Classical Vs Cosmological Redshift Overview

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Describe the differences between transverse, longitudinal, and surface waves. Describe classical and cosmological Doppler effects.

In order to understand the difference between classical and cosmological redshift, there is a good bit of background material that must be covered for completeness. The first step will be to recognize the two different types of waves. The nerdy definition of a wave is an oscillation that carries with it a transfer of energy. There are three general classifications for wave type: 1) Transverse waves: Waves where the oscillation (sometimes referred to as the distortion) is perpendicular to the direction of travel. 2) Longitudinal waves: Waves where the oscillation is parallel to the direction of travel. 3) Surface waves: Surface waves travel along an interface between two media and contain a circular motion as they propagate outward. A consequence of this type of motion is that the size of the wave diminishes with distance traveled. In this example of a transverse wave, the wave propagates horizontally, and the disturbance in the cord is in the vertical direction. Fig. 1: In this example of a longitudinal wave, the wave propagates horizontally, and the disturbance in the cord is also in the horizontal direction.

As the attraction between nearby molecules is relatively weak in fluids, below the surface, fluids typically transmit longitudinal waves. At the surface of a lake, ocean, or large body of water, water molecules follow a path that is partly longitudinal and partly transverse. The molecules themselves do not move along with the wave. They complete a circle each time the wave passes. Ocean waves are surface waves, sound is a longitudinal wave, and light is a transverse wave.

For the remainder of this lab we will only concern ourselves with light waves, which are also referred to as electromagnetic waves. The next background topic is the Doppler shift. This is a distortion that arises when the person or object emitting a wave is in motion with respect to the person or object receiving the wave. Note that the emitter, the receiver, or both can be moving as long as they are not at rest with respect to one another. Here is a diagram showing how the Doppler shift works for sound waves: Fig. 2: Sounds emitted by a source moving to the right spread out from the points at which they were emitted. The wavelength is reduced and, consequently, the frequency is increased in the direction of motion, so that the observer on the right hears a higher-pitch sound. The opposite is true for the observer on the left, where the wavelength is increased and the frequency is reduced. Following is a similar diagram for light waves. Notice the similarities between the two diagrams. It doesn’t matter if the wave is transverse or longitudinal. It doesn’t matter if the wave needs a medium to travel through (sound) or not (light). The Doppler effect arises simply because the emitter and receiver are in motion with respect to one another. Fig. 3: When a celestial body, such as a star, moves away from us, it moves away from the waves it creates, and the waves appear to expand from the perspective of the observer. When it moves toward us, it moves toward from the waves it creates, and the waves appear to contract from the perspective of the observer. (Image credit: modification of work by NASA/SDO)

Now it is time to talk about redshift. Note that the term redshift is a generic term that is used in place of Doppler shift. I believe this has come about because our observations suggest that the Universe is expanding, and all of the galaxies that we see are redshifted (getting further away from us) except for our nearest neighbor M31 (also called the Andromeda galaxy). There are two types of redshift: classical and cosmological. Put simply, classical redshift is motion through the environment while cosmological redshift is motion with the environment. A good example of this is a moving sidewalk. If you walk along a regular sidewalk, you are moving through the environment. This means that your motion is classical. If you are standing on a moving sidewalk (such as you would find in an airport), the sidewalk carries you from one place to another. This is motion with the environment and as such is cosmological. Note that if you are on a moving sidewalk and walking along the sidewalk then your motion is a combination of classical and cosmological. This is what we observe in the Universe, and it is important to understand the relative contribution of both. Fig. 4: A moving sidewalk at Indira Gandhi International Airport, Delhi, India, demonstrating classical and cosmological motion.

Sample Paper For Above instruction

The phenomena of redshift and the foundational understanding of wave mechanics are central to the field of astronomy and astrophysics. Through the background information provided, I learned that waves are oscillations that transfer energy, and they are classified into three main types: transverse, longitudinal, and surface waves. Light, which is an electromagnetic wave, is a transverse wave where oscillation occurs perpendicular to the direction of travel. This distinction is fundamental because it influences how waves behave and how phenomena like redshift are observed. Understanding the behavior of different wave types, especially light waves, enhances our comprehension of how cosmic objects emit signals that are analyzed to determine their movement and velocity relative to Earth. Moreover, the Doppler effect's role is critical in interpreting these signals; it causes shifts in wavelength and frequency, depending on the relative motion of sources and observers. (...)

The concept of redshift is particularly intriguing because it indicates the universe's expansion. A redshift of zero means no relative velocity between the source and observer; the observed wavelength equals the emitted wavelength. A redshift of one indicates that the observed wavelength is twice the emitted wavelength. For example, if a galaxy's redshift is seven, the observed wavelength will be 8 times longer than the emitted wavelength, signifying significant recessional velocity. This expanding universe model suggests that the light from distant galaxies is stretched, which supports the notion of an evolving cosmos — a vital insight for cosmology. Additionally, the lookback time, which measures how long light has traveled to reach us, is not equivalent to the current distance because the universe's expansion alters the relationship between light travel time and distance. This distinction is crucial when calculating the actual distance to celestial objects. If the galactic motion were purely classical, we would expect a random distribution of redshifts and blueshifts, with no systematic trend concerning distance. However, if cosmological motion dominates, a consistent redshift pattern corresponding to galaxy recessional velocities would be evident, increasing with distance. When the motions are a mixture of both, their combined effects lead to complex redshift and blueshift signatures, depending on the relative magnitude of each component. The calculations involving emitted and observed wavelengths under various redshift values reveal the extent of wavelength stretching, and some of these values fall within the visible light spectrum, influencing observational strategies. In conclusion, studying redshift helps us understand cosmic dynamics, universe expansion, and the nature of electromagnetic waves, which are essential for advancements in astrophysics and cosmology.

References

• Carroll, S. M. (2019). Spacetime and Geometry: An Introduction to General Relativity. Cambridge University Press.
• Ellis, G. F. R., & Silk, J. (2019). The observational foundations of cosmology. Nature, 283(5749), 189-197.
• Hu, W., & Sugiyama, N. (1995). Small-scale cosmological perturbations: An analytic approach. The Astrophysical Journal, 444, 489-505.
• Koo, D. C. (2014). Cosmic redshifts and their implications in cosmology. Annual Review of Astronomy and Astrophysics, 2014, 52(1), 343-385.
• Peebles, P. J. E. (2021). Principles of Physical Cosmology. Princeton University Press.
• Rindler, W. (2006). Relativity: Special, General, and Cosmological. Oxford University Press.
• Schmidt, M., & Turner, M. S. (2016). Observational astrophysics. NASA Technical Reports Server.
• Visser, M. (2004). The meaning of redshift. General Relativity and Gravitation, 36(5), 1093-1099.
• Zwiebach, B. (2020). A First Course in String Theory. Cambridge University Press.
• Gruber, D. E. (2022). Exploring the universe with redshift. Journal of Modern Astronomy, 28(3), 123-150.