Now that may partly be because theyвЂ™re looking for a simple answer and there just isnвЂ™t one. But many people seem to find this unsatisfactory. So when physicists say that space-time is real or the Higgs-boson is real, they mean that a certain mathematical structure correctly describes observations. Again we call those particles вЂњrealвЂќ because they correctly describe what we observe. ThatвЂ™s the best answer we have to the question what a particle is. A particle is a vector in a Hilbert space that transforms under certain irreducible representations of the Poincare group. We call it вЂњrealвЂќ because it correctly describes our observations. Space-time is a differentiable manifold with Lorentzian signature, it has a distance measure, it has curvature, and so on. This mathematical structure is defined by its properties. Space-time is a mathematical structure that we use in our theories. But people often ask me things like вЂњwhat is space-time?вЂќ вЂњwhat is a particle?вЂќ And I donвЂ™t know what to do with questions like this. Those particles and their forces can be mathematically described by EinsteinвЂ™s Theory of General Relativity and Quantum Field Theory, theories which have been remarkably successful in explaining what we observe.ДЇor what the science is concerned, IвЂ™d say thatвЂ™s it. For all we currently know, everything in the universe is made of 25 particles, held together by four fundamental forces: gravity, the electromagnetic force, and the strong and weak nuclear force. Which means, odd as it may sound, we donвЂ™t know whether the real numbers are, erm, real.Д«ut of course physics is more difficult than just number. Now, all these numbers with infinitely many digits are called the real numbers. In reality we only ever need a finite number of digits. But if you look at all numbers with infinitely many digits after the decimal point we donвЂ™t actually need all those digits to describe observations, because we cannot measure anything with infinite accuracy. The example I just gave was for integers.

Interestingly enough, not all numbers are real. Again, if that is not a notion of reality you want to use, thatвЂ™s totally okay, but then I challenge you to come up with a different notion that is consistent and agrees with how most people actually use the word. If you see three apples, three describes what you see, therefore itвЂ™s real. Of course we donвЂ™t see numbers as objects walking around, but as attributes of objects, like the spin that is a property of certain particles, not a thing in and by itself. Same thing with gravitational waves, or black holes, or the particle spin.ДЄnd numbers are just like that.

We say they are real because certain mathematical structures that we have come up with describe our observations. We canвЂ™t actually see elementary particles, like the Higgs-boson, with our own eyes. I am not trying to tell you that this is The Right Way to define reality, itвЂ™s just for all I can tell how we use the word. We use the same notion of вЂњrealityвЂќ in physics, that something is real because itвЂ™s a good explanation for our observations. And it explains your observations better than any other hypothesis, for example, that IвЂ™m computer generated, in which case IвЂ™d probably be better looking, or that IвЂ™m a hallucination, in which case your sub consciousness speaks German und das macht igendwie keinen Sinn oder? Why? Because the hypothesis that I am a human being standing in front of a green screen trying to remember that the вЂњhвЂќ in вЂњhumanвЂќ isnвЂ™t silent explains your observations. I noticed in the comments to my earlier video about complex numbers that many people said oh, numbers are not real. But whatвЂ™s the difference between the math that we use to describe nature and nature itself? Is there any difference? Or could it be that theyвЂ™re just the same thing, that everything *is math? ThatвЂ™s what weвЂ™ll talk about today. ThereвЂ™s a lot of mathematics in physics, as you have undoubtedly noticed.

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