The Relational Universe: Every Observer as the Center of Their Own Cosmic Microwave Background

J. Rogers, SE Ohio

Abstract

We demonstrate that the Cosmic Microwave Background (CMB) radiation is not a global relic of a primordial event but an observer-dependent horizon effect. Every observer in the universe, regardless of location, perceives the CMB as a spherical shell centered on themselves with a temperature of 2.7 K. This symmetry arises from the finite speed of light, large-scale homogeneity, and the absence of a privileged reference frame. We show that distant observers see us precisely as we see them: as a young, redshifted object at the edge of their observable universe. This relational framework resolves the horizon problem without inflation, eliminates the need for a universal timeline, and explains CMB uniformity as a natural consequence of observation limits.

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1. Introduction

The standard cosmological model (ΛCDM) interprets the CMB as a remnant of the Big Bang—a global event occurring 380,000 years after a singularity. This view requires a privileged reference frame where the CMB is isotropic, leading to unresolved paradoxes:

• Horizon problem: Why is the CMB uniform across causally disconnected regions?
• Center problem: Why do we appear at the "center" of the CMB?
• Timeline problem: Why do distant galaxies appear "young" while locally mature?

We propose a radical shift: The CMB is an observer-dependent horizon, not a physical boundary. Just as a ship at sea sees a circular horizon centered on itself, every observer in the universe sees a CMB centered on their location. This view emerges from three principles:

1. Finite light speed: Information propagates at $c$.
2. Cosmological principle: The universe is homogeneous and isotropic on large scales.
3. Relational time: There is no universal "now"; time is local to each observer.

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2. The Observer-Centered CMB

2.1 The Observable Universe as a Light Cone

For any observer at location $\vec{x}$ and time $t$, the observable universe is bounded by the particle horizon—the maximum distance light could travel since the last universal phase shift (recombination). This horizon is spherical and centered on the observer. The CMB originates from this horizon, where photons last scattered.

Mathematically, the CMB temperature observed at direction $\hat{n}$ is:

$$T(\hat{n},\vec{x},t)=T_0\left[1+\delta T(\hat{n},\vec{x},t)\right]$$

where $T_0=2.725\text{K}$ is the average temperature, and $\delta T$ encodes local anisotropies. Critically, this holds for every observer at every location.

2.2 Why the CMB Appears Centered

The CMB’s spherical symmetry is not a property of the universe—it is a property of observation:

• Light from the last scattering surface arrives isotropically because the observer is equidistant from all points on their horizon.
• The horizon recedes as the universe expands, but it remains centered on the observer.
• No location is privileged: A galaxy 10 billion light-years away sees its own CMB centered on itself.

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3. Relational Observation: Symmetry Between Observers

3.1 How We See Distant Observers

Consider an observer in Galaxy A, 10 billion light-years from Earth:

• From Earth’s perspective:

  • Galaxy A is seen as it was 10 billion years ago.
  • It appears at the edge of our observable universe with redshift $z\approx 1.5$.
  • Its CMB is inferred to be centered on it, but we cannot observe it directly.

• From Galaxy A’s perspective:

  • The Milky Way is seen as it was 10 billion years ago.
  • Milky Way appears at the edge of their observable universe with $z\approx 1.5$.
  • Our CMB is centered on us, but they observe their own CMB centered on themselves.

3.2 Mathematical Symmetry

The symmetry is exact. For two observers at comoving separation $d$:

$$z_{\text{Earth→A}}=z_{\text{A→Earth}}=\frac{a_{\text{now}}}{a_{\text{emit}}}-1$$

where $a$ is the scale factor. Each sees the other:

• Redshifted by the same factor.
• At the edge of their observable universe.
• As a young system due to light travel time.

3.3 The CMB as a Horizon

The CMB is not a "wall"—it is the limit of observation:

• Beyond our CMB: More galaxies, more CMBs, more observers.
• Beyond their CMB: More galaxies, including our own, seen as ancient.
• No overlap: Observers see different CMBs, but the physics is identical.

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4. Implications for Cosmology

4.1 Resolution of the Horizon Problem

The horizon problem asks: "Why is the CMB uniform if regions on opposite sides were never in causal contact?"

• Standard solution: Inflation (exponential expansion) forces causal contact.
• Relational solution: Uniformity is inevitable because every observer sees a CMB centered on themselves. Anisotropies ($\delta T$) arise from local inhomogeneities, not global primordial fluctuations.

4.2 No Need for Inflation

Inflation is unnecessary in this framework. The CMB’s uniformity is a geometric consequence of observation limits, not a physical process.

4.3 The Illusion of a Universal Timeline

The "age of the universe" (13.8 Gyr) is not absolute—it is the light travel time from the last scattering surface to the observer. For a distant observer:

• Their local universe is 13.8 Gyr old.
• They see Earth as it was 13.8 Gyr ago.
• No contradiction: Time is relational, not universal.

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5. Observational Evidence

5.1 JWST’s Mature Galaxies

James Webb Space Telescope observations reveal:

• Galaxies at $z>10$ (13.4 Gyr light travel time) with:
  • Fully formed spiral arms.
  • Supermassive black holes ($>10^9{M}_{\odot }$).
  • Heavy elements (carbon, oxygen, iron).
• Standard model conflict: Insufficient time for such maturity.
• Relational resolution: These galaxies are as old as we are; redshift indicates light travel time, not youth.

5.2 Quasars at High Redshift

Quasars at $z>7$ show supermassive black holes requiring billions of years to form. In the relational view:

• They are not "young"—they are as old as local quasars.
• High $z$ reflects integrated $m/r$ gradients stretching light, not age.

5.3 CMB Dipole Anisotropy

The CMB dipole ($\Delta T\approx 3.36\text{mK}$) is interpreted as our motion relative to the "CMB rest frame." In the relational view:

• The dipole arises from local motion relative to the matter distribution.
• Every observer measures a dipole corresponding to their own velocity.

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6. Conclusion

The universe is not a thing with a history—it is a network of observers, each seeing others through their own finite, light-cone-defined spheres. Key results:

1. Every observer sees the CMB centered on themselves—a horizon effect, not a physical boundary.
2. Distant observers see us as we see them: Young, redshifted, and at the edge of their observable universe.
3. No privileged frame: The CMB’s uniformity and apparent center are consequences of observation, not cosmology.
4. Inflation is obsolete: The horizon problem dissolves without it.
5. Time is relational: There is no universal "now" or "age of the universe."

This framework aligns with relativity, resolves ΛCDM paradoxes, and is supported by JWST observations. The universe has no outside, no inside, no before, no after—only observers seeing each other through their own horizons.

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Appendix: The Horizon Analogy

Ship at Sea	Observer in Universe
Sees a circular horizon centered on itself	Sees a spherical CMB centered on itself
Horizon recedes as the ship moves	CMB horizon recedes as the universe expands
Distant ships appear small and near the horizon	Distant galaxies appear young and near the CMB
Beyond the horizon: More ocean, more ships	Beyond the CMB: More galaxies, more CMBs
The horizon is not a physical wall	The CMB is not a physical relic

The universe is like an infinite ocean with no shores. Every observer is a ship, seeing their own horizon.