There are countless objections to the logical possibility of backward time travel, but rarely do i find discussions pertaining to the displacement of matter that backward time travel would inevitably cause.
Let me give an example of what i mean. Say you have invented a time machine prototype that's about the size of an apple. You are able to adjust a dial on it so that it can appear at any time in the past or future that you desire. Now lets imagine you put the device on a table in the kitchen at 8pm friday and set it to travel back in time exactly one day. It arrives at the same place on the table at 8pm thursday.
Now things get tricky when we try and imagine HOW it gets there. In my experience there are two common assumptions made about the path of the machine. It either (a) vanishes from its position and enters some form of "time-warp" dimension only to reappear at the set time, or (b) remains in its position and witnesses time unfold backwards all around it (like in H.G Wells' novel).
In (a) we can plainly see a violation of the basic laws of the conservation of energy. At 8pm thursday at point P on the table we find a physical object that did not exist one moment prior, meaning that the total mass of the universe has increased immediately by the mass of the time-machine. Similarly, the total mass of the universe a moment after 8pm friday decreases by the mass of the device.
If we adopt the many-worlds hypothesis for such a situation, and say that a new universe is created at 8pm thursday, a universe with slightly greater mass, then we would have to say the same for 8pm friday, where a universe is created with slightly smaller mass. What, then, happens to the original universe (assuming it cannot increase or decrease in mass)?
(b) seems slightly more consistent. But the problems are obvious. So the time machine is set and turned on. What happens? If it obeys the laws of conservation of energy, it must remain at P even after it is set. In fact, it would be difficult to determine whether anything at all has happened. From the perspective of someone inside a machine though, the world is witnessed in backwards motion. Or is it? If the machine must remain at P even after it is set, so too must the person inside. We can asume that neither the device nor the person inside is experiencing a backward flow of time AFTER 8pm friday, so they would in fact experience forward flow as normal. So then, what EXACTLY is experienced at P at exactly 8pm? Does the person experience the backward movement of time before 8pm and the forward movement of time after 8pm simultaneously?
My final objection can be seen in both scenarios. What happens if, at 8pm thursday, at point P on the kitchen table, someone has left another object? Would the time machine displace the matter of the coffee cup you left there accidentally? Can two things exist in the same point in space and time?