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your dog is most likely at some point in time and space, obeying the laws of physics
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It is impossible to catch your dog, because even if you know where exactly your dog is, you will lose all the information about its momentum and thus would not know how fast you should chase your dog to catch it.
@ AnowarJaman; A dog is a very macroscopic object and has no wave nature in real world; so uncertainty principle is too approximate here.
@62scruffy: If somehow you can arrange a worm-hole and travel to multiverse you may see many replica of your dog in other universes; you need not worry. Just concentrate to create a worm-hole or some type of such travelling machine, you'll meet him for sure !