# Scientist, Space, Observation The Age of the Universe

When people think about universe, they usually have two questions: how big is it and how old it turns out that the second of these questions can be answered, rather precisely if you want to know why our universe is about 14 billion years old. This is the rise place and time to be a lower bound on the age of the universe can be obtained from simple experiments on earth. Already, this bound is confirmed with astronomical observations. To do this, a simple estimate for the age is derived from the current expansion rate of our universe. Finally, the age is computed rather accurately with einstein’s general relativity. The second part of the video will walk you through the key concepts that lead to general relativity and an expanding universe, but let’s start on earth here on earth. You can find more than 90 different chemical elements. On the other hand, during the so called big bang nuclear synthesis in the early stage of our universe, only hydrogen and helium had been created abundantly all. The chemical elements you find on earth today were produced by nuclear reactions inside a star and only were released after its supernova explosion. The lifetime of a star is at least a few billion years. Moreover, the oldest rocks that have been found on earth are 4 billion years old. Therefore, our universe should be older than the oldest rocks on earth in the lifetime of our reactor star together, a reasonable, lower bound for the age of our universe is about 10 billion years.

Next, let’s have a look at the expansion of our universe. How does an expanding universe look like when galaxies are observed from earth? Almost all of them seem to move away from us, as it is shown in the animation. Moreover, galaxies that are further away from us seem to move away faster than galaxies nearby. The faster a galaxy moves away from us, the more its light is shifted towards red light. One shortly says that the light of the galaxies is redshifted. In 1929, the physicist edwin hubble, first measured the redshift or the speed of galaxies and plotted it against the distance of the galaxies here, revealed the simple relationship between the distance of the galaxies and their speed away from us. The constant of proportionality is called hubble’s constant and it has a value of about 70 kilometers per second per megaparsec. Hubble’S constant is the scale for the expansion rate of the universe. With this scale, one can estimate how long the expansion should have lasted for what is the meaning of 70 kilometers per second per megaparsec. One megaparsec is a convenient unit to measure astronomical distances. It is the same as 3.3 million light years. One light year is the distance that light can travel within one year, which is about 9.5 trillion kilometers. Finally, one megaparsec corresponds to 31 million trillion kilometers a galaxy at such a distance moves away from the earth with the speed of 70 kilometers per second, when the megaparsec in hubble’s, constant, is expressed in kilometers, one is left with the expansion rate of 2.

3 times 10 To the minus 18 one over second, the reciprocal value has the unit of time and it corresponds to 14 billion years. This is the cosmological time scale that is directly related to the expansion rate of the universe, and it turns out that it is a rather accurate estimate for the age of the universe. It should be obvious that neither of the previous arguments really nailed down the age of the universe. It should be older than 10 billion years, but by no means does it have to be 14 billion years old, twice as old or even older. The argument with the expansion rate just gives an order of magnitude estimate due to the expansion of the universe. The separation between galaxies becomes larger and larger. When we go back in time, the galaxies were much closer to each other, when general relativity is used to trace back the history of the universe, the distances between all galaxies vanished 14 billion years ago. Shortly before this moment, the universe was so hot that all particles, as we know them today, disintegrate and turn into a hot and dense plasma, and even earlier we lose confidence in what was going on. Since we don’t know how to describe the physical processes at such high energies, by now, we have reached a tiny fraction of the first second of the existence of our universe. The expansion rate changes during the evolution of the universe. It strongly depends on the matter.

Energy content that fills the universe and its dependence on time can be inferred from einstein’s field equations of gravity. These equations are the main conclusion of the framework of general relativity. They can successfully describe black holes gravitational waves and, in our case, an expanding universe. Although this formula looks rather simple in general, this line is a shortcut for 10 incredibly complicated equations. However, in the case of an expanding universe, they can be simplified and solved quite easily. The left hand, side of the equation, describes the curvature of the four dimensional space time. It simplifies, in our case to the well known friedman equation, where a is the time dependent scale factor of the universe, all distances scale with this function, if it has the value 2, all distances double, if it has the value 3, all distances are 3 times larger And so on, on the right hand, side there is the meta energy density of the universe on large scales. The galaxies are distributed rather evenly. Therefore, the meta energy density can be assumed to be the same everywhere and only depending on time. This equation can be used to calculate the age of the universe. The beginning of time corresponds to the moment when the scale factor of the universe is zero. The current time is obtained when the universe has reached the current expansion rate. However, if our universe was only filled with regular matter whose density shrinks proportional to the growth of the volume of space, the current edge of the universe would be less than 10 billion years.

Luckily, supernovae observations indicate that 70 of the matter, energy density of the universe, is dark energy that is not diluted by the expansion of space. This modifies the right hand, side of freeman’s equation, and it gives an age that is only little less than 14 billion years. It’S not necessary that you understand these computations, because can you repair your car by yourself? Can you cure a broken bone? We have specialists for every concern in our lives, so let scientists do these computations and just remember why they can do it because they have a well tested theory of gravity and they make assumptions about an expanding universe and its matter. Energy composition, based on observations and experiments. This concludes the first part of this video about the age of the universe. Let me know what you think in the comments and if you are curious for a few more details on the way to this result, then stay seated and keep on watching the hardest. Part of friedman’s equation is the left hand side where the geometry of the space time is computed. It actually takes a full page of symbolic calculations to obtain this expression. The starting point is the metric of the space time for an expanding universe from there. The christopher symbols are computed. They can be used for the calculation of the curvature that is here expressed by components of the richie tensor. These components are finally combined to the einstein tensor, which represents the left hand, side of einstein’s field equations, combined with the energy momentum tensor of a homogeneous and isotropic matter, distribution, one of einstein’s field equations reduces to the friedman equation that was used for the determination of The age of our universe, let’s have a closer look at the metric, that is the dynamic field, and it describes the geometry of the space time.

It is actually not difficult to understand. All you really need is pythagorean’s theorem applied to distance measurements in two dimensions. The square of the distance between two points is related to the difference of the x coordinates delta x and the difference of the y coordinates delta y because of the right triangle. This simple theorem can be rewritten as a matrix product. The coordinate differences are combined to row and column vectors and a 2 by 2 matrix is called the metric of this geometry. It doesn’t look so simple in general in polar coordinates, the distance is not simply related to the sum of the squares of the coordinate differences. Only when small distances are considered, a similar relation can be obtained in polar coordinates. The metric depends on the position where the distance is going to be measured. Observers at different places use their own coordinate systems that can be shifted with respect to our coordinate system. They will measure different coordinates for the points a and b. Nevertheless, all observers will agree on the distance between the two points, a and b independent of their position and choices of coordinates. Similarly, observers that look into another direction use coordinate systems that are rotated with respect to our coordinate system. They will even measure other coordinate differences in x and y direction. Nevertheless, again, all observers are going to measure the same distance between the two points. Therefore, the distance between two points is an observer, independent, intrinsic geometric property.

This independence of position and orientation of the observer is the guiding principle of relativity and it will be generalized to larger classes of observers until finally, every observer is equally acceptable as a measuring observer, no matter how fast she moves or how close he is to the Event horizon of a black hole. If you want to include observers that move with velocities close to the speed of light, this metric has to be extended to the space time. Metric let’s have a look at one experiment. First, consider a very long train car where it takes light six seconds to go from one end to the other. When einstein pushes the button in the middle of the car, the light has to travel for three seconds before it reaches the end of the car and the doors open on both ends. Simultaneously, einstein who rests inside the car will make the same observation, no matter how fast the train is moving. He pushes the button and three seconds later, both doors will open. He labels the event for the opening of the right door with coordinates three seconds and 3 light seconds and for the left door, 3 seconds and 3 light seconds. The first coordinate measures the time when the event takes place and the second coordinate measures. The position where the event takes place, amazingly, when the train is moving with 60 percent of the speed of light. The scientist lawrence on the platform of the train station makes a completely different observation, although the train is moving the light flashes travel with the same speed of light in either direction.

The front part of the car is moving away from the light signal, and the back part of the car is moving towards. The light signal. Lawrence observes that the back door opens after 1.5 seconds and the front door opens only after 6 seconds. The different set of coordinates that he uses can be understood as a so called lorenz coordinate transformation. The time that you measure with a clock is a coordinate. Much like a space coordinate that you measure with a ruler in the same way x and y coordinates mix during rotations time and space coordinates mix during loren’s transformations. The perception of time and perception of simultaneity depends on the state of motion of an observer. Neither of them are absolute and invariant concepts. We have learned that the distance between two points is invariant under rotations and translations. Now there is a similar metric distance that does not change under lorenz transformations. A matrix with this property has to include space and time for one spatial dimension. This metric is given by minus dt, squared plus dx squared, and it is easily generalized to three spatial dimensions. If you worry about the different units between spatial and time coordinates, you can multiply the time with the speed of light, which is one for our choice of coordinates to get the dimension of length. The final generalization sets the stage for an expanding universe. The spatial components of the metric are multiplied with a scale factor that can arbitrarily depend on time.

This function of time describes the expansion of the universe. Once it is known we can find out when the universe was born at a equal to zero, and we can understand what the faith of the universe will be from the metric. One can calculate the curvature of space time according to a very generic procedure. The first derivatives of the metric are combined in two christopher symbols. They contain the information about the forces that observers feel in their locations, for instance, for a rotating observer. They contain coriolis and centrifugal forces in a curved spacetime. They describe gravitational and tidal forces. In the case of the expanding space time, the non vanishing crostover symbols contain the first derivatives of the scale factor function. The curvature of the space time allows to distinguish between gravitational and non gravitational effects. One important curvature quantity is the richie tensor, which is given by a combination of derivatives and products of christopher symbols. For the surface of a two dimensional sphere, the richie tensor would only depend on the radius of the sphere for the expanding universe. The non vanishing components of the richie tensor contain first and second derivatives of the scale vector a the einstein tensor. On the left hand, side of einstein’s equations is a combination of the richie tensor and its trace. It indicates a non vanishing curvature of the space time, which must be balanced with a corresponding energy matter, content that fills the universe. The time time component of einstein’s equations exactly corresponds to the friedman equation, which was used to calculate the age of the universe.

The remaining parts of the equations provide information on how the meta density dilutes during the expansion, the calculations presented, will be rather tedious. If you want to perform them by yourself, it is advisable to use algebra software, as shown here. The definitions for the christopher symbols and the curvature quantities are quickly implemented and the corresponding left hand. Side of the field. Equations is calculated almost instantly. As a final remark, i want to mention that space and time are dynamic quantities and their perception depends on the state of the observer and the meta distribution inside the universe. This implies that space and time most likely do not exist independently of our universe. If einstein’s equations are by and large a faithful description of the dynamics of our universe, then it doesn’t make sense to ask questions like what was before the big bang and what lies outside of our universe. It is indeed very unlikely that the big bang was ignited in a pre existing space time. It is much more intuitive to assume that space and time were created simultaneously, with only matter at the instance of the big bang. The nature of gravity can be identified with the curvature of the space time. What is the nature of space and time? Are these fundamental physical quantities or are they much like temperature, just an average property of even more fundamental degrees of freedom? If so, einstein’s equations would also only be an average of some more fundamental physical theory that describes the dynamics of these more fundamental objects.

The search for such a theory has been the driving force for a lot of activity in theoretical physics during the last century.

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