Some Puzzles About the Universe

I pose three interesting questions relating to the enormity of the universe and man’s conception of space on a macrocosmic scale.

Questions

1. Imagine that a pole stretched across the diameter of universe. I am sitting at one end of the pole and Mr X is sitting at the other end of the pole. Now, I push my end of the pole. How long would it take for Mr X’s end of the pole to move?

2. If I have a piece of paper that is 0.1mm thick, how many times would I have to fold it in half for its thickness to exceed the diameter of the Universe? For example, after 1 fold it will be 0.2mm thick, after 2 folds it will be 0.4mm thick etc. After how many folds will it be greater than 100 billion light years thick? This is obviously not feasible in practice for many reasons including the low maximum number of times that paper can be folded in half. Excluding these practical limitations, what is the number of times that a piece of 0.1mm thick paper needs to be folded in half to exceed the Universe’s diameter? The diameter of the entire Universe (as opposed to visible Universe) is a contentious figure. For ease of calculation let us assume that it is 100 billion light years.

3. Imagine that you have a piece of string that is placed around the circumference of the universe in a circle (let’s call this X.) You then add an extra metre of string to X and now have a slightly larger circle (let’s call this Y.) You now have two very large circles composed of string. Circle X has a circumference 1 meter less than circle Y. In the diagram below, circle X is the black circle and circle Y is the blue circle. How far away is A from B?

 

Answers

1. Contrary to macroscopic based “common-sense,” the pole does not move instantaneously. When I push my end of the pole, a wave (similar to a shock wave) is sent through the atoms in the pole. Every material has its own speed of sound. This pole will move at the speed of sound of the material that makes up the pole. It will therefore take an inconceivably long amount of time for Mr X’s end of the pole to move- he will be dead before it moves.

2. It is first necessary to standardize the units of distance. 100 billion light years is equal to 10^24 km. A 0.1mm thick sheet of paper can fit 10^7 times into the 1 kilometer standardized distance. This results in 10^31 sheets of 0.1mm thick sheets of paper needed to be stacked on top of each other to span the Universe’s diameter. In Microsoft excel, the answer will be reached if one types in a box =LOG(10^31,2)

Microsoft Excel will spit out the results 102.9798. This number should be rounded up to 103 as one can’t perform a fraction of a fold. This means that approximately 103 folds of a paper in half are required for it to span the diameter of the Universe. The low result of 103 occurs due to the exponential increase in thickness when the paper is folded. Due to the contentious precise diameter of the Universe, the precise number of fold is probably in the 100 to 104 range.

3. Most people expect the distance between A and B to be some very tiny fraction of a millimetre. This is not the case. The distance between A and B is actually 15.93 cms. It does not matter what size circle X and circle Y are, as long as 1 meter in circumference is added onto circle Y, then circle Y will always be 15.93 cms away from circle X. For instance, imagine if I were to get a pea and place string around the circumference of it. Imagine that I then obtained string 1 meter longer than the string around the pea and placed it outside the pea’s circumference, in a circle. The distance between the two placed pieces of string would be 15.93 cms. This was the same figure as the universe answer! The same answer holds true for any circumference.  

Needless to say, these questions are theoretical questions and there are obviously countless logistical and scientific laws prohibiting these practical occurrences. Consequently, objections such as “the pole will break because it’s too long” do not suffice as the intended answer.

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