First, Guest. This should finally give you your answer. All that time you thought when I said I can explain my actions, but never did, you must have thought I was lying. Well below is a pet theoretical work I have been doing. When I asked that algebraic question you punnelled me for so many times, was because when I expressed the equations for the field density below, I just wanted to make it as proper as possible - the way Maxwell would have written it. Trivial to you maybe, but not to me.
First deriving the property of our electric field $$\mathbb{E}$$ takes the form of:
$$\mu_0 D= c^2 \mathbb{E}$$
Rearranging gives:
$$\frac{\mu_0 D}{c^2}= \mathbb{E}$$
Squaring both sides, and then multiplying by the permitivvity gives:
$$\epsilon_0 (\frac{\mu_0 D}{c^2})^2= \epsilon \mathbb{E}^2$$
We will now employ our rules, having a conservative electric field irrespective of any external magnetic changes. Now I consider the equation:
$$\mathbb{E}^2(qt^2)^2 \int v dt= I^2$$
Again we take a similar route and do the following:
$$\epsilon_0 \mathbb{E}^2(qt^2)^2 \int v dt= \epsilon_0 I^2$$ [*]
If we take one half of the quantity $$\epsilon_0 I^2$$ where $$I$$ is the inertial moment, gives us on the right hand side a relation to the field density (hence Guests insideous attempts to make me reveal why I asked certain questions),
$$I \sqrt{\epsilon_0} = u_eqt^2 \frac{1}{2}\int v dt$$
where the left hand side has been simplified to give one whole value of the inertial moment. This equation as I interpret it, describes the electric field strength as being inversely related to the inertial moment of the particle, and so this would be related to a certain type of electromagnetic inertia.
The equation with the star [*] is like most of the equations, describing a charge in an electric field in a state of motion.
The electric field is something which describes spacetime surrounding electrically-charged particles or even a time-varying magnetic field. However, the above is seen in light of a conservative electric field with no magnetic field present. Thus the electric field in this case can be seen as exerting a force on particles.
If a field can exert a force on a particle, why may it not give rise to a force associated similar to that of an inertial force?
The force resisting acceleration could very well be related to the field densities acting as a type of electromagnetic inertia.
Einstein never ruled out completely the cause of inertia, but in a series of work, he did show it was possible that the inertial energy of a system could cause inertia, which is slightly different to the above, but shares a fascet in which (and I can thank CPT bork for this) that the field density can be verbally replaced but not mathematically equivalent to an energy desnity itself, since the electric field is not a field which has the dimensions of energy.
The conservative field equations I have been using, are themselves a type of equation of motion, where the integral must govern a change in position, with a velocity which by choice of the observer, can change. It's linear however, but this can still invoke a more complicated set of dervations I would have presumed which we could allow a system to experience a varying magnetic field.
Einstein, as I said, involved the genious idea that perhaps the rest energy of a material system is what causes the inertia of matter, but in a sense, energy and matter are but fascets themselves of the same manifestation under Einsteins mass-energy relationship - but, with a little thought, I question the methodologies of using energy to explain inertia alone. Afterall, saying energy is responsible for inertia in a material system is just trivial as saying matter is what causes the inertia of trapped energy - neither really are enlightening to the cause of inertia itself, other than something pointing to the inherent structure of the particle (intrinsic structures).
In response to Einsteins idea, it was then a consideration to see if we could see the above equations, in a slightly different light, this time concerning energy.
I came to the equation:
$$\epsilon_0 \frac{(\frac{\mu_0 D}{c^2})q^2t^4}{t^2} \delta \int v dt= \epsilon_0 E_0 \ell$$
where $$E_0$$ is for inertial energy and $$\ell$$ is basically a distance travelled, with obviously dimensions of L. Here I have used a minilizing integral on the change of position, which in the sense is meant to indicate it takes the least energy required to move that distance. This means that it satisfies a ground state of energy, so I am assuming this eq. can be altered to the following form;
$$\epsilon_0 \frac{(\frac{\mu_0 D}{c^2})q^2t^4}{t^2} \delta \int v dt= \epsilon_0 (\hbar \omega) \ell$$
Where $$\hbar \omega$$ is the lowest frequency, or ground state of energy per unit volume of spacetime.
I then considered a rest inertia, and I decided it catagorically and fundamentally cannot exist for particles subjected to UP. Because of the UP, particles are never at complete rest, if they where, their locations would be predictable, and that is completely forbidden with total accuracy. So if rest inertia was to simply be related to mass as $$I_0=M_0$$, this could only apply to macroscopic bodies.
I'm am still trying to reconcile how to unify the energy in concordance with an understanding of my hypothesis concerning electromagnetic inertia.
I am going to ask if anyone can help me if I have made any mistakes. As I have said, many times, my knowledge on calculus is mediocre to the scientists here. So a little help would be appreciated. Thank you in advance.
First deriving the property of our electric field $$\mathbb{E}$$ takes the form of:
$$\mu_0 D= c^2 \mathbb{E}$$
Rearranging gives:
$$\frac{\mu_0 D}{c^2}= \mathbb{E}$$
Squaring both sides, and then multiplying by the permitivvity gives:
$$\epsilon_0 (\frac{\mu_0 D}{c^2})^2= \epsilon \mathbb{E}^2$$
We will now employ our rules, having a conservative electric field irrespective of any external magnetic changes. Now I consider the equation:
$$\mathbb{E}^2(qt^2)^2 \int v dt= I^2$$
Again we take a similar route and do the following:
$$\epsilon_0 \mathbb{E}^2(qt^2)^2 \int v dt= \epsilon_0 I^2$$ [*]
If we take one half of the quantity $$\epsilon_0 I^2$$ where $$I$$ is the inertial moment, gives us on the right hand side a relation to the field density (hence Guests insideous attempts to make me reveal why I asked certain questions),
$$I \sqrt{\epsilon_0} = u_eqt^2 \frac{1}{2}\int v dt$$
where the left hand side has been simplified to give one whole value of the inertial moment. This equation as I interpret it, describes the electric field strength as being inversely related to the inertial moment of the particle, and so this would be related to a certain type of electromagnetic inertia.
The equation with the star [*] is like most of the equations, describing a charge in an electric field in a state of motion.
The electric field is something which describes spacetime surrounding electrically-charged particles or even a time-varying magnetic field. However, the above is seen in light of a conservative electric field with no magnetic field present. Thus the electric field in this case can be seen as exerting a force on particles.
If a field can exert a force on a particle, why may it not give rise to a force associated similar to that of an inertial force?
The force resisting acceleration could very well be related to the field densities acting as a type of electromagnetic inertia.
Einstein never ruled out completely the cause of inertia, but in a series of work, he did show it was possible that the inertial energy of a system could cause inertia, which is slightly different to the above, but shares a fascet in which (and I can thank CPT bork for this) that the field density can be verbally replaced but not mathematically equivalent to an energy desnity itself, since the electric field is not a field which has the dimensions of energy.
The conservative field equations I have been using, are themselves a type of equation of motion, where the integral must govern a change in position, with a velocity which by choice of the observer, can change. It's linear however, but this can still invoke a more complicated set of dervations I would have presumed which we could allow a system to experience a varying magnetic field.
Einstein, as I said, involved the genious idea that perhaps the rest energy of a material system is what causes the inertia of matter, but in a sense, energy and matter are but fascets themselves of the same manifestation under Einsteins mass-energy relationship - but, with a little thought, I question the methodologies of using energy to explain inertia alone. Afterall, saying energy is responsible for inertia in a material system is just trivial as saying matter is what causes the inertia of trapped energy - neither really are enlightening to the cause of inertia itself, other than something pointing to the inherent structure of the particle (intrinsic structures).
In response to Einsteins idea, it was then a consideration to see if we could see the above equations, in a slightly different light, this time concerning energy.
I came to the equation:
$$\epsilon_0 \frac{(\frac{\mu_0 D}{c^2})q^2t^4}{t^2} \delta \int v dt= \epsilon_0 E_0 \ell$$
where $$E_0$$ is for inertial energy and $$\ell$$ is basically a distance travelled, with obviously dimensions of L. Here I have used a minilizing integral on the change of position, which in the sense is meant to indicate it takes the least energy required to move that distance. This means that it satisfies a ground state of energy, so I am assuming this eq. can be altered to the following form;
$$\epsilon_0 \frac{(\frac{\mu_0 D}{c^2})q^2t^4}{t^2} \delta \int v dt= \epsilon_0 (\hbar \omega) \ell$$
Where $$\hbar \omega$$ is the lowest frequency, or ground state of energy per unit volume of spacetime.
I then considered a rest inertia, and I decided it catagorically and fundamentally cannot exist for particles subjected to UP. Because of the UP, particles are never at complete rest, if they where, their locations would be predictable, and that is completely forbidden with total accuracy. So if rest inertia was to simply be related to mass as $$I_0=M_0$$, this could only apply to macroscopic bodies.
I'm am still trying to reconcile how to unify the energy in concordance with an understanding of my hypothesis concerning electromagnetic inertia.
I am going to ask if anyone can help me if I have made any mistakes. As I have said, many times, my knowledge on calculus is mediocre to the scientists here. So a little help would be appreciated. Thank you in advance.