[Still off-topic] Physics

[Steven D'Aprano]

On Fri, 4 Mar 2016 09:19 pm, Oscar Benjamin wrote:

>> As far as the reaction of matter and anti-matter, we've known for about a
>> century that mass and energy are related and freely convertible from one
>> to the other. That's the famous equation by Einstein: E = m*c**2. Even
>> tiny amounts of energy (say, the light and heat released from a burning
>> match) involve a correspondingly tiny reduction in mass.
> 
> This is also incorrect and suffers from the same misinterpretation as
> above. Mass and energy are not interchangeable in the sense that you
> can exchange one for the other with e=mc^2 giving the exchange rate.

Hmmm. Well, it's actually a bit more complicated than that. It depends by
what you mean by "converting" mass to energy. We can give at least one
sense in which it is true that mass is converted to energy, and likewise at
least one in which is it not true.

For example, we might say that even if mass-energy equivalence means that
mass and energy are in fact the same sort of thing, we can nevertheless
convert from one to another in the same way that one can convert from
kinetic energy to potential energy, or heat energy to rotational energy.

The Stanford Encyclopedia of Philosophy has a good discussion of the various
interpretations of mass-energy equivalence:

http://plato.stanford.edu/entries/equivME/


And of course, regardless of whether or not mass "really is" converted to
energy or not, using the language of conversion is the standard way to talk
about it:

https://www.physicsforums.com/threads/energy-mass-conversion.177827/

Unfortunately, mass is one of those concepts that seems easy to define, but
actually is anything but!

http://www.physics-online.ru/MessageFiles/6642/EJP-Roche-05.pdf


> Rather mass and energy are *the same thing*. Although they are
> different concepts defined in different ways and having different
> dimensions and units they are inseparable: e=mc^2 gives us the
> proportion in which the two appear together.

So apart from being different concepts defined in different ways with
different dimensions and different units, they're exactly the same?

Right-o.


Wikipedia says:

"... mass–energy equivalence is a concept formulated by Albert Einstein that
explains the relationship between mass and energy. It states every mass has
an energy equivalent and vice versa ..."

https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence

but beware because the Wikipedia article "appears to contradict itself".

Mass-energy equivalence is a simple formula, an important formula, and well
understood in practice. But what it actually "means" in theory is anyone's
guess. And so, on the principle that an analogy that is utterly wrong in a
technical sense but understandable is better than a complicated and complex
explanation that is utterly incomprehensible, I'm going to stick to talking
about mass/energy conversions :-)



-- 
Steven