Monday, 4 August 2025

You are standing in a field looking at the stars. Your arms are resting freely at your side, and you see that the distant stars are not moving. Now start spinning. The stars are whirling around you and your arms are pulled away from your body. Why should your arms be pulled away when the stars are whirling? Why should they be dangling freely when the stars don't move?

ChatGPT said:

This is a version of Mach’s principle—a deep philosophical and physical question about inertia and rotation, and how they relate to the rest of the universe.


What's happening?

  • When you’re not spinning, the stars are still. Your arms hang loosely—no force is acting on them other than gravity.

  • When you spin, the stars appear to whirl around you, and you feel your arms pulled outward. This is due to what we call centrifugal force—an apparent force that seems to push objects outward when they’re in a rotating frame of reference.


The paradox

Why should the distant stars—so far away—have any connection to whether your arms are pulled outward or not?

This question challenges the idea that acceleration and rotation are purely absolute. It leads to:


Mach’s Principle (as Ernst Mach posed it)

Mach speculated that:

The inertia of any object is the result of its interaction with the mass of the entire universe.

That is:

  • When you spin, your acceleration is relative to the distant stars.

  • The stars define the reference frame.

  • The resistance you feel (inertial forces like the centrifugal pull on your arms) is not due to some abstract space, but because you are rotating with respect to the distant matter in the universe.


In Newtonian mechanics:

  • Newton would say you are spinning with respect to absolute space, and the centrifugal force is an effect of that absolute rotation.

In Machian or relational views:

  • You're spinning relative to the fixed stars, and that's why the centrifugal force arises.

  • If the stars weren’t there (if the universe were empty), maybe you wouldn’t feel any outward pull at all.


Einstein and General Relativity

Einstein was influenced by Mach and tried to incorporate these ideas into General Relativity. While GR doesn't fully implement Mach's principle, it does partially honor it:

  • In GR, mass and energy shape spacetime.

  • Some solutions (like the Gödel universe or rotating shells of mass) show that local inertial frames can be affected by distant mass distributions—this is called frame-dragging or the Lense-Thirring effect.


Bottom line

  • Your arms are pulled outward because you are rotating with respect to the mass-energy content of the universe.

  • They dangle freely when you’re at rest with respect to it.

  • This suggests that inertia and centrifugal force are not just "internal" to your body or motion, but somehow entangled with the entire cosmos.

A single body in an empty universe would not know what it means to spin. Motion requires relation. Inertia, too, may be a form of cosmic entanglement.

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