**ERIC Number:**EJ1203560

**Record Type:**Journal

**Publication Date:**2019-Feb

**Pages:**6

**Abstractor:**As Provided

**ISBN:**N/A

**ISSN:**ISSN-0031-921X

An Intuitive Approach to Cosmic Horizons

Neat, Adam

Physics Teacher, v57 n2 p80-85 Feb 2019

How far, in space, can we see? And can we see an object whose Hubble recessional velocity exceeds the speed of light? Maybe you've thought about these questions before, or perhaps you've seen them discussed in the literature or mentioned in the media. With the recent popularity of inflation and Big Bang cosmology, they're hard to avoid. The discussion that follows is an attempt to resolve some common misconceptions--often seen in the popular literature--concerning the above two questions, and to do so in a way that appeals to kinematical intuition. A simple thought experiment will be used to initiate the discussion and to answer the question, "Can we see objects with faster-than-light recessional velocity?" Hubble's law, along with a simple assumption about the kinematics of light in expanding space, will be used to derive expressions, customarily derived in a general relativistic context, that allow cosmologists to determine our observational limits and define our cosmological horizons. Some of the results may surprise you. Before we delve into the topic fully, though, let's first lay some theoretical groundwork. Distant objects travel away from us faster than the speed of light, and it's no violation of special relativity. This strange fact is a consequence of one of modern cosmology's most elementary postulates--space is expanding. The distance between two vastly separated objects in our universe increases with time, not because the objects are moving through space, but because the space in between them is expanding. In a universe where space expands uniformly, the Hubble recessional velocity (recessional velocity due merely to spatial expansion) is related to the distance between objects by the following very simple equation, often referred to as Hubble's law: v[subscript r]= HD, where v[subscript r] is recessional velocity, "D" is separation distance, and "H" is the Hubble constant. Two major implications of this law are (1) recessional speed increases linearly with distance at any one moment in time; and (2) there is no limit to an object's recessional speed. Not only is faster-than-light recession not prohibited, it's what all matter does outside a radius of "D = c/H." A natural question that may arise in response to the above two points is, "If something is traveling away from me faster than light (FTL), can I see it?" If the object never slows down, one may reason, how can light from me ever catch up with that object; and, by symmetry, how can light from that object ever catch up with me? Reasoning this way, FTL objects seem to be beyond our observational reach. To reinforce this conclusion, consider the effects of redshift. Our special relativistic intuition might tell us that redshift approaches infinity as the recessional velocity of the emitter approaches the speed of light. If light from an FTL object "could" reach us, would it not be redshifted out of existence, i.e., an infinite amount? A related question about our observational limits is, "Given that the universe is finite in age, how far, in space, can we see?" One might reason: If the universe is 14 billion years old, and light travels at a constant rate of c, the greatest distance a photon can have traveled since the beginning of time is 14 billion light-years. This must therefore be the greatest distance we can see (assuming perfect transparency). There may exist more distant objects, but their light will not have reached us yet. To restate the above two conclusions: we cannot see objects receding from us faster than light, and we cannot see anything farther away than "c x age" of universe. It's not uncommon to find conclusions, or reasoning, similar to that above in introductory-level accounts or physics-for-the-layperson descriptions. Both conclusions, however, turn out to be wrong.

Descriptors: Motion, Physics, Scientific Concepts, Light, Astronomy, Time, Science Education, Equations (Mathematics)

American Association of Physics Teachers. One Physics Ellipse, College Park, MD 20740. Tel: 301-209-3300; Fax: 301-209-0845; e-mail: pubs@aapt.org; Web site: http://aapt.scitation.org/journal/pte

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A