LEONHARD EULER (1707- 83)

1755 – Switzerland

‘Analytical calculus – the study of infinite processes and their limits’

Swiss mathematician. His notation is even more far-reaching than that of LEIBNIZ and much of the mathematical notation that is in use to-day may be credited to Euler.

The number of theorems, equations and formulae named after him is enormous.
Euler made important discoveries in the analytic geometry of surfaces and the theory of differential equations.

Euler popularised the use of the symbol ‘Π‘ (Pi); e  , for the base of the natural logarithm; and i , for the imaginary unit.
Euler is credited with contributing the useful notations  f (x) , for the general function of x ; and  Σ , to indicate a general sum of terms.

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ALBERT EINSTEIN (1879-1955)

1905 – Switzerland

  1. ‘the relativity principle: All laws of science are the same in all frames of reference.
  2. constancy of the speed of light: The speed of light in a vacuüm is constant and is independent of the speed of the observer’
photo portrait of Albert Einstein &copy:

EINSTEIN

The laws of physics are identical to different spectators, regardless of their position, as long as they are moving at a constant speed in relation to each other. Above all the speed of light is constant. Classical laws of mechanics seem to be obeyed in our normal lives because the speeds involved are insignificant.

Newton’s recipe for measuring the speed of a body moving through space involved simply timing it as it passed between two fixed points. This is based on the assumptions that time is flowing at the same rate for everyone – that there is such a thing as ‘absolute’ time, and that two observers would always agree on the distance between any two points in space.
The implications of this principle if the observers are moving at different speeds are bizarre and normal indicators of velocity such as distance and time become warped. Absolute space and time do not exist. The faster an object is moving the slower time moves. Objects appear to become shorter in the direction of travel. Mass increases as the speed of an object increases. Ultimately nothing may move faster than or equal to the speed of light because at that point it would have infinite mass, no length and time would stand still.

‘The energy (E) of a body equals its mass (m) times the speed of light (c) squared’

This equation shows that mass and energy are mutually convertible under certain conditions.

The mass-energy equation is a consequence of Einstein’s theory of special relativity and declares that only a small amount of atomic mass could unleash huge amounts of energy.

Two of his early papers described Brownian motion and the ‘photoelectric’ effect (employing PLANCK’s quantum theory and helping to confirm Planck’s ideas in the process).

1915 – Germany

‘Objects do not attract each other by exerting pull, but the presence of matter in space causes space to curve in such a manner that a gravitational field is set up. Gravity is the property of space itself’

From 1907 to 1915 Einstein developed his special theory into a general theory that included equating accelerating forces and gravitational forces. This implies light rays would be bent by gravitational attraction and electromagnetic radiation wavelengths would be increased under gravity. Moreover, mass and the resultant gravity, warps space and time, which would otherwise be ‘flat’, into curved paths that other masses (e.g. the moons of planets) caught within the field of the distortion follow. The predictions from special and general relativity were gradually proven by experimental evidence.

Einstein spent much of the rest of his life trying to devise a unified theory of electromagnetic, gravitational and nuclear fields.

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GERD BINNIG (GERMANY b.1947) & HEINRICH ROHRER

1980 – Switzerland

‘Scanning Electron Microscope’

SEM image of Caffeine crystals. Credit: Annie Cavanagh. Wellcome ImagesSEM image of Diatom frustule.SEM image of Moth Fly

If a needle charged with electricity is placed extremely close to the surface of a metal or semi-conductor a miniscule but measurable electric current, known as a ‘tunneling current’ will leap the gap. This current is extraordinarily sensitive to the width of the gap. The size of the tunneling current therefore reveals the distance between the needle tip and the surface.

Photograph of Gerd Binnig - worked on the scanning-tunneling electron microscope ©

GERD BINNIG

Photograph of Heinrich Rohrer - worked on the scanning-tunneling electron microscope ©

HEINRICH ROHRER

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Related sites

scanning electron microscope (serc.carleton.edu/)
how-sem-works (nanoscience.com/)
high voltage electron microscopy (esi.nagoya-u.ac.jp)(2013)