Selected Questions -Answers From All Experts Astronomy Forum (Gravity Wells)

Question -

I actually have two questions, I know that the answers may be highly
theoretical because of limited knowledge we have of black holes, but any
answer - even theory - is welcome.

1. If a photon has no mass, how come light is drawn into a black hole?

2. What method of propulsion do black holes use the move themselves
through space? How is their movement in a vacuum achieved?

Thanks for your time mate

Answer -

You are quite correct in assuming that the answers are 'highly
theoretical', and I don't see how these can be made much simpler than
provided below.

First, a physical definition. For a term we call "inertia". This is any
resistance to change in position or motion.

You can think of it as a kind of "foundational" mass. It is the most
basic, fundamental concept we have by which "mass" can be recognized.

That is, when we perform an experiment and find that 'X' (whatever 'X' is)
exhibits a resistance to change its position or motion.

Keeping that thought in mind, we come to the photon. We already know that
light carries energy, usually expressed in a simple form as:

E = hf

where h is the Planck constant, and f is the frequency of the light.

But what many general readers do not know is that light also carries
momentum. For example, whenever light is emitted from some source there is
a tiny but definite "recoil" effect. (Something like you experience from
the stock of a rifle, if you've ever fired on a rifle range).

This recoil betrays the presence of what we call "momentum" to do with the
photon.

This is given by the product of one over its speed (1/c) times the energy,
E. Writing the momentum as p:

p = E x (1/c)  = E/c


We already have a good hint that photons have mass-inertia associated
with them from Einstein's equation:

E =  m c ²     (E = mass x speed of light squared).

Therefore, the mass is:

m =  E /   c ² (Energy divided by speed squared).

This equation (above) can be combined with the earlier one we obtained

 (E   = p c) to give:

m = p / c

Thus, the "mass" associated with a photon is its momentum divided by its
speed, c.

Other experiments validate this, including one in which a (true) radiometer is
bombarded with light, and turns it vanes - spins them around. This is a
result of the pressure of light exerted on the vane surfaces. (You perhaps
have seen this device in action, though most of them are really toys that
operate on a different principle from the real ones).

Basically, light cannot possibly exert any "pressure" unless it also
carries mass, or inertia.

Having said all this, it is important to recognize that in all these cases
I've noted we are looking at photons MOVING!

Once they cease to move, they no longer exhibit mass.

Thus, what you are really thinking of when you say "if a photon has no
mass", is REST MASS. The mass it exhibits when at rest.

And, of course, this is zero.

Hopefully, you can see from the above, that there is no contradiction. The
light that is prevented from escaping from black holes or drawn into them,
is moving - NOT at rest. Hence, it exhibits all the properties of mass or
inertia.


Regarding your second question, black holes like the stars they collapsed
from occupy specific regions of space-time. Hence, they are not
"propelled" like rockets or anything.

Rather, as part of a dynamical system (say the galaxy) they will move in
accord with the Newton's law of gravitation - given their distance from
the mass center of the galaxy, and the nature and masses of nearby bodies.

Since space itself is a vacuum, this motion is no more mysterious than the
planets of our Solar System moving "through a vacuum". Vacua provide no
impediment to motion, and indeed, every body in the cosmos will move under
the influence of the gravitational forces at work in its neighborhood.

The bottom line is that the presence of gravity means that NO body in the
universe can remain "still" or "motionless".

Peculiarities of the Fine Structure Constant

Spacing of spectral line shifts depends on the fine structure constant. It's been found that different spectra are obtained in the lab vs. obtained from distant quasars with light passing through gas clouds.

In the table presented in my March 18th post, the fine structure constant is shown on the last line with a value of  a   =  1/ 137.035999139 or approximately, 1/ 137.   Note the value is the same irrespective of the system of measurement because this constant is a pure number - there ate no units attached- unlike the other constants I covered.  Indeed,  a    is an amalgamation of several other constants including the electron, the speed of light and the Planck constant. We can write, for example,


 a   =  1/ 4p e _o    { e² / ħ c }   where:     ħ  =   h/ 2p


Physicists keep track of the fine structure constant by using quasars. Also called "QSOs" for quasi -stellar objects, these are active galactic nuclei of extremely high luminosity powered by supermassive black holes. As shown in the diagram above, on its way toward Earth the QSO's light passes through gas clouds which absorb light of particular frequencies producing gaps - also called absorption lines - in the otherwise continuous spectrum.  The typical profile of such an absorption line is shown below, this one centered at a wavelength of 5889.95 angstroms:

As can be seen from the absorption line profile there is a variation in the line "darkness"  with the maximal degree at line center where the absorption coefficient is greatest. This then falls off in what we call the "line wings".   (Note here that  D u_D  is the Doppler half-width of the line.)  The point is that the locations of these absorption lines depend on the fine structure constant. Thus, variations in the spacing of the lines in space or time might indicate the value of  a    has changed.

Is there evidence for such variations? In 2011, in a paper appearing in Physical Review Letters, John Webb of the University of New South Wales and colleagues reported the fine structure constant increases in one direction in the sky and decreases in the opposite direction. Almost if some special axis was running through the universe. Of course, no physicist would be content with such "specialness" or uniqueness. By the cosmological principle such behavior of a   ought not depend on directions. (And in this regard even Webb counts himself as a skeptic, as he should).

In fact, a compelling alternative explanation has been put forward by Michael Murphy of Swinburne University of Technology in Melbourne, Australia.  He suggests the logical take that telescope calibration issues are to blame for the apparently changing value of a.   Using measurements free of calibration issues, the value of  stays put, as Murphy et al reported in the Monthly Notices of the Royal Astronomical Society.   See also:

https://arxiv.org/abs/1606.06293


It should be noted, however, that Murphy et al's findings do not rule out actual variations in  a  with respect to the part of the sky observed by Webb in 2011.

Here's an interesting side thought to ponder: What if, instead of a   = 1/137 (approximately) it had been 1/ 130? Say during the birth of the universe. Then it seems clear the cosmos would have been set on a path to being barren, empty.

As an interesting historical aside, Sir Arthur Eddington arrived at a value of a   = 1/136 by taking the ratio of two "naturally occurring units of action". ('Great Ideas and Theories of Modern Cosmology', 1961, p. 178).  He chose one unit of action as the quantum for radiation, or  ħ  =   h/ 2p  and the second as the action for elementary particles, or e² / c.   Then, taking:

{e² / c}/  ħ  =  1/ 136

Curiously, Eddington wasn't bothered by the divergence (from a   = 1/137 )  , and just introduced a "fudge factor". This "was for obscure reasons that are difficult to understand". Perhaps, in the end, he was simply mesmerized by a kind of 'numerology' . Eddington also came up with a quadratic equation: 10x²  +    136x +  1 = 0,  linking his  fine structure result with the mass ratio of the proton to electron, i.e. in terms of the ratio of its two roots. From there, Eddington parlayed his fine structure and other pure number results into a kind of "universal theory" linking every aspect of the cosmos in a kind of romantic quest. Much like Kepler before him, with his "harmonic geometry"  in which the five Pythagorean regular polyhedra dictate the structure of the universe and reflect God's plan through geometry.

We shouldn't be too hard on Sir Arthur  (or Johannes Kepler) as he wasn't the first scientist to be taken in by numerical relationships, "harmonic" ratios, and "precision" theoretics. Nor will he likely be the last.  Even today we behold "scientists" seriously working on the so-called "anthropic principle". This  nonsense is based on the fallacy (due to a misunderstanding of physics units, dimensions) that there is an implicit "fine tuning". This in turn depends on a putative "fine precision" - but that is almost always based on the choice of units.

Thus, saying stupidity like "if the neutrino mass were 1 part in 10 ³⁵  smaller there'd be no expansion of the universe" is like saying that if Lebron James were 1 part in 10 ¹⁶  shorter he'd not have been a great basketball player! 

New Work Now Underway To Update Basis For S.I. Units Via Fundamental Constants

Above: Diagram showing the fundamental units of the S.I.  (International System of Units) - inner circle, which in a new endeavor will be defined by the seven fundamental constants occupying the outer circle.

Table showing fundamental constants and their role in the universe, current values.

Fundamental constants, units and dimensional analysis lay the groundwork for physics, since above all physics is a science of measurement and obtaining correct values while recognizing the associated errors is essential. We begin with the base  and derived units for the S.-I. system given in the link below:

http://physics.nist.gov/cuu/Units/units.html


These are now all in the process of being updated, revamped (by 2018),   based on use of fundamental constants as opposed to clumsy, arcane and too abstract ways of definition.  For example, up until 1983, the meter - the fundamental unit of length  - was defined:

"The length that is exactly 1,650, 763,73 time the wavelength of the orange light emitted when a gas consisting of the pure krypton nuclide of mass number 86 is excited in an electrical discharge."

That was recognized as too unwieldy and so since 1983 the new definition is in terms of the fundamental constant c, the speed of light in a vacuum:

"The meter is the distance light travels in a vacuum in 1/ 299, 792, 458th of a second ."

The string of digits in the denominator merely reflects the current high precision value of c , or c = 299, 792, 458 meters per second. The other base S.I. units also need to undergo similar redefinitions.

For example, the kilogram (basic unit of mass) is:

"the mass equal to the mass of the International Prototype of the Kilogram (IPK, also known as "Le Grand K" or "Big K"), currently housed as a 137-year old chunk of platinum -iridium metal in  a vault outside Paris".

How weird is that? Also, what if a reckless bug were to somehow climb onto it and get permanently affixed and altered the mass by one millionth of a kg? No big deal? Wrong! A big deal because then the whole standard mass is thrown off.

Then there is the Kelvin, the unit of temperature, currently defined as referenced to the temperature and pressure (standard) at the "triple point of water" or where it exists concurrently as solid, liquid and gas. A totally arbitrary definition that gives more physicists indigestion than you'd like to believe and need to be changed to a more rational basis.

Add in now the ampere which is currently defined:

"The current produced that - when flowing through two infinitely long parallel wires one meter apart- would produce a force between them".

This is also somewhat of an arbitrary and wacky definition given it is impossible to manufacture two infinitely long copper wires (or other) and hence to create a current that can be measured realistically.

So all these units are now in the process of revision, updating.  The next one up is the kilogram which will be revised based on refining Planck's constant- which we've seen multiple times before -  e.g. in the posts on Quantum Mechanics I did in the late summer of 2014.

The value of the Planck constant is currently:

h = 6.62607  x 10^-34 kilograms time meters squared per second

Or writing in shorter form:

h =  h = 6.62607  x 10^-34 kg m ²/ s

To get h to the point it can be used to redo the kilogram physicists (actually a specific subset called metrologists) need to get the measurement accuracy to two millionths of a percent, or at least out to seven decimal places.  Further, several measurements, preferably from different sources, need to be done and all need to agree.

Once that hurdle is crossed, the value of the Planck constant can first be fixed, then the kilogram:

So if we have h fixed, then:

kg = h/  (m ²/ s )

The meter is already defined in terms of c, as shown above, and the unit for time, the second, is given as independent of varying astronomical time, or:

"the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom."


While that sounds nerdy and clumsy too, it is defined to a specific atomic transition event, and is measurable. It also - as I said - removes the definition from solar observations, and the vagaries introduced by Earth's varying rotation rate.

Several teams are now working on the Planck aspect. One is using a device called the watt-balance to compare the electromagnetic force to the force exerted by gravity.   This may sound difficult if not impossible, but thanks to new quantum mechanical methods of producing voltages it's no big deal. An object's mass can be directly related to the Planck constant.

In another method, physicists are making use of exact (perfectly formed) spheres of silicon. Since atoms in the sphere are placed in a 3D crystal grid, the number of atoms can be deduced from the volume of the sphere. The result is the Avogadro constant, e.g.  from the table shown above:

N_A  =  6.022140857  x 10 ^23/  / mole

Other constants will also need to be reworked, and one of these - the fine structure constant - poses particularly hairy challenges, and will be the sole topic of a future post.

For now, we are confident by late next year a new set of fundamental units - based on 7 fundamental constants- will be ready for application.

Once this threshold is crossed, we can be more confident in our calculations requiring actual physical quantities.  Remember, a physical quantity is comprised of basic units which have one of the dimensions (M, L, T, etc.).

For example:

Velocity or speed is defined:  L T ^{- 1}

Or  length (L) per unit time

Similarly, an acceleration would be: L T ^{- 2}

And a volume would be:   L³


Force would be expressed:  M L T ^-2


Or,  simply mass (M) times acceleration ,( L T ^-2) according to Newton's 2nd law, F= ma.

Looking at Basic Atomic Physics (1)

1.The Rutherford Model of the Atom.

 What may be called the first foray into basic atomic physics by which further theory could be built upon, commenced with the Geiger and Marsden experiment – first suggested by Lord Rutherford in 1909. The basic setup is depicted in the rough sketch below:

Fig. 1: Basic Layout of the Geiger-Marsden Experiment

From the Rutherford experiment design, Geiger and Marsden made use of a source of alpha particles to bombard a thin metal foil, on the other side of which was a detecting zinc sulfide screen. They found that while most alpha particles arrived at A, in the direction shown, a few also scattered to positions at B and C which could be detected when the screen at A was moved to the other positions.  The nature of the scattering and deflections (especially some alpha particles at very large angles) was such that there had to be a highly concentrated charge or “nucleus” at the center of the atom. Since the alpha particles are relatively massive (at about 4.002 amu each) the deflections at wide angles meant nearly all the atomic mass was concentrated in the center of the atom and electrons were in the distant outer regions.

Rutherford thereby proposed a model of the atom in which nearly all the mass was concentrated in a very small nucleus while the electrons were scattered at some distance away. This is depicted below in Fig. 2.

Fig. 2: The Rutherford Model of the atom The key consequence was that the Rutherford experiment, carried out by Geiger and Marsden, showed that the “pudding pie” model of J.J. Thomson was incorrect. If Thomson’s model was correct, then the expected deflection could be no larger than 0.0001 radians or less than a degree. Since the observed deflections were in some cases more than 100 degrees, it failed the experimental test. Despite this success, Rutherford’s model still hadn’t won the day. It was largely accepted because it could quantitatively alpha-scattering by thin foils. His model could not: 1) explain line spectra in atoms, including both absorption and emission lines, 2) account for the stability of atoms and could only account for half the nuclear mass. 2. The Bohr  Model of the Atom. The Bohr Model of the atom, proposed by Neils Bohr, directly challenged the Rutherford model by showing how the observed emission and absorption lines of spectra could be explained. At the heart of Bohr’s model was simplicity, with the hydrogen atom – for example – configured to a miniature solar system with the nucleus at the center and the electron in orbit around it. Fig. 3: The Bohr Model of the atom. From the diagram the electron (e) orbits at a radius r from the central nucleus of charge Ze. As with the planets, a centripetal (inner directed force) F acts toward the center.  Bohr’s major concept was to quantize the electron orbits. He proceeded by first quantizing the angular momentum of the orbit: m vr  = nh/ 2p  = n ħ where  ħ  =  h/ 2p   is the Planck constant divided by 2p. The Planck constant, first proposed by Max Planck, is: h = 6.626069 x 10- 34 J-s Then the value of ħ  = 1.0546 x 10- 34 J-s Next: both sides are squared: (m vr ) 2 =  (n ħ)2 So:  m2 v2 r 2 =  n2 ħ2 And:  v2  =  n2 ħ2     / m2  r 2 Now, Bohr looked at the total energy of the H-atom in terms of it kinetic (K) and potential (V) contributions, so: E = K + V  =    ½ m v2  -  k e2  / r E = K + V  =   k e2  /  2r    - k e2  / r =  - k e2  /  2r     (Since  ½ m v2   =  k e2  /  2r ) Now solve for r (actually the quantized r n ): r n  = [  n2 ħ2/ m2 v2 ] ½ But  from the kinetic energy equivalence: v2 =  k e2  /  mr =  n2 ħ2   m2  r 2 \    r n  = [n2 ħ2   / m k e2  ] The Bohr radius is just the value when the principal quantum number n = 1, so : r o  = [ ħ2   / m k e2  ]   = 0.0529 nm = 5.2917 ×10−11 m This is just the most probable radius, i.e. distance between proton and electron, in the hydrogen ground state. Now, to obtain the quantized energy (E n) we substitute the value for r n  into the total energy equation: E =  - k e2  /  2r     =  - k e2  /  2[n2 ħ2   / m k e2 ]    E = - m k 2 e4  /  2n2 ħ2   =  - m k 2 e4  /  2 ħ2     [1/ n2] = - 13.6/ n2    Where the last quantity  is in eV, or electron volts. Here the n refers to the energy level, ground state is n = 1, so can allow the computation of energy for a given level. Or, the energy for a photon emitted from an atom when an electron makes a transition – say from n = 2 to n = 3. Such a situation is shown below:

Fig. 4: A few energy (electron) transitions made in Hydrogen

     An important point is that the quantized angular momentum postulate (m vr  = n ħ) restricts the possible circular orbits to defines sizes according to the quantized radii (r _n  etc.). Thus the normal state of the atom, say hydrogen, will be that for which it has the least energy or the ground state – corresponding in the case of hydrogen to the Bohr radius. Some transitions for different spectral series are shown below:

Fig. 5. Some Energy transitions in the Hydrogen Bohr atom

     As shown in Fig. 4, emission occurs when an electron in the atom, say hydrogen, makes a transition from a higher to a lower energy level, accompanied by the emission of a photon with a defined energy E = hf = h (c/ l). Consider for example, a transition from the n = 2 to the n = 1 level, as depicted in the lower right of Fig. 4 and in the first line of the Lyman series of Fig. 5.

The energy at the n= 2 level is:

E(n=2) =  - 13.6/ n²   = - 13.6/ (2)²      =  - 13.6/4  (eV)

Now, 1 eV =  1.6 x 10^-19 J  so:

E(n=2) =  - 13.6/4  (eV) =  -(3.4) x 1.6 x 10^-19 J  =

 -5.4 x 1.6 x 10^-19 J 

The n= 1 level has energy:

E(n=1) =  - 13.6/ n²   = - 13.6/ (1)²      =  - 13.6  (eV)

E(n=1) =  -(13.6)  x 1.6 x 10^-19 J  = -21.8 x 10^-19 J 

Then the energy difference is:

E2 – E1 = [- 5.4 – (-21.8)]  x 10^-19 J  = 16.4 x 10 ^-19 J 

From this, the wavelength of the photon emitted can be found. Since E = hf = h (c/ l):

l =   hc/ (E2 – E1) 

l =    (6.626069 x 10^{- 34} J-s)(3 x 10 ⁸ m/s)/ 16.4 x 10^-19 J 

l =    1.21 x 10 ^-7 m 

The frequency can be found from:

f = (c/ l) = (3 x 10 ⁸ m/s) / 1.21 x 10 ^-7 m  = 2.47 x 10 ¹⁵ Hz

Insight problem:  Using Fig. 5 as a basis, compute the energies and wavelengths of the photons emitted when the electron in the hydrogen atom makes the 1^st, 2^nd and 3^rd Balmer transitions.

Quantum Mechanics: As Mystifying Now as 100 Years Ago

A new survey of physicists working in the field of quantum mechanics (including a poll reported in a recent preprint on the physics arXiv server¹),) discloses that the so-called experts remain as mystified as ever. The semi-serious poll of 33 key thinkers on the fundamentals of quantum theory shows that opinions on some of the most profound questions are fairly evenly split over several quite different answers.


For example, votes were roughly evenly split between those who believe that, in some cases, “physical objects have their properties well defined prior to and independent of measurement” and those who believe that they never do. Despite the famous idea that observation of quantum systems plays a key role in determining their behavior, 21% felt that “the observer should play no fundamental role whatsoever”.

Regrettably, QM is not a descriptive field, i.e. amenable to straightforward English interpretation. It is primarily a mathematical theory. If one ventures outside the bounds of the mathematical descriptions to offer English interpretations, one risks nonsense. I believe it was Feynman, in a Preface to his 'Lectures in Physics', Vol. III, who remarked that once one tries to use purely English descriptions to button hole QM he or she will "disappear down a rabbit hole, never to appear again."

For readers who want a comprehensive and understandable book that provides the basis for the Copenhagen Interpretation, I recommend Heinz Pagels `The Cosmic Code' (Bantam, 1982) - which will dispel a lot of incorrect perceptions and assumptions that have accumulated over the past 25 years. In his book, Pagels endorses the best policy in quantum mechanics as simply being a `fair witness'. That means absolutely avoiding embellishment and exaggeration of the results, including projection of personal `fantasies'. If one insists on reading more into quantum measurement results than their statistical significance allows, self delusion ensues.

Back to the poll devised by Anton Zeilinger of the University of Vienna, together with Maximilian Schlosshauer, now at the University of Portland, Oregon, and Johannes Kofler at the Max-Planck-Institute of Quantum Optics in Garching, Germany. It was then disseminated at a meeting of the Templeton Foundation where attendees were given 16 multiple-choice questions on key foundational issues in quantum theory.

Disagreements over the theory’s interpretation have existed ever since it was first developed, but Zeilinger and his colleagues believe that their poll might be the first to interrogate the full range of views held by experts. A previous poll at a 1997 quantum mechanics workshop in Baltimore asked attendees the single question of which interpretation of quantum theory they favored most.

Probably the most famous dispute about what quantum theory means was that between Albert Einstein and his peers, especially the Danish physicist Niels Bohr, on the question of whether the world was fundamentally probabilistic rather than deterministic, as quantum theory seemed to imply. One of the few issues in the new poll on which there was something like a consensus was that Einstein was wrong. Quantum theory IS probabilistic!

This is because most quantum physicists still adhere to the comprehensive, original interpretation of quantum theory developed in the 1920s: the so-called Copenhagen interpretation. This proposed that the physical world is unknowable and in some sense indeterminate, and the only meaningful reality is what we can access experimentally. The mathematical underpinning was perhaps first explicated by Max Born, who showed the quantum wave function (PSI) was a statistical artifact, not a real physical wave.

Consider: you want to find the probability that some particle will be found in a region of length a. The probability is given as an integral in terms of the wave function (PSI):  INT (-oo to + oo) PSI* (PSI) dx

where PSI =

A sin (2π x/ a) exp (- iEt/h/2π)

and PSI* = A sin (2π x/ a) exp (iEt/ h/2π)

with h/ 2π = 1.054 x 10 ^-34   J-s (modified Planck constant h)


Obviously, without doing the full integration, the complex functions for PSI and its complex conjugate (PSI*) cannot be identified with any real world entity. Hence (Max) Born's conclusion to treat the wave function as primarily statistical in nature is amply justified.

As the earlier Baltimore meeting, the Austrian poll found the Copenhagen interpretation to be favored over all others, including the Stochastic interpretation of David Bohm and Brian Hiley (which treats PSI as a physically real wave) and the ‘Many World’ interpretation of Hugh Everett. Even so, only 42% of the voters endorsed the Copenhagen. However, the same 42% also admitted that they had switched interpretation at least once. And whereas a few decades ago the options were very few, says Schlosshauer, “today there are more ‘sub-views’.”

The most striking implication of the poll is that, while quantum theory is one of the most successful and quantitatively accurate theories in science, interpreting it is as plagued with as many controversies as it was at the outset.  According to Schlosshauer “Nothing has really changed, even though we have seen some pretty radical new developments happening in quantum physics, from quantum information theory to experiments that demonstrate quantum phenomena for ever-larger objects. Some thought such developments would push people one way or the other in their interpretations, but I don't think there’s much evidence of that happening.

However, he says there was pretty good agreement on some questions, adding.

“More than two-thirds believed that there is no fundamental limit to quantum theory — that it should be possible for objects, no matter how big, to be prepared in quantum superpositions like Schrödinger’s cat. So the era where quantum theory was associated only with the atomic realm appears finally over.”

Wow! So we can now look at the superposition effect experienced in rockets and automobiles?

Other notable views: 42% thought that it would take 10–25 years to develop a useful quantum computer, whereas 30% placed the estimate at 25–50 years. Meanwhile in the much debated role of measurement in quantum theory — how and why measurements affect outcomes —the votes split with 24% regarding it as a severe difficulty and 27% as a “pseudoproblem”.

Zeilinger and colleagues do not claim that their poll is rigorous or necessarily representative of all quantum researchers. John Preskill, a specialist in quantum information theory at the California Institute of Technology in Pasadena, suspects that “a broader poll of physicists might have given rather different results”.

Perhaps the most amazing line of agreement from all participants is that quantum theory does its job so well yet stubbornly resists answering our deeper questions. Maybe this "contains a lesson in itself,” according to Schlosshauer. In fact, the most revealing answer may well have been that 48% believe that there will still be conferences on the foundations of quantum theory in 50 years time.

I would not dispute that at all!