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Talk:Logical Flaws in E=mc² (view source)
Revision as of 01:53, February 25, 2016
, 01:53, February 25, 2016→Changing the Speed of Light: More carefully considered reply.
:::::::For the benefit of your benighted alarm, you said E=mc<sup>2</sup> was a definition when you actually compared its case with the case of "Newton's" as you put it, equation, F=ma, which is a definition. [[User:VargasMilan|VargasMilan]] ([[User talk:VargasMilan|talk]]) 01:01, 23 February 2016 (EST)
:::::::For the benefit of your benighted alarm, you said E=mc<sup>2</sup> was a definition when you actually compared its case with the case of "Newton's" as you put it, equation, F=ma, which is a definition. [[User:VargasMilan|VargasMilan]] ([[User talk:VargasMilan|talk]]) 01:01, 23 February 2016 (EST)
::::::::Yeah, I had a hunch that that was the nature of your misunderstanding. [[User:SamHB|SamHB]] ([[User talk:SamHB|talk]]) 20:53, 24 February 2016 (EST)
:::::In response to SamHB, it is not a scientific rebuttal to say that other equations might also break as ''c'' changes speed. Maybe other equations are flawed too, or maybe they aren't. E=mc<sup>2</sup> obviously does break as ''c'' changes speed, and thus cannot be true.--[[User:Aschlafly|Andy Schlafly]] ([[User talk:Aschlafly|talk]]) 21:13, 22 February 2016 (EST)
:::::In response to SamHB, it is not a scientific rebuttal to say that other equations might also break as ''c'' changes speed. Maybe other equations are flawed too, or maybe they aren't. E=mc<sup>2</sup> obviously does break as ''c'' changes speed, and thus cannot be true.--[[User:Aschlafly|Andy Schlafly]] ([[User talk:Aschlafly|talk]]) 21:13, 22 February 2016 (EST)
::::::Well, I guess you seem to be saying that equations of physics break when fundamental constants change. Would this include the de Broglie formula <math>p = E/c\,</math>? Or the equation of appearing in electromagnetism <math>c^2 = \epsilon\mu\,</math>? If the speed of light were to change, would existing de Broglie "matter waves" have their momentum change? Would the constant <math>\epsilon\,</math>, or <math>\mu\,</math>, change? For E=mc<sup>2</sup>, if the speed of light were to double, would the potential energy in an object quadruple? Or, alternatively, would the mass attributable to that energy be divided by 4? Or would the equation have to be replaced with E=mc<sup>2</sup>/4? If the latter, having E become mc<sup>2</sup>/4 instead of mc<sup>2</sup>, that would indeed be a failure of E=mc<sup>2</sup>. Is that what you are suggesting? That is, are you admitting that E=mc<sup>2</sup> now, but would have to change to something else, leaving E and m the same, for a change in c? [[User:SamHB|SamHB]] ([[User talk:SamHB|talk]]) 00:21, 23 February 2016 (EST)
::::::Well, I guess you seem to be saying that equations of physics break when fundamental constants change. Would this include the de Broglie formula <math>p = E/c\,</math>? Or the equation of appearing in electromagnetism <math>c^2 = \epsilon\mu\,</math>? If the speed of light were to change, would existing de Broglie "matter waves" have their momentum change? Would the constant <math>\epsilon\,</math>, or <math>\mu\,</math>, change? For E=mc<sup>2</sup>, if the speed of light were to double, would the potential energy in an object quadruple? Or, alternatively, would the mass attributable to that energy be divided by 4? Or would the equation have to be replaced with E=mc<sup>2</sup>/4? If the latter, having E become mc<sup>2</sup>/4 instead of mc<sup>2</sup>, that would indeed be a failure of E=mc<sup>2</sup>. Is that what you are suggesting? That is, are you admitting that E=mc<sup>2</sup> now, but would have to change to something else, leaving E and m the same, for a change in c? [[User:SamHB|SamHB]] ([[User talk:SamHB|talk]]) 00:21, 23 February 2016 (EST)
:::::::I apologize for the lack of lucidity in what I wrote just above; I was distracted by VargasMilan's [[anklebiter|nipping at my heels]].
:::::::I assume that you are allowing that, for example, the loss of mass due to potential energy in the alpha decay of Radium is .0052288 amu, that the combined kinetic energy of the alpha particle and the recoiling Radon atom is 4.870596 MeV, and that the ratio, once one wades through the amu->kilogram and MeV->Joule conversions, is 1.11<math>\times</math>10<sup>-17</sup> kilograms per Joule, or 9<math>\times</math>10<sup>16</sup> Joules per kilogram. And that similar results are obtained for other interactions. But that these results depend on the speed of light being the square root of that, or (recognizing the unit equivalence of 1 Joule being 1 kilogram meter-squared per second-squared) 3<math>\times</math>10<sup>8</sup> m/s. So you are saying the formula should be E=m<math>\times</math>9<math>\times</math>10<sup>16</sup> Joules of kinetic energy released per kilogram of mass lost. And that that formula, with its numeric ratio 9<math>\times</math>10<sup>16</sup>, is correct for all times and all places in the universe, and just happens to be the square of the speed of light in the current epoch but not at other times or other places.
:::::::That's an interesting idea. First let me say that there is no credible evidence that the speed of light has ever changed in the history of the universe. (I'm going to be editing the "c decay" page soon.) I don't remember the details, but I think I read some articles about speculation that the fine structure constant may have changed in cosmic time. As you know, the speed of light appears in the fine structure constant. Researchers have done calculations about how spectral lines of elements would shift if the fine structure constant changed, and about how the abundance of Uranium fission decay products would change. It is possible to separate out various aspects of spectral line shift from the uniform redshift of cosmic expansion. The characteristic differential spectral line shift was not observed, placing a tight small bound on possible changes in the speed of light since early cosmic time. Analysis of the fission product abundance in the Oklo "natural nuclear reactor" got inconclusive results for very tiny shifts. But "tight bounds" doesn't mean that any possible change is exactly zero.
:::::::There are other formulae that involve the speed of light, and involve photons, which we can directly receive from deep cosmic time. (We don't have access to any Radium atoms from 10 billion years ago.) A particularly noteworthy one is de Broglie's formula <math>p = E/c\,</math> or <math>E = pc\,</math>. This applies only to particles with (rest) mass of zero, that is, photons. There are compelling reasons (rooted in relativity) why this is so. So perhaps you are saying that the formula should actually be <math>E = 3\times10^8 p\,</math>, where the numeric constant is in meters per second. And that that ratio just happens to be the speed of light in the current epoch.
:::::::Unlike Radium atoms, these photons actually travel across the cosmos, so they would experience a change in the speed of light. There are a number of possibilities:
:::::::*The speed of a photon is the speed of light at the instant it was emitted. This would imply that, in the present epoch, there could be photons, from distant galaxies, traveling at different speeds. The fundamental principle that the speed of light is the same for all observers in all states of motion (the principle of the Michelson-Morley experiment) only applies to "home grown" photons, which are the only kinds we normally see. If the experiment were conducted with photons from distant galaxies it might get different results.
:::::::*Or maybe photons change speed as they travel through space.
:::::::*If the quantity in Broglie's formula is actually always the numeric value <math>E = 3\times10^8 p\,</math>, rather than the speed of light in the epoch in which it is being measured, Broglie's formula isn't correct except in the current epoch.
:::::::*But if the quantity in Broglie's formula is always the speed of light wherever the measurements are made, then photons change energy, or momentum, as they travel through space. This would violate the principles of conservation of energy or of momentum.
:::::::I really don't know which possibilities you have in mind. I admit that I haven't pondered these possibilities, and I'm not aware that anyone else has either.
:::::::[[User:SamHB|SamHB]] ([[User talk:SamHB|talk]]) 20:53, 24 February 2016 (EST)