ZikZak

Aarghe. Will it never die. I am teaching a summer course on Relativity (SR & GR) at approximately the sophomore level. Just about all of them were taught in high school physics that the reason nothing can travel faster than light is that things get so massive that there isn't enough energy in the universe to accelerate them to c.

This really cheeses me off. Maybe it's just a pet peeve, but this "relativistic mass" nonsense is frelling *everywhere.* I hate it, and I can't stand that this is the reason people are still, today, routinely given for the impossibility of travel at c. I don't know a single actual real physicist that ever uses the concept of relativistic mass, and there are some VERY good reasons why not. Among these are: (1) it breaks mass invariance for particles. Electrons are no longer all of the same mass. (2) It breaks the gravitational mass / inertial mass equivalence principle. Kinetic energy gravitates differently from rest energy. Students who are taught that mass increases with speed often believe that if you get something moving fast enough, you can increase its mass arbitrarily until it has enough gravity to become a black hole. When they are told this cannot happen, they are rightly very confused. (3) And most importantly, it makes students believe that the "speed of light barrier" is a dynamic phenomenon having to do with masses, inertia, forces, and accelerations, when nothing could possibly be farther from the truth. It is all about kinematics plus the invariance of the speed of light. In my course, we don't even talk about mass until the very end of SR, long, long after we have derived the velocity addition formula and its implications for travel at c.

It's also unfortunate because the concept of relativistic mass overemphasises the popular misconception that E=mc^2 **IS** Relativity, when in fact, it is only one of many interesting derived relations. Actually, it's E = (gamma) mc^2, but everyone drops the gamma for some reason in high school, which again confuses the issue between rest energies and kinetic energies. "Relativistic Mass" is just total energy, so why give it a new name like "relativistic mass?" Just to confuse people?

Now that the Rant Of Frustration is over with, does anyone else get irritated by this or is it just me?

Theophage

If people would only use more than 10% of their brains, they would realize that it is the relativistic mass that causes the electrons to orbit the nucleus of the atom counterclockwise in the southern hemisphere, which according to the second law of thermodynamics means bees shouldn't be able to fly.

Smullyan-esque

I think it is OK as a first approximation, but just like essentially EVERYTHING in science, "it is more complicated than that".

Relativistic mass does gravitate, and it does affect momentum, so calling it "mass" isn't totally crazy. It just leads to some false implications. But the other alternative is to teach them the whole, complicated story, from the very beginnning. And that just isn't practical, or educationally effective.

The dynamic phenomena of masses, inertia, and so on, derive from the speed of light limitation, not the other way around, but that requires people to do a bunch of math at a very high level, so it is often just easier to let them have their illusions until they are ready for the correct explanation.

Oh, and the gamma thing. My high school physics teacher handled that quite easily. He explained that you can get rid of gamma, if you define your units properly. So, E does equal mc^2, for the correct units of measurement. Otherwise (as for SI units), you need a conversion factor.

The part that really bugs me is that the students don't ever seem to be willing to realize that they DON'T already know the whole story. I get the same thing in my Algebra classes when I finally tell them that, Yes, you CAN take a square root of a negative. Complex numbers just freak them out.

Jesse

How does that make sense? For the same object moving at different velocities in your frame, its total energy in your frame will be different...how can you account for that just by using the right set of units? Certainly the right choice of units can make the constant c disappear, but I don't see how you can remove the object's velocity, which is a variable rather than a constant, from the equation.

On the subject of relativistic mass, while I don't think it's good to use for individual particles, it is helpful for newcomers to understand that for a composite system composed of many particles, the inertial mass of the entire system will be proportional to the sum of (rest energy of each particle, based on E = mc^2 with m as the rest mass) + (kinetic energy of each particle) + (binding energy of system, i.e. difference in potential energy between system's current state and the potential energy if you separated all the particles to an arbitrarily large distance from one another). So, for example, a heated brick will weigh more than the same brick when cold because of the increased kinetic energy, and an atom weighs less than the sum of the weights of the individual particles that make it up because the potential energy is less in the bound state. This is a good way of thinking of E=mc^2 I think, with E standing for the sum of all forms of energy in the composite system, and m being the apparent inertial mass of the system (difficulty in accelerating it).

barbos

No, it does not, energy-momentum tensor gravitate

Craig

Are you sure they are actually taught that in school? I hear a lot of people say that too, but I think it's more of an urban legend type thing than something that's taught (and that will make it both harder to get rid of and more common).

Jesse

I don't see why you say it's just about kinematics rather than dynamical issues involving energy and inertia--if you ignore energy issues, there's no logical reason you couldn't have an object whose velocity as a function of time v(t) in some inertial coordinate system starts at some v<c and at a later time goes to some v>c. The reason this is physically unrealistic is that it would require infinite energy in this frame (not to mention infinite proper acceleration), which is a dynamical argument. And even from a dynamical standpoint SR does not forbid the possibility of tachyons which always go faster than light (although it implies that if signals could be sent faster than light, they could also be sent backwards in time, so this would require us to sacrifice causality).

Of course you don't need "relativistic mass" to explain why the energy to accelerate a massive object to light speed would be infinite, you can just use the formula for total energy of an object with nonzero momentum:

E^2 = m^2*c^4 + p^2*c^2

...with p the relativistic momentum , which goes to infinity as v approaches c. And a little algebra shows that the above formula is equivalent to the equation you mentioned earlier, E = gamma*mc^2, with gamma = .

mester74

I don't know about the speed of light thing, but I am sure I was taught "relativistic mass" in high school, with rest mass being usually denoted as m0 and relativistic mass m = gamma*m0. I am not sure about the college physics course though. We used Landau & Lifschitz - does anyone remember?

Smullyan-esque

The E = mc^2 formula is only for rest mass. If the object has some velocity, the formula gets much more complicated. It has been a while for me, but it is something like E^2 = m^2 c^4 + something something.

Smullyan-esque

All this does is replace a phrase the student has some vague understanding of (althought not perfectly accurate) with a phrase the student doesn't understand at all.

Or you can avoid teaching students about relativity until after they learn tensor calculus. This would mean that 99.99% of the population wouldn't even have a rudimentary understanding of the past 100 years of physics.