**THE HIGGS BOSON AND THE
SPACETIME METRIC**

(Revised June, 2016)

JOHN A. GOWAN

**email:
jag8@cornell.edu
johngowan@earthlink.net
home page
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E-Book
Abstract**

Currently, there seems to be (at least) two interpretations of the activity of the Higgs boson: 1) the older, original interpretation of the Higgs as the scalar or gauge boson which determines therest massesof the weak force Intermediate Vector Bosons (IVBs - the "W" and "Z"), and through the IVBS, of the elementary particles as well (an interpretation I can understand and endorse); 2) a newer (additional? alternative?) interpretation consisting of a "Higgs ether" which acts as the source of particle mass in the sense ofinertial resistanceto acceleration. In this latter interpretation, all elementary particles interact with a universal Higgs field in proportion to their mass, and it is this interaction or "Higgs ether drag" which causes the inertial resistance to acceleration we recognize as mass. It is this latter interpretation which I cannot understand or endorse, as it seems to have no ability to explain the inertial mass of composite particles (baryons), or Einstein's relativistic mass. However, replacing the "Higgs ether drag" hypothesis (but retaining the Higgs scalar role) with a "gravitational field drag" concept does allow us to understand the mechanism of relativistic variability in the metric and energetic parameters of mass, and crucially preserves the equivalence between gravitational, inertial, and rest mass, including that of composite particles.

Table of Contents:

Abstract

Introduction

The Higgs Field vs the Spacetime Metric

Gravity

Mass, Energy, Time

Links

In terms of Newtonian or low-velocity mechanics, the inertial resistance of mass to acceleration is simply explained by the conservation of energy. Energy is obviously required to accomplish an acceleration, in direct proportion to an object's mass (F = ma). Intuitively, there is nothing particularly mysterious about mass or inertial resistance at low velocity. Classically, the concept of mass was no more unusual than the concepts of energy, space, or time; the equivalence between gravitational "weight" and inertial mass was its greatest mystery. Einstein explained that puzzle (accelerating spacetime) but introduced new ones: according to the high-velocity mechanics of Special Relativity, inertial mass increases with increasing velocity, and likewise "clocks run slow and meter sticks shrink", destroying the classical simplicity of metric symmetry and energy conservation. Energy conservation and causality nevertheless prevail, of course, but it requires a changed (or "warped"/"curved") metric to do so, and a new understanding of the relation between free and bound electromagnetic energy (E = mcc), as well as between gravitation, space, and time.

More recently still, a new question regarding the scalar origin of the mass of the elementary particles has been raised, a question answered by positing the "Higgs" mechanism (as originally suggested by Peter Higgs, among others). The Higgs boson acts as a mass scalar which determines the masses of the weak force IVBs (Intermediate Vector Bosons), and subsequently, acting through the IVBs, "gauges" the specific masses of the elementary particles (formalized in the mathematics of the electroweak unification of the "standard model" by Glashow, Weinberg, and Salam, 1979 Nobel Prize). We might put this more simply by saying the Higgs boson gauges the mass-energy of the electroweak unified-force symmetric energy state, elementary particles (quarks, leptons) and IVBs included.

In his book "__Nothingness: The Science of
Empty Space__" by Henning Genz (English Translation 1999,
Perseus Books Pub. L.L.C.), on pages 228-237, Genz provides an
illuminating explanation of the "Higgs" field and particle,
currently the "Holy Grail" of particle physics. As I read and
reread this section, I was struck with the similarity between
Genz's description of the interaction of the Higgs field with a
particle, and my own notion of the interaction of the spacetime
metric with a particle's gravitational field. In Genz's
description of the Higgs mechanism, the interaction of a
particle with the Higgs field provides the particle's attribute
of inertial mass (resistance to acceleration); in my conception,
a particle's inertial mass or resistance to acceleration is
simply the consequence of the interaction of the particle's
gravitational field with the metric field of spacetime ( a
notion bearing some similarity to Mach's ideas on the subject,
since the metric of spacetime is influenced by the gravitational
field of the entire universe).

I am here considering the distinction between Einstein's "rest mass" energy content (E = mcc) of an elementary particle (quarks, leptons), which is evidently scaled by the Higgs boson, and the inertial mass due to acceleration (or the gravitational mass or "weight") of the same particle. "m" is presumed to be the same quantity in all three cases, and must be, for energy conservation reasons, which is the rationale for this discussion. However, to attribute the inertial mass of acceleration to an interaction between the Higgs scalar and elementary particles (as a sort of modern-day "ether drag") is to lose the identity between rest mass and inertial mass in non-elementary particles, since in the latter case the binding energy component of rest mass (which is huge in composite particles such as baryons - as much as 99%) cannot be attributed to the Higgs interaction. Binding energy is not an elementary particle - how is the Higgs supposed to recognize it? However, we preserve this identity (necessary for energy conservation) by attributing a particle's inertial mass of acceleration to the interaction between the spacetime metric and a particle's gravitational field, as we know the gravitational field is an exact measure of the total bound energy content of a particle (Gm), whatever the source of that bound energy may be. (See also: "A Description of Gravitation"). Crucially, this formulation also preserves the identity between gravitational "weight" and inertial mass, as in Einstein's "Equivalence Principle".

The gravitational field of a massive particle is
produced by the intrinsic (entropic) motion of the particle's
time dimension, exiting space at right angles to all three
spatial dimensions, and dragging space along with it (see: "The
Conversion of Space to Time"). The spatial dimensions
self-annihilate at the gravitational center of mass, leaving
behind an uncancelled (because it is "one-way") metrically
equivalent temporal residue, which in turn moves on down the
time line into history, pulling more space with it, repeating
the self-feeding entropic cycle forever. *A gravitational
field is the spatial consequence of the intrinsic motion of
time.* Time is the primordial entropy drive of bound
energy, producing matter's entropic conservation domain
(history), the analog of space in the case of free energy
(light). Time is produced by the gravitational annihilation of a
metrically equivalent quantity of space. The converse
interaction occurs via the gravitational conversion of mass into
light (as in stars). Hence the three dimensional intrinsic
motions of light, time, and gravity are connected in an energy
and symmetry-conserving triangle. (See: "Entropy,
Gravitation, and Thermodynamics").

Even though the Higgs may be an attribute
of the spacetime metric (acting as the weak force mass scalar),
setting the energy scale for the IVBs and by extension for the
rest masses of the elementary particles via the IVBs, this is a
one-time electroweak interaction regulating the production of *single*
elementary particles; the Higgs field does not continue to
interact with particles (as a sort of "ether drag") to produce
their inertial resistance to acceleration. Instead, this latter
role is played by the spacetime metric, interacting with a
particle's gravitational field, an interaction which produces a
particle's inertial resistance to acceleration, and precisely in
proportion to its total mass (Gm), whatever the source of that
mass may be. It also seems highly unsatisfactory to attribute
part of a composite particle's *inertial* mass of
acceleration to the interaction of its elementary components
with the Higgs boson, and another part (binding energy, for
example) to some other, non-Higgs type of inertial interaction:
"inertial mass" should arise from a single source to retain its
identity with "rest mass" and "gravitational weight". The "Higgs
field" may be necessary to gauge the energy scale and regulate
the specific *rest mass* or quantized bound energy content
of the weak force IVBs and the various elementary particle
species (quarks and leptons) the IVBs subsequently produce, but
has nothing further to do with their mass as observed in
inertial resistance to acceleration (or gravitational "weight").
The quantization of the Higgs and IVBs is necessary to ensure
the invariance of the *single* elementary particles they
produce. (See: "The
Higgs Boson and the Weak Force IVBs".) Even though the
Higgs may be viewed as a scaling property arising from the
metric itself (a "metric" particle), and as establishing through
the IVBs the rest masses of particles, this is not the specific
attribute of the metric which creates inertial mass as defined
by resistance to acceleration. Energy conservation, as well as
Einstein's "Equivalence Principle", requires that the "m" in
"rest mass" (E = mcc), inertial mass (resistance to
acceleration: F = ma), and gravitational "weight" ("gm" in an
equivalent local field), are all equal, whatever their source.

Let us take note at this juncture of the
relationship between mass, energy, and time, which we find not
only in the non-obvious notion that gravitation, which is
exactly proportional to and produced by mass (Gm), creates time and
the temporal entropy drive of bound energy (through the
annihilation of space and the extraction of a metrically
equivalent temporal residue); but also in the famous set of
equations relating "frequency" and energy: E = h*v*
(Einstein-Planck); E = mcc (Einstein); h*v* = mcc (de
Broglie) (the time component is implicit in *frequency).*
This subtle relationship emerges again in the notion of the
increase of a particle's mass with relativistic motion in
Einstein's Special Relativity, an otherwise puzzling result
which is explained through the concept that a particle's
inertial mass (resistance to acceleration) is entirely due to
the interaction of its gravitational field with the metric field
of spacetime.

The "mass" or inertial resistance to
acceleration offered by a particle is due to the interaction and
interference of the particle's gravitational field with the
metric field of spacetime. The forced interaction between these
two metric fields, one asymmetric and the other symmetric (or at
least different), also produces the anomalous results of
relativistic motion in the spatial, temporal, and mass
parameters of the moving or accelerated system, as discovered by
Einstein (slowing of clocks, shrinking of meter sticks,
increasing particle mass). Because (in this view) the inertial
mass of the system is from the outset attributed to the
interaction of its gravitational field with the metric field of
spacetime, the relativistic increase of mass with accelerated
motion is seen as a natural outcome of the interaction,
interference, and especially the feedback between the temporal
(or "frequency") components of these two metric fields, and the
connection (mentioned above) between frequency, time, energy,
and mass (including the covariance of space with time). Recall
that although the gravitational field of an individual particle
may seem to be weak, it extends throughout the Universe. A
gravitational field distorts spacetime and its metric (as per
Einstein); forcing this distorting influence through the
(universal) metric field of spacetime (as in accelerated motion)
requires energy, which is the source of the particle's
resistance - and in exact proportion to the particle's mass
(Gm).

The equivalence of gravitational and inertial
mass ("weight" vs resistance to acceleration - leading to
Einstein's "Equivalence Principle") is due not only to the
reciprocal character of the spacetime accelerations of gravity
vs (for example) rocket engines (spacetime accelerating through
the rocket vs the rocket accelerating through spacetime), but to
the interaction in both cases of a particle's gravitational
field with the metric component of (identically but
reciprocally) accelerating spacetime (the spacetime metric
accelerating through our gravitational field vs our
gravitational field accelerating through the spacetime metric).
Likewise, the vanishing of "g" forces in orbit or free-fall
corresponds to the vanishing of the forced (accelerated)
interaction between these two metric fields. Time is a common
feature of gravity, acceleration, and even mass (as we saw
above, through "frequency": h*v* = mcc). In contrast to
immobile, massive matter, note in this connection that light,
whose "inertial" state is "intrinsic" motion in space with
"velocity c", has neither mass, a time dimension, nor a
gravitational field, and consequently and significantly, *has
no inertial resistance to acceleration *(as in reflecting
between two mirrors). (See: "Does Light
Produce a Gravitational Field?")

(See also: "The Mysteries of Mass" by Gordon Kane, *Scientific
American,* July 2005, pp. 41-48; and: "When Fields
Collide" by David Kaiser, *Scientific American,* June
2007, pages 63 - 69.)

CERN announced the discovery of a "Higgs-like" boson on 4 July, 2012, at approx. 125 GEV. (See: Science Vol. 337 13 July 2012 pp. 141-143) (see also www.sciencemag.org)