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

On Wed, 7 May 2025 1:02:26 +0000, rhertz wrote:

This is from DeepSeek:
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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.
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>
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Your assertion touches on a fundamental principle in physics, and the
reaction you received might stem from a misunderstanding or
oversimplification of how conservation laws work in real-world systems.
Let's clarify the physics involved and address your challenge.
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1. Conservation Laws in Physics
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Linear Momentum (p = mv) and Angular Momentum (L = Iω or L = m r² φ̇)
are exact conservation laws in isolated systems (no external
forces/torques). These are not "purely theoretical" but are rigorously
verified in experiments and engineering (e.g., spacecraft maneuvers,
particle collisions).
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On Earth or in low-Earth orbit, systems are not perfectly isolated due
to:
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Friction/drag (dissipating momentum into heat/air molecules).
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External forces (gravity from the Moon/Sun, atmospheric particles, solar
radiation pressure).
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Non-ideal collisions (energy loss to sound/deformation).
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However, this doesn’t invalidate the conservation laws—it just means you
must account for all interacting parts (e.g., Earth + object +
atmosphere). If you include every exchange of momentum (e.g., air
molecules gaining momentum when a ball slows down), the total momentum
is conserved.
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2. Your Challenge: Conservation in the Universe
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Angular momentum is conserved in the universe if you consider the entire
closed system. For example:
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A spinning star collapsing into a neutron star speeds up (conserving L:
I decreases, ω increases).
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Planets orbiting stars: if the Sun’s mass slowly vanished, Earth’s
angular momentum would be transferred to the Sun’s remnant or
gravitational waves.
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On cosmological scales, tidal torques between galaxies exchange angular
momentum.
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Proof: No known physical process violates angular momentum conservation.
Even in general relativity, the total angular momentum (including
spacetime curvature effects) is conserved for asymptotically flat
spacetimes. Experiments (e.g., LIGO, spacecraft navigation) rely on
this.
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3. Why the Forum’s Reaction?
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They may have misinterpreted your claim as denying conservation laws in
principle, rather than noting their practical complexity in non-isolated
systems. On Earth, we often use approximations (e.g., ignoring air
resistance for short timescales), but the laws hold exactly when all
interactions are included.
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The silence might reflect difficulty in articulating how to account for
all momentum transfers in a real-world Earth-bound system (e.g.,
tracking every air molecule’s motion).
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4. How to Resolve the Debate
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For Earth/near-space: Admit that momentum conservation is obscured by
external forces, but emphasize that it’s not violated—just harder to
measure because momentum leaks into the environment (e.g., Earth’s
rotation absorbs angular momentum from satellites via tidal forces).
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For the universe: Cite astrophysical examples (above) or textbooks like
Landau & Lifshitz’s Mechanics (§14: "Angular momentum is conserved in
any closed system, regardless of internal forces").
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For experimental proof: Refer to:
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Satellite gyroscopes (e.g., Gravity Probe B confirming frame-dragging,
which respects angular momentum conservation in curved spacetime).
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Particle physics (collisions where initial/final angular momentum sums
match).
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5. Key Point
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Conservation laws are always valid, but their apparent violation arises
when we artificially exclude parts of the system. Your critics likely
assumed you were rejecting the laws outright, while you were (correctly)
noting the challenges of applying them to open subsystems like objects
on Earth.
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If you reframe your argument as "Momentum conservation is often
practically obscured on Earth due to external interactions, but it holds
universally when all exchanges are accounted for," you might find more
agreement. The universe doesn’t break physics—we just need to include
all the physics.
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thanks
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You're very welcome! I'm glad I could help clarify things. Physics can
get heated (pun intended) when discussing fundamental principles, but
it's all about understanding the nuances.
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If you ever want to dive deeper into specific cases (e.g., how tidal
forces transfer Earth-Moon angular momentum, or how spacecraft
navigation accounts for perturbations), feel free to ask. Or if you'd
like a sharp, quotable rebuttal for your forum, I’d be happy to help
craft one.
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Keep questioning—that’s how science moves forward. Even if others react
strongly, you’re pushing for precision, and that’s valuable.
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Cheers to clear physics! 🚀

There is a WORLD of difference between DeepSeek and ChatGPT,
the latter being quite inferior.  DeepSeek's answer presents
clearly what I was alluding to in my post.  It made one error,
though, when it presumed that Hertz wasn't in denial of
conservation laws :-).  I hope he now understands that such
laws are quite accurate.  Otherwise, every Tom, Richard and
Harry would be building perpetual motion machines and Dean
drives (https://en.wikipedia.org/wiki/Dean_drive)