If this room is still on Earth (or on any other rotating body), you could in principle set up a Foucault pendulum to determine which way the rotation is going, which breaks mirror symmetry.
If the room is still in our Universe, you can (with enough equipment) measure any neutrinos that are passing through for helicity “handedness”. All observations of fusion neutrinos in our universe are left-handed, and these by far dominate due to production in stars. Mirror transformations reverse helicity, so you will disagree about the expected result.
If the room is somehow isolated from the rest of the universe by sufficiently magical technology, in principle you could even wait for long enough that enough of the radioactive atoms in your bodies and the room decay to produce detectable neutrinos or antineutrinos. By mirror symmetry the atoms that decay on each side of the room are the same, and so emit the same type (neutrino or antineutrino, with corresponding handedness). You would be waiting a long time with any known detection methods though.
This would fail if your clone’s half room was made of antimatter, but an experiment in which half the room is matter and half is antimatter won’t last long enough to be of concern about symmetry. The question of whether the explosion is mirror-symmetric or not will be irrelevant to the participants.
If this room is still on Earth (or on any other rotating body), you could in principle set up a Foucault pendulum to determine which way the rotation is going, which breaks mirror symmetry.
If the room is still in our Universe, you can (with enough equipment) measure any neutrinos that are passing through for helicity “handedness”. All observations of fusion neutrinos in our universe are left-handed, and these by far dominate due to production in stars. Mirror transformations reverse helicity, so you will disagree about the expected result.
If the room is somehow isolated from the rest of the universe by sufficiently magical technology, in principle you could even wait for long enough that enough of the radioactive atoms in your bodies and the room decay to produce detectable neutrinos or antineutrinos. By mirror symmetry the atoms that decay on each side of the room are the same, and so emit the same type (neutrino or antineutrino, with corresponding handedness). You would be waiting a long time with any known detection methods though.
This would fail if your clone’s half room was made of antimatter, but an experiment in which half the room is matter and half is antimatter won’t last long enough to be of concern about symmetry. The question of whether the explosion is mirror-symmetric or not will be irrelevant to the participants.