You keep chopping and changing formulae. One bit valid for photons only, another bit valid for electrons, and you don’t seems to see that you can’t do this.
p= E/c is only valid for photons. It becomes asymptotically more accurate as a massive particle approaches c, but it is never exact.
Back to the start. p is momentum. p * v = Energy. As v => c nothing changes. It is just that this term in the total equation for energy starts to dominate over the m[sub]0[/sub]c[sup]2[/sup] term. But you can’t claim that momentum is energy. Momentum times velocity is energy. In both classical or relativistic physics.
Right at the start you claimed that the p term in the full equation represented potential energy, then changed to kinetic energy. Basically saying that the term pc (momentum times c) was energy times c. Which is meaningless. Everything since seems to be an attempt to continue to ignore the fact that the p term is multiplied by velocity whenever energy is being calculated, whether that velocity is relativistic, c, or something small, doesn’t matter.
“Moving the goal posts” is what you have done for this entire derailment, starting from your assertion that “p” is a measure of energy rather than momentum. My cite is every university level basic physics text published in the last seventy years, and can you please stop sidelining the discussion about how nuclear fusion produces energy by arguing fundamental terminology with at least two posters with advanced degrees in physics?
rat_avatar, the discussion went astray fairly early when you stated that “p” in the dispersion relation was “potential” and, when this error was pointed out, you didn’t reply with, “Ah, of course. My mistake.” Rather, it looks like you were (are still?) defending that statement, if indirectly. Are you? If so, note that none of your cites every call this “p” “potential”. It’s always the momentum. You won’t ever find a cite that says this “p” is “potential”.
I actually can’t quite tell what you are trying to demonstrate. You say, for instance:
Can you point to where someone said p was not related to E? I see explicitly the opposite, e.g.,
Do you agree that two related things can be fundamentally different, despite their inter-relation?
Several of your expressions are also incorrect, either due to typos or to misunderstandings. This one:
has been addressed. In particular, p=E/c only holds in the special case of m=0, and thus not for electrons. Here’s a cite. Or this one.
Similarly, this expression:
is not what your cite shows. The “m” on the left should not be the same as the “m” on the right. They are not the same quantity. Note the very important subscript “0” on one of those quantities in your cite. (Incidentally, the unadorned “m” on that page – the “relativistic mass” – has been discarded in the modern era as an unhelpful quantity to bother talking about. It adds no value for the math, and it adds confusion in the language.)
These missteps make it hard to follow what you are trying to say. So, what are you trying to say?
You are cherry picking the Planck–Einstein relation, while ignoring the implications of the de Broglie hypothesis and the de Broglie relations
As stated above I abandoned attempts to get those to display in this message board due to limitations of this board.
And as stated above,
The relativistic energy expression is **the **tool used to calculate binding energies of nuclei and the energy yields of nuclear fission and fusion.
Anyway, I was going to try to set up the math to describe the OP’s question, but as I have caused thread drift just by trying to even explain the concept that there are really no massless particles in classical mechanics, and that classical concepts of momentum and KE don’t work when trying to describe yields, I will admit defeat and not even attempt to approach the nice implications of E = mc^2 in relation to fusion.
But to describe fusion , using the relativistic energy of a particle, expressed in terms of its momentum is pretty important.
I am sorry I failed to describe the implications or importance of that concept.
Sure, quoting an equation that uses nu. But I was quoting equations with velocity in them, and they use a vee. You explicitly referenced the equations I posted. They are not equations in frequency. None of your quoted derivations in any posting use frequency. They are all in velocity. In all of them v is velocity.
If you think it is frequency you are utterly lost.
Which two sets? This is the first mention of sets in the thread.
I haven’t seen anyone dispute that. Can you point to anywhere that anyone has disputed that?
Where? Be more specific. Use the quote feature (something the board does have) to point out my incorrect statement(s). You keep asserting that people are saying false things but not quoting the presumed false statements. Since there aren’t actually any false statements, it’s hard to guess which statements you think are false unless you tell us explicitly.
Do you mean Newtonian? Classical mechanics is fine with massless particles. Non-classical means quantum, not relativistic. (Just making sure we’re using the same terms.)
Can you explain where this trivial statement is so critical to your point? The sentence you quoted simply says, “momentum times the constant c is proportional to momentum”, but that’s tautological. All that sentence is offering is that using the constant c alongside momentum all the time makes the units work out nicely. As above, I haven’t seen anyone dispute that. Have you?
In this post and my last one, I’ve given three examples where you have made strong statements of correction when in fact no one has ever disagreed with the point you say they have. Can you pick any of those three and say where you see someone disagreeing with it? Otherwise I continue not to know what you’re trying to point out.
Multiple physicists have repeatedly demonstrated the errors in your assertions. At this point, you appear to be just trolling for reactions rather than even making a substantive argument.
Of course, and when we set those to “1”, we don’t need to include those constants in the equations, just as you have done. But the equations we were discussing contained the constant “c” explicitly, so one assumes it is not set to “1”.
rat avatar: Why are you asking for a cite that momentum is not energy? Do you want a cite that velocity is not mass? How about a cite that acceleration isn’t distance? These things are defined in physics, and momentum and energy are defined as two different things. No one makes lists of all the things that are not each other.
Even if it has the value 1 - which it often does, it still has units and dimension. They don’t go away no matter what the value. If they did, the equation would be nonsense. You get the right numeric value, but you can’t reason about or manipulate things without the metadata. You just have to trust that the units you get are the right ones. Which is often fine, if you are only working out values.