Lookback Homeward, Angel

Time Line of the Universe, Credit: NASA/WMAP Science Team

The farther away in the cosmos we look, the farther into a faster expanding *past* of the universe we see, not a faster expanding future.

We wrongly believe the expansion of our universe is accelerating because the red shift of distant stars increases with distance. However, Lookback time, the time it takes starlight to reach us, should lead us to interpret red shift evidence in the opposite direction, i.e. the older the light we receive, the greater the shift and the higher the speed of recession. If older = redder = faster then the recession is slowing down.

Since the canonization of Hubble’s Law, the vast majority of scientists have accepted that the Visible Universe  is expanding. But is the expansion accelerating or slowing down? Observations and calculations based on the standard interpretation of Hubble’s Law  increasingly indicate an accelerating rate of expansion, necessitating the invention of a mysterious “dark energy” to explain such counter-intuitive, gravity-defying observations. However, I will offer an argument for decelerating expansion that is consistent with modern observations but which depends on an unconventional interpretation of Hubble’s Law. Wikipedia introduces Hubble’s Law as follows:

“Hubble’s law … is the name for the astronomical observation in physical cosmology that: (1) all objects observed in deep space (intergalactic space) are found to have a doppler shift observable relative velocity to Earth, and to each other; and (2) that this doppler-shift-measured velocity, of various galaxies receding from the Earth, is proportional to their distance from the Earth and all other interstellar bodies. In effect, the space-time volume of the observable universe is expanding and Hubble’s law is the direct physical observation of this process.^[1] It is considered the first observational basis for the expanding space paradigm and today serves as one of the pieces of evidence most often cited in support of the Big Bang model.”

Doppler shift due to stellar wobble caused by an exoplanet (Photo credit: Wikipedia)

All this is inferred from observations that waves striking an observer appear higher in frequency if the observer and source are getting closer, and lower in frequency if the observer and source are getting farther away from each other. The amount of this frequency shift (known as a Doppler shift or Doppler effect) in light waves is proportional to the speed at which the source and observer are moving relative to each other. If the observed frequency of light is increased, as when the source and observer are getting closer, this is called a blue shift. If the frequency is decreased, as when a light source and observer are getting farther away from each other, this is called a red shift. Hubble’s Law is based on two different categories of measurements made by astronomers that appear to always have a constant proportion to each other, called Hubble’s Constant (H₀). We typically use the Hubble’s Constant ratio to determine the velocity (v) of objects like stars and galaxies that we see in deep space. The H₀ ratio involves:

1. the distance (D) of extra-galactic light sources. This is inferred by various methods of contrasting their “true” brightness or luminosity with their “apparent” brightness (the greater the difference in these values, the farther away an object is thought to be)
2. the direction of motion and velocity (v) of the light sources relative to us. This is inferred from the frequencies of the light we receive (sources with higher red shifts are thought to be moving away from us at higher speeds).

Hubble’s Law is sometimes expressed by the equation v = H₀D. Although Hubble’s Law is often cited (perhaps for the sake of simplicity) as evidence that “all” galaxies have been mutually moving away from each other for about 14 billion years, we know that exceptions exist. In some cases galaxies still remain close enough together to gravitationally affect each others shapes and motions. Some appear to be headed on collision courses, or to currently be in the process of colliding with each other. Our galaxy is expected to collide and merge with the Andromeda galaxy in about 4.5 billion years. However, it is still thought that the great majority of galaxies are moving away from the majority of other galaxies with the exception of those which are close enough (in galactic groups or clusters) for their mutual gravitational attractions to have overcome the forces which are spreading most galaxies out and away from each other. The primary cause of the apparent general movement of galaxies away from one another is usually considered to be some sort of “Big Bang.”

According to the Big Bang model, the Universe expanded from an extremely dense and hot state and continues to expand today. A common analogy explains that space itself is expanding, carrying galaxies with it, like spots on an inflating balloon. The graphic scheme above is an artist’s concept illustrating the expansion of a portion of a flat universe. (image and description from Wikipedia: Big Bang)

However,  all this is not without plenty of uncertainty and controversy. In the article on Doppler Shift, Wikipedia says:

“For waves that propagate in a medium, such as sound waves, the velocity of the observer and of the source are relative to the medium in which the waves are transmitted. The total Doppler effect may therefore result from motion of the source, motion of the observer, or motion of the medium. Each of these effects are analyzed separately. For waves which do not require a medium, such as light or gravity in general relativity, only the relative difference in velocity between the observer and the source needs to be considered.”

Light from a distant quasar passes through numerous intervening gas clouds in galaxies and in intergalactic space. These clouds subtract specific colors from the beam. The resulting “absorption spectrum,” recorded by Hubbles Space Telescope Imaging Spectrograph (STIS) determines the distances and chemical composition of the invisible clouds. (Photo credit: Wikipedia)

But this ignores the fact that the speed and frequency (color) of light may be affected by various materials (such as water or intergalactic gas) or fields of force (such as magnetic, gravitational, or perhaps even Higgs fields) through which it may pass. We generally assume intergalactic space to be a near-perfect vacuum in most places–in other words, we assume  that any known or unknown medium or media, if  present, will not have altered the generally isotropic, universe-wide observations of light reaching us from distant galaxies in a way that would significantly alter the cosmological principle or the calculations underpinning Hubble’s Law. Is that a reasonable assumption? In billions of years of travel, how much absorption & re-radiation, filtering, gravitational lensing, etc. is the average galactic image subjected to? The great variety of effects upon light produced with simple glass lenses and even pinholes in paper should make us very humble about interpreting the radiation we get from deep space, which has passed through “only-god-knows-what” in its very long journey. In fact, many of the assumptions involved in measuring the brightness, distance, velocity, and red shift of distant objects and the properties of galaxies and intergalactic space are controversial, resulting in values for Hubble’s Constant, for example, that vary from 50 to 100 (km/s)/Mpc. As a result of such discrepancies,  some scientists think the universe will expand forever and some think it will ultimately stop expanding and start collapsing under the force of mutual gravitational interaction. Under most current interpretations, the latest data (especially that which concerns “standard candles” of brightness such as type 1a supernovae) increasingly seem to favor unending expansion. But is there an alternate interpretation that might fit the latest measurements and even hold up irrespective of any intervening deep-space materials or forces either known or as yet unknown? I will suggest one presently.

“The age and ultimate fate of the universe can be determined by measuring the Hubble constant today and extrapolating with the observed value of the deceleration parameter, uniquely characterized by values of density parameters (Ω_M for matter density and Ω_Λ for dark energy). A “closed universe” with Ω_M > 1 and Ω_Λ = 0 comes to an end in a Big Crunch and is considerably younger than its Hubble age. An “open universe” with Ω_M ≤ 1 and Ω_Λ = 0 expands forever and has an age that is closer to its Hubble age.” (image and description from Wikipedia, Hubble’s Law)

This, so far, is a very brief and simplified summary of Hubble’s Law and some of its implications, leaving out many details and issues. I am not qualified to weigh in on the controversies surrounding any of the variables and measurements briefly outlined above. But I do have some bones to pick with every discussion of Hubble’s law and (by extension) every discussion of big bang and expansion cosmology I have read in the past 45 years. The bone that always catches in my craw is the damned accelerating expansion thing. And I have some other questions related to time and space which, if they remain unanswered, render any of the cosmological models I know of so ambiguous as to be meaningless. If the expansion of the universe is a relativistic expansion of a space-time continuum, what evidence do we have that such a relativistic expansion would produce any measurable change in the distances between galaxies? All our metrics of distances between cosmic objects rely on the distance traveled by radiation in a given unit of time. If space and time are both expanding, what are we actually measuring if we measure one in terms of the other? And what if the speed of light has changed over the course of deep, cosmic time? What if we could measure the distance between earth and a receding galaxy with a physical yardstick? If galaxies are receding because of the expansion of space-time itself, wouldn’t the space between the atoms and molecules in the yardstick expand as well, at least once it reached out beyond the space-time-compacting gravity of Earth? (And BTW, how might we distinguish, mathematically, the gravity of Earth from the effects of acceleration that might be created by an expanding Earth?) The usual answer to such conundrums is that local forces dominate between nearby atoms and molecules, overriding the universal expansion which occurs at large scales. Still, if the space between atoms and molecules were expanding,  in lock-step with other universal changes, how would we know? But such matters are not the real topic of this essay. I mention them only to suggest the degree to which our current cosmological narratives are underpinned by assumptions which are, as yet, neither provable nor falsifiable. For the most part, however, the general correlation between distance and red-shift and the correlation between red-shift and velocity seem relatively uncontroversial: Relatively Uncontroversial Fact #1: In general, the greater the apparent red-shift of an object, the faster it is moving away from us (and we from it). Relatively Uncontroversial Fact #2: In general, the greater the apparent distance of a light-producing object from Earth, the greater its apparent red-shift. Understandably, most everyone draws the conclusion from these two facts that the expansion of the universe has been accelerating and still is. As far as I can tell, the “dark energy” and “open universe” hypotheses have no other foundations aside from the standard interpretations of Hubble’s law, i.e. that red-shift appears to increase with distance and distance with time. If red-shift increases with distance and distance increases with time, then by simple, deductive reasoning red-shift increases with time; or in other words, the expansion of the universe is accelerating. The logic:

1. Socrates is a man.
2. All men are mortal.
3. Therefore, Socrates is mortal.

But what if, unknown to us, some men were potentially immortal? or what if Socrates was an extraterrestrial space alien rather than a “man”? (Cue Twilight Zone theme song …) Since the amount of mass in the universe, even including dark matter,  currently appears too small to counteract the rate of acceleration computed according to our standard interpretation of Hubble’s Law, the universe appears to be “open” (i.e. it will continue to expand “forever”). But so far our only explanation for such a startling state of affairs is based on cosmic inflation and dark energy. These are “dark hypotheses,” little better than “insert explanation later” place-holders. On the other hand, what if  we drew the opposite conclusion from Fact 1 and Fact 2 above; concluding that the expansion of the universe is decelerating, based on Relatively Uncontroversial Fact 3: the greater the distance of an object from Earth, the longer it takes its light to reach us. This is the lookback time (t_L). When we receive light from an object that is one billion light-years away we see, by definition, a signal emitted one billion years ago. If, from its apparent red-shift, we drew a conclusion about the relative velocity at which the Earth and the source are moving away from each other in the present moment, we would be getting information across a one-billion-light-year distance instantaneously, wouldn’t we? Is that possible, or does that contradict basic physics and information theory in the sense of  information about the relative velocity of earth and distant objects being transmitted to us faster than the speed of light? If instead we interpreted that same red-shift data as information that is one billion years old, it tells us the speed and direction of the light source and observer one billion years ago rather than at the moment that the data is collected and measured by us. This seems more consistent, IMHO,  with known physics and information theory, and it would logically reverse the usual correlation of expansion speed with time, providing evidence for a decelerating expansion. Instead of v = H₀D, an alternative equation for Hubble’ Law for cases when lookback time (t_L) is significant might be:

 v = H₀ /D

or

     v = H₀/t_L  since in this expression distance (D) = Lookback time (t_L)

Does the apparent red shift of deep space objects represent the relative velocity between the light source and Earth at the time of observation, as is generally assumed; or the relative velocity at the time of emission, as I propose; or some third possible (but mysterious) value somewhere between those two? Apparently, the scientific community sees no problem so far with the standard expressions and interpretation of Hubble’s Law and  I have not encountered any discussion of an information theory paradox or any problem with the standard interpretations of the Doppler effect for cases involving significant lookback times. Can this be explained by the fact that we have no exacting standards of reference or controlled experiments involving significant amounts of lookback time? After all, it is very difficult to combine high relative velocities and significant amounts of lookback time in tightly-controlled experiments on earth and get results that exceed the margin of error. One issue raised by my hypothesis concerns the basic definition of relative motion in cases that involve significant amounts of lookback time. We usually consider a relative velocity or relative direction to specify relations between two or more objects at a given instant in time. When lookback time is significant, then by definition we have incomplete data about any possible changes in relative motion between the time an electromagnetic signal is emitted and the time it is received. When we measure relativistic changes in mass, length, or time-keeping in things that are rapidly orbiting the Earth (like atomic clocks on GPS satellites or changes to particles in a big accelerator) we are dealing with direct, well-controlled comparisons–for example, the speed of  identical clocks on earth and in orbit, or particles with precisely measurable energies and velocities. In such cases we have clear controls and standards of reference. Even then, experimental results can be ambiguous and even baffling, such as the results in state-of-the-art versions of the double-slit experiment which suggest that the nature of quantum reality (i.e. particle vs wave interference effects) can be changed retroactively by successive observations. But when we compare the velocities of very distant, very ancient stars and galaxies, and the “proper” vs apparent Doppler-shifted frequencies of their radiation, do we really have clear controls and standards of reference? Scientists go to amazing, heroic, and often very convoluted lengths trying to estimate extra-galactic distances, luminosities, velocities, frequencies, and frequency shifts. Yet it appears to me that the variables are often difficult, if not impossible, to define in non-circular terms; and the best estimates of true, absolute, or “proper” values are still only educated guesses in may cases. However, it seems to me that we might test the standard and alternative (lookback-significant) equations for Hubble’s Law with precision-engineered lasers on high-orbit satellites that could change their relative velocities in very controlled amounts between the times a signal of known “proper” frequency (frequency minus any Doppler effect) was emitted and the time that a shifted signal was received. I am not aware that any such experiments aimed at confirming the relationship between lookback time and the Doppler effect have ever been performed or even proposed, despite the fact that countless experiments with rapidly-moving satellite-based  electromagnetic and optical instruments at one or both ends have been performed for many other purposes. IMHO such experiments might also reveal (or perhaps even calibrate) other aspects of the relationships between space, time, motion, and gravity that still remain ambiguous long after Einstein. So far, the only controlled space-time calibrations I’ve heard of concern satellite clocks or particle accelerators. We know that things like Doppler effects and gravitational lensing effects occur in deep space, but knowing how to measure and interpret them correctly for deep-space objects is still more a “dark” art than a science. But I get all my astrophysics from the popular media, so WTF do I know?

Poor Richard

Related:

• Accelerating Universe? Not So Fast

• Lal, Ashwini Kumar (2010) ‘Big Bang Model : A Critical Review’, Journal of Cosmology (USA), vol. 6, pp. 1533-1547 (viXra e-print pdf)
• Cosmological Look-Back Time
• DISTANCE MEASURES IN COSMOLOGY, David W. Hogg