All around us, throughout the universe, and at every scale, there is continual change occurring.
Now the kinds of transformation that are possible in the circumstances in which they can occur are governed by the laws of physics.
And yet we recognize that there are fundamental phenomena involving change, which the laws of physics don't seem to adequately capture for us.
For example, think about information. Increasingly, our society is based on information.
We know that it can be created, that it can flow and can be transformed.
But what is its fundamental nature? Is there really only one kind of information?
Here in Oxford, my colleagues David Deutsch and Kiara Maleto, with support from the Templeton World Charity Foundation.
Are endeavoring to create a new language for physics, in which these questions can be made precise and then fully answered.
Science explains the physical world, everything that's out there, including ourselves, at the fundamental level,
in terms of laws of nature, that is laws of motion, the law of gravity, electricity, magnetism, and so on.
Over the centuries since the scientific revolution, one thing that hasn't changed very much is the mode of explanation of our fundamental laws.
So, for example, if we see a comet in the sky, and can measure where it is, and which direction it's going and how fast,
we can use the laws of motion to tell us where it will be at any other time in the future.
But sometimes that question is not the one we want the answer to.
Sometimes we don't want to know necessarily where the comet will go if nothing gets in the way.
We want to know where it can be made to go, given certain resources, such as rockets, fuel, and most importantly, knowledge.
That is the sort of question that is addressed by constructive theory.
Now, information is essential both in science and in everyday life, even most are now that we live in a world where there are billions of computers all interconnected with one another.
What does the existence of information tell us about the laws of physics?
Well, in constructive theory, we can answer this question exactly in what we call the constructive theory of information.
And with that theory, we bring information directly into fundamental physics.
Information is very different from anything else we have in fundamental physics.
It's not an observable, it's not like the velocity or the charge of particle, and it somehow transcends the physical systems that contain it.
It can be embodied in the transistors within a computer.
It can be spoken aloud in vibrating molecules of air, and it can even be instantiated in the flags of an air traffic controller.
And yet, the meaning of the message stays the same if information transcends physical systems.
How can there be a physical theory of information?
How can we free information from its dependence on particular physical systems, and yet retain its deep connection with the laws of physics?
Well, you can't see information in a physical object unless you also know how the object could have looked if it had had other information in it.
And that is called the counterfactual property of information, and it is easy to express in constructive theory because constructive theory is all about what is possible and impossible.
And the only other thing that's needed is that the information when it's received can be distinguished by the recipient from all these other possible ways it could have been, and also passed on to other recipients.
Now, these two properties of information, the counterfactual property and the copyability are both easy to state in constructive theoretic terms, and without referring to any particular type of physical system.
The very next step, which involves imposing a condition that's very natural in constructive theory, leads directly to all the most important properties of quantum information, which is at the heart of the new and rapidly growing field of quantum technology.
So, the constructive theory of information expresses the regularities in the laws of physics that permit the existence of information in our universe.
These regularities permit things like computation, communication, and even the existence of living organisms, which evidently contain information about their own design.
And all these regularities can be expressed exactly in terms of possible and impossible transformations, and this is why constructive theory suddenly opens the doors to these concepts and brings them directly into fundamental physics.
A DNA molecule is an information storage and retrieval device, and so is a computer drive that holds something like the design of a new iPhone.
Now, these two objects, the molecule and the drive, are physically very different. They have in common that they both hold information, but it's information of a special kind, the kind that can cause transformations in other objects, much larger than themselves.
And we call that kind of information an abstract constructor or knowledge.
Living things are made of atoms, just like galaxies, planets, or rocks.
But unlike these, living things look much more like designed objects, such as cars, robots, or iPhones.
But of course, living organisms haven't been the output of an intentional design process. They haven't been produced by a factory.
It's a scientific theory, Darwin's theory of evolution, that explains how living organisms can have come about through the undirected process of variation and natural selection.
The centerpiece of the explanation is a physical object. It's a DNA sequence that codes for the organism's design.
This is what biologists call a replicator, because it can be copied from generation to generation by the cell it lives in.
And for replication to be possible, the cell must be capable of undergoing self-reproduction.
That is to say it must be capable of constructing another instance of itself with high accuracy.
Self-reproduction and replication are the basic mechanisms of life.
Their accuracy is so remarkable that some physicists have been wondering how they can occur with such an accuracy under simple laws of physics.
Constructed theory explains that they can and why.
An accurate self-reproducing bacterium must contain a recipe, a sequence of elementary instructions to construct a bacterium.
And that's the fundamental thing that a bacterium has in common with, say, an iPhone factory.
For the factory, the recipe is the program that contains the design of an iPhone.
For the bacterium, the recipe is the DNA sequence.
And self-reproduction happens by copying the recipe in the DNA sequence and by reconstructing the rest of the cell by executing the recipe step by step.
And one such step that is crucial for high accuracy to be achieved is error correction.
Error correction for the bacterium is when anything that has gone wrong in the copy of the recipe is corrected.
And for the iPhone factory is quality control when faulty and products are discarded.
Without error correction, an arrow catastrophe would occur.
And this is because both the bacterium and the iPhone are highly complex structures.
This plays one small bit and nothing works anymore.
Which is why things like viruses that don't use our correction must stay simple under our laws of physics.
And the striking thing is all this can be expressed exactly within fundamental physics.
That's because the basic principle of construct a theory is that any transformation that isn't forbidden by the laws of physics is possible.
And that means that it can be performed in practice given only enough knowledge.
So construct a theory can let us understand how knowledge and knowledge creating systems, such as humans, work.
Construct a theory draws its fundamental distinction between transformations that are possible and those that are impossible.
So construct a theory recasts physics into a new form capable of tackling these deep questions like what is information or what makes complex life forms possible.
We believe that constructed theory has the potential to change the way we think about the universe and our own place within it.