Gravitational Lensing Exposes Further Discrepancy in Hubble Constant - Past 5 Standard Deviations

We know the standard model of Big Bang cosmology, known as ΛCDM, incorporates how the assorted cosmological components outwardly behave. Dark energy, the model presumes,

• Dark Energy - Evidence for a New Law of Physics?

 Takes the form of a cosmological constant Λ, or a constant energy density per unit volume of vacuum. And dark matter is cold—that is, nonrelativistic—and interacts only via gravity and possibly the weak force.

Now it turns out (Phys. Today, March, p. 14) discrepancies are showing up in the measurements of the Hubble constant H0 - based on gravitational lensing techniques.  To fix ideas, the ΛCDM model predicts that the universe today should be expanding at a rate of 67.4 ± 0.5 km/s/Mpc. But a direct measurement of H0 based on observations of standard candles—Cepheid variable stars  (e.g. Measuring Stellar and Celestial Distances )

 And type Ia supernovae—give a different value: 74.0 ± 1.4 km/s/Mpc.

Now we learn that new collaborative research led by Sherry Suyu, from H0LiCOW (H0 Lenses in COSMOGRAIL’s Wellspring)  uses gravitationally lensed quasars to independently measure H0. The group’s latest result, 73.3 + 1.7 − 1.8 km/s/Mpc, agrees well with the standard-candle value. Combining the H0LiCOW and standard-candle measurements gives an H0 of 73.8 ± 1.1 km/s/Mpc, which differs from the ΛCDM value by 5.3 standard deviations.

As I noted in a previous blog post e.g

Arriving at a More Refined Hubble Constant

There has been ongoing work on improving the value of   such as described in the link to an Astrophysical Journal preprint paper in the above blog post link.  In the current research related to the  H0LiCOW work, it is crucial to note the link to a theoretical basis called "time delay cosmography".   Reference to the graphic shown (compliment of Freddie Pagani, ibid.)  can be instructive in understanding how the gravitational lensing works.

Basically, when a quasar or other luminous distant object lies in the line of sight of massive object, i.e  foreground galaxy, its light is deflected so strongly that multiple images appear (see the extreme right frame of the graphic)

The challenge in any direct measurement of H0 is in gauging the distances to faraway astronomical objects; their velocities relative to Earth, in contrast, are readily inferred from the redshifting of their radiation. Standard candles are appealing because their luminosities are known, so their distances can be calculated from how bright they appear on Earth. In H0LiCOW’s complementary measurement, the researchers studied quasars whose light is so strongly deflected by foreground galaxies that they appear as multiple distinct images, as shown in the figure. Because the light in each image traverses a path of a different length, fluctuations in the quasar’s light show up in the lensed images at different times. 

Measuring those time differences, which are on the order of weeks, doesn’t directly yield Dd (the distance from Earth to the lens) or Dds (the distance from the lens to the quasar). But it does constrain their combination, which is enough information to calculate H0 from the objects’ known redshifts. In 2017 the collaboration published a first result based on three lensed quasars (see Physics Today, April 2017, page 24). The current work extends the analysis to six quasars.  Below are shown the light curves from four lensed images of the quasar shown in the top graphic.

These curves were collected over 13 years from the COSMOGRAIL collaboration.  Note that fluctuations in the quasar's intensity appear first in the curves A and C, then in light curve B. Finally, two weeks later in light curve D.   The key point is that sufficient information is obtained - using 1 to 2 m telescopes- to get H0.

Basically, given the two angles, q1  and  q2   are small, the difference in path lengths shown(top graphic)  will be proportional to:   (Dd  Ds )/ Dds  .   Here  the denominator refers to the distance from the galaxy to the quasar.  Now, the difference in light travel time, which includes the effects of general relativity and the cosmic expansion, is proportional to the same value.  Recall in the case of general relativity, we are looking at the deflection of light as a result of encountering a massive object along its path, e.g.

Here the light from a star at an actual position S2 is seen to deflect by some angle  a    thereby altering the image position to that seen at S1. This is a direct result of the effect of the gravitational field of the Sun on the light rays. The true direction is thus alone the ray ES2 while the deflected position is along the ray ES1.  By more formally arriving at the geometry below:

We can obtain for the deflection angle, :

 a   = - 4 GM/ b   or (in cgs units): 

 a       = - 4 GM/ b c²  

Finally, in obtaining H0  we note the importance of the lensing galaxy's mass distribution.   This is needed to calculate the deflection angles,   q1  and  q2 .These, again, are analogous to the angle  a  computed in the example above. 

 These results in tandem  lessen the likelihood that the H0 discrepancy is due to some unappreciated systematic uncertainty in the standard-candle measurement.  Taken at face value, they seem to point toward a need to revise the ΛCDM (Standard) model. 

For those interested in further details, see:  K. C. Wong et al., Mon. Not. R. Astron. Soc., in press, https://arxiv.org/abs/1907.04869.)

Is There Really A "Discrepancy" In The Hubble Constant? Is It Truly A Constant?

According to Dennis Overbye, writing recently in the NY Times "there is a crisis brewing in the cosmos, or perhaps in the community of cosmologists". He adds that some astronomers believe  the universe seems to be expanding too fast.   Further, recent measurements of the distances and velocities of faraway galaxies don’t agree with a hard-won “standard model” of the cosmos that has prevailed for the past two decades. The latest result shows a 9 percent discrepancy in the value of the Hubble constant, which describes how fast the universe is expanding.

First, a bit of background: thanks to astronomer Edwin Hubble cosmology was put on a more secure observational footing on the basis of his "Hubble law". It is encapsulated by the graph shown below:

This relation between distance D  to an extra-galactic object  e.g. quasar, galaxy cluster) and its recessional velocity (v), has since come to be known as Hubble's law and is  expressed:

v = cz = HD

where H is known as the Hubble constant, c is the speed of light and z is the red shift.

This quantity z measures the extent to which spectral lines, say L1 and L2,  are shifted to the red  (longer wavelengths) compared to the normal spectrum, say of an element like hydrogen. The greater this shift the higher the velocity of recession.

The image below illustrates this for two extragalactic objects:



In fact 'H' is more technically the Hubble "scale factor".  The REAL Hubble constant (H o ) is the scale factor (a) divided by the distance in megaparsecs  MPC (km) where 1 parsec = 3.26 light years.

If then currently MPC (km)   =   3.08 x 10  ¹⁹     km/ Mpc  then:

H o =   a / MPC(km)   =  2.26 x 10 ^-18  s ^-1

Then the age of the cosmos can be obtained from:  t o =  1 / H o =

 (1 /   2.26 x 10 ^-18  s ^-1 )   =   4.4 x 10 ¹⁷  s   = 1.3 x 10 ¹⁰  yrs. or 13 billion years in age

The scale factor a, called the "Hubble constant",  is currently a »  70 km/ sec/Mpc. But as I reported last summer, e.g.

http://brane-space.blogspot.com/2016/06/arriving-at-hubble-constant.html

has since been refined to a = 72.8  km/ sec/Mpc.

Clearly then what we call the Hubble constant depends on the accuracy of a, and this in turn depends on the latest techniques to attain more exact values.  As I noted in the preceding link the newer,  more exact value has been based on refining the universe’s current expansion rate to unprecedented accuracy, reducing the uncertainty to only 2.4 percent.

However, an uncertainty of even just 2.4 percent means we cannot be talking about a real physical constant, but only an approximate factor that determines the proportionality value H in the Hubble law.  This is important to process before continuing.  My point is that the "discrepancy" with the standard model is a separate issue, because the standard model itself is still under scrutiny, although it's gained much more traction with the discovery of the Higgs boson.

This elicits the question of whether this small "mismatch" (Overbye's term)  is truly an indicator of  how well we know the cosmos. According to  Wendy Freedman of the University of Chicago, who has spent most of her career charting the size and growth of the universe:

“If it is real, we will learn new physics,”

Perhaps. But I don't think the 'new physics' will enter until we also are able to incorporate the role of dark energy, which has been identified as the primary agent responsible for the accelerated expansion. Relevant to this we invoke what can be called a cosmological "equation of state" (think of something like the equation of state for an ideal gas, e.g. P = nkT) for the vacuum energy presumed to underlie most theories of  dark energy . This is:

w = (Pressure/ energy density) = -1

One advantage is that this equation of state is consistent with Einstein's general theory of relativity - which one could say approaches the status of a 'basic law of physics'. 

In this case, the existence of a negative pressure is consistent with general relativity's allowance for a "repulsive gravity" - since any negative pressure has associated with it gravity that repels rather than attracts. (See, e.g. 'Supernovae, Dark Energy and the Accelerating Universe', by Saul Perlmutter, in Physics Today, April, 2003, p. 53.) Of course, simple algebra applied to the above also shows that the energy density would have to be negative, e.g. energy density =  - (pressure).

Specifically the term (r + 3p) acts as a source of gravity in general relativity, (where r = energy density).

 Set:  0 = (r + 3p),   then the pressure :

 p =  -r /3   (or  r  = - 3p)

 and if:  p <  (r /3) we have gravity that repels.

To ascertain the proportions of dark matter and dark energy one uses graphs derived from supernova  data with corrected apparent visual magnitude m v , redshift (z),   to give different combinations of  W _dark to W _matter over the range. However, only one of the graph combination bests fits the data. Currently this yields:

Wd_ark = 0.68 and  W_matter = 0.27


As a result,  astronomers have accepted that the universe consists of roughly 5 percent atomic matter by weight, 27 percent dark matter and 68 percent dark energy . The last is what's speeding up the cosmic expansion.

Back to the link above for my earlier post last summer citing a team led by Adam Riess of Johns Hopkins University and the Space Telescope Science Institute, using the Hubble Space Telescope and the giant Keck Telescope on Mauna Kea in Hawaii . They obtained a value with  only 2.4 percent uncertainty - but as I pointed out-   this is still nowhere near acceptable constant territory. Check any table of physical constants - actual ones, like the Newtonian G, or speed of light c - for comparison.

The claim of Overbye  in his piece is that this "made waves because it meant that, if true, the Hubble constant as observed today was now clearly incompatible with a result of the lower slower value of 67 inferred from data obtained in 2013 by the European Planck spacecraft of relic radiation from the Big Bang."

But how big were these "waves",  really? Those  Planck mission observations revealed the universe when it was only 380,000 years old  and these are considered "the gold standard of cosmology."  But how reliable and trustworthy is this gold standard?  Interestingly, whether the standard cosmic recipe might now need to be modified  depends on whom you talk to.

Personally, I side with the higher  H values because I place more confidence in the supernova data and observations, redshifts derived therefrom, than the Big Bang Plank observations. Heresy? Maybe, but there it is. Also, Prof.  Riess has admitted that the Planck mission measured the Hubble constant only indirectly as one of several parameters, i.e. in the standard model of the universe. So why would you place more faith in those measures than the supernovae data?

Bolstering this POV, another group called H0LiCOW (short for H0 Lenses in COSMOGRAIL’s Wellspring),  from the Max Planck Institute for Astrophysics in Garching, Germany, reported its own value of 72 km/ sec/Mpc , also inconsistent with the lower value from the Planck space mission’s analysis.  This interjects the question of whether the "Big Bang' results might themselves be spurious and based on as yet undetected systematic or other errors. Or, perhaps the Standard Model itself needs revision. (See addendum).

Stay tuned, because the issue isn't resolved yet, but for my money, the high z supernova data hold the key. Until I see much more consistency in the results from the "Big Bang"- Standard model teams.
--------------------------------------
Addendum on the Standard Model- Higgs boson discovery:

The so-called 'Standard Model' is generally defined as the symmetry:

SU(3) x SU(2) X U(1)

where each of the above denotes a specific matrix, or more exactly a group. See, e.g.

http://brane-space.blogspot.com/2010/04/looking-at-groups.html

In the case of SU(2) we describe it as the "special unitary group" which has the form:

S =

(a.........-b*)
(b..........a*)

where a*, b* are complex conjugates and we have (aa* + b*b) = 1. Thus the elements of SU(2) are the unitary 2 x 2 matrices with DET (determinant) = 1. These groups thus define the behavior of a specific class of subatomic particles. Spontaneous symmetry breaking would therefore resolve this combination into constituent parts, e.g.: SU(3) associated with the 'color force' of quarks:

 SU(2) x U(1)

associated with the electro-weak force.

One possible symmetry breaking (quark -boson format) is:

SU(3) x SU(2) X U(1) -> SU(3) + SU(2) x U(1)

which would occur at a particular ambient temperature (T_qb) for the universe at some epoch (E_qb) in the past. In the foregoing, the synthesis of SU(2) and U(1) into the locally gauge invariant electro-weak theory requires a mechanism which confers mass to three vector bosons while leaving the photon massless. This 'mass-giving' mechanism is called the Higgs Field or Higgs mechanism, and it demands the existence of one or more massive, spin-0 bosons otherwise called Higgs bosons.

Enter now the putative discovery of the Higgs, thanks to the large hadron collider, which  was announced at CERN. Dr. Rolf Heuer, director general of CERN, while referring to the new discovery as "a historic milestone"  nevertheless cautioned that it was too soon to know for sure if the new particle (coming in at 125 billion electron volts) is actually the long sought particle.

The problem? The culmination of analyses of over 800 trillion proton-proton collisions over the 2 years leading up to the announcement generated a quandary. When buttonholed,  the physicists admitted they  actually knew little. The CERN results were mostly based on measurements of two or three of the dozen different ways, or “channels,” by which a Higgs boson could be produced and then decay. Worse, there were hints that some of the channels were overproducing the Higgs while others might have been underproducing. In either case, false positives or false negatives, one had to look askance at the initial results.

The upshot? There may not have been a real Higgs discovered but a spurious 'mirage' imitating some of its properties but more a confection of the data than based in reality. Also, assuming a genuine signal or find, it may not have been unique but only ONE of two or three different Higgs bosons. Much like the case of the neutrino, which was once believed to be one entity only, but we now know is THREE: the electron neutrino, the tau neutrino and the muon neutrino, see e.g. http://brane-space.blogspot.com/2012/06/solving-neutrino-puzzleand-matter.html

Dark Matter And Dark Energy In The Universe

Graph showing the plot of magnitude (M) vs. red shift z for Type 1a supernovae,  showing the universe is accelerating.(From: Perlmutter, Physics Today, April, 2003, p. 53)

Continued questions at All Experts.com suggest many still do not understand the differences between dark matter and dark energy. Both of these are critically important to our conception of the cosmos given they impinge on conclusions that we can draw on the nature of the cosmos - including whether it displays "order" or can be considered to be "created", i.e. by an outside agent.

In the case of order, as I've noted before, it is difficult to make such an argument given  the universe has been shown to contain ordinary,  visible matter at only 7% of the total, with fully 93% exhibiting a “dark component” - of which nearly 70% was dark or vacuum energy, the rest dark matter. (See, e.g. Physics Today, July, 2000, p. 17). Given these components, the extent of any order can't be properly assessed, and the issue of creation has been shown to be superseded by greater understanding of the nature of quantum fluctuations and virtual particles.

Dark matter came on the cosmological scene first, back in 1933, when Fritz Zwicky's measurements of galaxy clusters highlighted a ‘missing mass’. He found that the mass needed to bind a cluster of galaxies together gravitationally was at least ten times the apparent mass visible. This mass, because it was inferred but not directly detectable, became the first ‘dark matter’. Around the same time there were observations of stellar motions in the galactic plane by Dutch astronomer Jan Oort. He found there had to be at least three times the mass visibly presenting in order for stars not to escape the galaxy and fly off into space.

By the late 1970s, astronomers realized there were other forms of dark matter. Among the most discussed candidates were black holes, marking the end stage of evolution for very massive stars. In the black hole, the gravity is so strong that no light escapes and the mass typically is much greater than that of the Sun. These objects can only be detected indirectly, e.g. as a member of a binary (double) star system, to infer its presence from the intense x-rays given off when the companion star’s gaseous layers are sucked into it.

Dark matter itself occurs in either baryonic or non-baryonic forms, depending on whether the matter reacts with radiation or not. If it doesn’t, it’s non-baryonic. Baryons include protons and neutrons, while non-baryons include electrons and neutrinos.

Non-baryonic dark matter further breaks down into cold dark matter and hot dark matter. The terms hot and cold are not so much indicative of current temperatures, as the phase of the early universe at which the particular dark matter ‘decoupled’ from the hot radiation background. An early decoupling implies a higher ambient background radiation temperature of the primeval cosmos. A later decoupling correlates to a cooler temperature. Perhaps the most widely studied candidate of hot dark matter is the neutrino.

By contrast, cold dark matter candidates tend to have larger mass and amongst the most likely suspects are: gravitinos, magnetic monopoles, and primordial black holes. However, there are a couple of exceptions to this, which include: WIMPs and Axions.

Dark energy didn't emerge conceptually until the late 1990s when the first Type Ia supernovae measurements came to the fore. By  early 1998, the type Ia supernova results of two groups: the Supernova Cosmology Project (based at UC Berkeley) and the High- Z Supernova Search - led by Brian Schmidt of Mt. Stromlo Observatory in Australia, began to show tightening error bars.

Why Type 1a supernovae? First, because they’re bright enough to isolate in different galaxies – hence there’s a cosmological dimension. Second, they exhibit a uniform, consistent light spectrum and brightness decay profile (all supernovae diminish or ‘decay’ in brightness after the initial explosive event). This applies to all galaxies in which they appear so they function as cosmic standard “candles”. Third, all Type 1a’s betray the same absorption feature at a wavelength of 6150 Angstroms (615 nm) - so have the same spectral “fingerprint”.

Basically, the majority of plotted Type 1a supernovae data points (see graph) congregated along the upper of the two plot lines  This placed them firmly in the region of the graph we call “accelerating universe”. On the other side of the diagonal is the "decelerating region". An additional feature of the accelerating side is 'vacuum energy'.

To get an insight, we can examine the equation that underpins cosmic expansion and whether it is accelerated or not (cf. Perlmutter, Physics Today, 2003)

R"/R = - {4p / 3} G r (1 + 3 w)

Here R is a cosmic scale factor, R" is the acceleration (e.g. second derivative of R with respect to time t), G is the Newtonian gravitational constant, r  the mass density. We inquire what value w must have for there to be no acceleration or deceleration. Basic algebra shows that when w = -1/3 the whole right side becomes zero. The supernovae plot data constrains w such that it cannot have a value > (-1/2). Most plausibly, w, the ratio of pressure to density is (Perlmutter, ibid.)

w = (p / r) = -1

This is consistent with Einstein's general theory of relativity - which one could say approaches the status of a 'basic law of physics'. In this case, a negative pressure (check by solving for p)  meshes with general relativity's allowance for a "repulsive gravity" - since any negative pressure has associated with it gravity that repels rather than attracts.

Some might argue that such cosmic repulsion shows a "new law" of physics, but it's merely extending the existing concept of gravitation to show it has a repulsive as well as attractive aspect, and has always been consistent with Einstein's general theory of relativity.

What’s to become of the cosmos if the acceleration is ongoing? Clearly, photons emerging from whatever cosmic object (star, nebula etc.) can never catch up to the rapidly expanding space-time. This means that over time, fewer and fewer objects will be visible to any sentient observers. Eventually, all cosmic objects will “vanish” from the scene and all observers – if any remain- will be plunged into dark, featureless skies.

Is Pope Francis Correct? Can God "Co-Exist" With the Big Bang?

Attention has once more turned to the words of Pope Francis who, in a recent address to the Pontifical Academy of Sciences, appeared to endorse the Big Bang theory of cosmology. In his speech he raised eyebrows when he opined that there was no contradiction between having a belief in God and acceptance of cosmic expansion.  He said:

"When we read about creation in Genesis we run the risk of imagining God was a magician, with a magic wand able to do everything, but that is not so." 

He went on to add:

"Evolution in nature is not inconsistent with the notion of creation, because evolution requires the creation of beings that evolve"

Well, apart from some circular reasoning that is still not a totally valid statement. My major quibble is with the use of the words "creation" and "evolution" in the same sentence. Generally, in terms of definitions, they mean two different things and we acknowledge them to be mutually exclusive: if a being has been 'created' its genome is already complete and there is no need to evolve. If a being is evolving then it hasn't been created. "Creation" then denotes a completeness not present with evolution.

The problem with theistic evolution in any form, of course, is that it also pre-supposes a governing purpose and envisions God as some kind of divine watch maker.

From earliest times both philosophers and theologians have debated the question of whether the universe has a purpose.

Those who saw some divine purpose invariably believed the cosmos had to have been “created”. Most of these creationists appealed to a subjectively perceived evidence of “design” in the universe as an argument for the existence of a special divine creator. William Paley (1743- 1805), for example, drew attention to the complexity of structures occurring in both astronomy and biology, arguing that they could not possibly be a product of blind chance. (The Vatican, to its credit, has taken care to reject intelligent design).

In this respect, he may be said to be the father of intelligent design (ID) – now making the rounds as the latest manifestation of the belief that some kind of “irreducible complexity” is embedded in physical- biological reality that dictates one must invoke an external, “intelligent designer”.

The viewpoint of Science in general, and modern physics in particular, is totally opposed to this. This opposition has arisen not merely from logical arguments, but from experiments and observations in quantum mechanics, statistical mechanics and cosmology. In the light of these advances, Paley’s (not to mention ID’s) deficiencies are now evident.

Both physicists and biologists, for example, now recognize many systems in which order and complex activity can emerge spontaneously. In this article, I show how such recognition leads the dispassionate observer to dispense with any notion of cosmic purpose that transcends mere existence in its own right.

A biological example, based on in-vitro experimental studies of cancer tumors, is the individual tumor cell.[1] The cell appears as a fluctuation, able to develop by replication. A cosmological example is the instantaneous formation of the universe by a possible quantum fluctuation[2] that arises when one treats the conformal part of space-time as a quantum variable.

A more prosaic example is the aurora, such as I observed near Chena Hot Springs, Alaska in March of 2005. This particular aurora displayed two perfectly symmetrical parallel green “tubes”, arcing from north to south horizon. Did an intelligent designer craft two natural fluorescent tubes in the sky? Not at all. The inimitable procession to order (observed over two hours) was dictated by the (pre-existing) presence of the auroral oval around the pole and the polar electro-jet, after impinging electrons from the solar wind began to decelerate into the oval and form currents in sheets. These were then shaped by the ambient magnetic field of Earth into the two parallel tubes visible near Chena.

What do the above examples disclose? Basically, that William Paley’s famously naïve argument: “A watch must always have a Watchmaker, so also the universe must have a Maker or Creator.” is flawed and outdated.

The analogy is flawed, first, because the universe is not a mechanical contrivance like a watch. Apart from the fact that – for the most part (certain limited domains in celestial mechanics excepted) the ‘clockwork universe’ was dispelled when quantum theory emerged. Unfortunately, while the practicing physicist has long since had to adopt an indeterminate, non-mechanistic world view (e.g. guided by the experimental results from quantum physics), the same cannot be said for non-physicists, including theologians, philosophers and multitudes of laypersons.

These groups continue to labor under erroneous assumptions of causality and “order” generated almost exclusively by an ignorance of modern physics. For example, an ignorance of the fact that simultaneous measurements at the atomic level are fundamentally indeterminate. Technically, for one of the most common forms of the Heisenberg Uncertainty Principle, this may be expressed (in terms of position x, the Planck constant h and momentum p = mv):

[x, p] = -i h/ 2 p

In term's of Bohr's (Complementarity) Principle, the variables x (position) and p(momentum) are regarded as "mutually interfering observables". This is why only one can be obtained to precision, while you lose the other. In another sense, one can think of approaching a particle in such way (or with such apparatus) that it suddenly gets 'wavy'. At a particular stage of resolution, as the late David Bohm noted, the particle aspect vanishes and you apprehend a wave. But during some interim threshold one can regard it as a wavicle. Of course, if Heisenberg's principle didn't apply - meaning we could know both the position and momentum to the same degree of accuracy, then: [x, p] = 0 such that x*p – p*x = 0 spells out non-interference.

In cosmological terms, the whole concept of “order” has been relegated to a minor and tiny niche of the extant cosmos. For example, the recent balloon-borne Boomerang and MAXIMA UV measurements to do with Type I a supernovae, have disclosed a cosmic content:[3]

7% - ordinary visible matter

93% - dark component, of which:

- 70% is DARK (vacuum) energy and

- 23% is dark matter

In effect, 93% of the universe can’t even be assessed for “order” since it can’t be seen. In the case of dark matter, one can only discern its presence indirectly by the visible effects on neighboring matter. In the case of dark energy, the underlying physical basis isn’t even known – though we know the result is an increase in the acceleration of the universe (arising from a cosmic repulsion attributed to dark energy).

This is all critical, since in the past apologists of teleologism (the belief that purpose and design are part of nature) have cited a perceived “orderliness” as a revelation for the “handiwork” of an intelligent Mind, or Creator. Alas, this falls through the cracks if most of the universe is disorderly, or dark-energy-matter. Indeed, by current assessment – and discounting plasma abundance, one may reckon that even rudimentary order is evident in barely 0.00001% of the cosmos. And this can all be explained or accounted for by appeal to scientific reasoning or hypotheses. For example, the nebular hypothesis, whereby the original solar nebula progressively collapsed under the force of gravitational attraction, can account for the formation of the solar system.

Another point missed by these apologists is that there has always been a profound confusion between the principles of sufficient reason and causation. According to the former: “Nothing happens without a sufficient reason”. As Mario Bunge has observed[1]:

“Giving reasons is no longer regarded as assigning causes. In Science, it means to combine particular propositions about facts with hypotheses, laws, axioms and definitions. In general, there is no correspondence between sufficient reason and causation.”

As an example, let's say I fire electrons from a special "electron gun" at a screen bearing two holes some distance away, e.g.

At first glance, one might reasonably conclude that the electron motion is singular and follows one unique path. That is, that each fired electron traverses a single, predictable path, following stages 1, 2, 3 and so on, toward the screen. This is a reasonable, common-sense sort of expectation but alas, all wrong! The problem is that common sense is useless in the domain of quantum mechanics.

According to the most widely accepted interpretation of quantum theory[1] , the instant the electron leaves the "gun" it takes a large number of differing paths to reach the screen. Each path differs only in phase, and has the same amplitude as each of its counterparts, so there is no preference. How does the electron differ from the apple? It takes all paths to the screen, the apple takes only one (at a time) to the wall. And the electron exhibits phases (as a wave) while the apple doesn't. The electron's wave function can be expressed:

U = U (1) + U (2) + U(3) + . . . . . . U (N)

Here the total wave function for the electron is on the left hand side of the equation, while its resolved wave amplitude states (superposition of states) is on the right-hand side. If they are energy states, they would correspond to all possible electron energies from the lowest (1) to the highest or Nth state (N). There is absolutely no way of knowing which single state the electron has until it reaches the screen and an observation is made, say with one or other special detector (D). This is illustrated in Fig. 1, with each number denoting a given electron state and path.

Prior to reaching the screen the electron exists in a superposition of states or "wave packets". Is this description statistical, or individual? This depends. The wave function has a clear statistical meaning when applied to a vast number of electrons. But it can also describe a single electron as well.[1] In the example just cited, all the energy states refer to the same electron. However, if all electrons are identical, the statistical and individual descriptions coincide.

Germane to the point made earlier, i.e. that there is no correspondence between sufficient reason and causation, one finds that in a large number of cases, the approaching electron goes through both holes in the screen – not just one. This is totally counterintuitive to one steeped in the traditions of Newtonian or classical mechanics. For example, if a baseball were hurled at a wall with two six inch diameter apertures near to each other – it would go through one or the other – but not both! Of course, the electron deviates from such classical behavior precisely because of its wave nature – as demonstrated in the famous Davisson-Germer experiment that verified that particles exhibit wave properties.

The point emphasized here is that this deviation means that in specific spheres (mainly in science, specifically in modern physics) conventional logic and thinking are of little or no use. A number of researchers, authors, for example Hilary Putnam, have argued that the distributive law of classical logic is not universally valid[6] Much of his reasoning (which is beyond the scope of this article) has to do with the peculiar nature of Hilbert spaces that are part and parcel of the underpinning of quantum mechanics.

Interestingly, it is this very indeterminacy that also resides at the core of many quantum bootstrap models, allowing for the spontaneous inception of the cosmos. People have serious problems with such models and ways of thinking because: a) they fail to appreciate the lack of correspondence between sufficient reason and causation, and b) they fail to understand that causality predicated on classical logic is no longer applicable to many areas of modern physics.

While further conceptual/conceptual development remains (the work of science is never final) it is clear that any postulated purpose in the cosmos can already be regarded as a redundant anachronism. If the cosmos can “bootstrap” itself into existence via quantum fluctuation, and acquire “order” (even in highly limited domains) via the implicit laws of statistical and thermal-quantum physics – then it has no need of a “creator” (or “designer”) and no purpose other than to exist. No extraneous being is necessary to ensure its continued stability or existence. More bluntly, the addition of such a being doesn’t advance the quality of our research, or improve our predictions by the most remote decimal place. Hence, to all accounts such a being (or purpose) is totally superfluous.

Thus do humans, as generic offshoots of the cosmos, have any purpose other than to be. If they seek an additional purpose, they must craft and forge this subjectively of their own accord – rather than looking for it on high.
 

Does this imply that the concept of “God” is outright useless, null and void? Not at all. It merely requires that we re-think the concept so that it is consistent with the absence of higher or extraneous purpose. As Bernard d’Espagnat notes [7]:


“The archaic notion that is conveyed by the words ‘Lord’ and ‘Almighty’ will presumably never recover its full efficiency for lulling the ontological qualms of mankind. For a religious mind, turning towards being should therefore become a subtler endeavor than the mere acceptance of the heavenly will stated in the Bible, formulated by the priests, and exhibited by miracles.”

Finally, the abolition of extraneous higher purpose should not incur any psychic loss for humanity. As Marilyn French has aptly observed:

“It is a loss of dignity to define humanity as a race defined to please a higher Being, rather than as a race whose only end is to please itself. The ‘gift’ of purpose to the human race is thus very expensive: one can fulfill one’s God-given purpose only by sacrificing felicity while one is alive.”

In the end, as I have noted before, it all hinges on one's definition of "God".  Francis then is definitely correct that there is no inconsistency of God belief with the Big Bang - but that is only applicable if we refrain from invoking a personal deity and opt for an impersonal but transcendent Being instead. More on this in a future post.


[1] Garay, R.P. and Levefer, R.: 1978, Theoretical Biology, 417, p. 73.

[2] Padmanabhan, T. 1983, ‘Universe Before Planck Time – A Quantum Gravity Model, in Physical Review D, Vol. 28, No. 4, p. 756..

[3] See: Physics Today, July, 2000, page 17.

[4] Bunge, Mario: 1979, Causality and Modern Science, Dover Publications, p. 231.

[5] Due to Richard Feynman. See, Herbert, N.: (1985), Quantum Reality - Beyond the New Physics, Doubleday, New York, pp. 115-117.

[6] Putnam, H., ‘Is Logic Empirical?’ in R. Cohen and M. P. Wartofski (eds.), Boston Studies in The Philosophy of Science 5 (Dordrecht, Holland: D. Reidel, 1968). Reprinted as ‘The Logic of Quantum Mechanics’ in H. Putnam, Mathematics, Matter and Method, Cambridge University Press (1976).