Reminded me of Brownian motion

The Japanese meteorological satellite, Himawara, captures the image of a Earth every 10min. This image is from last week.

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From Stephen Hawking’s - Singularities and the Geometry of Spacetime, 2014

the Minkowski space

The cylinder represents R1 ×S3 where two spatial dimensions have been suppressed. The shaded region is the part conformal to Minkowski space.

This representation is a bit difficult to grasp as it is hard to visualise objects in four dimensions or to draw diagrams of them. However, it can be simplified using the fact that Minkowski space, as all the other solutions to be described, has spherical symmetry.

the Schwarzschild solution

The Penrose diagram of the t−r plane of Minkowski space. The dotted lines represent curves of constant r.

The Schwarzschild solution represents the spherically symmetric gravitational field outside some massive body. All the experiments which have been carried out to test differences between the general theory of relativity and Newtonian theory are based on predictions by this solution.

Eur. Phys. J. H DOI: 10.1140/epjh/e2014-50013-6

© EDP Sciences, Springer Verlag 2014

Radial Triangles - 171004

Diver

More of my work

Spaceman

Black holes aren’t black

They’re very dark, sure, but they aren’t black. They glow, slightly, giving off light across the whole spectrum, including visible light.

This radiation is called “Hawking radiation”, after the former Lucasian Professor of Mathematics at Cambridge University Stephen Hawking, who first proposed its existence. Because they are constantly giving this off, and therefore losing mass, black holes will eventually evaporate altogether if they don’t have another source of mass to sustain them; for example interstellar gas or light.

Smaller black holes are expected to emit radiation faster compared to their mass than larger ones, so if – as some theories predict – the Large Hadron Collider creates minuscule holes through particle collisions, they will evaporate almost immediately. Scientists would then be able to observe their decay through the radiation.

Faraday’s Law of Electromagnetic Induction

The ball (also a magnet) is falling quite a bit slower than expected (despite the slow motion). This can be attributed to Faraday’s Law:

When a conductor is exposed to a changing magnetic field there is a current created within the conductor. Or more technically a magnetic flux changing over time produces an electromotive force across a conductor.

That’s not the whole explanation though…

Lenz’s Law

When the magnet is falling the current in the cylinder is producing a magnetic field as well. Lenz’s Law states:

 The induced current will produce a new magnetic field that will oppose the change in magnetic flux.

The produced field applies a force to the magnet resisting its fall. If the tube is long enough the magnet will reach a constant velocity because the magnetic force and weight will cancel each other out (no net force).

This works like air resistance on a falling object. Eventually the resistance completely counters the gravitational acceleration of the object.

Faraday’s and Lenz’s Laws basically tell us that the faster the magnet moves the more the conductor (tube) will resist the magnet’s fall.

Watch this Veritasium video on the same concept and see this phenomenon in real time.