The Paradox of the Human Body Smeared Across Time
Doug Marett (2010)
Can physical objects connected together in space also be physically connected through time? When you are standing on the surface of the Earth, you are upright in a gravitational gradient . According to General Relativity (GR), time is passing more slowly at the surface of the Earth and the speed of time increases the further we move away. This implies that for a person standing on the Earth, the time at your head is moving forward faster than the time at your feet. Ultimately at any given moment one part of your body is in the future (your head), and another part (your feet) are in the past. But your head is physically connected to your feet. How can you be physically connected to something in the past or the future? If I reach and touch my feet, am I literally reaching into the past? From the perspective of relativity, the only way for time to reverse would be for light to go faster than C. In touching my toes, am I violating an immutable law?
On a rotating Earth with its angular velocity and gravitational potential, a literal interpretation of GR would imply that every single atom of our body must be in a slightly different timeframe - we do not exist physically in space in the here and now, but rather are smeared across a gradient of time. Every time I walk, the signal from my brain to move my legs must travel back in time to activate my past feet to move forward, and this action from the past then articulates my torso in the future to lurch ahead - the ultimate paradox of eliminating the concept of an absolute time is that we end up with the idea that a single object exists in multiple timeframes simultaneously. This contradicts our own definition of time - that the future is distinct from the past - and thereby the future and the past can not in any way involve simultaneity.
In Minkowski spacetime, if every atom of every object is defined by spacetime points (x,y,z,t), when my hand (in the future) touches my toes (in the past), the spacetime points of my fingers must translate through coordinates t to reach the spacetime points in the past. The action cannot be carried out without time travel. Since the action is reversible, this time travel must be possible both forward and backward. This would make time travel trivial - but because time travel has never been shown experimentally to occur, it could not possibly be trivial (a contradiction). One cannot say that the slowing of clocks such as in the Haefle and Keating experiment is proof of relativistic time travel, since the same effect should happen in Lorentzian relativity where time is absolute, and these two explanations are experimentally indistinguishable.
Finally, it has been argued  that the temporal region of spacetime that is perceived to be the "present" is defined by the speed of our thought processes (say on the order of a fraction of a second), and as such allows for our body to be stretched temporally across spacetime, since the time difference from one end of the object to the other is much shorter than can be perceived. However, this returns to the idea, common in Quantum Mechanics, that the impossible can happen, as long as we can't perceive it to happen! Perderantism, which is implied from the idea of the human body smeared across time, requires an objective spacetime existing regardless of perception, thus any subjective agreement that the present does not include the future or the past, does not invalidate the fact that it would have to in any substantivalist interpretation of spacetime. .