Emergence of Special Relativity from Causal Sets


Causal Set Theory (CST) is one of the current serious attempts at creating a discrete model of the fine level structure of spacetime. It relies on a small number of basic assumptions. It is accessible to non-experts. The plausibility of some of the effects of special relativity can be seen quite simply without any mathematics. In this post I am going to show in diagrams how this happens. You won’t need any technical knowledge here, you won’t need to know anything about special relativity, and you won’t have to look at a single equation. (For those interested, I’ll quarantine some equations and technical details in sections in a coloured font, but there is no need to look at these if you don’t want to.)

Currently there is a lot of early stage theoretical investigation going on in CST. Some of it is looking into special relativity. This post will show the sort of ideas that are being thrown around. In particular I’ll be trying to show intuitively how time dilation, length contraction and increase in mass are quite natural in CST.

It is precisely the discrete nature of CST that allows this more intuitive understanding of special relativity. Keeping track of a finite number of points is much simpler than keeping track of an infinite number of them. Basically, CST lends itself to visual explanation much better.

So without any nasty infinities to bother us, let’s go…
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Higgs and the Luminiferous Aether

One Ring to rule them all, One Ring to find them,

One Ring to bring them all and in the darkness bind them

– J R R Tolkien

Peter Higgs (* 1929)

Peter Higgs (* 1929) (Photo credit: Wikipedia)

The recent release of conclusive evidence of the existence of a Higgs(-like) particle is truly a significant step in the development of human knowledge. So as an adherent of digital physics (DP) it is natural for me to consider whether that fits well with DP or if it’s problematic. Well the good news is that I think it fits very nicely indeed and I’d like to weave a tale that tries to explain why. It will touch on various things such as special relativity, wave-particle duality, and other details of particle physics. But most importantly of all, it will be presented with graphics vastly improved on my previous pathetic effort.

When I started mulling over DP, I was interested in thinking through any and all of the known facts of particle physics and see how they stand up to digital models. I wanted to see if I could identify some fact that was unambiguously at odds with DP, so that I could stop wasting my time and move on with my life. I often thought I’d come up against one, but by perseverance it was always possible to see that you couldn’t actually completely rule out DP on the grounds of any known fact. Of which I was aware.

Except for one…. Continue reading