Selected Questions (And Answers) From All Experts Astronomy Forum (Big Bang, proper time, quantum cosmology etc.)

The following were culled from cosmology questions asked on the All Experts Astronomy forum over 2010--2012:


1-What is the evidence for the Big Bang and how was it discovered?

The evidence for the Big Bang is the 2.7 Kelvin degree, cosmic background radiation. The key aspect that makes it evidence is that it has the same intensity in all directions- wherever one observes in the sky. No ordinary radiative or local explosive source (e.g. supernova) would produce such a characteristic. The only feasible explanation to account for it would be a vast “explosion” occurring in the distant past and affecting the entire universe. Its entire volume.

The isotropic (all directions) radiation was discovered during a sky survey at the Bell Laboratories in 1965, by Arno Penzias and Robert Wilson. They had pointed their radio telescope in different directions in the sky and received the same “buzz” no matter where they observed. After rigorous data reduction (removal of data detritus and effects of bat guano), plus later confirmation of the “universal buzz” - it was later identified by Robert Dicke as the cosmic microwave background radiation (CMB), the radio remnant of the Big Bang, they realized they’d discovered the relic radiation left over from the Big Bang.

In 1978 the pair received the Nobel Prize in Physics for their discovery

2- If there was a Big Bang can we say the universe had a beginning, or not? What came before the Big Bang?

Asking ‘what came before the Big Bang’ is like asking ‘what’s north of the north pole?’ It’s the kind of question that at first glance seems logical, but really isn’t. The key thing here is that the time continuum we use to measure instants or epochs starts at the Big Bang, using the Hubble constant. Going to epochs before the Big Bang isn’t feasible because there is no temporal template to go by.

Though we can use the current Hubble constant to measure the proper time since the Big Bang as 13.7 billion years we can’t go any further than that. Or, into any “negative times” – as defined “before the Big Bang”. The reason is that so far there is no physically operational meaning to these.

3- You mentioned “proper time” – what’s that?

Proper time   τ   is defined in terms of the relativistic factor  (from special relativity):

g  =   [(1 - v  ²/c²)  ^-1/2]  

where v is a specific velocity- say of an observer’s frame, c is the speed of light.

Then the proper time is:   dτ   = dt/ g

Reversing the above, we can say that when the (relativistic) clock advances by increment dτ   then  the clock time that elapses on Earth is given by:

dt  =    g   dτ  

Why use proper time? Basically, because normal time measures are unreliable and subjective owing to relativity. For example, even saying or asserting the energy is greater or less at one time (t2) than time (t1) is impossible since energy (like mass, time, length) varies depending on the observer’s frame.

For example, consider the energy of an object moving at velocity v in the simple diagram below:


But, to the observer O moving in a reference frame with the same velocity, the object appears at rest so its kinetic energy = 0. In more technical consideration, on the basis of the Lorentz transformation (google!) the energy E’ in a new frame will depend on the energy E in an older frame according to:

E’ =  g _o (E –  v _o  p _x )

Where  v _o is the velocity and  p _x   the momentum in direction (x).

The factor  g _o   =   1  / [(1 - v _o ²/c²)^½]  


The point is that the energy in the new frame E'  depends on the momentum in the old frame, p _x . If this momentum is not conserved, then energy won’t be conserved in the new frame.

Note here that the relation of the new p' _x momentum  to the old,  p _x is:

p' _x    =  g _o (p _x   –  v _o  E/   c² )

Bottom line, unless one employs corrections using proper time to make energy estimates or statements, he will end up talking nonsense.

For example, let’s say you are looking at an object receding at a velocity of 0.5 c, and assert based on careful ordinary time measurements that it emerged 1 billion years after the Big Bang. Or – 12.7 billion year removed from your observation. But how does this compare to the proper time?

We have: dτ  = dt/ g

Where dt = 12.7 billion yrs.

g  = [1 – (0.5c/c) ²]  
 
 = 1/  Ö[1 – (0.25)] = 1/  Ö[0.75] = 1.155

Then the proper time interval dτ   is: (12.7 x x 10 ⁹  yr)/1.155 = 1.1 x x 10¹⁰  yr

Or 11 billion years not 12.7 billion.

This obviously also means that one cannot say or assert that from the Big Bang there has been “an infinite” amount of time, or instants. No, there hasn’t, and one can do the computation for the actual time interval using the proper time format.


4- What is meant by Quantum Cosmology and how does it work? Can it explain the Big Bang?

Quantum cosmology means that we use terms, conditions and parameters that are peculiar to the quantum level – for example quantum variables – in examining how they might work in explaining aspects of cosmology and yes, origins.

Quantum cosmology also is not for the faint of heart, or those who haven’t done a lot of physics – including taking quantum physics courses. In other words, one can’t simply approach its basis or claims using common sense or even ordinary logic. I believe it was Richard Feynman in one of the prefaces to his lectures who wrote: “Don’t even try to go down the rabbit hole of understanding quantum mechanics, or you will be lost forever.”

What he meant by that is that we don’t approach quantum formulations on the basis of trying to understand them, like one might wish to understand how an electronic amplifier works. We approach them from the mathematics we use, and let those math results lead the way.

At least one theory of the origin of the cosmos uses quantum cosmology in what we call “quantum bootstrapping”. This means, formulating a quantum fluctuation which could have incepted the cosmos via the Big Bang.

The starting point for these sorts of theories actually resides in a real world phenomenon. Particle production is one- wherein particles are created then quickly destroyed with energy release.

The typical pi meson (call it p ) lasts 10 ^-16 sec then vanishes yielding two gamma ray photons in its wake,viz.

 p    -> g   +   g

Thus, rest energy is real energy and is capable of doing work. In the case of the pion above, the total mass 2.4 x 10^-28 kg, is converted to electromagnetic energy.

The amount of the energy can be estimated using the Heisenberg Uncertainty Principle in the energy-time format:

D E D t   <  ħ  (where   ħ   is the  modified Planck constant: 

 h/ 2p =   1.05 x 10^-34 J-s

Thus,  if the time uncertainty for disappearance of the pi meson is:  D E = 10^-16 s

Then the energy available that comes off is:

   D E =    ħ  / D t   = 1.054 x 10 ^-18  J = 6.5 eV

In the same manner, a number of theoreticians (e.g. T. Padmanabhan) have speculated the universe could have emerged like the pi meson using the same basis for energy arising out of “nothing”.

Padmanabhan’s full paper: Universe Before Planck Time – A Quantum Gravity Model, can be found in Physical Review D, Vol. 28, No. 4, p. 756.

The Vatican's Big Bang Conference: Does George Lemaitre's "Theory" Prove A Supernatural God?

The news this past week out of Rome is the Vatican celebrated the big-bang theory. What? Big Bang? The theory whereby the cosmos incepts from an "explosion" (super dense state) and needs no external divine agents? Yep, one and the same, but the Vatican is not deterred and believes firmly there need be no conflict between its proclamations and the findings of modern cosmology.

So it's not entirely odd that the Vatican Observatory has invited some of the world's leading scientists and cosmologists to talk about black holes, gravitational waves and space-time singularities as it honors a Jesuit cosmologist  (George Lemaitre) who is considered one of the fathers of the idea that the universe began with a gigantic explosion.

The May 9-12 conference honoring Lemaitre was held at the Vatican Observatory, founded by Pope Leo XIII in 1891 to help correct the notion that the Roman Catholic Church was hostile to science. The perception has persisted in some circles since Galileo's heresy trial 400 years ago, but let's face it the perception is not entirely without foundation.  Recall, for reference, how Stephen Hawking noted in his book, 'A Brief History Of Time', how Pope John Paul II warned against trying to investigate the "moment of creation" at one cosmology conference Hawking attended at the Vatican.  Of course, this is the very moment one does want to investigate - or at least as close to it as possible.

Hawking's formulation of the universe's inception spontaneously can be described via the diagram below:

This was explored in detail in the episode God and the Origin of the Universe in the "Planet Green"  'Curiosity' series some five years ago. By the end of the program even a person with no mathematical background could grasp Hawking's simple arguments which followed from gravitational time dilation, e.g. the slowing of clocks as experienced near black holes or other gravitating masses.

Understanding Hawking's arguments even at a basic level, requires a few preliminaries. First, at a basic logic level, we agree and understand that to have causal agents or causality we require time. If there is no time evident or existent, then there can be no nexus or connection from event A to event B. It is time- the chronometric passage of some interval- which allows one to say, e.g.

(Event A) -> (Event B)

If on the other hand, the two events occurred with no time passage, one wouldn't be able to infer causality, say that Event A "caused" B.

Second, we need to grasp at least at a qualitative and rough quantitative level that time slows down in the vicinity of gravitating masses. The way this is approached is usually by using what's called a "metric tensor" such as shown in the bottom half of the lower diagram There are 16 components in this tensor, each of which can be measured by means of clocks...atomic or other. For the form of the metric tensor shown, we have elements conforming to a spherically symmetric distribution with r the radius or distance from the center.

See also my earlier post on general relativity, e.g.

http://brane-space.blogspot.com/2014/12/a-look-at-general-relativity-and_27.html


To operate in a typically curved space-time (x,y,z,t) one will usually use what's called the "interval" such that:

ds² = {1 - 2GM/r}dt² - {1 + 2GM/r}(dx² + dy² + dz ²)

The key component used in gravitational time dilation measurements is the one at the very upper left of the matrix which we denote by g _0o. All experiments on gravitational time dilation can be regarded as direct measurements of the g _0o component of the metric tensor. For all comparisons with actual experiments, it's convenient to express chronometers at two different distances, say:

dτ2/ dτ1 = [g _0o(2)]^1/2  / [g_0o (1)] ^1/2

it's convenient to use fractional deviations, e.g.

Dτ/ τ = (dτ2 - dτ1)/ dt ~ GM {1/r1 - 1/r2}

The clock rate can also be related to the frequency f. If a clock registers a large elapsed time it must be ticking fast, and if a small elapsed time, ticking slow. Thus the frequency difference, D f, must be proportional to D τ, or:

Df/f = (f2 - f1)/f =  D τ/ τ ~ GM{1/r1 - 1/r2}

Cutting to the chase and sparing readers a lot of algebra, one ends up with:

D τ/ τ = g [ D r/ c² ]

As a terrestrial application, say D r = 10 km (the typical height attained by an aircraft) the time dilation is:

Dτ/ τ = 10 ^-12 

Now switch to the Hawking's black hole example, and one finds as one approaches the center of the hole, at which r = 0, there is no time, period. This is also the point of maximal gravitational acceleration, call it g = ¥, or infinite. Thus:

Dτ/τ = ¥ [ 0/c² ]= D f/f = 0

In the above we have assumed the reference clock is right at the black hole center, and the difference is now 0. Then the time elapsed is zero. This is confirmed - well, the tendency of clocks to slow in g-fields is confirmed by hydrogen -maser clocks and others. (See, e.g. 'Gravitation and Spacetime', by Ohanian and Ruffini, p. 183. In effect, one simply extrapolates to the most extreme g-field, present in black holes, to infer no time passage that can be reckoned by any chronometer.

If there is no time passage, there can be NO cause! There can be nothing which causes the universe in the first place, hence...no "supernatural agent" as "creator". Since we already agreed that for causality to operate time must exist, then conversely, if we find time doesn't exist then there can be no cause or causal agent.

Hawking's final argument, illustrated by the top illustration in the lower diagram, is simply that the cosmos (originally with less diameter than a proton) simply "popped" into existence much like we currently observe particles in pair production doing the same via spontaneous quantum fluctuations using the energy-time uncertainty principle. The basic principle underlying these pair production processes is the energy-time uncertainty principle: dE dt > h/2π where h is the Planck constant of action. . Thus, a brief fluctuation occurring over time dt can produce a change in energy dE, which may be sufficient to produce particles. The energy has an estimated magnitude given by the uncertainty principle.

Hawking's other point is that the manifestation of mass in the cosmos always has a complementary action in forming negative energy. He used the analogy of a person forming a large mound or hill by digging into the ground. The larger the hill formed, the bigger the hole from which the hill was excavated. All that negative energy is now scattered across space, as bound systems via gravitational potentials. These potentials represent negative energy reservoirs. For example, gravitational potential energy, say associated with a planet's g-field might be expressed: V(r) = - GMm/r.

If all the positive and negative energy contributions are tallied, the total comes to zero. This zero energy indicates that no agents acted to create the cosmos. We didn't need a "hole digger" to get positive mass from "digging a negative energy hole" because it already inhered in the subatomic cosmic hyperdense state. Moreover, we're still seeing -observing the effects of the initial repulsion of the unstable primeval "atom" as all parts of the cosmos continue to accelerate during the expansion of space.

However, the head of the Vatican Observatory, Brother Guy Consolmagno, says you can believe in both God and the big-bang theory. He bases his argument on Lemaitre's theory of the "primeval atom" and - to give credit where it is due - Lemaitre was the first to explain the recession of distant galaxies (called the "expansion of the universe").   He arrived at this result by solving the equations associated with Einstein's theory of general relativity, see e.g. the content in the link above. According to a Vatican press release:

"He understood that looking backward in time, the universe should have originally been in a state of high energy density, compressed to a point like an original atom from which everything started".

But is this enough basis to believe in both God (as a supernatural entity) and the big bang theory? Not really, and Brother Guy does not bother to go into the further details that it was actually a trio of physicists (Ralph Alpher, Hans Bethe and George Gamow) who get more credit for the big bang theory via their 1948 paper published in Physical Review. That trio actually came closest to predicting the major outcome, the temperature of the cosmic microwave background temperature.  That is, there exists a "relic" radiation comprised of thermal microwaves from the big bang detectable even today. Further, the spectrum must match that of a black body.

They did this by way of a meticulous assessment of primordial nucleosynthesis at that epoch and assuming that the latter was radiation dominated. Gamow himself made an original estimate of the CMB at 10 K (some sources say 50 K) but his collaborating students Ralph Alpher and Robert Herman, later refined that to 5 K in a further paper (Physical Review 74 (12): 1737–1742, 1948).  By 1965, Arno Penzias and Robert Wilson at Bell Laboratories discovered the CMB at 2.7 K. 

There is some dispute here concerning the "ABC" paper as it was called, and that in fact it was a Canadian cosmologist - Andrew McKellar - who predicted the CMB temperature first and most accurately in a 1940 paper. This paper emphasized "excellent coincidences obtained between the wave lengths of three of the unidentified, sharp, interstellar lines and lines arising from the lowest states of the CH, NaH, and CN molecules"   and hence “the maximum ‘effective’ temperature of interstellar space would be 2.7K”. 

My point in respect of the preceding is that while Lemaitre did great original work he did not make any actual predictions, say for what background cosmic temperatures would be detected.  And hence his hypothesis fell short of being an actual big bang THEORY.  Remember, a theory is a hypothesis which has actually made predictions that have been confirmed.  Alpher, Bethe and Gamow met this standard, Lemaitre did not.

Brother Guy Consolmagno's remark to the Vatican and international press that "Christians believe in a supernatural God who is responsible for the existence of the universe" is fine as a statement of faith, but alas, is not scientific. Nor is it based on any objective scientific evidence.  He added that "our science tells us how He did it" but again, that begs the question of why one needs to insert a special supernatural agent-creator at all. Hawking's work - as I showed - indicated this is superfluous.

These distinctions are important and even Lemaitre conceded his conclusions were largely based on faith, not science, i.e. when he reminded Pope Pius XII "the creative act of God was not something that happened 13.8 billion years ago, it is happening continually".   In other words, as a Christian this is what he believes - but it is not a scientific conclusion. At least not in terms of a supernatural deity.

As I noted in my ASTRONOMY magazine article:  ‘The God Factor’ (Astronomy Forum, March, 1990), science selectively excludes problems for which no practical method of inquiry exists. The supernatural, which is neither measurable or verifiable, falls into this category and that includes ‘God’ - if depicted as "causeless" and "supernatural". More to the point, we tend to regard unproven, non-evidentiary agents claimed by virtue of belief alone as evocative of superstition. 

The key fallacy embraced by the Vatican appears to be ignotum per ignotius : postulating an unknown agent or cause to account for a not well understood process or entity, e.g. consciousness or the origin of the cosmos.

Congressman MORON BROUN: "Science is from the Pit of Hell!"

"YEEEESSS, I'M THE ONE THAT INVENTED THE BIG BANG THEORY, EVOLUTION AND EMBRYOLOGY! FROM THE PIT OF HELL!"


 Yes, another Confederate congress-ass cum yahoo - this time from JOH-JUH. He is Rep. Paul Broun, a Republican (which I can believe) and a "medical doctor" (whose patients I am truly sorry for ...if that is so) who recently yapped at a Sept. 27 Sportsman's Banquet that "Evolution, The Big Bang Theory and Embryology are ALL lies from the Pit of Hell".

And to make it crystal clear, this bozo added:

""And it's lies to try to keep me and all the folks who are taught from understanding that they need a savior"

Errr.....no. Evidently they like you need something more tangible: COMMON SENSE and intellect!

Incredibly, this jackass sits on the House Committee on Science, Space and Technology. No, seriously! And for that, we all ought to be concerned because the fool has essentially tabbed the basic core of modern science has having been gestated within a fantasy bogey land existing only in his febrile mind.

Let's take the Big Bang Theory first! It's been essentially confirmed with the discovery of the 2.7K isotropic microwave radiation (by Penzias and Wilson, in 1965) and for which they won a Physics Nobel Prize.  Is Broun therefore asserting the Nobel Prize Committee was put together in the "pit of Hell" to award a Nobel Prize for the Big Bang's consummate discovery? If so, he needs to resign forthwith from his committee.

The Big Bang is also supported by the recent detection of the Higgs boson. How or WHERE does the Higgs enter the picture? The so-called 'Standard Model' is generally defined as the symmetry:


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

where each of the above represent different matrices

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. WIth the Higgs discovery, this temperature T_qb has been identified and with it the epoch and the mass -conferring mechanism post Big-Bang.

Then again, the observed cosmic expansion and the Hubble constant (H _o ) associated with it allows us to compute the age of the universe itself, from the putative beginning in the Big Bang. Currently, we have  H _o ~ 70 km/ sec/Mpc, where Mpc denotes ‘megaparsec’ – and each parsec has 3.26 light years.

The above is little use, however, without changing a lot of units and ensuring their consistency. The key initial step is to obtain the megaparsec equivalent for kilometers:

MPC(km) = (c) (86400)(365.25)(3.26)x 10^6

where c = 300,000 km/sec, the velocity of light

Then: MPC(km) = 3.08 x 10^19 km/Mpc

Now, what is usually colloquially called the "Hubble constant" is in reality the Hubble scale factor (a = 70 km/ sec/Mpc). The REAL Hubble constant (H_o) is the scale factor divided by MPC(km):

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


then, t_o = 1/ H_o = 1/ {2.26 x 10^-18 /s} = 4.4 x 10^17 s

Which,when converted, is about 1.3 x 10^10 yrs. or 13 billion years in age.

Of course, we see here why Broun-Moron wouldn't accept the Big Bang since according to yesterday's AP story on him, he "believes the universe is about 9,000 years old as is the Earth and was made in 6 days."

Again, HOW the fuck can this fool be a member of any Science and Technology committee? Are we now into appointing blithering imbeciles? Well, given the fact that if the repukes take the Senate they intend to appoint Tom Coburn ("Global warming is a HOAX!") I guess we are.

Then there's Evolution which as a theory means it's really confirmed FACT!

For example, the theory of evolution as it applies to the elements of common descent, predicts humans and chimpanzees ought to have very nearly the same cytochrome-c protein sequence. This has been found to be the case. It also predicts that the two ape chromosomes designated 2p and 2q ought to be fused in the human to be one: designated '2'. The theory of evolution has also predicted the full evolutionary development of foraminfera and this is validated.

If Broun doesn't accept evolution, then he's flunked the most basic test for qualification to sit on a congressional Science and Technology committee.

What we need is for this turkey to have the full faith of his stupid convictions and resign immediately. If he believes science has been confected in the 'pit of Hell' he has no business sitting on ANY science -associated committee!