Theoretical High Energy Physics - Science topic

the singularity is unphysical. your answer can only be answered by a quantum gravity, which avoids singularities. .the singularity of a black hole is nothing but another word for the failure of geneal relativity at the planck scale. hence it makes no sense to ask for.the natue of the singularity

There's nothing particularly new to report about these resonances. The statement about the pion is wrong: it carries orbital angular momentum in theory and in fact. Its trajectory is described in terms of the cross section for observing it-more precisely its own decay products. The calculation is standard and described in any textbook on particle physics.

Dear Stefano,

Thank you for your comment. Like Martin pointed out, nature does behave differently at different scales. I want to know if it is reasonable to have a metric that is also scale dependent.

One of my interests is deformations of algebras as a means of generalizing symmetry. So for example, both SR and QR can be seen as deformations of Galilean relativity and classical mechanics respectively. Taking Minkowski spacetime with Poincare symmetry and deforming it give either dS or AdS. At this point the isometry group is rigid and cannot be deformed further. The mathematics does not tell you the value of the cosmological constant (just as it doesn't tell you the value of x or hbar).

Experiments suggest that at least on large scales the cosmological constant is positive. Loop quantum gravity seems to introduce a positive cosmological constant to rid the theory of IR (large scale) divergences. On the other hand many theories make use of the AdS/CFT correspondence and assume an AdS spacetime. This also gives some impressive results. There is interesting physics in the singleton representations of AdS (discovered by Dirac all the way back in 1963). 

My question is whether it is possible to reconcile these approaches. I think that if it is then it could lead to interesting new physics.

1.    As the question for the first answer see the attachment. Where you'll see two regions of energy are there E1 & E2. E2 is encirculated by E1, because the lesser energy region always surrounds the high energy region.

2.    As the emitted wavelengths are 5896 A and 5890 A, both are inside the range of our visible light i.e. 390 to 700 nm. So this spectrum should be visible.

3.    These emission lines could be detected by an electromagnetic (E-M) radiation detector.

The problem is that it only has an appreciable effect over a very short distance and the mass of the reflectors would be far greater than the effect.

Hossein,

Why is it that people vote down the question?  It must be that they do not understand its importance.  If we knew all there was to know about the sub-atomic then this would be a meaningless question, however we know only what "Theory" tells us and that is obviously wrong.

There needs to be a new model to the atom and we have known this ever sense Niels Bohr proposed the current model more than 100 years ago.  

Even at the time Bohr knew that this was only a way to look at the atom and not the answer, yet we look at it at the truth.

The question puts into question our reasoning behind theory that has no bases in reality.  If there is objection to this line of questioning then logic has no place in science.

Where are the researchers that understand logic?

Dear Ilian,

you are missing orbital angular momentum in the equation, which can be carried by the atom-photon system. That's the resolution to the "paradox".

Angular momentum conservation holds for the *total* angular momentum, which combines both orbital angular momentum and spin contributions.

Furthermore, even in the n=5 shell, there are states with l=0 (s-orbitals), l=1 (p-orbitals), and so on. Those do not even need any other type of angular momentum.

I hope this helps.

Best regards,

Alex

Gluons don't become massive in the infrared limit-that statement is incorrect.  Nor is the statement about the gluon jet losing kinetic energy correct, either. The references to the two slit experiment aren't relevant.  It's useful to consult textbooks or lectures on the subject, that's now background knowledge, e.g. 

The statement ``the emitted gluon at finite energy becomes a spatial coordinate singularity'' is meaningless and the statement that the gluon propagator doesn't have a spectrum beyond the first Gribov horizon is meaningless, also. What the Gribov ambiguity means is, simply, that it's not possible to fix the gauge uniquely, one must use coordinate patches in field space. Cf. http://projecteuclid.org/euclid.cmp/1103904019 

However, when performing a tree-level computation one isn't sensitive to the Gribov ambiguity, since one is working in the coordinate patch  about the identity in field space, anyway. 

Finally, the quoted text doesn't have anything to do with any comparison between a tree-level calculation and a higher loop calculation, so is completely irrelevant to the issue. It certainly doesn't produce either a mass gap or an example of color confinement. Cf. http://arxiv.org/abs/1008.1936 for how gluon jets are studied.

It means that, since the gauge bosons that mediate charged current processes, i.e. the W-bosons, contribute to the processes that affect the mass difference between the two kaon states, the mass of such bosons is constrained by what's known about the mass difference of the kaons. This is what happens in the Standard Model, too, incidentally, regarding the mass of usual W bosons. It suffices to write down the expressions for the amplitudes, using the corresponding Feynman rules. So it might be useful to review how it's realized, already, in the Standard Model.

Dear Biswajoy,

perhaps you still remember that people decided to search for tau neutrino at CERN  (CHORUS and NOMAD) since the hot+cold dark matter model was considered appealing. I just mean that this kind of activity has been pursued since ever and they are known to be risky.

Indeed, we have changed the cosmological model since some 10 years. Many papers have used it to obtain measurement of neutrino masses, see e.g. a couple of PRL past year (one of them linked below).

The new (ΛCDM) cosmological model is based on many observations, including those of Saul Perlmutter, Brian P. Schmidt and Adam Riess (Nobel in Physics 2011). But it has a lot assumptions of and it is still a model. Various datasets are included for the inference, affected by various systematics. The papers I have linked in the beginning of this discussion, in fact, claim that they have cleared out the issue. Can we trust their analysis and conclusions?

An essential facet of the discussion is, in fact, the following question; what are the possible systematic errors that we could have missed and could affect the determination of neutrino mass? The likelihood that allows us to estimate the neutrino mass, that I mentioned several times above, has been derived assuming that the known errors are fairly assessed and no big systematic error is present.

I guess one can discuss this point within known physics or astrophysics; or one can try to perform checks using various data; or even one can start to imagine (speculative) cases when important modifications are expected. Due to the importance of the point, and the strong bound presently provided by cosmology, all these activities seem to be  worthwhile.

Dear Biswajoy,

the neutrino to anti neutrino oscil is helicity suppressed, was first described in http://journals.aps.org/prd/abstract/10.1103/PhysRevD.23.1666 Regarding the counting and parametrization was exhaustively desrbed in http://journals.aps.org/prd/abstract/10.1103/PhysRevD.22.2227 and the symmetric presentation given there is BETTER than PDG for LNV processes. The PDG form is more convenient for standard oscillations only  CHEERS

You may see the following reference.

The Two Loop beta Function for a G(1) x G(2) Gauge Theory

D.R.T. Jones, Phys. Rev.  D25, 581 (1982).

If I understand the question (assuming 4D and initial condition usually consider for ordinary inflation), you are describing a scalar-tensor theory. These theories can be mapped to f(R)-models. If you start from an f(R), through a conformal transformation you just obtain a scalar degree of freedom coupled with the metric as in scalar-tensor models. Starobinsky model is nothing but a f(R)=R+R^{2}, inflaton is just the extra scalar degree of freedom propagating in this model. You can also obtain the precise potential in this case.  

Tom,

usually everything is quite clear (using Noether):

The symmetries of the Poincare group are related to conservation laws. One has 10 generators and one has 10 laws (energy, momentum, angular momentum and center of mass). The translations correspond to momentum and energy. The rotations correspond to the angular momentum and center of mass.

For the classification of particles you have to include the charges. The corresponding Noether symmetry comes from quantum mechanics (QM). It is the (local) phase shift leading to gauge invariance (and the appearance of gauge fields). Or, charges are connected with the complex structure of the wave function in QM (and the choice of the phase). The Poincare group has nothing to do with charges. Therefore I don't see why one should relate the generators of the Poincare group to particles. According to the representation theory of Wigner, you will get the mass (continuous) and the spin (in units of 1/2) from the representation of Poincare group.

Torsten

Akira, all what you write is so off the mark and so surrealistic than we don't even know where to begin with to answer you. I already gave up for a long time. You have only read the books that reinforce your prejudices, and/or suitably misconstrued other ones. Your knowledge on the very matter, on the scientific community, on the methods, on the history must be very thin to utter such absurdities. Your motivation is only to put down the scholars, and not to seak the truth, so a discussion with you is pointless. You want to think that they are all mislead? All right, think so, it's your problem, not ours.

Quantum mechanics have been discovered independently by Schrödinger and Heisenberg, and in different forms.  But Schrödinger has proved that they are mathematically equivalent.  There was also an american physicist who discovered it even before De Broglie's thesis.  But his paper has not been accepted for publication for deemed to be too abstract. It has been destroyed, but Schrödinger saw it, and said that it was the same thing as his own work. This story is very little know, I can't find the references again. So, three identical and independent copies of the same theory, in different settings, there is certainly something in it.  Before the debate between Bohr and Einstein, and before the famous EPR paper, quantum mechanics was thought to be perfectly rational, even though not intuitive, not "anschaulich." It explained quite naturally the empirical rules of Bohr and Sommerfeld, without the irrational-magical tinge they carry.  In only two or three years after its official birth, quantum mechanics has been applied succesfully to a wealth of problems.  Since then, despite much efforts, and even despite the rationalist movement, no better theory could be found.  The only rôle we could ascribe to the "anti-rational hysteria," is that these invaluable papers could be published, contrary to with the stringent and arbitrary policy of the American Physical Society.  De Boglie who sparked this revolution was not in Germany.

Can they scatter gravitational waves ?

See for example:

Does a domain wall emit gravitational waves? -- General-relativistic perturbative treatment

Hideo Kodama, Hideki Ishihara, Yoshihisa Fujiwara

arXiv:gr-qc/9401007

You can read this paper.

"Orbital angular momentum" is a label characterizing a representation of the group of spatial rotations on a space of orbital wave functions describing a certain finite number, N, of particles in non-relativistic quantum mechanics. Now, it is assumed (for good reasons) that orbital wave functions are single-valued functions on the configuration space of those N particles, which is an N-fold Cartesian product of physical space, \mathbb{E}^{3}. Then the group that is represented on any space of orbital wave functions is SO(3), rather than its universal covering group SU(2). One now observes that only integral angular momenta correspond to representations of SO(3). That's it! - However, if one studies particles with "intrinsic angular momentum", i.e., spin, one finds that spin can also be half-integral, because, on the state space of particles with spin, the group SU(2) is represented, rather than SO(3). It is usually claimed that particles with half-integral spin (electrons, protons, neutrons,...) are fermions, while particles with integral spin (the nucleus of Helium_{4}, ...) are bosons. This "connection between spin and statistics" can only be understood or "explained" in relativistic local quantum (field) theory.

To Andrew Messing: The first proof of the connection between spin and statistics in relativistic, local quantum theories of freely moving particles is due to Markus Fierz and was published by him in 1939. At the time, Fierz was a twenty-seven years old postdoctoral researcher with Pauli. In 1940, Pauli published a somewhat simpler proof. The general connection between the spin and the quantum statistics of fields and particles in relativistic local quantum field theories on space-times of dimension at least 4 was derived by Lüders and Zumino: Half-integral spin corresponds to Fermi statistics, integral spin corresponds to Bose statistics. (In space-times of dimension 2 or 3, other forms of quantum statistics, called braid-group statistics are possible. There remains a connection between spin and braid-group statistics; but it is more subtle.)

I think there was some confusion here because in the discussion it should have been stated clearly what is a linear function of what. Secondly, we are talking of mathematical models of physics; if we add all the dirty side effects nothing is linear anymore. In Maxwell's theory, the em fields are linear functions of the charged sources and currents that are around, but if you take into account that these sources back react, then the combined equations become non-linear.

Only in this sense, the question posed is a meaningful one: if we keep the sources and currents fixed, then our mathematical models say that the em fields are linear but the gravity fields are not.

In mathematical terms, this can be explained by the fact that the local gauge group in electromagnetism is Abelian (i.e. the effect of two consecutive gauge transformations does not depend on the order) while in gravity it is non-Abelian (the effect of two consecutive curved coordinate transformations does depend on the order). Physically, this means that gravity carries energy and momentum (although this depends on the curved coordinates chosen), so gravity generates gravity, while em fields are electrically neutral.

All of this did not require the consideration of quantum mechanics. In ordinary quantum mechanics, what I say above is still valid. But now, even the vacuum has vacuum fluctuations of charged particles and they cause non-linearities in light when you include the back reaction of the vacuum.

First, allow me to clarify that invariance and symmetry are often used as synonyms: for instance, we may say that a ball is spherically symmetric, or that it is invariant under the three-dimensional rotation group. These mean the same thing.

Also, symmetries aren't conserved (not in the usual meaning of the term). However, symmetries can lead to conservation laws. Specifically, when you have a Lagrangian theory that is invariant under some transformation (i.e., it has some symmetry), there is a conservation law associated with that symmetry. (This is the essence of Noether's theorem, named after the remarkable German mathematician Emmy Noether.)

Having said that, I think the gist of your question is whether or not in physics, Lorentz invariance is exact or approximate. As far as we know (notwithstanding speculative theories) it is exact. That is, our best classical theories, special and general relativity, are built on the notion of exact Lorentz invariance (at least in infinitesimal neighborhoods, i.e., "local" Lorentz invariance). Similarly, quantum field theory, being a relativistic theory, is manifestly Lorentz invariant.

There are other theories that break Lorentz invariance. These theories are often proposed to address important questions, e.g., in cosmology. However, as of yet they have no experimental support.

Dear Riaz, why not to ask people from BRAHMS directly? Other way to find an answer is to read carefully relevant published papers from BRAHMS. 

Following is a link to an article which deals with acceleration on quantum scale. It contains a new wave equation which is developed by merging Newton's inverse square law with Schrodinger wave equation. Here the particles are not in bound state / stationary state. Specific case of electron positron creation is shown in the table.

This is a very important question. Matter cannot exist outside of the time dimension. We can visit different points in space but never at the same time. Einstein is right in that space and time are inseparable but time is not the same as space. The space dimensions are isotropic but time has a direction defined by the entropy gradient.

Then there is the question of whether time is quantised The RG consensus is "not" but I think it must be, if energy is quantised.

The Higgs field is a scalar field that couples linearly to a spinor field via the term psi*psibar in the Lagrangian, which has the same form as the usual mass term. This scalar field is peculiar as it also adds a "potential" term to the Langrangian that has a negative minimum at a non-zero value. That minimum drives the vacuum state of the Higgs field into a non-zero value m. This m acts then as the spinor mass. This mechanism works but suffers from some ambiguity with respect to the involved parameters. It is also unclear whether it is a fundamental field or an emergent property of the vacuum state of the interacting field theory, perhaps along the lines of superconductivity.

Please don't forget that there is a large (order 10^-3) dipole term in the CMB, generally interpreted as a simple red/blue shirt indicative of our velocity with respect to the CMB rest frame (a thoroughly classical explanation). (This was the only CMB anisotropy known for over two decades, roughly 1970 - 1992.)

The Gribov copies don't have anything directly to do with quark confinement. They are a property of Yang-Mills theories, when the gauge-fixing term (e.g. the Faddeev-Popov determinant) can have normalizable zeromodes. This fact is logically distinct from the behavior of the Wilson loop or the behavior of the 't Hooft loop (its dual).

Vacuum permittivity (aka. the "electric constant") is just a way to measure the strength of the electromagnetic interaction. In the best theory that we have, quantum electrodynamics, this role would be fulfilled by the fine structure constant α, which is related to ε0 by a simple formula (i.e., they represent the same thing.) In other words, ε0 (or α) is not a property of free space, it is a property of the electromagnetic field.

The curious thing is that for zero value of the Higgs scalar

it has more potential energy than a non-zero value of the

scalar. This non-zero value is the VEV. This situation is

depicted in the picture above. Then how do we define a vacuum ?

There are two alternatives.

1) Where the value of Higgs field is zero.

2) Where the energy of Higgs field is zero (minimum)

The first choice is true vacuum and second choice is

false vacuum. But universe has chosen to stay in the

false vacuum. Isn't it ironic ?

A VEV of a fermion will break Lorentz invariance, which is a good

space time symmetry. When you minimize inflaton potential it will

naturally pick up nonzero VEV due to couplings with doublet Higgs.

Here I assume that inflaton is a singlet scalar.

Otherwise if inflaton transforms under extra gauge groups, then to

break them you will require a VEV of inflaton.

There isn't any theoretical dilemma. Until 1998, it was thought that neutrinos were massless-so they traveled at the speed of light. However there wasn't any particular reason that forbade neutrinos to be massive, or required them to be massless. Since it was known that their mass is very small, the simplest hypothesis, that was, also, consistent with experiments, until 1998, was that the mass was, in fact, zero.

The absence of right handed neutrinos means that their putative mass terms require a slightly more complicated mechanism (the seesaw mechanism) but that is understood theoretically. There are currently experiments that try to test whether neutrinos could acquire their mass through Yukawa terms or not (whether they are not their own antiparticle, or they are).

Since 1998 it is *known* from the discovery of their flavor oscillations that neutrinos are not massless-therefore they don't travel at the speed of light. However their masses are so small, that their speed is *very* close to the speed of light.

On the other hand, there is a theoretical reason the photon is massless and that is gauge invariance: the unbroken U(1) symmetry of the Standard Model ensures that the photon remains massless-thus, it travels at the speed of light in vacuum.

You can diagonalize M in general by first diagonalizing

M^dagger M and then diagonalizing M M^dagger. These

matrices are hermitian. Let us say that the first one is

diagonalised by a unitary transformation A

A (M^dagger M) A^-1 = diagonal

then you diagonalise M M^dagger by an unitary

transformation B

B (M M^dagger) B^-1 = diagonal

Then the biunitary transformation on M is

A M B^-1 = diagonal -------------> Eq.1

for quark mass matrices,

U_L M U_R^\dagger --> U_L=A and U_R=B

The proof is through making M upper/lower

triangular. You can see numerical recipes

algorithm part and also, many references are there.

This was a very hot topic but about 20-30 years ago. The only result of these searches was a lower limit on the proton lifetime, which was quite discouraging to continue experiments on this subject. Most of these experiments were converted into the dark matter searches. Some theoretical studies ( https://journals.aps.org/prd/abstract/10.1103/PhysRevD.72.095003) of the lepton and baryon number violation were also quite pessimistic concerning a chance to detect such processes at the LHC. So up to my knowledge there are no new developments in this field.

You are absolutely right. Indeed if one uses the most common definition for the spectral index (according e.g. to "The Primordial Density Perturbations" by D. Lyth and A. Liddle) which is given by n-1 = d ln(P(k))/d ln(k), where n is the spectral index an P the spectrum of the curvature perturbations, one gets that P is proportional to k^(n-1) (assuming n = cst.!). Therefore the spectrum is scale invariant for n=1. For non-constant n you have to take into account the running of the spectral index.

Biswajoy,

As I understand, if one assumes that the dark matter is cold (CDM), it's considered to interact only through gravitation. Self-gravitation in CDM-only simulations produces the cuspy-halo problem, which is, I think, most often ignored.

The prior reference, http://en.wikipedia.org/wiki/Cuspy_halo_problem, concludes:

"One approach to solving the cusp-core problem in galactic halos is to consider models that modify the nature of dark matter; theorists have considered warm, fuzzy, self-interacting, and meta-cold dark matter, among other possibilities."

See: http://en.wikipedia.org/wiki/Warm_dark_matter

There was a calculation of s,t,u parameters involving one loop

calculations involving standard model fields. Those could

differentiate between different models of new physics. For example

supersymmetry was preferred over technicolor models.

In that spirit, some calculations should exist, which will tell

us about the chances of discovering superpartners or

other new physics candidates.

Meanwhile I have found some constructions in hep-th/0612021 (and refs therein). Is there more?

Slightly revised answer given on different thread by Dima here on Researchgate https://www.researchgate.net/post/Can_anyone_help_with_Dirac_matrices_choice:

Short answer: The (indefinite) Hermitian form \bar \psi \phi is the invariant Hermitian form, unique up to real factor, defined by the abstract data of a Clifford algebra and an irreducible spinor representation. Here invariant means that the vector space of which the Clifford algebra is build, acts Hermitian.

The \gamma^0 in

\bar\psi \phi = \psi^\dagger \gamma^0 \phi

comes from choosing an orthonormal basis and (skew) Hermitian \gamma matrices (i.e. a Hermitian gamma^0 for the one timelike and skew Hermitian matrices \gamma^i for the space like basis vectors) This then defines an explicit spinor representation and the textbook form above of the invariant Hermitian form.

Long answer

For a real even dimensional vector space V with a non degenerate quadratic form g, consider the abstract Clifford algebra Cl(V,g). It has a unique [1] irreducible spinor representation \Delta. It carries a unique (up to real scalar) _but- _not_ _necessarily_ _positive_ _definite_ Hermitian form h such that the action of a vector in V is Hermitian (see below for a construction). This is the form that physicists write as

\bar\psi\phi = h(\psi, \phi).

If we already have _some_ Hermitian inner product ( , ) on \Delta then we can represent h as

h(\psi, \phi) = (\psi, H\phi)

for some ( , ) hermitian linear map H: \Delta \to \Delta which is determined by

(v\cdot)^* H = H (v\cdot)

where ^* is the hermitian conjugate with respect to ( , ). This also shows why h is unique up to a scalar: if h' is a different invariant form, then the H (with respect to h') commutes with all elements of V, hence commutes with the whole Clifford algebra, hence is a (necessarily real) scalar.

Now how come H is always gamma^0 in physics textbooks?

First physicists choose an orthonormal basis e^a with g(e^a, e^a) = 1 for a = 1 .. p (the time like basis vectors) and g(e^a, e^a) = -1 for the remaining q = n - p (the space like basis vectors). Then they _choose_ a matrix representation on C^{2^n/2} to get "gamma matrices"

\gamma^a = \gamma(e^a)

Having chosen spinors concrete complex column vectors we have available the normal inner product ( , ) = ( )^\dagger ( ), but because the spinor basis defined by the columns is arbitrary (we can think of them as coming from some abstract spinor representation \Delta and then choosing a completely arbitrary basis \psi_1, \psi_2, ...\psi_{2^{n/2}} for \Delta and unlike, the (functorial) tensor representations, the choice of a basis for V does not in any way induce a choice of basis for \Delta ) , it has has, nothing to do with the invariant hermitian form h except that, as above, h can be written as

h(\phi, \psi) = phi^\dagger H \psi

for some Hermitian matrix H which is determined by

\gamma^a^\dagger H = H\gamma^a for i = 1, ... , n (*)

Now we can always choose a matrix representation such that the \gamma^a are Hermitian for the time like and skew Hermitian matrices for the space like basis vectors ((in the usual sense that \gamma^a^\dagger = \pm \gamma^a). Then if p = 1, we see by inspection that H = \gamma^0 is a solution to equation (*). Thus, the \gamma^0 in the textbook form of the invariant form actually comes from choosing gamma matrices that are (skew) Hermitian and having just one time dimension.

So why can we choose the gamma matrices Hermitian or skew Hermitian depending on the sign of g(e^a, e^a)? This is standard but looks suspiciously like what we are trying to prove so lets prove it here. By going to the complexification we can get a new complex "genuinely" orthonormal basis f^1 \cdots f^n with g(f^a, f^b) = \delta^{ab} of V\tensor \C, by judiciously multiplying the basis e^1, ... e^n with factors of i = \sqrt{-1}. Clearly, a matrix representation of Cl(V,g)\tensor \C = Cl(V\tensor \C, g\tensor \C) such that the \gamma(f^a) are Hermitian is the same thing as a representation of Cl(V, g) such that the \gamma(e^a) = \gamma^a are (skew) Hermitian. But since (f^a)^2 = 1 we have (f^a)^{-1} = f^a, so finding a representation with \gamma(f^a) Hermitian is the same thing as finding a representation such that the \gamma(f^a) are unitary. But such a representation is easy to find: just consider the Clifford group G generated by the f^a inside CL(V\tensor \C, g\tensor \C). By the commutation relations

G = \{\pm 1, f^a, f^af^b (a&lt; b), f^af^bf^c (a < b< c), ....\}

is finite and so its representations can be chosen to be unitary.  

I mean the natural units. For masses, in eV/c^2.

electron neutrino: 2^1 eV/c^2

electron: 2^{19} eV/c^2

quark up: 2^{21} eV/c^2

quark down : 2^{22} eV/c^2

all that within experimental error margins

This follows from the construction of unitary (ray) representations of the rotation group in three or more dimensions, where one discovers the condition that 2s+1 must be integer.

Unitary ray representation because we describe spin by Quantum Mechanics.

Note: There is not a similar restriction in two dimensions, where quantum spin in principle may vary continuously (cf. the theory of anyons).

Dear Robert

Even if Higgs boson is related firmly to special relativity but this can be considered as an approximation to the more general case which is working with curved space time. This is logical because Higgs boson worked with mass and mass is related to curvature of space time. Isn't it?

SR deals just with Galilean systems, those moving relative to each other at a constant speed with no rotation.

The transformation rules between these systems follow the Lorentz equations.

If the frames "are rotated at fixed angles" the Lorentz transformation will include this.

If the frames "are in rotation changing their angles" then SR and the Lorentz transforms will no longer hold valid and General Relativity dealing with accelerated systems must be used.

You are not reporting a result with a smaller error than the LC. If your least count is 0.1, then you measure a value of 1, then the real value could be anywhere between 0.95 and 1.05, otherwise your apparatus will measure 0.9 or 1.1. The apparatus is effectively using the round function (as opposed to the floor or ceiling functions).

You can measure a value of 0, which really means a value between -0.05 and +0.05, but there is no physical meaning. If you takes lots of measurements of the same quantity then the error will decrease by a factor of 1 / sqrt( n )

Note that it is the square of the orbital angular momentum that is zero (quantum-mechanically) in the s-state. The orbital angular momentum itself has strong fluctuations and it is zero only on average. If you want to imagine the s-state classically, then think that the electron is orbitting around the nucleus, but this orbiting does not have a prefered trajectory, i.e. it goes in all directions around the nucleus. In quantum mechanics such parallel "events" are allowed due to the principle of superposition.

Brehmsstrahlung radiation is not pure photon event, it portraits the interaction of accelerated (decelerated) charged particles and photons. The point is, the spontaneous symmetry breaking (SS) accomplish the re-summation of multiple processes that lead to an effective rest mass for some particles, besides providing a well defined vacuum state. And the question is, it the setting of the SSB can leave for itself phenomenological traces beyond the rest masses and if the SSB can be considered an "event" and not just the change of reference. If we picture the gradual setting of a rest mass (due to the setting of an SSB "event") for a charged particle then a Brehmsstrahlung effect is expected. The question is if such a production of photons in an still opaque universe has the chance to leave observable effects.