(Roughly) Daily

Posts Tagged ‘space-time

“‘Space-time’ – that hideous hybrid whose very hyphen looks phoney”*…

Space-time curvature [source: ESA]

Space and time seem about as basic as anything could be, even after Einstein’s theory of General Relativity threw (in) a curve. But as Steven Strogatz discusses with Sean Carroll, the reconciliation of Einstein’s work with quantum theory is seeming to suggest that space and time might actually be emergent properties of quantum reality, not fundamental parts of it…

… we’re going to be discussing the mysteries of space and time, and gravity, too. What’s so mysterious about them?

Well, it turns out they get really weird when we look at them at their deepest levels, at a super subatomic scale, where the quantum nature of gravity starts to kick in and become crucial. Of course, none of us have any direct experience with space and time and gravity at this unbelievably small scale. Up here, at the scale of everyday life, space and time seem perfectly smooth and continuous. And gravity is very well described by Isaac Newton’s classic theory, a theory that’s been around for over 300 years now.

But then, about 100 years ago, things started to get strange. Albert Einstein taught us that space and time could warp and bend like a piece of fabric. This warping of the space-time continuum is what we experience as gravity. But Einstein’s theory is mainly concerned with the largest scales of nature, the scale of stars, galaxies and the whole universe. It doesn’t really have much to say about space and time at the very smallest scales.

And that’s where the trouble really starts. Down there, nature is governed by quantum mechanics. This amazingly powerful theory has been shown to account for all the forces of nature, except gravity. When physicists try to apply quantum theory to gravity, they find that space and time become almost unrecognizable. They seem to start fluctuating wildly. It’s almost like space and time fall apart. Their smoothness breaks down completely, and that’s totally incompatible with the picture in Einstein’s theory.

s physicists try to make sense of all of this, some of them are coming to the conclusion that space and time may not be as fundamental as we always imagined. They’re starting to seem more like byproducts of something even deeper, something unfamiliar and quantum mechanical. But what could that something be?….

Find out at: “Where Do Space, Time and Gravity Come From?, ” from @stevenstrogatz and @seanmcarroll in @QuantaMagazine.

* Vladimir Nabokov


As we fumble with the fundamental, we might send far-sighted birthday greetings to Jocelyn Bell Burnell; she was born on this date in 1943. An astrophysicist, she discovered the first pulsar, while working as a post-doc, in 1957. She then discovered the next three detected pulsars.

The discovery eventually earned the Nobel Prize in Physics in 1974; however, she was not one of the prize’s recipients. The paper announcing the discovery of pulsars had five authors. Bell’s thesis supervisor Antony Hewish was listed first, Bell second. Hewish was awarded the Nobel Prize, along with the astronomer Martin Ryle.

A pulsar— or pulsating radio star– a highly magnetized, rotating neutron star that emits a beam of electromagnetic radiation. The precise periods of pulsars make them very useful tools. Observations of a pulsar in a binary neutron star system were used to  confirm (indirectly) the existence of gravitational radiation. The first extrasolar planets were discovered around a pulsar, PSR B1257+12.  And certain types of pulsars rival atomic clocks in their accuracy in keeping time.

Schematic rendering of a pulsar


Jocelyn Bell Burnell


Written by (Roughly) Daily

July 15, 2022 at 1:00 am

Pieces of pi…

In 2010, Japanese engineer Shigeru Kondo set a record, calculating the value of pi to 5 trillion digits… then last October, he smashed his own mark, identifying the first 10 trillion decimal places.  (He used a home-made computer that ran so hot that the temperature in his apartment was over 100 degrees…)

The quest will no doubt continue– pi is an irrational number that exerts an irrational fascination.  Meantime, readers can take a peek at this work-perpetually-in-progress.  Web design firm firm Two-N has created this nifty visualization and search tool, allowing one to find any one of the first 4,000,000 digits of pi:

Bonus: “50 Interesting Facts About Pi


As we ruminate on randomness, we might send carefully-calculated birthday greetings to Hermann Minkowski; he was born on this date in 1864.  Minkowski developed the geometry of numbers and used geometrical methods to solve difficult problems in number theory and mathematical physics; he is probaly best remembered for realizing that his former student Albert Einstein’s special theory of relativity (1905), presented algebraically by Einstein, could also be understood geometrically as a theory of four-dimensional space-time.  Einstein embraced the geometric approach in the development of his theory of general relativity– and the four-dimensional space (the three physical dimensions plus time) involved has since been known as “Minkowski spacetime.”

Minkowski’s best friend was “mathematical hotelier” David Hilbert.


Written by (Roughly) Daily

June 22, 2012 at 1:01 am

%d bloggers like this: