  We propose a theory that preserves spin-summed scattering and decay rates at
tree level while affecting particle spins. This is achieved by breaking the
Lorentz group in a non-local way that tries avoiding stringent constraints, for
example leaving unbroken the maximal sub-group SIM(2). As a phenomenological
application, this new physics can alter the spins of top-antitop pairs (and
consequently their entanglement) produced in $pp$ collisions without impacting
their rates. Some observables affected by loops involving top quarks with
modified entanglement receive corrections.
