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Beautiful proofs (#4) - When Gauss was a young child...

The legend goes something like this:

Gauss’s teacher wanted to occupy his students by making them add large sets of numbers and told everyone in class to find the sum of 1+2+3+ …. + 100.

And Gauss, who was a young child (age ~ 10) quickly found the sum by just pairing up numbers:

Using this ingenious method used by Gauss allows us to write a generic formula for the sum of first n positive integers as follows:

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Physicist Create a Fluid With Negative Mass

Physicists from Washington State university have created a liquid with negative mass meaning that when you push it, instead of accelerating in that direction, it accelerates backwards.

Matter can have a negative mass much the same way that particles can be negatively charged. Newton’s second law of motion (F=ma) tells us that mass will accelerate in the direction of the force so we can deduce that matter with a negative mass would do the opposite and accelerate against the force.

To create the conditions for negative mass, Peter Engels and his team started by cooling rubidium atoms to a Bose-Einstein condensate meaning they reached very near absolute 0. The researchers used lasers to trap the atoms in an area less than 100 microns across and allow high energy particles to escape cooling them further. Then to create negative mass, the physicists applied a second set of lasers to change the way atoms spin back and forth. They then removed the first set of lasers causing the rubidium to rush out and appear to hit some sort of invisible wall; behaving as if it had a negative mass.

What’s great about this is the control we have over the negative mass without any other complications. This gives us a new tool we can use to engineer experiments in astrophysics looking at neutron stars, black holes, dark energy and a lot more.

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