Ever since the excitement of the “god
particle” came about, I wondered whether when the final time came to meet our
creator in whatever elementary particle form, I would be subjected to a god
field in which I could be expelled because I had no notion of the god particle.
This field would not spare me even if I am a chemist with an “incorrigible”
appreciation of the fundamentals of physics. At the risk of increasing my
diabetes mellitus because of the excess stran on my mental faculties, I decided
to take a long walk to pick up my daily milk and focus a little in interpreting
in my way some of what has been written on the god particle so as to be
accepted in a god-field. I guess what I have come up with is expressed in this
blog, trying m best to avoid cutting and pasting, is a viewpoint with the
statutory warning that all views expressed in this blog may have little to do
with reality. In the context of god particle this does not seem to be a
deterrent.

There are two views on the god particle as expressed in the cartoons above. The left expresses the trivial way the god particle influences the ordinary man. The one on the right expresses the actual experimental situation when the finding of a particle depends on a statistically relevant blip on a screen. It is the relevance of this blip that forms the basis of the god particle. What makes it significant is the amount of money spent on it.

In philosophicsl/religious treatises/testaments on the origin of matter/life one inevitably ends up starting with a philosophy or with a bang. The Old Testament of some Hebrews would have the world being created in seven days nearly 6000 years ago, being off by a factor of a million or so. This kind of error is sometimes allowed in cosmology. That it started suddenly is the common philosophical point and therefore similar no matter what Michael Moore would say abut it. After all, there is this (theologically) much debated line

There are two views on the god particle as expressed in the cartoons above. The left expresses the trivial way the god particle influences the ordinary man. The one on the right expresses the actual experimental situation when the finding of a particle depends on a statistically relevant blip on a screen. It is the relevance of this blip that forms the basis of the god particle. What makes it significant is the amount of money spent on it.

In philosophicsl/religious treatises/testaments on the origin of matter/life one inevitably ends up starting with a philosophy or with a bang. The Old Testament of some Hebrews would have the world being created in seven days nearly 6000 years ago, being off by a factor of a million or so. This kind of error is sometimes allowed in cosmology. That it started suddenly is the common philosophical point and therefore similar no matter what Michael Moore would say abut it. After all, there is this (theologically) much debated line

*One day is with the Lord as a thousand years, and a thousand years as one day (2 Peter 3:8)*

which means that 6000 years translates
to 6000 x 365,000 ~ 2,2 billion years (assuming, of course that the period of
earth’s rotation and revolution remains relatively the same). This is a
respectable value. The Hebrews interpret Hosea 5:14-6:2

*After two days he will revive us; on the third day he will restore us, that we may live in his presence*

as the 2

^{nd}millennium after Christ when Israel was created and that the third millennium will be the time when the Israelites will be restored with their Messiah.
A different (as well as more accurate)
chronology is in Hindu cosmology in which one day in the life of

*Brahma*, the creator, is 4.3 billion years. This is the*pralaya*period when the universe is created/destroyed during*Brahma*’s day and takes rest during Brahma’s night for the same period. This process continues for 100 Brahma years which is 300 trillion years. The point here is that during the day it is*adristam*(causality) that rules when every effect/cause is caused/effected. The day starts, say, with the creation of a particle which could be a ray of light (stream of photons), if you want to be biblicaly correct. It is this disturbance that starts off the*adristam*cycle and when that ends it is night and nothing exists because there is no causality to perceive beginning and ends.*Brahma*, the maker of the universe?) in a state of rest (say, in the

*yogi*c

*savasana*pose, Fig 1, left). In this pose the mind is ideally quiet and the eyes are closed so that no light there is perceived and it is night. The body is balanced

*on*a point (fulcrum) and is parallel to a horizontal, defined for some (Euclidean or non-euclidean) geometry. A ray of light appears when the body opens its eyes and he asks why. He has a problem to solve. The mind becomes active. The blood goes to his brain. The head becomes heavier (this was demonstrated first, I think, by JBS Haldane) and the body is tilted from the horizontal (Fig 1, right, click to expand).

If the medium above and below the
horizontal were different then the consciousness of the man would wake him into
the (lower) medium he is immersed in. When

*Brahma*is not solving problems (no*adristam*) he will be balanced again to enter the dark phase which he won’t be aware of although*Brahman*(the supreme god) would know the difference.
The tilting of the body may be taken
as a breaking of symmetry as far as the distribution of weight about the
horizontal for the given geometry is concerned. The breaking of symmetry is
essential to the theories for the formation of new particles. In essence the
breaking of symmetry changes the way a force due to a field acts and this in
turn may be interpreted in terms of a new particle (with a new mass) being
formed because the effect of a force is
determined by the mass. We have shown a potential energy scheme along a
coordinate which is some property (“expectation value”) of interest.

The stability of a particle is usually
discussed in terms of its energy along a particular coordinate.In order to simplify matters we may consider the
expectation value to be the spatial position of the particle. If the particle
is displaced along the

*z–*axis (perpendicular to the valley of the Mexican Hat) there would be a change in energy. However, there is no change in energy when the particle is displaced parallel to the plane of the valley.
In the left of
Fig 2 we have a featureless black ball resting at the middle of a single
minimum potential (blue line). The potential has a double
minimum which appears due, say, to a change in sign of the coordinate. The
change in sign of the coordinate could result in a change in sign of some
applied field; e.g., the arrows could indicate a change in magnetic field
direction due to a reveral in direction of the current flow in a coil. As long
as the feature-less ball is insensitive to the direction of the new applied
field it will remain at the bottom of the single-minimum potential However should the ball have a component that
interacts with the applied field it will slide down to one of the minimum of
the double-minima potential. For example, if the ball has an “up” oriented
magnetic moment it will stabilize in the well created by the “up” field. In
this process the symmetry of the double well potential is broken.

Such double-well potentials are sometimes visualized as a
“Mexican hat” (Fig 2) potential which is cylindrically symmetric in the sense
that there is a rotational symmetry about the zero of the “expectation value”
coordinate. A ball is precariously
(unstable) balanced on top of the hat (Fig 2 left) and the ball slides down to
a happier, more stable position. Once it slides down the symmetry is broken, no
matter which side it slides down.

The mexican hat first came into my
consciousness when I heard in my very early days (late 1950s early 1960s) the music of the mexican hat
dance. It was probably at this time (in my reckoning) that the Mexican Hat Potential was coined which could be important in understanding the way popular culture becomes important in popularizing scientific concepts. The dance that is the most classic is said to be the

*El Jarabe Tapatio*(see http://www.youtube.com/watch?v=zE6qVVffM1Q 1.5 million views) the original form of which was banned by the Spanish banned because it was too sexy. Parts of the dance shown below are from another less popular youtube video (225 hits). I can’t help pointing out as an aside that the term*Jarabe*, according to the Wikipedia, comes from the Arab word ‘xarab” which they say means ‘herb mixture” but which we know as “sharab’ or intoxicating liquor (e.g.,*jhoom barabar jhoom sharabi*, http://www.youtube.com/watch?v=W03OI-F7kdg).
I struggled (remarkably unsuccessfully at that time) with the
Mexican Hat potential when I was trying to understand the Jahn-Teller
distortion in molecules when an outer electron occupies orbital (~spatial) states which are
degenerate (energetically) equivalent. For such Jahn-Teller effects the
distortion is usually studied in terms of molecular normal mode (pattern of
motion in which all parts of the system move sinusoidally with the same
frequency and with a fixed phase relation) vibrational coordinates, Q (see Fig 3
left bottom) for, say Cu

^{2+}atoms with one*d*- electron in doubly degenerate*(**e**g*)*orbital states, the arrows indicate direction of vibrating motion) The first order potential energy function for linear coupling between the normal modes for simple harmonic oscillators and the occupied electronic energy levels yields a double well potential.*The Mexican hat potential is always cited when discussing the Higg’s particle or “god particle”. It is important nevertheless to understand some aspects of real-life chemistry and physics that has applied the Mexican hat potential to routinely observed processes before one moves towards discussions on the Higg’s boson. I struggled (remarkably unsuccessfully at that time) with the Mexican Hat potential when I was trying to understand the Jahn-Teller distortion in molecules which occupy orbital (~spatial) states which are degenerate (energetically) equivalent. For such Jahn-Teller effects the distortion is usually studied in terms of molecular normal mode (pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation) vibrational coordinates, Q

_{q}

_{,}

_{e}(see Fig 3 left bottom for, say Cu

^{2+}atoms with one

*d*- electron in doubly degenerate

*orbital states, the arrows indicate direction of vibrating motion) Landau and Teller were among the first (late 1930s) to discuss the stability of molecules with orbitally degenerate state. The first order potential energy function for linear coupling between the normal modes for simple harmonic oscillators and the occupied electronic energy levels yields a double well potential.*

The Mexican Hat potential has a
continuum of minima in the plane of the valley (the

*xy*plane). In this case, one may have other interactions that break the symmetry.
In the case of the Jahn-Teller effect
when there is strong linear as well as higher order quadratic couplings between
the electronic states and vibrational modes in the molecule the Mexican hat
becomes warped (right of Fig 3). For example in metal-ligand, ML

_{6}, octahedral symmetry the warping can give a Mexican hat with “hills” (higher energy) and “valleys” instead of one feature-less valley. For example, rotation about the*z-*axis by an angle f could give 3 “valleys”s at f = 0^{o}, 120^{o}and 240^{o}and three “hills” at f = 60^{o}, 180^{o}and 300 degrees for an electron in a doubly degenerate (*e*)_{g}*orbital. The three “valley”s could correspond to three equivalent elongating distortions of octahedral symmetry as shown in Fig 3 (right, below; dashed lines indicating longer metal-ligand distance). The contour map of the potential energy surface shows the location of the “valley”s and “hill”s. It should be easy to see that for, say, axially asymmetric second order couplings the depths of the “valley”s could change and the stabilityof the various distortions could change.*_{ }
The Mexican hat potential surface of Fig 3 left is
thus a simplification. It may be appropriate to rename the “Mexican Hat”
potential surface may instead be called a “lemon squeezer” surface (see Fig 2) when
there are many “hill”s amd “valley”s. In Fig 2 a severly distorted “squozed”
lemon rests at the bottom-most potential in a symmetry broken state

Complications come in when, for instance, what seems to be straight in our coordinate
system, is not straight when viewed from another perspective. For example, what
is straight trajectory on a flat land, will be curved when we take the
curvature of the land into account, and differently curved when one takes the
axis of earth’s rotation or earth’s revolution. Similarly, if an object is
hurled into space, its trajectory will depend, say, on its mass, shape,
electrical charge, its magnetic moment etc., when there are gravitational,
viscous, electric, magnetic fields, etc.

The
Mexican Hat potential is also sometimes known as the “wine bottle” potential when
there is punting at the bottom of the bottle. The
lowest-energy state of the system is not at the symmetry point at the top of
the punt but is down in the trough of the wine bottle. The occupation of the
trough at any point will break the symmetry. Another way which we think is
useful (not only because it could be new) is to the bottle is held parallel to the earths
gravitational field --- say, parallel to the vertical bars of the window
grill of a cheap-ish apartment builing in Pune (Fig 4, left). If one manages
to tilt the apartment complex without changing the direction of the
gravitational field (Fig 4, right; this usually happens when the wine in the
bottle reaches the dregs stage) and the bottle is still thought to be held
straight, there is more liquid on one side and the symmetry of the “wine
bottle” potential is broken.
The
tilting of a bottle could be taken as the beginning of a swirling motion
where liquid flows in the trough because of an introduction of a swirling
motion introduce by the combined action of a tilt and rotational motion. If the liquid had no resistance to flow,
say, because of a continuum of minima in the Mexican Hat potential--- it was
a superfluid --- the flow will be perpetual once the initial flow of liquid
was started. In this case it is not straightforward to imagine a tilt if the
fluid had no charge. But once the fluid is imagined to be a flow of perpetual
current then the fluid may be thought to be a superconducting current and the
direction of tilt would be related to the direction of the magnetic field that
is expelled by a superconducting current (Meissner effect).
The physics of the swirling or rolling of a ball in the “wine bottle”
or “Mexican Hat” potential is looked upon sometimes as a transformation under
continuous symmetry of the way the total energy of the system is expressed
(its Hamiltonian operator). There is one mode which is thought to be gapless
or no energy change on traversing the degenerate levels of the minimum
potential. This is called the Goldstone Theorem and the massless mode is the
Goldstone mode. The Goldstone mode is described usually by referring to a
ferromagnet in which all the magnetic moments (taking up a direction in a
magnetic field) are aligned in one direction (Fig 5, top, magnetic moments
indicated by arrow). This arrow may refer to any direction. In Fig 5, middle,
the finger of god reaching out to Adam in Michael Angel’s painting in the
Sistine chapel would reach out in the same spiritual direction for all
aadmi (hindi for man = adam). There are some critical points that arise
from the system being infinitely large because, I suppose, one cannot roll up
infinity into a three-dimensional ball or even flatten it into a
two-dimensional disc. In this way an infinitesimally small point and an
infinity become equivalent as they cannot be divided.
Peter Higgs gave an
illuminating talk at Kings College, London, on 24
^{th} November 2010
(my wife completed sixty that day) which he titled “My Life as a boson”.
t is
perhaps best to get Higgs’ viewpoint from this talk:-
The feature of spontaneous symmetry breaking is
that you have some continuous symmetry that is broken by the ground state of
the condensed-matter system. If it is of infinite volume, which of course a
ferromagnet never is, then the ground state is degenerate. But if you were in
an infinite ferromagnet then there would be a spontaneous magnetization, which
could point in any direction, and you would think that the system was no longer
rotationally invariant.The Mass of particles
One of the more discussed topics in modern particle physics seems to be
the origin of mass. This should be strange to us since we have been brought
up in the belief that the central feature of Newton’s view is the
conservation of mass so that mass is the crucial defining property of matter.
There should be no origin because all of us, including elementary particles
are born with a mass. Mass can be redistributed, but neither created nor
destroyed. In modern physics there is no equivalent fundamental concept for
mass.It turns out that in special relativity it is energy that is conserved,
and in general relativity gravity responds to energy through space-time
curvature and not mass.
There seems to be a new way to look at properties of physics, which is
the property of emergence. It emerges from the interaction of smaller entities
which themselves do not show it. For instance, the P,V,T of a gas of atoms or
molecules are not anticipated from the property of a single atom or molecule though
they may depend on the properties of those individuals. When the physicists consider emergence, mas appears as an
approximate, emergent property of matter so that the understanding of the
origins of mass of standard matter (colour gluons, up- and down- quarks,
electrons and photons) depends on
understanding the properties of the relevant elementary quanta.
“
I would like to emphasize that
this theory of the origin of the mass of standard matter makes no reference
to symmetry breaking in the electroweak sector, nor to the Higgs condensate,
nor of course to the Higgs particle.” (Frank Wilczek, in Origins of Mass,
2012
It is useful to familiarize one-self with mass being expressed in
terms of energy as electron-volts. From the well known expression
E
= mc, mass is
expressed in units of eV/^{2}c^{2}, where eV
is an electron volt, c is the speed of light in a vacuum. Most times mass is simply expressed terms of
1/c^{2} units as electron
volts, eV. 0.51 MeV is the rest mass of an electron or
positron and an electron-positron annihilation yield nearly 1 MeV of energy;
0.94 GeV is the mass of a proton, 200 MeV energy released in fission of ^{239}Pu
or ^{235}U atoms.
The next
term one need to be (as usual vaguely) familiar with is The Standard Model (SM). comprises a set of fermionic fields whose
quanta of excitation are fermions with spin ½ such as electrons, protons,
quarks, etc. The Fermions obey Pauli
exclusion principle by which two
fermionic particles cannot occupy the same state at the same time and which leads
to the Fermi-Dirac statistics. There is also a bosonic field whose quanta of
excitations are bosons following the Bose-Einstein statistics in which two
bosons can occupy the same state at the same time. I am not clear why Fermi, an
Italian, is associated with statistics of fermions that gives others their
space and Bose, a Bengali developed a
statistics where one is used to one’s space being overcrowded. Actually a
Bengali is unaware of the existence of others as long his wisdom can flow uninterrupted,
non-contradicted (resistance less) preferably at the same time and space in perfectly coherent incoherence. That is why the Bengalis are so loved
A little about
gauge and gauge theory
In simplest terms, I think, a change in gauge
may be looked upon as the way we convert our measurement systems on going
from America to Europe (e.g., feet to metres, gallons to litres, pounds to
kilograms, dollars to euros). This is one example of a gauge transformation
in which we have changed our measurement coordinates (gauge) with changes in
our location. We do not change the absolute (a more difficult concept to
define, perhaps, especially when we are talking of god-like terms) value
(gauge invariance, --- “
What’s in a name?
that which we call a rose/By any other name would smell as sweet;/ So Romeo
would, were he not romeo call’d”) of the
property being measured. Put this way, gauge theory is straightforward. Gauge invariance must be maintained to ensure that the results are not
dependent on the choice of gauge.
IThere is also Wigner’s statement that the
invariance of observables under certain transformations implies the existence
of an unitary operator on the various states. If the unitary operator commutes (Abelian
group operation does not depend on the order they are applied as in the
addition of integers, with the unity operation being addition with 0 as an
integer) with the operator (Hamiltonian) that describes the dynamics of the
system, it gives to characteristics (spectrum or observables) that describe the
system. However, there are systems (such as those with long-range coherence including
superconductors, superfluids, iferromagnets) in which the physical observable (local
symmetry) does not reflect the invariant global symmetry of the system. This is
the spontaneous symmetry breaking, as noticed by Higgs’ observer inside a
ferromagnet (see above).
n the more complicated world of particle physicists, gauge theory is applied to areas (I don’t venture to understand) such as string theory and loop quantum gravity where, essentially, point particles are replaced by one-dimensional string-like ( sutra?)
objects and their path in space trace surfaces instead of lines and are
described by appropriate languages from topology and geometry.
A gauge
boson is a particle that carries an interaction between elementary particles by
the exchange of these gauge bosons between them. Thus photons (mass ~ 0 GeV)
carry electromagnetic interactions, the two W
^{±} (mass 80.4 GeV) and Z
bosons (91.2 GeV) carry weak interactions and the gluons (mass 0 GeV) carry the
strong interaction. All of these have spin = 1; except for the W_{0}^{±} boson which have charge ± 1, the others are charge neutral.
The
Lagrangian equations (that describes the state of a dynamic system in terms of
position coordinates and their time derivatives that summarises the dynamics of
the system) express a gauge invariance that cannot have a mass term so that it
implies that gauge fields are massless and a mass cannot change as Newton said
they won’t. Gauge symmetry offers
a way to describe interactions due to invariance
properties of Lagrangians. The gauge
principle provides a method to transform a Lagrangian that is invariant with
respect to global Abelian symmetry from
the U(1) group (unitary transforming) into a Lagrangian that is invariant with respect to local
symmetry, or gauge-invariant.
By having a
spontaneous symmetry breaking such that new background forces can be
introduced, one may overcome the concepts of gauge invariance and introduce/add
a mass because of a change in the background. Such a change cannot be a
consequence of the initial starting equations. It is put in by hand due to the
spontaneous changes in symmetry (as we did, we think, by the “drunken” building
in Fig 4). This is a key step in the Salam-Weinberg electroweak theory.
Curvature and Mass
The mass of a particle
(say, the earth) placed in the wine-less end of the bottle (see inset of Fig 4,
left) would be different from that when immersed in the wine-full end (see
inset of Fig 4, right) of the bottle, for example. If we take the tilt (director)
angle as a measure or gauge then the extent of tilt may be taken as a
measure of the change in the gauge. The
director characterizing the local direction of tilt is a two-dimensional vector
sicne it depends on the position in the trough. The continuous rotation
symmetry along the bottle axis is broken in the director. The symmetry breaking
occurs spontaneously in the tilted bottle. All directions are equivalent long the
central symmetry axis (there is no change in energy) as long as the tilt angle
is the same.
The
curvature up the side of the wine bottle is often called a “mass". In the
big bang theory this curvature has a relationship with real physical mass, The
relationship between curvature and mass
is
reminiscent of the mass of a charge carrier in an energy vs wave-vector (E vs k) plot in band theory of solids Fig 6, left). The energy of a
free electron, E, has
a parabolic dependence on Its wave vector, _{free}k,
such that E µ _{free}k^{2}/m_{0}, m being the mass of a free electron. _{0} In the presence of an attractive potential
such as in a periodic lattice of a crystal, the energy, Eµ _{crystal} k^{2}/m*, where m* is an effective mass. In the periodic potential of the lattice,
the E vs k diagram shows allowed and forbidden region. In
an extended zone scheme shows an energy band which are separated by band gap.
Going by the curvature, it is apparent that the opening of a gap would lead to
changes in curvature and therefore to changes in mass.
It is true
that in the late 1950s and early 1960s the exclusive particle physics community
was frustrated in their progress with particles and their origin. In particular
the problem seemed to be to find a mechanism that gives a photon a mass. It was
at this point that Nambu listened to Schrieffer (both graduate students at that
time) and speculated on the way the broken symmetry gives mass to fermions.
Again referring to Higgett’s 2010 talk at King’s college he writes *referring
to Fig 6, right)
“
the analogy that I think Nambu noticed was with the
Dirac theory of a spin-half fermion. If you have a massless Dirac particle
there are excited states of positive energy and there’s the sea, and there is
no gap between them, but if you have a massive particle then those are split
apart. There is an energy difference between the sea and the states of the
fermions, so there is a BCS-like gap of 2mc.” ^{2}.
This is basically the way in which Nambu’s BCS model involving spontaneous
symmetry breaking generates fermion masses
In the Nambu-Goldstone mode, the ground state is not invariant under the symmetry. Instead, there is a continuous family of exactly degenerate, not invariant, ground states that are related by the generator of the broken symmetry. For every spontaneously broken symmetry there is a particle species with zero mass which are called Goldstone particle or Goldstone bosons when they are spin-less. The currents of broken symmetries create these particels from the vacuum. One may have the ball in the bottle of Fig 6 to be a ball infinite dimension
The
“wine-in-the-tilted-bottle” model requires to be modified to make a proper
connection with the Higgs’ model. In the
first place the tilt in the wine bottle need not be so exaggerated. The tilt
may be treated as a perturbation around the ring wirh a wave number,
k.
We may may make the tilt infinitesimally small or k tending to zero..When the relaxation time of
the perturbation becomes long compared to the relevant time scale there is
perpetual flow... as in a superconductor. The wine at the bottom of the “wine bottle”
potential will then be seen as that shown in Fig 7 with a phase mode and an
amplitude mode. It is the amplotude mode from the curvature that gives mass to the boson.On the Mass of a Photon
The massiveness of a photon goes against some of our most cherished lessons from what we think is fundamental physics. A consequence of Maxwell’s description of
electromagnetism is the constant speed of
all
electromagnetic radiation in vacuum. However, many of the properties of light
is obtained from universal constants such as the Planck’s constant, h, and the velocity of light, c, and a
spin angular momentum h/2p, for a frequency, v. As it turns out, the idea of a finite
photon mass does not contradict developments in classical electromagnetism or
quantum electro dynamics (QED). Experiments to find limits to the rest mass
of a photon shows it to be less than 10^{-50} 9.
With a
nonzero photon mass, the usual Maxwell equations transform into the so-called
Proca equations which are valid for the charge carriers in superconductors and
for, the basis for understanding massive photons and the London penetration
depth, l
((the distance magnetic flux can penetrate into a superconductor). It
turns out that the damping of a magnetic field inside a superconductor is
totally caused by the photon having a finite mass. The propagator (the
probability amplitude for a particle to travel from one place to another in a
given time) for a massless photon with distance _{L}r fall off as 1/r. When a
photon obtains a finite mass with a Compton wavelength 1/m, the propagator drops as exp(-_{A}m_{A}_{}r)/_{ }r. The London penetration depth, l ~ 1/_{L}m.
As early as 1992 in a paper titled “On the London equations” (_{A}PNAS,
1992, v. 89,no. 22, 10673–10675.] Sternberg had shown how the classical London
equations for superconductors can be written in a form that yield the Proca
equations. The abstract of this paper has the sentence: In particular, the field itself acts as its own charge carrier.
The Higgs field has non-zero strength
everywhere and the particles such as W
^{±}, Z
and photons _{0} aquire
mass by interacting wit the Higgs field. Since the field carries its own charge
carrier, the Higgs field should have a Higgs particle. The Higgs amplitude of
the vibrational amplitude up- and down- the sides of the Mexican Hat potential
(or wine-bottle potential, Fig 7) has a rest mass that the Large Hadron
Collider experiments were looking for. The mass of the Higgs particle as
determined by experiment (126 GeV ~ 133 mass of protons) would correspond to an
atomic nucleus of atomic number 133. This value is close to the value of the
fine structure constant of ~ 137. This value gives the relativistic limits of
stability for the mass of an atom.
Anderson found in 1963 in a paper
entitled Plasmons, Gauge Invariance, and Mass that when
a superconducting Fermi liquid is charged, the scalar zero-mass excitations become
longitudinal plasmon modes of finite mass of a superconductor. It has been pointed
out (including by Higgs) that Anderson’s proposal was a speculation since he did not discuss any relativistic model so that he could not demonstrate
(through Lorentz invariance) how the Goldstone theorem could be avoided.
A
critical question would be whether such a Higgs boson mass value allows
to extrapolate the standard model to very large energies witout leading to
vacuum instabilities (which is an end-of-the-world scenario, in my
understanding, at least for some particles). The most critical ingredient in
evaluating this instability is the top quark with a mass of ~ 173.2 GeV. Whether
the electroweak vacuum is stable or not up to the largest possible high-energy
scale, would depend critically on a precise determination of the Higgs boson
and top quark masses. An estimate by Alekhin and co workers show that the mass
of the Higgs boson is at the brink of a stability (see Fig 8, click to expand for reading the legend).,
This
must be exciting from a Russian roulette point of view since the stability of
our universe would depend on the theoretical models for the “god particle”.
The Higgs field that
permeates all space and gives mass to some bosons including photons now becomes
conceptually similar to the
luminferous
ether , that is a material substance that causes light to have an unique
velocity as it passes through it. The famous experiments of Michelson and
Morley disproved this concept when they showed that the measured velocity of
light did not depend on the direction of the Earth’s motion seemingly
demolished this theory and established the special theory of relativity and
Einstein’s story became a folklore. Higgs electro-weak field is a modern
relativistic, quantum mechanical, non-Newtonian resurrection of the ether.
When Einstein applied
his general theory of relativity to the structure of the cosmos, Newtonian laws
still guided scientific efforts and to be consistent with Newton his model,
Einstein had to have in his model an infinite Euclidean three-dimensional space
with the mass (or density, r) being distributed
uniformly. It seems that Einstein
realized that for such a model the universe would be unstable to collapse or
expansion. For Newtonian gravity, in which the gravitational field is
conservative, one uses the Poisson equation (Ñ
^{2}F = 4pkF) for a scalar gravitational potential,
F. Einstein found it necessary to add a
cosmological constant, l, that modifies the
Poisson equation (to Ñ^{2}F + lF)= 4pkF) to his field equation. By
doing so, it seems, Einstein had introduced a new repulsive force on every
particle that balanced the catastrophic consequence of an attractive forces due
to the distribution of mass, Einstein himself required a justification of the cosmological
constant, l, by empirical observation. The
cosmological constant was required by Einstein to get a quasi-static
distribution so as to obtain “ ... the
fact of the small velocities of the stars.”.Beginning of Time: Setting up a SupercurrentIn
superconducting coils a supercurrent can be set up by having the rate of change
of an external magnetic field with time being not equal to zero. Taking this up
in some way may mean that the fact that a supercurrent is important in setting
up the Higgs field or generating the Higgs particle can only be done at the
beginning of time itself ... or at the origin of the time coordinate itself
when the Minkowski spacetime is three dimensional space alone. I don’t know if
this makes some sense to the special relativity people as they always have the
past and future light cones meeting at the origin. It is perhaps because of this that in real time time, when time exists, mass is given to gauge bosons and the realisation of existence begins. Causality or Adristam comes into being.
I hope it makes some sense in the context of the beginning of the day in the life of Brahma. The cosmological constant was thought by Einstein to be the residual space-time curvature when matter was created/removed. It would therefore seem that at time t = 0, some supercurrent contributing to the relativistic gauge field still existed. So whether Brahma’s days and night may continue in cycles there is the eternal Brahman overseeing this cycle.There is no Creatio ex Nihilo?In the meanwhile Shiva continues with his dance of creation and destruction as Brahman said he should (I think). In the meanwhile, we may add our "aum" to te sparklers from the experiments on the Higgs particle in the spirit of Diwali --- our own Festival of Lights |