I am proposing a rigorous thought experiment at the intersection of physics and the philosophy of science. The goal is to test whether we can, by applying a set of strict methodological constraints, arrive at a single, fundamental formulation of physical laws.

This challenge is not based on new physics, but on "Mathematical Hygiene" (MH) - a principle demanding absolute correspondence between mathematical symbols and their operational, relational meaning.

---

Part 1: The Rules of the Experiment (The Principles of "Mathematical Hygiene")

For this experiment to be pure, we must temporarily agree to follow four disciplines. (I will refer to them as A.1–A.4).

* A.1. The Principle of Ontological Economy:

A theory must be founded on the smallest possible set of primitive, operationally defined concepts (e.g., observable relations or transformations). All other constructs (fields, potentials, curvature) must be derivative functions of this primitive basis.

* A.2. The Discipline of Minimal Representation:

The number of symbols in a "hygienic" formula should equal the number of independent physical ideas. Using, for example, a tensor T_μν (10+ components) to describe the simple idea of "energy density" is "semantic inflation."

* A.3. The Principle of Hierarchical Sufficiency:

All derived constructs must be unambiguously derivable from the primitive basis. New physics cannot be "smuggled in" under the guise of mathematical convenience.

* A.4. The Discipline of Epistemic Hygiene:

Every symbol in a theory must carry an "interpretive passport" linking it to an empirical, relational (dimensionless) meaning. Symbols without passports (e.g., t=0 or x=0 in an empty universe) are "grammatical artifacts" and must be eliminated.

---

Part 2: Example Application of MH (Kinematics)

Let's apply this filter to an icon of physics: the invariance of the SR interval.

Test Subject: dτ² = dt² - dx² (with c=1)

MH Verdict: This equation is fundamentally "unhygienic."

Justification:

1. Violation A.4 (Passport): The symbols dt and dx are not primitives. They are differentials of t and x.

2. Violation A.1 (Container): t and x themselves imply the existence of an a priori coordinate grid - a "hidden container" we impose on reality. This container has no "interpretive passport" in the absence of events.

3. Violation A.4 (Units): Even if we accept dt and dx as "measurable," they are measured in seconds and meters - arbitrary human conventions, not fundamental relational (dimensionless) quantities.

"Hygienic" Derivation (Kinematics):

To "cleanse" this law, we must use only dimensionless, relational primitives:

1. Amplitude Primitive (Motion): The ratio of an object's velocity to the universal speed limit. This is β = v/c. It has a clean "passport."

2. Phase Primitive (Time): The ratio of an object's proper time to the observer's time. This is β_Y = Δτ / Δt. It also has a clean "passport."

The physical law is the Lorentz factor: β_Y = √(1 - β²).

If we write this as a closure identity, we get the "hygienic" form of the law of kinematics:

β² + β_Y² = 1

Note: no d's, no t or x, no meters or seconds. Just two pure, dimensionless primitives in an algebraic identity.

---

Part 3: The Challenge (Gravity)

Now, here is the task for you.

We must apply the exact same MH logic to gravity.

We must completely reject the formalism of GR (G_μν, g_μν, differentials) as the peak of "semantic inflation" and "hidden containers."

The Task: Find the fundamental "hygienic" closure identity for gravity, analogous to β² + β_Y² = 1.

Guiding Questions:

1. How do we define the "hygienic" Amplitude Primitive for gravity (let's call it κ)?

* It must be dimensionless.

It must describe the intensity* of gravity.

2. How do we define the "hygienic" Phase Primitive for gravity (let's call it κ_X)?

* It must be dimensionless.

It must be the analogue of β_Y (i.e., it must describe the observable gravitational time dilation*).

3. What is the necessary algebraic closure identity that connects κ and κ_X?

---

Rules of Engagement:

For the sake of a pure experiment, I ask all participants to adhere strictly to the MH methodology (A.1–A.4).

The goal is not to prove "GR is wrong," but to test a hypothesis: Will strict epistemological discipline force all participants toward the same, inevitable algebraic structure?

I await your derivations.

11 minutes ago, Anton Rize said:

I am proposing a rigorous thought experiment at the intersection of physics and the philosophy of science. The goal is to test whether we can, by applying a set of strict methodological constraints, arrive at a single, fundamental formulation of physical laws.

This challenge is not based on new physics, but on "Mathematical Hygiene" (MH) - a principle demanding absolute correspondence between mathematical symbols and their operational, relational meaning.

---

Part 1: The Rules of the Experiment (The Principles of "Mathematical Hygiene")

For this experiment to be pure, we must temporarily agree to follow four disciplines. (I will refer to them as A.1–A.4).

* A.1. The Principle of Ontological Economy:

A theory must be founded on the smallest possible set of primitive, operationally defined concepts (e.g., observable relations or transformations). All other constructs (fields, potentials, curvature) must be derivative functions of this primitive basis.

* A.2. The Discipline of Minimal Representation:

The number of symbols in a "hygienic" formula should equal the number of independent physical ideas. Using, for example, a tensor T_μν (10+ components) to describe the simple idea of "energy density" is "semantic inflation."

* A.3. The Principle of Hierarchical Sufficiency:

All derived constructs must be unambiguously derivable from the primitive basis. New physics cannot be "smuggled in" under the guise of mathematical convenience.

* A.4. The Discipline of Epistemic Hygiene:

Every symbol in a theory must carry an "interpretive passport" linking it to an empirical, relational (dimensionless) meaning. Symbols without passports (e.g., t=0 or x=0 in an empty universe) are "grammatical artifacts" and must be eliminated.

---

Part 2: Example Application of MH (Kinematics)

Let's apply this filter to an icon of physics: the invariance of the SR interval.

Test Subject: dτ² = dt² - dx² (with c=1)

MH Verdict: This equation is fundamentally "unhygienic."

Justification:

1. Violation A.4 (Passport): The symbols dt and dx are not primitives. They are differentials of t and x.

2. Violation A.1 (Container): t and x themselves imply the existence of an a priori coordinate grid - a "hidden container" we impose on reality. This container has no "interpretive passport" in the absence of events.

3. Violation A.4 (Units): Even if we accept dt and dx as "measurable," they are measured in seconds and meters - arbitrary human conventions, not fundamental relational (dimensionless) quantities.

"Hygienic" Derivation (Kinematics):

To "cleanse" this law, we must use only dimensionless, relational primitives:

1. Amplitude Primitive (Motion): The ratio of an object's velocity to the universal speed limit. This is β = v/c. It has a clean "passport."

2. Phase Primitive (Time): The ratio of an object's proper time to the observer's time. This is β_Y = Δτ / Δt. It also has a clean "passport."

The physical law is the Lorentz factor: β_Y = √(1 - β²).

If we write this as a closure identity, we get the "hygienic" form of the law of kinematics:

β² + β_Y² = 1

Note: no d's, no t or x, no meters or seconds. Just two pure, dimensionless primitives in an algebraic identity.

---

Part 3: The Challenge (Gravity)

Now, here is the task for you.

We must apply the exact same MH logic to gravity.

We must completely reject the formalism of GR (G_μν, g_μν, differentials) as the peak of "semantic inflation" and "hidden containers."

The Task: Find the fundamental "hygienic" closure identity for gravity, analogous to β² + β_Y² = 1.

Guiding Questions:

1. How do we define the "hygienic" Amplitude Primitive for gravity (let's call it κ)?

* It must be dimensionless.

It must describe the intensity* of gravity.

2. How do we define the "hygienic" Phase Primitive for gravity (let's call it κ_X)?

* It must be dimensionless.

It must be the analogue of β_Y (i.e., it must describe the observable gravitational time dilation*).

3. What is the necessary algebraic closure identity that connects κ and κ_X?

---

Rules of Engagement:

For the sake of a pure experiment, I ask all participants to adhere strictly to the MH methodology (A.1–A.4).

The goal is not to prove "GR is wrong," but to test a hypothesis: Will strict epistemological discipline force all participants toward the same, inevitable algebraic structure?

I await your derivations.

What a load of pompous, AI-generated ballocks. 😆

17 minutes ago, exchemist said:

What a load of pompous, AI-generated ballocks. 😆

You already showed your glaring incompetence in other thread, so im not surprised. Goodbye.

Edited October 25Oct 25 by Anton Rize

The frequent use of quotation marks seems to weaken the precision and, ironically, introduce more "semantic inflation" rader than reduce it.

4 minutes ago, Anton Rize said:

You already showed your glaring incompetence in other thread, so im not surprised. Goodbye.

I'm afraid I must concur with Exchemist. Your theory is definitely UNhygienic.

Unhygienic in the sense that you have taken the English language, Ai mixed it up with some sciency words, then took a huge, steaming shit all over it.

7 minutes ago, Ghideon said:

The frequent use of quotation marks seems to weaken the precision and, ironically, introduce more "semantic inflation" rader than reduce it.

Good point Hahaha! I guess we limited by our language or at least I am.

7 minutes ago, pinball1970 said:

I'm afraid I must concur with Exchemist. Your theory is definitely UNhygienic.

Unhygienic in the sense that you have taken the English language, Ai mixed it up with some sciency words, then took a huge, steaming shit all over it.

You overcomplimenting AI's abilities and underestimating mine. "steaming shit" is not a constructive argument isn't it? "Your theory" is a misplaced term in this context. There's a difference between theory and methodology I suggest you google it. In the end its just 4 premises:
A1
A2
A3
A4

Which one you finding resemble a "steaming shit"?

Edited October 25Oct 25 by Anton Rize

Just now, Anton Rize said:

is not a constructive argument isn't it? "

No, I was attempting something else, humour.

Are telling us that your post is not Ai generated?

Just now, pinball1970 said:

Are telling us that your post is not Ai generated?

Post is written by me but I use AI to translate it in to English and reformat latex in to Unicode. I understand that there's a lot of AI generated crap around but if you assuming that every well structured argument is AI generated the again you overcomplimenting AI's abilities and underestimating mine.  

You didn't answer my question:

8 minutes ago, Anton Rize said:

In the end its just 4 premises:
A1
A2
A3
A4

Which one you finding resemble a "steaming shit"?

1 minute ago, Anton Rize said:

Which one you finding resemble a "steaming shit"?

Steaming shit was a reference to your post's lack of hygiene.

Just now, pinball1970 said:

Steaming shit was a reference to your post's lack of hygiene.

Is it all you are capable of? Shallow view and overgeneralisation without any substance? If so - please leave.

57 minutes ago, Anton Rize said:

Is it all you are capable of? Shallow view and overgeneralisation without any substance? If so - please leave.

Do you want me to pull it apart? I can do that if you prefer?

36 minutes ago, pinball1970 said:

Do you want me to pull it apart? I can do that if you prefer?

This is exactly what this post is made for. Considering the fact that its your 4th message here and you still not sure about the purpose of this post - I highly doubt that you can. But will be happy if proven wrong - that's the hole point. Be my guest.

4 hours ago, Anton Rize said:

MH Verdict: This equation is fundamentally "unhygienic."

Justification:

1. Violation A.4 (Passport): The symbols dt and dx are not primitives. They are differentials of t and x.

2. Violation A.1 (Container): t and x themselves imply the existence of an a priori coordinate grid - a "hidden container" we impose on reality. This container has no "interpretive passport" in the absence of events.

3. Violation A.4 (Units): Even if we accept dt and dx as "measurable," they are measured in seconds and meters - arbitrary human conventions, not fundamental relational (dimensionless) quantities.

"Hygienic" Derivation (Kinematics):

To "cleanse" this law, we must use only dimensionless, relational primitives:

1. Amplitude Primitive (Motion): The ratio of an object's velocity to the universal speed limit. This is β = v/c. It has a clean "passport."

2. Phase Primitive (Time): The ratio of an object's proper time to the observer's time. This is β_Y = Δτ / Δt. It also has a clean "passport."

The physical law is the Lorentz factor: β_Y = √(1 - β²).

If we write this as a closure identity, we get the "hygienic" form of the law of kinematics:

β² + β_Y² = 1

Note: no d's, no t or x, no meters or seconds. Just two pure, dimensionless primitives in an algebraic identity.

If they are mathematically equivalent, then why does it matter? Seems like this is just personal preference. The utility in equations doesn’t rest on the “purity” of the expression; the ease of use and how it’s learned/taught matter as well. Other factors are what we measure in experiments and what we do to solve problems. Personally, I always disliked “compact” equations that had to be deciphered to put them in physical terms.

Offering something up as “better” or “easier” is flawed. Much like relativity shows with various quantities, these are not absolutes. One has to say for whom it’s better or easier.

You also cherry-picked an example that has unitless terms, related to your pet project, but not all physics is like that, unless you make the expressions more complicated.

As far as adopting this goes: Hard pass

Thank you for jumping in @swansont

10 hours ago, swansont said:

If they are mathematically equivalent, then why does it matter?

Mathematical equality ≠ same ontological clarity. Replacement of ontology with mathematical artifacts is a well known problem in physics raised by Sean Carol, Nima Arkani-Hamed and many more.

10 hours ago, swansont said:

The utility in equations doesn’t rest on the “purity” of the expression; the ease of use and how it’s learned/taught matter as well.

Exactly! the ease of use and how it’s learned/taught directly depends on amount of abstract coordinates like t, x that require interpretation. They are not primitive observables but representational choices: they depend on frame and synchronization conventions. What’s operationally invariant are proper-time intervals and relational, dimensionless ratios. MH targets exactly this distinction between representational coordinates and observable structure. Two equally correct formulations are not pedagogically equivalent - the one with fewer abstract, non-operational symbols conveys the physics more transparently.

10 hours ago, swansont said:

Personally, I always disliked “compact” equations that had to be deciphered to put them in physical terms.

Ironically the standard form is the one who has to be deciphered to put it in physical terms (coordinate constructs like t and x). This is a great example of replacing ontology with mathematical artifacts. You just proved my point.

10 hours ago, swansont said:

Offering something up as “better” or “easier” is flawed.

Absolutely - that’s why this is framed as an experiment, not an assertion.

10 hours ago, swansont said:

You also cherry-picked an example that has unitless terms, related to your pet project, but not all physics is like that, unless you make the expressions more complicated.

you’re right that not all physics is naturally dimensionless. That’s exactly why I framed gravity as an open task under the same MH constraints - to see whether equally “hygienic” primitives can be identified there. In other words, the SR example is step 1, not the conclusion.



Finally comment with substance not just personal attacks. Thank you @swansont

22 hours ago, Anton Rize said:

xample, a tensor T_μν (10+ components) to describe the simple idea of "energy density" is "semantic

This is done all over the shop in physics, you be writing out a lot of clunky equations otherwise. Einstein's tensor, Dirac's spinor, Lorentz's factor, h bar.

You used v/c which you call beta, as a sub for dx/dt? Two things first you are doing the thing above and second v is still there even though you are not writing it out, dx/dt.

13 hours ago, Anton Rize said:

Mathematical equality ≠ same ontological clarity. Replacement of ontology with mathematical artifacts is a well known problem in physics raised by Sean Carol, Nima Arkani-Hamed and many more.

Not everyone considers it a problem, nor, I suspect, is the problem with all of physics.

13 hours ago, Anton Rize said:

Exactly! the ease of use and how it’s learned/taught directly depends on amount of abstract coordinates like t, x that require interpretation. They are not primitive observables but representational choices: they depend on frame and synchronization conventions. What’s operationally invariant are proper-time intervals and relational, dimensionless ratios. MH targets exactly this distinction between representational coordinates and observable structure. Two equally correct formulations are not pedagogically equivalent - the one with fewer abstract, non-operational symbols conveys the physics more transparently.

Beta, your variable of choice, is not an invariant.

13 hours ago, Anton Rize said:

Ironically the standard form is the one who has to be deciphered to put it in physical terms (coordinate constructs like t and x). This is a great example of replacing ontology with mathematical artifacts. You just proved my point.

I think you proved mine. Replacing the measurable variables x and t is the abstraction, and would be a pedagogical nightmare in trying to teach introductory physics, or teach relativity as an introductory topic, before Newtonian mechanics.

13 hours ago, Anton Rize said:

Absolutely - that’s why this is framed as an experiment, not an assertion.

you’re right that not all physics is naturally dimensionless. That’s exactly why I framed gravity as an open task under the same MH constraints - to see whether equally “hygienic” primitives can be identified there. In other words, the SR example is step 1, not the conclusion.

This is backwards, though. Scientific proposals are tested by falsification, not by looking at trivial cases where the idea works.

@pinball1970
And you call it "pull it apart"? I cant even understand your argument. Can you express yourself a bit clearer?




@swansont
Two clarifications:
(i) I don’t claim β is Lorentz-invariant; it’s an operational, dimensionless primitive within a chosen frame. What I call “invariant” is the form of the closure identity (e.g. β^2+βY^2=1), not each component separately.
(ii) x,t become “measurable” only after conventions (synchronization, frame, units). They are representational choices, not primitives.
MH targets exactly this: primitives first (operational, dimensionless), coordinates later as derived bookkeeping.
Pedagogy is a separate (and open) question; ontology shouldn’t be outsourced to convenience.

2 hours ago, Anton Rize said:

you express yourself a bit clearer?

Seems pretty straightforward. You are substituting different terms in the established equations for no particular reason.

You did not want to derivatives but you have v/c, v is the derivative of x w.r.t. to t.

Also what is c? Why not express that in terms of the fine structure constant?

Why stop there? Your substitutions seem arbitrary.

6 hours ago, Anton Rize said:

@swansont
Two clarifications:
(i) I don’t claim β is Lorentz-invariant; it’s an operational, dimensionless primitive within a chosen frame. What I call “invariant” is the form of the closure identity (e.g. β^2+βY^2=1), not each component separately.

Any equation can be written that way. F=ma can be written as F/ma = 1

This is just preference; equality is a useful concept. In solving problems the equation might need to be rearranged anyway

But nobody needs to indulge another’s preference or OCD or whatever.

6 hours ago, Anton Rize said:

(ii) x,t become “measurable” only after conventions (synchronization, frame, units). They are representational choices, not primitives.

How do you measure beta?

6 hours ago, Anton Rize said:

MH targets exactly this: primitives first (operational, dimensionless), coordinates later as derived bookkeeping.
Pedagogy is a separate (and open) question; ontology shouldn’t be outsourced to convenience.

Pedagogy might be a separate question but it’s an important one. You’re giving ontology a greater emphasis but I don’t see what’s revealed by your approach.

32 minutes ago, swansont said:

Any equation can be written that way. F=ma can be written as F/ma = 1

Unless of course a or m or both = 0.

Which also applies to anything Anton Rize writes.

Nor do I accept his use of 'emergence' or we could be saying things like

if 2p + 3q =7 and p + q = 1 then it emerges that p is -4 and q is 5.

That is not what I understand by emergence.

Nor can nabla 'emerge' from anything.