough experience myself (hence I am asking for your viewpoint) but I have always thought of the light model in that way (if there even IS a way to think about it) and I was just hoping u might see it like that as well. Anyway........