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That is, what is the largest number one could possibly come across in the physics of the universe? I would assume it might have something to do with the maximum number of combinations of possible states. For example, Tegmark provides a number listing the probably distance in an infinite universe to the next identical copy of yourself as 10^(10^28) metres. Opinions? [BTW, claiming "infinity" in the multiverse is cheating...]

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  • $\begingroup$ Speed of light is one (in some unit) $\endgroup$ – Paul Dec 16 '14 at 10:38
  • $\begingroup$ Might be interesting, according to Wolfram alpha (wolframalpha.com/input/…) the number of planck volumes in the observable universe is roughly 8*10^164 $\endgroup$ – Joshua Lin Dec 16 '14 at 11:04
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    $\begingroup$ And the number of ways of arranging them... $\endgroup$ – user56903 Dec 16 '14 at 11:05
  • $\begingroup$ This question is completely ill-defined. Just take some power sets or something; you'll get as high as you want. $\endgroup$ – Danu Dec 16 '14 at 12:50
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The number of protons in the universe is estimated to be $10^{80}$ and is called Eddington's Number, $N_{Edd}$, named after the British astronomer Arthur Eddington.

This falls short of the family Googol, which is $10^{100}$ which in turn falls way short of a Googolplex, $10^{Googol}$.

Apparently a physicist at the University of Alberta, Canada, Don Page, calculated the longest finite time that has so far been explicitly calculated by any physicist, as: $10^{10^{10^{10^{10^{1.1}}}}}$ years.

Then there are numbers such as:

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  • $\begingroup$ How is Graham's number "applicable to the universe"? Or any of the others apart from Eddington's number? $\endgroup$ – Rob Jeffries Dec 16 '14 at 10:49
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    $\begingroup$ Graham's number, related to Ramsey theory, "a branch of mathematics that studies the conditions under which order must appear". This seem applicable to the cosmology, even if it is not commonly applied. $\endgroup$ – iantresman Dec 16 '14 at 10:53
  • $\begingroup$ Cheers, good to give it a name, but the total number of sub-atomic particles is a bigger number, so that's presumably what the OP is asking for. I'm sure elemental particles isn't the biggest universally-applicable number, though. $\endgroup$ – Astravagrant Aug 27 '15 at 12:19
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This is not a very sensible question unless you limit it to a dimensionless number of discrete things. You certainly cannot talk about anything with units, because you can pick whatever units you like to make something a very large number, though a ratio of two temperatures, densities etc. measured in the same units could be permissible.

Eddington's number for the number of protons in the observable universe of $10^{80}$ is a contender, but must clearly be fewer than the number of quarks in the observable universe (not that the quarks are observable!).

Once past this though you can make up a very large number by saying something like how many possible quantum states can these protons occupy.

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Estimated number rather than maximum number of combinations , from what i found is $$ 5* 10^{96}$$ ,Planck density, the density (in kg/metre3) of the universe at one unit of Planck time after the Big Bang. Reference here.

According to Don Page, physicist at the University of Alberta, Canada, the longest finite time that has so far been explicitly calculated by any physicist is $$10^{10^{10^{10^{10^{1.1}}}}} years $$ which corresponds to the scale of an estimated PoincarĂ© recurrence time for the quantum state of a hypothetical box containing a black hole with the estimated mass of the entire universe, observable or not, assuming a certain inflationary model with an inflaton whose mass is $10^{−6}$ Planck masses. Reference link.

There is also mention of TREE(3) here, which is lots of math.Its from Kruskal's tree theorem* and Ackermann function . *conservation of mass

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  • $\begingroup$ I raise that by a Googol for the decay time of photons. $\endgroup$ – CuriousOne Dec 16 '14 at 10:46
  • $\begingroup$ I just tried to answer the question literally . I agree that the question is flawed in that "Largest number is mathematically meaningless " but i think if the question is edited probably we can arrive at some numbers $\endgroup$ – Gowtham Dec 16 '14 at 11:18
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This is a nonsensical question because we can pick ANY scale we like for our basic units and the numerical values that pop out of calculations will, as a result, be all over the place. Some folks like to argue that there has to be some highest energy/lowest spatial and temporal scale, but that's only correct for our particular era of the universe. Scales beyond these limits can exist, if we allow for horizons like the big bang or for a phase transition like a big rip (which may create a new horizon on the "other side" of the event). What scale is relevant behind that horizon, or if it can even be translated into our understanding of scales is completely unknown at this moment.

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  • $\begingroup$ Well, restrict it to numbers that appear in the literature then $\endgroup$ – user56903 Dec 16 '14 at 10:37
  • $\begingroup$ They are just as arbitrary. $\endgroup$ – CuriousOne Dec 16 '14 at 10:42
  • $\begingroup$ They will have at least passed some kind of peer review, as opposed to "I think it's a zillion grillion" $\endgroup$ – user56903 Dec 16 '14 at 10:43
  • $\begingroup$ Theoretical predictions of numbers that can't be checked experimentally do not even pass the basic definition of science. $\endgroup$ – CuriousOne Dec 16 '14 at 10:47
  • $\begingroup$ That's a lot of physics you have just excluded there $\endgroup$ – user56903 Dec 16 '14 at 11:06