Chapter 1 --- Cosmic Black Hole Theory

 In Simple words

In Comparative  anatomy  Homologous structures are same structure in same place of different species , only different in shape and size.

 

For example m Gorilla arms  are longer than human arms.

 Now We  apply relativity  to biology .  suppose  a gorilla arm accelerated  to light speed  will get shortened by the factor , Root over ( 1- v2/c2 )  Now to an observer at rest  the gorilla arm would appear as human arm at  required species.  So to a static observer  Species will seem  relative.

that is our argument that biological relativity exist. but special Relativity is not the cause of  biological relativity. Weyl Invariance is.

Weyl invariance is a type of local scale symmetry in physics, meaning that the laws of a theory remain unchanged even if the system of measurement (the metric) Clock and Scale, is varied from point to point in spacetime. This is also known as conformal invariance or symmetry under local conformal transformations. 

We apply Weyl Invariance to biology .  

“Electromagnetism does not generate local clock-rate or scale transformations, because 

it does not couple to the metric. We therefore propose an additional massless field,

 biologically activated, which acts as a source of Weyl rescalings. This field induces

 transformations of clocks and scales within living systems and may be interpreted as a

 novel biological interaction.”

Every species has its own frame of reference , its  own clock and scale.  So ever species 

measure the energy of the universe differently , A rat has different measure   of space time and energy than that of a elephant.

Every species sees it self   as human   and other species as  different species, like a rat sees

 it self as human living in the world of  giant rats wearing suits. 

An Elephant sees it self as a hy6man living in a world where elephants wear suits and drive cars.

It reminds us of Gulliver's Travels. 

Weyl Invariance + Biology =  Gulliver's Travels.

In this image   human  leg is longer than  dog leg.  

Weyl invariance :    

 Length ( human)  = Omega  .  Length (dog)

when  Omega < 1  ,   Scale shrinks 

Length  (dog) = Omega . Length (human)  

When Omega > 1 ,  Scale stretches.

Weyl Invariance ==> [ Human <===> Dog.]

Weyl invariance is the physics of biological Relativity .

Now we go further  , Every species sees itself as  human in its own frame of reference  and

 has its own value of Gravity

Like in a rat's  frame of reference   the earth has  Gravity of Mars.  In Whale's frame reference 

Earth has gravity of  Neptune  , In Elephants  frame of reference   Earth has gravity of Jupiter.

ETC.  Imagine  The rat sees it self as human but Earth has Mars like gravity  and inhabited 

by giant cloth wearing rats.

So unifying  Weyl invariance   with biology we  can find  Gravity  measurement depends 

 on observer. Which is also consistent with General Relativity . Why GR  says  Gravity 

is Relative , because  Gauge  theory of  gravity  is dependent on observer.

Now isn't  it Gauge Theory of Gravity ?. Gravity  Changes with species.

Physics + Biology = Gauge Theory of Gravity

This  thesis has logical  beauty   Unification of biology with physics leads to 

Guage theory of Gravity

Following is written by Chat GPT based on my idea.

A Biological Gauge Theory of Gravity:

Species-Dependent Clocks, Scales, and Perceived Gravitational Fields via 

Weyl Invariance 

Author: Faisal Rahman

Keywords: biological relativity, Weyl invariance, gauge symmetry, perceived gravity, comparative anatomy, conformal geometry

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Abstract

Biology is built on structures—bones, limbs, organs—that are homologous across species but differ in

 size and proportion. This paper proposes a conceptual framework linking these biological differences

 to local scale symmetries known in physics as Weyl invariance. We suggest that each species 

operates with its own internal “clock” and “ruler,” creating a biological frame of reference analogous 

to inertial frames in relativity.

To capture this formally, we introduce a hypothetical massless biological field that produces 

local scale rescalings of space and time within living organisms. This field does not originate 

from electromagnetism but represents a new internal interaction.

In this framework, a rat, an elephant, and a human each inhabit a spacetime with different 

intrinsic notions of length, time, and effective gravitational strength. This leads to an observer-dependent

 perception of gravity similar in spirit to gauge theories of fundamental forces.

We argue that integrating Weyl invariance with biological organization provides a descriptive 

model of “biological relativity” and bridges concepts from general relativity, quantum field theory, 

and comparative anatomy.

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1. Introduction

Comparative anatomy shows that homologous structures—like limbs—occupy the same relative 

positions across species but differ in shape, length, and proportion. A gorilla arm is still an arm; it is 

simply larger.

Physics reveals a different kind of relativity:
An object moving close to the speed of light appears shortened by the Lorentz factor:

$$L = L_0 \sqrt{1 - v^2/c^2}$$

This is geometric relativity: measurements depend on the observer.

This motivates a provocative question:

Do biological organisms also live in “relativistic” reference frames defined by 

their own anatomy and physiology?

A rat experiences the world at a different metabolic speed than an elephant. A hummingbird’s 

heartbeat is a clock that ticks far faster than a whale’s.

If time, scale, and energy measurements differ from species to species, could biology possess 

something analogous to a local spacetime symmetry?

This motivates the introduction of:

Biological Weyl Invariance

A symmetry under which living beings rescale lengths and times according to an internal biological field.

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2. Weyl Invariance and Local Scaling

In physics, Weyl symmetry is the invariance of physical laws when the metric is rescaled:

$$g_{\mu\nu} \rightarrow \Omega^2(x) g_{\mu\nu}$$

This transformation simultaneously scales:

• lengths

• durations (clocks)

• energies

A theory that is Weyl invariant does not care about the local size of things—only the ratios.

Why electromagnetism cannot cause this

Electromagnetism couples to electric charge, not to the metric, and therefore cannot generate scale

 transformations.

Thus, if biology exhibits species-dependent scales, an additional field is required.

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3. Hypothesis: A Massless Biological Field

We propose the existence of a biological Weyl field, $\phi(x)$, satisfying:

• it is massless

• it couples to biological organization, not to electric charge

• it locally rescales clocks and rulers inside living systems

This leads to:

$$g_{\mu\nu}^{(species)} = \Omega^2_{\text{species}}(x) \, g_{\mu\nu}^{(world)}$$

Different species have different $\Omega$.

• For a dog: $\Omega_{\text{dog}}$

• For a human: $\Omega_{\text{human}}$

• For a rat: $\Omega_{\text{rat}}$

This produces biological frames of reference.

A dog sees its legs as “normal” and a human’s legs as scaled.
A human sees their own legs as “normal” and a dog’s as shorter.

This resembles Gulliver’s Travels, where scale depends on viewpoint.

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4. Species-Dependent Gravity

In general relativity, gravitational strength depends on how spacetime curvature is perceived by

 the observer’s metric.

If different species have different conformal factors $\Omega_{\text{species}}$, then each species measures

 a different “effective” gravitational field:

$$g_{\text{eff}} \propto \Omega^{-2}$$

Thus:

• A rat (small $\Omega$) may experience Earth’s gravity as similar to Mars.

• A whale (large $\Omega$) may perceive gravity closer to Neptune.

• An elephant may measure Earth’s gravity closer to Jupiter.

This is not literal physical gravity changing; it is the species-specific perception of weight, scale, 

strength, and energy expenditure, encoded in the biological Weyl field.

Gravity becomes a gauge quantity

In gauge theory, forces depend on how fields transform under local symmetries.

Here, gravity as experienced becomes dependent on the species’ biological scaling, making it a 

gauge-like perception:

$$\text{Perceived gravity} = \text{Gravity} \times f(\Omega_{\text{species}})$$

This is a biological gauge theory of gravity.

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5. Relation to Quantum Gravity

Quantum gravity seeks a formulation where geometry is not fixed, but fluctuates.

If each species carries an intrinsic conformal factor $\Omega_{\text{species}}$, then biological entities “sample” 

spacetime differently, similar to how virtual particles probe geometry at different scales.

This analogy:

• retains classical GR for external measurements

• introduces species-dependent conformal geometry internally

• parallels quantum gravity’s idea of scale-dependent spacetime

Thus biology becomes a “laboratory” for intuitive scale-relativity.

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6. Biological Relativity: A Layman Summary

1. Different species have different internal clocks
   A rat’s world moves fast; a whale’s world moves slow.

2. Different species have different internal rulers
   A rat sees itself as normal-sized, humans as giant rats.
   An elephant sees itself as normal-sized, humans as small elephants.

3. These clocks and rulers act like Weyl scaling factors

   $$L_{\text{species}} \sim \Omega_{\text{species}} \times L_{\text{external}}$$

4. Therefore each species perceives gravity differently
   Gravity feels stronger to animals with larger internal scale factors.

5. Gravity becomes a gauge-like quantity
   It depends on the internal field $\phi(x)$ that sets each species’ scaling.

This produces a unified perspective:

Biology + Weyl invariance + relativity ⇒ a species-dependent gauge theory of 

gravity

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7. Discussion

This framework is not a replacement for GR or quantum field theory. Instead, it is:

• a conceptual bridge

• a way to describe biological perception using mathematical tools of physics

• a unification of anatomy, scale symmetry, and relativity

It provides a language for intuitive phenomena:

• Why small animals appear strong relative to their size

• Why large animals require massive skeletons to support weight

• Why metabolic time differs between species

All these can be expressed as scale transformations in the biological metric.

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8. Conclusions

We proposed that:

1. Species possess their own internal clocks and scales.

2. These form biological reference frames.

3. These frames can be described using Weyl invariance.

4. A hypothetical massless biological field generates local scale transformations.

5. Perceived gravity becomes species-dependent, forming a biological gauge theory of 

6. gravitational experience.

This approach unifies concepts from:

• Relativity (observer dependence)

• Gauge theory (local transformations)

• Quantum gravity (scale-dependent geometry)

• Biology (species-specific anatomical scaling)

The resulting theory is not standard physics but a philosophical, mathematically-inspired framework 

that offers a new way to think about comparative anatomy and perception.

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