High Energy Physics - Science topic

It basically goes from a few Hz (for certain axion/ dark-matter experiments ) over the Khz to Mhz range (NMR based axion search"CASPER") with a big activity now between 100 Mhz and about 50 Ghz (all sort of cavity based axions search..Primakoff effect) and then lots of infrared, visible to UV PM (photomultipliers and PM like devices (solid state) devices e.g. for scintillator readout

Thanks for the articles to help me understand the problem. It seems to me that the change in the diameter of the drops from voltage and current can occur as follows. With an increase in the arc power (product of current and voltage), the metal temperature rises. Surface tension decreases with increasing temperature as a result of the thermocapillary effect (dependence of surface tension on temperature). You can write down the droplet separation condition, process the experiments that you indicated, and get a real change in surface tension with increasing current. Perhaps it is possible to get the drop-off frequency. In principle, this could be the material for a new and possibly joint article. I will be glad to be of service.

le 18 novembre 2020

Cher André,

Je vous remercie beaucoup pour les matériaux en ce qui concerne votre nouveau livre qui est intitulé Introduction à l’électromagnétisme selon Maxwell (Mécanique électromagnétique), par André Michaud. Félicitations pour la publication de cet oeuvre vraiment magnifique chez Generis Publishing!

Je viens de lire la table de matières, qui est remarquablement pleine de sujets très intéressants, et le tableau est à la fois assez profond, et en même temps, clairement présenté et certainement bien organisé, comme d’habitude.

Bien que mon français ne soit aussi fort qu’auparavant, quand j’ai été en train d’enseigner plusieurs cours consacrés à l’enseignement de la littérature française à l’université d’Indiana et à l’université de Washington, et aussi un tout petit peu au Centre Méditerranéen à Nice, et j’avais l’habitude de penser en français tout le temps, néanmoins, il me semble que c’est plus facile pour moi de lire les articles scientifiques et bien recherchés, surtout comme les vôtres, qui sont tellement bien écrits en français plutôt qu’en anglais. Je ne sais pas la raison. C’est peut-être parce que j’ai suivi un bon nombre de cours dans les sciences, il y a longtemps, bien sûr, et d’ailleurs, j’ai enseigné de temps en temps à l’université un cours de traduction de textes en arts et sciences de français à anglais intitulé “Reading Comprehension in the Arts and Sciences”.

Merci bien de m’envoyé cet excellent travail purement scientifique! Quant à moi, je viens de recevoir des nouvelles de mon article à publier dans le livre sur l’intelligence artificielle en Juin 2021 et je suis contente.

Avec mes meilleurs salutations, Nancy

Schwinger discussed the electromagnetic mass of electron in his paper in 1983:

Note, this was written by the Author - Schwinger, who got Nobel price for QED theory containing infinities and renormalization of mass + charge of electron.

At present, Standard model assumes all the mass of the electron comes from its Yukawa coupling to the Higgs field:

Hi, if I understood your question currently - you want to create a muon beam that doesn't have a point source but multiple point sources such that the generation area resemble a rectangle? - if that is the case, I suggest two things - look into using CRY (https://nuclear.llnl.gov/simulation/doc_cry_v1.7/cry.pdf) to generate the initial muon flux and then in the PrimaryGeneratorAction.cc file create a nested for loop (2 loops) to create an array of such point sources that would effectively create the rectangular source that you need.

Hints:

1) Define a particle Gun:

% particleGun = new G4ParticleGun();

2) Define a generation point and angle:

% particleGun->SetParticlePosition(G4ThreeVector(x, y, z));

% particleGun->SetParticleMomentumDirection(G4ThreeVector(( xu,yu,zu ))

3) Loop over x and y points to create the rectangle

I think both of you have already been in the right track. It seems that the only reason magnetic monopole evaded detection was because of its weak strength. It requires large number of collection of neutrons and the earth is the perfect case to test it. Gauss law for magnetic monopole will be exactly the same as for the electric charge.

Now the only broken symmetry is that there don't seem to exist enough of opposite polarity magnetic monopoles the same number as the north magnetic monopole that we have. This makes me to speculate the existence of the perfectly organized antimatter universe where south magnetic monopole is abundant but north magnetic Monopole is rare.

Best regards,

Eue Jeong

Very good the coment of prof Radu A.Vasilache. sure, about GW laser the problems change.

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 Sumit,

I think yes it is there. For reference I am quoting site. Excellent approached was forwarded to take intense study in USA.

Please go through the article site given below. Some of the points I am highlighting for your concern. This may be little helpful to you.

Particularly inside the giant planets of our solar system, several chemical processes are predicted to significantly influence the evolution and internal structure of these celestial bodies. One famous example is the transition from molecular hydrogen to metallic hydrogen, which may also be accompanied by hydrogen-helium de-mixing and subsequent helium precipitation inside Saturn. States of matter constitute the deep interiors of most planets in our solar system3 and a steadily increasing number of extrasolar planets.

Some experimental investigation- This work was performed at the Matter at Extreme Conditions (MEC) instrument of LCLS, supported by the U.S. Department of Energy Office of Science, which provided for structural and chemical characterization.

The high-pressure and high-temperature environment may also result in chemical activity: methane is predicted to first dissociate and form polymeric hydrocarbon chains before deeper towards the planet interior core, a full species separation into metallic hydrogen and carbon in the form of diamond may occur. These diamond particles have a higher density than the surrounding ice fluid, and thus, the isolated carbon will precipitate towards the rocky core. Depending on the temperature at the boundary of the rocky core and the ice layer, either a layer of solid diamond or liquid carbon will form. Another possible precipitation process inside Neptune or Uranus may be the formation of ammonia hemihydrate (H2O)(NH3)2 compounds that are predicted to remain stable up to 500 GPa

Solid samples of hydrocarbons are convenient initial materials to mimic the ice mixtures of icy giant planets in the laboratory. While methane is present in the atmospheres of these planets, longer hydrocarbon chains are expected to form in the ice layers. The samples are compressed and heated using the pulsed high-energy drive laser available at MEC (15 J–32 J pulse energy in 10 ns pulses focused to spot sizes of 150 μm–250 μm in diameter). Within a few picoseconds, the target surface is transferred into a rapidly expanding plasma state, which in turn drives a shock-compression wave into the cold material behind the ablation front. In order to mimic planetary interiors, the sample can be compressed in two stages. This reduces the entropy increase in the overall compression process and thus the induced heat. For example, polystyrene will reach temperatures much higher than inside most planetary interiors when compressing to pressures above 100 GPa with a single shock. In our experiment, we used polystyrene samples with a thickness of 83.4 μm.

Finally, as the free hydrogen created by the carbon-hydrogen separation around 150 GPa and 5000 K is expected to be metallic, the experimental platform described may also provide opportunities for further studies of this exotic state of matter that is thought to shape the magnetic fields of giant planets.

Hope it work out for you.

Ashish

If by ``quantum mechanics" is meant the non-relativistic quantum dynamics of a point particle, the minimum symmetry is time translation invariance, which implies energy conservation and the definition of the Hamiltonian.

So far, the Supersymmetry has not been very succsesful in physics. However, mathematically, it is a very beautiful subject, which may explain why it stood so long with theoretical physics.

It is a very interesting and gut issue.

Basically nobody really dont know what did happen in this periode .

All theories are based upon our knowledge to particle physics and is our best estimate and guess . It means we have to be very careful coming up with an exact theory and banish new way of thinking.

Kurt Wraae

Exactly, if you applied the z-score normalization, then just calculate the inverse transformation using your HHbbb statistics (multiplying predictions by the standard deviation and then adding the mean).

I could follow your schematic when i download it.

It is okay and it will suction properly from the basic point of view. But i have only one question why do you not connect 220 ohm in series with the gate of the right transistor to make the circuit symmetrical for the the positive and negative half cycles of the damped oscillations.

Connecting the two gates together is not allowed in your circuit as the two gates must have different potentials. From the beginning it is rejected.

Could you show me the current in the circuit during the discharge process?

In summary this circuit can work well from the conceptual point of view.

Best wishes

@Christian Baumgarten  I think he ask if electron can round in different direction like stop the earth and round them to the other side ;)

Dear Eder problem is that spin Has nothing to do with round because is not a ball !!!

best  

Basabendu, take  φ₁⁰ and φ₂⁰ which are two neutral members of  φ₁ and φ₂. They will invariably mix with each other at electroweak scale because there is no other quantum number which will distinguish between them. Then form combinations cos α φ₁⁰+ sin α φ₂⁰  and  -sin α φ₁⁰ + cos α φ₂⁰. You will get an expression for the mixing angle α in terms of model parameters from the minimization conditions of Higgs potential.

In the Higgs potential, after substituting appropriate VEVs (for simplicity take them real) of two Higgs doublets, among other terms, you should obtain, (φ₁⁰)², (φ₂⁰)² as well as φ₁⁰φ₂⁰ terms with appropriate coefficients, which will form a 2x2 mass matrix in (φ₁⁰, φ₂⁰) basis. Upon diagonalization this matrix yields the mixing angle α in terms of model parameters. New basis obtained after diagonalization is actually the mass basis which you are seeking.

To make a long story short: It is known that in (relativistic) quantum field theory models of fields obeying parastatistics can be reformulated in terms of fields carrying ordinary statistics which transform as tensors under some global gauge group, the important point being that the local observables (gauge invariant operators) coincide in both formulations. Thus the notion of parastatistics  does not introduce "new physics" and can be avoided by the usage of (non-abelian) symmetry groups.  For example, a parafermion of order 2 can equivalently (with regard to the observable content)  be described as an ordinary fermion with internal symmetry group SU(2).  

For an introduction into this topic and further references see Chapter IV.1 in the book of   R. Haag   "Local Quantum Physics.  Fields, Particles, Algebras"  Springer  1992

Dear Gaurav,

this is a very model-dependent question. In particular, you have not specified the representation (i.e. the charges) of the scalars you are looking for.

Example collider limits can be found on pdgLive:

However, there can be many other limits e.g. from consistency arguments on the scalar potential or from LFV or similar.

Thus, I am afraid, there is no simple answer in case you were asking for only two numbers.

Best regards,

Alexander

Of course it can. The width is controlled by the ways the particle interacts with others. And that's one way to detect, indirectly, the presence of unknown particles. 

However it's the other way around: the higher the value of the width in units of energy, the shorter the decay time is, so the faster the particle decays. 

For the Kerr (-Newman) black holes this is given by the Komar integral belonging to the Killing field, associated to the SO(2) isometry group. For details, see e.g. my GR- book (Springer 2013), eq. (8.187).

The vev is the ``distance'' of the minimum of the Higgs potential from the origin. So in the 2D plot it would be the radius of the circle, where the potential attained its minimum value. 

The physical meaning is a bit more subtle. 

In a representation independent way, charge conjugation matrix can be defined as, C^-1γ_μC=-γ_μ^T. If you plug in gamma matrices in Majorana representation (which is purely imaginary) in this basic definition you should get explicit form of C matrix. A charge conjugated spinor should reduce to ψ^c=-iγ₂ψ*=ψ.

Here C is indeed an operator which acts on Dirac spinors (four component objects) and which can be represented by a 4x4 matrix. C does not commute with electric charge operator (or any other charge such as B, L,..). It is therefore not possible to have a simultaneous eigenstate of charge conjugation operator and electric charge operator. States without having any charges can be eigenstates of C, with eigenvalues plus or minus unity, known also as C parity.

Now left handed Majorana mass is ν̅_Lν_L^c and relabeling L→R yields right handed Majorana mass term. Let us denote these by m_L and m_R and the Dirac mass as m_D, then, m_ν= m_L + m²_D / m_R. In case you are studying a three generation case then replace m_L, m_R, m_D by 3x3 complex matrices written in generation space and m²_D by m_D^†m_D.

to reconsider is that measuring/observation influences the particles as well as estimating probability: by squaring the wave amplitude; for we could consider the inverse, i.e. the square root to realize that a particle cannot be located in two different places simultaneously (square root assigns to one value: two values: +/-).

Rs^3 4/3Pi is a measure of its volume as seen by an outside observer, which is the volume of a sphere in Euclidean space of radius Rs. Christodoulou and Rovelli wrote about the "largest volume" that can be bounded by the event horizon. See arXiv:1411.2854 [gr-qc]. Even though a Schwarzschild black hole looks the same forever to an outside observer, its volume actually gets larger with time. However, there is no unique volume that one can assign to a black hole because 3-volumes depend on the choice of spacelike hypersurfaces. The size of a BH is related to the horizon radius but its volume is related to length contraction and infinite curvature, therefore the volume is zero in Riemann sense. However, the mass of BH does not reside inside its radius, but is concentrated in the singularity with infinity density and zero volume.The coordinate radius and the proper radius would be zero. This is a prediction of GR as an incomplete theory, defining a singularity as a point (!) of infinite density in space. At the same time, a singularity appears as a consequence of a geodesically incomplete spacetime, therefore it is not a point or set of points in spacetime, The dimension or volume of a singularity does not make sense without a theory of Quantum Gravity.

 Nice comment by Mr. Shashikant Phatak. Thank you. But I want to add something that the pair production mechanism you have mentioned is high energy gamma photon materializes to particle-antiparticle pairs in the presence of a third body. The third mainly some high Z atomic nucleus is required because of the 4-momentum. 

But in the process of Schwinger mechanism the entire mechanism is different. Here the fermionic vacuum state gets polarize in the presence of the strong external electric field. So in that context the vacuum persistence probability is not unity between initial and final state.  One can have, this vacuum persistence probability <0|0>|^2=exp{-2S_eff/h{bar}}. This effective action has imaginary part due the vacuum polarization which leads to particle generation.

Hi Ming,

You can contact the authors of the code from http://www.pulsar.nl/gpt/

You need to pay for the license.

Oznur

Nano-structures, Superfluids and superconductors

Dear Newton,

okay, now I understand the question properly... so let's hope I can use this understanding to now provide you with a satisfactory answer.

Both, even and odd CP states, are trivial, in the sense that CP is not violated. However, this holds for the *individual* neutrino mass eigenstates, whereas the parameter delta is kind of an "overall" CP-violation parameter that combines information from all three generations.

For example, we might be in a situation where the first two neutrino mass eigenstates are odd under CP, whereas the third one is even. Thus, when applying a CP transformation, we would have the action \nu_{1,2} -> -\nu_{1,2} whereas \nu_3 -> \nu_3. However, one can rotate away all unphysical phases and the only phase that remains is \delta (in that sense it does contain information from all three generations). From my understanding, in the above case, we should after re-phasing obtain \delta=0 (even though the individual CP-phases of \nu_{1,2} are non-zero, but nevertheless trivial). This would also hold if all three mass eigenstates were even, or for any other combination of *only* even and odd. This you can easily try when playing around with a few example matrices (e.g. use the MPT package and its documentation).

In that case, we would see *no* difference in any physics of neutrinos compared to antineutrinos. E.g. the oscillation probabilities for neutrinos experience a change \delta -> -\delta when going from neutrinos to antineutrinos (see e.g. Eqs. (23) and (35) - (39) in hep-ph/0402175). Only if something non-trivial is going on within at least some of the generations, this will materialise in actual CP violation in an experiment.

Best regards,

Alexander

Dear Niels

the quantum oscillator is at the basis of any physical structure as that of the field. I have found a sub structure in the quantum oscillator  that might help us know the elementary particles and their physical behavior. I think further study may well explain issues that are similar to those outlined by you.

Yes, the Cauchy-Riemann condition is true for all analytic real valued functions. In which case they can be used to prove that the class of analytic real valued functions consists of the real constants.

But the Cauchy-Riemann conditions does not hold for arbitrary functions of two variables, regardless of they are real-, imaginary-, or complex-valued. 

Xrays and gamma rays are nothing but photons of different energies. X rays are emitted by atoms when electrons jump from higher to lower energy states. Gamma rays, on the other hand are emitted by nuclei. Using the equation E=hν we see that higher energy photons have higher frequencies and hence smaller wavelengths. Roughly speaking  X rays have 10^-8 > λ > 10^-12  meters and gamma rays have 10^-10 > λ > 10^-14 meters. As you have noticed, these ranges do have an overlap. There is no deep physical reason for the fact that the wavelength ranges overlap. It is a matter of nomenclature.

Thank you for your question about the LHC. You certainly have some misunderstandings, so I will try to clear them up:

Thank you again for your question.

The speed of light is defined to be 299 792 458 m/s.

* Please (i) calculate the energy E required to accelerate a mass of 1 kg to the speed of 299 792 457.99 m/s, and (ii) calculate how much mass M at rest you can create from that energy (by use of the formula M=E/c²).

* Estimate (i) the the total energy E_sun released by the sun in one year, (ii) the mass M_sun you can create from that energy, and (iii) the velocity v obtained by an electron if all that energy was used to accelerate it (assuming 100% efficiency, including no radiative losses).

* Estimate (i) the total energy within the "visible" part of the universe, and (ii) the velocity an electron would obtain if all that energy was used to accelerate it.

* Find the largest double precision floating point number which can be represented in your computer, and multiply the energy of the universe with that number. To which velocity could you accelerate the electron with the resulting amount of energy? Do you think it has gotten close enough to the speed of light?

By modifying physics at a higher energy scale, I think you can do almost anything.

The question is whether the standard model is stable on its own, or has another negative minimum for very large field values. The answer to the last question is much more subtle than often discussed, since most properties of the effective potential, and the field on which is depends, are gauge dependent and dependent on the renormalization scale. More discussions can be found in the linked papers.

Anisotropic pressure means that the principal stresses are not all equal.Thus, I understand the original question proposed by Hasrat, as equivalent to: Does spherical symmetry implies that all principal stress are equal?

The answer to the above question is :NO.

Spherical symmetry has two implications.

1)There may be two different principal stresses, but not three as in the more general (non spherical) case.

2)Neither one of them depend on the adapted spherical coordinates.

Stability is no the issue here.

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.

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

Thank you Prof, El-Naschie for your advise

I can't providing any specific data. But I think it would be more usefull to you to find the BH curve of your steel. The permeability depends of the working point. You may ask to your steel provider.

OK André, we will see when the LHC restarts (supposed to be in March)

We observed Meissner effect  and flux trap in large (cm^3) Pb samples, see WT et al, PHYSICAL REVIEW B 85, 184522 (2012) and  WT et al APPLIED PHYSICS LETTERS 101, 162603 (2012), does this answer your question?

But: *How* do you see that there is no coulomb scattering? Do you look at the process in in your sensitve detector or stepping action? I check it with

Cowan-Reines neutrino experiment. Here an electron anti-neutrino scatters a proton to produce a neutron and a positron. Reines got Nobel prize in 1995. Neutrinos are produced in a nuclear reactor and then aimed at a water tank. Positrons then emit gamma rays which are detected by photo multiplier tubes.

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.

Theoretically yes. A sinusoidal phase grating (no absorption) where the amplitude of the phase shift is pi/2. This grating would only have 2 orders, +1 and -1. 

If all you want is to get rid of the +/-2nd orders all you have to do is to make sure the line-to-space ratio of the grating is 1. This ratio gets rid of all the even diffraction orders. If you also make sure the grating is a perfect phase grating then you'll also get rid of the 0th order. 

Read section 2.5.1 in my thesis (http://kth.diva-portal.org/smash/get/diva2:398800/FULLTEXT01.pdf), it's 1.5 pages and has the formula for the efficiency of gratings (absorption and phase) with a rectangular grating profile. 

Take a look at EdX course on effective field theory

@Yurij: I said about "extract information" and not "capture information"... its hard to find what you want if you expect to find it in the way you want it :)

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. 

I am not quite sure, But this article may help

N. E. CHRISTENSEN at £11.: Electronic Structures of Semiconductors under Pressure 23 phys. stat. sol. (b) 198, 23 (1996)

Link : http://users-phys.au.dk/nec/Papers/necPSS/PSS19823.pdf

OR 

Pressure dependence of the direct band gap in tetrahedral semiconductors

Phys. Rev. B 58, 12579

First, I think you may be thinking about a global conformal transformation. In the context of (relativistic) Bohmian mechanics and scalar theories of gravity, the conformal transformation is local: the magnitude of the conformal rescaling varies from point to point, which is what leads to dynamical behavior.

A conformal spacetime transformation amounts to a change in the gravitational constant. A local conformal transformation, therefore, amounts to a variable gravitational constant. Conversely, a variable gravitational constant can be absorbed into a conformal transformation; this is how the variable gravitational constant of Jordan-Brans-Dicke theory can be eliminated by a conformal transformation from the Jordan frame to the Einstein frame. Of course, since the transformation is local, it is described by a scalar field, and as a result of that transformation, the scalar field will couple to other fields. The phenomenological interpretation is that a particle trajectory that is a geodesic in the Jordan frame is the trajectory of a particle that responds to a nonmetric scalar "fifth force" in the Einstein frame, and thus not a geodesic in that frame.

Conformal transformations are of course angle preserving. In the context of relativistic spacetime, this has the special significance that they leave light cones (in the case of a local conformal transformation, infinitesimal light cones) invariant. More generally, Maxwell's laws for electromagnetism are invariant under a conformal transformation (in four dimensions). Furthermore, the Weyl tensor (which is also known as the conformal tensor), which describes, among other things, free gravitational waves in empty space, is also invariant under conformal transformations.

The relationship between conformal transformations and Bohmian mechanics is well desrcibed in this paper: http://arxiv.org/abs/0810.2786. The essence of the argument is that we first introduce a scalar theory of gravity, and observe that the resulting metric is always proportional to the Minkowski metric, therefore the theory amounts to introducing a local conformal transformation; and then, using a suitably chosen stress-energy tensor representing matter yields equations that are the defining equations behind the de Broglie-Bohm interpretation.

By the way, the full conformal group in 4 dimensions has 15 degrees of freedom; in addition to the 10 degrees of freedom of the Lorentz-Poincare group, five additional degrees of freedom are introduced by a) a conformal rescaling, and b) an inversion, followed by a translation, and then a second inversion. This latter bit is referred to as the special conformal transformation. However, the metric is invariant up to a rescaling under the conformal group, which is why we are only interested in that one degree of freedom. (Matter, on the other hand, may transform differently.)

Since the electromagnetic interaction conserves spin, parity and charge conjugation quantum numbers (J^PC), the Heisenberg uncertainty principle allows the photon to "fluctuate" into another uncharged particle with same J^PC for a short time.  The photon can thus fluctuate into the charge=0 rho, omega, phi and J/Psi vector mesons, since all have the same J^PC=1^--.

Since these vector mesons can interact via the strong interaction in addition to the electromagnetic, and the strong interaction is much stronger than the electromagnetic interaction, when the photon fluctuates into a vector meson its interaction strength is greatly enhanced.  This leads to the model of "vector meson dominance" for photon energies in the 0.5<E_gamma<3 GeV range, where the photon interacts dominantly as an uncharged hadron with J^PC=1^--.

Of these 4 vector mesons, the rho has the lowest mass and so its contribution to "vector meson dominance" is the most prominent for photon energies 0.5<E_gamma<1 GeV.  The omega meson has similar mass to the rho, but its decay modes are more complicated and so it is not seen in as many reaction channels as the rho.  At higher photon energies (1-3 GeV), the phi and J/Psi also become important as they become closer to being "on shell".

With a femtosecond laser you can do this experimentally, by placing the glass slide on a translation stage and moving the slide through the focus. If the energy of the laser is high enough you will start to see voids form.  After that it becomes an issue of controlling the stage position, and turning on and off the laser.

To detect if a void is forming you can probably use another CW beam and monitor the scattering.  

Off the top of my head it will be the same way but you need to add the energy of the meta-stable into the final state.  Just a guess though.

Well, some times ago I've looked at this problem,

J.Math.Phys. 45 (2004) 3659-3675; DOI: 10.1063/1.1782671' 

e-Print: quant-ph/0310128 | PDF

It happened to be closely related to different unitary noneqivalent representation of CCR (Canonical Commutation Relation) algebra and to Galilei equivalence principle in nonrelativistin quantum mechanics. Quite an inspiring stuff. Unfortunaly, generalization for n>1 space dimensions is mathematically highly  nontrivial, related to the quantum billiard problem, not to mension about more fancy shapes of the box.

Nuclear matter is a hypothetical substance consisting of huge number of nucleons ( protons and neutrons) interacting through nuclear forces only - no Coulomb forces. In an infinite nuclear matter volume and number of interacting nucleons are infinite, but the ratio of the two is finite. Infinite volume implies translational invariance which means absolute positions don't matter only difference in positions matter. Infinite volume also implies that there are no surface effects.

For compact stars such as neutron stars, the composition is not only neutrons( about 80%) and protons( about 10%) but also include electrons(10%) and does not exhibit translational invariance and is not necessarily charge neutral. Unlike nuclear matter, Neutron star's matter is therefore different type of matter called 'stellar matter' or 'neutron star matter'.

For finite regions and finite nuclei one would need a model that include surface effects and Coulomb interactions. The liquid drop model mentioned earlier by Gry is one such model.

The most official answer I have always heard is that three is a minimum for CP violating phase. But not a strong argument.

Extra dimensions seem to like three generations, as it is known from compactification of superstrings, usually getting the number of families from some topological parameter. With extra dimensions, but without superstrings, some of my university teachers did a paper years ago: https://inspirehep.net/record/11555?ln=es (Phys.Rev. D26 (1982) 691-697)

My own guess is a very retorted mechanism: use the quarks as preons for the yet-to-be-found susy scalars. This is only possible with three generations.

Daniel,

Above the temperature 200 MeV where the QCD--hadron phase transition occurs, the

hadrons are represented by their free quark subconstituents in rhermal equilibrium. They contribute more degrees of freedom than hadrons, forming a dense medium of quark matter. This phase transition occurs about 1 microsecond after Big Bang.

When the universe cools below the phase transition the  quarks become bound in hadronic matter; the separation between quarks in the nucleons increases, and the interaction between any two quarks in a nucleon cease to interact with quarks in neighbouring nucleons.

Your question is: just how unlikely is it that more than two or three quarks get bound in the same hadron at that brief moment of the QCD--hadron phase transition. To answer it one needs a good model, but I think it is reasonable that multi-quark hadrons would be rare. Perhaps such states exist in the interior of neutron stars or quark stars. A quark star is really what you are asking for.

The metric tensor g_{mu nu} has 10 components. Of these 10, it is g₀₀ that determines how fast a local clock goes (when its velocity is zero, and is seen from a distance). So g₀₀ takes the place of the gravitational potential. In general relativity, gravity is not a single vector field (3 vector components) but a more complicated object with 36 independent components. The single gravitational potential field is replaced by the metric tensor with 10 components (of which 4 can bet set to zero by choosing your coordinates right). If you think general relativity is not elegant, that's a question of taste. Realising how efficiently it takes care of equivalence of gravitational and inertial mass, while respecting space-time relativity, without any ambiguity, I find the theory extremely elegant, in big contrast with any alternative that has been proposed.

BTW - I found a very approachable article reviewing cosmological acoustic oscillations at http://dx.doi.org/10.1063/1.2911177 - and http://aether.lbl.gov/bccp/PDFs/BAO.pdf - to be very helpful...

The measure is, also, important, else the result of the integration *won't* have the requisite properties.Both metric and measure are important. And by measure is meant, also, the prescription for dealing with the singularities, i.e. what happens when x and x' coincide. In Euclidian signature the solution is unique-in Lorentzian signature a prescription is required. This, of course, is standard material in mathematical methods for physics courses. For the subject at hand, cf. http://www.rand.org/content/dam/rand/pubs/research_memoranda/2006/RM2820.pdf

The RHIC collider has produced a lot of polarized-proton research, including lots of collisions with the spin vectors pointing toward each other as the particles collide (as well as other configurations). See, eg, http://arxiv.org/abs/hep-ex/0701048 . Although the protons are destroyed in this process, it isn't generally described as 'annihilation', since at every point in time there are quarks present.

Similar polarized electron-electron experiments have also been run, and these definitively show that the electrons do not annihilate regardless of the directions of their spin vectors during the collision.

If you'd like to learn more, the term for spin vectors that are pointed along their velocity vector is "Longitudinally Polarized". There are countless papers on the subject of these collisions.

No-we do know what the cosmological constant means and its effects in the solutions to the Einstein equations. We do not know of any matter that can exert negative pressure, so the question, whether with the cosmological constant alone it is possible to quantitatively describe spacetime is perfectly well-defined-and it does seem to work, as the supernova measurements indicate.

I reckon you can find the required info and more in LEP design report. Here you go: http://cds.cern.ch/record/102083/files/cm-p00047694.pdf

Regards, Oznur

Hello!

It can be determined from the quarter-point of the elastic scattering angular distribution. It is the angle where the elastic differential cross section relative to the Coulomb-point (or Rutherford) one is 0.25. This angle relates to the grazing trajectory. The grazing angle can be calculated using the formula for the distance of the closest approach in the Rutherford scattering. When this distance is equal to the sum of the radius of the projectile and the radius of the target, the projectile trajectory corresponding to the grazing angle touches the surface of the target nucleus.

Cheers,

Alexis

The electro-weak unification states in very simple words means that at very high energies both were actually one force. And this force must be mediated by some bosonic particle. Did this mediator get split into a massless photon, and very massive Ws and Z bosons?

Actually it depends on what you mean by "unification". If you define it through the concept of simple groups (think it physically as having only one gauge coupling), then a rigorous unified (and unbroken) phase is actually reached only at very high energies (and not within the SM, at least not exactly), of the order of 10^16 GeV, in the context of GUT theories. Only there the "mediator" you are talking about is actually "unique", in the sense that it is in an irreducible representation of the gauge group (that, by the way, contains also the strong force at that point). But take care not to confuse it with the concept of "spontaneously brake", that by definition tells you that your theory is invariant under some gauge group while the vacuum is not (completely).

On the other hand, if one thinks to unification in a less rigorous way, I mean by looking to electromagnetic and weak forces coming both from a more general principle (gauge invariance of the lagrangian under SU(2)_L X U(1)_Y), then ok: they are unified. But using this definition it has less sense to ask at which energies they unify, I hope you'll agree with me. But also with this less stringent concept of unification, the gauge bosons of the *two* "factors" of the gauge group (not only "one mediator"), after electroweak symmetry breaking, get mixed to give you one massless photon plus three, massive, bosons. One could say that the word "unification" was given to this phenomenon because two distinct (at that time) forces, with distinct experimental features, could be explained by one single principle.

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.)

Article "Periodic quantum gravity and cosmology" predicts innumerable particles. The particles of standard model are shown to be just the tip of the iceberg. According to this theory, to look for the fundamental building block of the universe is not a very wise thing to do.

If a spherically symmetric, pulsating object could generate gravitational radiation, this would be scalar radiation. However, a mass cannot generate such radiation because of the shell theorem/Birkhoff's theorem, which states that outside a spherically symmetric object, the object's field will be identical to the field of a similar point mass located at the center.

Next, dipole radiation is produced by charge separation: for instance, an antenna can radiate electromagnetic waves if positive and negative electric charges in it are separated by a voltage. This cannot happen for gravity though, because there is no negative gravitational charge (i.e., no negative mass).

So the "simplest" gravitational mode that there is is quadrupole radiation. This radiation leaves its imprint on the cosmic microwave background in the form of tensor perturbations.

Scalar perturbations, in contrast, are not due to gravitational waves, they arise as a result of the varying distribution of mass density across the Universe.

So to sum up, the mechanisms behind the two perturbations are very different: Scalar perturbations are caused by the presence of matter with variable mass density and hence, variable gravity (but no waves/radiation!) whereas tensor perturbations are caused by freely traveling gravitational radiation (i.e., waves).

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 ?

The idea is simple. In order to get a not-so-homogeneous universe today, the assumption goes, the primordial universe had to have small random density (scalar) fluctuations which grew into the stars and galaxies of today. Some of these initial density fluctuations would be small in size. Others would be large in size. Are small and large fluctuations equally likely to occur? If so, then if you took two pictures of the early universe and magnified one a thousand times, it would still look exactly the same as the other. This is scale invariance. On the other hand if, say, the early universe favored tiny fluctuations over large fluctuations, then the two pictures would not look the same; the original picture would contain predominantly small fluctuations, the magnified one, predominantly large fluctuations.

If you plot the amount of fluctuations against size (in other words, wavelength), you get a power spectrum. If the amount of fluctuations on all scales is the same, the plot would be a horizontal line. However, if we have, say, more fluctuations at small scales and less at larger scales, the plot will have a slope. This slope can be approximated by assuming a simple exponential relationship. The exponent is usually expressed as n - 1, where n is the spectral index. So n = 1 means an exponent of 0 and a horizontal line (scale invariance); any other value means some deviation from scale invariance.

Hi Oznur, Yes, you can change the kinetic energy of your particle via the SteppingAction, but you have to get the current track through the step. For example:

G4Step()->G4Track()->SetKineticEnergy (const G4double aValue). This is, however, a bit of a roundabout way to do a physical process. Something must be creating this gain in energy. I'm assuming a uniform electric field is creating your linear gain of kinetic energy. Why not just apply an electric field in Geant4?

Hope that helps,

Cheers,

Evan

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 in