Hence, the plausibility of the causality of Smolin's Autodidactic Universe.The
Laws of the Universe Are Changing | RealClearScience
Slum-dunk? No, there is only more research to be funded to search for what can
be detected.
For this peasant? A great working theory.
-----Original Message-----
From: Lawrence Crowell <goldenfieldquaterni...@gmail.com>
To: Everything List <everything-list@googlegroups.com>
Sent: Fri, Dec 30, 2022 10:04 am
Subject: Re: Physics? Ok Astronomers view 2 distant Water Worlds so following
the physics I ask..
On Wednesday, December 28, 2022 at 11:41:36 PM UTC-6 Bruce wrote:
On Thu, Dec 29, 2022 at 4:34 PM Brent Meeker <meeke...@gmail.com> wrote:
On 12/28/2022 9:01 PM, Bruce Kellett wrote:
On Thu, Dec 29, 2022 at 3:29 PM Brent Meeker <meeke...@gmail.com> wrote:
Of course one reason there are "laws of physics" is what my late friend Vic
Stenger called Point Of View Invariance. This was his generalization of Emmy
Noether's theorem that showed every symmetry implied a conservation law.
That is not strictly true. It is only continuous symmetries of the Lagrangian
that imply conservation laws -- not all symmetries. For example, the symmetries
of a square under rotation and reflection do not generate any conservation
laws. Neither do discrete symmetries like parity and charge conjugation.
So momentum is conserved because we want any law of physics to be invariant
under translation of a different location. Energy is conserved because we want
the laws of physics to be the same at different times, etc.
It is not what we want, it is what we find. We find that nature is invariant
under these continuous transformations, so we build those symmetries into our
laws.
Vic called in POVI because he wanted to extend it to transformations in
abstract spaces, e.g. gauge invariance. Of course the invariance depends on
the "point of view" in a sense. Things didn't look at all space translation
invariant to Aristotle. Galileo said ignore that your ship is moving along the
shore, just look at the dynamics in the cabin. So we discovered these
symmetries by learning what ignore as well as what to measure.
The real point is that the laws are discovered, not imposed. The fact that
continuous symmetries correspond to conservation laws was discovered only very
much later. Most of the history of physics is about discovering what works --
what the laws might be. POVI was thought of only very late in the game, and is
not a fundamental insight.
Bruce
This begins to look a bit similar to the debate over whether mathematics is
objectively real or something invented. Emmy Noether gave consideration to
that boundary term we usually discard when deriving the Euler-Lagrange formula
to show that a symmetry was involved with this term. This symmetry and that
this boundary term is zero meant a conservation law. A law of physics
considered as such is something associated with covariant and invariant
properties of space, spacetime or an abstract space under some set of
transformations. Is this principle, a law of laws should we say, something that
is discovered or is some objective aspect of a mathematical reality?
The type D, II, III and N solutions, black holes = D and gravitational waves =
N, are vacuum solutions with the Weyl tensor C_{abcd} that wholly determines
the curvature. The Weyl curvature is an operator on Killing vectors, such that
Killing vectors are eigenvalued with the Weyl curvature C_{abcd}K^bK^d =
λK_aK_c. The type N solutions have Killing vectors that have zero eigenvalue
C_{abcd}K^d = 0. Type III spacetimes have λ = 0 and type II and D have
nontrivial eigenvalues that are unequal for C_{abcd} and *C_{abcd}, for * the
Hodge dual with C_{abcd}K^bK^d = λK_aK_c and *C_{abcd}K^bK^d = λ’K_aK_c for λ ≠
λ’ and λλ ≠ 0. These Killing vectors define symmetries and thus conservation
laws. A timelike Killing vector defines conservation of energy, a spacelike
Killing vector defines conservation of momentum, and a Killing bi-vector or one
derived from such defines conservation of angular momentum. That is a total of
1 + 3 + 6 = 10 Killing vectors. These eigenvalued equations should make one
think of the Schrodinger equation. Indeed for a timelike Killing vector K_t =
√(g_{tt})∂_t so that this gives a general wave equation HΨ[g] = iK_t∂Ψ[g]/∂t,
which for g_{tt} = 1 is the Schrodinger equation. The ADM approach to general
relativity give NH = 0 and the Wheeler-deWitt equation HΨ[g] = 0. General
relativity does not automatically define conservation laws. Conservation laws
only occur with certain symmetries of spacetime. This often occurs where there
is an ADM mass defined by an asymptotic condition of flatness or some other
spacetime with constant curvature at a distance.
Conservation laws appear as asymptotic or boundary terms. The AdS/CFT
correspondence of Maldacena shows that a nonlocal quantum gravity theory
corresponds to a local conformal field theory on the conformal boundary of the
anti-de Sitter spacetime. The anti-de Sitter (AdS) spacetime has constant
negative curvature. This is a negative vacuum energy, where this has some
correspondence with string theory, such as the type I string theory has a
negative energy vacuum and its first excited state is a negative energy state.
The AdS_4 has a correspondence with black hole physics. The AdS spacetime is
not the spacetime of the observable universe. It is though in line with the
theory of Emmy Noether, also work by Hurzebruch, and even the old Gauss-Bonnet
theory.
Physical spacetime is more similar to de Sitter spacetime, and is the
Friedmann-Lemaitre-Robertson-Walker spacetime with positive energy. This means
curvature is positive, which involves how space is embedded in spacetime, and
this does not have conservation laws. If that space is a sphere S^3 the
constant vacuum energy on this space grows with the evolution of this space and
volume growth. This is one reason that people tend to prefer the flat space
model, where vacuum energy is net "infinity" and remains so. However, there is
nothing to prevent vacuum energy density from changing. The phantom energy
model leading to a big rip of the cosmos is possible, and the curious
discrepancy between CMB and SNII data, with the Hubble constant H =
70km/sec-Mpc and H = 74km/sec-Mpc respectively, appears to resist analysis
meant to show it is zero. If the phantom energy model should be realized then
conservation of energy, even with an infinite flat space, is gone.
The expansion of the universe also means we will not be able to observe much
physics that could be called “pre-cosmic,” or the quantum gravitation of the
pre-inflationary universe. Because of inflation and this 60-efolds of
expansion, expansion by ~ 10^{29}, a Planck scale region was expanded from
10^{-33}cm to 10^{-4} cm. Since inflation began at 10^{30} sec in the early
universe, any Planck scale fluctuation involved with the generation of the
universe would have been 10^{-23}cm, and was expanded to 10^6 cm --- beyond the
scale of the then observable universe ~ 10cm. After inflation the observable
universe with a scale of ~ 10cm an possible Planck scale process was stretched
by more normal expansion to 10^{10} light years, and might appear as some order
anisotropy in the CMB. Using blackbody physics, these quanta would have been a
tiny aspect of the early universe. These would be very difficult to find in the
CMB. Beyond that, we cannot observe anything. Any pre-cosmic physics emerged
from something smaller than the Planck scale and is expanded beyond any
measurable scale on the CMB.
John Wheeler said that the ultimate law of physics is there is no law. We may
then have something similar to this, where what we call the laws of physics are
just local emergent pattern in the observable universe. At large the universe
may simply have no conservation laws and ultimate there are globally no
physical laws.
LC
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to everything-list+unsubscr...@googlegroups.com.
To view this discussion on the web visit
https://groups.google.com/d/msgid/everything-list/e45935c8-1aa6-44a6-94a4-09e43c6a2bd0n%40googlegroups.com.
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to everything-list+unsubscr...@googlegroups.com.
To view this discussion on the web visit
https://groups.google.com/d/msgid/everything-list/301845347.2626329.1672416814898%40mail.yahoo.com.
