Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Bill S on 23/10/2010 22:50:37
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If cosmic strings exist they pack a lot of mass into a very small space in terms of any unit length; one would expect this to mean that they would exert enormous gravitational attraction, i.e. to cause extreme local curvature of spacetime.
Some popular science books suggest that the tension on the string would counterbalance this attraction, making them gravitationally inert, while others point to the potential these strings would have for gravitational lensing. Can both be right? [???]
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OK, so nobody wants to talk about cosmic strings. [:-'(]
I shall try an appeal to the mathematically minded.
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, 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.
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I am sorry Bill, but I haven't done the maths. Cosmic Strings have only one spatial dimension - and even if they don't (i know that contradicts first half of sentence) then the cross section is proton-size or lower (ie sub femtometre). A string about a mile long will have mass similar to the earth! All a bit mind-boggling - or in fact very mind-mangling
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Thanks imatfaal, in order to have any chance with this mathematical stuff I have to convert it into imagery I can work with. Your mile-long string is a good image.
Cosmic Strings have only one spatial dimension
Lower dimensionality is something that bothers me a bit. I can accept that if any position on a line can be completely specified using only one co-ordinate, it can be said to have only one dimension; but on a practical level, surely, as soon as you lose any one of the three spacial dimensions the object ceases to exist. Any good images to help with that?
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The problem with most physics from SR/GR onwards is its lack of easy imagery. Things move too fast, are too small, too big, etc. Dimensions are difficult to get ones head around as soon as we leave our inherited comfort zone. Read Flatland - it helps one disengage from reality and try and see other perspectives.
On your question of "losing" 2 dimensions ... the way I think of it; there cannot exist a function f(x) that produces a value for every point on a 2 dimensional plane, you need a function of f(x,y). however a function in one variable can describe every point on a one dimensional string; it maybe a very complicated function but you only need one input variable. I think the thrust is to stop thinking of dimensions as axes on a cartesian co-ordinate graph and think of them in terms of description of the variables of a function.
The surface of a ball is called a sphere by mathematicians - a 2-sphere is the two dimensional surface of a three dimensional ball (ie surface of the earth). It is quite obvious that this 2-sphere exists in a 3-d space, however from any point it is only necessary to provide 2 pieces of information to uniquely determine any other point. The solid ball also exists in 3-d space but you require 3 pieces of information to determine any point (same as sphere with added distance from centre)
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Thanks Imatfaal. Read Flatland - twice - amazing insight!
A few years ago I wrote down my thoughts about dimensions as I was trying to make sense of them. You have condensed into a few lines what took me several pages. What I was really trying to do was get a grip on the idea of time travel, so it was necessary to ask the next question: what would it be like if I could enter an extra dimension, or a scenario in which there were less than 3 dimensions of space? You will not be surprised to learn that that was where I ran into real trouble. I have no problem with the co-ordinates of lower dimensions, just trying to think what it would look/feel like in the physical world.
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If cosmic strings exist they pack a lot of mass into a very small space in terms of any unit length; one would expect this to mean that they would exert enormous gravitational attraction, i.e. to cause extreme local curvature of spacetime.
Some popular science books suggest that the tension on the string would counterbalance this attraction, making them gravitationally inert, while others point to the potential these strings would have for gravitational lensing. Can both be right? [???]
There is sort of a lensing effect caused by the string. It can surely alter the direction of light. One must keep in mind that, for example, a straight cosmic string cannot exert a gravitational force on any object.
The spacetime around the string (i.e. outside of the material from which it is composed) the string itself alters the topology of that space making the changge in the direction of the light possible. I'll get to add this to my website someday. Until then you it can be found in the GR literature. I can find a reference if its important to you?
Best wishes
Pete
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There is sort of a lensing effect caused by the string.
Presumably this should be: "There would be.....", or is there hard evidence for cosmic strings.
A reference would be wonderful - only hope I can understand it [:I]
Thanks
Bill.