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# Tired light

Tired light is a class of hypothetical redshift mechanisms that were proposed as an alternative explanation for the redshift-distance relationship as alternatives to the Big Bang and the Steady State cosmologies, both of which proposed that Hubble's law was associated with a metric expansion of space. The concept was first proposed in 1929 by Fritz Zwicky, who suggested that photons lose energy over time through collisions with other particles. Alternative models of gravity that do not produce an expanding universe sometimes appeal to tired light to explain Hubble's Law. Today, tired light is remembered mainly for historical interest, and almost no scientist accepts tired light as a viable explanation for Hubble's Law.

## History and reception

Tired light was an idea that came about due to the observation made by Edwin Hubble that distant galaxies had redshifts proportional to their distance. Redshift is a shift in the spectrum of electromagnetic radiation toward lower energies and frequencies, usually attributed to recessional velocity. Before Hubble's observations, all observed redshifts were attributable directly to a mechanism similar to the Doppler Effect. In these situations, objects moving away from us exhibit a shift toward the red end of the optical spectrum while objects moving toward us exhibit a shift toward the blue end (blueshift). Hubble and other scientists observing the redshifts associated with distant galaxies attributed their redshifts to motion away from us. Bizarrely, the relation held in all directions and so could not be attributed to normal movement with respect to a background which would show redshifts and blueshifts. Everything was moving away.

Immediately upon publishing this results, Willem de Sitter who was working with Einstein's Theory of General Relativity recognized that these observations fit with a particular solution to the Einstein equations now known as the FRW metric. This solution explains that distant objects are observed with greater wavelengths than were emitted by the objects because they are moving with an expansion of the universe. In this formulation, there was still an analogous effect to the Doppler Effect, though relative velocities are not really well-defined for such situations.

Not everyone accepted this interpretation immediately. General relativity was notoriously difficult to understand and many of the astronomers were skeptical that this was the only possible explanation. Some, like Edward Milne proposed that there was a giant explosion that could explain redshifts (see Milne universe). Others thought that there might be systematic effects that made the observation suspect. Along this line, Fritz Zwicky proposed a "tired light" mechanism in 1929. Zwicky suggested that photons might slowly lose energy as they travel vast distances through a static universe by interaction with matter or other photons, or by some novel physical mechanism. Since a decrease in energy corresponds to an increase in light's wavelength, this effect would produce a redshift in spectral lines that increase proportionally with the distance of the source. The term "tired light" was coined by Richard Tolman in the early 1930s as a way to refer to this idea

Tired light mechanisms were among the proposed alternatives to the Big Bang and the Steady State cosmologies, both of which relied on the general relativistic expansion of the universe of the FRW metric. Through the middle of the twentieth century, most cosmologists supported one of these two paradigms, but there were a few scientists who worked with the tired light alternative. As the discipline of observational cosmology developed in the late twentieth century and the associated data became more numerous and accurate, the Big Bang emerged as the cosmological theory most supported by the observation evidence, and it remains the accepted consensus model in the current parametrization of the state and evolution of the universe. Additionally, a number of studies have shown that the "tired light" hypothesis is not a viable explanation for cosmological redshifts.

Redshift is directly observable and used by cosmologists as a direct measure of time, often referring to age in terms of redshift rather than years. The Big Bang is the end of this scale of time corresponding to a redshift of infinity. The relation between universal expansion and redshift is observationally confirmed through a great variety of tests, though alternative hypotheses such as tired light remain historical interest. So-called alternative theories of gravity that do not have an expanding universe need an alternative explanation to explain the correspondence between redshift and distance that is sui generis to expanding metrics of general relativity. Such cosmologies are sometimes referred to as "tired-light cosmologies", though not all authors are necessarily aware of the historical antecedents.

## Tired light models

A number of tired light mechanisms have been suggested over the years:

### Zwicky's models

Zwicky investigated a number of redshift explanations, ruling out some himself (Zwicky, 1929):

• The Compton Effect:

"... light coming from distant nebulae would undergo a shift to the red by Compton effect on those free electrons [in interstellar spaces] [...] But then the light scattered in all directions would make the interstellar space intolerably opaque which disposes of the above explanation. [...] it is evident that any explanation based on a scattering process like the Compton effect or the Raman effect, etc., will be in a hopeless position regarding the good definition of the images"

• Gravitational potential:

"One might expect a shift of spectral lines due to the difference of the static gravitational potential at different distances from the center of a galaxy. This effect, of course, has no relation to the distance of the observed galaxy from our own system and, therefore, cannot provide any explanation of the phenomenon discussed in this paper."

• The Gravitational "Drag" of Light:

"... [a] gravitational analogue of the Compton effect [...] It is easy to see that the above redshift should broaden these absorption lines asymmetrically toward the red. If these lines can be photographed with a high enough dispersion, the displacement of the center of gravity of the line will give the redshift independent of the velocity of the system from which the light is emitted."

Zwicky also notes, in the same paper, that according to a tired light model a distance-redshift relationship would necessarily be present in the light from sources within our own galaxy (even if the redshift would be so small that it would be hard to measure), that do not appear under a recessional-velocity based theory. He writes, referring to sources of light within our galaxy: "It is especially desirable to determine the redshift independent of the proper velocities of the objects observed".

### Hubble and Tolman's "energy loss" treatment

Following after Fritz Zwicky in 1935, Edwin Hubble and Richard Tolman compare recessional redshift with a non-recessional one, writing that they:
"... both incline to the opinion, however, that if the red-shift is not due to recessional motion, its explanation will probably involve some quite new physical priciples [.. and] use of a static Einstein model of the universe, combined with the assumption that the photons emitted by a nebula lose energy on their journey to the observer by some unknown effect, which is linear with distance, and which leads to a decrease in frequency, without appreciable transverse deflection

### Finlay-Freundlich Red Shift Hypothesis

In the early 1950s, Erwin Finlay-Freundlich proposed a redshift as "the result of loss of energy by observed photons traversing a radiation field.". R.A. Alpher noted "No generally accepted physical mechanism has been proposed for this loss" , though P.F. Brown ".. proposed that the energy lost reappears as neutrino pairs resulting from the exchange of a graviton between two photons.

## General features of tired light models

The simplest form of a tired light theory assumes an exponential decrease in photon energy with distance traveled:

$E\left(x\right) = E\left(0\right)e^\left\{-x/R\right\},$
where $E\left(x\right)$ is the energy of the photon at distance x from the source of light, $E\left(0\right)$ is the energy of the photon at the source of light, and R is a large constant characterizing the "resistance of the space". To correspond to Hubble's law, the constant R must be several gigaparsecs.

## Criticisms

Any "tired light" mechanism must solve some basic problems, in that the observed redshift must:

• admit the same measurement in any wavelength-band
• not exhibit blurring
• follow the detailed Hubble-relation observed with Supernova data (see accelerating universe)
• explain associated time dilation of cosmologically distant events.

As part of a broader alternative cosmology, other observations that need explanation include:

To date, no established mechanism to produce such a drop in energy has been proposed that reproduces all the observations associated with the redshift-distance relation. Scattering by known mechanisms from gas or dust does not reproduce the observations. For example, scattering by any mechanism would blur an object more than observed. In general, cosmologists consider classical tired light models to have too many problems to be worth serious consideration. Tired light alone does not provide a full cosmological explanation and so cannot reproduce all the successes of the standard big bang cosmology. No tired light theory is known that by itself correctly accounts for the observed time dilation of distant supernovae light curves , the black body spectrum or anisotropy of the cosmic microwave background, and the observed change in the morphology, number count, and surface brightness of high redshift galaxies and quasars. Furthermore, the fact that the age of the oldest stars is roughly equal to the inverse of the Hubble constant emerges naturally from a Big Bang cosmology, but is an unexplained coincidence with most tired light models.

In 2008, Blondin et al. showed that even processes that take macroscopic amounts of time such as various elapsed times are slowed down by the same redshift factor as the light frequency.

## Notes

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