The Essential Inability to Know Anything: How Time Renders Us Ignorant

We usually think of scientific research as the process of formulating a hypothesis based on past experience and laws deduced from them, and then of verifying or disproving that hypothesis using experiments.

Take the example of the Higgs boson. The Standard Model of Quantum Mechanics suggested that it may exist, and previous experiments and theoretical considerations pointed to an energy range (or mass range, for E=mc²) where it could possibly be found. That's the theory. The experiment has been conducted at the Large Hadron Collider (LHC) near Geneva, and data collected by the detectors of LHC have been studied and analysed to see if traces of this elusive particle can be found, or if its existence can be ruled out (which outcome now seems almost completely unlikely).

Or, we can take the example of a much cheaper experiment with which you can verify, any number of times, that teapots placed close enough to Earth tend to accelerate toward the centre of the planet. Or that a die thrown over a table will eventually come to rest on one of its sides; and, if the experiment is repeated many times, approximately in sixth of the cases it will rest on the side marked with six dots.

We expect the repeated verification of the effect of gravity on the teapot and the behaviour of the die because we regard the experiments as independent, with everything in the starting position being re-set to some defaults when we try the experiment again. Indeed, when we learn how to calculate (classical) probabilities, we are told the die will show "one" in one sixth of all rolls because the outcomes are equivalent, and the rolls (experiments) are independent. But is that really true of the experiments?

As a macroscopic object, a die obeys the laws of classical physics with very good approximation. As it leaves the fingers, rotates in the air and collides with the table, its movement is predicted very well by classical mechanics. That is, its movement is deterministic, and the outcome, in theory, is determined by how the die has been thrown.

That, in turn, is determined by how the muscles in the fingers and arm contract, which is determined by how the neurons fire that control them, and, ultimately, what they do in the brain of the person throwing the die. His or her cognitive and mental processes must be influenced by what the die showed the previous times. Rolling a die again and again might be events, but because of this, they are hardly independent.

And this is always true, not only when the system includes a person or something that has memory to recall the outcome of previous experiments. Even the die will lose some molecules with every collision with the table, and its scratches and dents will effectively "remember" its whole history. Admittedly, there is usually a lot of noise in the feedback loop: the muscles don't contract completely in line with the neurons, and the collisions between the die and the table magnify tiny fluctuations in the initial movement of the die to the point that it becomes very hard to predict the outcome from the initial set-up of the experiment. But only very difficult, and not impossible: in theory, the effect of all previous experiments is there; they cannot be escaped.

But why stop there, on the level of experiments? The effects of all physical events propagate at the speed of light. By the time we have the chance to react to one, the information about it has practically reached all particles in our planet. Therefore, the only way to make sure that two experiments are truly independent is to conduct them separated by some large distance and almost at the very same time, so that the outcome of one would not be able to reach the other. But it's not clear that this would help, either. We already know that if the experiments are clearly linked, for example because we measure both members of a specially prepared pair of photons, then we will always see correlation between the outcomes of the experiments because when we conduct one of them, we get "entangled" (quantum-mechanically-speaking) with that outcome, and will only see the correlating part of the other experiment. In fact, this is true of all experiments. After any interaction with a system (including measuring the outcome of an experiment), we hopelessly get entangled with it, which, going forward, can mean that we will see a world in which the outcome must have happened in one way and not the other (simply because in that world, it did happen that way).

This all leads to one conclusion: that because we see time as steadily progressing, no two events we see (or have seen) are truly independent. That is, an experiment can never be repeated under the same conditions, which is a prerequisite for it to be able to verify or disprove a theory. In other words, no theory about the physical world can be independently proven to be true or false.

And it also means that the world seems to be free to decide how to behave in any experiment independent of what has been measured before. (Or, if we don't think the world we see must be consistent, then, well, in any experiment.) If we haven't ever definitely, positively, absolutely, undeniably and reliably ruled out the existence of dragons or unicorns, then they are still free to appear around the corner of Piccadilly and Regent Street.

And if the world is consistent, we'll never know what it's really like. We only know the world we lock ourselves in bit by bit, with each entanglement following an experiment or experience, as henceforth we expect the world to behave consistently with what we first saw. When we look at the world around us and experience it, we may not be actually discovering it, but actively participate in its creation--and not only in a psychological or cognitive sense, but in a very real, physical one.