INTRO

This system is nothing more than dimensional analysis: Distance, Mass, Time and Charge, into which hard data can be substituted for real results. For example, for M substitute the mass of an electron or an elephant and see the result.

Given that it is just dimensional analysis it is very, very hard to go wrong.

BASIS OF ARGUMENT

Where D (metres) is the reduced Compton wavelength of mass M (kg) then Planck's constant h = 2piDMc. The symbol D denotes displacement or distance. ±2pi denotes intrinsic angular momentum.

DM = h/2pic and because h, 2pi and c are all absolute constants then DM (m kg) is also an absolute constant. Nothing more than dimensional analysis.

DM is just as constant as c and it places significant physical constraints on the universe just like the speed of light does.

MOTION, MATTERWAVES

In Planck units DM = 1 for anything with a Compton wavelength, e.g. protons, neutrons and electrons. Thus D1M1 = D2M2 resulting in every action having an equal and opposite reaction per unit of time. In every matter interaction, time is variable while DM remains constant.

A matterwave, one particle displaced one wavelength in accordance wave/particle duality, is 2piDM = h/c. The matterwave constant is also absolute. Compton-scale matterwaves are 137 times smaller than putative, intra-atomic de Broglie standing waves.

Where Q is Coulomb charge, the Fine Structure Constant, 1/137 = alpha = Q^2/DM. (Ref Note 1).

ENERGY, INERTIA

Mach and Einstein were wrong: inertia is "relativistic mass" and a photon of light is inertia in transit.

1. With special relativity, where the only input is kinetic energy, mass cannot reach c due to the build up of inertia. Kinetic energy and inertia are therefore the same.

2. E = Mc^2 and in every experiment to date mass and inertia have been proven to be equivalent. Therefore inertia is equivalent to energy.

3. Mass does not spontaneously accelerate: it must first gain more inertia which it does by absorbing energy.

4. The inertia of a mass that is accelerating due to gravity does not change because it is not absorbing kinetic energy. (Ref Note 2.)

5. DM = 1 in Planck units. Therefore M = 1/D = the inverse of displacement = inertia. The particle is the wave. The inertia of the particle is the inverse of the particle's wavelength which means inertia can be considered an ordinary wavenumber.

6. DM = (delta D)(delta M). As mass goes faster its wavelength shrinks inversely. The wavelength of transmitted light is the relativistic version of lambda = hc/E = (delta 2piD).

The wavelength of light encodes the relativistic change in matterwave-length of a particle which is also the change in its inertia. The wavelength of light transmits inertia.

7. Photons with a wavelength of (delta 2piD) transmit energy and momentum but not mass. Waves have momentum because they transmit 1/D inertia, not mass.

Time T for particles is T = D/v (i.e. displacement/velocity).

Momentum, Mv = v/D = 1/T, is the frequency of the matterwave. The relativistic version adds inertia to momentum which changes the matterwave-length but not its rest mass: the Lorentz transformation shows this clearly. At any velocity inertia is relativistically variable while mass remains in a rest state.

The wavelength D of a matterwave at any given time is due to 1/D inertia, not mass M.

Despite being counterintuitive, energy is transmission of inertia.

The fact that light is a product of 2piD proves that Compton-scale matterwaves both exist and are the norm.

EXAMPLE USING THIS SYSTEM

To enumerate Bohr's hydrogen: Q^2/nDM = v/c = alpha/n = nD/r.

In Bohr's hydrogen angular momentum rMv is:

rMv = nh/2pi = nDMc

Time is measured differently for mass and inertia:

- time T for particles is T = D/v (displacement/velocity)

and from rMv above, where r is a geodesic distance

- time t for photons is t = r/c = nD/v (displacement/velocity).

So in hydrogen t/T = n. That is, (time for inertia) / (time for mass) is quantum. (Ref Note 3.)

2pir/c = n2piD/v so a photon orbits the nucleus once at radius r in the time it takes a particle to travel n matterwave-lengths at velocity v at the same radius.

An electron near a proton is accelerated by Coulomb force and will radiate energy. As the electron emits a photon it drops towards the proton and when it reabsorbs the photon it jumps back up a higher energy level.

In other words the electron oscillates like a wave, vertically relative to the proton, while displacing D tangentially to form a matterwave each time it absorbs and re-emits its own 1/D inertia.

Mass M emits 1/D, displaces D, reabsorbs 1/D. Repeat ad infinitum.

In hydrogen, a particle travels just n matterwave-lengths between photon interactions. Therefore electrons would not have enough time, by orders of magnitude, to orbit a proton between photonic interactions that would alter both their energy level and course. Due to the presence of other charges each particle would be electromagnetically confined within limited regions of each atomic shell, e.g. a 2p lobe.

Photons orbit the nucleus of an atom, particles don't. The Schrödinger wave equation maps photons, aka inertia, not matter. As light is a product of 2piD matterwaves and not of 2pir standing waves, the entire concept of de Broglie standing waves is superfluous.

Notes:

1. Q^2 = (q^2 10e-7) (kg m)

2. Dark matter is chargeless mass without inertia so it can be gravitationally accelerated to exceed the speed of light. Inertia is limited to c while mass isn't.

There appears to be no law preventing instantaneous transfer of angular momentum states between entangled particles if there is no inertia involved.

3. For reference the "quantum of time", the chronon, is theta = 2D/3c (seconds). Since D is dependent on 1/D inertia, chronons would not be quantum.

So what's the point to be discussed?

You talk about photons in terms of "inertia in transit" which does not single out photons in any way. All energy moving from A to B would be inertia in transit.

You also say that dark matter is without inertia, which is sure to be doomed as a useful physical concept. Not that anybody has tried to accelerate a galactic halo, though. Anything containing energy must possess inertia.

Dimensional analysis only gives you a zeroth-order approach to physics. It weeds out lots of possible silly mistakes and allows you to qualitatively predict the parametrics of physical problems. But trying to guess the whole of physics from dimensional analysis is akin to figure out global economics by counting beads.

19 hours ago, joigus said:

So what's the point to be discussed?

It's necessary to define 1/D inertia and show its relationship to wavelength D to then demonstrate how beautifully simple an atom really works:

Mass M emits 1/D inertia : displaces wavelength D : reabsorbs 1/D. Repeat ad infinitum.

This then shows how Mach and Einstein, De Broglie and Schrödinger were wrong.

It's not good that they continue to teach kids stuff that's incorrect. It's also wrong for you to disparage something without reading it or understanding it. I believe that you should not to be part of the problem but should strive to be part of the solution.

4 hours ago, Mosian said:

It's necessary to define 1/D inertia and show its relationship to wavelength D to then demonstrate how beautifully simple an atom really works:

Mass M emits 1/D inertia : displaces wavelength D : reabsorbs 1/D. Repeat ad infinitum.

This then shows how Mach and Einstein, De Broglie and Schrödinger were wrong.

It's not good that they continue to teach kids stuff that's incorrect. It's also wrong for you to disparage something without reading it or understanding it. I believe that you should not to be part of the problem but should strive to be part of the solution.

How can I be part of a problem? What problem? What is it that's wrong with physics that you set out to put right? OTOH, this doesn't look like a discussion on classical physics. It seems more like a speculation to me.

And you didn't address any of my criticism. It's not about 'disparaging' anything. It's about stating clearly what it is that you're addressing. And then addressing any possible criticism.

6 hours ago, Mosian said:

This then shows how Mach and Einstein, De Broglie and Schrödinger were wrong.

You can only show them to be wrong by having their models not match experiment. Does that happen?

On 5/3/2025 at 5:46 AM, Mosian said:

Given that it is just dimensional analysis it is very, very hard to go wrong.

Kinetic energy in a Newtonian system. Lorentz factor in relativity. Law of Malus. Energy-momentum equation in relativity. Image location in optics.

Please derive these using only dimensional analysis.