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Assuming that alternate histories arise as proposed by the many worlds interpretation of quantum mechanics, that is, from 'branching' events, where each possible outcome gives rise to a new timeline, I was wondering how that would feed through into the numbers of timelines in which there was a perceptible difference to (for example) the Earth.

The sort of events that the many worlds theory considers when determining whether there are multiple outcomes are those at the quantum- the subatomic - level. For example changes of energy level by electrons, radioactive decay and so on.

Even if a timeline branches, that does not mean there will be perceptible differences between the two (or more) timelines that result from the branching event. For example, a galaxy ten billion light years away is still part of our universe, and physics implies that branching events are as likely to occur there as they are in our galaxy. However, events so far away are extremely unlikely to make any perceptible difference to the Earth or anything on it. The same applies to a branching event taking place where even a chance of its being observed by something beyond its immediate vicinity is very, very low, such as in the dark matter that makes up the vast majority of the universe, or in the heart of a star (stars making up the vast majority of the 'visible' matter in the universe), or in a molecule of gas in interstellar space. In fact, the same could probably be said for a branching event anywhere other than within the biosphere of the Earth, and probably even for most events within the biosphere.

For the sake of argument, I am assuming that any timeline branching could result in a locally perceptible difference. That is, one that can be relatively easily detected close to where the branching event takes place and so have an impact on how events proceed from that point in time. This is unlikely to be the case in reality, where I would imagine that most branching events cause a microscopic change that then causes no macroscopic differences, with only a (probably tiny) minority causing a chain reaction of increasing changes to the point that they have an effect on a macroscopic - noticeable - scale. It is also likely that the further in the past the branching point occurred there more likely it is that changes will have had a chance to propagate up to a macroscopic level.

However, I have no idea how one might calculate the fraction of branching events that do result in macroscopic changes, that is, the sensitivity of the environment at a given point to microscopic changes, so this is very much a 'best case' estimate.

That being so, assuming (as seems reasonable) that branching events occur at random across the entire universe, then I would say that the chance of a timeline being perceptibly different to another comes down to the ratio between the mass of the universe (that is, the entire set of particles in which branching events that can split a timeline take place) and that of the region in which one is interested in the branching events. Basing these estimates on ratios of masses removes the need to account for the numbers and types of atoms and subatomic particles in different locations.

So based on this, the chances of a timeline showing perceptible differences to another within a given region is given below:

Region Mass (kg) Fraction of Timelines with
Change Inside Region
of Interest For Mass Of
Number of Timelines with
Changes Outside Region
of Interest for Every
One Within Region For Mass Of
Whole Universe All Stars Whole Universe All Stars
Whole Universe
(including dark matter)
6.0 x 10+53 1 - - -
All Stars in Universe 3.0 x 10+52 0.05 1 20 -
Our Galaxy 1.2 x 10+42 1.9 x 10-12 3.9 x 10-11 5.2 x 10+11 2.6 x 10+10
The Solar System 2.0 x 10+30 3.3 x 10-24 6.7 x 10-23 3.0 x 10+23 1.5 x 10+22
The Earth 6.0 x 10+24 1.0 x 10-29 2.0 x 10-28 1.0 x 10+29 5.0 x 10+27
Earths Biosphere 1.1 x 10+16 1.8 x 10-38 3.7 x 10-37 5.5 x 10+37 2.7 x 10+36
A Human Being 70 1.2 x 10-52 2.3 x 10-51 8.6 x 10+51 4.3 x 10+50

1. The 'Fraction of Timelines with Change Inside Region of Interest' columns give the fraction of timelines in which the branching event that caused the timeline to split occurred within the region of interest. This is calculated by comparing the mass of that region to the mass of either the whole universe (for the numbers in the 'Whole Universe' column) or the mass of all of the stars in the universe (for the results in the 'All Stars' column).

2. The 'Number of Timelines with Changes Outside Region of Interest for Every One Within Region' columns give the number of timelines in which the branching event occurred outside the region of interest for every timeline where it occurred. So, for example, for every timeline in which a branching event occurred within a given human being, there will be nearly 1052 (that is, nearly ten thousand trillion, trillion, trillion, trillion) timelines where it did not.

Note that the numbers given here are for a single branching event. Because each timeline created from a given branching event continues to branch further as time progresses, each additional branching event multiplies these numbers by themselves, so that after n branching events, the number of timelines is that for a single branching event raised to the power of n.

Depending on the frequency with which branching events occur - and I would imagine they happen much more often than once per second and perhaps more often than once per the Planck Time of some 5.4 x 10-44 seconds - the number of timelines would become utterly vast very, very quickly. There are some 1080 atoms in the universe, so it does not take many branching events for the number of timelines to exceed that number by a vast amount, even if the region of interest is the size of a galaxy...

The age of the universe in seconds is some 4.3 x 1017 seconds. Thus there have been some 8 x 1060 Planck Time intervals since the start of the universe. So there could be the 'Number of Timelines with Changes Outside Region of Interest for Every One Within Region' raised to the power of 8 x 1060 timelines, or anything up to some 10113. Which given that it is some 1033 (that is, one billion, trillion, trillion) times the number of atoms in the universe is a lot!

All of this means that finding timelines with differences perceptible to an Earth-based observer with a human level of perception would be very difficult, and require traversing vast numbers of apparently identical timelines (by whatever means) to reach. It also means that finding a specific timeline is likely to be very difficult. Finding it twice without some distinguishing feature to home in on is likely to be even more so...

Send any comments to me at tony {dot} website {at} clockworksky {dot} net.

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