- #1
H_A_Landman
- 59
- 8
Here's a puzzle that has been bothering me lately. I take as given the following:
Combining (2) and (1c), we seem to have the implication that an electrostatic potential should change the mass of an electron. We know the frequency is changed. We know frequency equals mass. We should be able to logically conclude that the mass is changed.
Now clearly, that conclusion is wrong. If an electric potential changed the mass of electrons, then we would see changes in the size, mechanical strength, color, and other physical properties of the spheres of Van de Graaff generators when we charge them up, but this doesn't happen.
Further, I know directly that the charge/mass ratio of electrons is not altered, because I ran that experiment myself in 2010, inside the sphere of the giant Van de Graaff at Boston Museum Of Science. I got a solid null result, with the only noticeable effect being a slight fuzzing of the electron beam (probably attributable to EM noise from the nearby generator). Within the 5% accuracy of the equipment, there was no observable change from about -1 MV to +1 MV potential. Since the mass of an electron is about half an MeV, the prediction from (2) is that at -1 MV the frequency should be roughly 3 times as great as for an electron at 0 V and therefore(?) by (1c) the mass should triple. If this effect actually existed, it should not be subtle and hard to detect.
So, I'm not confused about the physical reality. I hope. What I am confused about, is why there is an apparently valid argument that the mass should change, when it doesn't. Why, in this case, does frequency NOT equal mass? Does the de Broglie relation not apply universally? If so, when does it apply, and when does it not?
Am I just missing something really simple and obvious here?
- [itex]E = h\nu[/itex] (Planck) energy equals frequency
- [itex]E=mc^2[/itex] (Einstein) energy equals mass
- [itex]mc^2 = h\nu[/itex] (de Broglie) mass equals frequency
- The phase frequency of an electron is altered by an electromagnetic potential. For a static electric potential [itex]V[/itex], this causes a phase shift [itex]\Delta\phi=-\frac{qVt}{\hbar}[/itex] that corresponds to an increase (decrease) of the electron phase frequency when [itex]V[/itex] is negative (positive). This is the same frequency change that shows up in different-energy solutions to the Schrodinger equation.
Combining (2) and (1c), we seem to have the implication that an electrostatic potential should change the mass of an electron. We know the frequency is changed. We know frequency equals mass. We should be able to logically conclude that the mass is changed.
Now clearly, that conclusion is wrong. If an electric potential changed the mass of electrons, then we would see changes in the size, mechanical strength, color, and other physical properties of the spheres of Van de Graaff generators when we charge them up, but this doesn't happen.
Further, I know directly that the charge/mass ratio of electrons is not altered, because I ran that experiment myself in 2010, inside the sphere of the giant Van de Graaff at Boston Museum Of Science. I got a solid null result, with the only noticeable effect being a slight fuzzing of the electron beam (probably attributable to EM noise from the nearby generator). Within the 5% accuracy of the equipment, there was no observable change from about -1 MV to +1 MV potential. Since the mass of an electron is about half an MeV, the prediction from (2) is that at -1 MV the frequency should be roughly 3 times as great as for an electron at 0 V and therefore(?) by (1c) the mass should triple. If this effect actually existed, it should not be subtle and hard to detect.
So, I'm not confused about the physical reality. I hope. What I am confused about, is why there is an apparently valid argument that the mass should change, when it doesn't. Why, in this case, does frequency NOT equal mass? Does the de Broglie relation not apply universally? If so, when does it apply, and when does it not?
Am I just missing something really simple and obvious here?