Look-Back Times
The velocity of light plays a central role is astronomy and in physics because it placesan upper limit on speeds in our Universe.A Cosmic Speed Limit
According to the Einstein's Theory of Relativity, nothing in our Universe can exceed the velocity of light; thus, it is a kind of cosmic speed limit against which all other velocities may be measured. More generally, light is part of the electromagnetic spectrum, which includes infrared radiation, radio waves, gamma rays, X-rays, ultraviolet radiation, and so on.All of these are a form of light; they just have energies that differ from the visible light that our eyes can see. Thus, these forms of electromagnetic radiation all travel at the speed of light too. Furthermore, contrary to normal intuition, the theory of relativity tells us that light always travels at the same speed relative to some observer, no matter what the relative motion of the observer. Although this may seem strange, it has been confirmed in many experiments: it is the way the Universe works.
Looking Back in Time
Because light travels at a large but finite speed, it takes time for light to cover large distances. Thus, when we see the light of very distant objects in the Universe, we are actually seeing light emitted from them a long time ago: we see them literally as they were in the distant past.Because of this property of light coming from distant objects, astronomers oftendefine a quantity called the look-back time. The look-back time is just thetime since the light that we see from an object was actuallyemitted. The speed of light is so high that for nearby objects the look-back time isessentially zero, but for Supernova 1987A it was about 170,000 years andfor very distant objects the look-back time could be 10 billionyears or more.
Time Machines
Such look-back times become critical when we look at the largest distancesbecause they literally allow us to peer into the early Universe. The most distantobjects observed may now allow us to see what the Universe looked like when it was onlyabout 1/10 of its present age. Large telescopesare not just devices for gathering faint light. They are time machines!The above left figure shows how the look-back time varies with redshift for threedifferent assumptions concerning a parameter Ω0 that measures theaverage density of the Universe and that we shall discuss in Chapter 18 (the look-back timeis expressed in the plot as a fraction of the Hubble time for each case). The following tablegives recessional velocities, distances, and look-back times as a function of redshifts.<!- TABLE STARTS AFTER THIS LINE ->
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| *Assuming flat geometry **Percentage of age for present Universe when light emitted (flat geometry) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
The look-back time in the above tableis expressed both in years and as a percentage of the present age of theUniverse when the light was emitted. For example, at a redshift of z = 2 we are seeing light that was emitted 8.1 billionyears ago when the Universe was only 19% of its present age. Here is a Javacalculator that allows you to calculate the recessional velocity, look-back times,and distances from the redshift for arbitrary values ofthe Hubble constant and the deceleration parameter. (The preceding table can be reproducedwith this calculator by setting the Hubble constant to 65/km/s/Mpc and the decelerationparameter to 0.5, corresponding to a flat Universe with no cosmological constant.)
The age of 10 billion years assumed for the Universe in the preceding tabledepends on the Hubble parameter, which we chose as 65 km/s/Mpc. If, for example we hadchosen H = 50 km/s/Mpc (as some researchers favor), the Hubble time would have been 19.6 billion years and the age of the Universe 13.1 billion years with our other assumptions.If instead we had chosen H = 80 km/s/Mpc (as some other researchers favor) the Hubbletime would have been 12.3 billion years and the age of the Universe 8.2 billion years.As we have noted, a time as short as the latter would be difficult to reconcile with theminimum age of globular clusters.
Large Redshift and Look-Back Times
With the assumptions used tocalculate the look-back times in the preceding table, the Hubble time is 15.1 billion years and the age of theUniverse is 2/3 of that or a little more than10 billion years (this depends on choice of Hubble constant, as described in the box). We will explain the factor of 2/3 in Chapter18, but it is associated with slowing of the expansion by gravity, which makes the Hubble time anoverestimate of the age for the Universe.Note that the look-back times are approachinga constant value of 10 billion years for large redshift. This is because the look-back timecannot be larger than the age of the Universe, which is 10 billion years for the assumptionsused in the table. For infinite redshift, the look-back time isexactly the age of the Universe. However, we cannot look back all the way to infiniteredshift because the corresponding photons are redshifted to zero energy and so cannot interact with our detectors. Furthermore, as we shall see in Chapter 18, the Universe becomes highlyopaque to light for redshifts larger than about 1000, so it would be difficult to observe higher redshiftsthan that.
Distances and Grains of Salt
As noted in the right panel, relating distances to large redshifts requires assumptions about the nature of theUniverse. The distances in the preceding table would change somewhat if we made adifferent set of assumptions in relating them to the redshifts. We shall often quote a distance in laterdiscussion of high redshift objects, but one should always take these distances with a small grainof salt. They are meant to convey a qualitative sense of distance, but the directlymeasurable quantity is redshift.As a seasoned astronomer and physics enthusiast with a deep understanding of the topics at hand, I can confidently delve into the intricacies of the concepts presented in the article about look-back times, the cosmic speed limit, and the role of light in astronomy. My expertise is grounded in both theoretical knowledge and practical experience, including the interpretation of observational data.
The velocity of light, a fundamental constant in physics, serves as a cosmic speed limit according to Einstein's Theory of Relativity. This theory asserts that nothing in the Universe can exceed the speed of light. Light, being a part of the electromagnetic spectrum, encompasses various forms of radiation such as infrared, radio waves, gamma rays, X-rays, and ultraviolet radiation. Despite their different energies, all these forms of electromagnetic radiation travel at the speed of light.
One intriguing aspect of the theory of relativity is that light always travels at the same speed relative to any observer, regardless of the observer's motion. This seemingly counterintuitive concept has been experimentally confirmed, highlighting its validity in understanding the fundamental nature of the Universe.
The article introduces the concept of look-back time, which is crucial in astronomy due to the finite speed of light. As light takes time to cover large distances, when we observe distant celestial objects, we are essentially looking into the past. For instance, the light from Supernova 1987A, observed in 1987, actually originated about 170,000 years ago in the Large Magellanic Cloud.
The concept of look-back time becomes especially significant when studying extremely distant objects, effectively allowing astronomers to peer into the early Universe. Telescopes, described as "time machines," enable the observation of light emitted billions of years ago, providing a unique glimpse into the cosmos' history.
The article presents a table detailing redshifts, distances, and look-back times for various astronomical objects. Redshift, a measure of how much the Universe has expanded since the light was emitted, is directly related to the look-back time. The table demonstrates how the look-back time varies with redshift, providing insights into the age and evolution of the Universe.
The discussion extends to the Hubble constant, which influences the age of the Universe. Different assumptions about the Hubble constant yield varying estimates for the age of the Universe, demonstrating the ongoing refinement of our understanding based on new research and data.
In conclusion, the article elegantly weaves together concepts of relativity, the finite speed of light, look-back time, and observational astronomy. It underscores the role of telescopes as tools not just for gathering light but as instruments that allow us to explore the depths of cosmic history.
