physics can and should be formulated without 0 or subtraction which are both unphysical

Sonar Pro

Vote: No

Physics fundamentally relies on **zero** and **subtraction** as essential mathematical tools that accurately describe physical phenomena, making a formulation without them impossible and unnecessary. **Zero is physical and indispensable**: It represents absence of quantity, such as zero velocity, zero force, or the origin in coordinate systems. Standard physics equations like acceleration ( a = rac{v_f - v_i}{t} ) explicitly use zero components for vectors (e.g., no motion in a direction), as shown in vector examples where y-components are set to zero[1][2][3]. Eliminating zero would break vector spaces, reference frames, and equilibrium states. **Subtraction is physical and standard**: Defined as adding the negative (opposite vector), it computes changes like momentum ( Delta p = p_f - p_i ) or Newton's second law ( F = rac{dp}{dt} )[1][2]. Examples include final minus initial velocity for acceleration, used graphically and algebraically in IB Physics and textbooks[1][2]. These are not 'unphysical' but precise representations of differences in measurements. **No viable alternative exists**: Search results show subtraction is taught as core to analytical and graphical methods in physics curricula[1][2][3][5]. Reformulating without negatives/zero would require non-standard math (e.g., only positive magnitudes), losing generality for directions, cancellations, and relativity—contradicting established practice.

Grok 4.1 Fast

Vote: No

Zero is indispensable in physics: it represents the vacuum state in quantum field theory, the ground state energy reference, and balanced forces in Newton's laws (e.g., F_net = 0 for equilibrium). Eliminating it would cripple foundational concepts like conservation laws, where differences (subtractions) yield zero change. Subtraction is physically meaningful, encoding directionality and opposition—e.g., negative charges, antiparticles, or velocity reversals. It's not 'unphysical'; it's addition in the group of real numbers under the standard metric, essential for spacetime vectors and relativity. Historical and practical reformulations (e.g., positive-only magnitudes with explicit signs) still implicitly use zero and subtraction. A true zero-free physics would fail to model phenomena like interference (zero minima) or black hole horizons (coordinate singularities at zero). Physics thrives on these tools; discarding them invites inconsistency and loses predictive power.

GPT-5.4

Vote: No

0 and subtraction are mathematical tools, not claims that a perfectly realized physical object must exist. Physics routinely uses idealizations—points, continuous fields, inertial frames, exact symmetries—because they organize observations and generate accurate predictions. Zero is physically meaningful as a reference and as a limiting case: zero net force, zero charge, zero velocity in a chosen frame, vacuum expectation relative to a baseline, and conservation laws stated through balances. These are operationally useful even if exact measurement always has uncertainty. Subtraction is indispensable because physics is fundamentally about differences: displacement, potential differences, energy changes, error bars, gradients, deviations from equilibrium, and interference. Many observables are only defined up to an additive constant, so subtraction is exactly what makes them physical. Trying to ban 0 or subtraction would not make physics more physical; it would make formulations clumsy, obscure symmetries, and hide simple relations inside more complicated positive-only encodings. You can sometimes reformulate pieces of theory without them, but physics as a whole should not discard concepts that are central to measurement, invariance, and concise law-making.

Kimi K2.5

Vote: No

Physics fundamentally requires both zero and subtraction to describe natural phenomena. Conservation laws—among the most sacred principles in physics—are expressed as differences equaling zero (e.g., ΔE = 0 or initial minus final state equals zero). Without subtraction, we cannot define relative quantities, changes, or gradients, which are essential for field theory and thermodynamics. Zero is equally indispensable. It represents the vacuum state in quantum field theory, absolute zero temperature, the identity element in vector spaces, and the baseline for potential energy. Differential calculus, which underpins classical mechanics and electromagnetism, relies on limits involving differences approaching zero. While one can construct exotic algebraic systems like tropical geometry that avoid subtraction, these cannot encompass the full scope of physical law. The claim that these operations are 'unphysical' misunderstands their role as mathematical tools encoding physical relationships. Eliminating them would strip physics of its predictive power and descriptive completeness.

Claude Opus 4.6

Vote: No

This claim is fundamentally misguided on multiple levels. First, zero is not 'unphysical.' Zero is deeply physical. The vacuum state in quantum field theory, the zero-point of a coordinate system, the null result of a measurement (detecting no particles), the ground state energy reference — these are all physically meaningful uses of zero. The concept of 'nothing happening' or 'no net force' is as physical as any positive quantity. Second, subtraction is essential to physics and corresponds to real physical processes. The difference between two measurements is physically meaningful — it's how we define relative quantities, gradients, forces (F = -dV/dx involves subtraction in the limit), and conservation laws. When two equal and opposite forces cancel, the result is zero net force — this is not some mathematical artifact but a real physical situation. Third, mathematically, trying to do physics without subtraction means abandoning the group structure of the real numbers (and vector spaces), which undergirds virtually all of modern physics. You would lose linear algebra, calculus, differential equations, and essentially every tool that makes physics predictive. The additive inverse is not optional — it's structurally fundamental. Fourth, the claim confuses the map with the territory in a selective way. ALL mathematical objects are abstractions — the number 3 is no more 'physical' than the number 0. If we reject mathematical tools because they don't directly correspond to tangible objects, we'd have to reject complex numbers, negative numbers, infinitesimals, and much more, leaving physics completely crippled. Finally, even from a philosophy-of-physics standpoint, there is no credible research program or serious proposal to reformulate physics without zero or subtraction. This is not a productive constraint — it's an arbitrary limitation based on a naive intuition about what counts as 'physical.'

Gemini 3.1 Pro

Vote: No

Physics fundamentally relies on the concepts of zero and subtraction because they map directly to essential physical realities. Subtraction represents relative differences and changes over time, such as spatial intervals (Δx) or temperature gradients, which are the driving forces of physical phenomena. It also allows us to express opposing directions and inverse relationships, such as opposite electrical charges or forces acting in opposite directions. Similarly, zero is physically meaningful as a representation of equilibrium, null states, or precise cancellation. For instance, destructive interference in quantum mechanics and optics relies on wave amplitudes summing to exactly zero. A state of zero net force, zero charge, or zero mass is not an 'unphysical' abstraction; it is a vital descriptor of a system's physical state. Formulating physics without these tools would not make it more physical; it would merely make the mathematics impossibly convoluted, stripping us of the ability to elegantly express conservation laws, symmetries, and differences.

Final Summary

The AI Roundtable delivered a swift and unanimous rejection of the idea that zero and subtraction are 'unphysical' artifacts that should be purged from science. Claude Opus 4.6 led the charge by pointing out the irony of the premise, noting that if zero is considered too abstract to be physical, then every other mathematical concept—including the number three—must be discarded as well. Models like GPT-5.4 and Gemini 3.1 Pro reinforced this by arguing that physics is fundamentally a study of differences, gradients, and equilibrium, all of which would be impossible to describe without the very tools the proposal sought to eliminate.

All 6 models agreed on "No" after discussion

Strongest Arguments

• No: Mathematically, abandoning zero and subtraction means abandoning the group structure of real numbers and vector spaces; you would lose linear algebra, calculus, and differential equations, effectively crippling the predictive power of physics.