Mike, have you ever seen the Relativator slide rule manufactured by Atomic Laboratories? If not, then congrats, because you basically redesigned it :-)
The inner disk of the Relativator has a 10 decade logarithmic eV scale from 1 eV to 1e10 eV. Gauge marks are included for particle energies, including marks at 3.73e9 eV for the alpha particle and 9.4e8 eV for the proton. The 10 decade logarithmic ɣ-1 scale gives the ratio of kinetic energy to rest energy, with a range from 1e-6 to 1e4. The outer scale labeled β is the same v/c scale you designed, but covers the range 0.0015 to 0.999999995, and is read against the ɣ-1 scale.
Hi Eamonn. Yes, I've seen the article in Symmetry. I continuously search for one but have never seen one for sale. Indeed, it certainly was an inspiration for my post. And thanks for posting the link!
Yes, unfortunately they don't come up for sale very often. However, now we know how to generate the scales, thanks to your article, so a homemade linear version shouldn't be too difficult to build.
To solve the first problem above on the Relativator, move the gauge mark for the proton rest energy (9.4e8 eV) opposite 1 on the ɣ-1 scale. Move the pointer to the kinetic energy, 2.5e8 eV, on the inner scale and read v/c = .614 on the outer beta scale.
The second problem is solved by moving the alpha particle rest energy gauge mark (3.73e9) on the inner scale opposite 1 on the ɣ-1 scale. Move the pointer to v/c = 0.165 on the β scale and read the kinetic energy = 5.5e7 eV on the inner scale.
For the third problem, the section of the β scale opposite the section of the ɣ-1 between 1e-3 and 1e-2 is the new b0 scale you are asking for. The problem can be solved on the Relatavitor by moving the proton rest energy gauge mark on the eV scale opposite 1 on the ɣ-1 scale, then moving the cursor to 3.5e6 eV and reading v/c = 0.083 on the β scale under the cursor.
Mike, have you ever seen the Relativator slide rule manufactured by Atomic Laboratories? If not, then congrats, because you basically redesigned it :-)
Here is a link to an article about the Relativator published in Symmetry Magazine in 2006: https://www.symmetrymagazine.org/sites/default/files/legacy/pdfs/200512/artifact_relativator.pdf
The inner disk of the Relativator has a 10 decade logarithmic eV scale from 1 eV to 1e10 eV. Gauge marks are included for particle energies, including marks at 3.73e9 eV for the alpha particle and 9.4e8 eV for the proton. The 10 decade logarithmic ɣ-1 scale gives the ratio of kinetic energy to rest energy, with a range from 1e-6 to 1e4. The outer scale labeled β is the same v/c scale you designed, but covers the range 0.0015 to 0.999999995, and is read against the ɣ-1 scale.
By the way, here's another article with more pictures. https://www.physicsforums.com/threads/relativator-the-circular-slide-rule-for-physicists.767964/
Hi Eamonn. Yes, I've seen the article in Symmetry. I continuously search for one but have never seen one for sale. Indeed, it certainly was an inspiration for my post. And thanks for posting the link!
Yes, unfortunately they don't come up for sale very often. However, now we know how to generate the scales, thanks to your article, so a homemade linear version shouldn't be too difficult to build.
No, it shouldn't be. ;-) And with just a bit of extrapolation of the concepts, we can even make a circular version.
To solve the first problem above on the Relativator, move the gauge mark for the proton rest energy (9.4e8 eV) opposite 1 on the ɣ-1 scale. Move the pointer to the kinetic energy, 2.5e8 eV, on the inner scale and read v/c = .614 on the outer beta scale.
The second problem is solved by moving the alpha particle rest energy gauge mark (3.73e9) on the inner scale opposite 1 on the ɣ-1 scale. Move the pointer to v/c = 0.165 on the β scale and read the kinetic energy = 5.5e7 eV on the inner scale.
For the third problem, the section of the β scale opposite the section of the ɣ-1 between 1e-3 and 1e-2 is the new b0 scale you are asking for. The problem can be solved on the Relatavitor by moving the proton rest energy gauge mark on the eV scale opposite 1 on the ɣ-1 scale, then moving the cursor to 3.5e6 eV and reading v/c = 0.083 on the β scale under the cursor.