Re: ChatGPT: Momentum conservation idealization and the faikire of the Noether theorem,

Asking Grok: At the beginning of time nor momentum conservation neither
energy conservation didn't exist (cosmological time t=0). How come these
"laws" evolved from nothing
WATCH GROK RETORTING TRYING TO DEFEND CLASSIC PHYSICS BY USING THEORIES
BEYOND QUANTUM PHYSICS, WHICH ARE STILL BEING DEVELOPED (AND FAILING).
GROK, AS WELL OTHER AI ENGINES CAN'T ADDRESS THIS TOPIC WITHOUT MIXING
EVERY THEORY AVAILABLE TO DEFEND THESE TWO BASIC AND LOCAL LAWS.
ENJOY.
****************************************************
Can you tell me what theories about angular momentum conservation
support that such law exist since t=0, at the very start of the
currently accepted Big Bang that created the Universe? For me, at t=0,
the angular momentum of the "primordial atom" didn't evcn existed. How
come this law evolved from nothing, 14 billion years ago.
The question of how angular momentum conservation applies at the very
start of the Big Bang, at t=0t=0, is deeply tied to fundamental physics,
cosmology, and the nature of the early universe. Let’s break it down,
addressing the core of your question: how angular momentum conservation
could exist or emerge from the Big Bang, given the notion that the
"primordial atom" (a historical term for the initial state) might have
had no angular momentum.
1. Angular Momentum Conservation and Its Basis
Angular momentum conservation is a consequence of rotational symmetry in
physical laws, as described by Noether’s theorem. If the laws of physics
are invariant under rotations (isotropic), then angular momentum is
conserved. This principle is fundamental in classical mechanics, quantum
mechanics, and general relativity, and it’s expected to hold in most
physical contexts unless specific conditions break this symmetry.
In the context of the Big Bang, we need to consider:
    Whether the universe at t=0t=0 (or as close to it as our theories
allow) had conditions that allowed for angular momentum conservation.
    How the initial state of the universe, which is often modeled as a
singularity or a highly dense quantum state, relates to this
conservation law.
2. The Big Bang and the Initial State (t=0t=0)
The currently accepted model of the Big Bang, based on general
relativity and cosmology, describes the universe as emerging from an
extremely hot, dense state. At t=0t=0, the classical picture of the Big
Bang involves a singularity—a point of infinite density and temperature
where spacetime curvature becomes infinite. However, this singularity is
not a physical "object" like a primordial atom with well-defined
properties (e.g., spin or angular momentum). Instead, it’s a
mathematical limit where our classical theories (general relativity)
break down.
Key points about the initial state:
    The "primordial atom" is a historical and somewhat misleading term
from early cosmology (e.g., Lemaître’s hypothesis). Modern cosmology
does not describe the universe as a single particle but as a quantum or
relativistic state of spacetime and energy.
    At t=0t=0, the universe is not well-described by classical notions
of angular momentum because spacetime itself is undefined. We need a
quantum theory of gravity (e.g., string theory or loop quantum gravity)
to describe this regime, and such theories are still speculative.
    Immediately after t=0t=0, during the Planck epoch (t<10−43t<10−43
seconds), the universe was governed by quantum gravitational effects,
and classical concepts like angular momentum may not apply directly.
3. Theories Supporting Angular Momentum Conservation from the Early
Universe
Several theoretical frameworks and cosmological models address how
conservation laws, including angular momentum, might apply or emerge in
the early universe:
a. Symmetry in the Early Universe
    Rotational Symmetry and Noether’s Theorem: The conservation of
angular momentum relies on the isotropy of space (no preferred
direction). Observations of the cosmic microwave background (CMB)
suggest the universe is highly isotropic on large scales, supporting the
idea that rotational symmetry was present in the early universe. If the
laws of physics were rotationally invariant from the moment spacetime
emerged, angular momentum conservation would hold as a fundamental
principle.
    Quantum Cosmology: In quantum cosmological models (e.g., loop
quantum cosmology), the universe avoids a true singularity, and the
initial state is described by a quantum wavefunction. These models often
assume fundamental symmetries, including rotational invariance, implying
that angular momentum conservation is built into the fabric of the
universe from the start.
b. Inflation and the Early Universe
    The inflationary epoch (t∼10−36t∼10−36 to 10−3210−32 seconds) is a
cornerstone of modern cosmology. Inflation posits that the universe
underwent rapid exponential expansion, smoothing out any initial
anisotropies or irregularities.
    If the pre-inflationary universe had any net angular momentum,
inflation would dilute it to negligible levels due to the immense
expansion. This is consistent with observations: the universe today
shows no significant net rotation (i.e., no large-scale angular
momentum).
    However, local angular momentum (e.g., in galaxies or stars) could
arise later from quantum fluctuations amplified during inflation, which
conserve angular momentum locally due to the underlying symmetry.
c. Quantum Gravity and the Planck Epoch
    In the Planck epoch (t<10−43t<10−43 seconds), the universe was so
dense that quantum gravity effects dominated. Theories like string
theory or loop quantum gravity speculate that spacetime itself may have
been quantized, and conservation laws might emerge from the symmetries
of the underlying quantum framework.
    For example, in string theory, the fundamental objects (strings)
obey symmetries that include rotational invariance, suggesting that
angular momentum conservation could be a feature of the fundamental laws
even at the earliest moments.
    Some models propose that the universe’s initial state was a quantum
vacuum with zero net angular momentum, but quantum fluctuations could
produce particle pairs or fields with locally conserved angular
momentum.
d. Primordial Black Holes and Spin
    Some speculative models suggest that primordial black holes could
have formed in the early universe. Black holes have angular momentum
(described by their spin parameter), and their formation would obey
conservation laws. If such objects existed, their angular momentum would
be part of the universe’s total budget, conserved from their formation
onward.
    However, at t=0t=0, no such objects are thought to exist, as the
universe was a singular or quantum state.
4. Why Angular Momentum Conservation Seems to "Evolve from Nothing"
Your intuition that the "primordial atom" had no angular momentum is
reasonable, as the initial state at t=0t=0 is not a physical object with
classical properties like spin. Here’s why angular momentum conservation
still holds and appears to "emerge":
    No Net Angular Momentum: The universe as a whole likely has zero net
angular momentum, both at the start and today. This is supported by the
lack of observed large-scale rotation in the CMB or galaxy
distributions. Conservation laws don’t require non-zero angular
momentum; they just require that the total remains constant (e.g., zero
stays zero).
    Local Angular Momentum: Angular momentum in the universe today
(e.g., spinning galaxies, stars, or particles) arises from local
processes, such as gravitational collapse or quantum fluctuations, which
conserve angular momentum locally. These processes trace back to the
post-Big Bang era, not t=0t=0.
    Emergence of Classical Laws: At t=0t=0, classical concepts like
angular momentum may not apply due to the quantum gravitational nature
of the universe. As the universe expanded and cooled, classical
spacetime emerged, and with it, the familiar conservation laws rooted in
symmetries like isotropy. The "evolution" of angular momentum
conservation is thus tied to the emergence of classical physics from a
quantum regime.
5. Challenges and Open Questions
    Singularity and Quantum Gravity: Since general relativity breaks
down at t=0t=0, we lack a definitive theory to describe whether angular
momentum conservation holds in the singular or quantum state. A complete
theory of quantum gravity is needed to resolve this.
    Initial Conditions: Some cosmologists argue that the universe’s
initial conditions (e.g., zero net angular momentum) are a "choice" or
constraint of the universe’s birth, possibly explained by anthropic
reasoning or a multiverse framework. Others see it as a natural outcome
of symmetry.
    Testing Early Symmetries: While the isotropy of the CMB supports
rotational symmetry, it’s an observation from t∼380,000t∼380,000 years
after the Big Bang. Extrapolating back to t=0t=0 relies on theoretical
assumptions, and some models (e.g., ekpyrotic or cyclic cosmologies)
propose alternative early dynamics that could affect conservation laws.
6. Conclusion
Angular momentum conservation likely exists as a fundamental principle
from the earliest moments of the universe due to the rotational symmetry
of physical laws, as dictated by Noether’s theorem. At t=0t=0, the
universe was not a classical "primordial atom" with defined angular
momentum but a singular or quantum state where classical conservation
laws may not directly apply. However, as spacetime emerged in the Planck
epoch and beyond, the isotropy of the universe ensured that angular
momentum conservation held. The universe likely started with zero net
angular momentum, and local angular momentum (e.g., in galaxies) arose
later from conserved processes like quantum fluctuations or
gravitational dynamics.
The "evolution" of this law from "nothing" reflects the transition from
a quantum gravitational regime to a classical spacetime where symmetries
like isotropy became manifest. While we lack a complete theory of
t=0t=0, current models (inflation, quantum cosmology, string theory)
strongly suggest that angular momentum conservation is a universal
principle rooted in the symmetries of the cosmos, present as soon as
spacetime itself emerged.
If you’d like me to dive deeper into a specific theory (e.g., loop
quantum cosmology or string theory) or explore related concepts like the
universe’s isotropy, let me know!
No. Tell me instead the same problem with the conservation of energy
since cosmological time was zero.
The question of how the conservation of energy applies at the very start
of the Big Bang, at t=0t=0, is a profound one, touching on fundamental
physics, cosmology, and the nature of the universe’s initial state. Your
concern about the "primordial atom" (a historical term for the initial
state) having no defined energy, and how energy conservation could
emerge from "nothing" 14 billion years ago, is a key issue in modern
cosmology. Let’s address this systematically, focusing on theories and
models that explain energy conservation since t=0t=0.
1. Energy Conservation and Its Basis
Conservation of energy is a cornerstone of physics, rooted in Noether’s
theorem, which links it to time-translation symmetry: if the laws of
physics are the same at all times, energy is conserved. In classical
mechanics and special relativity, energy conservation is
straightforward. However, in general relativity (which governs
cosmology), energy conservation is more complex due to the dynamic
nature of spacetime itself.
In the context of the Big Bang:
    At t=0t=0, the universe is modeled as a singularity or a quantum
state where classical notions of energy may not apply.
    We need to explore whether energy conservation holds in this extreme
regime and how it emerges as the universe evolves.
2. The Big Bang and the Initial State (t=0t=0)
The Big Bang model describes the universe as originating from an
extremely hot, dense state. At t=0t=0, general relativity predicts a
singularity—a point of infinite density and temperature where spacetime
curvature diverges. This is not a physical "primordial atom" with
well-defined properties like energy but a mathematical limit where
classical physics breaks down. Quantum gravity is needed to describe
this regime, and such theories remain speculative.
Key points about t=0t=0:
    The singularity is not an object with measurable energy in the
classical sense. Instead, it represents the breakdown of spacetime.
    In the Planck epoch (t<10−43t<10−43 seconds), quantum gravitational
effects dominate, and classical energy conservation may not directly
apply.
    The "primordial atom" concept (from Lemaître’s early cosmology) is
outdated; the initial state is better thought of as a quantum or
relativistic configuration of spacetime and energy.
3. Theories Addressing Energy Conservation from t=0t=0
a. Energy Conservation in General Relativity
    Challenges in Cosmology: In general relativity, energy conservation
is not always straightforward in an expanding universe. The
stress-energy tensor’s conservation (∇μTμν=0∇μ​Tμν=0) ensures local
energy conservation, but globally, energy is not always conserved in a
simple way due to spacetime expansion. For example, photons lose energy
as they redshift in an expanding universe, which can seem like a
violation of energy conservation.
    Zero-Energy Universe Hypothesis: One influential idea, proposed by
physicists like Edward Tryon and developed by others, suggests the total
energy of the universe is zero. This arises because:
        Positive Energy: Matter, radiation, and kinetic energy
contribute positive energy.
        Negative Energy: Gravitational potential energy, due to the
attractive nature of gravity, is negative.
        In a flat universe (consistent with CMB observations), the
positive energy of matter and radiation can exactly balance the negative
gravitational energy, yielding a total energy of zero.
        At t=0t=0, if the universe began with zero total energy, energy
conservation is trivially satisfied: the total energy remains zero as
the universe evolves. This avoids the need for an initial "source" of
energy, as the universe could emerge from a quantum fluctuation with no
net energy cost.
b. Quantum Cosmology and the Initial State
    Quantum Fluctuations: In quantum cosmology, the universe’s birth is
often modeled as a quantum fluctuation in a vacuum state. The Heisenberg
uncertainty principle allows for temporary violations of energy
conservation on short timescales, potentially enabling the universe to
"tunnel" into existence with zero net energy. Models like the
Hartle-Hawking "no-boundary proposal" or Vilenkin’s tunneling universe
suggest the universe could emerge from a quantum state where energy
conservation is preserved in a quantum sense.
    Loop Quantum Cosmology (LQC): In LQC, a branch of loop quantum
gravity, the Big Bang singularity is replaced by a "quantum bounce." The
universe transitions from a contracting phase to an expanding one, and
energy conservation is maintained through the quantum dynamics of the
bounce. The total energy before and after the bounce is constrained by
the underlying symmetries, though the exact nature of this energy at
t=0t=0 is quantum mechanical.
    String Theory: In string theory, the universe’s initial state might
involve a compactified or higher-dimensional configuration. Energy
conservation arises from the symmetries of the string landscape, but at
t=0t=0, the classical notion of energy may be replaced by quantum
operators or brane dynamics.
c. Inflation and Energy Conservation
    The inflationary epoch (t∼10−36t∼10−36 to 10−3210−32 seconds)
involves rapid exponential expansion driven by a hypothetical scalar
field (the inflaton). The energy of the inflaton field is converted into
matter and radiation during reheating, preserving energy locally.
    The zero-energy universe hypothesis is compatible with inflation:
the negative gravitational energy grows as spacetime expands, balancing
the positive energy of the inflaton and later matter/radiation.
    Inflation also smooths out any initial energy inhomogeneities,
ensuring that the universe’s large-scale energy distribution aligns with
conservation principles as classical spacetime emerges.
d. Quantum Gravity and the Planck Epoch
    During the Planck epoch (t<10−43t<10−43 seconds), the universe was
so dense that quantum gravity dominated. Classical energy conservation
may not apply directly, as spacetime and energy are quantized.
    In speculative frameworks like string theory or loop quantum
gravity, energy conservation is expected to emerge from the symmetries
of the quantum gravitational theory. For example, if the fundamental
laws are time-translation invariant at the quantum level, a form of
energy conservation would hold even in the pre-classical regime.
    Some models propose that the universe’s initial state was a quantum
vacuum with zero average energy, but quantum fluctuations could produce
particle-antiparticle pairs or fields, with energy conserved in the
quantum mechanical sense.
4. Why Energy Conservation Seems to "Evolve from Nothing"
Your intuition that the "primordial atom" had no defined energy, and
that energy conservation emerged from "nothing," is insightful. Here’s
how this apparent paradox is addressed:
    Zero Total Energy: The universe may have started with zero total
energy, as in the zero-energy universe hypothesis. If the positive
energy of matter and radiation balances the negative gravitational
energy, no initial energy is required, and conservation is satisfied
trivially (zero remains zero). This idea suggests the universe could
arise from "nothing" (a quantum vacuum) without violating energy
conservation.
    Quantum to Classical Transition: At t=0t=0, the universe was likely
in a quantum gravitational state where classical energy conservation
doesn’t apply. As the universe expanded and cooled, classical spacetime
emerged, and with it, the familiar form of energy conservation rooted in
time-translation symmetry. The "evolution" of energy conservation
reflects this transition from a quantum to a classical regime.
    No Classical "Source" Needed: The universe doesn’t require a
pre-existing reservoir of energy. Quantum cosmological models suggest
the universe could bootstrap itself into existence via quantum
fluctuations or tunneling, with energy conservation enforced by the
underlying quantum dynamics.
5. Challenges and Open Questions
    Singularity and Quantum Gravity: The classical singularity at t=0t=0
is a barrier to understanding energy conservation, as general relativity
breaks down. A quantum gravity theory is needed to describe whether
energy conservation holds in this regime and in what form.
    Global vs. Local Conservation: In an expanding universe, global
energy conservation is not always well-defined, but local conservation
holds. The zero-energy universe hypothesis resolves this by proposing a
globally conserved total energy of zero, but this is a theoretical
assumption, not directly observable.
    Initial Conditions: Why the universe has zero (or near-zero) total
energy, if true, remains an open question. Some attribute it to
anthropic principles or multiverse scenarios, while others seek a
fundamental explanation in quantum gravity.
    Testing Early Physics: Observations like the CMB and large-scale
structure probe the universe at t∼380,000t∼380,000 years, not t=0t=0.
Extrapolating energy conservation back to the Planck epoch relies on
theoretical models, and alternative cosmologies (e.g., ekpyrotic or
cyclic models) may propose different energy dynamics.
6. Conclusion
Energy conservation since t=0t=0 is supported by theories that leverage
the universe’s symmetries and quantum origins. The zero-energy universe
hypothesis suggests the total energy was zero at the start, with
positive matter/radiation energy balanced by negative gravitational
energy, satisfying conservation without requiring an initial energy
source. Quantum cosmological models, such as those in loop quantum
cosmology or string theory, propose that the universe emerged from a
quantum state (e.g., a fluctuation or bounce) where energy conservation
is maintained in a quantum sense. As classical spacetime emerged after
the Planck epoch, energy conservation took its familiar form, rooted in
time-translation symmetry.
The apparent "evolution from nothing" reflects the transition from a
quantum gravitational regime, where classical energy is undefined, to a
classical universe where conservation laws govern. The universe likely
required no pre-existing energy, as it could arise from a quantum vacuum
with zero net energy. While the exact nature of t=0t=0 remains
speculative due to the lack of a complete quantum gravity theory,
current models strongly suggest that energy conservation is a
fundamental principle, either trivially satisfied (zero total energy) or
emergent from the symmetries of the early universe.
If you’d like a deeper dive into a specific framework (e.g., the
zero-energy hypothesis, loop quantum cosmology, or inflation’s role), or
if you want to explore related topics like the role of dark energy in
conservation, let me know!