Copyright © 2002 jsd
Let’s start with a demonstration of wave propagation.
Procure some light, flexible chain, at least six feet long. I’m imagining the beaded chain that they use for making pull-cords for overhead lamps, and for controlling certain types of window-shades – but anything will do if it’s strong enough, flexible enough, and not unduly heavy.
Next, procure a similar length of nice flexible rope that has the same mass per unit length as the chain. Discrepancies of 20 or 30 percent in the mass per unit length won’t matter much; just do the best you can.
Splice one end of the rope to one end of the chain, to make a combination that is half rope and half chain. Have two assistants hold the ends of the combination, or better yet, fasten the ends to suitable supports. Don’t make it unreasonably tight, just tight enough that it doesn’t drag on the floor or other obstacles.
Whack the rope with a broomstick or some such. Whack it near the end, near the support. You can easily produce a wave pulse that propagates along the rope. When the pulse gets to the splice, it will propagate onto the chain and keep going.
The wave has some properties, such as its shape, that are more-or-less preserved as it propagates along.
According to the reductionist viewpoint, wave is “really” just a bunch of rope-particles or chain-particles moving up and down. Also note that the wave cannot exist separately from the medium.
|It would be quite extreme to say that there is no such thing as a wave; there is just a rope or chain wiggling ways that conspire to make us think there is a wave.||The non-extreme view accepts that the wave is embodied in the rope or chain ... but we also recognize that the wave is a wave.|
The reductionist viewpoint is sometimes useful but sometimes not. Whether the reductionists like it or not, the wave has properties that transcend its embodiment in a particular medium. Over on one side of the room the wave is a bunch of rope-particles moving up and down. Then it propagates over to the other side of the room and becomes a bunch of chain-particles moving up and down. But still we recognize it as the same wave. The wave is the same, even though the medium has changed completely.
We can say that the wave moves from left to right across the room – even though the medium does not move left to right. The medium ends up exactly where it started. We can talk about the velocity of the wave, even though no part of the medium is moving with that velocity except possibly by accident.
It is non-controversial to recognize that the rope is made of an organic polymer, and the chain is made of metal.
|It would be quite extreme to say that there is no such thing as a rope or chain; there is just a bunch of organic polymer molecules that conspire to make us think there is a rope, and a bunch of metal atoms that conspire to make us think there is a chain.||The non-extreme view accepts that the rope “is” a bunch of polymer molecules ... but it is also a rope. The chain “is” a bunch of metal atoms ... but it is also a chain.|
Saying there is no such thing as a wave is just a silly as saying there is no such thing as a rope. The reductionist viewpoint is sometimes a valid way of looking at things – but it is not the only valid way of looking at things.
You can take the reductionist viewpoint if and when you like. But you would be tragically limiting yourself if that were the only viewpoint you were able to take. And it would be quite unwise and unkind to ask other folks to adopt such narrow views.
Some of the things we said about waves can also be said about energy.
There are many forms of energy. Sometimes it is embodied in the gravitational potential energy of objects. Sometimes it is embodied in the kinetic energy of objects. Sometimes it is embodied in electromagnetic radiation. However, as far as we know, energy never exists in isolation; it cannot exist separately from some sort of embodiment.
Still, energy has important properties that transcend any particular embodiment. Just as a wave can propagate from the rope to the chain and still be recognized as the same wave, energy can flow from the rope to the chain and still be recognized as the same energy.
Some people loudly insist that energy is not a “thing”. That indicates a remarkable non-understanding of what energy is, and/or what a thing is. Energy is a somewhat abstract thing. It is not a tangible material thing. But it is still a thing.
My opinion is supported by my dictionary (Random House) which gives 21 definitions for the word “thing”. Of these, items 3, 4, 5, 6, 7, 8, 11, 13, 15, 16, 18, 19, 20, and 21 clearly refer to abstract and/or intangible things.
Saying that energy cannot be a “thing” is beyond pedantry – it’s just plain wrong.
Chief among the properties that we ascribe to energy per se is the local conservation law. That is: Energy cannot be created or destroyed. Any decrease in the amount of energy in a given region must be balanced by a simultaneous increase in the amount of energy in an adjacent region. (For details on this, see reference 1.)
Saying that energy isn’t “real” is like saying that waves don’t really exist, or like saying that rope doesn’t really exist.
I am using the word “real” as the antonym of “fictional”. (All my dictionaries approve this usage.)
To my way of looking at it, waves are real. I don’t care whether the wave is tangible or even visible; the important point is that waves are created, propagated, and destroyed according to strict natural laws. Ropes are also real. Of course they can be created from scratch, they can be destroyed, and they can behave in complicated ways – but only according to natural laws. Energy is just as real as waves, and as real as ropes. Energy may be intangible and almost invisible, but it obeys laws that are simple, strict, and very well understood.
There are a few other abstractions that are just as real, just as nonfictional as energy. The list includes:
A great deal of physics – and especially physics teaching – is representational. We build models that represent the physics. Sometimes we represent things with equations; sometimes we represent them with pictures, or mechanical models, or whatever.
The question is not whether or not to build models; we are going to build models. The only question is which models are more (or less) faithful representations of the underlying reality.
For example, electric field lines are neither perfectly good nor perfectly bad representations of the electric field vector.
What’s more interesting is that the electric field vector is not even the best available representation of the field! The E-vector is notoriously not relativistically covariant. It is not even part of any useful 4-vector.
The clever way to represent the electromagnetic field is as a bivector. This bivector is relativistically covariant, which means that if you draw a picture of it, everybody (in every reference frame) agrees that is the right picture. This is in dramatic contrast to electric field lines, which different observers would draw differently.
Almost all the usual objections to “field lines” can be removed by drawing the bivector instead. Yeah, I know drawing bivector fields is harder than drawing lines, but it’s not impossible. A number of good examples can be found in reference 2. Some more modest examples can be found in reference 3 and reference 4.
Copyright © 2002 jsd