# How to distinguish between the spectrum of an atom in motion and the one of a scaled atom ?

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Galaxies are moving dragged by the space expansion. When atoms are in motion the doppler effect will shift the spectra of the emitted photons.

The proton-to-electron mass ratio, $\frac{m_e}{m_p}$ has been measured constant along the history of the universe, but nothing can be said about the constancy of the electron or proton's masses.

The photon's energy obey the Sommerfeld relation, $E_{jn}=-m_e*f(j,n,\alpha,c)$, as seen here, and it is evident that a shifted (1) spectrum is obtained with a larger $m_e$.

The spectra lines are not only due to the Hydrogen atom; there are other spectral lines due to molecular interactions, due to electric/magnetic dipoles, etc, and so the electromagnetic interaction,the Coulomb's law, $F_{}=\frac{1}{4\cdot \pi\cdot \varepsilon}\cdot \frac{q1\cdot q2}{d^2}$ must be analyzed.

If we scale all masses by the relation $\alpha(t)$ (not related with the above fine structure constant), where $t$ is time (past), and also scale the charges and the distances and time by the same factor, gives exactly the same value $F_{}=\frac{1}{4\cdot \pi\cdot \varepsilon}\cdot \frac{q_1\cdot q_2\cdot \alpha^ 2(t)}{d^2\cdot \alpha^2(t)}$. Thus the system with and without the transformation behaves in the same manner. The same procedure shows that the universal gravitational law is also insensitive to the scaling of the atom (2). This should not be a complete surprise because the scaling of masses, charges, time units and distances is routinely used on computer simulations that mimic the universe in a consistent way.

The conclusion is that there is no easy way to distinguish between the spectrum of an atom in motion and the one of a scaled atom.

The photons that were emitted by a larger atom in the past are received now without any change in its wavelength.

The mainstream viewpoint, not being aware that scaling the atom gave the same observational results, adopted the receding interpretation long time ago. As a consequence the models derived from that interpretation (BB, Inflation, DE, DM, ) do not obey the general laws of the universe, namely the energy conservation principle.

My viewpoint offers a cause for the space expansion.  Most physicists are comfortable with: 'space expands', period, without a known cause.

Physics is about causes and whys, backed by proper references.
I used the most basic laws to show that another viewpoint is inscribed in the laws of nature.

When I graduated as electronic engineer, long time ago, I accepted naively that the fields (electrostatic and gravitational) are sourced by the particles, and expand at $c$ speed, without being drained. But now, older but not senile, I assume without exception, that in the universe there are no 'free lunches' and thus the energy must be transferred from the particles (shrinking) to the fields (growing).

This new viewpoint is formalized and compared to the $\Lambda CDM$ model in a rigourous document, with the derivation of the scale relation $\alpha(t)$ that corresponds to the universe's evolution, at:
A self-similar model of the Universe unveils the nature of dark energy
preceded by older documents at arxiv:
Cosmological Principle and Relativity - Part I
A relativistic time variation of matter/space fits both local and cosmic data

Can someone provide a way to distinguish between the spectrum of an atom in motion and the one of a scaled atom ?

maybe by probing the atom's nucleus and find the isotope ratio's abundance, D/H evolution and other isotopes as Mr Webb did with Mg (1998 paper) when in search of the $\alpha$ variability.

PS: To simplify the argument this question skips some details and to avoid misrepresentations a short resumé is annexed.

(1) - after the details are done it is a redshifted spectrum at the reception

(2) - LMTQ units scale equally by $\alpha(t)$, $c,G,\varepsilon$ and the fine structure constant $\alpha$ are invariant.

## A short introduction to the self-similar dilation model

The self-similar model arises from an analysis of a fundamental question: is it the space that expands or standard length unit that decreases? That analysis is not an alternative cosmological model derived from some new hypothesis; on the contrary, it does not depend on hypotheses, it has no parameters besides Hubble parameter; it is simply the identification of the phenomenon behind the data, obtained by deduction from consensual observational results. The phenomenon identified is the following: in invariant space, matter is transforming in field in a self-similar way, feeding field expansion. As a consequence of this phenomenon, matter and field evanesce while field expands since the moment when matter appeared. As we use units in which matter is invariant, i.e., units intrinsic to matter, we cannot detect locally the evanescence of matter; but, as a consequence of our decreasing units, we detect an expanding space. So, like the explanation for the apparent rotation of the cosmic bodies, also the explanation for another global cosmic phenomenon (the apparent receding of the cosmic bodies) lays in us.
In units where space is invariant, named Space or S units, matter and field evanesce: bodies decrease in size, the velocity of atomic phenomena increases because light speed is invariant but distances within bounded systems of particles decrease. In standard units, intrinsic to matter, here called Atomic or A units, matter and all its phenomena have invariant properties; however, the distance between non-bounded bodies increases, and the wavelength of distant radiations is red-shifted (they were emitted when atoms were greater). The ratios between Atomic and Space units, represented by M for mass, Q for charge, L for length and T for Time, are the following:

$$M=L=T=Q=\alpha(t)$$

The scaling function $\alpha(t)$ is exponential in S units, as is typical in self-similar phenomena:    $$\alpha(t_S)=e^{-H_0 \cdot t_S}$$

Mass and charge decrease exponentially in S units, and the size of atoms decrease at the same ratio, implying that the phenomena runs faster in the inverse ratio; as A units are such that hold invariant the measures of mass, charge, length of bodies (Einstein concept of reference body) and light speed, they vary all with the same ratio in relation to S units. In A units, space appears to expand at the inverse ratio of the decrease of A length unit; the space scale factor in A units, a, is: $$a=1+H_0 \cdot t_A$$
Therefore, space expands linearly in A units.
In what concerns physical laws, those that do not depend on time or space (local laws), like Planck law, are not affected by the evolution of matter/field and hold the same in both systems of units. The laws for static field relate field and its source in the same moment; as both vary at the same ratio, their relation holds invariant and so the laws – the classic laws are valid both in A and S units. The electromagnetic induction laws can be treated as if they were local, therefore holding valid in both systems, and then consider that, in S, the energy of waves decreases with the square of field evanescence (the energy of electromagnetic waves is proportional to the square of the field). In A, due to the relationship between units, the energy decreases at the inverse ratio of space expansion while the wavelength increases proportionally. This decrease of the energy of the waves (or of the photons) is a mystery for an A observer because in A it is supposed to exist energy conservation, which is violated by electromagnetic waves. The phenomenon is observed in the cosmic microwave background (CMB) because the temperature shift of a Planck radiation implies a decrease of the density of the energy of the radiation with the fourth power of the wavelength increase and space expansion only accounts for the third power (this is perhaps the biggest problem of Big Bang models, so big that only seldom is mentioned). Note that induction laws can be treated as time-dependent laws and the evanescence of the radiation be directly obtained from the laws; that introduces an unnecessary formal complication. Finally, there are the conservation laws of mechanics, which require a little more attention.
Although it is not usually mentioned, the independence of physical laws in relation to the inertial motion implies the conservation of the weighted mass summation of velocities and square velocities of the particles of a system of a particles. As the A measure of mass is proportional to the weighted mass, these two properties are understood as the conservation of linear momentum and of kinetic energy. Therefore, the correct physical formula of these conservation laws depends on the weighted mass and is valid in both systems of units; for simplicity, the A measure of mass can be used instead of the weighted mass; for instance, for the conservation of square velocity: $$\sum_i{\frac{m_i}{m_{total}}\cdot v_i^2=\text{const}}\Leftrightarrow \frac{1}{2}\sum_i{(m_A)\cdot v_i^2}$$
In the first expression the system of units is not indicated because the equation is valid in both systems; in the second equation, velocity can be measured in A or S (has the same value in both) but the measure of mass has to be the A measure. The second expression is the conservation of kinetic energy in A.
The conservation of the angular momentum is the only law modified in A units because the relevant measure of curvature radius is the S measure; the angular momentum L can be written as
$$\textrm{L}=\mathbf{r}_s\times m_\text{A}\mathbf{v}$$
This is the quantity that holds invariant in an isolated system; the usual A angular momentum, function of $r_A$
$$\textrm{L}_\text{A}=\mathbf{r}_\text{A}\times m_\text{A}{v}$$, of an isolated system increases with time:
$$\left ( \frac{d\textrm{L}_\text{A}}{dt_\text{A}} \right )_0=H_0\textrm{L}_0$$
This means that the rotation of an isolated rotating body increases with time. For an S observer, this is consequence of the decrease of the size of the body; an A observer can explain this considering that it is consequence of the local expansion of space, that tends to drag the matter.
Note that there is no conflict with the data that support standard physics because this effect is not directly measurable by now; yet, this insignificant alteration has an important consequence: the expansion of planetary orbits.
A note on the value of constants in both systems of units. To change from one system to the other is like any change between two systems of units, but there is a difference: units are time changing one another. As a consequence, a constant in A may not be constant in S. For instance, the Planck constant change in S with the square of the scaling law (a simple image of the physical reason is the following: orbits radii are decreasing in S and also their associated energy; so, the wavelength of emitted radiation is decreasing with orbit radii and also the energy, which implies a Planck constant decreasing with the square of the scaling). Field constants are the exception: they hold constant in both systems of units. The Hubble constant is different: it is constant in S but not in A (in A, the Hubble constant is just the present value of the Hubble parameter). In short, the Hubble constant is the only time constant and is a S constant, field constants are constant is A and S and the other constants, including Planck constant, are relative to atomic phenomena and are constant in A; naturally, the dimensionless relations, like the fine structure constant, are independent of units.
Only the classical fundamental physical laws have been considered because that is what is required, the ground on which the analysis of all the rest of physics can be made, special and general relativity included.

edited Jun 12, 2014

Hi @HelderVelez,

it seems this post is intended to discuss and review a paper of yours by the PhysicsOverflow community, which would make it a perfect  submission to our Reviews section, which is dedicated to exactly such applications. If you like, you can ask for such a submission to be created by a superadministrator here. First, the submission would contain not much more than a link to and the important data of the paper, but you can then claim authorship and edit the sumbission by adding a summary, such as for example the content of the above post. Other people will then write reviews for you in the answers and additional discussions can take place in the comments.

Specifically, concerning your ideas, I think you have to be a bit careful to properly distinguish between (theoretical) transformations of the system (the scaling transformation can be among them), and real dynamical motions of objects.

Ok, as it is clear that you are the author, we could probably also simply convert this question into a submission and add the content as the summary of the paper, if you like ?

I'm friend and a sort of colaborator of the author and I will ask his oppinion. I knew this model since 1992 but the formal derivation of the model was completed by 2011. This post is only an application to show the potential of this viewpoint. The linked doc is a fully derived formal new theory without any ad-hoc hypotheses. The author is from outside of the academia and it is very difficult to be accepted for review in such conditions.  Imo, it would be interesting to submit it to review in this comunity.

Ok, I realized later that the author was not you ... So I think we could create a submission for the paper of your friend pretty fast and he could claim authorship later, if you like.

Yes, you can proceed with the submission and I'will be around and will tell him about this development.  Thanks.

@Dilaton: I've a more recent version, extended with the implications on the electromagnetism. May be that I should upload this version, after the approval of my friend.  (coincidently it's file name is Dilation3.pdf ;) )

:-D

The author needs some time, until monday, to revise the last version and we will focus our attention on that. The first link in the post, version of 2011, is correct and self-contained, and it has  plenty of material to discuss and it is a good option but, If you can wait, we would like to upload the most recent version.  I've with me the new Abstract that I can post here as an 'answer'  to antecipate some thoughts.

m_e needs to be smaller, not larger, to make a redshift with the scaling law you give.

You spotted it correctly. The energy at emission is greater, but at the reception it is redshifted. I posted a short introduction to the theory to provide more context. The simple post was intended to to show that physical laws included the possibility of the scaling of the atom, as I think you understood, and the reading of the linked document is beneficial.

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Just scaling down m_e only works to rescale spectra for monatomic atoms, and then only if you ignore nuclear recoil (see V. Kalitvianski's answer). Rescaling m_e doesn't work for molecules, where the rotation and vibration spectra depend on the nuclear mass and moment of inertia. The vibration and rotation spectra of simple molecules are rigidly redshifted, not just the monatomic lines. Whenever you can distinguish observed rotation/vibration spectra for H2, DH, CH4, H2O and O2 in a distant cloud, this is enough to ensure that the proton mass, deuteron mass, deuteron binding force, H_2 binding length, C12 and O16 nucleus mass, and C-H, O-H, O-O bond lengths and angles are preserved relative to the purported new scale, so that if one mass is rescaled, all the masses are rescaled.

In order to rescale universally low-energy non-gravitational physics, you need to do a renormalization group step. It's a very convoluted thing, you need to shift the masses of the electron, the up and down quark, and the strong coupling constant, so that all the nuclei scale down in mass, relative to the gravitational scale. By dimensional analysis the effect is equivalent to making "G" vary with time, and this is proposed by Dirac in the large-numbers hypothesis: http://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis . The theory you are proposing is a large-number-hypothesis theory, with a particular specific time-dependence designed to reproduce the entire redshift of distant matter.

Doing this has an impact on star stability, since gravity is becoming weaker in the past uniformly, so that the rate of light-production is altered. In the linked Wikipedia article, this historical argument is made by Teller in 1948 to give a bound on large-number variations. This has an effect on the Earth--- the sun can't maintain 5 billion years of constant shining, the Earth's orbit and temperature can't be stable for so long, if the mass of everything keeps going up over cosmological time. The historical bounds on large-number theories should easily exclude your theory, at least if the same parameter changes happen on Earth.

From these constraints, you can conclude that a model of this sort can work only if it has us in a preffered center--- since we don't have variations of parameters over cosmological time, but the distant objects do. This is a violation of the Copernican principle.

The direct observational tests to exclude this idea are more difficult, you could theoretically look at broadening effects on spectral lines, since stationary and moving objects would have different broadening, but this is probably unobservable. But I think just to be sure the idea is not true, the bounds on large-numbers are sufficient.

answered Jun 11, 2014 by (7,720 points)
edited Jun 11, 2014

I made the post more clear and included a short introduction to the theory that, I hope, address all of your concerns.

The $G,c,\varepsilon$ are kept constant as seen in the dimensional equation when all four base units are scaled.  And the same with the adimensional constant $\alpha$. But it is probably a surprise that the constant of Planck is dependent on the scale of the atom as a dimensional analisys puts in evidence.
This is the first scale theory where all constants are kept invariant, besides BB that has 6 parameters instead of one, and it provides no cause for the expansion (the metric is not a cause, it only describes).

About the centre of the universe: it is exaclly the opposite; the presumption that the actual size is unique ('absolute') and no other incarnation of the atom is viable is limited.

The equations can tell us if the atom can scale or not and the data tell us if the atom scaled or not.  The study is done and available to be studied.

Dirac ?  not at all.

Keeping G fixed and changing m_e and m_u m_d and g_s appropriately to rescale all the spectra is exactly the same thing as keeping m_e, m_u, g_s  fixed and making G vary. It's exactly the same thing. There is no difference. The question is only whether you define the unit of mass to be the Planck mass, in which case G is obviously fixed, or the proton or electron mass, in which case you have a varying G theory.

Your response, that the "equations will tell us which is varying" is incorrect, because the equations depend on your choice of units. I have chosen to use units where the atomic spectra are fixed, because this is the easiest way to find a literature refutation of the idea in the theory. You have chosen another way of choosing units, where G is fixed, and then it looks like all the masses are rescaled, and the strong coupling fiddled with.

Do you agree, or not, that my simple procedure proved that "those 2 equations show that scaling of the atom, the way I did, gave a shifted spectra" ?  (a)

Scaling the atom was choosed to be defined as: to keep $G,\varepsilon,c$ as constants and to vary the atomic properties of mass/length/charge/time units with the same factor. (b)

It is useless to invoke the actual system of units we use, SI, Planck, etc,.. because all the realizations of the unit's systems are based in the atomic properties, called 'atomic system' through all the paper (c), in contraposition to a Space (S) system. It is useless to invoke a varying $G$ or any other varying scenario besides the one defined in the paper, as above said. Those other variations  (page 2- Dirac's LNH,Canuto,Hoyle and Narlikar,Wesson,Meader and Bouvier ),..., are not under scrutiny now.

I expected that you (based in a previous answer of yours) try to anchor your position on the constancy of the Planck constant (length or mass). By dimensional analysis the Planck constant has dimensions $ML^2T^{-1}$ therefore it scales as $\alpha^2$ thus, although an atomic observer (A) will measure it as a constant, an invariant observer (S) will see its value changing as the atom's size change. If us, as atomic observers did not found any contradiction in the laws using $h$ then any other atomic observer inhabiting a diferent atom incarnation will use the same equations and arrive to the same conclusions.

Not relevant to our discussion, an aside: Knowing what I know now, any attempt to bring the total mass of the universe (m_u in your comment?) to any unit definition is extremelly abusive, because it depends on a choosed cosmological model and it can not be directly measured; and the same for any black-hole's characteristic, or whatever unrealizable measure process.

(a) (b) by your previous comments I understood that you agreed, but I can be wrong in the interpretation.

(c) reading the paper is beneficial because it is the only way to know new ways of thinking, and the new conclusions expressed there that no one had expressed before. You can not presume that it adds notingh to your preconceptions. In that way the time can be used to talk on why/where you disagree with the expressed position.

There is nothing to read. If you rescale all spectra to redshift, you rescale all energies down by a factor, and all atomic length-scales get blown up by the same factor. This is in units where G is fixed. This is equivalent to changing G and keeping the atomic scales fixed, the two are related by a unit transformation. In fact, this is the best way to say what "changing G" means in a way that is unit-invariant--- all atomic scales are dilated relative to a (fixed) Planck scale. I have said it three times, and you keep on saying it's not true. It is true, and it is not hard to see either. I didn't read anything, there's no point, I already understand this.

I'm writing in the benefit of those wanting to read.

What is the role of $G,c,\varepsilon_0$ in the physics laws? They represent how space allows the response of the battle - space versus matter; and space is not null, it has properties; the  $\varepsilon_0$ is ... of vacuum is there to remind us. Let X be a function of matter properties X=f(M,L,T,Q). Then Ron is saying that the outcome F of the battle (which determines the dynamics):  $F=G\cdot X$ is equivalent to 1- fiddle with $space-G$ or 2- fiddle with $matter-X$.  I can't see how either physically neither mathematically. Change G then F has a different outcome. What I point is that it exists another mathematical function of M,L,T,Q  that have the same result of f() and, thus, the outcome is not changing.

If you want to know the limitations involved in the scaling of a geophysical model find 'Scaling Laws' inside it, and think: The perfect solution, if at hand, is to scale the atoms.

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We measure everything, including the atom, with the atom.  There is no external reference.

The mass unit, in all units system is the mass of a determined colecction of atoms, put the number

The mass of the electron is a tiny fraction of  a mass unit, put the number.

Wat is the mass of an atom? It is a tiny fraction of  a mass unit, put the number.

This is a circular definition because we measure the atom with itself thus, the atom can be of any size.

Try with length unit and find it is linked to atom' radius.

Thus, the atom can be of any size. It is inscribed in our atomic model that the atom can scale.

Thus, while others are thinking of 'absolute energy scale' and of the absolute size of the atom, I cant find references to that.

The best and the accepted way to say that I'm wrong is to present a reference document on the absolute atom's size.  Until then I'will keep saying that the atom scale, there is no Dark Energy, no Dark matter, no BB, and also I've the best argument to maintain: there is no BlackHoles (this argument is after Ron's hint, thanks).

May be that reading the above linked paper you can say what is wrong inside of it, and deny my statements (any reasoning, math, physics). Go on.

answered Jun 15, 2014 by (-10 points)

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