It is proposed that there exists a basic interaction ${\mathcal{L}}_V$, not involving the photon, whose strength is similar to the of electromagnetism and which violates isospin, $C$, $\mathrm{CP}$, and $T$ invariance "maximally," while conserving $P$ and $\mathrm{CT}$. Simultaneously, it is assumed that electromagnetism conserves $C$, $\mathrm{CP}$, and $T$. It is proposed that such an interaction arises through the coupling of a vector-meson field ${V_{\mu }}^0$ to a hadronic current $J_{V_{\mu }}$ with strength $g_V$ comparable to the electric charge $e$ (if $V^0$ is not too heavy). It is also assumed that $V^0$ is not involved in other basic interactions (apart from gravity). Some arguments are provided to show that $V^0$ should be heavier than at least $3m_{\pi }$. Possible ways of producing and detecting the $V^0$ meson, which acts as an $I$-spin schizon like the photon, are discussed. It is suggested that the problem of the sign of the $n-p$ mass difference and that of the forbiddenness of the $\eta \to 3\pi$ decay based on partial conservation of axial-vector current, current algebra, softness of any one pion, and the conventional electromagnetic interaction, may be resolved owing to the existence of the $V^0$ interaction. A specific model for ${\mathcal{L}}_V$, based on Lévy's generalization of the $\sigma$, model to $\mathrm{SU}\left(3\right)\mathrm{}$, is presented to demonstrate that $\eta \to 3\pi$ forbiddenness is avoided in this model via the contribution of the $V^0$ interaction. One expects to see (under the proposed hypothesis) noticeable ${\pi }^{+}-{\pi }^{-}$ energy asymmetry in the $\eta \to {\pi }^{+}+{\pi }^{-}+{\pi }^0$ decay, no such asymmetry in the $\eta \to {\pi }^{+}+{\pi }^{-}+\gamma$ decay, no noticeable $T$-violating effects in the $\gamma +d\rightleftarrows n+p$ reactions, and an electric dipole moment of the neutron in the region ${10}^{-22\mathrm{}}-{10}^{-23\mathrm{}} e$ cm. It is suggested that these measurements should enable us to choose between ${\mathcal{L}}_V$ and other existing theories of $\mathrm{CP}$ violation.

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