# Wave analogies

1. Mar 7, 2009

### Mentallic

So I've been told that electromagnetic waves oscillate like flicking a rope up and down or a ripple in a pond. In the first example, from a side view, the rope can be considered to be a line, or 1-dimensional. However, once the ropes starts oscillating to represent waves, width must also be taken into account to view the wave, so it becomes 2-D. Similarly for the pond, the surface of the water can be considered 2-D from a birds eye view, but to view the ripples, it takes the 3rd dimension of height. Following this pattern, if we were to view the light waves being emitted from a light bulb (3-D environment), we would need a 4th spatial dimension?
I haven't studied quantum theory or any other topics that relate to these ideas, but I'm curious as to whether electromagnetic waves physically oscillate in a way that we couldn't possibly perceive them (4-D) which just defies logic at this point. So what is actually going on here?

2. Mar 7, 2009

### jambaugh

Remember that these are analogies and not models. The distinction here is that in an analogy some things are held in common but others differ whereas in a model all relevant features are isomorphic and you can use the model to predict behavior in the system in question. You can't infer anything from an analogy you only use it to clarify and classify types of behavior.

The one thing you can see in all these analogies is superposition of waves and what this implies e.g. interference, beat frequencies, standing waves, frequency decomposition, etc.

Be careful also extrapolating from low dimensional examples (1 & 2). Things are possible in higher dimensions which are not possible in lower dimensions. For example torsion waves (picture those slow motion pictures of a dog shaking water off its fur. His head twists back and forth and this twisting propagates down his fur.)

You left out the example of the pressure waves in air (or any compressible material) which do not require extra dimensions.

However in the case of E-M fields and waves you can model by adding an extra dimension (see Kaluza-Klein theory).

Be careful of your wording "(4-D)" doesn't "defy logic" it just defies your ability to visualize. We can logically describe higher dimensional spaces mathematically. We can make logically sound conjectures about their existence or behavior... and that logic may or may not show the conjectures fit empirical observations.

Finally let me point out that whether one postulates extra dimensions or not is really immaterial within the physics. A conjecture is physically meaningful if it describes what we expect to see happen (independent of what we think "is" apart from what we can see happen) and a conjecture is considered correct (or at least confirmed) if what it describes actually does occur in physical observations.

3. Mar 7, 2009

### Mentallic

Alright, so what conjectures can be made about the behaviour of E-M waves in our 3-D world? Are they oscillating in a way that we can visualize them, or is their physical behaviour especially plain, without any vibrations/oscillations, which might suggest they do in fact extend their waves into a 4th dimension?

The difference here with the sound waves is that unlike the E-M waves, they require a medium, and the way in which they move can be represented with analogies that don't require extra dimensions to show their movement, thus, no 4th dimension is required to describe the movement of sounds waves in our 3-D world.

If I have interpreted what you're trying to say correctly, it's that the E-M waves do in fact 'wave' in a fashion that can be visualized in the 3rd dimension, while the predecessing analogies of 1-d and 2-d are inferior in that they require another dimension.

4. Mar 8, 2009

### Klockan3

E-M waves are actually not normal waves at all, they are just electric and magnetic fields going from + to - in a harmonic fashion.

It is not an extra dimension since a dimension is a place where every point is unique, instead electric fields are just properties of our current dimension, just like how different points can contain different mass bits etc. As such when sound waves propagate through the medium "density" you can just as well say that E-M waves propagates through the medium "Electro and magnetic fields".

5. Mar 9, 2009

### Mentallic

I was never told this before. The teacher probably felt sorry for us and decided to save us the pain of more confusions
ok so if the E-M waves can be represented on a graph, even though they're fields, not waves. Does this have something to do with the 'harmonic fashion' they travel in? (sorry I don't understand what this harmonic fashion is).

6. Mar 9, 2009

### Klockan3

Harmonic waves are those who follow the normal sinus curve.

And yes you can graph them, when you do you put field strength on one axis and position on the other, its no more a dimension than a graph showing how velocity changes with position on an accelerating car.

Anyway, look at this:
http://en.wikipedia.org/wiki/Maxwell's_equations
Look at the third and fourth equation, you see there that both E and B (magnetic and electric) fields can be created through change in the other, and as such when you pair them together like they are in an electromagnetic wave you get a never ending loop of them going into each other.

Its quite a bit the same how electric potential distributions follows exactly the same formulas as static temperature distributions, it doesn't mean that they are equal in any way except mathematically.

7. Mar 10, 2009

### jambaugh

That depends on your power of visualization. But yes. Can you visualize an electric field? Can you visualize a magnetic field? Now imagine you grasp a charge and crack it like a whip. You will perturb the E field and as it changes it induces a perpendicular B field.

Undulations of the E field induce undulations of the B field which reinforce the undulations of the E field ad infinitum as the wave propagates.

Grasp a bar magnet and crack it sideways and you get the same sort of wave. The E-M wave is sort of a double wave with the E component riding the B component and vis versa.

In three dimensions you have 1dim for the direction of propagation, 1 dim for the transverse E undulation and one dim for the perpendicular transverse B undulation.