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The Accidental Truth in Flat Earth Theory

March 27, 2021

I have never addressed or even really considered this particular conspiracy theory of the flat earth, and this is because it is clearly mostly motivated by a kind of wish fulfilment style of reasoning a bit similar to old ideas of the Earth as being at the center of the Universe, on the one side, and on the other side it is promoted by fraudsters trying to discredit all other conspiracy theories in the process. I am not going to go into the typical arguments either for or against. But to summarise them, there is claims about the faked stuff in the moon landings, magnetic issues with the south pole, and there is the possibility of seeing further on the horizon than should be possible. And, in general, there is just the fact of for many people, they won’t believe it because they are never going to see it with their own eyes, and don’t trust any others. Here is a good representative conversation of this perspective for those who want to pursue and get that context a bit further who have not heard this kind of stuff before:

The kernel of accidental truth to it that I want to explore in this post is the notion of the relativity of curvature. This is connected with the relationalist view of space and time, and tells us basically, that for any curvature in the objects around us and the space around us, we can equivalently attribute it to curvature in our own frame of reference. Take the case of the star behind the sun whose light was curved round the edge of it and so it appeared in a different place than was expected, by an amount that corroborated the amount of curvature to be effected by Einstein’s General Theory of Relativity. You could say there is a curvature in that space near the sun, caused by gravity, or you can equivalently say there is a curvature/corresponding distortion in your frame of reference caused by looking near the sun. Like when looking through a magnifying glass. As opposed to how things look just outside of that magnifying glass. Indeed, this is potentially all that is really happening with supposed curvature of space. Because it is corroborated by recent scientific advances with gravitational lensing and like phenomena which are used to measure smaller changes and perturbations near gravitational objects in order to detect things such as exo planets.

So the kernel of truth is that space is not “really” either curved or flat, and can be seen equivalently as either, because there is not “really” any space, there is only a relational network of objects. Contrariwise, the kernel of falsity in the mainstream view is that most people, even today, are still stuck in Newton’s notion of absolute space, despite of Einstein, partly because this particular relativity of curvature and equivalence of flat and curved frames of reference was not made clear or was misunderstood. Though you can see it illustrated by Einstein’s classic accelerating lift thought experiment that creates, within that frame of reference, an equivalent curvature to a gravitational field, with light taking a bent path across that lift as it travels through it.

The misunderstanding in the mainstream view seems related to this felt need even now for us to hypostatise our models of things and take them for reality itself. So, in general relativity , we take some curved models of space and time, and the desire is to find the one “true” model of the curvature. Yet, for all the searching, there has still not been decided if there is any overall curvature to the space of the universe. All we have our localised pockets of curvature caused by areas with big gravitating objects like in solar systems or near black holes. The suggestion of relativity of curvature, which is basically my own idea that I came up with as far as I am aware, is that there won’t be any overall curvature to the universe, for it would mean space is something more than a relational network of things.

The perceived apparent absoluteness, homogeneousness and near flatness of space is made initially difficult to explain with the relational approach, but a good explanation can be found in the Janus approach and shape dynamics approach of Julian Barbour, for which I would refer you to his website . In this approach there is no privileged metric tensor for measuring space with: Size is a purely relative concept, as it needs to be in a relational approach, and the distinctions we perceive instead come from shape distinctions, i.e. relational distinctions in the patterns of how objects are related to each other.

What this can illustrate to us all as a general moral, is that we should avoid arrogance in our perspectives. It would be easy to dismiss flat earth theory, and rightfully so, for some of the reasons I mentioned and for many others, but in the result you may miss the accidental though misguided kernel of truth to it of the relativity of curvature and miss out on your own prejudice and error of presuming some sort of hypostatised model of an absolute Newtonian space.

The real debate around relationalist views of space and time is actually still a live and ongoing debate in current theoretical physics. And in that sense the conspiracy prone types would do well to not rush to their own pet theories but instead be open to exploring relationalist models of space and time. The ideas are very abstract and difficult to visualise, but they are an open field of current exploration which does not involve having to retreat some conspiracy where the whole academic world and mainstream are making up a false narrative purely on purpose, which only makes you powerless in the end against forces in the world all conspiring against you.

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