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We did not identify the black hole in full detail yet. Does  it has an event horizon or apparent horizon. We are trying to modify our theory to resolve the problem of singularity. Is the black hole without singularity still be a black hole? What is the main character of the black hole, the singularity or the event horizon.
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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
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the spin of Δ(1232) is 3/2 ,but its decay product,like nuclear is 1/2,pion is 0, so the spin isn't consistent before and after decay reaction .Is some of the spin angular momentun translate to orbital angular momentum?So what is the trajectory of a free particle that carries orbital angular momentum?
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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.
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Observational data indicates that the cosmological constant has a positive value, resulting in a de Sitter spacetime. In loop quantum gravity, the IR divergences in the Ponzano-Regge model can be made to disappear through q-deforming SU(2) to SUq(2). The classical limit of this Turaev-Viro model is GR with positive cosmological constant.
On the other hand, anti de Sitter spacetime has a number of (potentially) desirable properties as well, for example the AdS/CFT correspondence. This correspondence is used in Light Front holographic QCD and seems to offer some insights into confinement as well as meson and hadron spectroscopy (arxiv:1407.8131). AdS also admits a positive energy operator making it more suitable for a particle interpretation. There has been some work (mostly by Flato and Fronsdal) describing photons and leptons as composites of singleton representations that live in an AdS spacetime.
Would it be possible and sensible to describe spacetime as being anti de Sitter at very small scales and de Sitter at cosmological scales? Perhaps this would be possible through a bi-metric model?
To me it seems that such a model would offer the best of both worlds (LQG without IR divergences, agreement with cosmological observations, AdS/CFT, singleton representations). I am just not sure if such a model would be possible and if it even makes sense to think along these lines. I would very much value any comments people may have.
Thanks in advance!
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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.
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You have a well-insulated box filled with sodium vapor. The box has been left for a long time. Suppose you punch a small hole into the box and observe the energy distribution around the strong yellow sodium lines at 5896 A and 5890 A. What would the energy distribution look like? Would you see spectral lines? If so, would you see absorption or emission lines?
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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.
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What is the parameter or mechanism that needs to be considered in order to design a spacecraft that could bend and stretch the fabric of space-time?
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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.
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The Nobel Prize in Physics 1965 was awarded jointly to Sin-Itiro Tomonaga, Julian Schwinger and Richard P. Feynman "for their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles".
QED rests on the idea that charged particles (e.g., electrons and positrons) interact by emitting and absorbing photons, the particles that transmit electromagnetic forces. These photons are “virtual”; that is, they cannot be seen or detected in any way because their existence violates the conservation of energy and momentum.
In quantum electrodynamics (QED) a charged particle emits exchange force particles continuously. This process has no effect on the properties of a charged particle such as its mass and charge. How is it describable?
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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?
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It is well known that Bohr model is not totally right. But I recently discovered a very curious inconsistency (if I am right) which I haven't seen explained anywhere.
The first postulate of Bohr theory is that the Orbital momentum of the electron is quantized L=mvr=nh  (where h  means the Dirac constant). This means that if there is a transition between level n=5  to n=1  (Balmer series) the orbital momentum changes by 4h  !!! Based on this rule and his second postulate Bohr finds the right energy for this transition (and all others as well). But this transition is a release of just one photon and a photon has spin 1h  . It can add to L as (h,0,−h)  . So it can change the orbital momentum with 1,0  or −1  and not by 4.  I'm very surprised to make such conclusion.
Am I wrong here?
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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
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By the 1950s, when Yang–Mills theory, also known as non-abelian gauge
theory, was discovered, it was already known that Quantum Electrodynamics (QED) gives an extremely accurate account of electromagnetic fields and forces. So it was natural to inquire whether non-abelian gauge theory described other forces in nature, notably the weak force and the strong or nuclear force. The massless nature of classical Yang–Mills waves was a
serious obstacle to applying Yang–Mills theory to the other forces, for the weak and nuclear forces are short range and many of the particles are massive. Hence these phenomena did not appear to be associated with long-range fields describing massless particles. In the 1960s and 1970s, physicists overcame these obstacles to the physical interpretation of non-abelian gauge theory. In the case of the weak force, this was accomplished by the Glashow–Salam– Weinberg electroweak theory. By elaborating the theory with an additional “Higgs field,” one avoided the massless nature of classical Yang–Mills waves. The solution to the problem of massless Yang–Mills fields for the strong interactions has a completely different nature. That
solution did not come from adding fields to Yang–Mills theory, but by discovering a remarkable property of the quantum Yang–Mills theory itself, called “asymptotic freedom”.Asymptotic freedom, together with other experimental and theoretical discoveries made in the 1960s and 1970s involving the symmetries and high-energy behaviour of the strong
interactions, made it possible to describe the nuclear force by a non-abelian gauge theory in which the gauge group is G = SU(3). The non-abelian gauge theory of the strong force is called Quantum Chromodynamics (QCD). But classical non-abelian gauge theory is very different from the observed world of strong interactions; for QCD to describe the strong force successfully, it must have at the quantum level the mass-gap and related color confinement
properties. Both experiment—since QCD has numerous successes in confrontation with experiment—and computer simulations carried out since the late 1970s, have given strong encouragement that QCD does have the properties of mass-gap and color confinement cited above. But they are not fully understood theoretically. In the attached link, http://dx.doi.org/10.13140/RG.2.1.1637.3205 the theoretical understanding of mass-gap and related color confinement property have been provided during mathematical calculation of the gluon emission cross section for QCD process by taking over the corresponding results from closely related aforesaid QED process under the assumption that color interactions in perturbative sector are “a copy of electromagnetic interactions.
As such, the direct mathematical calculation for QCD process has been
avoided because the presence of point-like Dirac particles inside hadrons through Bjorken scaling and the carriage of a substantial portion of proton’s momentum by neutral partons, as revealed by the ‘asymptotic freedom’ based analysis of the data on deep inelastic scattering of leptons by nucleons, do not constitute direct evidence that the aforesaid Dirac particles and neutral partons can be identified with quarks and gluons respectively for making QCD the correct physical theory.
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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.
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WR mass is constrained from KL-KS mass differences in LR model.What does it mean and from where  it comes? A detailed calculation will be helpful.
LR - Left Right
W_R - right handed W boson
KL,Ks - K-Long and K-short,two neutral kaon state
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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.
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When we compare various cosmological determinations of neutrinos masses, Primack et al, 4.8 eV (1994); Allen et al, 0.6±0.3 eV (2003); Battye et al, 0.3±0.1 eV (2014) and finally Palanque-Delbrouille et al, 0.02±0.06 eV (2015), we see that the results have kept changing in the course of the time; moreover, they contradict each other.
However, the most recent one, appeared after Planck data, is quite impressive and agrees with the conventional picture of the neutrino mass spectrum, expected to obey a hierarchical pattern, and that implies the lower bound of 0.05 eV.
Evidently, this result is of great importance for the search of neutrino mass in laboratory. Do you consider the new result from cosmology reliable? Which systematic effects could threaten it? And, assuming it is correct, how could we test it in laboratories?
Reference to the new work:
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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.
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We do not know whether the neutrino is a Dirac particle or a Majorana particle. If neutrino turns out to be a Majorana particle then two additional phases are to be introduced in the 3x3 lepton flavor mixing matrix. Why these phases cannot be removed by field redefinitions. In the two generation case, we know that in the CKM matrix there is no CP violating Dirac phase. Similarly, will the Majorana phases disappear in the two generation case, or, will they continue to be non-zero even in the 2x2 mixing case. In which experiments will they show up.
References:
  1. J. Schechter and J. W. F. Valle, Phys. Rev. D 23, 1666 (1981)
  2. J. Schechter and J. W. F. Valle, Phys. Rev. D 22, 2227 (1980)
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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
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I have started to study the AdS/CFT correspondence by reading Minahan's introductory review (arXiv:1012.3983). The first equation of that review is the expression for the leading contribution to the $\beta$-function:
$$
\beta(g)=-{g^3\over16\pi^2}\left({11\over3}N-{1\over6}\sum_iC_i-{1\over3}\sum_j\tilde C_j\right),
$$
where $C_i$ are quadratic Casimirs due to bosons and $\tidle C_j$ are those due to fermions. The author cites Gross and Wilczek (1973) as a source of the formula. But there it looks a bit differently:
$$
\beta(g)=-{g^3\over16\pi^2}\left({11\over3}N-{4\over3}\sum T_j\right),
$$
where $T_j={d(R_j)\over d(G)}\tilde C_j$, $d(R)$ and $d(G)$ are dimensions of the representation and of the group.
Forget about the boson contribution (Gross and Wilczek were not interested in it). But the fermion contribution contains there the factor $-4/3\times{d(R_j)\over d(G)}$ instead of $-1/3$ in Minahan's article. The factor 2 is related to the fact that Gross and Wilczek considered Dirac fermions, while Minahan considers the Weyl fermion. Ok. But we are left with the extra $2{d(R_j)\over d(G)}$ factor, which I am unable to cancel.
Could anybody explain me this factor? May it be related somehow to supersymmetry?
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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).
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Researchers in the fields of cosmology and gravitation, which are also expert at high energy physics .
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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.  
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A fuller statement of the question:
What consequences arise (regarding nature or theories) if some of the 10 Poincare-group generators do not correlate with behavior of Z and W bosons, and/or (hypothetical) gravitons?
Background:
I may have developed math sufficient to provide an analog for elementary particles to the periodic table for elements.  To the extent the resulting catalog of particles pertains to nature, it provides (for all 17 known ordinary-matter particles, some yet-to-be-found ordinary-matter particles, dark-matter particles, dark-energy particles, gravitons, and some other zero-mass bosons) spins, some information about interactions, some masses, numbers of generations (for fermions), and relevant numbers of generators related to the Poincare group (and special relativity).
Findings:
  • The following particles would correlate with all 10 generators of the Poincare group: leptons, photons, the Higgs boson, and composite (yes, not elementary) particles such as pions and protons.
  • The following particles world correlate with 7 generators of the Poincare group: Z boson, W bosons, graviton, and some other zero-mass bosons.
  • The following particles would correlate with symmetries other than those discussed above: quarks, gluons, and some other particles.
Parallel question:
To what extent would the above findings violate known experimental or observational data?
Reference:
"Theory of Particles plus the Cosmos," especially table 2.8.2 in section 2.8.  (See attachment.)
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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
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Kuhn says leading physicists accepted Newton's theory of gravitation before astronomical measurements were accurate enough to decide the issue ["Structure of Scientific Revolutions" 1962]. Other than this aged example, is there any case in which physicists accepted a new or modified basic theory of physics based on a mathematical derivation from well-accepted theories, before direct empirical evidence was available? The Higgs boson and cosmic inflation have something of this flavor: these theories had substantial credibility before empirical evidence was available because they explained phenomena that were left unexplained by existing theories, but they were not fully accepted in the canon of physics.
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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.
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Domain walls or boundaries are expected to form when a discrete symmetry is broken spontaneously.
REF:
Y. B. Zeldovich, I. Y. Kobzarev and L. B. Okun, Zh. Eksp. Teor. Fiz. 67 (1974) 3
[Sov. Phys. JETP 40 (1974) 1]; T. W. B. Kibble, J. Phys. A9, 1387 (1976); A. Vilenkin, Phys. Rept. 121 (1985) 263
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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
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The algebra of angular momentum operators in QM are very general and apply equally well to orbital as well as spin angular momentum. However, when we are through with the algebra we get 0,1/2,1,3/2,2,5/2,3 ..... etc as the possible ang. mom. values in units of h-bar. We have particles of both types of spin-- scalars, electrons, photons, baryons, gravitons etc. But why don't we have systems with 1/2, 3/2, 5/2 (in h-bar units) of orbital angular momentum?
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"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.)
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The gravitational and coulomb potentials are identical, particularly in the weak gravity limit. The Coulomb interaction remains linear in very high field intensities, such as electrons in nuclear fields. However gravitational field interaction in strong gravity limit (but much less than the strength of nuclear field) is highly non linear. The perihelion of orbit of Mercury in the gravitational field of the Sun is an example of non linearity of gravitational interaction. On the other hand no such phenomenon has been observed in this so called electron's orbits around nucleus.     
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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.
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I want to know whether Lorentz symmetry is conserved for all the velocity ranges or not?
Is the Lorentz invariance completely related to Lorentz symmetry; i.e. if Lorentz symmetry conserved then Lorentz invariance is also conserved or there are certain conditions where the Lorentz invariance conserved while Lorentz symmetry is not? what are they if there are such conditions.
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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.
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Rapidity distribution.
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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. 
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There are many physical problems in which the acceleration causes phenomena of interest. For example, the radiation of accelerated charge. This phenomena must be, obviously. of quantum nature, but, the available descriptions start from classic principles. On the other hand, both in Relativity as in quantum physics, the accelerated systems are strongly "hard of to study". The question goes to inquiry about the state of our mathematical tools for the description of accelerated systems in quantum mechanics.
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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.
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When using propagators and potentials (like the Yukawa one), time is not explicit. Should we use different forms of the propagators and the potentials in a 4d spacetime with time being a 'regular' spacedimension (except for its irreversibility)? Does the incompleteness of particle physics theories come from the fact that time is always treated separately?
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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.
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The Higgs boson or Higgs particle is an elementary particle initially theorised in 1964,whose discovery was announced at CERN on 4 July 2012. The discovery confirms the existence of the Higgs field, which is pivotal to the Standard Model and other theories within particle physics. It would explain why some fundamental particles have mass when the symmetries controlling their interactions should require them to be massless, and why the weak force has a much shorter range than the electromagnetic force.
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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.
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The question has following implications
1) What does the term anisotropy mean ?
2) Because universe is homogeneous and isotropic in general
how does one expect anisotropies ?
3) Is it a purely quantum effect ? or is it possible to have
classical explanations of this phenomenon ?
4) Is there a definite pattern in the anisotropy ? If so
how to explain that pattern ?
5) What are theoretical implications for inflationary theories ?
6) Does anisotropies give any indications on the nature
of dark matter. For example is DM cold or warm ?
I am adding a figure; source is
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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.)
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How can I prove that the Gribov problem is related to quark confinement? We know in QCD, perturbation theory can not be applied in infrared region, so does this have anything to do with Gribov copies? If we restrict the integration region in the fundamental modular region, can IR singularity be removed?
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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).
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Permittivity of free space
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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.
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Vacuum expectation value (VEV) of the Higgs scalar is responsible for fermion
masses and also masses of the W+ W- and Z gauge bosons. Does it mean
that the Higgs particle can extract energy out of vacuum and convert it to a
new form in which gauge bosons and fermions are massive ? For quarks
one can also have QCD correction to masses which are
unrelated to Higgs VEV
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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 ?
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Inflaton is the scalar field that causes inflation. Why it is assumed that it is a scalar field with very weak interaction?
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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.
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The relativistic equations of energy and momentum forbid the possibility that anybody with nonzero rest mass reaches the speed of light because both quantities tend to infinity. In the case of the photon and neutrino, the problem is saved annulling their masses, so that the equations lead to an indetermination, and opens thus the ability to assign the value E = pc for both quantities. But on the other hand, the measurements indicate that neutrinos have nonzero mass. The question is how this theoretical dilemma is resolved.
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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.
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If I understand correctly, then any matrix can be diagonalized with real and +ve diagonal entries via a bi-unitary transformation. My question is, given a matrix, are the unitary matrices unique?? Is there any common textbook that provides a simple proof of this fact?
The next part of my question involves the quark sector of the Standard Model. In the gauge basis, the "mass matrix" of the quarks is a general complex one. We can then rotate the left and right handed fields separately to go to the mass basis. Now, my problem is that they are called "mass eigenstates" and the masses are called "eigenvalues". But, the Yukawa matrix in the original gauge basis is an arbitrary complex one which does not necessarily have "eigenvalues" in the usual sense of the term. So, is there any way to understand the meaning of the term "mass eigenstate" in this context ?
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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.
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Proton lifetime is believed to be comparable to the lifetime of the
universe. What is the most recent experimental numbers of
proton lifetime ? What are the unified models which are ruled
out by the latest data of proton lifetime ?
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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.
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If density perturbations are scale invariant then the dependence should be more like k^0, where k is the wave number. Then why do we define that scale invariant perturbations has spectral index 1. What is the advantage of this choice?
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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.
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There are several small satellite galaxies of milky way. Namely, Draco, Sextans, Carina, Fornax and others. What do we know about how dark matter is distributed in these satellites? Do we know about the amount of dark matter contained in these galaxies?
Any technical or non-technical information is welcome.
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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."
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Unless there is a symmetry reason to protect the Higgs mass near the
electroweak scale, one loop effects will give large corrections. Is it
super-symmetry or is it something else ? Or is it some extra dimensional
mechanism which is working ? Or is it purely fine tuning of parameters ?
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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.
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Please advise.
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Meanwhile I have found some constructions in hep-th/0612021 (and refs therein). Is there more?
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We can extract \sqrt{\gamma^0} but not L^\dagger L = \gamma^0, hence the \gamma^0 is a slap-on over the (covariant) operator, not over the wave-function. What does this represent physically? Is there a C (chg. conj.) operator that exists abstractly (answer: no)?
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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.  
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Their masses are powers of 2 in the Planck length basis. Do you have an explanation for that? Calculations must be done in the (x,y,z,t) space.
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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
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The spin of particles is a rational number s=p/q, where the numerator p is a non negative integer and the denominator q is equal to two. I want to know if there is an explanation why other values of the integer q are forbidden. What is the origin of the step equal to 1/2 of the Planck constan h?
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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).
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The Higgs boson interaction gives mass to matters according to standard model. Does that represent the reason of space time curvature in general relativity?
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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?
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Special relativity (SR) is valid only in Inertial frames. Lorentz transformations (LT) includes both rotations as well as boosts. But rotations gives accelerated frames so how can we connect these SR and LT? In other words, how does this "rotation" give Lorentz Invariance?
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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.
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Suppose Least Count (LC) for some apparatus say 0.1 . But often we used to write 0.1/2 as least count. How this factor "1/2" come into the picture of LC ? We cannot able to measure anything beyond LC by definition. Then why this "1/2" ? Off topic but if you know the answer, please share so that I can understand it clearly...
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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 )
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For example in a hydrogen atom, the electron is orbitting the nucleus which implies the electron should have some angular momentum, but we say in the ground state (n=1) the angular momentum (l) is zero. Is there any contradiction here..? Can anyone explain this in detail..?
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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.
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I know that the symmetry breaking event happened when the universe was opaque, nevertheless the balance between the population of photons and other particles might change due to the expected deceleration processes. The corresponding pressures due to such populations might change, so I wonder if there is any chance that there is some pattern in the evolution of the universe that might reveal extra features of the symmetry-breaking event. One could naively expect that it it is not just a change of reference system since the dynamics are different before and after the event. Is there any chance of tracing a contribution to the profile of the spectrum of the cosmic background radiation?
I know there are interesting questions about the problem of propagating such a symmetry breaking event, domain walls, etc.
I wonder also if the negative mass term (quadratic coupling) of the Higgs would give to it some "special dynamics" before the event, and what would be the classical gravitation interactions for such special dynamical objects. I just wonder if there might be some sort of echoes of the symmetry breaking mechanism (beyond the acquisition of rest-mass for some particles).
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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.