The Thermal Bell Test: A Parameter-Free Prediction

If the ether programme stands or falls on a single experiment, this is the one.

The Problem

Quantum entanglement produces correlations that violate Bell's inequality. The standard CHSH parameter for a maximally entangled state reaches $|S| = 2\sqrt{2} \approx 2.83$ , exceeding the classical bound of $|S| \leq 2$ . This has been confirmed in every Bell test since Aspect's 1982 experiment.

But what happens when you heat the system up?

In standard quantum mechanics, entanglement is degraded by decoherence — coupling to the environment. The degradation depends on implementation-specific parameters: the decoherence rate $\gamma_0$ , the measurement time $\tau$ , and the details of the noise bath. The functional form is exponential:

|S_{\text{QM}}(T)| = 2\sqrt{2}\,\exp\!\left(-\gamma_0\tau\,n_{\text{th}}\right) \tag{8.90}

In the ether framework, the mechanism is fundamentally different. The ether's zero-point field (ZPF) carries the entangled correlations via long-range electromagnetic order. At finite temperature, thermal photons contaminate the ZPF signal. Each detection event is independently classified as "signal" (from the ZPF) or "thermal" (random noise), with thermal probability $p = 2n_{\text{th}}/(1 + 2n_{\text{th}})$ .

Theorem 8.8

The result is Section 8.7 — the thermal depolarisation of Bell correlations:

\boxed{|S(T)| = \frac{2\sqrt{2}}{(1 + 2n_{\text{th}}(\omega, T))^2}} \tag{8.81}

where $n_{\text{th}} = (e^{\hbar\omega/k_BT} - 1)^{-1}$ is the Bose–Einstein thermal occupation number.

The critical temperature — below which Bell violation persists — follows from $|S(T_{\text{crit}})| = 2$ :

T_{\text{crit}}(\omega) = \frac{\hbar\omega}{2.449\,k_B} \tag{8.87}

Why This Prediction Matters

Three features make this prediction exceptional:

1. It is parameter-free. The ether prediction depends only on the mode frequency $\omega$ and the temperature $T$ — both experimentally controlled. There are no adjustable parameters. The standard QM prediction has one free parameter ( $\gamma_0\tau$ ).

2. The functional form differs qualitatively. Algebraic degradation (power law with exponent 2) versus exponential degradation. These produce visibly different curves that are distinguishable with modest statistics.

3. It is testable with existing technology. Superconducting circuits operating at 5–10 GHz in dilution refrigerators have already demonstrated Bell violation at $\sim 20$ mK. The critical temperature at 10 GHz is $T_{\text{crit}} = 0.196$ K. A temperature sweep from 10 mK to 1 K would map the entire degradation curve.

The Ratio Test

The cleanest discrimination requires no curve fitting at all. Measure $|S|$ at two temperatures $T_1$ and $T_2$ , and compute the ratio:

R = \frac{\ln(|S(T_1)|/|S(T_2)|)}{\ln(n_{\text{th}}(T_1)/n_{\text{th}}(T_2))}

The ether predicts $R = -2$ (algebraic, exponent 2). Standard QM predicts a value that depends on $\gamma_0\tau$ . A single pair of measurements discriminates the two frameworks.

What's at Stake

If the algebraic degradation is confirmed, it will be the most consequential result in quantum foundations since the original Bell tests. It would mean that quantum entanglement is not a primitive feature of nature but an emergent property of a physical medium — the ether's long-range zero-point correlations.

If the standard exponential prediction holds, the ether's quantum sector is falsified. The gravitational programme (Sections 3–4) would survive — it does not depend on the quantum mechanism — but the unified framework would be broken.

Either way, the prediction deserves to be tested. The full derivation is in Section 8. You can explore the prediction interactively with our Thermal Bell Calculator.