So when people say light exists as a particle and a wave, I understand what it means in terms of different behavior, but what “is” a wave? A photon is a light particle, is a light wave “made” of anything? Is a light wave just a way that a photon expresses itself? Is it just “energy”? But then, what is energy? Is a microwave “made” of anything, or is it just a way of describing how heat/light behaves under certain conditions?
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A wave is a back-and-forth change in something that travels along that something.
A sound-wave is an increase and decrease in pressure that travels along the air/water/whatever.
Light is a wave in what is known as the electromagnetic field where it oscilates back and forth.
The confusion seems to be from the fact that when you get down to extremely small scales, things start to behave with characteristics associated with *both* waves and particles. This includes light.
A Photon is a discreet packet of light energy, but that energy still has a wavelength and will behave in partivular manners associated with that wavelength, such as resonance and refraction.
A “microwave” is actutually just light within a specific range of wavelengths, as are radio-waves and gamma rays.
Ocean wave is described by a wave equation. A wave equation said that a point on the surface of water receive an acceleration opposite and proportional to the relative height of that point compared to those around it. More abstractly, the relative height value at a point will change by accelerating toward the relative height values at points near it. Of course, people don’t just declare that ocean wave follow wave equation just like that, we derive it from basic physic principles: Newton’s mechanics.
But now that we have a wave equation, we can apply it to many settings, as long as the physical principles give you the same equation. The wave equation describe how a “field” change. A field is something that assign a number to each point on a surface or in space at each point in time, and the wave equation describes how these values change over time.
So now we have light. The wave behavior of light is described by the theory of electromagnetic field. The physics of that field is described by Maxwell’s equation, which is completely different from ocean wave’s Newtonian physics. But yet – as it turns out – we still derive the wave equation from it. Because we get the same equation as the equation for ocean wave, we also call it a wave. Of course, there are some differences, but the mathematics similarities are enough to call it by that name. The field in electromagnetism describes the strength of electric and magnetic force, while the field in ocean wave describes the height of the water surface. Electromagnetism is also 3 dimensions in space, while ocean wave is 2 dimensions.
This will sound hand-wavey (no pun intended) as these are such fundamental concepts, but it sounds like you’re pretty close to being able to answer your own question. A wave is indeed a “behavior”, or really a set of behaviors that in simple terms can be described as a moving disturbance. A wave itself is not “made” of anything, but rather it describes how “things” such as particles behave. With “things” themselves being extremely general, seeing as spacetime itself is a “thing” that may not be tangible in an intuitive sense but does exhibit wave-like behavior.
Waves can be thought of as “carrying” energy in a sense, but it would be misleading to say they “are” energy. What is energy is a question that I’m not sure how to answer very well and understandably.
As far as photons, heat, light and microwaves. Light, microwaves, and all of the other electromagnetic waves are really just different wavelengths in photons, i.e. different levels of wave-like behavior. These things are not heat, but they are a means in which heat is transferred between atoms in a process called electromagnetic radiation.
A wave is a repeated variation of… something. If the variation can be described in terms of a *frequency* (how often the variation repeats) a *wavelength* (how far apart the repeated bits of the variation are) and an *amplitude* (how much the… something… varies within each repetition) then it’s a wave.
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