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*Mar*
Mathematics-Vs-Reality
II think that all Planetary movements, actually every movement of
everything in Astronomy is mathematically precise and accurate. There can
be interference from any force. But the why in the case of absolute zero
the interference is assumed? Why?
Chat gpt
This is an excellent question, and you’re zeroing in on a deep idea: *if
the universe follows precise mathematics, why does absolute zero have a
“no-go” rule while planetary motion does not?* The key is *what kind* of
mathematics is involved.
------------------------------
*1. Planetary motion is mathematically precise — but not perfectly rigid*
Planetary motion follows *deterministic physical laws* (Newton’s laws,
General Relativity). Given initial conditions, the motion is mathematically
defined.
However:
- Planets are *never isolated*
- There are always perturbations: other planets, radiation, tidal
effects, quantum fluctuations, spacetime curvature
- We handle this using *approximations and corrections*
So the motion is:
- *Law-governed*
- *Predictable to high precision*
- *Not exact in the mathematical sense of a closed system*
In fact, the solar system is *chaotic* over long timescales—tiny
uncertainties grow exponentially.
------------------------------
*2. Absolute zero is different in kind, not degree*
Absolute zero is not “hard to reach” because of practical interference. It
is forbidden because of a *fundamental limit*, not because of uncontrolled
forces.
The key difference:
*🔹 Planetary motion:*
“Here is an equation describing how the system evolves.”
*🔹 Absolute zero:*
“No physical process can make temperature exactly zero.”
This comes from *the Third Law of Thermodynamics* and *quantum mechanics*,
not from experimental imperfections.
------------------------------
*3. Why interference matters for absolute zero but not for planets*
*A. Temperature is not just motion*
Temperature measures the *statistical distribution of energy states* in a
system.
At 0 K:
- All particles would have to be in the *single lowest quantum state*
- No entropy
- No uncertainty in momentum
Quantum mechanics forbids this.
By the *Heisenberg Uncertainty Principle*:
- If a particle is confined, it must have non-zero momentum
- That momentum corresponds to energy
- This is *zero-point energy*
So even in *perfect isolation*, motion cannot vanish.
This is not “interference” from outside — it is *intrinsic*.
------------------------------
*B. Planetary motion does not require a forbidden state*
Nothing in physics says:
- “A planet must not have exactly zero acceleration”
- “An orbit may not be perfectly elliptical”
But physics *does* say:
- “A system cannot reach a pure ground state with zero entropy”
- “You cannot extract the last bit of thermal energy”
Absolute zero is a *boundary that physical laws prohibit crossing*.
------------------------------
*4. Mathematical precision ≠ physical realizability*
This is the crucial idea.
Physics uses mathematics to describe:
- What *can happen*
- What *cannot happen*
Both are equally precise.
Examples:
- You can mathematically describe a particle with exact position and
momentum — but physics forbids it.
- You can mathematically describe negative temperatures — and physics
allows them in special systems.
- You can mathematically describe 0 K — physics says it is unreachable.
So mathematics is not violated. It is *constrained*.
------------------------------
*5. Why astronomy doesn’t face this limit*
Astronomical systems:
- Are macroscopic
- Governed by classical limits
- Not required to reach an extremal quantum state
Thermodynamic extremities (like 0 K):
- Are *limit points*, not reachable states
- Similar to reaching the speed of light or infinite density
We can approach them arbitrarily closely — but never reach them.
------------------------------
*6. A useful analogy*
Think of a mathematical curve:
[
y = \frac{1}{x}
]
- You can get arbitrarily close to ( y = 0 )
- But you never reach it
Absolute zero is like that asymptote:
- Mathematically defined
- Physically unreachable
Planetary motion is like moving *along* the curve, not trying to hit the
asymptote.
------------------------------
*7. Bottom line*
- ✔ The universe follows precise mathematics
- ✔ Planetary motion is accurately predictable
- ❌ Absolute zero is not blocked by “random interference”
- ❌ It is blocked by *fundamental physical laws*
- ✔ Mathematics allows it; physics forbids reaching it
So the difference is *not inconsistency*, but *category*:
*dynamical evolution vs forbidden boundary state*.
If you want, we can go even deeper—into *why nature seems to forbid exact
extremes at all*.
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