The figure I found recently for the density of a cosmic string, if such a thing exists, was 10ˆ16 tons per centimetre. Notwithstanding this odd mix of imperial weight and metric length, I put my limited maths to the test trying to get a picture of what this really implied. My thoughts went like this:
If we take a cautious view of the width of a cosmic string, and consider it as having a width roughly equal to the diameter of an average atomic nucleus, then we are looking at a width of about 10ˆ-14 of a metre; that would translate to about 10ˆ-11 of a millimetre.
What that means is that if you were to place 10ˆ11 of these strings side by side, closely packed, they would cover just one millimetre. This would give you a ribbon with a width of 1mm. and a thickness of 10ˆ-11mm.
If you were to gather 10ˆ11 of these ribbons and place them one on top of another, you would have a “cord”, the cross section of which would be 1mm²
Finally, if you were able to cut a length of 1mm from this “square string”, this would give you a cubic millimetre.
For the moment let’s not think about what would happen if this tiny cube lost its tension!
What would be the mass of this cubic mm?
Taking 10ˆ15 tons per millimetre as the density of a string; we needed to place 10ˆ11 strings together to form a ribbon, thus the ribbon would have a density of 10ˆ15 X 10ˆ11 = 10ˆ26 tons per millimetre. We needed 10ˆ11 ribbons to form our square-sectioned cord, so the density of the cord will be 10ˆ26 X 10ˆ11 = 10ˆ37 tons per millimetre. It follows that our tiny cube will have a mass of 10ˆ37 tons.
OK. Now I know it would be a waste of time going to the gym in the hope of ever being able to lift this. I also suspect that if it came to Earth it would fall right to the centre of the core; but how does it compare with the density of the Earth?
If the mass of the Earth is taken as about 6 X 10ˆ21 tons (let’s round that to 10ˆ22 tons), then our cube will have a mass that is somewhat more than 10ˆ15 times greater than that of the whole Earth. In other words, our tiny cube would have as much mass as one thousand trillion Earths.
Perhaps some kind person would check my maths, without laughing too much.
