I absolutely can't wrap my mind around this
That much is obvious
the acceleration is linked to charge which is linked to potential energy which is linked to bremsstrahlung and the reaction force. The only variables is really mass and distance, but distance doesn't matter so much. Changing the mass will alter acceleration thus bremsstrahlung and the reaction force but it won't alter potential energy or charge.
If you knew how to quantify those things using mathematics it'd be a lot clearer. Previously you've made the argument you can do conceptual things and let others worry about the quantitative stuff but this is a demonstration of how that attitude
fails. I suggest you learn from this.
This case itself is not special, its a perfectly ordinary scenario.
You said you were considering the case where they move very slowly, as this minimises the accelerations and thus means the amount of energy emitted by the 2q charge is approximately 4 times that of the 1q charge but, as I've explained, this
isn't the exact result. In this non-relativistic limit you're able to say "The 4:1 ratio is close to true" but for relativistic setups, where you allow the particles to undergo a lengthy amount of acceleration then you'll find that the ratio drops to
less than 4:1 as the braking radiation on the 2q charge means it doesn't accelerate as quickly as it would do without the braking radiation and thus over the time until collision the 2q charge will emit
less than 4 times the 1q charge.
And to be honest, I can't be sure that the standard bremsstrahlung equation is even relevant in contemporary QED so I definitely don't inted to say the full model is wrong :shrug:
Please explain how you are in a position to say what is or isn't relevant to contemporary quantum electrodynamics when you don't understand its quantitative structure, you don't understand its qualitative structure, you don't know what relevance these phenomena have to experiments like particle colliders and you don't know any of the courses a student would need to have done to even get onto a quantum field theory course.
You are in a position of
total ignorance when it comes to any mainstream physics,
especially high level stuff like quantum field theory, so please tell me why you think your comments are in any way substantiated.
You are right, this interdependency is non-trivial - even with minimal acceleration, something which I have not recognized before. It cant be accounted for using the simple equation I have given.
And the reason you didn't recognise it before is because you never looked. You didn't bother to try to find out what the model actually is, you didn't bother to find out about any experiments, you didn't bother to try to understand it at all, you simply plucked a few equations which you didn't understand the origins of (and thus didn't realise you can't apply them blindly to all situations) from Wikipedia.
Wouldn't you agree however that the reaction force will be 4 times greater for 2q than for q ?
For a given acceleration.
To give an example consider the following thought experiment :
Consider a rollercoaster. The cars on them move along a preset path with a preset velocity. If you gave a rollercoaster car a charge Q and then let it go around the track it'd emit some amount of energy (assume this doesn't alter its velocity, the car goes a preset speed regardless), E(Q). Suppose now you do the same thing and you give the car a charge of 2Q. It will emit E(2Q) = 4E(Q). Twice the charge, 4 times the energy emission.
That is what you're talking about.
But that isn't how the particles in your example behave, when they emit braking energy they will experience a force which acts against them and thus their overall acceleration will be
lower. Each particle has the same mass so for a given force they'll accelerate the same amount. But they don't experience the same forces, the 2q charge will experience more braking and thus will experience a smaller acceleration. The energy output of 2q will be 4 times that of 1q
provided their motions are identical but they won't be, the extra braking slows the 2q charge somewhat and it'll emit less energy overall thus it'll emit
less than 4 times what the 1q charge does.
I've explained this several times now. Yes, the formula for the energy emission is quadratic in the charge but it also depends on the motion of the particle. The motion of the 2q charge is affected more and it moves slower and thus does not emit as much as it otherwise would if it moves as faster as the 1q charge.
Again, this would be simple for you to grasp if you could do what is basically high school physics. Once again your lack of mathematical ability/knowledge retards the development of your physics understanding.
Right, but if this domain includes the entirety of possible solutions then you can be certain that something is awry. But also there is canonical momentum and I don't even know what else ... I will have to put in some effort to find out.
You explicitly said its only valid for very low speeds, so by your own admission it doesn't apply exactly. And please don't pretend you know about canonical momentum, you can't even understand a Taylor expansion. You're just throwing out buzzwords to try to make it seem like you're well read and putting in effort but its obvious you aren't. When you admit you can't do high school calculus going on to name drop things which aren't encountered until degree level or beyond only further adds weight to the view you're an ignorant hack who isn't above lying.
A very conservative approximation is that the kinetic energy of the object will be between 1-3 x and the emitted radiation will be 5 x . In this domain you will still have difficulty conserving momentum if you only consider photons and kinetic energy.
Well done on getting what I said completely wrong. The emitted energy is
less, not more. And you don't 'still' have momentum issues, in electromagnetism, quantum electrodynamics and relativity its conserved at all velocities and configurations. No amount of you stumbling around in the dark butchering equations you don't understand in the hopes they'll say what you want them to say will negate the
fact QED, EM and everything else in physics at present have consistent momentum conservation and have had this tested in experiments to the limits of our ability. No model violated momentum conservation in any configuration, no experiment has ever violated it either.
I really can't understand why you're continuing with this. Time after time its demonstrated you haven't got a clue, you don't know the models, you misrepresent mainstream work (which you haven't read), you have no understanding of the scientific method, you argue against
reality and when you try to come off as if you understand it but there's just a crossed wire in communication you demonstrate clearly that you
don't understand it. Dropping buzzwords only serves to make your ignorance manifest.