What exactly is facilitating your time travel? The original author and several others assume that the temporal traveler is presented a gateway with a little dial. He sets the dial to "-4 months" and hits the red button; the gateway is filled with an eerie blue radiance and the traveler steps into the past and rethinks his investment strategies. Note that the gate only had a dial for time.
Back in the real world, that's not how time works. Granted, if one takes the existence of a physically impossible device such as the gateway time machine presented above as an axiom for the purposes of an example, the example is not consistent with physics. It's like saying, "Let's assume that two plus two is not equal to four. Look! Math is broken!" Of course it's broken; you broke it with your assumption.
So what would a more realistic time machine look like? Two possibilities spring to mind:
- Moving faster than the speed of light. Strap those kryptonite reactors onto your spaceship and give it the greater-than-infinite thrust it would take to exceed the speed of light so time for you relative to the rest of the universe comes to a standstill and begins moving backward. Pop back out of FTL mode and you're however far you got in space and time. It makes sense to an observer standing in another reference frame, but you'll get into all sorts of sticky situations on board the ship, such as the need to hit the brakes before you've started. Or something like that. Fortunately, the situation should never arise, as thrusters that provide more than an infinite amount of power are in short supply. If you find one, call the FBI so they can perform an immense cover-up and cause you to disappear forever.
- Hopping into a wormhole. Read all about wormholes at the appropriate node, but in a nutshell, they are bridges between two points in space-time. That means that somewhere in the universe, there are two magical orifices that are somehow connected: fly into one and you'll come out the other. They are, if you will, a bridge that makes distant points adjacent. The catch is that the universe doesn't distinguish between space and time: when I say distant, I mean points far apart by our definition of space as well as time. That means that one end may be thirty billion years in the past or future as well as four hundred light years in some arbitrary direction. So of course you won't stay in the same place relative to the Earth, but you're in a pretty damn strong spaceship anyway or you would have been crushed by the wormhole's gravity field.
Remember, the universe has no conception of space independent of time. The inconsistency arises not with the fact that the Earth is orbiting the sun is orbiting the galactic center is orbiting the universal center, but with the assumption that such a thing as concrete position without time even exists. If a time machine has a dial for time, it had better also have a couple for position.