Timeline for Relativistic beamed photon propulsion
Current License: CC BY-SA 3.0
7 events
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| Feb 4, 2015 at 6:34 | comment | added | user12262 | @Rob Jeffries: "I think that is a can of worms and there is another Am.J.Phys. paper that I need to track down" -- Am.J.Phys., ha? More power to you! (I may not be able to follow this for a while; hope the OP still is. Mulling over "parametrization": a "final result, function of $t$" may involve "$f_{\text{beam}}~t$" but also "$f_{\text{beam}} \times L_{\text{take-off}} / c$" for the "entire spectrum"; perhaps "$\frac{L_{\text{take-off}}}{c~t}$", too.) "I removed a couple of my (at least partly incorrect) comments above" -- Good thing I quote. (I had misspelt "the factor" above; tough! ;). | |
| Feb 3, 2015 at 21:44 | comment | added | ProfRob | Do you want me to write down the equation of motion (that is what I have shown in the rest frame of the mirror) and the equation of energy conservation in the frame of the laser? i.e. $d\gamma/dt =$ ? I think that is a can of worms and there is another Am.J.Phys. paper that I need to track down to check my result - possibly more tomorrow. In the meantime I removed a couple of my (at least partly incorrect) comments above, to keep the debate concise. | |
| Feb 3, 2015 at 19:51 | comment | added | user12262 | @Rob Jeffries: "the doppler shift formula is not what you have used in the case of an accelerating receiver." -- True. (I missed that. On, to the drawing board! ;) So, I'd expect some dependence on "$f_{\text{beam}}$", parametrized (at the outset) by $\frac{A}{c~f_{\text{beam}}}$ (in comparison to $\beta$, or to $c$) ... Meanwhile I'm still curious about your derivation of "reflected power in the source system". | |
| Feb 3, 2015 at 12:55 | comment | added | ProfRob | Yes, I see. Perhaps then it is that the $\beta$ you are using in the doppler formula is not measured at the time the photons were emitted by the laser. This matters because of the acceleration. A (very) brief search suggests that the doppler shift formula is not what you have used in the case of an accelerating receiver. | |
| Feb 3, 2015 at 1:46 | comment | added | user12262 | @Rob Jeffries: "[...] the fact that fewer photons hit the mirror [...] as the mirror recedes with speed v in the same frame." -- I agree: this "kinematics" must be taken into account. I claim: I do take it into account, and together with the "plain dilation factor $\sqrt{1 - \beta^2}$" I derive $\sqrt{\frac{1 - \beta}{1 + \beta}}$ as final "one-way" Doppler result. You, AFAIU, want to apply the "kinematics factor" again, "on top" of that. That's incorrect: Doppler dilation of photon frequency and of "pulse rate" follow from the same calculation. (Has this been asked/solved at PSE?) | |
| Feb 2, 2015 at 21:12 | comment | added | user12262 | @Rob Jeffries: "Just a thought: Your first equation is just the doppler shift of individual photons." -- Yes. "But don't you have to account for the fact that fewer photons per second impact the mirror as it goes faster?" -- Accounting for this gives a (partial) factor $\frac{1}{1 + \beta}$, AFAIU; and together with the "dilation factor $\sqrt{1 - \beta^2}$" obtains the relativistic doppler factor in the first place. So why "double accounting"?? "an extra factor of $(1-\beta)$ [...] would lead to agreement with my result." -- True, but not quite convincing by itself ... | |
| Feb 1, 2015 at 18:06 | history | answered | user12262 | CC BY-SA 3.0 |