### Meditations on time

I have been thinking a lot recently about relativity (Started drafting this post over a year ago). After having made my last post on black holes I have been watching a lot more on general relativity as well as reading lost in Math and The Fabric of the cosmos. The only reason I can consume so much is because audible allows me to listen at up to 3.5x which when played out loud feels very much like the information downloading from the matrix.

One comment from this video was that as a result of special relativity, light trapped in a perfectly reflective massless box will act as if it has mass.

I haven’t been able to explore this in enough detail to truly understand it but it seems that mass can be an emergent property of the energy. Clearly, this is shown in e=mc^2 but the idea that the mass form of the energy can emerge in the first place.

The other train of thought I have been playing with is the idea that light is the propagation of causality and that causality itself is time.

That makes sense in terms of the speed of light being constant from every reference frame. If light is the propagation of causality through space, it makes sense that causality would have a single speed.

A lot of this comes down to the problems that arise from trying to pin down what time is. For most people, there is an intuitive sense of what time is, perhaps people will raise things like clocks, perhaps even more fundamental clocks like sundials.

The problem is that there are places where those coarse definitions of time break down.

The rising and falling of the sun, at least away from the equator, changes its timing (days getting longer and shorter) and even noon changes a little. Not enough that it matters from everyday experience but when you try to do things more precise when you try to measure time on the order of milliseconds, days change their length each day. If you try to measure things on the order of a second, the year changes it’s length quite chaotically of order a second each year.

To our collective intuition about time, these things don’t matter but when you try to look close enough the discrepancies make our intuition of a concept we agree to call time, less and less well defined. To start with, how can the length of a day changed from day to day, even by a few milliseconds?

If there are 86400000 milliseconds in a day. If you define the millisecond to be that small fraction of the time between consecutive noons then the length of the day, by definition can’t change.

The problem here, sticking to celestial definitions of time, is that the number of milliseconds between the noons of solstices (The number of milliseconds between the longest and shortest days of the year, each at noon on the respective day) changes when counted based on a definition of milliseconds from consecutive noons. That discrepancy points to the fact that the collective definition of time is not as fundamental as we believe it to be.

There must be something in this concept of time, but perhaps it needs to be defined differently to a celestial definition.

Since SI unit of time, the second, is precisely defined to be “The duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" (at a temperature of 0 K).

This is a more consistent definition and allows for incredible accuracy. Enough to facilitate technology like GPS but in my mind, it isn’t dissimilar to a definition based on celestial bodies.

Our understanding of reality gives us reason to believe that this particular process should be consistent over time, and it seems to be the most consistent we have observed.

All of these definitions of time are based around the same principle, something happens and then it happens again.

For each, we have a model for what cause results in the periodic effect. That relates to other things we understand about time, which makes time to be the flow of cause and effect.

For a large group of things, the flow between their cause and their effect are consistent fractions of each other.

To me, it is a realisation that our observation of time, that which forms our intuition, is based around similar ratios between the causal links we observe in life.

In the book the case against reality, one of the assumptions about existence which the author challenges is that space and time exist at all, that they aren’t just things we construct to have an efficient way to interpret the world such that we can seek higher fitness in a more abstract game of evolution than one imagines when thinking of Darwinian evolution.

One concept which I have slowly been generating from both the case against reality and “the order of time” is that it might be better to abstract away this intuition for time as this continuous flow, ever divisible and ever-present and instead think of time as fundamentally these cause->effect relationships.

Thinking about these relationships in terms of a network of causes and effects it makes sense to think of time as the propagation of causality.

When thinking about time as the propagation of causality it makes sense that there is a universal speed limit, a limit to the amount of causal propagation that can happen, for an amount of propagation elsewhere.

This has lead me to the idea that perhaps the time dilation caused by relativity can be thought of as similar to that which is imposed by EVE online. A computational limit.

This might be a concept taken too far by a person whose livelihood is computation, much like how the universe is devised in terms of the technology of the day, “the clockwork universe” etc.

I feel like there is something more fundamental about computation, however.

There are limits of computation which intuitively I feel if broken in physics would permit their braking in general. Of course, this depends on the axioms used in the proofs of the limits, which are different for each limit.

It makes sense to me that physics would limit the amount of mass in a given volume, and the speed at which causality propagates would have a speed. For whatever speed causality propagates at it is the ratios that are important. That to me indicates that every timing event, every element of cause-effect is not just limited by the speed of light but on some level defined by the speed of light. The traversal through the system might not be that of unimpeded light when measured from entrance to exit, but when all the distances involved in all the interactions are considered, the total is such that the apparent slower speed is simply an under measurement of the true total distance.

Special relativity then is trivial and intuitive, if for any process, any measurement of time you can conceive of it as just a measure of the speed of the propagation of causality through space. Then by moving you are increasing the propagation required, the total distance that has to be travelled to result in the effects, so you will measure a reduction in the propagation of time.

That is why a moving clock will slow down when compared to a stationary one, the causal loops must always travel at the same speed.

The idea of building the universe from the propagation of causal effects is something Stephen Wolfram explores in more depth in his book "A new kind of science".

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