The obvious answer is that we can't remember the future because it hasn't happened yet, but this cannot be the whole story, after all Albert Einstein once stated that:
"people...who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion".
There are two ways to look at time: either it's something that flows as the present moves away from the past and towards the future, or it's something that is static, the past is just as real as the future, and our experience of the present is an illusion. The former idea is known as the tensed theory of time, and the latter is known as the tenseless theory of time[2a].
The tensed theory is the most natural way to think of time and, if this theory is correct, then we are right to conclude that we can't remember the future because it hasn't happened yet. The problem is, there's no physical theory that requires time to flow, and Einstein's theories of relativity specifically state that the tensed theory of time is incorrect[4a].
Special relativity states that two observers that are moving relative to each other must both measure the speed of light to be the same. This means that either of the two properties that movement relies on - space or time - must differ between observers. The first consequence of this is known as the relativity of simultaneity. This shows that the concept of the present is relative because events that appear simultaneous in one reference frame may not do so in another.
Einstein described his theory of general relativity as taking "away the last remnants of physical objectivity from space and time"[4b]. This is because a number of different coordinate systems can be used to map the universe, all giving the same results. There is no way to know which system is 'correct' and so there is no absolute system, or prior geometry to the universe[4c].
According to Einstein's theories of relativity, space and time cannot exist independently, and so are best thought of as a single entity known as spacetime. Since there can be no time without space, there's no such thing as time outside of the universe, and therefore nothing to measure the flow of time against. If there's no such thing as the flow of time, then all times are equally real, and the universe can be thought of as a complete and unchanging 'block' of four-dimensional spacetime.
Given that the tenseless theory of time is correct, and that the future is as real as the past, then it makes sense to ask why we can't we remember the future. This is not the first time that a scientific theory has contradicted our common sense view of the world. The idea that the Earth orbits the Sun at a 100,000 km/h contradicts the common sense view that we should all fall off something that is moving so fast, and it can be argued that quantum mechanics conflicts with the common sense view that there is only one reality.
It's natural to think that time flows from the past to the future, as this is how we understand cause and effect to work, however on a microscopic level all physical processes would still make sense if time were reversed. Some have considered whether we could have evolved to experience the flow of time because it provides an evolutionary advantage[2b]. If this were true, then our brains could have developed the ability to only remember the past in order to create this illusion.
The illusion of the flow of time may have evolved to mimic the thermodynamic arrow of time, which is defined by the law of entropy, also known as the second law of thermodynamics. This states that a closed system will become increasingly disordered over time, assuming that its components move in a random way. Despite what the name suggests, it's not an unbreakable law but a statistical principle. A state of order may randomly arise from a state of chaos, it's just extremely unlikely.
If our perception of the flow of time is an illusion created by the brain, then it may also be possible that creatures have evolved to experience time flowing backwards, to remember the future, or even to experience the world without the concept of the present. Some propose that it's not possible for a conscious being to remember the future because if they knew what they were going to do, then they could choose to act differently, therefore proving that their future memory was false and creating a paradox.
Others worry that a tenseless view of time contradicts our notion of free will, even with the illusion of the flow of time. This is because, if our future is just as real as our past, then it must be 'fixed', whether we know it or not. This problem is not exclusive to the tenseless view of time. The behaviour of people is entirely predictable in theory since our decisions are correlated with neuronal assemblies that are large enough to be described classically.
Many neurophysiologists have confirmed that human behaviour can be predicted. In 2008, Chun Siong Soon and colleagues showed that you can predict a person's free choice up to ten seconds before they are aware of what they will do.
Determinism is not necessarily incompatible with free will, however. This is because the two concepts are not mutually exclusive. We are considered to be acting freely when we act consistently with our character. In fact, people may question the freedom of our actions if we began to act drastically out of character. In 1954, philosopher Alfred Jules Ayer suggested that free will should be contrasted with constraint, not determinism.