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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Life, The Mathematical Universe Hypothesis and Everything

The Mathematical Universe Hypothesis (MUH) is a science philosophy that says that our universe is nothing more than a mathematical structure. It also says that all definable mathematical structures are universes that are just as real as ours.

It doesn’t seem to be taken too seriously. The person who proposed it, Max Tegmark, refers to his MUH papers with the perspective “Every time I’ve written ten mainstream papers, I allow myself to indulge in writing one wacky one” under his home page link “Crazy Science”. Maybe this is just a disclaimer because it’s on an MIT site and he’s a well respected member of the scientific community.

Well I’m not. And I think it should be taken seriously and I’d like to explain why. But my approach will be from a finitist point of view, that any definable finite and discrete mathematical structure is a real universe. I’ll also be presuming that our universe is finite and discrete.

In this post I’ll show you some things most people haven’t seen. I’ll stretch your imagination to think of reality differently. I’ll show you You Tube clips that are truly stunning. And if these things don’t blow you right out of your chair then you’re simply reading the wrong blog.

Then as a bonus I’ll show how the MUH provides answers to some of the Big Questions, such as Why is there something rather than nothing?, What happened before the universe? and What is the meaning of life?

But I’ll begin with something simple and ask: What is strange about this picture?

Source: Public Domain

Source: Public Domain

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The GZK Test of Whether We Are In a Simulation

The world of Digital Physics is generally immune from appearing in mainstream media. But some nights ago, during an insomnia induced late night TV viewing, on a mainstream news source (either BBC or Al Jazeera English, can’t remember which) I saw a piece on Are We In a Computer Simulation? And the term Digital Physics was bandied about.

A google search showed activity in various mainstream news websites that appeared to feed off an article at the MIT Technology Review website that you can find here, which talks about an arXiv technical article that you can find here.

Interlaced tracks at Amsterdam Centraal

Interlaced tracks at Amsterdam Centraal (Photo credit: Daniel Sparing)

It talks about the universe being a regular cubic lattice of points, with an observable effect occurring when light travels parallel to the lines of the lattice, sort of like getting your car tyres stuck in tram tracks.

So what can we make of this? Continue reading

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

A Cool Digital Physics Blog

So far I’ve been pretty good at saying what I’m going to do: develop algorithms that show how particular aspects of physics can occur in a locally randomised discrete network. Well someone’s already doing it. It’s Alex Lamb over at How To Build A Universe. I particularly like his post Making Waves 4 where he has created a wave in his random network that propagates as an expanding circle, encounters a wall with two slits, and then creates an interference pattern from the bits of wave going through each slit. This is a great result.

Why The Big Bang? Part 3: Networks

“Space is big. You just won’t believe how vastly, hugely, mindbogglingly big it is. I mean, you may think it’s a long way down the road to the chemist’s, but that’s just peanuts to space.”       –     Douglas Adams, The Hitchhiker’s Guide to the Galaxy

In the previous two parts I discussed two ideas:

                That the universe is finite.

                That any computable mathematical structure exists in the same sense as our universe exists.

I would now like to suggest the general form of structure our universe takes: that of a network or graph. I’ll be considering a network to be a finite number of points, some of which are connected and some are not. That’s it. For example:

Network

Clunky graphics I know, but I’m working on it. Continue reading

Why The Big Bang? Part 2: Existence

“All is number”       –        Pythagorean School

In Part 1 I attempted to present some of the philosophical reasons why we may think infinity is a pretty dodgy concept. I now want to address the second and third questions I posed

What do we mean when we say mathematics exists?

What do we mean when we say the universe exists?

Much has been said about reality and existence, probably way too much. I’m not trying to introduce new ground here, just present a view that I think goes nicely with the idea that everything is finite. That view is known as the Mathematical Universe Hypothesis (MUH) an idea originated by Max Tegmark. It states that our universe is nothing more nor less than a mathematical structure. It implies that any mathematical structure exists in the same sense that our universe exists. I won’t elaborate on this in great detail (I hope to in a later post) but I’d like to give some brief motivation to this idea. Continue reading