Three Conditions Leading to a Unified (Quasi-Newtonian) Physics

It is shown that the total escape speed u (i.e. from all the masses in space), which depends on the total gravitational potential U through the relation u = (−2U), tends to c; then, under the 1 condition c = u, and assuming (as a 2 condition) the light as composed of longitudinally-extended, elastic (i.e. variable length) and massive particles, (photons), emitted at speed u referred to the initial location (O) of their source, we show that c referred to O becomes invariant despite any motion of its source from O. We revised the Doppler effect for the light, the gravitational redshift cause, the time dilation, highlighting the differences with respect to the Relativity. In the 2 part, considering (3 condition) the electron charge as a point-particle fixed to the electron surface and facing the atom nucleus during the electron orbit, the light-matter interaction becomes a consequence of the particular impacts between these photons and the circling electrons: e.g., on H atom, we found 137 circular orbits only, the last one being the ionization orbit, where the electron orbital speed becomes vi = c/137. [Classical physics, under the assumption that a circling electron should produce (like a macroscopic electric circuit), an electro-magnetic radiation, implies that this claimed effect has to cause the electron fall into its nucleus: on Section 2.5, we show that the e.m. radiation of a circling electron only happens between two circular orbits].

its initial location O (where the photons emission starts), is invariant with respect to O; 2) Doppler effect equations for the light, slightly different from the relativistic ones; 3) The compensating velocity, (to restore the resonance source-absorber on Harvard Tower Experiment), has same value but contrary direction with respect to the one predicted by GR; 4) The variation of U from ground to GPS satellite level, implying a decrease of c and consequently a decrease of the frequency of the photons emitted by atomic clocks at that altitude, give them an increase of their counted time (inducing them to run faster); 5) High gravitational redshifts are due to the increase of c (inducing the increase of the photons length λ) during their path toward the Earth where |U o | >> |U →∞ |.
On the 2 nd part, under the third condition claiming that the electron charge can be considered as a point-particle fixed to the electron surface, and facing the atom nucleus during the electron orbit, we got these results: On H atom: 6) n = 1, 2, •••, 137 electron circular progressive orbits, not an infinite number; n also represents the number of admitted photons (of the same ray) absorbed (or 9) The electron radial speed (due to the impacts photons-electron) becomes 2 n w = c/137 2 constant for every circular orbit; along the orbit #137, the electron orbital speed becomes which is a scalar, (called escape speed), representing the value of the velocity u, (referred to M), a massive particle needs to reach the infinity; hence the relation represents the condition, as for a point-particle m, to be provided with the absolute escape velocity u (absolute means here referred to M) whereas considering a generic point O, represents the condition, regarding m, to be provided with the relative escape velocity u O , where relative means here referred to a generic point O; (anyhow, our claimed variable length of photons, during their emission from a source S gives them an invariant speed referred to any considered point O, in spite of any velocity v OS ).
Regarding the possibility to define the escape speed from two or more masses, we point out that considering M as a real mass, the potential U, in a considered point, has to be regarded as the sum of the partial potentials U n due to each partial mass M n composing the mass M; therefore, as for two masses, we have ( ) ( )  (6) representing the total escape speed.
For instance, the escape speed from the Earth surface, due to Earth and Sun only, becomes ( ) ( ) Journal of Modern Physics dius, and d the distance Earth-Sun giving u E,S ≅ 42 km/s, while the escape speed from our Galaxy can be roughly expressed as u g ≃ (2M g G/d g ) ½ where M g ≃ 10 42 kg is our Galaxy mass and d g ≃ 30 kly ≃ 3 × 10 20 m the distance between the Earth and our Galaxy centre, giving u g ≃ 8 × 10 5 m•s −1 . Now, the mass of universe, by some authors, is estimated [1] [2] [3] to be M u ≅ 10 53 kg; about the same value is given through the number ( ≅ 10 22 ) of observable stars [4] [5] [6], and since from Earth the distribution of the masses appears to be homogeneous and isotropic, under our assumption U ∞ = 0, we may assume their density as decreasing toward the infinity like a function ρ = ρ c e −as being ρ c ≅ 9.2 × 10 −27 kg/m 3 the critical density.
Writing the mass of universe as and since, on Earth, the variation of potential due to an increase of the distance ds, can be written dU = −dm G/s with dm = ρ4πs 2 ds and ρ = ρ c e −as , the potential on Earth becomes ( ) .
We can therefore infer that, on Earth, u 0 = c 0 , giving The equality c = u, which implies the massiveness of light, means that, along any free path, the speed of light only depends on the value of the potential along that path.
The equality c = u is also supported by a cosmological reason: in fact, if c > u the energy of light will be lost forever and furthermore the observable masses, following the always increasing mass of light going toward the infinity, will also tend to the infinity moving away from each other. On the contrary, if c < u, all the masses in space, (having speed lower than u), will tend to a gravitational collapse, whereas for c = u, the mass of light, tending to the infinity in an unlimited time, appears to be the necessary mass to avoid the two events (collapse or dispersion).

Annual Variation, on Earth, of the Total Escape Speed
On Earth, a small variation of the total escape speed u o , from Equation (11) written as u 2 = −2U yielding 2u = −2dU/du, can be written as  (12) where ΔU is the variation of the total potential on Earth, mainly due to the variable distance Earth-Sun; so, between Aphelion and Perihelion, where a = (1 + e)d and p = (1 − e)d are the respective distances Earth-Sun, with e (=0.0167) the eccentricity of the Earth's orbit and d ≅ 1.5 × 10 11 m the average distance Earth-Sun, and since pa ≅ d 2 , and (a -p) = 2ed, we get with M S = 2 × 10 30 kg the mass of the Sun, and we note that Δu AP is compatible with the accuracy of the value of the speed of light in vacuum (on Earth) c 0 = 299,792,458 m•s −1 .

Definition of Photons and Their Speed
The Galileo's velocity composition law (since different parts of a moving object may have different velocity) is strictly valid for point-particles, and therefore the light cannot be a succession of point-particles (otherwise it should follow this Galileo's law), hence we may infer that the light, to comply both this law and the equality c = u, could be composed of particular particles, photons, (whose physical characteristics are then shown on §2.2), as defined: Longitudinally-extended, elastic (variable length) and massive particles emitted by a source during an emission time T at speed c = u moving individually or along rays, (continuous succession of photons where every tail corresponds to the front of the next one). Photons speed: the measurement of the speed of a point-particle (or regarding an object, its barycentre), is defined through the ratio v = d/t with d the distance between two Observers (O 1 and O 2 ) and t (=t 2 -t 1 ) the time the particle/barycentre needs to cover such a distance; on the contrary, every photon may have different length with respect to two Observers, (like, for instance, an elastic thread during its stretching), hence to define the speed of one photon, we must consider its length λ divided its transit time T t (time the whole particle needs to cross one Observer). Therefore the relation represents the speed of one photon referred to a considered Observer, whereas the relation c = d/t, written as t t c d t n nT T where n is the number of photons (of one ray) each of them having length λ, and where t = nT t is the transit time of the n photons, represents the average speed of the light along d.
with the sign + if photon and source have opposite direction; then showing that the speed of a photon referred to an Observer fixed to the source initial location, (O), is invariant despite any motion of the source with respect to O.
The frequency of the light referred to a generic Observer O, on our bases, has to be defined as ν = n/T t with n the number of photons, of the same ray, crossing the Observer during their transit time T t . Hence, for T t = 1 s, we have ν = n meaning that the frequency corresponds to the number of photons, same ray, transiting in 1 s, while, for n = 1, the frequency becomes We point out that the photons frequency emitted by a source S, under the condition υ OS = 0, has to be equal to the one observed by O; this is also valid if O and S belong to different potential, (e.g., the equality of the number of balls falling from the top of a tower with respect to an Observer at the tower base), and therefore the condition υ OS = 0 always implies ν S = ν O whatever is the distance source-observer.
[We also point out that, according to the Relativity, (due to the claimed constancy of c and because of the Doppler effect), an Observer in relative motion from a source should observe different wavelength as well as different frequency for emitted light; on the contrary, on our results, if the source is fixed to its initial location (the ground on Earth), the length of the emitted photons is invariant, while c and ν are varying, as hereafter shown].
Referring now to Figure 2, let P be an observer (represented at different times, by P A and P B ) moving with velocity v OP from O along the same direction of the photons while the source S is moving from O with velocity v OS contrary to them; we assume the photon AB totally emitted at the time the front A reaches P A (for simplicity as t = 0). [In fact, after this emssion, the source may even disappear]. Now, the transit time T P of the photon AB is given, see Equation (18) Figure 2. The Observer P moves from P A to P B during the transit time T P of the photon AB while the source is moving from its initial emission location O.
[In short, the motion of S (from O) causes a variation of the photon length, while the relative motion observer-source varies the observer transit time and its related frequency].
On next Figure 3, we analyse the parameters c, λ, ν of five configurations regarding a source S, the considered frame O (practically the Earth's surface) and an Observer P.

Doppler Effect for the Light, New Equations
The Equation (17) represents our longitudinal Doppler effect for the light, while the general case of this effect, assuming υ OS << λ (hence OP ≅ PB), see Figure   4(a), can be written as with α the angle between the direction of λ O and v OS . As for the Transverse Doppler effect, see Figure 4(b), in general, we have ( ) As for a source circling around an Observer P, the Figure 5 shows that the length of the photon λ emitted when its source is fixed to O, becomes λ O when S is circling with velocity v OS .  [The succession of the photons λ represents a ray if S is at rest with P, while the succession λ 1 → λ 3 represents a ray if S is circling around P, with O, B, C the emission points of the circling source]. Then, assuming λ O > λ, we have ( ) while the photon transit time, being T the emission time of λ becomes with r the orbit radius, ω the source angular speed, giving to any photon, speed c O = c.

Re-Visitation of the Harvard Tower Experiment (HTE), Time Dilation, Gravitational Redshift
General Relativity predicts that the gravitational field of the Earth will cause a photon emitted downwards (towards the Earth) to be blueshifted: scope of HTE experiment was to detect this shift of light. A Mossbauer source S was placed on the top of a tower (height h ≅ 22 m) emitting photons toward the tower base where an Absorber went out of resonance; the experiment did not clarify if the non-resonance was due to a variation of λ or ν; indeed, because of the claimed constancy of c, both of them should have varied their initial values during the path tower-base.
According to our bases, we have different evaluations of this experiment. Let us first consider S at the base and A at its top, see Figure 6.
It is a fact that if S and A are at relative rest at the same level (e.g. both on the ground), then A is in resonance and it is also a fact that other experiments effected at this regard, e.g. Blatt, [7], show that if S moves toward the absorber, not contrarily, the absorber goes out of resonance: indeed, if S is fixed to the ground, the length of emitted photons (as previously shown) is constant, whereas if S moves with respect to its initial emission location (the ground), the photon length varies, thus we may infer that the resonance is physically related to the constancy of the length of photons.  Now, referring to Figure 6, if S, on the ground, emits photons reaching A at height h, because of the variation of potential, following our relation c = (−2U) ½ , it will be c 0 → c h ; since S and A are at reciprocal rest, it turns out that, as shown just after the Equation (20), it is always ν h = ν 0 (in spite of any variation of potential between S and A) yielding λ h = c h /ν h . Therefore, with r 0 the radius of Earth (hence r h = r 0 + h) and M E the mass of Earth, writing the (11) as c 2 = −2U, we get 2c = −2dU/dc hence from r 0 to r h and since Δc = −ΔU/c with ΔU = U Eh - (where ΔU = gh); then for ν h = ν 0 we have and since λ h < λ 0 , contrary to Relativity, A observes a blue-shift effect.
Thus, to restore the resonance via Doppler Effect (DE), see Figure 6(b), S has to recede from A in order that the photon length could increase, see Equation (17), from λ h to ; therefore, equating the relative variation of the photon length due to the DE, that is (λ h − λ 0 )/λ 0 = −υ/c, to the one due to the altitude, Δλ/λ 0 , as given by (28), we get  Well, it is known that atomic clocks give an increase of their counted time in altitude (T h > T 0 , hence ν h < ν 0 ), therefore taking these clocks from ground to h, their frequency ν h has to follow the same decrease as c h ; this implies λ h = λ 0 so the frequency of photons emitted in altitude becomes ( ) showing an increase of λ from the top to the base. Hence the absorber, on the base, will state, contrary to GR, a red-shift, hence, to compensate it via Doppler shift, see Figure 7, S has now to move toward A; on the contrary, according to GR, A and S should recede from each other. We also highlight two points: − The increase of λ for photons moving from h to the ground, gives a reason to the gravitational red shift related to far sources.
with T h the counted time of one photon emitted by a h-clock, while T 0 by a g-clock. Thus the variation of the counted time between the two clocks, for every   to a clock at the Earth's centre E, we can write T 0 ≅ T E ; thus, the difference between the two transit times T h and T 0 (≅ T E ) due to their relative motion, is Then, as above, is the variation of the number of photons emitted by a h-clock in 1 s; so the variation of the counted time, in one day, is showing a decrease of the counted time for a g-clock due to their relative mo- which is also predicted, (with different reason), by GR. To prevent this effect, before launching, the daily counted time (T 1d ) of clocks, has to be decreased by ≅38 μs.
In short, the time dilation is a consequence of the variation of U, hence of c: indeed, as show on §2.3, the admitted/emitted frequency on H atom (and of course the one of the other elements) varies together with c.

Gravitational redshift
As for the Relativity, the only way to explain high cosmological redshifts is the Doppler effect, (which implies an incredible universe expansion at a speed υ u ≅ c), whereas, on our results, disregarding the reciprocal motion between a (far) source and an Observer on Earth, which implies ν = ν 0 , we get c/λ = c 0 /λ 0 , where ν 0 , c 0 and λ 0 are the values on Earth, hence for c 0 > c one gets λ 0 > λ, that is a red shift observed on Earth; therefore, the shifts here observed can be expressed as with U 0 the potential on Earth, U the one on the source. Thus, apart from Doppler effects, z turns out to be the variation of c (as well as λ) during the path of light toward a different potential. In particular, with s the distance Earth-source, for s < ≅45 Mpc, [11], (roughly corresponding to −0.01 < z < +0.01) if U (potential on the source) is, in absolute value, higher than the potential on Earth U 0 , the (41) gives, on Earth, z < 0 (blue shift), and vice versa for |U| < |U 0 |; thus, for s < ≅45 Mpc, these red/blue shifts indicate that the potential, may increase or decrease with respect to |U 0 |. In the range ≅0.01 < z < ≅0.20, (where z follows the Hubble's law), the (41), written as shows that, for z << 1, U depends linearly on z, as Hubble's law; then, for s → ∞, U → 0, hence z → ∞, see Table 1.
[For s > ≅45 Mpc, z is always positive, hence we may infer that our galaxy is practically near/close to the middle of the masses of universe (where |U| has the max value)].

Electron Structure and Photon-Electron Impact Point
On our basis, (light composed of our photons), the interaction light-matter requires that to move a circling electron toward outer orbits, the impact photon-electron has to occur, see Figure 8(a), in a radial way, (giving origin to the radial velocity w), otherwise, other impacts could cause the electron fall into the nucleus, due, for instance, to an impact where the velocity of photons and electron have contrary direction.
To be radial, the impact must occur in a specific point, fixed to the electron surface, we call it Impact Point, which, during the electron, orbit, has to face its nucleus, (up to its removal), giving to the electron one rotation every orbit; the impacting photons have to approach the nucleus, as shown on Figure 8(b), perpendicularly to the electron orbit plane, providing, to the electron, a radial velocity w.
Moreover, we can infer that the charge of the electron, has to correspond to the Impact Point (I p ), so we may infer that each photon front is provided with a positive charge, while its tail with an equal negative one. In fact, the photon may be represented as an electric bipole.

Physical Characteristics of Photons
The total energy of a mass m is 2 E mc = also proved [12] by the evidence of nuclear reactions like n pd γ + + , hence this energy has to be valid for the (massive) light too, thus writing their energy as  in our case, n r ≅ 3 × 10 18 rays, and we point out that, as for a given power P, the higher is the frequency, the lower is the number of rays, as shown by (50)  whose validity is confirmed, see  with ν n the photons admitted frequency along the n-th circular orbit and since, as claimed on Section 1.4, ν (=n/t) is the number of photons (of the same ray) crossing an observer during the time t, the integer n represents the number of photons absorbed by the electron during the photon-electron impact time t and this number, for all the H atom circular orbits, is an integer starting with 1 along the electron ground-state orbit.

H Atom Parameters and Meaning of Quantum Numbers
The massiveness of light implies a finite impact time during which the electron is circling, and supposing, for now, that, for n = 1, the photon frequency ν 0 should be equal to the electron frequency along the ground-state orbit, that is ν e0 = υ 0 /2πr 0 , where r 0 , see conf. (c) is the electron ground-state orbit, with υ 0 its orbital speed, we could write 0 e0 1 ν ν = (first assumption); (62) to verify this ratio or to find the correct value, we may start from the experimental value of the 1 H ground-state ionization energy W 0 (electron extraction work) corresponding to the same as along n r .

Electron Radial Speed, Ionization Condition, Electron Radius
To apply properly the Conservation of momentum (CoM) to the impact photon-electron, the atom nucleus has to be considered fixed as origin in the common centre of gravity nucleus-electrons. On H atom, referring to Figure 9(c), an inelastic impact photon-electron, since photon and w, see Figure 8, have same direction, the (52), gives   hence the ionization, requiring 1 w υ = , could happen for n = 137, but the number of admitted photons, along r 0 , is n = 1. Now, along the progressive orbit # n, the admitted photons frequency is if the electron charge would be coincident with the electron barycenter along its effective orbit 0 r′ ; indeed, the photons admitted frequency is related to the effective distance r 0 , where the effective photon frequency is therefore 0 ν . In fact, we introduce 0 ν ′ to determine the value of 0 υ′ (ground-state electron effective orbital speed).

Absorption/Emission Effect; Claimed Fall of Circling Electrons
Referring to Figure 11 representing the Absorption of photons into a circling electron, let us assume the nucleus mass m N >> m e so to consider the nucleus fixed in the atom centre of gravity B. Now, the expression of the total energy of the system photon-electron is given by e r r T E U K K = + + + where E (=mc 2 ) is the energy of the incident light, U r (=−e 2 /4πε 0 r) is the potential due to electrostatic attraction acting on the electron, K e (=½m e υ 2 ) is the electron orbital kinetic energy, and K r (=½m e w 2 ) its radial kinetic energy related to its radial speed w due to the impact photon-electron.
Regarding the Absorption/Emission effect (elements on gaseous state), see Figure 11, along circular orbits it is K r = 0 and moreover, at the end of absorption, along the orbit r 2 , (where the photons have been absorbed), it is E 2 = 0; hence between two circular orbits r 1 and r 2 , the (101) gives Then, according to (71) we have r 1 = r 0 n 2 and r 2 = r 0 k 2 (with k > n as r 2 > r 1 ), thus Figure 11. Absorption/Emission effect: (a) Incident photons are absorbed by the electron which moves toward wider orbits; (b) Emission: the electron moves toward inner orbits emitting photons.
and plugging the (74) written as ν 0 = e 2 /8πε 0 hr 0 , we find which is the photons frequency between two circular orbits, where n represents the progressive specific number of each circular orbit and where k turns out to have, for each of them, the values k = n + 1, n + 2, •••, n i which are, one by one, the number of the remaining external circular orbits, and where n i is the ionization orbit; on H atom, n i = 137. Claimed fall of a circling electron into its nucleus: an electrical current emits an electro-magnetic radiation and therefore it is claimed that the circulating electrical charge of an electron should also emit an e.m. radiation yielding the electron, in a short time, to fall into the nucleus; but on our results, a free electron, moving, for instance, along a copper wire under an electrical potential difference, when entering into an atom influence, (at that moment the electron charge will return to face the atom nucleus), will release the necessary photons to reach the atom energy level corresponding to the energy previously received (during the absorption effect). Indeed, along circular orbits, it is w = 0, therefore the absorption/emission of photons cannot happen along circular orbit, that is why the circling electrons are absorbing/emitting photons only between circular orbits, and therefore, the e.m. radiation is due to the emitted photons during their re-entry toward inner orbits; at this regard, the photons emission is necessary for the electrons not to fall into their nucleus.

Photoelectric Effect: Number of Involved Photons
Between the electron ground-state orbit r 0 and its extraction orbit r → ∞ (intending on microscopic scale), the (101) On ground-state, as also shown between Equations (102) and (103), it is

Conclusions
This paper is mainly based on three conditions: c = u (with u the total escape speed); a certain structure of the light (massive photons having variable length); the electron charge like a point-particle facing the atom nucleus during the electron orbit.
On these bases, we gave a classical reason to the apparent constancy of c, then we showed that the time dilation turns out to be an effect of the variation of the total gravitational potential U (inducing a variation of c) and we also showed that the high gravitational red shifts are also due to the same reason; we also showed that the quantum numbers are nothing else than the numbers of photons admitted on free atoms along an integer number of electron orbits; then we gave a reason why the circling electrons cannot fall into their nucleus, and we also showed that the ionization of free atoms happens when the electron radial speed (due to the impact photons-electron) equals the electron orbital speed.