Tuesday, June 9, 2020

Teleportation and time-travel

Let’s assume:

  1. Faster-than-light travel is metaphysically possible in a special relativistic world.

And let’s assume:

  1. In a special relativistic world, no (inertial) reference frames are metaphysically privileged.

Now, if faster-than-light travel occurs, then one travels from space point z1 to point z2 during a length of time t < d(z1, z2)/c according to some reference frame F1. The arrival location then is not in the light-cone centered on the departure point (and light-cones do not depend on reference frames). But if the arrival point is not in the light-cone centered on the departure point, then there is a reference frame F2 according to which the arrival is earlier than the departure. (For the forward light-cone centered on a point a is just the set of points of space-time that are later than or simultaneous with a according to all frames. So if you’re not in the forward light-cone centered on a, you are earlier than a according to at least one frame.)

But no frame is privileged by (2). Moreover, if faster than light travel is possible, then faster than light travel is possible at any finite speed, since anything else would be unacceptably ad hoc. So if faster than light travel is possible according to F1, it is possible according to F2. So let’s suppose that you traveled from z1 to z2 and arrived −δ units of time earlier according to F2 (for some δ > 0). Then add another spot of faster than light travel from z2 to z1, at a speed high enough to ensure you arrive at z1 in δ/2 units of time. Then according to F2, you moved from z1 to z2 and back to z1 and arrive −δ + δ/2 = −δ/2 units of time after the beginning of your journey.

So according to F2 you time-traveled backwards at the same spatial location. But backwards time-travel at the same spatial location in one reference frame implies backwards time-travel according to all frames (because it implies going into one’s backwards light cone).

So, we’ve argued:

  1. If (1) and (2) are true, then it is metaphysically possible to travel absolutely backwards in time,

where absolute backwards time-travel is time-travel backwards according to all inertial frames. (I assume that most people working in philosophy of time know this.)

And there is good reason to believe (1) and (2). Indeed, (2) seems definitional. And (1) seems pretty plausible, especially given an omnipotent God. After all, surely God could make you travel to alpha Centauri and back by Christmas of this year. Note, though, that a part of (1)—and perhaps this is the controversial part?—is the possibility of a special relativistic world.

I am not sure what to make of this.

1 comment:

Michael Gonzalez said...

I think William Lane Craig has done the right thing by denying special relativity, in favor of a Neo-Lorentzian approach with a preferred reference frame. After all, if God accelerates you faster than c, in which reference frame does He do so? Does He have a particular one like some object occupying space? He can't occupy them all without having contradictory beliefs and a scattered, incoherent mental state. I just think Newton was right to establish the absolute, privileged frame for both space and duration as being based in God, and I think Craig has done some great work in giving a variety of reasons (only some of which involve God) for preferring a Lorentzian approach over an Einsteinean one.