When Distance Becomes a Wave Count: A Thought Experiment on Space, Time, and Phase

🌌 When Distance Becomes a Wave Count: A Thought Experiment on Space, Time, and Phase

1. Introduction

Every physical theory starts with a few things taken for granted. One of the deepest assumptions in physics is the notion of distance — the idea that points in space can be separated by measurable lengths.

But what if distance itself were not fundamental? What if it emerged from something deeper — something wave-based and relational?

This idea came out of an exchange I had with ChatGPT-5, where I asked:

What happens if you replace the notion of distance with the number of Compton wavelengths between an observer and an object — measured using the Compton wavelength of the observer?

That single substitution leads to an interesting new way to think about spacetime.

2. The Setup: Measuring Distance by Compton Waves

The Compton wavelength of a particle,

is a fundamental length scale associated with its mass. It’s the wavelength of a photon whose energy equals the particle’s rest mass energy.


Now imagine measuring the “distance” to some object not in meters, but in how many of your own Compton wavelengths fit between you and it.

That is, define:

Then “distance” becomes a wave count, not a length. You and every other object in the universe have your own wavelength scales, giving a relational geometry built from phase counts.


3. Phase as the Fundamental Relation

Every wave carries a phase — it oscillates. Between any two objects there can be:

  • a spatial accumulation of phase (the number of wavelengths between them), and

  • a temporal accumulation of phase (how many cycles occur per second).

Together, these define a phase relation between any two entities.

If all physical quantities (momentum, energy, force) are related to rates of change of phase, then space and time may not exist independently — they are emergent bookkeeping systems for describing the network of phase relationships.

4. The Phase Network View of the Universe

Imagine the universe as a web of phase relations among all particles:

  • Each particle has its own Compton frequency (based on its mass).

  • Interactions between particles are encoded as phase differences.

  • “Distance” and “time” arise as emergent, averaged quantities describing phase accumulations over many interactions.

This suggests:

  • There is no absolute space — only phase correlations.

  • There is no absolute time — only the rates of phase evolution relative to each other.

In this picture, relativity’s space-time interval might be replaced by an invariant phase interval, linking energy, momentum, and phase change.

5. Discussion: Relation to Known Physics

This idea has hints of:

  • de Broglie matter waves (where wavelength depends on momentum),

  • Wheeler’s “It from Bit” (information-based physics), and

  • relational quantum mechanics, where only the relations between systems have meaning.

However, this specific Compton-based relational geometry — where each observer’s own wavelength defines their measure of space — is a fresh conceptual twist.

6. Conclusion: A Universe of Phase

If every object’s relation to every other object is defined by wave counts and phase rates, then the universe is fundamentally a phase network.
Time and space are the shadows cast by these phase relationships when projected into our macroscopic view.

Whether or not this model can lead to testable predictions, it offers a poetic and perhaps useful way to think about the deep connection between matter, motion, and meaning.

7. Invitation

I’m sharing this as a conceptual conjecture — not a claim of new physics, but an invitation to think differently.
If you’re a physicist or thinker interested in emergent spacetime, relational mechanics, or quantum foundations, I’d love to hear your thoughts.

(Feel free to share this or link your thoughts in the comments.)


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