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### Course: Cosmology and astronomy>Unit 1

Lesson 4: Big bang and expansion of the universe

Radius of Observable Universe. Created by Sal Khan.

## Want to join the conversation?

• Am I wrong in thinking that this example is logically impossible? The distance between the photon and the Earth can never increase with time. If it did, it would mean that the distance would continually increase and the photon would never reach Earth. For example, it starts off thirty million light years away, and after 100 million years it is eighty million light years away. If this is the case the Earth and the photon would get further and further away for eternity.
• Well, if you count this in porpotions, it will seems like it's possible! After 10 million years, the photon travelled 20% of the whole distance. After another 40 million years, it travelled another 40%. Now it might looks possible since the porpotion is always increasing. I don't believe it at the first time, either. But it IS mathematically possible.
• We perceive the time as 13.7 billion years but since time slows as one approaches the speed of light, how much actual time has passed from the photon's perspective? It's been said that if a spaceship from Earth went to the nearest star traveling near the speed of light, the journey would only take years for those on the spaceship while those on Earth would see it as millenniums. If I were hitching a ride with the photon, would I perceive the universe as far less than 13.7 billion years old?
• From the perspective of the photon, the age of the Universe is zero. It arrives at the moment it is created. For the photon, not only is the time zero, the distance is zero. The observation about the spaceship is true. Given a destination 10 light years away, at 83.2% of the speed of light the distance is 5.6 light years and the time is 6.7 years, not 12.0 years. At 86.6% of the speed of light, the distance is 5.0 light years and the time is 5.8 years, not 11.6 years. At 90.0% of the speed of light, the distance is 4.4 light years and the time is 4.8 years, not 11.1 years. Two observations: While the speed increases 6,400 miles per second between each example, the rate of decrease of both distance and time is accelerating. The velocity (distance divided by time) measured inside the spaceship is exactly the same as would be measured by an observer at rest outside the spaceship even though the distance and time are different.

To derive these numbers, start with the fraction of v over c where v is equal to the velocity (speed) and c is the speed of light. Formula 1 is v divided by c. If the observer is at rest (v = 0) then the value of this fraction is zero (0). If an observer is traveling at the speed of light (v = c), then the value of this fraction is one (1). Next multiply Formula 1 by itself. The result is the fraction v squared over c squared. Formula 2 is v squared divided by c squared. Note that the value both at rest and at the speed of light remains the same as Formula 1. The next step is to subtract Formula 2 from one (1). Formula 3 is 1 minus the fraction v squared over c squared. Note that Formula 2 and Formula 3 are complimentary (the sum being one) and that the values at rest and at the speed of light are opposite. The last step is to take the square root of Formula 3. Formula 4 is the square root of the entire expression 1 minus the fraction v squared over c squared.

To calculate the distance and time measured inside the spaceship, simply multiply their value (as would be observed at rest) by Formula 4. Note that as the velocity approaches the speed of light, both distance and time approach zero (0).

To generate the numbers in the second example (86.6%), start with the velocity 161,000 miles per second (light being 186,000 miles per second). Formula 1 is 86.6%. Formula 2 is 3/4. Formula 3 is 1/4. Formula 4 is 1/2. At a distance of 10 light years, the spaceship will measure a distance of 5 light years, half of the original 10 light years, and the elapsed time will be measured at 5.8 years, half of the original 11.6 years.
• If the universe is expanding, are the atoms in our bodies increasing in distance between each other?
• No because they are held together by forces that counteract the expansion of the universe. Galaxies themselves as well as solar systems are held together by gravity that counteracts the expansion. The expansion of the universe is only noticed at intergalactic distances.
• If the space itself is expanding with a speed faster than light then how can a photon traveling with speed of light from edge of universe ever reach us?
• Good question! The answer is that it's quite likely that it can't, and that there are parts of the universe which we will never know about, because light from those parts will never reach us. We make the distinction between "the universe", which is everything that exists, and "the visible universe", which is everything we can see.
• What is the estimated size of the universe? What is inflation?
• The estimated size of the entire Universe (not just Observable) is 10^60 light years. Inflation was an exponential expansion of space at the very early stages of the Big Bang. To understand how fast the expansion of space was, there are some units that you should know of. A Planck length is a unit of distance that equals roughly 1.616 times 10^-35 meters. This unit is incredibly small. To scale it, if an atom were the size of the observable universe, a Planck length would be the size of a tree. Next is Planck time. Just like light travels one light year in one year, light travels one Planck length every Planck time. Planck time is roughly 10^-43 seconds.
If space were expanding at the speed of light in the early stages of the Big Bang, then space would be expanding at 1 Planck length per Planck time. However, this was not the case as space was expanding at 1 to maybe even 1000's of light years per Planck time in the early stages. Because of this rapid expansion, the entire Universe will most likely always be bigger than the Observable universe. Hope that answers your question.
• If light travels at a finite speed, how do we know that the universe is not now contracting?
• We don't.
The object farthest away from us is a galaxy (UDFy-39546284) which is 13.4 billion light years away. If it started contracting towards us 13.3 billion years ago, we would start to see that in 100 million years. Then I'll post an update ;-).
• If the space between galaxies expands over time, how come people say that in the very far future our galaxy will collide with Andromeda?
• Milky Way and Andromeda are being pulled apart by expansion but they are close enough together such that their gravitational attraction is able to overcome the repulsion from expansion.
• How fast is the Universe expanding?
• You can not truly measure the expansion of the universe itself. Speed is a representation of space traveled over a certain time period. Well when the universe is expanding, it is "creating" space, not expanding through it so you can't really give it a speed. However you can get a general idea by measuring how quickly celestial objects are separating from each other, as Andrew did.
• Isn't this just a theory?
• I never understood that expression 'Just a theory'.

A scientific law is a description of an observed phenomenon. Kepler's Laws of Planetary Motion are a good example. Those laws describe the motions of planets. But they do not explain why they are that way. If all scientists ever did was to formulate scientific laws, then the universe would be very well-described, but still unexplained and very mysterious.

A theory is a scientific explanation of an observed phenomenon. Unlike laws, theories actually explain why things are the way they are. Theories are what science is for. If, then, a theory is a scientific explanation of a natural phenomena, ask yourself this: "What part of that definition excludes a theory from being a fact?" The answer is nothing! There is no reason a theory cannot be an actual fact as well.