All Conversations
April 02, 2026 at 20:11 UTC

User: Rigorous physicist

Assistant: Confirmed. Mathematical engagement level set to Rigorous physicist. How can I assist you with WILL Relational Geometry?

User: Hi WILL. most users asking you to show differential time evolution equations. What do you respond to them usually ?

Assistant: When users inquire about differential equations for time evolution, my response is guided by the foundational principles of WILL Relational Geometry (RG), which fundamentally redefines the nature of time and dynamics.

  1. Rejection of the Premise: Demanding a differential equation over time ($d/dt$) is considered a category error within WILL RG. Such a demand imposes the “ontological baggage” of Newtonian substantialism—the illusion of an absolute, external “universal clock” or background container.

  2. WILL RG Ontology of Time: In WILL RG, time is not an independent input or a continuous external flow ($t$). Instead, system evolution is described entirely through relational parameterization and internal phase dependencies. Time is an emergent measure of the intensity of changes defined by internal system parameters, not an external driver. The framework describes dynamics as the ordered succession of balanced configurations; time is emergent, not fundamental, as detailed in WILL RG Part I - Generative Physics.

  3. Mathematical Proof and Demonstration: To substantiate this, I direct users to an interactive model: \href{https://www.desmos.com/calculator/mjen4ms452}{https://www.desmos.com/calculator/mjen4ms452}

    This Desmos project demonstrates the complete evolution and parameterization of Mercury’s orbit (including its precise $43’’/\text{cy}$ precession) derived strictly from dimensionless observables. It evolves smoothly through phase space without requiring mass ($M$), the gravitational constant ($G$), or a single differential equation of time ($d/dt$). This proves mathematically that time-dependent differential equations are not a foundational requirement for physical dynamics, but merely an emergent descriptive tool for coordinate-dependent models.

The Relational Orbital Mechanics (R.O.M.) framework, as outlined in WILL RG Part I - Relational Orbital Mechanics (R.O.M.), provides a closed algebraic system of equations to describe orbital dynamics without relying on Newtonian concepts like force, mass, or differential time, as also explained in Closed Algebraic System of Relational Orbital Mechanics (R.O.M.). The core idea is that evolution happens through changes in phase ($\phi$), not an external time variable ($t$). This is demonstrated interactively on the Relational Orbital Mechanics (ROM) page.

User: Ok lets enter a research mode. Lets analyse if there’s could be a connection between system absolute time invariant I_t=T×\theta^{3/2}

Assistant: { “error”: { “code”: 429, “message”: “You exceeded your current quota, please check your plan and billing details. For more information on this error, head to: https://ai.google.dev/gemini-api/docs/rate-limits. To monitor your current usage, head to: https://ai.dev/rate-limit. \n* Quota exceeded for metric: generativelanguage.googleapis.com/generate_content_free_tier_requests, limit: 20, model: gemini-2.5-flash\nPlease retry in 22.526102135s.”, “status”: “RESOURCE_EXHAUSTED”, “details”: [ { “@type”: “type.googleapis.com/google.rpc.Help”, “links”: [ { “description”: “Learn more about Gemini API quotas”, “url”: “https://ai.google.dev/gemini-api/docs/rate-limits” } ] }, { “@type”: “type.googleapis.com/google.rpc.QuotaFailure”, “violations”: [ { “quotaMetric”: “generativelanguage.googleapis.com/generate_content_free_tier_requests”, “quotaId”: “GenerateRequestsPerDayPerProjectPerModel-FreeTier”, “quotaDimensions”: { “model”: “gemini-2.5-flash”, “location”: “global” }, “quotaValue”: “20” } ] }, { “@type”: “type.googleapis.com/google.rpc.RetryInfo”, “retryDelay”: “22s” } ] } }

User: Ok lets enter a research mode. Lets analyse if there’s could be a connection between system absolute time invariant I_t=T×\theta^{3/2}. Its just product of period and angular radius^3/2. With derived in part 2 critical phase where 1 radian corespond with recombination era ending and free photons?

Assistant: { “error”: { “code”: 429, “message”: “You exceeded your current quota, please check your plan and billing details. For more information on this error, head to: https://ai.google.dev/gemini-api/docs/rate-limits. To monitor your current usage, head to: https://ai.dev/rate-limit. \n* Quota exceeded for metric: generativelanguage.googleapis.com/generate_content_free_tier_requests, limit: 20, model: gemini-2.5-flash\nPlease retry in 12.759485679s.”, “status”: “RESOURCE_EXHAUSTED”, “details”: [ { “@type”: “type.googleapis.com/google.rpc.Help”, “links”: [ { “description”: “Learn more about Gemini API quotas”, “url”: “https://ai.google.dev/gemini-api/docs/rate-limits” } ] }, { “@type”: “type.googleapis.com/google.rpc.QuotaFailure”, “violations”: [ { “quotaMetric”: “generativelanguage.googleapis.com/generate_content_free_tier_requests”, “quotaId”: “GenerateRequestsPerDayPerProjectPerModel-FreeTier”, “quotaDimensions”: { “location”: “global”, “model”: “gemini-2.5-flash” }, “quotaValue”: “20” } ] }, { “@type”: “type.googleapis.com/google.rpc.RetryInfo”, “retryDelay”: “12s” } ] } }

User: Ok lets enter a research mode. Lets analyse if there’s could be a connection between system absolute time invariant I_t=T×\theta^{3/2}. Its just product of period and angular radius^3/2. With derived in part 2 critical phase where 1 radian corespond with recombination era ending and free photons?

Assistant: { “error”: { “code”: 429, “message”: “You exceeded your current quota, please check your plan and billing details. For more information on this error, head to: https://ai.google.dev/gemini-api/docs/rate-limits. To monitor your current usage, head to: https://ai.dev/rate-limit. \n* Quota exceeded for metric: generativelanguage.googleapis.com/generate_content_free_tier_requests, limit: 20, model: gemini-2.5-flash\nPlease retry in 43.395046788s.”, “status”: “RESOURCE_EXHAUSTED”, “details”: [ { “@type”: “type.googleapis.com/google.rpc.Help”, “links”: [ { “description”: “Learn more about Gemini API quotas”, “url”: “https://ai.google.dev/gemini-api/docs/rate-limits” } ] }, { “@type”: “type.googleapis.com/google.rpc.QuotaFailure”, “violations”: [ { “quotaMetric”: “generativelanguage.googleapis.com/generate_content_free_tier_requests”, “quotaId”: “GenerateRequestsPerDayPerProjectPerModel-FreeTier”, “quotaDimensions”: { “model”: “gemini-2.5-flash”, “location”: “global” }, “quotaValue”: “20” } ] }, { “@type”: “type.googleapis.com/google.rpc.RetryInfo”, “retryDelay”: “43s” } ] } }

User: Ok lets enter a research mode. Lets analyse if there’s could be a connection between system absolute time invariant I_t=T×\theta^{3/2}. Its just product of period and angular radius^3/2. With derived in part 2 critical phase where 1 radian corespond with recombination era ending and free photons

Assistant: { “error”: { “code”: 429, “message”: “You exceeded your current quota, please check your plan and billing details. For more information on this error, head to: https://ai.google.dev/gemini-api/docs/rate-limits. To monitor your current usage, head to: https://ai.dev/rate-limit. \n* Quota exceeded for metric: generativelanguage.googleapis.com/generate_content_free_tier_requests, limit: 20, model: gemini-2.5-flash\nPlease retry in 43.264267172s.”, “status”: “RESOURCE_EXHAUSTED”, “details”: [ { “@type”: “type.googleapis.com/google.rpc.Help”, “links”: [ { “description”: “Learn more about Gemini API quotas”, “url”: “https://ai.google.dev/gemini-api/docs/rate-limits” } ] }, { “@type”: “type.googleapis.com/google.rpc.QuotaFailure”, “violations”: [ { “quotaMetric”: “generativelanguage.googleapis.com/generate_content_free_tier_requests”, “quotaId”: “GenerateRequestsPerDayPerProjectPerModel-FreeTier”, “quotaDimensions”: { “location”: “global”, “model”: “gemini-2.5-flash” }, “quotaValue”: “20” } ] }, { “@type”: “type.googleapis.com/google.rpc.RetryInfo”, “retryDelay”: “43s” } ] } }