Today is March 14, which many celebrate as Pi Day since the month and day mark 3.14, which is approximately pi (π).It is also Albert Einstein’s birthday, so it seems fitting to ask whether π can exist in a universe as Einstein described it. Just for fun, I’m going to outline why the answer is no, and then explain why that answer is wrong.
The value of π (3.14159…) is defined as the ratio of the circumference of a circle to its diameter. But in a physical universe where (as Einstein demonstrated) space is curved, the ratio of circumference to diameter isn’t π. For example, if you drew a circle around the Earth, the ratio of circumference to diameter would actually be a little less than π. This is because the mass of the Earth curves space around it, making the diameter of your circle a bit longer than it should be.
This is actually a way you could define a region of space as being curved. Draw a circle around a region of space, find the ratio of circumference to diameter, and if the value is less than π then that region of space is curved. The smaller the ratio, the more strongly that region of space is curved. If you drew a circle around a black hole, its diameter would be infinite, so the ratio would be zero.
So if we define π as the ratio of circle’s circumference to diameter in physical space, then π would actually have lots of values depending the curvature of space around the circle, and none of them would be 3.14159…
Of course that isn’t how π is defined. The circumference/diameter definition applies for a mathematically ideal circle, where space isn’t curved. It can also be defined in other ways, such as an infinite series π = 1 – 1/3 + 1/5 – 1/7 + … The geometry definition is just a simple (and perhaps the oldest) one. The key point is that π is a mathematical concept, not a physical one.
So even though physical space is actually curved, π still exists and has the value we all know and love. So celebrate the day, because it is a perfect excuse to have a slice of pie.
Image: Paul Smith
You’ve likely seen a representation of the big bang. A sea of dark silence, and then…Bang! A flash of light emanating from a point, then expanding outward. The universe has begun…
Popular science loves to portray the big bang this way. It was even portrayed this way in the new Cosmos series. The only problem is that isn’t how the universe began, and portraying it this way raises all sorts of misconceptions.
In reality, there was no outside darkness into which the big bang appeared. The big bang didn’t begin at a point in space and time, it was space and time. If you want an accurate picture of the big bang, it shouldn’t be from the outside looking in. It should be from within the big bang itself. If we could travel backward in time, we would see a universe where galaxies rush together. The background temperature of the Universe would increase as it contracted. The stars would fade and evaporate into primordial gas. The galaxies would dissipate into hydrogen and helium gas. For a while the universe would be dark.
A more accurate representation of the big bang would be light and heat in all directions. Credit: Planck/IPAC
Eventually the temperature and density of the universe would be high enough that it would visibly glow with its own internal heat. In every direction we would see a glow of light. The light would grow brighter as the temperature rises. It would soon reach a temperature of about 3000K, or about the temperature of the surface of a red dwarf star.
Except the light and heat would be in all directions. Everywhere you looked you would see a bright reddish glow. You would be surrounded by a gas of hydrogen and helium. At this point the universe would be only about 380,000 years old.
The idea of traveling backward in time sounds like science fiction, and in a way it is. But that bright reddish glow can still be seen today. As the universe expanded the glow has faded and cooled, so that now it is a dim background of microwaves. But it is still there. It is an image as close to the big bang as we can directly observe.
The big bang didn’t begin at a point, it began everywhere.
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