Now...why would the same NOT apply for a time machine ??? Why would a time machine that travels back 5 minutes not be bound by the SAME inertial reference frame as the laboratory from which it travels ?????
I can't find fault with this.
But there is a difficult problem which arises from attempting to reach a significant answer regarding a hypothetical situation--one unknown to physics.
When the time machine is operating, can one move it? Is it actually there in the lab between departure and arrival? If not, why can't something move through that space? If it is there, why can't it be moved spatially? But if it is there what is it that is moving through time?
If time travel is nothing more than an exact backtracking of the time machines history, then it doesn't actually go anywhere. Doesn't that mean the voyager moves independently of the machine? That is, assuming he goes backward in time.
There are reasons why he can't actually do this, among which are (1) the thermodynamic arrow of time--how do you put Humpty-Dumpty together again?--(2) cause and effect, and (3) in a somewhat similar vein,the circumstance that events are recorded in history in a specific sequence. Given these objections, wouldn't a reasonable person conclude time travel must have be purely fictional as it is generally presented?
The only promising possibility I can see would be if the time travelers mind traveled back (traveling forward in time involves assumptions about the future)to his body at a specific point in the past and possessed it (?) If his actual body travels to where he already has the 'same' body there is a problem with the Conservation of Energy law, as far as I can see.<font color="green}*[/color">
This is only a beginning of the problems. In a Time Travel Fiction forum, I present the story of a certain "Freddy" who is given a trip to the future by his pals as a prank. Upon reaching a point ten years in the future in ten minutes, Freddy exits his machine to find his fellow club members much older. They ask him, "Where have you been for the last ten years?" Freddy replies he saw them only ten minutes ago. They remind him that they have all the proof in the world that ten years have passed (which would have been the case if it had been a real trip). His pals, without a time travel machine,get to the agreed upon date in the future at exactly the same time as Freddy does by time traveling (perhaps we should say traveling in time faster than time).
If one wishes to introduce "parallel time lines," or even "time dilation," feel free to do so as an exercise in speculative fiction.
Please don't mention the term 'paradox'.