The concept of infinity is endlessly fascinating. For philosophers, for mathematicians and of course children. We have all wondered about how any number can be infinite, because we can always imagine making a larger number: infinity plus one. The concept of infinity is also discussed in the context of the physical sciences. However, frequently people neglect to mention that there are no infinite quantities in physics. None? Well, I don’t think so. I think that infinity is fundamentally a mathematical concept and in reality something else always happens that interferes with the extremity of physics that would happen near an infinite quantity of anything.
Are you sure? Well ‘No’.
I agree that in the physical sciences, the word infinity is often used. I remember being taught at school that when one’s eyes were relaxed they were ‘focussed on infinity’. I wondered about that phrase for a long time, but in the end I concluded it was just poetry. It means one’s eyes were set so that parallel light would be focussed onto one’s retina. If the light had indeed come from infinity, it would – of course – not have reached us yet.
What about the singularity around an electron? At Sussex University, Dr David Bailin taught me that a ‘bare’ electron would have infinite mass and infinite electrical charge. I was told that the particle that we observe and call ‘an electron’ is actually a hypothetical ‘bare electron’ plus its ‘re-normalised cloud of virtual electrons and positrons’. This cloud is created by the intense electric field around the infinite electrical charge. What that means is that in reality we never observe an electron to have infinite mass, but theoretical physicists imagine a real electron as being composed of a hypothetical singular particle plus another phenomenon that hides the singularity. The upshot of this is that a ‘bare electron’ is a mathematical concept – not a physical one. When we look at electrons we never observe an infinite property.
Similarly, it is populalry stated that a black hole is a ‘gravitational singularity’ – an infinitely strong peak of gravitational intensity. But of course we have no observations on this and based on everything we know, we would expect that as the field intensity increased – ‘something’ would happen. Currently, we have no idea what that ‘something’ is. But there is certainly no experimental evidence that a gravitational singularity actually exists. The intensity can reach any amazingly large number. It can reach an intensity which is so alarming that it takes my breath away. But as long as a number can be associated with it – it is not infinite. I am prepared to be ‘boggled’ by large numbers but not ‘baffled’ by an unphysical concept.
What about the Big Bang? At the time of the Big Bang – something is supposed to have exploded for reasons we have not yet figured out. Amazingly it seems that the vast universe hat we observe, and all the energy in it, was once packed closely together in the space occupied by a proton. So the universe was once unimaginably hot and dense. Do I mean infinitely hot and dense? No, not infinitely so, just orders of magnitude beyond any regular conception of temperature or density.
What about the Universe? Well there are many different conceptions of the Universe – and we have data from the cosmic microwave background indicating that the furthest structures that we can see are at most around 40 billion light years distant. Beyond that there is certainly something else, but we just don’t know what. But surely, I hear you ask, one can always keep going? Well actually, we just don’t know! In some conceptions one can, and in others one can’t. But there is no reason to suppose that the Universe is infinite – only that it is even more uncomfortably large than we previously conceived.
So is infinity unphysical? Well I think so. I would love to hear of an example of an infinite quantity, but actually I just don’t think that an infinite ‘anything’ makes any sense at all. And as a measurement scientist I would be very interested to know of the uncertainty of measurement of an infinite quantity: infinity plus or minus what?