pretendy

Science, maths and computers.

Some perspective Light travels at a speed of 299,792,458 metres per second exactly. No matter how fast you, or the light source is traveling, go try measuring it and you’ll find that this is exactly the case. At this speed, it takes light: 18 milliseconds to travel between London and New York 0.13 seconds to circumnavigate the equator of the Earth 1.4 seconds to travel to us from the Moon 8.4 minutes to travel from the Sun 4.15 hours to travel from the Sun to Neptune, the most remote planet in the Solar System 17 hours to travel to the current location of Voyager 1, the farthest man made object from Earth ~0.8 years to travel from us to the Oort Cloud, a hypothesised spherical cloud of icy comets centered around the Sun, which marks the boundary of the solar system 4.2 years to travel to us from Proxima Centauri, the nearest star to Sun. 1,100 years to travel to us from the centre of our own galaxy, the Milky Way 100,000 years to travel across the whole disc of the galaxy itself 2.5 million years to travel to us from the Andromeda galaxy, our nearest neighbour 110 million years to travel across the Virgo Supercluster, our small, local little corner of the universe After this it stops making sense to say “a distance x”, as the expansion of the universe warps our perception of distance on these immense timescales. Therefore, when you hear radio static, 1% of that is said not to originate from a place, but rather a time, roughly 13.5 billion years ago - the cosmic microwave background from the time of recombination at the dawn of the universe. TL;DR: The universe is big. (Photo: pretendy)

Some perspective

Light travels at a speed of 299,792,458 metres per second exactly. No matter how fast you, or the light source is traveling, go try measuring it and you’ll find that this is exactly the case.

At this speed, it takes light:

  • 18 milliseconds to travel between London and New York
  • 0.13 seconds to circumnavigate the equator of the Earth
  • 1.4 seconds to travel to us from the Moon
  • 8.4 minutes to travel from the Sun
  • 4.15 hours to travel from the Sun to Neptune, the most remote planet in the Solar System
  • 17 hours to travel to the current location of Voyager 1, the farthest man made object from Earth
  • ~0.8 years to travel from us to the Oort Cloud, a hypothesised spherical cloud of icy comets centered around the Sun, which marks the boundary of the solar system
  • 4.2 years to travel to us from Proxima Centauri, the nearest star to Sun.
  • 1,100 years to travel to us from the centre of our own galaxy, the Milky Way
  • 100,000 years to travel across the whole disc of the galaxy itself
  • 2.5 million years to travel to us from the Andromeda galaxy, our nearest neighbour
  • 110 million years to travel across the Virgo Supercluster, our small, local little corner of the universe

After this it stops making sense to say “a distance x”, as the expansion of the universe warps our perception of distance on these immense timescales. Therefore, when you hear radio static, 1% of that is said not to originate from a place, but rather a time, roughly 13.5 billion years ago - the cosmic microwave background from the time of recombination at the dawn of the universe.

TL;DR: The universe is big.

(Photo: pretendy)

Happy Birthday Hubble

Today the Hubble Space Telescope celebrates its cake day, having spent 22 years collecting some of the most iconic images in science. Though possibly the most successful unmanned space program to date, its manufacture was beset by a decade of technical setbacks.

When it was finally launched in 1990, within a few weeks it became apparent that there was a major problem with its optical system. Images it returned were ten times more blurry than what they were supposed to be. The problem was identified to be a misshapen primary mirror.

Though it was one of the finest mirrors ever cut, boasting smoothness almost to the atomic scale, it was found to be ever so slightly too flat - by about 2µm at the edges. This lead to the catastrophic aberrations present in the images it brought back.

It was too costly at the time to bring it back to Earth for a refit and too impractical to conduct a refit in space. Instead, engineers came up with an ingenious solution - to fit it with extra optics which would act as a monocle, correcting the aberration. This ‘hack’ was done by astronauts of STS-61 Endeavour and worked like a charm.

Data collected by Hubble since then has had a tremendous impact on astronomy, astrophysics and cosmology.

However, I think that its served an even higher purpose. Before Hubble, we had but a glimpse of the beauty of outer space. However, in the 22 years of its operation it has given us a whole encyclopaedia of the richness and diversity of galaxies, nebulae, stars, supernovae etc.

Images like the Pillars of Creation have become culturally iconic and significant. When I was little, I was enthralled by these images, and I’m sure Hubble is partially responsible for some of my early interest in science. In fact, I’m absolutely sure this can also be said of many other students of my generation who grew up with Hubble.

On behalf of these people I say: Hubble, we salute you!

On this day, 18th April 1955, one of the greatest scientists of history was on his deathbed. Suffering from internal bleeding caused by an aneurysm, he refused surgery saying: “I want to go when I want. It is tasteless to prolong life artificially. I have done my share, it is time to go. I will do it elegantly.” His name was Elbert Ainstein (I think I got that right…wait…) His face has become synonymous with science, his name with intelligence and he’s the only person yet to have the prestigious title of Time’s Person of the Century. How can one man have had such an impact on the world? Despite the ubiquity of his name, it is impossible to stress exactly how important this guy was. He didn’t just revolutionise some area of physics, he created new sciences altogether and his legacy can be found everywhere. Here are just five of many reasons why he’s awesome Annus Mirabilis: In the year 1905 he released four papers that were to change the face of physics. He explained the photoelectric effect, providing some of the grounds from which quantum theory was built. He explained Brownian motion using a statistical treatment of atomic theory. He single-mindedly developed special relativity which is one of the most notoriously mind-bending theories students have to encounter. Finally, before the year was out, he showed how matter was equivalent to energy, with his famous equation E=mc^2. General Relativity. Expanding on his work on special relativity, he generalised it to, well, general relativity. He described how matter and energy could warp the shape of space itself. One of his predictions was that large, massive objects would bend the path of light traveling around them. While he argued this from completely independent theoretical grounds (his papers were notorious for not referencing many if any other papers), his predictions have been confirmed time and time again by different observations. Cosmology Armed with general relativity, he applied his theories to the cosmos and constructed a model that described the structure and shape of the universe. In order for his model to produce a static universe, like he thought it had to, he was forced to introduce a term called the cosmological constant. Later in his life he said that the introduction of this was his biggest mistake ever. However, modern cosmologists have been forced to re-include the cosmological constant to account for the effects of dark energy!  Phonons. He considered the vibrations of individual atoms in a solid, and using quantum theory he postulated that each atom created quasi-particles called phonons which propagated lattice vibrations. Though his model wasn’t 100% accurate, a slightly refined version (thanks to Debye) is currently one of the best approximations we have for acoustic waves in solids. Bose-Einstein. Expanding on work by Bose, he developed the statistics for particles we now call bosons - particles of integer spin. He realised that particles of light, photons, could be considered to be like a gas of indistinguishable particles. Not only do these statistics really well explain the energy distributions of such particles, but they predict a new state of matter: Bose-Einstein condensates. These have been well observed and studied at low temperatures. It is impossible to overstate how incredible this man’s mind really was. I would go so far as to say that there has never been a single person who has changed the face of science more. Albert Einstein died on the morning of the 18th of April 1955, at his home in Princeton.

On this day, 18th April 1955, one of the greatest scientists of history was on his deathbed. Suffering from internal bleeding caused by an aneurysm, he refused surgery saying: “I want to go when I want. It is tasteless to prolong life artificially. I have done my share, it is time to go. I will do it elegantly.”

His name was Elbert Ainstein (I think I got that right…wait…)

His face has become synonymous with science, his name with intelligence and he’s the only person yet to have the prestigious title of Time’s Person of the Century.

How can one man have had such an impact on the world? Despite the ubiquity of his name, it is impossible to stress exactly how important this guy was. He didn’t just revolutionise some area of physics, he created new sciences altogether and his legacy can be found everywhere.

Here are just five of many reasons why he’s awesome

  1. Annus Mirabilis: In the year 1905 he released four papers that were to change the face of physics. He explained the photoelectric effect, providing some of the grounds from which quantum theory was built. He explained Brownian motion using a statistical treatment of atomic theory. He single-mindedly developed special relativity which is one of the most notoriously mind-bending theories students have to encounter. Finally, before the year was out, he showed how matter was equivalent to energy, with his famous equation E=mc^2.
  2. General Relativity. Expanding on his work on special relativity, he generalised it to, well, general relativity. He described how matter and energy could warp the shape of space itself. One of his predictions was that large, massive objects would bend the path of light traveling around them. While he argued this from completely independent theoretical grounds (his papers were notorious for not referencing many if any other papers), his predictions have been confirmed time and time again by different observations.
  3. Cosmology Armed with general relativity, he applied his theories to the cosmos and constructed a model that described the structure and shape of the universe. In order for his model to produce a static universe, like he thought it had to, he was forced to introduce a term called the cosmological constant. Later in his life he said that the introduction of this was his biggest mistake ever. However, modern cosmologists have been forced to re-include the cosmological constant to account for the effects of dark energy! 
  4. Phonons. He considered the vibrations of individual atoms in a solid, and using quantum theory he postulated that each atom created quasi-particles called phonons which propagated lattice vibrations. Though his model wasn’t 100% accurate, a slightly refined version (thanks to Debye) is currently one of the best approximations we have for acoustic waves in solids.
  5. Bose-Einstein. Expanding on work by Bose, he developed the statistics for particles we now call bosons - particles of integer spin. He realised that particles of light, photons, could be considered to be like a gas of indistinguishable particles. Not only do these statistics really well explain the energy distributions of such particles, but they predict a new state of matter: Bose-Einstein condensates. These have been well observed and studied at low temperatures.

It is impossible to overstate how incredible this man’s mind really was. I would go so far as to say that there has never been a single person who has changed the face of science more.

Albert Einstein died on the morning of the 18th of April 1955, at his home in Princeton.

Why is the night sky dark? This is a question that at first sounds a bit stupid, but the observation that the night sky is dark is in fact a deeply profound one that provides much of the basis for modern cosmology. The question which has now come to be known as Olbers’ paradox goes something like this: “In an infinite and static universe with an infinite amount of stars, why is the night sky dark?” Why? The argument was that if you looked at any point in the sky and drew your line of sight, it would eventually reach a star. In other words, along every possible direction, there should be a star, and hence light should be coming from every point in the sky. No, really, why? This is a bit of a wishy-washy argument when posed in terms of words, so let’s try some maths: Imagine that throughout the universe, the density of stars (number per cubic lightyear, say), let’s call it n, remains roughly constant. Now, imagine that we construct a series of spherical shells surrounding the Earth, and that each has a thickness dr. See the main picture to see what I mean. What we want to do is count up the number of stars, N, in a shell. For a shell a distance r away, we multiply its volume by the star density: Now let’s work out how bright that shell is. We can assume that each star has a total luminosity of L, but we have to take into account the fact that the further away a star is the fainter it appears. In fact, the apparent brightness, F, of any star varies like: The brightness of a thin shell - which we’ll call dJ- is just the number of stars times the brightness of each! Now we integrate over all space, i.e., add up the contribution from every consecutive shell all the way to infinity. In other words, the total brightness of the sky, J, is infinite! Okay but WHY? The essential reason for this is the fact we said that the brightness of a star decreased by an inverse square law, but the number of stars increased by a regular square law. The two r^2 terms cancelled each other out and we found that each shell had the same brightness! Therefore when you add up an infinite number of same-brightness shells the answer you get is ∞. Oh. So? Well, this is obviously not true when we look up at the sky, so there must be a problem somwhere. Like most things in science, the problem lies within our initial assumptions, namely: ‘the universe is static and infinite’. We have shown that this just can’t be true! The night sky being dark forces the universe to have a finite size and age! Edgar Allen Poe was eerily accurate when he postulated that no light reaches Earth from beyond a certain distance - corresponding to the age of the oldest stars. Cosmology caught on to this idea and introduced the concepts of the big bang, universal expansion, and the cosmic horizon in order to account for this seemingly trivial darkness problem. Think of this next time you look at a starry sky. We see faint objects as they were hundreds, thousands, millions and billions of years ago (the time it has taken light from them to reach our eyes). At the farthest depths of what our most powerful telescopes can make out are objects from the beginning of the universe itself, and beyond that… nothing. We can see the edge. It’s black. Cool.

Why is the night sky dark?

This is a question that at first sounds a bit stupid, but the observation that the night sky is dark is in fact a deeply profound one that provides much of the basis for modern cosmology.

The question which has now come to be known as Olbers’ paradox goes something like this: “In an infinite and static universe with an infinite amount of stars, why is the night sky dark?”

Why?

The argument was that if you looked at any point in the sky and drew your line of sight, it would eventually reach a star. In other words, along every possible direction, there should be a star, and hence light should be coming from every point in the sky.

No, really, why?

This is a bit of a wishy-washy argument when posed in terms of words, so let’s try some maths:

Imagine that throughout the universe, the density of stars (number per cubic lightyear, say), let’s call it n, remains roughly constant. Now, imagine that we construct a series of spherical shells surrounding the Earth, and that each has a thickness dr. See the main picture to see what I mean.

What we want to do is count up the number of stars, N, in a shell. For a shell a distance r away, we multiply its volume by the star density:

Now let’s work out how bright that shell is. We can assume that each star has a total luminosity of L, but we have to take into account the fact that the further away a star is the fainter it appears. In fact, the apparent brightness, F, of any star varies like:

The brightness of a thin shell - which we’ll call dJ- is just the number of stars times the brightness of each!

Now we integrate over all space, i.e., add up the contribution from every consecutive shell all the way to infinity.

In other words, the total brightness of the sky, J, is infinite!

Okay but WHY?

The essential reason for this is the fact we said that the brightness of a star decreased by an inverse square law, but the number of stars increased by a regular square law. The two r^2 terms cancelled each other out and we found that each shell had the same brightness! Therefore when you add up an infinite number of same-brightness shells the answer you get is ∞.

Oh. So?

Well, this is obviously not true when we look up at the sky, so there must be a problem somwhere. Like most things in science, the problem lies within our initial assumptions, namely: ‘the universe is static and infinite’. We have shown that this just can’t be true! The night sky being dark forces the universe to have a finite size and age!

Edgar Allen Poe was eerily accurate when he postulated that no light reaches Earth from beyond a certain distance - corresponding to the age of the oldest stars. Cosmology caught on to this idea and introduced the concepts of the big bang, universal expansion, and the cosmic horizon in order to account for this seemingly trivial darkness problem.

Think of this next time you look at a starry sky. We see faint objects as they were hundreds, thousands, millions and billions of years ago (the time it has taken light from them to reach our eyes). At the farthest depths of what our most powerful telescopes can make out are objects from the beginning of the universe itself, and beyond that… nothing.

We can see the edge. It’s black.

Cool.

I'm a physics student at the University of Warwick, UK.

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