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With the bare minimal force required to not drop it, Rita

holds a refrigerator magnet — not the lame flexible ones that just stick to a fridge, the good ones that can actually hold papers and photos — up against the mirror.

If there were different universes,

this would be placing the pole of two magnets against each other.

I contend that these would be the same poles, which repel each other; if you've ever done this, you know this repulsion tends to push the magnets sideways relative to each other.
@Dr Xorile, in comments, suggested the symmetry of the alternate universe would mean the poles would in fact be opposites. This makes no real difference; that would cause the magnets to "snap" together from their magnetic attraction.

Either way, the magnets will exert force on each other and they will move accordingly.

It is trivial to show that, in fact, nothing happens.
So Rita proves Joe's conjecture is false.

Joe might argue that Law 7, or Rita's grip itself, still explains this.

Strong enough magnets should demonstrate the effect before actual surface contact, keeping Law 7 out of play. Hanging the magnet from some string would prevent any argument that Rita's hold on the magnet is preventing it from moving. My kids have fridge magnets strong enough, and a good few of my souvenir magnets also qualify, and I doubt my household is particularly unique in this.

With the bare minimal force required to not drop it, Rita

holds a refrigerator magnet — not the lame flexible ones that just stick to a fridge, the good ones that can actually hold papers and photos — up against the mirror.

If there were different universes,

this would be placing the pole of two magnets against each other.

I contend that these would be the same poles, which repel each other; if you've ever done this, you know this repulsion tends to push the magnets sideways relative to each other.
@Dr Xorile, in comments, suggested the symmetry of the alternate universe would mean the poles would in fact be opposites. This makes no real difference; that would cause the magnets to "snap" together from their magnetic attraction.

Either way, the magnets will exert force on each other and they will move accordingly.

It is trivial to show that, in fact, nothing happens.
So Rita proves Joe's conjecture is false.

Joe might argue that Law 7, or Rita's grip itself, still explains this.

Strong enough magnets should demonstrate the effect before actual surface contact, keeping Law 7 out of play. Hanging the magnet from some string would prevent any argument that Rita's hold on the magnet is preventing it from moving. I have kitchen magnets strong enough (those shown in a comment below, for example), and a good few of my fridge souvenir magnets also qualify, and I doubt my household is particularly unique in this.

With the bare minimal force required to not drop it, Rita

holds a refrigerator magnet — not the lame flexible ones that just stick to a fridge, the good ones that can actually hold papers and photos — up against the mirror.

If there were different universes,

this would be placing the same pole of the magnets against each other, which repel each other; if you've ever done this, you know this repulsion tends to push the magnets sideways relative to each other.

Since this won't happen,

we know Joe's conjecture is false.

Joe might argue that Law 7 still explains this.

Strong enough magnets to demonstrate the effect without actual surface contact negates Law 7. My kids have fridge magnets strong enough to do this, and a good few of my souvenir magnets also qualify.
Rita's force in holding the magnets, too, can be eliminated with little difficulty with suitable application of string, making the magnet strength required to show the (absence of) effect quite minimal.

With the bare minimal force required to not drop it, Rita

holds a refrigerator magnet — not the lame flexible ones that just stick to a fridge, the good ones that can actually hold papers and photos — up against the mirror.

If there were different universes,

this would be placing the pole of two magnets against each other.

I contend that these would be the same poles, which repel each other; if you've ever done this, you know this repulsion tends to push the magnets sideways relative to each other.
@Dr Xorile, in comments, suggested the symmetry of the alternate universe would mean the poles would in fact be opposites. This makes no real difference; that would cause the magnets to "snap" together from their magnetic attraction.

Either way, the magnets will exert force on each other and they will move accordingly.

It is trivial to show that, in fact, nothing happens.
So Rita proves Joe's conjecture is false.

Joe might argue that Law 7, or Rita's grip itself, still explains this.

Strong enough magnets should demonstrate the effect before actual surface contact, keeping Law 7 out of play. Hanging the magnet from some string would prevent any argument that Rita's hold on the magnet is preventing it from moving. My kids have fridge magnets strong enough, and a good few of my souvenir magnets also qualify, and I doubt my household is particularly unique in this.

With the bare minimal force required to not drop it, Rita

holds a refrigerator magnet — not the lame flexible ones that just stick to a fridge, the good ones that can actually hold papers and photos — up against the mirror.

If there were different universes,

this would be placing the same pole of the magnets against each other, which repel each other; if you've ever done this, you know this repulsion tends to push the magnets sideways relative to each other.

Since this won't happen,

we know Joe's conjecture is false.

With the bare minimal force required to not drop it, Rita

holds a refrigerator magnet — not the lame flexible ones that just stick to a fridge, the good ones that can actually hold papers and photos — up against the mirror.

If there were different universes,

this would be placing the same pole of the magnets against each other, which repel each other; if you've ever done this, you know this repulsion tends to push the magnets sideways relative to each other.

Since this won't happen,

we know Joe's conjecture is false.

Joe might argue that Law 7 still explains this.

Strong enough magnets to demonstrate the effect without actual surface contact negates Law 7. My kids have fridge magnets strong enough to do this, and a good few of my souvenir magnets also qualify.
Rita's force in holding the magnets, too, can be eliminated with little difficulty with suitable application of string, making the magnet strength required to show the (absence of) effect quite minimal.