On The Relativity of Redshifts: Does Space Really 'Expand'?

📝 Abstract

In classes on cosmology, students are often told that photons stretch as space expands, but just how physical is this picture? Does space really expand? In this article, we explore the notion of the redshift of light with Einstein’s general theory of relativity, showing that the core underpinning principles reveal that redshifts are both simpler and more complex than you might naively think. This has significant implications for the observed redshifting of photons as they travel across the universe, often refereed to as the cosmological redshift, and for the idea of expanding space.

💡 Analysis

In classes on cosmology, students are often told that photons stretch as space expands, but just how physical is this picture? Does space really expand? In this article, we explore the notion of the redshift of light with Einstein’s general theory of relativity, showing that the core underpinning principles reveal that redshifts are both simpler and more complex than you might naively think. This has significant implications for the observed redshifting of photons as they travel across the universe, often refereed to as the cosmological redshift, and for the idea of expanding space.

📄 Content

AUSTRALIAN PHYSICS 95 53(3) | MAY–JUN 2016 On The Relativity of Redshifts: Does Space Really “Expand”? Geraint F. Lewis Sydney Institute for Astronomy, School of Physics, A28 The University of Sydney, NSW 2006 In classes on cosmology, students are often told that photons stretch as space expands, but just how physical is this picture? Does space really expand? In this article, we explore the notion of the redshift of light within Einstein’s general theory of relativity, showing that the core underpinning principles reveal that redshifts are both simpler and more complex than you might naively think. This has significant implications for the observed redshifting of photons as they travel across the universe, often referred to as the cosmological redshift, and for the idea of expanding space. Stretching Photons In an expanding universe, the light from distant galaxies is redshifted, with the wavelength of observed spectral features being longer than those measured in the labora- tory. To anyone who has taken an undergraduate course on cosmology, the source of this redshifting is obvious, having been told that photons “stretch” as the space ex- pands. This statement is often accompanied with a pic- ture like Figure 1, with a blue photon stretched into a red photon as space expands during its journey between two cosmological observers. All of this is pretty satisfying, and life can happily con- tinue. But with a little more thought, a few niggling is- sues appear. If expanding space can stretch a photon, a photon that is extremely tiny, is expanding space stretch- ing atoms and molecules? Is expanding space stretching stars and galaxies? And are Brooklyn and its inhabitants expanding with the universe, as discussed in the won- derful scene in Woody Allen’s “Annie Hall”. When faced with such questions, you may turn to Google and find out what the experts have to say, and you may find your- self rather surprised. Figure 1: Typical diagram demonstrating how expanding space stretches photons as they travel across the universe. John Peacock, author of “Cosmological Physics”, at- tacks the misconceptions in cosmology, noting that “[t]he worst of these is the ‘expanding space’ fallacy” [1]. But Peacock is just one cosmologist, and you may turn to others for further scientific insight, but you’ll find no solace there. Cosmological giants, Martin Rees and Ste- ven Weinberg, tell us “…how is it possible for space, which is utterly emp- ty, to expand? How can nothing expand? The answer is: space does not expand. Cosmologists sometimes talk about expanding space, but they should know better.” So experts tell us that space doesn’t expand! Just what is the layperson to make of this? And if space doesn’t expand, just what stretches a photon traveling across the universe? To start to answer these questions, we need to take a step back and really understand the mechanism of the redshifting of light in a relativistic universe. Three Types of Redshift? When flipping through a physics textbook, students are typically told that there are three different redshifts seen within Einstein’s relativity, each applicable in particular circumstances. These are; Doppler Redshift: first encountered in the flat space- time of special relativity, this concerns the observation of photons by observers who are moving relative to one another. Gravitational Redshift: a classical consequence of general relativity, observers at different locations in a gravitational field measure different wavelengths when exchanging photons. 96 AUSTRALIAN PHYSICS 53(3) | MAY–JUN 2016 Cosmological Redshift: a staple of cosmology classes, this is the case where observers exchange photons over cosmological distances in an expanding universe. These appear to be distinct physical processes, and gov- erned by quite different equations. But let’s again ask ourselves the mechanism by which the redshifting oc- curs. We’ve already seen what students are told that in the cosmological case. In the case of the gravitational redshift, photons apparently lose energy as they climb out of a gravitational potential. But what about the first case considered above, the Dop- pler shifting of special relativity? Just where does the red- shifting occur in this scenario? Understanding this is key to understanding relativistic redshifts in general. But let’s start with a photon moving in a gravitational field Of Gravity and Rockets As already mentioned, the gravitational redshift appears to occur as photons lose energy as they climb in a gravi- tational field, a situation we can represent schematically shown in Figure 2. Considered one of the classical test of general relativity, this phenomenon was experimentally verified in 1959 by Robert Pound and Glen Rebka in the Harvard tower ex- periment, where photons were sent on journeys up and down a 22m path and their energies measured, finding precise agreement with the predictions of g

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