|HPS 0410||Einstein for Everyone|
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John D. Norton
Department of History and Philosophy of Science
University of Pittsburgh
None of the universes discussed so far are ours. To determine which universe in Einstein's great book is our universe we need to know a little more about ours. Two facts have proven decisive in selecting our universe: the distribution of matter in the universe and its motion.
How is matter distributed in our universe on the largest scale? To answer we need to get a sense of just what that largest scale is. Let us step up to it:
Within our solar system, the distance from the sun to the earth is 93 million miles; light requires 8.3 minutes to propagate from the sun to the earth. Pluto is much farther away from the sun, 2700 to 4500 million miles depending on the position in its orbit.
Our solar system is just one of hundreds of billions of stars that form our galaxy, the Milky Way. It is vastly bigger than our solar system. Its main disk is 80,000 to 100,000 light years in diameter. It is worth pausing to imagine what that means. A light year is the distance light travels in one year: 5,880,000,000,000 miles. Just one light year is already enormous. If we decide to send a light signal to some randomly chosen star in the Milky Way, it will require many tens of thousands of years to get there. That is already longer than recorded history. If some being there decides to send a signal in response, will there be anyone here to receive it?
Here's how the Milky Way looks to us from the inside as a broad luminous band made up of many stars spread across the sky.
Here's an artist's conception of how it looks from the outside:
The remaining stars of the universe are grouped into other galaxies. Here's our nearest galaxy, the Andromeda galaxy, M31, which is about 2 million light years away:
Finally, on the largest scale, luminous matter is roughly uniformly distributed through space in galaxies separated by millions of light years. Here's an image from the Hubble telescope:
The images above were drawn from the NASA website, http://www.nasa.gov/, January 14, 2007. NASA provides these images copyright free subject to the restrictions on http://www.simlabs.arc.nasa.gov/copyright_info/copyright.html
This familiar picture of the universe on the largest scale is a quite recent discovery. As late as 1920, it remained unclear whether all the matter of the universe was collected in one place, the Milky Way; or whether the Milky Way was just one galaxy of many scattered through space. This question was the subject of what came to be known as the "Great Debate" that happened in the Baird auditorium of the Smithsonian Museum of Natural History on April 26, 1920 . There two astronomers battled. Harlow Shapley defended the theory of island universe and Heber Curtis argued for the many galaxies of stars view that ultimately prevailed.
These galaxies are the basic units of matter of modern cosmology. They are the molecules of the cosmic gas that is the subject of modern cosmology. The theory proceeds by assuming that they form a continuous fluid, much as we routinely assume that water or air is a continuous fluid, even though we know it is made of molecules; or that sand dunes are continuous, even though they are made of grains of sand. As long as we take a distant enough view of galaxies, molecules or sand grains, they blend into their neighbors and appear to form a continuous distribution of matter.
The galaxies form the luminous part of the matter of the universe. Recent investigations are showing that there is a lot more matter in the cosmos. It is prefixed by "dark...". Dark energy permeates all space and plays a major role in cosmic dynamics. Dark matter provides the additional gravitational pull needed to hold galaxies together.
Einstein, in 1917, presumed that on the largest scale we would see a uniform distribution of stars all roughly at rest. In the course of the 1920s, in the aftermath of the Great Debate, it became clear that the basic unit of cosmic matter would be the galaxy and not the star. That by itself changed little at the fundamental level of theory. What did change our cosmic theorizing a lot was an observation about light from distant galaxies pursued most famously by Edwin Hubble towards the end of the 1920s. That observation became the single most important observational fact of modern cosmology.
Mount Wilson telescope
What Hubble observed was that light from distant galaxies was redder than light from nearby galaxies.
More importantly, there was a linear relationship between the distance to the galaxy and the amount of reddening. Double the distance and you double the reddening; triple the distance and you triple the reddening; and so on.
How was this reddening to be interpreted? Hubble inferred that it revealed a velocity of recession of the galaxies. The redder the light the faster the galaxies were receding.
Hubble arrived at this interpretation through an effect familiar from optics and acoustics, the Doppler effect. Every sound or light wave has a particular frequency and wavelength. In sound, they determine the pitch; in light they determine the color. Here's a light wave and an observer.
If the observer were to hurry towards the source of the light, the observer would now pass wavecrests more frequently than the resting observer.
That would mean that moving observer would find the frequency of the light to have increased (and correspondingly for the wavelength--the distance between crests--to have decreased). That increase in frequency is a shifting of the light towards the blue end of the spectrum.
The converse effect would happen if the observer were to recede from the light source. The light's frequency would diminish and the light would redden.
|For light, this effect depends only on the relative motion of observer and source. So if the observer were at rest and the light source moved, exactly the same thing would happen.||This is no longer true in the case of sound. Then there is a medium that carries the sound waves, the air, and we get slightly different results according to which of the observer or sound emitter is moving with respect to the air. There is nothing analogous to the air for light--there is no luminiferous ether!|
The Doppler effect is familiar from everyday life. When an ambulance approaches us with its siren on, we hear a higher pitch because it is approaching. As it passes and then recedes, we hear the pitch suddenly drop. There has been no change in the sound emitted by the siren. The ambulance driver hears no change in the siren pitch. All these changes happen as a result of the relative motion between you and the ambulance siren by means of the Doppler effect.
Hubble inferred from the red shift of light from distance galaxies to a velocity of recession of the galaxies. The further a galaxies is from us, the faster it recedes. The relationship is linear, a fact to be explored in a moment.
Hubble arrived at the basic fact that all modern cosmologies try to accommodate: the universe is undergoing a massive expansion.
I'll mention here for later reference that the use of Doppler's principle as a way of interpreting the red shift has limited application. When we have developed a full cosmological model using general relativity, we'll see that the presumptions above of a static space with observers and galaxies moving in it will fail. Instead we shall see that the reddening of light from distant galaxies comes from a stretching of space itself while the light propagates to us. Doppler's principle provides a useful, classical approximation of the effect.
Hubble found a linear relationship between the velocity of recession and the distance to the galaxy. What that means can be seen in the table:
|Distance to galaxy
|Velocity of recession
There is an obvious rule built into this table and it is known as "Hubble's Law":
|Velocity of recession
|=||20||x||Distance to galaxy
(millions of light years)
The magic number of 20 in this formula carries a lot of the content. In effect is it telling us that we need to assign 20 kilometers per second of velocity of recession for every million light years of distance between us and the galaxy. This number, which is one of the most important cosmic parameters, is known as Hubble's constant.
Built into Hubble's law is also a notion of the age of the universe. To see it, consider a galaxy a million light years distant from us. If its speed of recession was the same in all history, we can compute how long ago the matter of that galaxies was here. Similarly we can compute how long ago the matter of a galaxy two million light years distant was here. And we can compute how long ago the matter of a galaxy three million light years distant was here.
A remarkable fact follows from the linearity of Hubble's law. All the times computed will come out to be the same. They will simply be one divided by Hubble's constant (with the units appropriately adjusted). The time we have computed is a time at which all the matter of the universe was coincident. That marks the beginning of the universe--we now call it the "big bang." This is very pretty. We proceed from observations about galaxies to Hubble's law with its constant on to the age of the universe.
|Age of Universe||=||1||/||Hubble's constant|
The Hubble age of the universe is roughly 14 billion years.
Copyright John D. Norton. March 2001; January 2007, February 16, 23, October 16, November 10, 2008, March 31, 2010, January 1, March 18, 2013.