In order to travel through the fourth dimension, we must obtain some kind of satisfactory conveyance, a time machine. Ideally, this temporal conveyance device would allow one to remain tethered to an adjusted anchor point within the three-dimensional space (exact point of origin) or else allow for one's return to a similar point of origin within that same three-dimensional space.
Indeed in many cases, the latter would be beneficial and the former might prove devastating to any would-be time travelers.
If one were to somehow remain anchored to one's exact location in three-dimensional space whilst traveling forward into time, the best-case scenario would be that one would become marooned in outer space. This becomes evident when one remembers that the exact point of origin (currently located safely on the surface of Earth) would soon move as Earth orbits the Sun and moves further still as it rotates. The entire solar system and everything in it would also be orbiting further distant objects with ever-increasing mass. The entire Milky Way galaxy rotates about a central hub (Galactic central point) some 26,000ly away. At the center of our beautiful, if unremarkable galaxy is a supermassive black hole, about 4 million times the mass of our own sun (Sol.)
Even an adjusted anchor point (if possible) could prove deadly if surface changes occurred during travel. We understand that two objects cannot effectively occupy the same three-dimensional space at the same time. Given humanity's persistent trend to build upon the Earth's surface, a new building inserted into the exact point of origin would become a fatal obstacle for any living inhabitants suddenly fused into walls, beams, or solid surfaces.
Travel backward into history could also prove fatal if calculations do not adequately predict the exact location of objects within the conveyance's pathway. Arriving at one's correct adjusted point of origin in the past (2 million years ago) only to killed by being partially fused into a 200 ft tall prehistoric canopy tree is not an example of successful time travel, is it?
Further danger to craft or crew could arise if calculations are incorrect or do not effectively map out changes in Earth's changing topography. An error of this type could cause a craft to emerge at its "correct" destination, but hundreds or thousands of feet above the Earth's surface, or fused into the bedrock hundreds of feet below ground.
The resulting obstruction in either example could not be called a "collision" as a collision, by its very nature implies a real-time interaction of two or more bodies in motion, bound by the rules of the second law of thermodynamics. A temporal fusion event would likely release energy, light, gravitational waves, and unique subatomic signatures. Think of it as a trainwreck that takes place on a quantum scale. Temporal obstacles as well as any associated travelers would be irretrievably altered by these fusion events. If by some miracle a traveler were to survive such an event, they would be trapped at their new location in space-time without a functional device to get them back.It is likely that these subatomic signatures and gravitational waves would be detected in parallel universes which interact with our own. While it is unknown exactly how much energy would be released by a temporal fusion event, it may be similar to a tiny nuclear explosion. Production of novel subatomic particles (as are routinely generated by the LHC at CERN) would almost certainly occur.
In order to effectively navigate the fourth dimension (time) it is necessary to avoid catastrophic fusion events by mapping out various pathways prior to travel.
In order to arrive at an exact point in space-time, it is first necessary to accurately measure one's travel through the fourth dimension. A clock that measures movement through time, based on units of measurement at the Planck scale would be essential. Planck time is defined as the distance that it takes for a photon to travel one Planck length. An advanced quantum computer onboard the craft would first measure the rate of travel through the fourth dimension at baseline (resting at the point of origin.) On-board gyroscopes would feed telemetry data to the computer and provide for real-time adjustments and course correction if necessary.
In order to maintain certainty that the craft emerges within the correct universe, it would be necessary to perform several diagnostic tests prior to travel and upon arrival. One such test might include measuring the values of certain mathematical constants, like Pi. Measuring the value of Pi to a certain number of decimal places might help one to confirm if one had inadvertently crossed into a parallel universe with significantly different initial conditions, though that might be immediately obvious if the differences were highly significant.