- #26

krab

Science Advisor

- 896

- 2

Anton A. Ermolenko is correct in my view. I should add that by "correct", I mean by Occam's Razor: it results in a simpler description of reality.

In lower level physics courses in America, relativity is usually first taught in such a way that it is easier to compare with Newtonian mechanics. However, if you carry this to solving complicated problems relating to the dynamics of relativistic particles, it is way too cumbersome. One of its results is a distinction between "longitudinal" and "transverse" mass. Another is that pesky sqrt(1-v^2/c^2) factors appear everywhere.

I now believe it is the wrong way to teach relativity. My undergraduate education left me with the impression that relativity is very tricky, with many pitfalls. My later career turned out to be at an accelerator lab where it is essential to correctly describe trajectories of relativistic particles. To my surprise, I found the equations of motion are relatively (unintended pun) simple, and simple to derive, if one begins with 4-vectors and Hamiltonians. In 4-vector form, mass is rest mass; it is in a sense the norm of the 4-momentum. It is a useful concept because it is invariant. Defining mass in such a way that it depends on momentum only complicates life.

James Smith in his text Introduction to Special Relativity (1965) derives E=mc^2/sqrt(1-v^2/c^2) and then comments: "This raises a semantic question. Here is a new quantity that is the relativistic generalization of two classical quantities. Many treatments do just what we have temporarily done and call M=m/sqrt(1-v^2/c^2) the "mass", m the rest mass, and call Mc^2 the energy. But, if energy is always just c^2 times the "mass", this is not good economy with words or concepts. Furthermore, it seems desirable to have the word mass refer to an intrinsic property of the particle, and not to refer to a property of its motion. From now on this book will follow what is becoming quite general practice. The word energy will refer to the quantity mc^2/sqrt(1-v^2/c^2) . The word mass wil refer to m, the quantity many other treatments call the "rest mass"."

I am also quite close to the field of particle physics. No one says photons have mass. Everyone says photons are massless, without qualifying this by saying they are speaking of rest mass only.

In lower level physics courses in America, relativity is usually first taught in such a way that it is easier to compare with Newtonian mechanics. However, if you carry this to solving complicated problems relating to the dynamics of relativistic particles, it is way too cumbersome. One of its results is a distinction between "longitudinal" and "transverse" mass. Another is that pesky sqrt(1-v^2/c^2) factors appear everywhere.

I now believe it is the wrong way to teach relativity. My undergraduate education left me with the impression that relativity is very tricky, with many pitfalls. My later career turned out to be at an accelerator lab where it is essential to correctly describe trajectories of relativistic particles. To my surprise, I found the equations of motion are relatively (unintended pun) simple, and simple to derive, if one begins with 4-vectors and Hamiltonians. In 4-vector form, mass is rest mass; it is in a sense the norm of the 4-momentum. It is a useful concept because it is invariant. Defining mass in such a way that it depends on momentum only complicates life.

James Smith in his text Introduction to Special Relativity (1965) derives E=mc^2/sqrt(1-v^2/c^2) and then comments: "This raises a semantic question. Here is a new quantity that is the relativistic generalization of two classical quantities. Many treatments do just what we have temporarily done and call M=m/sqrt(1-v^2/c^2) the "mass", m the rest mass, and call Mc^2 the energy. But, if energy is always just c^2 times the "mass", this is not good economy with words or concepts. Furthermore, it seems desirable to have the word mass refer to an intrinsic property of the particle, and not to refer to a property of its motion. From now on this book will follow what is becoming quite general practice. The word energy will refer to the quantity mc^2/sqrt(1-v^2/c^2) . The word mass wil refer to m, the quantity many other treatments call the "rest mass"."

I am also quite close to the field of particle physics. No one says photons have mass. Everyone says photons are massless, without qualifying this by saying they are speaking of rest mass only.

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