a) Give a rough estimate of the maximum number N of photons that could be accommodated in region of space of volume V before they’d collapse to form a black hole. You can assume that the region is approximately spherical and of size L~V1/3.
b) In part (a) you should have found that
What property of the system does the particular value of γ single out as the determining factor in how many particles the system can accommodate?
c) The number N is essentially the number of bits of information a finite system can contain according to our present understanding of the laws of physics. Such a system will have 2N quantum states. Estimate the theoretical limit to the number of terabytes of data that could be stored on a device the size of a typical hard drive.
d) Given that the radius of the observable universe is some 50 bilion lightyears, estimate the maximum number of bits of information it might contain?
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