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Who is Charlene Werner, you might ask? Seemingly she is an optometrist who is a great proponent of homeopathy. However, she is mostly well known for her absolutely hilarious pseudoscience, as depicted in this video (don't be surprised if that video doesn't exist by the time you click on it, as Werner is busy sending cease-and-desist demands to everybody who posts the video).
The sheer stupidity of what she says in that video has been totally trashed in several blogs around the internet, so I'm not going to go through everything she says because that has been done already. Instead, I'm just going to concentrate on her misunderstanding of mathematical formulas in physics, and the "E=mc2" formula in particular, just as an intellectual exercise.
The relevant quote is:
You know that when light is energy, right? OK. And he [Einstein] gave us the theory that energy equals mass times the speed of light. E=mc2. OK. If we take that formula, and we think that there's a lot of mass, right? OK. If you collapse all the mass down into the universe, so that there is no space between the mass, do you know how much mass there is in the entire universe? You think you're a lot of mass, right?... Well, the whole universal mass can be consolidated down into the size of a bowling ball. That's all there is in the whole universe. So, how much mass are you? That's right, an infinitesimal amount. So if you take that formula, E=mc2, you can almost cross out mass. So the formula ends up being "energy = the speed of light."
(No, there's a lot more "mass" than that in the universe, but as said, I'll skip commenting on that and the other things she says, and concentrate only on the math.)
Werner seems to have a fundamental misunderstanding of what a physical formula is. She seems to think that it's some kind of metaphor, a vague description of the relationship between two phenomena. She seems to think that "E=mc2" means approximately the same thing as "there's some kind of relation between energy, mass and light". One also gets the feeling that she seems to think that the little 2 (the "square") is just for decoration, put there because it looks fancy, as she just mentions it but ignores it completely.
She seems completely unable to understand that this is not a metaphor or a vague description. This is a mathematical formula. Mathematical formulas are completely rigorous and obey very strict rules. You can't just shuffle things around however you want and expect it to remain valid.
So here's a list of things that she gets utterly wrong:
This is one of the reasons you know that, let's say, "velocity = volume" is nonsensical: Because the units don't match. On the left side we have meters/second as a unit, while on the right side we have liters. These just don't match, which means the equation is nonsensical.
The units on both sides of "E=mc2" match, although it might not be immediately apparent. The unit of energy is a joule. On the right hand side we have the unit of mass, kilogram, and the unit of speed, meters/second, squared. In other words, the overall unit of the right hand side of the equation is "kg·(m/s)2".
The unit joule is defined as "N·m" (newton times meter), and a newton is defined as "kg·m/s2". Hence a joule is defined as "kg·(m/s)2", which is the same as the units of the right hand side of the equation.
If you frivolously drop the mass from the equation (in other words the "kg" from the units) the units won't match anymore, which is why you know that "E=c2" (or "E=c" or whatever) is nonsensical.
The "speed of light", c, is just that: A certain speed. It has nothing to do with light itself (other than that light travels at that speed in vacuum). It's called "speed of light" because light (or, more precisely, electromagnetic radiation) is the most obvious phenomenon that travels at that maximum physical speed. (Any massless particle would travel at that same speed too, as a direct consequence of the theory of relativity.) This quantity could be called something else completely (such as "universal maximum speed" or whatever).
Even if the quantity c would be inherently tied to light and nothing else, equating them would still be utterly wrong. The speed at which something travels is not the same thing as that something. It's like saying that "the speed of that car" is the same thing as "that car". Obviously this is pure nonsense. It's a fundamental category error.
Again, it clearly seems like she thinks of "E=mc2" as some kind of vague metaphor, like a cryptic utterance of a wise prophet which has to be interpreted. No, it's math, not a metaphor.
If there's any deeper meaning to the E=mc2 formula, it's that it establishes an equivalence between energy and mass (rather than energy and light, as she postulates). It gives the exact ratio between the two (in other words, "this many kilograms of mass are equivalent to this many joules of energy".) And this is an exact, mathematical equivalence, not a vague metaphor.
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