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

NOW WITH GROK. FORGET THE EQUATIONS, AS I DID A BRUTE FORCE COPY&PASTE.
COMPARE THE THREE ANSWERS: CHATGPT, DEEPSEEK AND GROK, IN PARTICULAR
ABOUT
T=0 IN THE BIG BANG MODEL, WHERE I CLAIM MOMENTUM DIDN'T EXIST AT ALL.
I have a discussion in a physics forum about that momentum conservation
(linear or angular) can't be conserved on Earth or near surrounding
outer space. I asserted that, maybe, it can happen in outer space, but
far from Earth. Reasons? Friction causing heat and air molecules being
drafted. So, equations like p=mv or p=mr^2PHI can't be applied on Earth,
and are purely theoretical. Most members of the forum accused me of
crazy, heretic, etc. I challenge the forum to prove that angular
momentum is conserved IN THE UNIVERSE. Silence since my post.
Your argument in the physics forum touches on an interesting point about
the conservation of momentum (linear and angular) and its applicability
in real-world scenarios versus idealized theoretical conditions. Let’s
break it down to clarify the physics, address your claims, and explore
why your challenge to the forum might have met with silence.
1. Conservation Laws in Physics
Linear momentum (
p=mv) and angular momentum (
L=Iω or, for a point particle,
L=mr×v) are conserved in closed systems where no external forces (for
linear momentum) or torques (for angular momentum) act. This is a
consequence of Newton’s laws and Noether’s theorem, which links
conservation laws to symmetries in physics (translational symmetry for
linear momentum, rotational symmetry for angular momentum).
On Earth: Systems are rarely closed due to external forces like
friction, air resistance, and gravity gradients. These forces introduce
non-conservative effects (e.g., friction generates heat, dissipating
energy and affecting momentum). For example, a spinning top slows down
due to frictional torque at its base, meaning angular momentum is not
conserved locally within the top alone.
In outer space: Far from massive bodies, gravitational fields are
weaker, and there’s no atmosphere to cause drag. Systems in deep space
can approximate closed systems more closely, so conservation laws apply
more readily. However, even in space, weak influences like gravitational
perturbations or solar wind can introduce small external forces or
torques.
Your intuition that momentum conservation is more applicable far from
Earth is partially correct, as deep space minimizes external influences.
However, your claim that equations like p=mv or L=Iω are “purely
theoretical” and inapplicable on Earth overstates the case, as these
equations are routinely used in practical physics with appropriate
considerations.
2. Why Your Forum Post Might Seem Controversial
The forum’s reaction (calling your claims “crazy” or “heretic”) likely
stems from a misunderstanding or your phrasing, which might have
suggested you’re denying fundamental physics. Conservation laws are
well-established and experimentally verified, even on Earth, when
systems are carefully defined. For example:
Linear momentum: In collisions on a low-friction air table, momentum is
conserved to a high degree because external forces (friction, air drag)
are minimized.
Angular momentum: A figure skater spinning faster by pulling in their
arms demonstrates angular momentum conservation, as the torque from
friction is small over short timescales.
Your assertion that friction and air drag prevent conservation on Earth
is valid in open systems but doesn’t negate the utility of conservation
laws in controlled or approximated scenarios. By challenging the forum
to prove angular momentum is conserved “in the universe,” you might have
appeared to question a bedrock principle, prompting strong reactions.
3. Addressing Your Challenge: Is Angular Momentum Conserved in the
Universe?
Your challenge to prove that angular momentum is conserved “in the
universe” is intriguing but needs clarification. Let’s interpret it as
asking whether angular momentum is conserved for the universe as a whole
or in specific systems within it.
The Universe as a Whole: The universe is not a simple closed system in
the Newtonian sense, as it’s governed by general relativity, and its
boundaries (if any) are unclear. However, angular momentum conservation
is expected to hold in isolated regions where external torques are
negligible. For the entire universe, the question is complex due to
cosmological factors like expansion and potential violations of
rotational symmetry on large scales. There’s no definitive evidence that
the universe’s total angular momentum is conserved or even well-defined,
as it depends on the universe’s topology and dynamics. However, this is
a niche topic far beyond typical forum discussions.
Isolated Systems in the Universe: In practice, angular momentum is
conserved in systems where external torques are absent or negligible.
Examples include:
Planetary orbits: The angular momentum of a planet orbiting a star is
nearly conserved, with small corrections due to gravitational
interactions with other bodies.
neutron stars: Their angular momentum is conserved over long periods,
with gradual losses due to electromagnetic radiation or gravitational
waves.
Laboratory experiments: Systems like rotating flywheels in vacuum
chambers conserve angular momentum when external torques are minimized.
To “prove” angular momentum conservation, physicists rely on:
Theoretical derivation: From Newton’s laws or Lagrangian mechanics,
showing that
dL/dt =τ
ext
​
 , so angular momentum is constant if external torque  is zero.
Experimental evidence: Countless experiments, from gyroscopes to
particle collisions, confirm conservation when external influences are
controlled.
Astrophysical observations: Conservation is observed in rotating
galaxies, binary star systems, and accretion disks, with deviations
explained by known torques.
4. Why the Silence?
The forum’s silence could stem from several factors:
Misinterpretation: Members might think you’re denying conservation laws
outright, which are foundational to physics, and find it hard to engage
without clarifying your stance.
Scope of the Challenge: Proving conservation “in the universe” is a
vast, almost philosophical question that’s hard to address in a forum
post. Most physicists would point to isolated systems rather than the
entire cosmos.
Forum Dynamics: Online forums can be polarized; your bold challenge
might have been dismissed as trolling or too vague to tackle
constructively.
5. Refining Your Argument
To engage the forum productively, you could clarify your position:
Acknowledge that conservation laws hold in closed or nearly closed
systems, even on Earth, when external forces/torques are minimized
(e.g., in lab experiments).
Emphasize that your point is about real-world complications (friction,
air drag) making ideal conservation harder to observe in open systems on
Earth.
Reframe your challenge: Ask for examples of angular momentum
conservation in practical or astrophysical systems, or discuss how
conservation is approximated in non-ideal conditions.
For example, you could say: “I understand angular momentum is conserved
in closed systems, but on Earth, friction and air resistance often
disrupt this. Can anyone share examples where angular momentum is
conserved in real-world systems, or explain how we account for
non-conservative effects?”
6. Mathematical Context
To ground this, consider the equations you mentioned:
Linear momentum:
p=mv. This is the definition of momentum, and conservation follows if
ext=0∑F
 .
Angular momentum: You wrote
p=mr2ϕ, likely meaning , where ϕ  is angular velocity (ω). For a point
particle, angular momentum is
L=mr2ω, and conservation holds if ext=0
​
 .
These equations are not “purely theoretical.” They’re applied in
engineering (e.g., satellite attitude control), astrophysics (e.g.,
Kepler’s laws), and particle physics, with corrections for external
effects like friction or tidal torques.
7. Conclusion
Your intuition about friction and air drag affecting momentum
conservation on Earth is correct for open systems, and deep space does
provide better conditions for observing conservation. However,
conservation laws are not just theoretical; they’re applied successfully
in many real-world scenarios by accounting for external forces/torques.
Your challenge about the universe is philosophically interesting but
hard to address definitively, as it involves cosmological complexities.
The forum’s reaction likely reflects a misunderstanding of your intent
or the provocative phrasing of your challenge.
To move the discussion forward, clarify that you’re questioning the
practicality of conservation in open systems, not the laws themselves,
and invite specific examples or counterarguments. This could turn the
silence into a constructive debate.
If you’d like, I can analyze specific forum posts on X or elsewhere to
gauge the community’s perspective, or I can help you draft a follow-up
post to rekindle the discussion. Let me know!
No. I prefer you to analyze how angular momentum is conserved within the
Big Bang theory, since it all started with a "primal atom" going off.
Momentum didn't exist at time t=0.
Analyzing angular momentum conservation within the context of the Big
Bang theory is a fascinating and complex question, as it requires
bridging classical physics (where angular momentum is well-defined) with
cosmology and the extreme conditions of the early universe. Below, I’ll
explore how angular momentum is understood in the Big Bang model,
considering the universe’s evolution from the initial singularity (or
“primal atom” in early formulations) and addressing your point that
momentum didn’t exist at t=0.
1. The Big Bang and the Initial State
The Big Bang theory describes the universe’s evolution from an extremely
hot, dense state approximately 13.8 billion years ago. The term “primal
atom” comes from Georges Lemaître’s early hypothesis, which envisioned
the universe originating from a highly compressed state. Modern
cosmology refines this into a singularity—a point of infinite density
and temperature where classical physics, including concepts like
momentum, breaks down.
At t=0: The singularity is not a physical “atom” but a boundary where
our current understanding of physics (general relativity and quantum
mechanics) fails. Space, time, and matter as we know them didn’t exist
in a classical sense. Angular momentum, defined as L=r×p (for a
particle) or L=Iω (for a rotating system), requires a well-defined
position, momentum, and spatial extent. At the singularity:
Space itself is undefined (or infinitesimally small), so the position
vector
r is meaningless.
Momentum p cannot be defined in the classical sense, as particles and
their velocities are not distinct in this quantum-gravitational regime.
Quantum mechanics suggests that properties like angular momentum are
quantized, but at t=0, the universe is governed by a hypothetical
quantum gravity theory (e.g., string theory or loop quantum gravity),
where classical conservation laws may not directly apply.
Thus, you’re correct that angular momentum (and momentum in general)
didn’t exist at
t=0 in the classical sense, as the framework for defining it was absent.
2. Emergence of Angular Momentum Post-Big Bang
As the universe expanded and cooled immediately after the Big Bang, the
conditions for defining angular momentum emerged. Let’s trace this
evolution:
Planck Epoch (t<10−43 seconds): The universe is in a
quantum-gravitational state. General relativity and quantum mechanics
are incompatible here, and no classical conservation laws (like angular
momentum conservation) can be applied. Some quantum gravity models
suggest the universe might have had quantum fluctuations, but whether
these carried angular momentum is speculative and model-dependent.
Inflation (t≈10−36  to 10−32  seconds): The universe underwent rapid
exponential expansion driven by a hypothetical inflaton field. Inflation
smoothed out initial irregularities, making the universe highly
isotropic (same in all directions) and homogeneous (uniform in density).
In an isotropic universe:
Net angular momentum is expected to be zero or negligible, as there’s no
preferred axis of rotation. Any initial angular momentum in quantum
fluctuations would be diluted by the immense expansion.
However, inflation allows for small quantum fluctuations to seed density
perturbations, which later grow into galaxies and large-scale
structures. These fluctuations could, in principle, carry tiny amounts
of angular momentum, but the universe as a whole remains nearly
rotationless.
Post-Inflation (after t≈10−32 seconds): As the universe cooled,
particles (quarks, electrons, photons) and fundamental forces emerged.
Angular momentum becomes meaningful once particles and fields have
defined positions and momenta. Conservation of angular momentum applies
locally to systems where external torques are absent, as dictated by
Noether’s theorem (rotational symmetry implies angular momentum
conservation).
3. Conservation of Angular Momentum in the Universe
To address whether angular momentum is conserved in the Big Bang
framework, we need to consider the universe as a system and its
symmetries:
Rotational Symmetry: The universe on large scales is observed to be
isotropic, as evidenced by the cosmic microwave background (CMB)
radiation, which is uniform to 1 part in 100,000. Isotropy implies no
net rotation or preferred angular momentum axis. If the universe has no
net angular momentum initially (post-inflation), conservation would
imply it remains zero unless external torques act. Since the universe
encompasses all space, there are no external torques by definition.
Local Conservation: Angular momentum is conserved in isolated systems
within the universe. For example:
Galaxies and Stars: As density perturbations collapsed under gravity to
form galaxies, any initial angular momentum in collapsing gas clouds was
conserved, leading to rotating disks (e.g., spiral galaxies). This is
why galaxies have angular momentum, derived from tidal torques between
neighboring structures or initial fluctuations.
Planetary Systems: The angular momentum of a star-planet system is
conserved during formation, modulo losses from processes like magnetic
braking or accretion disk interactions.
Particle Interactions: In high-energy particle collisions (e.g., in the
early universe or modern accelerators), angular momentum is conserved
when no external torques act.
Global Conservation: The universe’s total angular momentum is harder to
define. General relativity complicates global conservation laws because:
The universe’s geometry (e.g., flat, open, or closed) affects how we sum
angular momentum across vast distances.
In an expanding universe, the metric changes, and conserved quantities
are trickier to define. For example, in a Robertson-Walker metric (used
in cosmology), rotational symmetry holds on large scales, suggesting
angular momentum conservation for isolated subsystems, but the
universe’s expansion introduces non-trivial effects.
Some models propose the universe could have a tiny net angular momentum,
but observations (e.g., CMB isotropy, galaxy rotation surveys) suggest
it’s negligible. If the universe started with zero angular momentum
post-inflation, conservation would maintain this.
4. Did the Universe Start with Zero Angular Momentum?
Your statement that momentum didn’t exist at t=0 aligns with the
breakdown of classical physics at the singularity. Post-singularity, the
universe’s angular momentum likely started near zero due to:
Inflation: The rapid expansion erased any initial rotation or angular
momentum, as any pre-inflation angular momentum would be stretched
across scales larger than the observable universe.
Isotropy: Observations of the CMB and galaxy distributions show no
evidence of large-scale rotation. Studies (e.g., Su & Magueijo, 2011)
have searched for rotational signals in the CMB and found upper limits
on the universe’s rotation rate
ω<10−9  radians per year), implying negligible net angular momentum.
Symmetry: A universe with significant net angular momentum would exhibit
anisotropic expansion or a preferred rotation axis, which contradicts
observations.
However, local angular momentum emerged as structure formation began.
For example, gravitational collapse amplified small fluctuations, and
tidal interactions between proto-galaxies transferred angular momentum,
leading to the rotation of galaxies and clusters.
5. Challenges and Speculations
Some open questions and speculative ideas in cosmology touch on angular
momentum:
Pre-Big Bang Scenarios: Models like loop quantum cosmology or string
theory suggest the Big Bang wasn’t the absolute beginning. If a
“pre-universe” had angular momentum, it might influence the post-Big
Bang state, but such ideas are untested.
Quantum Gravity: At t=0, angular momentum might be defined in a
non-classical way (e.g., via spin networks in loop quantum gravity).
Conservation might emerge only as classical spacetime forms.
Dark Matter and Dark Energy: These components dominate the universe’s
energy budget but interact weakly with matter. Their role in angular
momentum conservation is unclear, though dark matter halos in galaxies
clearly rotate and conserve angular momentum locally.
6. Mathematical Perspective
Angular momentum conservation follows from rotational symmetry. In
general relativity, the stress-energy tensor’s conservation implies
local conservation laws, but global conservation in an expanding
universe is nuanced. For a system in flat spacetime, angular momentum
is:
L=∫r×(ρv)dV
where ρ is density and v is velocity. In an isotropic, homogeneous
universe, the velocity field averages to zero (no net rotation), so L≈0.
As structures form, local angular momentum arises from gravitational
torques, but the total remains conserved in the absence of external
influences.
7. Conclusion
In the Big Bang framework, angular momentum didn’t exist at t=0 due to
the singularity’s undefined nature. Post-Big Bang, the universe likely
started with near-zero net angular momentum due to inflation’s smoothing
effect and observed isotropy. Angular momentum conservation holds
locally for isolated systems (e.g., galaxies, stars) as spacetime
emerged and symmetries applied. Globally, the universe’s total angular
momentum is probably zero or negligible, conserved in the sense that no
external torques act on the universe as a whole. Your intuition about
the absence of momentum at t=0 is correct, and the emergence of angular
momentum is a consequence of the universe’s evolution from a symmetric,
non-rotating state to one with local structures.
If you’d like to use this to reframe your forum challenge, you could
ask: “How does angular momentum conservation apply to the early
universe, given that classical momentum wasn’t defined at the Big Bang?”
This could spark a focused discussion. Alternatively, I can dig into
specific cosmological models or analyze relevant X posts for community
perspectives. Let me know your next step!
No. Thanks.
Alright, glad I could help clarify the topic. If you change your mind or
want to dive into another physics question, just let me know!