Do you think these expressions can be used interchangeably? I find little or no differene between the two meanings. Does this question need more context?
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Speaking from the eastern side of the Pond, I would understand them as being different:
When you say 'technically possible' you mean that it is something that can be done, if you just go by the book. Like, according to the manual of instructions, you can make it happen. Usually this term is used when the truth of the matter is that, whatever the book says, it actually cannot be done. So in a way, it's a non-answer.
To say something is 'physically possible' is just to talk about the mechanics of the operation. There is no consideration given to other relevant factors. Like, for example, you can say that it is physically possible for a child to crawl through a 100-foot-long sewer pipe which is big enough to accommodate the child's body. This doesn't mean that it is actually possible because there are other considerations like whether the child would have the courage to do that, especially if the sewer pipe in question is totally dark and probably infested with mice and other creepy-crawlies, not to mention that it would very likely also be partly filled with stinking sewage.