People doing intense exercise experience time warp, study finds

Research suggests those who push themselves when working out perceive time to move more slowly

If your sessions at the gym seem to drag on for hours, you are in good company. People who push themselves when working out report a form of time warp, making it feel as if they have been exercising for longer than they have, researchers say.

Adults who took part in 4km cycling trials on exercise bikes perceived time to have slowed down, scientists said, with the cyclists underestimating how long they had been pedalling for by about 10%.

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Unearthed notebooks shed light on Victorian genius who inspired Einstein

Michael Faraday’s illustrated notes that show how radical scientist began his theories at London’s Royal Institution to go online

He was a self-educated genius whose groundbreaking discoveries in the fields of physics and chemistry electrified the world of science and laid the foundations for Albert Einstein’s theory of relativity nearly a century later.

Now, the little-known notebooks of the Victorian scientist Michael Faraday have been unearthed from the archive of the Royal Institution and are to be digitised and made permanently accessible online for the first time.

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Einstein letter warning FDR of threat of Nazi nuclear bomb set to fetch $4m

Two-page letter written by physicist and fellow scientist, for sale at Christie’s, urged US government to invest in research

A two-page letter written by Albert Einstein warning Franklin D Roosevelt – then the president of the US – that Nazi Germany might harness nuclear research to invent an atomic bomb is going up for sale at Christie’s auctioneers in September with an estimate value of $4m.

Einstein’s letter – one of two the theoretical physicist drafted in a cabin on the north shore of New York’s Long Island with a fellow scientist, Leo Szilard – warned that the German government was actively supporting nuclear research and could make “extremely powerful bombs” like the kind that were eventually deployed by the US at the end of the second world war.

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Einstein’s handwritten calculations for theory of relativity to be auctioned for €3m

The rare document, which records attempts to explain an anomaly in the orbit of Mercury, is ‘a fascinating dive into the mind of the greatest scientist of the 20th century’

A crucial series of Albert Einstein’s calculations, scrawled down as the physicist struggled to account for an anomaly in the orbit of Mercury while developing his theory of general relativity, is set to be auctioned for an eye-watering estimate of up to €3m.

Christie’s France and auction house Aguttes, who will auction the manuscript in Paris on 23 November for an estimate of €2m-€3m, said it documents a crucial stage in the development of the theory of general relativity, and is “without doubt the most valuable Einstein manuscript ever offered at auction”.

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Astronomers detect light behind black hole for first time

Telescope picks up unexpected ‘luminous echoes’ – smaller, later and of different colour to bright flares

Astronomers have detected light behind a black hole deep in space for the first time.

Bright flares of X-rays were spotted bursting from a supermassive black hole at the centre of a galaxy 800m light years away, which is relatively normal.

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Albert Einstein letter with E=mc2 equation in his own hand sells for $1.2m

  • Only two similar examples of world-changing equation known
  • 1946 letter to physicist Ludwik Silberstein auctioned

A handwritten letter by Albert Einstein that contains his famous E=mc2 equation has sold at auction for more than $1.2m, about three times more than it was expected to get, a Boston-based auction house said on Friday.

Related: Albert Einstein's 'God letter' reflecting on religion auctioned for $3m

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100 years on: the picture that changed our view of the universe

Arthur Eddington’s photograph of the 1919 solar eclipse proved Einstein right and ushered in a century where gravity was king

A hundred years ago this month, the British astronomer Arthur Eddington arrived at the remote west African island of Príncipe. He was there to witness and record one of the most spectacular events to occur in our heavens: a total solar eclipse that would pass over the little equatorial island on 29 May 1919.

Observing such events is a straightforward business today, but a century ago the world was still recovering from the first world war. Scientific resources were meagre, photographic technology was relatively primitive, and the hot steamy weather would have made it difficult to focus instruments. For good measure, there was always a threat that clouds would blot out the eclipse.

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