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Physics: the structure of the input

From Lindgren’s geometric premise to the physical change a biological receiver must register.

BERM starts with a claim about physical structure. It then asks how a living receiver translates that structure into a change of state. This order matters: the geometry supplies relationships between inputs, the receiving operator supplies the biological coupling, and the downstream model carries the resulting state into behavior and civilization.

What enters this level

The 2025 Lindgren formulation: an electromagnetic four-potential contributes to the metric alongside the Minkowski background.

What carries forward

A receptor-specific input z, with its units, temporal structure and dependence on the receiver’s state. Biology uses this input to describe what changes next.

The physical premise

The starting point is the normalized 2025 form gμν = ημν + AμAν. The background term η distinguishes it from the 2021 singular formulation. This is the identified theoretical premise from which the following tensor relations are derived. Lindgren, Kovacs & Liukkonen 2025i.

gμν=ημν+AμAνg_{\mu\nu}=\eta_{\mu\nu}+A_\mu A_\nu

The proposition is relational: the total potential enters as a tensor product. BERM therefore retains the components and their relationships before asking what a particular receiving system can detect. A source label or one scalar technology index cannot by itself specify that structure.

Background and external input

Write the total potential as a background Ab and an external component a. Subtracting the background metric gives the exact identity below. The two cross terms retain the relationship between background and perturbation; the last term describes the external component’s own quadratic contribution.

A=Ab+a,δgμν=Ab,μaν+aμAb,ν+aμaνA=A_b+a,\qquad\delta g_{\mu\nu}=A_{b,\mu}a_\nu+a_\mu A_{b,\nu}+a_\mu a_\nu

This result is derived algebraically from the stated premise. It is still a tensor. A scalar biological response requires a declared contraction or observation operator. Where the computational notation retains a coefficient κ, it multiplies all three terms; its calibration belongs to that convention and the specified coupling.

The receiving operator

BERM conditionally derives a formal response operator by adding minimal matter–metric coupling and causal response theory. The resulting retarded tissue kernel maps δg to a selected observable. A receptor-specific temporal representation is written below: zᵣ is the measured input and Kᵣ the receiving operator. The state Sᵣ includes orientation, cofactors, redox state, biological phase and recovery history. Kubo 1957i.

zr(t)=∫0∞Krμν(τ;Sr(t)) δgμν(t−τ) dτz_r(t)=\int_0^\infty K_r^{\mu\nu}(\tau;S_r(t))\,\delta g_{\mu\nu}(t-\tau)\,d\tau

For example, z could be the logarithm of a reaction-rate ratio. In the normalized expression, a dimensionless z requires K to have units of inverse time. A change in membrane voltage needs a different operator and units. Naming CRY or an ion channel identifies a candidate biological implementation; the quantitative mapping must specify what that implementation measures.

The explicit coupling premise

The formal operator follows conditionally from BERM’s stated matter-coupling and response premises. Lindgren’s metric relation alone does not supply the gauge prescription, physical scale, tissue kernel, response sign, lag or human endpoint calibration. These remain open parts of L2. Component experiments constrain receiving states and downstream transitions while the physical bridge retains these explicit calibration tasks.

Read the conditional response-operator derivation →

Consequences of the structure

The tensor form yields a useful separation. With background, state and coupling fixed, reversing a separates the part that changes sign from the part that does not. This is a structural prediction of the chosen premise and, for a linear receiving operator, of its composed response.

δg(+a)−δg(−a)=2(Ab⊗a+a⊗Ab)\delta g(+a)-\delta g(-a)=2(A_b\otimes a+a\otimes A_b)δg(+a)+δg(−a)=2a⊗a\delta g(+a)+\delta g(-a)=2a\otimes a

A realizable comparison must define the potential convention, the physical stimulus and the observation operator together. A carrier-phase reversal is not automatically a reversal of the complete perturbation in this identity. With several time-varying inputs, the cross terms also retain their relative frequencies, directions and phases before biological temporal filtering.

Computed signal example

Same RMS, different time structure

Continuous sine waveRMS 1 · Peak 1.41

Normalized amplitude

Pulsed sine waveRMS 1 · Peak 3.16

Normalized amplitude

Time / repetition period

Active pulse windowBoth panels use the same fixed scale, −5…+5.

A shorter active time requires a higher peak here to keep RMS unchanged. Carrier frequency and repetition period stay fixed.

RMS = peak × √(d/2) = 1, where d is the active fraction. Every pulse contains complete sine cycles.

A synthetic comparison of physical inputs. It does not calculate a receptor response or establish which signal has a larger biological effect.

From field to observation

FieldState is BERM’s observation and estimation module. Physical state can generate both a measurement and a biological response; using the measurement to estimate that state reverses the direction of inference, not the direction of causation. The model therefore keeps local field measurements, exposure proxies and scenario parameters distinct.

Static fields, low-frequency fields, radiofrequency signals, pulsed magnetic stimulation and optical inputs each retain their own dose, spectrum, orientation and timing. The biological literature supplies receiver examples within these protocols. Their shared role is to identify which physical and physiological variables the coupling has to carry.

The next step is now precise: carry z into receptor activity, chemical and electrical state, clocks and hormone responsiveness. This is where one physical input can branch into several coordinated biological consequences.

Explore the connected explanations

The tensor derivation

Follow the algebra, its conventions and the steps needed for a scalar observable.

Mathematical structure

Equations, proposed response laws and the model’s computational representation.

Frequency and response

How spectral structure enters explicit receiver assumptions.

Measuring the physical state

Observations, uncertainty and estimation in the FieldState module.

Combining physical inputs

Read the existing superposition examples alongside the tensor structure.

Biological reception

Candidate receivers and the experimental systems that locate their responses.

Continue the explanation

Biology: a changing receiving system

Follow the input through receptors, clocks, hormone responsiveness and functional capacity.