Friday, June 3, 2016

Do We Live In Personal Universes?

It's generally useful to behave as if we all live in the same universe. Even if one agrees with quantum solipsism - the idea that one is the only person one knows exists and that the existence of the entire universe depends on you continuing to exist - walking around acting that way makes you look crazy and you're sure to piss off everyone around you if they do in fact also exist. Life is a lot easier to live if one accepts the postulate that other people really do exist even if it can't be proven - and even if they don't exist, behaving as if they do keeps your experience of reality consistent with the expectations your mind has built up over years of experience before you started questioning the reality of other people.

If one puts aside quantum solipsism, there is still a problem in knowing whether or not other people exist in the same universe as you or not. It turns out that one can only prove that other people's universe is consistent with your universe, and not that they are in the same universe.

The Observable Universe

Scientists sometimes mention the observable universe. The observable universe is basically the subset of the universe that we could possibly observe or otherwise be affected by. Because nothing can travel faster than the speed of light under relativity, it's not the case that some object in the universe an arbitrary distance away from Earth can affect Earth (although there are phenomena that do seem to violate the universal speed limit, they are either purely theoretical or confined to the quantum scale, so we will ignore them here).

Only objects that are no farther away than the speed of light times the age of the universe can have affected Earth, so one might guess that the observable universe is a sphere with Earth at the origin and a radius of about 13.8 billion light-years - the speed of light times age of the universe. However, the universe is also expanding, so 13 billion years ago many objects were much closer to us when they emitted light that we observe today. Taking the expansion rate of the universe into account, the actual radius of the observable universe is about 46.5 billion light-years. Also because of the expansion of the universe, there are a set of objects which will never enter the observable universe - they are becoming more distant fast enough that the light they emit will never reach us. In fact, because the universe expands exponentially but the rate of expansion of the universe is constant, objects in the observable universe slowly leave it!

Side note - because light takes time to travel to Earth, it's also the case that looking out into space is looking back in time. When we look out to the edge of the observable universe, we are seeing things as they were billions of years ago. If you go back far enough, the elemental composition of the universe was different, with heavy elements not yet having been synthesized in supernovas. In these conditions, stars and galaxies themselves often took different forms than they do today. Distant galaxies are usually bluer and more metal-poor because of their youth, for example.

The observable universe is relative to the point from which one looks out into the galaxy. Because its radius is so huge, the observable universe on Mars is very nearly identical to that on Earth - at its most distant, Mars is about 401 million km from Earth, or 0.0000423 light-years, or 0.0000000000000912% (9.12 e-14%) the radius of the observable universe. That is insignificant enough to consider the observable universe of Mars as the same as the observable universe of Earth for most purposes - any information that reaches Mars at the speed of light reaches Earth no more than about 24 minutes later, and vice versa. Compare to the age of the universe, that is nearly instantaneous.

But the difference is not zero. There is a slight difference between the observable universe of Mars and that of Earth, and while it's unlikely ever to matter, it's still not zero. It's still different.

Our Own Observable Universes

Earth is not a point in space, so similar to the difference between the observable universes of Mars and Earth, different locations on the Earth's surface have ever so slight differences in their observable universes. The differences are four orders of magnitude less than the greatest difference between Earth and Mars - the Earth's diameter is only about 12,742 km on average - but the difference is still not zero.

People are not points in space either, but because our observation and understanding of the universe arise from of the abstract viewpoint of our brains, we perceive the universe as if we were points in space. Because we are made of fermions, no two people can occupy the same point in space, so no two people can observe the universe from the same point. Thus, like Mars and Earth, we each have our own observable universes too. If we're having a conversation we might only be a meter apart - 9 orders of magnitude closer than the Earth and Mars at their most distant - but we are still a non-zero distance apart and we have different observable universes.

Being in different observable universes doesn't mean we are in different actual universes, however. As long as our observations of the universe are consistent, it only means we observe things at slightly different times - only if we observed a contradiction, like me observing a coin come up heads and you observing it come up tails, or me observing a distant supernova and you observing a star happily chugging along, would being in different observable universes show that we are in different actual universes.

But it also means that we can't prove that we are in the same actual universe. It only means that we can check our past observations against each other and determine whether or not they are consistent with the hypothesis that we are in the same actual universe.

There is a similar thought process some have explored regarding the fact that it takes time for light to enter your eye, cause chemical reactions in your retina, travel up your optic nerve, and be processed into information by your brain. This process means we are always observing the past, and the present ever eludes us. This is a valid observation, but different from the observable universe argument in that it speaks about our limits making observations, not about the content of the universe we are able to observe.

So, does it matter if we can't prove that we are in the same actual universe? Certainly, all our experience has been consistent with that hypothesis. And like quantum solipsism, running around saying that no one else is in the same universe as you is a great way to alienate friends and get committed.

But that's not the point. The point is to use things we can know to reason about the world and form a logical understanding of reality. And the fact that you and I are in different observable universes (assuming you exist :) ) means that neither I nor you can know that the other is also in the same universe. It means we either accept the loneliness that implies, or adopt some additional postulates into our worldview.

Personally, I find it more practical to accept the postulates and carry on with the assumption that other people are in the same actual universe as I. But it's good to know what beliefs you hold that are postulates, both because being logically explicit is mentally healthy and calling out your assumptions enables you to reason and understand other things more effectively. Plus, you never know when you'll see a coin come up heads that I see come up tails, and we'll suddenly realize we aren't in the same universe after all.

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