Note: This paper presents a provisional thought experiment, an initial exploration of a conceptual framework regarding fundamental physical quantities and conservation laws. It is intended to stimulate discussion and further investigation rather than assert definitive conclusions.
Abstract:
This paper proposes a conceptual framework centered on a single, dimensionless, universally conserved quantity, or stuff universal, denoted S_u. It is posited that all fundamental variable physical properties of a system (such as energy, mass, momentum, characteristic length, and characteristic time) are dimensional "aspects" or "manifestations" of this underlying S_u. The standard SI values of these properties are hypothesized to be S_u scaled by the corresponding (non-reduced) Planck units. This framework suggests that the conservation of S_u is the ultimate conservation law, from which all other known conservation laws (energy, momentum, etc.) derive as dimensional expressions of this singular principle. This reinterpretation aims to unify the understanding of physical properties and conservation laws, framing fundamental constants as the specific scaling factors that bridge the dimensionless S_u to our dimensional system of measurement.
1. Introduction: The Quest for Unity and the Role of Constants
A primary goal in fundamental physics is the unification of concepts and laws, seeking to describe diverse phenomena through a minimal set of principles. Current physics recognizes several distinct conservation laws (energy, momentum, angular momentum, charge, etc.) and utilizes a set of fundamental dimensionful constants (c, h, G, k_B, e) whose precise numerical values in SI units often appear arbitrary or "mysterious."
This paper explores the hypothesis that these distinct conserved quantities and constants might be understood more cohesively through the lens of a single, underlying, dimensionless, and universally conserved quantity, S_u (Universal Conserved Stuff/State). We propose that the measured SI values of variable physical properties are different dimensional "views" of this S_u, obtained by scaling S_u with the appropriate fundamental Planck units (constructed using c, h, and G).
This perspective builds upon the idea that fundamental constants primarily serve as scaling factors that bridge our arbitrary, human-defined SI units to the inherent, unit-independent proportionalities of nature [as explored in frameworks like the Physics Unit Coordinate System (PUCS) and Modular Unit Scaling].
2. Defining the Dimensionless Universal Conserved Quantity (
We provisionally define the dimensionless universal conserved quantity S_u by relating it to the total energy E of a system and the (non-reduced) Planck Energy E_P:
S_u = E / E_P (Eq. 1)
where:
E is the total energy of the system in SI units (Joules).
E_P is the (non-reduced) Planck Energy, E_P = t_Ph / (Hz_kg * c^2)).
Hz_kg is Planck's constant.
c is the definition of the meter versus the L~T equivalence.
t_Ph is the Plank time scale factored from G.
This is just removing the unit scaling for SI time, SI kg, and SI meter from the energy to get the true value of the dimensionless stuff that is being conserved in reality.
By this definition, S_u is dimensionless. We postulate that S_u is the fundamental quantity (or stuff) that is conserved in any closed physical system. The conservation of energy is then a direct dimensional consequence: if S_u is conserved and E_P is a universal constant, then E must be conserved.
3. Dimensional Aspects of
If S_u represents the fundamental dimensionless "amount of stuff" or "state content" of a system, we hypothesize that its various dimensional manifestations (what we measure as mass, length, time, momentum, etc.) are obtained by scaling S_u with the corresponding (non-reduced) Planck unit:
Energy Aspect (by definition):
E_SI = S_u * E_P (rearranging Eq. 1)
Mass Aspect:
m_aspect_SI = S_u * m_P (Eq. 2)
where m_P = Hz_kg / t_Ph is the (non-reduced) Planck Mass.
This implies that the "mass content" of the system, when viewed from this perspective, is its total dimensionless "stuff"
Length Aspect:
l_aspect_SI = S_u * l_P (Eq. 3)
where l_P = c * t_Ph is the (non-reduced) Planck Length.
This suggests a characteristic length scale associated with the system's total "stuff"
Time Aspect:
t_aspect_SI = S_u * t_Ph (Eq. 4)
where t_Ph = sqrt(G_SI Hz_kg / c^3 is the (non-reduced) Planck Time.
This suggests a characteristic time scale associated with the system's total "stuff"
Momentum Aspect:
p_aspect_SI = S_u * p_P (Eq. 5)
where p_P = m_P * c = Hz_kg * c / t_Ph is the (non-reduced) Planck Momentum.
This suggests a characteristic momentum magnitude associated with the system's total "stuff"
It is crucial to note that these "aspects" (e.g., m_aspect_SI, l_aspect_SI) are not necessarily the standard kinematic mass or specific geometric size of a particle or system in all contexts. Rather, they represent the magnitude that particular physical dimension would take if the total conserved S_u of the system were to manifest purely along that dimensional axis, scaled by the corresponding Planck unit of measurement scaling back to SI units of measurement. For instance, m_aspect_SI is the system's total energy E divided by c^2 (since S_u * m_P = (E/E_P) * (E_P/c^2) = E/c^2), representing its total mass-equivalent.
4. S_u Conservation: The Unifying Principle
The central tenet of this framework is that the Conservation of S_u is the singular, fundamental conservation law.
If S_u is conserved for a closed system, then all its dimensional aspects (E_SI, m_aspect_SI, p_aspect_SI, etc.), being direct scalings of S_u by universal constants (Planck units), will also exhibit corresponding conservation behaviors when the system is viewed from those dimensional perspectives.
For example, the conservation of total energy is explicit. The conservation of total linear momentum for a closed system would arise from the conservation of the "momentum aspect" of S_u, which in turn would be linked to the system's invariance under spatial translation (consistent with Noether's theorem, but re-grounded in S_u).
This implies that distinct conservation laws are not independent fundamental truths but are different facets of a single underlying conservation principle, made distinct by our dimensional framework of measurement.
5. Implications and Interpretation
Role of Planck Units: The (non-reduced) Planck units are not just characteristic scales where new physics might emerge, but serve as the fundamental conversion factors that translate the dimensionless S_u into the dimensional quantities we measure in SI (or any other unit system).
Role of These constants, which define the Planck units, are thus the essential components of these dimensional scaling factors. Their SI numerical values reflect the relationship between our arbitrary SI base unit scales and the inherent, unit-independent structure of reality represented by S_u and its manifestations.
Demystification of Quantization and Discrete States: If a system (like an electron in an atom) is constrained such that its energy E (and thus its S_u) can only take on discrete values, then all other "aspects" (m_aspect, p_aspect, l_aspect, t_aspect) must also be discrete, as they are all proportional to the quantized S_u. Quantization becomes a feature of the allowed states of S_u under certain boundary conditions.
Potential for Simplification: This framework offers a path to conceptually simplify the foundations of physics by reducing the number of independent fundamental conserved quantities and clarifying the role of dimensionful constants.
6. Challenges and Future Directions
This proposal is highly conceptual and requires significant development:
Rigorous Mathematical Formulation: S_u is currently defined via energy. But any aspect of a particle could be converted from its unit of axis of measurement to this same numerical value of stuff. A more fundamental definition, perhaps from action principles or information theory, might be necessary. How S_u relates to vector/tensor quantities like momentum or angular momentum needs precise formulation.
Derivation of Existing Laws: A key test would be the ability to rigorously derive all known conservation laws and their associated symmetries from the singular postulate of S_u conservation.
Connection to Existing Theories: How does S_u relate to concepts in Quantum Field Theory, General Relativity, or String Theory (e.g., the wave function, spacetime metrics, string states)?
Experimental Signatures: While S_u conservation directly implies energy conservation, are there novel, testable predictions that arise uniquely from this unified perspective, perhaps in extreme regimes (Planck scale, black holes)?
7. Conclusion
The concept of a single, dimensionless, universally conserved quantity S_u offers a potentially unifying lens through which to view fundamental physical properties and their conservation. By positing that measurable dimensional quantities are simply S_u scaled by the appropriate Planck units, this framework reinterprets fundamental constants as essential dimensional conversion factors. The conservation of S_u would then be the ultimate conservation principle, underpinning all others.
While this paper presents an initial and provisional exploration, the pursuit of such unifying ideas is vital for deepening our understanding of the fundamental structure of reality. Further theoretical development is required to explore the viability and predictive power of this S_u framework.
This is a starting point. It lays out the core idea, its components, and some initial implications and challenges. It could be expanded significantly in each section with more detailed derivations, comparisons to existing physics, and deeper philosophical discussion.
Appendix A: S_u as a Unifying Principle for Conservation Laws and a Reinterpretation of Noether's Theorem
A.1 Introduction: The Multiplicity of Conservation Laws
Standard physics recognizes a set of distinct conservation laws, including the conservation of energy, linear momentum, angular momentum, electric charge, and others. Noether's theorem provides a profound connection, linking each of these conserved quantities to a continuous symmetry in the underlying physical laws (the action or Lagrangian of the system). For instance, time translation invariance leads to energy conservation, spatial translation invariance to linear momentum conservation, rotational invariance to angular momentum conservation, and gauge invariance (e.g., U(1) symmetry) to charge conservation.
While Noether's theorem reveals a deep structure, it still presents these symmetry-conservation pairs as distinct fundamental principles. This appendix explores how the proposed dimensionless universal conserved quantity, S_u, could offer a more unified perspective, suggesting that these various conservation laws are different dimensional manifestations of a single, overarching conservation principle: the conservation of S_u.
A.2
As defined in the main body of this paper, S_u = E / E_P is a dimensionless quantity representing the total "stuff" or "state content" of a system, where E is the system's total SI energy and E_P is the (non-reduced) Planck Energy. We hypothesized that various dimensional physical properties are "aspects" of S_u, obtained by scaling S_u with the corresponding (non-reduced) Planck unit:
Energy: E_SI = S_u * E_P
Momentum Aspect: p_aspect_SI = S_u * p_P (where p_P is Planck Momentum)
Angular Momentum Aspect: L_aspect_SI = S_u * L_P_ang_mom (where L_P_ang_mom = S_u * ħ or S_u * h for non-reduced, representing Planck Angular Momentum, typically ħ)
Charge Aspect (Hypothetical): If charge conservation is also a facet of S_u conservation, there would be a corresponding "Planck Charge" q_P such that Q_SI = S_u_charge_aspect * q_P. This requires further development but illustrates the pattern.
A.3 Reinterpreting Symmetries as Measurement Axes for
The core idea of this reinterpretation is to view the "dimensions" or "degrees of freedom" associated with Noether's symmetries not as independent abstract spaces, but as different "axes of measurement" within our Layer 2/3 perceptual and descriptive framework. S_u, residing in the fundamental Layer 1, is inherently conserved. When we project our understanding or measurement of a system onto these different axes, the conservation of S_u manifests as the familiar dimensional conservation laws.
Time as a Measurement Axis for
The "dimension" of time in our physical laws allows us to track changes. Time translation invariance (physical laws don't change with time) corresponds, via Noether's theorem, to energy conservation.
In the S_u framework: Energy (E_SI = S_u * E_P) is the manifestation of S_u along the "energy/time measurement axis." If S_u is fundamentally conserved, its projection onto this axis (E_SI) will appear conserved when the system exhibits invariance with respect to translations along this (time) axis. The symmetry (time invariance) is thus seen as a condition under which the S_u's projection as "energy" remains constant.
Space as Measurement Axes for
The "dimensions" of space (e.g., x, y, z) allow us to describe location and extent. Spatial translation invariance (physical laws don't change with location) corresponds to linear momentum conservation.
In the S_u framework: Momentum (p_aspect_SI = S_u * p_P) is the manifestation of S_u along "spatial/momentum measurement axes." If S_u is conserved, its projection as "momentum" will appear conserved when the system exhibits invariance with respect to translations along these spatial axes.
Rotational Degrees of Freedom as Measurement Axes for
Rotational invariance corresponds to angular momentum conservation.
In the S_u framework: Angular momentum (L_aspect_SI = S_u * ħ) is the manifestation of S_u related to the system's state concerning rotational degrees of freedom or "orientational measurement axes." The conservation of S_u projected onto this aspect appears as angular momentum conservation under rotational symmetry.
Internal Symmetries (e.g., Gauge Symmetry) as Abstract Measurement Axes for
Gauge invariance (e.g., U(1) for electromagnetism) leads to charge conservation.
In the S_u framework: Electric charge (Q_SI) could be a manifestation of a particular "internal symmetry aspect" of S_u, projected onto an abstract "charge measurement axis." Its conservation would stem from S_u conservation when viewed through this particular internal symmetry.
A.4 Unification: One Conservation Law, Many Manifestations
This perspective suggests a profound unification:
Instead of multiple fundamental symmetries leading to multiple independent conservation laws, there is one fundamental conserved dimensionless quantity, .
The various symmetries identified by Noether's theorem (time translation, spatial translation, rotation, gauge invariance) are reinterpreted as fundamental invariances of the system when viewed along specific "measurement axes" corresponding to our dimensional framework (time, space, orientation, internal charge-space).
The different conserved dimensional quantities (Energy, Momentum, Angular Momentum, Charge) are the values that the single, conserved S_u takes when it is "projected" or "measured" along these different axes, scaled appropriately by the Planck units (which act as the dimensional conversion factors for each axis).
Noether's theorem remains a crucial mathematical link between the observed symmetries in our dimensional physical laws (Layer 4) and the observed conservation of dimensional quantities. However, the S_u framework proposes a deeper Layer 1 reality: these observed symmetries and conservations are reflections of the singular, fundamental invariance and conservation of the dimensionless S_u.
A.5 Conclusion for Appendix
The S_u concept offers a path towards viewing the array of known conservation laws not as a collection of disparate principles, but as interconnected facets of a single, underlying conservation of a dimensionless universal quantity. By reinterpreting the symmetries of Noether's theorem as different "measurement axes" onto which S_u is projected, this framework provides a potentially more unified and fundamental understanding of conservation in physics. This reinterpretation elevates S_u to a candidate for the ultimate conserved entity, with the Planck units serving as the bridges from this dimensionless reality to our dimensional perceptions and measurements. Further work is needed to formalize these projections and derive the full spectrum of conservation laws from this singular postulate.
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