Theoretical Astrophysics - Science topic

There seems to be something quite unclear about the interplay of elements stemming into different causal orders (we shall define them as expressions of different, hierarchically ordered complex systems [their concept, too, being such an expression]).

We cannot speak of absolute and homogeneously present and consistent "heat", with the same being held for "mass".

A fundamental problem therefore arises from mixing different levels of analysis, whose specific articulations tend to negate one another.

Electrons have spin because they live in a 4D spatial manifold and that is one of their degrees of freedom. The summation of all spins should be zero.

In other words, one can explain why electrons have spin without disobeying the law of conservation of angular momentum.

I don't deal with the geodesics model, and thus, I don't use spacetime.

I could benefit from your explanation of what do you mean by:

Observed Radial Momentum of Spacetime

By the way, you might want to watch a short video and read a short paper:

The Big Pop Cosmogenesis - replacement to the Big Bang

Big Pop Article

Such that we establish a common language.

Cheers,

Marco

Good deductive arguments have two properties: (1) validity and (2) soundness. Validity is entirely a formal property: it says that IF the premises are true then so is the conclusion; soundness says that not only is the argument valid, but its premises ARE true. Whether the premises are indeed true may be a matter of empirical discovery or of previous deductions or definitions (including deductions or definitions in mathematics). Sometimes it's just interesting to see what else a certain assumption commits one to and deduction can answer that question and sometimes also give us a good reason for rejecting that assumption (that is the rationale for reductio ad absurdum arguments, aka indirect proofs). It helps to keep in mind that the alleged shortcoming of deduction is not an indictment of its formal nature but a matter of the "garbage in, garbage out" principle.

Maybe a useful link

I agree with all your criticism.

JES

p.s.

It would be interesting to see a new theory evolve from your insight.

Hi John,

Instead of "reducing gravity", what about "reducing the mass of matter" once neutron degeneracy pressure is exceeded? For example, in a collapsing neutron star, what if the mass of those neutrons were to be reduced during the collapse?

Recall that a neutron is thought to get 99% of its mass from (1) a cloud of virtual gluons, and (2) the momentum of its quarks. Only 1% of the mass of a normal neutron is thought to come from its quarks interacting with a Higgs type field.

Which makes me wonder: if the quarks in each neutron can be "confined" by gravity instead of by gluons, there'd be no need for all that glue (and the associated mc^2). Also, as gravity confines the range for those quarks to move, their momentum might also be reduced (asymptotic freedom).

Which raises the question: in a collapsing neutron star, as all those neutrons become increasingly compressed by gravity, as the mass each neutron gets from gluons and momentum disappears, does this mean that the mass of a collapsing neutron star reduces as it shrinks?

Nigel

A universe can be created from nothing without any external laser or strong gravitational field. In QFT vacuum real particles can be created and annihilated thereafter provided their lifetime dt and energy dE satisfy the uncertainty relation, roughly dtdE~h where h is the Planck constant.

Owing to the uncertainty relation, borrowing a small amount of energy (dE~0) from vacuum is allowed for a long time. According to some estimates the total energy (including negative gravitational energy) of our Universe is precisely zero or very close to zero. Hence, if the Universe is created as a quantum fluctuation its lifetime can be almost infinite.

Dear Natalia S Duxbury.

The axions would be a good candidate for the dark matter for two reasons:

they haven't electric charge and their interaction with matter is very weak. The main problem is that these only speculative particles never observed.

Dear Ziaedin,

ZS: To make the problem easier suppose the OMG particle is approaching another particle. The observer in the frame of OMG particle can assume its own frame is standing still and the other particle is approaching it. In that case it takes one year for these two particles to meet.

Slow down, what event are you timing that from? We know when they meet but you have no starting point to define a duration.

ZS: But the same observer in the frame of OMG particle can also assume the OMG particle is speeding towards the other particle and thus the distance between them vanishes to zero which consequently reduces the time of travel to zero. The same two arguments can be repeated in the frame of other particle.

Yes, or in any other frame you choose, but if you want to say "it takes one year for these two particles to meet" you need an event at each end of that period, not just the meeting.

What you are saying is a completely standard aspect ant not a problem in any way, I would recommend you look up something called the "Parable of the Surveyors" to understand this better. I think it was originated by John heeler but you'll find several versions of it on the web.

A Virtual observatory provides user a virtual platform to get access to astronomical large data base, user friendly softwares for processing and analyzing the data. The Virtual Observatory India project (http://voi.iucaa.in/voi/abouVOI.htm) is one such platform. Link to other virtual observatory sites can be found at http://voi.iucaa.in/voi/linkstosites.htm.

"Minkowski formulation itself was a mathematical model designed to emulate Einstein’s results". I always assumed Minkowski space came before Special Relativity.

GR has not predicted a single galaxy's rotation (without invisible & arbitrary help) and its invisible helper has not been detected in any form after 40 yrs. It needs correction.

Researchgate doesn't allow for deletion of a question, so I will just replicate a derivation of Luminosity proportional to G^(-3).

Dr. David Arnett was generous to point out that he didn't agree with my argument using the thermonuclear chain reactions.  It is not clear that he disagreed with the final conclusion.

In any event, Dr. Arnett made an imprint on me.  Like a duckling recently hashed, Dr. Arnett's work was the first one I found modeling Luminosity.  So, he is like a (duckling) mother to me...:)

If, my idea were to be correct, it would probably have to be correct within the logical framework created by Dr Arnett's oeuvre.

So, I searched his work for equations of Luminosity of Supernovae.  Found one from 1980. I started with equation (40) and revied what influence a variable G would have on it. Since the radius of this Supernova varies according to Chandrasekhar radius or G^(-1/2), and since epoch-dependent Supernovae are scaled down Supernovae, their thermal energy (a volumetric integral) would scaled with G^(-3/2)... Left was the calculation of the mass of the Sun within that context.

I understood as Mass of the Sun, not as the mass of our current Star Sun, but as a unit of mass (currently matching the Sun's mass) but in the context of a Supernova.

The context of a Supernova means that radiative pressure outweighs gas pressure.  In that regimen, all the Gravitational dependence of the Sun's mass is included in its mass.

L (Sun) is proportional to Sun's mass.

The Luminosity of the star is also directly proportional to its surface area. That bring about another G(-1). The last G(-1/2) comes directly from a R factor.  So:

Thermal energy scales with G(-3/2)

Sun Mass has a dependence  of G^(-1)

Radius scales with G^(-1/2).

The total dependence of the Supernova Luminosity is the product of all these dependences or G^(-3).

So, I obtained the same result from my simple-minded physical reasoning using the infinitely more sophisticated work of Dr. David Arnett.

Below is the Hypergeometrical Universe Theory (HU) to the question of how environments with different Gravitation would affect the Absolute Luminosity of SN1A Supernovae.

The derivation starts with the work of David Arnett on type II Supernova.  We apply type 1A Chandrasekhar radius G dependence to the thermal Energy and to R0. We also scale a Sun Mass by modeling the Sun mass under different regimen - Low and HIgh radiative pressure.

This is an estimation to see if they expected dependence is consistent with astronomical observations, so the precise value is less relevant than the range.

Astronomical observations are consistent, within the logical framework of the Hypergeometrical Universe, with a G^(-3) dependence. That is exactly what one obtains using the High Radiative Regimen to evaluate the mass of the Sun G dependence.

That said, irrespective to which model we useed the range varied Between G^(-3.5) and G^(-3).

The relevance of this results is that in HU, G is inversely proportional to the 4D radius of the Universe. 

The Standard Cosmological Model considers that the Absolute Luminosity of a SN1a is constant or standardizable (variations due to different amount of ejecta are renormalizable through the empirical methodology WLR).

HU proposes the G is epoch-dependent, which would make SN1a to be epoch-dependent in a way that farther away SN1a had intrinsically weaker explosions and thus reduced Luminosity. Our adjustment of David Arnett's work indicated a G^(-3) Luminosity dependence.

That would result in an overstimation of the distances of Supernovae by G^(1.5).  After correction of the distances we can compare HU d(z) predictions with the astronomical observations.  See plot below:

The results below are consistent with 

Pauli exclusion in some stars leads to degeneracy and explanations of how and why stars have the sizes, temperatures, and compositions they appear to have.

Some red giants and other large stars are said to have electron degeneracy operating in some part of the star. It means the electrons are so close together that Pauli exclusion modifies the equation of state, Temperature, Pressure, and Volume.

White dwarfs are thought to be proton degenerate near the centers also leading to a different equation of state that may describe some part or maybe almost all of the star.

Neutron stars are believed to be neutron degenerate, with yet another equation of state.

Black holes can be regarded as degenerate time and space, which might simply disappear if some principle related to Pauli exclusion did not prevent it. The model is made of ZPE oscillators with virtual particle pairs packed so closely together that they can't vibrate independently. 

Most of these explanations are nearly a hundred years old, and are probably not the best available now, but some of them can be found in old books written by famous pioneers in Astrophysics.

I have some arguments about black holes that can't be resolved here, and don't change the answers to your question.

Since time and space can become degenerate in a high gravity case, time and space should also become degenerate in a case of high acceleration, and maybe in cases of extremely high kinetic energy.  It is discussed in other threads.

 Dear Thierry De Mees,

I have downloaded your book "Gravitomagnetism/Coriolis Gravity Theory" and will spend my winter break reading through it. As I recall, in the past, Voyager images lead researchers towards the Coriolis effect as an explanation for the Great Red Spot on Jupiter. Thank you.

Sincerely, 

Terry R. Fisher

To answer this: "I thought that Newton's gravity only acts on things with non zero mass, and consequently not on photons."  -- We have universality of free fall in Newton's theory (i.e. a weak form of the equivalence principle), so the trajectory of a particle in a gravitational field does not depend on the mass of a particle. That extends to zero or negative mass particles -- they all fall alike in a gravitational field.

The question then depends only on whether the kind of entities you consider interacts gravitationally. As long as you believe with Newton that light is made up of particles, you can (and von Soldner did in 1804) predict light deflection in a gravitational field. The answer is half the value predicted by Einstein in 1915 (but Einstein predicted the same value as von Soldner in 1911, albeit based on the wave picture of light).

If you believe that light is a wave phenomenon and no particles are involved, there is no reason in the Newtonial world view to assume it to interact with a gravitational field and then Newton's theory would predict zero deflection.

Thank you very much for the answers! So GaAs and InP must be direct band gaps and Si and Ga must be indirect band gap.

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.

This would make sense only if this angular momentum, defined at the boundary, where the Kerr metric is asymptotically flat, can be identified with the angular momentum of a quantum system. This system, however, is a quantum system in flat spacetime, so the fact that its angular momentum is that of a Kerr black hole doesn't seem relevant. In fact it's the other way around, cf. http://arxiv.org/abs/gr-qc/9710076

I think we have no sure theory to claim that we can determine which is matter and which is antimatter just by means of astronomic observation data. Of course if there is annihilation process just in progress, we can get some clues about antimatter in emission spectrum...

This is a very standard material, available in a number of text books.

Inflationary cosmological model was proposed by Particle Physicist Alan Guth and others in early 1980s. Essentially, at high energies, as particles behave as quantum fields, contribution of a quantum field to the energy density and pressure need not be zero. In the Planck era the lowest energy state of this quantum field might have corresponded to a false vacuum, generating a cosmological constant which is  10¹⁰⁰ times larger than what it is today, and resulting in a super-large repulsive force. Such a repulsive force stretches 3-D space which doubles in volume in every 10^-43 seconds. After 85 such doubling (in volume) temperature drops from 10³² K to near absolute zero. 

Ref:

Philadelphia, PA

Dear Wallis,

Its seems to me that your question concerns how black holes could radiate. You ask:

Black holes can't emit light waves, likewise they can't emit gravity waves and cannot exert gravitational force on matter outside. So how do the proponents explain two black holes pulling on each other, orbiting in the gradually closing binary system?

---end quotation

The key to the production of gravitational waves is not that massive objects emit gravity waves, but that the acceleration of massive objects does. Black holes, since they constitute massive objects, do curve space-time in their vicinity, however, and other objects follow the lines of curvature. In the LIGO discovery, it is the mutual acceleration of two black holes toward each other, and the consequent loss of angular momentum which is responsible for the emission of gravitational waves.

The oscillation of a charge produces electromagnetic radiation, and  the concept of gravitational radiation is analogous: accelerating masses emit gravitational radiation, though in most cases, and with small masses, this is negligible. Its takes the acceleration of gigantic masses to produce detectable gravitational radiation.

The hypothesis of gravitons does not really belong to the standard model of particle physics --which does not include gravity. Instead it belongs to proposals to extend the standard model to include gravitation. These proposals are much more speculative than the standard model. While gravitational waves were strongly and confidently predicted as a large-scale implication of Einstein's theory of general relativity, the concept of the graviton, as the supposed carrier of the gravitational force, is much more problematic, since this concerns extremely small scale phenomena, at or near the Planck length, and falls into the domain of proposals for theories of quantum gravity. Gravitational waves are an implication of GR, gravitons not.

In any case, if one follows the proposals for gravitons (Freeman Dyson, e.g., has expressed strong doubts that they could ever be detected), then they would arise as the quantum of the gravitational field in correspondence with gravitational waves. It is not that black holes, un-accelerated, or other massive bodies would be though to emit gravitons, instead, like the gravitational waves, they would be emitted by accelerating masses.

The two black holes are supposed to "pull on" each other, simply by following the curved space-time in their mutual vicinity. This is in accord with GR. But as they approach each other and there is a loss of angular momentum, the local curvature is repeatedly perturbed so as to produce the expanding gravitational radiation.

H.G. Callaway

No, the two statements don't imply any such suggestion. 

As pointed out earlier, an" intergalactic space density of DQV has a value of Planck density" is only Dr. Sorli's assumption, without any justification or smallest hint of physical background. It's a kind of new ether.

I should probably start by saying that the very Physics behind the occurrence of the "stiff" and "soft" equations of state is quite complicated. You can subdivide the EOS into regions: I. Nuclear saturation density; II. Supra-saturation nuclear density. Now for each case the stiffness/softness comes from two main ingredients: (a) EOS of symmetric nuclear matter; (b) EOS of pure neutron matter --> this one can be replaced by the nuclear symmetry energy. Now we can talk about the Physics behind the stiffness/softness for each case:

I. (a) The stiffness/softness is mostly controlled by the incompressibility parameter that can be more or less constrained by nuclear breathing modes. There are no big variations (for example it is well constrained to be about 200 < K < 260 MeV)

I. (b) The stiffness/softness is due variation of the nuclear symmetry energy. The large uncertainty comes from our poor knowledge on isovector channel of nuclear interaction. Physics of exotic nuclei close to dripline contain this information, however they are not yet readily available. This is a hot topic of research.

II. (a) The stiffness/softness is controlled by the skewness parameter (third derivative of energy per nucleon). The physics of finite nuclei is not sensitive to this variation, and therefore one can have models giving ranges of the EOS with maximum NS mass from 2 to 3 solar masses.

II. (b) Density dependence of the symmetry energy at suprasaturation is basically unknown. That is why we have a huge variations in the EOSs. 

I suggest you to further read this and references therein: https://www.researchgate.net/publication/232238087_Constraining_the_High-Density_Behavior_of_Nuclear_Symmetry_Energy_withthe_Tidal_Polarizability_of_Neutron_Stars

see arXiv 1311.6328 quant-ph.

please have a look at the paper by

Roles of Hyperons in Neutron Stars

Shmuel Balberg, Itamar Lichtenstadt

The Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel

and

Gregory. B. Cook

Center for Radiophysics and Space Research, Space Sciences Building,

Cornell University, Ithaca, NY 14853

some portions are copied for you below.

ABSTRACT

We examine the roles the presence of hyperons in the cores of neutron stars may

play in determining global properties of these stars. The study is based on estimates

that hyperons appear in neutron star matter at about twice the nuclear saturation

density, and emphasis is placed on effects that can be attributed to the general multispecies

composition of the matter, hence being only weakly dependent on the specific

modeling of strong interactions. Our analysis indicates that hyperon formation not only

softens the equation of state but also severely constrains its values at high densities.

Correspondingly, the valid range for the maximum neutron star mass is limited to

about 1.5 − 1.8 M⊙, which is a much narrower range than available when hyperon

formation is ignored. Effects concerning neutron star radii and rotational evolution are

suggested, and we demonstrate that the effect of hyperons on the equation of state

allows a reconciliation of observed pulsar glitches with a low neutron star maximum

mass. We discuss the effects hyperons may have on neutron star cooling rates, including

recent results which indicate that hyperons may also couple to a superfluid state in high

density matter. We compare nuclear matter to matter with hyperons and show that

once hyperons accumulate in neutron star matter they reduce the likelihood of a meson

condensate, but increase the susceptibility to baryon deconfinement, which could result

in a mixed baryon-quark matter phase.

Subject headings: stars: neutron — elementary particles — equation of state — stars:

evolution

– 2 –

1. Introduction

The existence of stable matter at supernuclear densities is unique to neutron stars. Unlike

all other physical systems in nature, where the baryonic component appears in the form of atomic

nuclei, matter in the cores of neutron stars is expected to be a homogeneous mixture of hadrons and

leptons. As a result the macroscopic features of neutron stars, including some observable quantities,

have the potential to illuminate the physics of supernuclear densities. In this sense, neutron stars

serve as cosmological laboratories for hadronic physics. A specific feature of supernuclear densities

is the possibility for new hadronic degrees of freedom to appear, in addition to neutrons and protons.

One such possible degree of freedom is the formation of hyperons - strange baryons - which is the

main subject of the present work. Other possible degrees of freedom include meson condensation

and a deconfined quark phase.

While hyperons are unstable under terrestrial conditions and decay into nucleons through the

weak interaction, the equilibrium conditions in neutron stars can make the reverse process, i.e.,

the conversion of nucleons into hyperons, energetically favorable. The appearance of hyperons in

neutron stars was first suggested by Ambartsumyan & Saakyan (1960) and has since been examined

in many works. Earlier calculations include the works of Pandharipande (1971b), Bethe & Johnson

(1974) and Moszkowski (1974), which were performed by describing the nuclear force in Schr¨odinger

theory. In recent years, studies of high density matter with hyperons have been performed mainly

in the framework of field theoretical models (Glendenning 1985, Weber & Weigel 1989, Knorren,

Prakash & Ellis 1995, Schaffner & Mishustin 1996, Huber at al. 1997). For a review, see Glendenning

(1996) and Prakash et al. (1997). It was also recently demonstrated that good agreement with these

models can be attained with an effective potential model (Balberg & Gal 1997).

These recent works share a wide consensus that hyperons should appear in neutron star (cold,

beta-equilibrated, neutrino-free) matter at a density of about twice the nuclear saturation density.

This consensus is attributed to the fact that all these more modern works base their estimates of

hyperon-nucleon and hyperon-hyperon interactions on the experimental constraints inferred from

hypernuclei. The fundamental qualitative result from hypernuclei experiments is that hyperon

related interactions are similar in character and in order of magnitude to nucleon-nucleon interactions.

In a broader sense, this result indicates that in high density matter, the differences between

hyperons and nucleons will be less significant than for free particles.

The aim of the present work is to examine what roles the presence of hyperons in the cores

of neutron stars may play in determining the global properties of these stars. We place special

emphasis on effects which can be attributed to the multi-species composition of the matter while

being only weakly dependent on the details of the model used to describe the underlying strong

interactions.

We begin our survey in § 2 with a brief summary of the equilibrium conditions which determine

the formation and abundance of hyperon species in neutron star cores. A review of the widely

accepted results regarding hyperon formation in neutron stars is given in § 3. We devote § 4 to

an examination of the effect of hyperon formation on the equation of state of dense matter, and

the corresponding effects on the star’s global properties: maximum mass, mass-radius correlations,

rotation limits, and crustal sizes. In § 5 we discuss neutron star cooling rates, where hyperons

might play a decisive role. A discussion of the effects of hyperons on phase transitions which may

occur in high density matter is given in § 6. Conclusions and discussion are offered in § 7.

– 3 –

2. Equilibrium Conditions for Hyperon Formation Neutron Stars

In the following discussion we assume that the cores of neutron stars are composed of a mixture

of baryons and leptons in full beta equilibrium (thus ignoring possible meson condensation and a

deconfined quark phase - these issues will be picked up again in § 6). The procedure for solving

the equilibrium composition of such matter has been describes in many works (see e.g., Glendenning

(1996) and Prakash et al. (1997) and references therein), and in essence requires chemical

equilibrium of all weak processes of the type

B1 → B2 + ℓ + ¯νℓ

; B2 + ℓ → B1 + νℓ

, (1)

where B1 and B2 are baryons, ℓ is a lepton (electron or muon), and ν (¯ν) is its corresponding

neutrino (anti-neutrino). Charge conservation is implied in all processes, determining the legitimate

combinations of baryons which may couple together in such reactions.

Imposing all the conditions for chemical equilibrium yields the ground state composition of

beta-equilibrated high density matter. The equilibrium composition of such matter at any given

baryon density, ρB, is described by the relative fraction of each species of baryons xBi ≡ ρBi

/ρB

and leptons xℓ ≡ρℓ/ρB.

Evolved neutron stars can be assumed to be transparent to neutrinos on any relevant time scale

so that neutrinos are absent and µν = µν¯ = 0. All equilibrium conditions may then be summarized

by a single generic equation

µi = µn − qiµe , (2)

where µi and qi are, respectively, the chemical potential and electric charge of baryon species i,

µn is the neutron chemical potential, and µe is the electron chemical potential. Note that in the

absence of neutrinos, equilibrium requires µe =µµ. The neutron and electron chemical potentials are

constrained by the requirements of a constant total baryon number and electric charge neutrality,

X

i

xBi = 1 ; X

i

qixBi +

X

ℓ

qℓxℓ = 0 . (3)

The temperature range of evolved neutron stars is typically much lower than the relevant

chemical potentials of baryons and leptons at supernuclear densities. Neutron star matter is thus

commonly approximated as having zero temperature, so that the equilibrium composition and

other thermodynamic properties depend on density alone. Solving the equilibrium compositions

for a given equation of state (EOS) at various baryon densities yields the energy density and pressure

which enable the calculation of global neutron star properties.

3. Hyperon Formation in Neutron Stars

In this section we review the principal results of recent studies regarding hyperon formation in

neutron stars. The masses, along with the strangeness and isospin, of nucleons and hyperons are

given in Tab. 1. The electric charge and isospin combine in determining the exact conditions for

each hyperon species to appear in the matter. Since nuclear matter has an excess of positive charge

and negative isospin, negative charge and positive isospin are favorable along with a lower mass

for hyperon formation, and it is generally a combination of the three that determines the baryon

density at which each hyperon species appears. A quantitative examination requires, of course,

– 4 –

modeling of high density interactions. We begin with a brief discussion of the current experimental

and theoretical basis used in recent studies that have examined hyperon formation in neutron stars.

3.1. Experimental and Theoretical Background

The properties of high density matter chiefly depend on the nature of the strong interactions.

Quantitative analysis of the composition and physical state of neutron star matter are currently

complicated by the large uncertainties regarding strong interactions, both in terms of the difficulties

in their theoretical description and from the limited relevant experimental data. None the less,

progress in both experiment and theory have provided the basis for several recent studies of the

composition of high density matter, and in particular suggests it will include various hyperon

species.

Experimental data from nuclei set some constraints on various physical quantities of nuclear

matter at the nuclear saturation density, ρ0 = 0.16 fm−3

. Important quantities are the bulk binding

energy, the symmetry energy of non-symmetric matter (i.e., different numbers of neutrons and

protons), the nucleon effective mass in a nuclear medium, and a reasonable constraint on the compression

modulus of symmetric nuclear matter. However, at present, little can be deduced regarding

properties of matter at higher densities. Heavy ion collisions have been able to provide some information

regarding higher density nuclear matter, but the extrapolation of these experiments to

neutron star matter is questionable since they deal with hot non-equilibrated matter.

Relevant data for hyperon-nucleon and hyperon-hyperon interactions is more scarce, and relies

mainly on hypernuclei experiments (for a review of hypernuclei experiments, see Chrien & Dover

(1989), Gibson & Hungerford (1995)). In these experiments a single hyperon is formed in a nucleus,

and its binding energy is deduced from the energetics of the reaction (typically meson scattering

such as X(K−, π−)X).

There exists a large body of data for single Λ-hypernuclei, which clearly shows bound states of

a Λ hyperon in a nuclear medium. Millener, Dover & Gal (1988) used the nuclear mass dependence

of Λ levels in hypernuclei to derive the density dependence of the binding energy of a Λ hyperon in at density ρ0 to be about −28 MeV, which is about one third of the equivalent value for a nucleon

in symmetric nuclear matter. The data from Σ-hypernuclei are more problematic (see below). A

few emulsion events that have been attributed to Ξ-hypernuclei seem to suggest an attractive Ξ

potential in a nuclear medium, somewhat weaker than the Λ−nuclear matter potential.

A few measured events have been attributed to the formation of double Λ hypernuclei, where two

Λ’s have been captured in a single nucleus. The decay of these hypernuclei suggests an attractive Λ−

Λ interaction potential of 4−5 MeV (Bodmer & Usmani 1987), somewhat less than the corresponding

nucleon-nucleon value of 6−7 MeV. This value of the Λ−Λ interaction is often used as the baseline

for assuming a common hyperon-hyperon potential, corresponding to a well depth for a single

hyperon in isospin-symmetric hyperon matter of -40 MeV. While this value should be taken with

a large uncertainty, the typical results regarding hyperon formation in neutron stars are generally

insensitive to the exact choice for the hyperon-hyperon interaction, as discussed below.

We emphasize again that the experimental data is far from comprehensive, and great uncertainties

still remain in the modeling of baryonic interactions. This is especially true regarding densities

– 5 –

greater than ρ0, where the importance of many body forces increases. Three body interactions are

used in some nuclear matter models (Wiringa, Fiks & Fabrocini 1988, Akmal, Pandharipande &

Ravenhall 1998). Many-body forces for hyperons are currently difficult to constrain from experiment

(Bodmer & Usmani 1988), although some attempts have been made on the basis of light

hypernuclei (Gibson & Hungerford 1995). Indeed, field theoretical models include a repulsive component

in the two-body interactions through the exchange of vector mesons, rather than introduce

explicit many body terms. We note that the effective equation used here is also compatible with

theoretical estimates of ΛNN forces through the repulsive terms it includes (Millener, et al. 1988).

In spite of these significant uncertainties, the qualitative conclusion that can be drawn from

hypernuclei is that hyperon-related interactions are similar both in character and in order of magnitude

to the nucleon-nucleon interactions. Thus nuclear matter models can be reasonably generalized

to include hyperons as well. In recent years this has been performed mainly with relativistic theoretical

field models, where the meson fields are explicitly included in an effective Lagrangian. A

commonly used approximation is the relativistic mean field (RMF) model following Serot & Walecka

(1980), and implemented first for multi-species matter by Glendenning (1985), and more recently

by Knorren et al. (1995) and Schaffner & Mishustin (1996) (see the recent review by Glendenning

(1996)). A related approach is the relativistic Hartree-Fock (RHF) method that is solved with

relativistic Green’s functions (Weber & Weigel 1989, Huber at al. 1997). Balberg & Gal (1997)

demonstrated that the quantitative results of field theoretical calculations can be reproduced by

an effective potential model.

The results of these works provide a wide consensus regarding the principal features of hyperon

formation in neutron star matter. This consensus is a direct consequence of incorporating

experimental data on hypernuclei (Balberg & Gal 1997). These principal features are discussed

below.

3.2. Estimates for Hyperon Formation in Neutron Stars

Hyperons can form in neutron star cores when the nucleon chemical potentials grow large

enough to compensate for the mass differences between nucleons and hyperons, while the threshold

for the appearance of the hyperons is tuned by their interactions. The general trend in recent

studies of neutron star matter is that hyperons begin to appear at a density of about ρB = 2ρ0,

and that by ρB ≈ 3ρ0 hyperons sustain a significant fraction of the total baryon population. An

example of the estimates for hyperon formation in neutron star matter, as found in many works, is

displayed in Fig. 1. The equilibrium compositions - relative particle fractions xi - are plotted as a

function of the baryon density, ρB. These compositions were calculated with case 2 of the effective

equation of state detailed in the appendix, which is similar to model δ = γ =

5

3

of Balberg & Gal

(1997). Figure 1a presents the equilibrium compositions for the “classic” case of nuclear matter,

nuclear matter. In particular, they estimate the potential depth of a Λ hyperon in nuclear matter

and also see:

Searching for Dark Matter Annihilation in M87

Sheetal Saxena, Dominik Elsässer, Michael Rüger, Alexander Summa, Karl Mannheim

Sep 20 2011 astro-ph.HE arXiv:1109.3810v1

 No  gravitational waves  radiated in spherically symmetric system, while axisymmetric situation can be.

Thank you for your answer. If your truth would be embarrassing for me, it would also embarrass such icons of soviet physics as Bogolubov and Landau, and I'd be totally fine with being part of that axis-of-shame :-) I agree that one has to be careful with ensemble averages when talking about inhomogeneous systems, for example, when describing soliton-like waves in active matter (see my Phys. Rev. E from 2013, and the Discussion on Ohta paper in 2014)). However, I disagree that hierarchy-equations like the BBGKY-hierarchy are useless in general. In your own papers, you also use such hierarchies of equations for multi-point correlation functions. In my opinion, for the ensemble average, one just has to imagine that only  the proper microscopic members that describe a particular inhomogeneous state are part of the ensemble. For example, for a single soliton, only those microscopic states should be  included that have the same density and momentum profile (coarse-grained over small cells in phase space) at the same time. Another argument to not dismiss BBGKY-like hierarchies is to consider the extreme case of a N-particle ensemble distribution that consists of products of delta-functions at time t. That means, all ensemble members have particles at the same positions with the same momenta and the BBGKY-equations would be equivalent to the evolution of a particular real system with those initial conditions. A more pragmatic argument: I recently used the first two BBGKY equations (adopted to my system) for self-propelled particles in a weakly-correlated limit where three-particle correlations are negligible compared to two-particle ones and I found perfect quantitative agreement with particle-based direct simulations. I didn't have to explicitly select the proper members of the ensemble, I did neither use thermodynamics nor Gibbs distributions, I just solved the time-dependent hierarchy equations until  a stationary state was reached. Thus, if you have an alternative theory, I suggest testing it quantitatively with Molecular Dynamics simulations and see how it does. In contrast to experiments, simulations can be adjusted to mirror all the approximations made in a theory and thus allow ``comparing apples with apples''. In my opinion, the more serious problem with kinetic theory is the closure of the hierarchy. You mentioned in your papers that you somehow close your equations at the two-particle level but I couldn't find any details. For self-propelled particles, there is parameter ranges where the three-particle correlations are stronger than the two-particle ones and the four-particle-ones are even stronger than three-particle ones and so on. Thus, in this strongly-correlated system, some type of generating function should be found that contains correlations to all orders, at least approximately, or a systematic closure for all multi-particle correlations is needed. In your papers, you mention discrepancies between experiments and theory. Could that also be due to neglecting these higher multi-particle correlations or using an inappropriate closure ?

 

The main source of uncertainty in photon diffusion time is related to the opacity in different layers of the sun as inferred from various solar models. Also this opacity will change as the sun evolves so the photon diffusion time is not constant. Convection in the interior of the sun also complicates this this issue.

A simple random walk calculation combined with a simple density gradient model for the sun is a relatively clean calculation.

http://adsabs.harvard.edu/full/1992ApJ...401..759M (a 2 page paper)

is a good source for this and is the source for the 170,000 yr timescale.

Dear Ludwig,

to be honest, your work is beyond my scientific horizon, but thank you for sharing. I´m going to try to understand.

Regards

Red shift can originate also in following cases.

1) The distance between a source and an observer does not change, but the source moves with velocity comparable with the speed of light. Then red shift in the source spectrum arises. It is interpreted as a result of relativistic slowdown of time on the source relative to the observer (it is called transverse Doppler effect).

2) Red shift arises if the observer is located in a region where the gravitation is less than near the source. In classical physics it means that photons surmount gravitation and thus lose energy. Red shifts in spectra of white dwarfs are explained in this way.

Q1: Probably not.

Coronal mass ejections will perturb the net magnetic field at the Earth's surface, but we regularly expose ourselves and other creatures to rapidly varying magnetic fields (stand at an electrically powered tram station...) and more slowly changing fields (have an MRI scan).

Dedicate attempts to induce nervous currents have been done.

As I am sure you know.

Eg.

Ham CLG, Engels JML, Van de Weil GT et al. Peripheral Nerve stimulation during MRI: Effects of high gradient amplitudes and switching rates. Journal of Magnetic Resonance Imaging 1997; 7(5): 933-937.

But the field strengths and magnitude of dB/dt were far larger than you would encounter from a CME-induced perturbation.

Dear Rogier,

a short answer to your question is: Yes, the Universe can be curved at super-large scales. A more detailed answer involves at least two aspects.

What do we know from observations?

From the observational point of view we know from a detailed analysis of the temperature fluctuations of the cosmic microwave background, combined with a local measurement of the Hubble expansion rate (the precise value does not matter too much here) that the curvature scale of the observable Universe is at least one to two orders of magnitude larger than the Hubble scale (the characteristic scale of the observable Universe), i.e. curvature still could be a few per cent effect. You ask if there could be curvature at scales 10 to 20 magnitudes larger than the observable Universe? The answer is yes. This could be the case.

What do we believe based on theoretical ideas?

Our standard model of cosmology relies on the idea of cosmological inflation.

Inflation predicts that the observable part of the Universe is very close to being flat. It does not predict that the curvature on scales much larger than the observable domain is exactly zero. Different models of inflation make different predictions about the super-large scales. Thus the answer is again, the Universe could be curved at those super-large scales. At the observable scales we expect a departure from flatness, but we expect that it is just a 0.1 per mille effect (a factor of 100 smaller than current observational constraint).

As far as I know the handedness of spiral galaxies

is determined by the citizen-science project Galaxy Zoo.

Michael Longo et al. found that there seems to be an

excess of left-handed spiral galaxies which might be

a sign of a rotating universe.

But in the meantime it turned out that there is a psychological

bias toward seeing left handed spirals.

Further reading:

Regards,

Joachim

The total entropy of the universe is not constant and there is no heat exchange with the "outside" that we know of. The entropy of the universe in the distant past was much lower and has been increasing ever since. The second law of thermodynamics states that the entropy of an isolated system always increases. Isolated means no heat flow in or out. In fact, many physicists would say that the "arrow of time" in the universe comes from the increasing entropy.

Also, in the paper, we are clearly saying that the cosmological term (which Einstein called the cosmological "constant") is not constant, nor are Einstein's equations "accepted", they are generalized. That is the whole point of the paper.