Mathematical UniverseMathematical Universe

Cambridge 2013Cambridge 2013

One may say the eternalmystery of the world is its COMPREHENSIBILIY

On 25th of November 1915, after a period of pain andstruggle, Einstein finally writes down the final form ofhis gravitational field equations.

Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie,Sitsungsberichte der Preussischen Akad. d. Wissenschaften,1, 1917, 142-152.

= 0

19221924

1927

ΛΛ > 0 > 0

1931

1929

Einstein’s equationsnew that much earlier

Supernova in NGC 4526

Acceleration of the Universe

Schwarzschild, K. (1916). "Über das Gravitationsfeld eines Massenpunktes nach der Einstein'schen Theorie". Sitzungsberichte der Königlich Preussischen Akademie der

Wissenschaften 1: 189–196.

The simplest kind of black hole in theory but one that could never occur in the real universe. A Schwarschild black hole doesn't rotate, has no electric charge, and exists in a spacetime with no other masses. There exist more realistic solutions to Einstein’s equations describing black holes (Kerr – rotates, no charge, Reissner-Nordstrom – charge, no rotation)

NGC 4261

NGC 7052

How did equations know about that?

Gravitational waves are ripples in the curvature of spave-time which propagate as a wave travelling outward from the source.

Einstein, A., "Über Gravitationswellen." Sitzungsberichte, Preussische Akademie der Wissenschaften, 154, (1918).

Two-dimensional representation of gravitational waves generated by two neutron stars orbiting each other.

AURIGA is the Antenna Ultracriogenica Risonante per l'Indagine Gravitazionale Astronomica, or "ultra-cryogenic resonant antenna for gravitational-wave astronomy." The detector consists of an aluminum cylinder 3 meters in length and weighing approximately 2.3 tons.

LIGO: laser interferometer

The Binary Pulsar PSR 1913+16

In 1993, the Nobel Prize in Physics was awarded to Russell Hulse and Joseph Taylor of Princeton University for their 1974 discovery of a pulsar, designated PSR1913+16, in a binary system, in orbit with another star around a common center of mass.

Using the Arecibo 305m antenna, Hulse and Taylor detected pulsed radio emission and thus identified the source as a rapidly rotating, highly magnetized neutron star. The neutron star rotates on its axis 17 times per second; thus the pulse period is 59 milliseconds.

The Vela Pulsar and its surrounding pulsar windnebula.

What equations did know before it has been detected?We have discussed:1. Expansion of the universe2. Acceleration of the universe – cosmological constant – dark energy (?)3. Gravitational collapse – black holes4. Gravitational waves

There are more such wonders:1. Three „classical tests”: bending of light, perihelion motion, gravitational red shift2. CMB – a window into the early history of the universe3. Origin of chemical elements in the universe4. Evolution of massive stars5. .............6. .............

In predicting some of these effects equations from various branches of physics had to becombined

Hertz once said of Maxwell's equations, "One cannot escape the feeling that ... Hertz once said of Maxwell's equations, "One cannot escape the feeling that ... they have an intelligence of their own, that they are wiser than we are, wiser they have an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally even than their discoverers, that we get more out of them than was originally put into them."put into them."

Hinrich Hertz

James Clerk Maxwell

WHAT DOES IT MEAN THATWHAT DOES IT MEAN THAT

THAT THE UNIVERSE IS MATHEMATICAL?THAT THE UNIVERSE IS MATHEMATICAL?

Common sense view:

Mathematics is a purely formal science;mathematical structures “are lacking causal powers”.

The role of matheatics in physics is purely descriptive.There is a physical world, and it just happens thatsome mathematical structures descibe it correctly (upto a certain approximation)

Let us take a look at the current practice of physicists...

The theory of weak interactions tells us that that this happens because the down quark, being a part of a neutron, transforms into the up quark, emitting an intermediating boson W- which, in turn, decays into an electron and antineutrino.

Is it a description?

Listen To The Sunset

Listen to the sunset, Hear its silent sighAs it falls down the horisenWarning, the moon is nigh

Listen to the sunsetHear its silent threatThat darkness will be upon usIt makes everyone upset

Listen to the sunsetThe vanity of its wordsHow beautiful this sunset isWith its colour, and birds

Katniss Everdeen

However, physicists, in their practice, treat this process in a radically different way. Elementary particles are but “places” within the mathematical structure and outside of this structure have no meaning at all. Physical “nature” of elementary particles, and their interactions with other particles, is entirely determined by the mathematical structure.

The beta minus decay is not described by mathematics; it is prescribed by it.

Analogy with hardwere and softwere.

Einstein has given us new worlds

Gotfried Wilhelm Leibniz in the marginof his Dialogue:

‘When God calculatesand thinks things through,the world is made’.