That all helps a lot, thanks.

I can’t tell if that quip is missing a smilie or not. When you were discussing this on CT, almostfamous wrote:

re: the units. doesn’t dimensional analysis not make sense if you could just equate mass to energy? that would be M=ML2T-2

i realize we aren’t talking about billiard balls anymore, but i thought dimensional analysis held up in most cases. unless, of course something has changed in the way physicists think about these things since early 2002, the last date at which i took a class in physics.

He makes an important point. Mass and energy are not the same, but physicists have to assume that they are in order to be able to explain what’s happening. The fact is, though, if mass is the equivalent of energy, then the dimensional inconsistency that almostfamous points out has to be swept under the rug and ignored. On the other hand, if they are not the same, which commonsense seems to insist, then the fact that they each can be changed into something else reveals that they are not fundamental entities, because that which can be changed into something else is obviously not fundamental. This indicates that the more fundamental entity is common to both mass and energy, and since both matter and radiation are related to energy by velocity, and velocity is space and time, then we ought to take the hint, and look to motion, s/t, as the fundamental constituent of the universe.

If a universal motion exists, it consists of a universal increase of space and time, delta s/delta t. We know that time progresses universally, because we observe it. However, we haven’t considered an analogous progression of space, because we haven’t observed it, except for the last 75 years or so (these things take a long time to sink in). Nevertheless, it’s really only a matter of a slight interpolation to assume that space has the properties of time, i.e. space, like time, progresses. In fact, it’s a sound scientific procedure to interpolate like this, much more justified scientifically than the wild, ad hoc, theoretical inventions so common today.

Of course, a hypothesis is justified by its results, and the above results are very encouraging (I don’t know if you think so. I can’t read the intent of your one-liner.) At any rate, this assumption opens up a whole new basis for physics in which the speed of light is viewed as the unit ratio of a universal progression of space and time, which redefines space and time as the reciprocal aspects of a universal motion that forms the reference system of all physical phenomena.

It’s just this type of fundamental change in the nature of space and time that people like Gross and Smolin are expecting, as I have been explaining in detail in a thread on the Bad Astronomy Universe Today discussion forum (see: The Reciprocal System of Physical Theory thread). If you want to know more, I’ll be happy to discuss it with you there.

Regards,

Doug

It’s more or less a coincidence that the theory of relativity and nuclear physics were developed at the same time. One might easily imagine a world where it was measurements of nuclear reactions and their mass loss that gave inspiration for the theory of relativity.

Interesting. Has anybody ever figured out why the rest mass is related to energy by velocity? We know that the space/time (note: not spacetime) dimensions of velocity squared are (cm/sec)^2, but if you try to find the dimensions of mass, or the dimensions of energy, on Google, you get something like this:

“The physical dimension of energy is defined as mass times length squared over time squared.”

Hmmm, that’s not very interesting. Try again. Whoa, now we find something different, “The unit of energy is the joule, with dimensions kg·m^2/s^2.” Grrrrr! Let’s try for the dimensions of mass… Turns out that we run into the same tautology, but if we dig hard enough we can find that the dimensions of mass can be expressed in terms of geometric units, which are meters per kilogram. Well at least we see something in common with velocity, but then this space unit is not much help really, because it’s just a unit of time expressed as length and mass expressed as the magnitude of four-momentum vector.

Geezzz, guys, can’t we do better than that? What if the space/time dimensions of energy were the inverse of the space/time dimensions of velocity, with dimensions s/l? Now that would be interesting! And it’s not all that unreasonable given the emphasis on symmetry these days, huh? I mean come on, what’s a little spontaneous symmetry swapping among friends?

Lets see now. With that little discovery, and Einstein’s un-American equation of mass,

M = L/V^2,

we get

m = t/s / (s/t)^2 = (t/s)^3, [1]

where s and t are units of space (length) and time (seconds). Now we’re getting somewhere, at last! Can we go further? What about momentum, p?

p = mv (we’ll use the more modern lower case letters), so from [1]
we get

p = (t/s)^3 * s/t = (t/s)^2.

Hmmm, what can we do with that? Well, we see that these dimensions are really similar to the dimensions of that enigmatic concept of action, or momentum times space, the foundation of the uncertainty principle. That’s interesting, because the energy of radiation is related to h by another form of velocity, a frequency, 1/t. Let’s see:

E = hv,

or with our new dimensions of energy,

h = E/v = (t/s)/(1/t) = t/s * t = t^2/s,

but, if frequency really is a velocity, the space unit is still there, it’s just used over and over again in a rotation, right? So, then, putting that ole sneaky space unit back where it belongs, let’s do that equation again,

h = E/v = (t/s)/(s/t) = t/s * t/s = (t/s)^2,

voila! How interesting is that? Momentum with the same dimensions as h, and a symmetry between the way mass and momentum relate to energy through velocity. Too bad we can’t come up with something like that, instead of that horrible four-momentum vector, Sean.

Would “the sums of the masses of the constituents plus the binding energy” be equal to the sums of the masses of the constituents plus the kinetic energy of the constituents plus the potential energy of the constituents? In other words, is the “binding energy” of a bound system the same as kinetic energy + potential energy for that system? This would sort of make sense, because I think the potential energy of a bound system would be negative, so this would be the difference between the depth of the potential well and the system’s total kinetic energy, and if you added enough kinetic energy so the two were equal, that would be the point where the system would tear itself apart (come unbound). Am I getting this right?

If so, then for me it’s a little easier to think of the implications of E=mc^2 as “both kinetic energy and potential energy contribute to the inertia of a bound system”–a hot brick is a little harder to accelerate than a cold one, and a compressed spring is harder to accelerate than a relaxed one. And because of the equivalence principle, this also means the hot brick and the compressed spring would weigh a little more too.