One of the most remarkable features of the world we live in is that we can make measurements that are consistent across space and time. By "consistent across space" I mean that you and I can look at the outcome of a measurement and agree on what that outcome was. By "consistent across time" I mean that you can make a measurement of a system at one time and then make the same measurement of that system at some later time and the results will agree.
It is tempting to think that the reason we can do these things is that there exists an objective reality that is "actually out there" in some metaphysical sense, and that our measurements are faithful reflections of that objective reality. This hypothesis works well (indeed, seems self-evidently true!) until we get to very small systems, where it seems to break down. We can still make measurements that are consistent across space and time, but as soon as we stop making measurements, then things start to behave very differently than they did before. The classical example of this is the two-slit experiment: whenever we look at a particle we only ever find it in one particular place. When we look continuously, we see the particle trace out an unambiguous and continuous trajectory. But when we don't look, the particle behaves as if it is in more than one place at once, a behavior that manifests itself as interference.
The problem of how to reconcile the seemingly incompatible behavior of physical systems depending on whether or not they are under observation has come to be called the measurement problem. The most common explanation of the measurement problem is the Copenhagen interpretation of quantum mechanics which postulates that the act of measurement changes a system via a process called wave function collapse. In the contemporary popular press you will often read about wave function collapse in conjunction with the phenomenon of quantum entanglement, which is usually referred to as "spooky action at a distance", a phrase coined by Einstein, and intended to be pejorative. For example, here's the headline and first sentence of the above piece:
More evidence to support quantum theory’s ‘spooky action at a distance’
It’s one of the strangest concepts in the already strange field of quantum physics: Measuring the condition or state of a quantum particle like an electron can instantly change the state of another electron—even if it’s light-years away." (emphasis added)
This sort of language is endemic in the popular press as well as many physics textbooks, but it is demonstrably wrong. The truth is that measurement and entanglement are actually the same physical phenomenon. What we call "measurement" is really just entanglement on a large scale. If you want to see the demonstration of the truth of this statement, read the paper or watch the video or read the original paper on which my paper and video are based. Or go back and read about Von Neumann measurements or quantum decoherence or Everett's relative state theory (often mis-labeled "many-worlds") or relational quantum mechanics or the Ithaca interpretation of quantum mechanics, all of which turn out to be saying exactly the same thing.
Which is: the reason that measurements are consistent across space and time is not because these measurements are a faithful reflection of an underlying objective reality. The reason that measurements are consistent across space and time is because this is what quantum mechanics predicts when you consider only parts of the wave function and ignore other parts.
Specifically, it is possible to write down a mathematical description of a particle and two observers as a quantum mechanical system. If you ignore the particle (this is a formal mathematical operation called a partial trace of an operator matrix ) what you are left with is a description of the observers. And if you then apply information theoretical operations to that, what pops out is that the two observers are in classically correlated states. The exact same thing happens for observations made of the same particle at two different times.
The final consequence of this, the one that grates most heavily on the intuition, is that your existence as a classical entity is an illusion. Because measurements are not a faithful reflection of an underlying objective reality, your own self-perception (which is a kind of measurement) is not a faithful reflection of an underlying objective reality either. You are not, in point of metaphysical fact, made of atoms. Atoms are a very (very!) good approximation to the truth, but they are not the truth. At the deepest level, you are a slice of the quantum wave function that behaves, to a very high degree of approximation, as if it were a classical system but is not in fact a classical system. You are in a very real sense living in the Matrix, except that the Matrix you are living in is running on a quantum computer, and so you -- the very close approximation to a classical entity that is reading these words -- can never "escape" the way Neo did.
As a corollary to this, time travel is impossible, because in point of metaphysical fact there is no time. Your perception of time is caused by the accumulation of entanglements in your slice of the wave function, resulting in the creation of information that you (and the rest of your classically-correlated slice of the wave function) "remember". It is those memories that define the past, you could even say create the past. Going "back to the past" is not merely impossible it is logically incoherent, no different from trying to construct a four-sided triangle. (And if you don't buy that argument, here's a more prosaic one: having a physical entity suddenly vanish from one time and reappear at a different time would violate conservation of energy.)