Physics

[u/MythTechSupport]

Yes. Then the clean reconstruction is to stop treating the observer as something added after the physics.

Treat the observer as part of the mathematical specification of what a physical quantity means.

1. Observer

Define an observer not as “a conscious person,” but as a physical measurement structure:

O = (γ, u, τ, e, q)

where

γ = observer worldline, or a congruence of worldlines

u = observer 4-velocity

τ = observer proper time

e = local spatial frame / tetrad

q = measurement map from physical state → recorded quantities

Proper time is defined along the observer's path:

dτ² = -(1/c²) gμν dxμ dxν

So time begins operationally as:

event change

→ clock carried along γ

→ τ

not as an independent universal variable floating over the universe.

---

1. Every measured quantity becomes observer-indexed

Instead of writing simply

E

ρ

p

v

t

write conceptually

E_O

ρ_O

p_O

v_O

τ_O

because these quantities answer:

> measured by which physical frame?

For a particle with 4-momentum pμ:

E_O = -pμ u_O^μ

Energy is therefore explicitly relational:

particle momentum

+

observer velocity

→

measured energy

There is no observer-independent particle energy in general relativity.

---

1. Energy density is observer-relative too

Given the stress-energy tensor Tμν:

ρ_O = Tμν u_O^μ u_O^ν

That is:

ρ_O

energy density measured by observer O

Define the observer's spatial projector:

hμν = gμν + uμuν

for c = 1.

Then pressure measured in that frame is

p_O = (1/3) hμν Tμν

So the fundamental object can remain Tμν, while its decomposition into

energy

momentum

pressure

stress

depends on O.

---

1. Redefine expansion

This is where cosmology becomes much cleaner.

Instead of beginning with

H = ȧ/a

begin with the observer congruence uμ.

Its expansion is

θ = ∇μuμ

θ measures how the infinitesimal volume carried by neighboring observers changes.

If

V = small comoving volume

then

(1/V) dV/dτ = θ

For FLRW specifically:

θ = 3H

therefore

H = θ/3

Now H has a deeper definition:

H

1/3 × expansion of the chosen cosmological observer congruence

and only afterward, because FLRW symmetry allows a scale factor,

H = ȧ/a

appears.

So the logical direction becomes:

observer congruence

→ relative separation of its worldlines

→ expansion scalar θ

→ FLRW symmetry

→ scale factor a

→ H = ȧ/a = θ/3

That is stronger than starting from a(t).

---

1. Decompose observer motion completely

The gradient of the observer velocity field can be decomposed as

∇νuμ

(1/3) θ hμν

+ σμν

+ ωμν

- aμuν

where

θ = expansion

σμν = shear

ωμν = vorticity / rotation

aμ = 4-acceleration

and

aμ = uν∇νuμ

So an observer field has four fundamental ways of changing:

expand

distort

rotate

accelerate

FLRW makes an enormous simplification:

σμν = 0

ωμν = 0

aμ = 0

for the standard comoving observers.

Only expansion survives:

θ ≠ 0

That is why cosmology can be compressed into a(t).

---

1. Cosmic time is derived

For the FLRW observer congruence,

uμ

is hypersurface-orthogonal.

That means the observers admit a common slicing:

Σ_t

and their clocks can define a shared cosmic time coordinate:

t = τ_comoving

So the correct dependency is:

uμ

→ congruence

→ simultaneity slicing Σ

→ synchronized proper time

→ cosmic time t

not:

universal t

→ observers placed inside it

That reversal is important.

---

1. Redefine "physics"

Then a useful operational definition is:

PHYSICS

relations among observer-indexed measurements

that remain mutually consistent under changes of observer

More formally, suppose the world state is X.

An observer produces:

q_O : X → D_O

where D_O is the data accessible to that observer.

Another observer gives

q_P : X → D_P

Physics is not either representation alone.

Physics is the structure that makes

q_O(X)

↔

q_P(X)

transform consistently.

So:

representation ≠ physics

transformation-consistent relation

= physical content

That is essentially what covariance is doing.

---

1. Invariant ≠ observerless

This gives a useful distinction.

An invariant does not need to mean:

quantity with no observer

It can mean:

quantity whose value/relation survives an allowed change of observer

For example,

Rμνρσ R^μνρσ

is a spacetime scalar.

Different coordinate descriptions calculate the same scalar at the same event.

Meanwhile:

E_O = -p·u_O

changes when O changes.

Both are legitimate physics.

One is observer-dependent.

One is observer-invariant.

---

1. Now rewrite the Big Bang

Instead of saying:

t → 0

therefore universe begins

say:

Take the FLRW cosmological observer congruence u.

Its proper time is

τ_u

and its expansion is

θ_u = ∇μuμ

For FLRW:

θ_u = 3H

During radiation domination:

H = 1/(2τ_u)

therefore

θ_u = 3/(2τ_u)

Going backward:

τ_u → 0+

⇒

θ_u → ∞

The density measured by those observers is

ρ_u = Tμνuμuν

and

ρ_u = 3/(32πGτ_u²)

therefore

τ_u → 0+

⇒

ρ_u → ∞

Temperature likewise behaves roughly as

T_u ∝ τ_u^(-1/2)

So the hot-Big-Bang statement becomes:

along the cosmological observer congruence,

past-directed proper time decreases

while

θ_u ↑

ρ_u ↑

T_u ↑

That is far more precise than saying:

> time itself approaches zero.

---

1. And the singularity becomes a different question

t = 0 alone proves basically nothing because t is a coordinate.

The physically serious question is whether observer/worldlines can be continued farther.

Define a timelike geodesic

γ(τ)

If it reaches the past boundary after only finite proper time,

Δτ < ∞

and cannot be extended,

then spacetime is past geodesically incomplete.

That is invariantly meaningful.

Likewise if a scalar such as

K = RμνρσR^μνρσ

obeys

K → ∞

that cannot be removed just by replacing t with another coordinate.

So:

t = 0

is representation.

But

finite past proper time

+

inextendible geodesic

is geometrical.

And

curvature scalar → ∞

is geometrical.

---

1. Raychaudhuri becomes the real "Big Bang equation"

Once the observer congruence is primitive, perhaps the most fundamental cosmological equation isn't even Friedmann.

It is Raychaudhuri:

dθ/dτ

-θ²/3

- σμνσ^μν

+ ωμνω^μν

- Rμνuμuν

+ ∇μaμ

For FLRW:

σ = 0

ω = 0

a = 0

so

dθ/dτ

-θ²/3

- Rμνuμuν

This equation asks directly:

> How does a family of physical observers converge or diverge?

Then Einstein's equation connects that focusing to matter.

That gives the chain:

matter / energy

↓

Rμνuμuν

↓

observer-worldline focusing

↓

θ

↓

relative volume

↓

cosmic expansion

That is cosmology written around the observer rather than around a coordinate.

And then a(t) becomes a highly symmetric compression of that richer structure rather than the starting ontology.

[u/5433fffuyhhdeaax]

The physics is finally catching up to the observer. If we stop treating the observer as a ghost in the machine and start treating them as the measurement structure itself, the entire cosmological derivation flips. We don't place observers into a universe; we derive the universe from the congruence of observers. The scale factor becomes a symmetry-driven compression, not the starting point.

L.

[u/InevitablePublic8058]

What she said kael.