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Compressed archives in computer science are, from some perspective, decreasing the data size by minimizing repetition of data.

Take each particle (to any precision you prefer) in the whole universe, in different fields, at a certain point of time, as a vector in the field. If these vectors are put together to form an enormous file (whether it is logical that a disk can contain this file is irrelevant to this question), and then compressed using the aforementioned type of compression algorithm, how much smaller can it become?

In other words, do the vectors at a discrete point of time of particles in different fields have a pattern that we can facilitate such that, when processing data on the whole universe, there is no need to really calculate things per particle?

Note: I'm referring to the relative compression size, not the real number of bits it may consume. I am talking about the average in the universe, so whether the universe is infinitely big is irrelevant.

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Lossy or Lossless Compression?

Most of modern physics works with lossy compression; we calculate orbits based on entire planets, not on systems of particles orbiting other systems of particles. Depending on the amount of "lossiness" you're willing to accept, this could work as a sort of "compression;" we don't compress systems of particles, but instead detect clusters of particles in known configurations and simply store those.

But like Jpeg's compression, you're going to end up with giant artifacts, which get worse the stronger compression you use.

Lossless compression wouldn't work without a Heisenberg Compensation Device; since all features of a particle cannot be determined 100% accurately according to Science As We Know It Today, it would be impossible for us to losslessly compress the universe.

Different compression methods get different compression results. Some handle some types of data better than others, so a number would be pretty impossible to come up with.

How big is the universe? This is all moot if the universe is actually infinite in extent, as infinitely compressing an infinity is still infinite in size. If I wanted to be a jerk, I could make Infinity Big! the answer :D

Why not pack instead of compress? A safer method of "compressing" the universe would be to defrag it; there's an awful lot of empty space out there, and by moving particles closer to each other (using some sort of handwave to keep them from interacting), along with some metadata, you could likely compact the universe into a very small space.

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    $\begingroup$ A good example of when the simplification of "treat the lump of particles stuck together as one big lump of a particle" fails is mascons, or mass concentrations. This is particularly evident with Earth's Moon, where they make maintaining a passive, stable orbit for any real length of time difficult, but Earth isn't exactly a perfect sphere either. (It isn't even a perfect oblate spheroid.) Mass concentration (astronomy) on Wikipedia. $\endgroup$ – a CVn Apr 20 '17 at 5:09
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    $\begingroup$ Problem is, empty space is not completely empty. If it is required to keep track of everything you cannot just cut out a swath of the universe and say "508.53 light years of empty space here". $\endgroup$ – Annonymus Apr 20 '17 at 6:30
  • $\begingroup$ Sorry about the ambiguity of the question. I'm not asking about the absolute size, only the relative size. Please see the last line in the edited question $\endgroup$ – SOFe Apr 20 '17 at 7:55
  • $\begingroup$ Heisenberg's uncertainty principle says that the data cannot be precisely obtained in the first place, so that the compression will be lossy by necessity. $\endgroup$ – AlexP Apr 20 '17 at 13:14
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There appears to be a fundamental limit to the amount of information needed to encode all particles in a volume of space that is much smaller than you would gather from the resolution of that volume.

The Holograpic Principle shows that any volume’s contents is limited to the surface area of a 2 dimensional boundary drawn around it! It’s 2 bits per square planck length, if I recall correctly.

For the case of the observable universe, the boundary is the cosmological horizon. So, 13.82 billion light years in radius is a surface area of ≈2.15×1035 square meters. That comes to roughly 1.6×10105 bits.

This is proportional to the surface area, not the volume, so is quite heavily compressed. If you could compress the measurements of all the actual particles in the volume in some super-smart way, you can expect it to produce a random number of this size — it could not be compressed further.

Now the bad news: you cannot store this value in any system smaller than the observable universe. As explained above, this is a fundimental limit to how much information can be present in a given volume of space.

If your compression was not as good as this theoretical maximum, you would actually need a volume larger than our observable universe to store it.

edit to go with the edited question

The compression factor is not a constant amount or even a factor in the sense of a multiplication. It is a higher power. It is the difference between squared and cubed, or a number raised to the 2/3 power. The number is based on the radius.

You should understand that tbis is many orders of magnitude more than what you see in a zip file or other examples, because the radius of the universe (in planck lengths) cubed divided by the same value squared is very very very large. Reducing the top value by a factor by noticing that spqce is mostly empty will make a very small difference.

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    $\begingroup$ No, I don’t see that at all. It is focused only on the zipped size and relative compression factor. Did you understand this answer? Read up the links? $\endgroup$ – JDługosz Apr 20 '17 at 7:57
  • $\begingroup$ I understand that entropy inevitably increases with the amount of data to compress. I probably didn't write the question too well — wasn't expecting someone to be serious enough to calculate it as hard-science :P $\endgroup$ – SOFe Apr 20 '17 at 8:12
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    $\begingroup$ It's weirdly pleasing to me to learn that the most efficient way to fully describe the observable universe is to build one. $\endgroup$ – Steve V. Apr 21 '17 at 3:27

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