Reduction of a Two Particle System to One (or Reductionism)

(or the problem with breaking physics into subfields QED, QCD 

from: https://chem.libretexts.org.../Quantum_Mechanical_H_Atom

$\mu$ is reduced mass

Reduction-ism and isolation are mainstream concepts, commonly applied principles, applied commonly as postulates in theoretical derivations (or should be applied/included).  As a matter of fact, the experimentalists often use the concept of reduced mass in much of their work and derivations when designing experiments to test theory:

$M=m_1+m_2$

$\mu={m_1m_2\over m_1+m_2}$

$x_{cm}={{m_1r_1+m_2r_2}\over{m_1+m_2}}$

$\mu<m_1$

$\mu<m_2$

$\mu={m_1m_2\over m_1+m_2}\approx m_1$ for $m_2\gg m_1$

$\mu={m_1m_2\over m_1+m_2}\approx m_2$ for $m_1\gg m_2$

${1\over\mu_i}=\sum_{i=1}^n{1\over x_i}={1\over x_1}+{1\over x_2}+\cdots+{1\over x_n}$    (eqn 1)*

$m^*={m_1m_2\over m_1+m_2}$

$err(i)=m^*-{1\over\mu_i}$

Q:How many terms does it take to make ${1\over\mu_i}=m^*$ (i.e., drive the error to zero)?

Let's deal with the proton - electron system, where:

$m_1=m_e$

$m_2=m_p$

$m_p\gg m_e$ $\therefore$ $m_2\gg m_1$ case, thus $m^*\approx m_1=m_e$

Note, again, $m^*<m_1$

$m_{ep}^*\equiv{m_em_p\over m_e+m_p}\approx m_e$

What is the error?

$err ={m_em_p\over m_e+m_p}-m_e$

$\;\;\;\;\,\,\,={-m_e^2\over m_e+m_p}$

$\therefore\;err<0$, i.e. the error is negative, thus, no matter how many terms are added to eqn 1, there will always be an error.  Adding any term actually increases the error.  This is the problem the mainstream has been engaging in repeatedly, over the last few decades - this is insanity!

A: No number of terms will make it fit, thus, this is why the proton radius cannot be determined by the mainstream scientists using their flawed approach.

So, QED, Quantum Electro Dynamics reduces the problem to electron-photon dynamics which work for most ordinary interactions, and QCD, Quantum Chromo Dynamic (LQCD??? or others attempting to address this issue???) basically is inside the proton, reductionism into quarks and gluons, etc, however, now matter how many terms they add, since the initial error is negative, they are adding more error and simply studying error terms and calling them particles.  And with high energies, they're studying transient disturbances in the vacuum.  Very funny and strange.

Talk about insanity.  The mainstreamers are Ghost Busting!

No matter how many terms, it will not fit, thus, convict. Quite opposite of if the glove does not fit, you must acquit.

There is likely formal and more detailed proofs of this concept, however, human dynamics and power struggles seem to make co-operation very challenging and expensive.

For future analysis (from a distant observer)

From a distance $R\gg r$, $r=R_1-R_2$ distance between the two particles:

(examine equations in the detailed form of a distance observer however, include near, intermediate, and far fields)

(could look at it using antenna engineering concepts)

An operator for reducing two particles to one and creation of error terms.

Charged him with committing a 9-11 @1:25
(famous Gomer & Barney Fife citizen's arrest scene makes mockery of integrity of the law and humans)

The Surfer, OM-IV 

Ω