Tag: Einstein

The Genesis of Relativity

“The distinction between past, present, and future is only a stubbornly persistent illusion.” – Albert Einstein

A comprehensive overview of the theory of relativity and its applications in astronomy would require a course in itself. The purpose of this post will be to give a brief overview of the subject and in particular, the history of its development as a theory. What I would like to stress that despite its fearsome reputation as being difficult to understand, the major concepts of the theory can be understood by the public. In its most advance form, the mathematics of relativity can provide a challenge to any student of physics. However, this is true of any area of physics. You will not find many physics students tell you that a graduate level electricity & magnetism course is a breeze. However, the subject of electricity & magnetism can be presented in a manner that the public can understand. The difficulties of relativity lie in that it deals with phenomena we do not ordinarily observe in our lives. Relativity provides accurate predictions in two areas where Newton’s Laws do not. These are when matter has velocity near the speed of light and/or is located near a large gravity well (such as a star or a black hole). However, I do want to stress that outside of these two situations, Newton’s Laws and Einstein’s Theory of Relativity give essentially the same results.

Beginnings

In the latter part of the 1800’s, physics was thought by many to be a dead science. Newton’s Laws were considered the final say in predicting the behavior of matter in motion. James Clerk Maxwell, using four equations, successfully provided a comprehensive explanation of the properties of electricity and magnetism. The major problems in physics and astronomy seemed to be solved. However, as the century came to a close, cracks were appearing in this assumption. One was the failure of Newton’s Laws to accurately predict the orbit of Mercury around the Sun. The perihelion (closest approach to the Sun) advanced 574″ (about 1/6 of a degree) per century, which is 43″ more than the 531″ advance predicted by Newton’s Laws. This advance is caused by the presence of the other planets in the solar system. For a time, scientists thought the extra advance in Mercury’s orbit was due to the presence of an undiscovered planet. As none was found, a new explanation was required. An image of the advance is depicted below. It is exaggerated to demonstrate the effect.

Credit: Rainer Zenz/Wiki Commons

Einstein’s Papers

In 1905, Albert Einstein, who was working as a technical expert in a Swiss patent office, published four landmark papers (in addition to his doctoral dissertation) revolutionizing physics.  This year is often called “annus mirabilis” or miracle year. The topics of these four papers are the following:

1. The photoelectric effect demonstrating light behaves as a stream of particles as well as waves. It was known at the time that a beam of light would knock electrons off a metal surface. This is similar to a baseball thrown on a beach. The impact of the ball will knock sand in the air. The accepted theory at the time was light consisted as a series of waves and this could not explain the photoelectric effect. Einstein showed that light behaves as a stream of discrete particles as well. Thus, light has a duality in that it behaves as a stream of particles as well as waves. This discovery is the foundation of quantum physics.

2. The second paper concerned the nature of Brownian motion explaining that heat is created by the motion of atoms and molecules. It was this paper that put the rest the ongoing debate if atoms existed as the constituent particles of matter.

3. The Special Theory of Relativity. This paper was concerned with the motion of objects in non-accelerating frames of reference.  This means gravity is not a factor in the Special Theory as opposed to the later developed General Theory of Relativity.

4. The mass-energy equivalence principle. This paper gave us that famous equation E = mc2.

The last two papers will be discussed below.

Albert Einstein circa 1905, Credit: Einstein Archives/Wiki Commons

 

The Special Theory of Relativity

As mentioned earlier, James Clerk Maxwell, in the mid-1800’s, formulated four basic equations outlining the properties of electricity and magnetism. One outcome of these equations is electromagnetic radiation travels at a rate of 3.0 x 108 m/s (186,282 miles per second). This rate of speed is constant regardless of the observer’s velocity relative to the radiation. What exactly does this mean? Think of yourself on a highway and your speed is 55 mph. The car in the lane next to you is moving at 60 mph. That car will pass you at a rate of 5 mph, as their velocity is that much faster than your velocity. Now, let’s ramp up the speed of your car to 186,277 miles per second. This is exactly five miles per second slower than the speed of light. Remember, light is just a form of electromagnetic radiation. Imagine a beam of light traveling in the lane next to your car. At what rate of speed would it pass you? All your life’s experience would lead you to answer five miles per second. But that would be the incorrect answer! The light beam would pass you at a rate of 186,282 miles per second as if you were standing still. This is true regardless of your velocity relative to the beam of light. The genius of Einstein was to realize that contrary to what we perceive, the speed of light is constant for all observers and time is variable as a function of your velocity. The Special Theory of Relativity leads to the following conclusions:

1. As an object (or person) approaches the speed of light, their clock slows down compared to a stationary observer. If you were to take a round-trip voyage 100 light years away and travel at 99.995 percent of the speed of light, you would only age two years but arrive back on Earth 200 years later. In popular entertainment, the original 1968 movie Planet of the Apes gives a reasonably accurate portrayal of this effect.

2. Mass of an object increases as it approaches the speed of light. In fact, the mass of an object approaches infinity as it approaches the speed of light. This is why the speed of light is the maximum speed obtainable in our universe. As its mass approaches infinity, the force required to accelerate it approaches infinity.

3. The length of an object appears to decrease to a stationary observer as it approaches the speed of light.

4. E = mc2. This is the equation that gives us the understanding of nuclear fusion that occurs in the Sun. As hydrogen fuses to form helium, the mass of the helium atoms is less than the mass of the original hydrogen atoms. The difference is converted to energy. The Sun converts 4.3 million tons of mass into energy each second. A fraction of which reaches the Earth providing the energy to sustain life.

General Theory of Relativity

After publishing his Special Theory of Relativity, Einstein spent the next ten years working out the General Theory of Relativity. It is general in that it applies to all reference frames, accelerating and non-accelerating. This theory was published in 1916 and provided a dramatically different way of looking at gravity. Unlike Newton, who postulated gravity was a force between two bodies, Einstein postulated that gravity represents a curvature in space-time itself. Lets look at an analogy. Think of a trampoline with nothing on it. This represents a universe with no mass in it. If you rolled a golf ball across it, the ball would move in a straight line. Now place a baseball (which could represent a planet) on the trampoline. The ball would depress the trampoline slightly. Now roll the golf ball again. As it approached the baseball, the depression in the trampoline would cause the golf ball to move in a curved motion. Now place a bowling ball (this could represent a star) on the trampoline. The depression becomes more pronounced and the path of the golf ball as it moves towards the bowling ball becomes more curved. In fact, if the golf ball got too close to the bowling ball, its path would curve into the bowling ball much like a meteor would fall to the Earth’s surface if captured by Earth’s gravity well.  The video below describes the difference between Newton & Einstein’s theories on gravity.

Experimental Proof

Einstein’s General Theory of Relativity predicted the advance of Mercury’s perihelion accurately. Remember, the predictions of relativity and Newton’s Laws diverge in two circumstances. When an object travels near the speed of light and when it is located near a large gravity well. Mercury is the closest planet to the Sun. This closeness is enough for predictions of its motion using the theory of relativity to vary slightly than Newton’s Laws. While this created a buzz in the physics community, relativity did not gain general acceptance until it passed an experimental test in 1919. Relativity predicts that light would be deflected by the Sun’s gravity.  A beam of light would follow the path of space-time. If space-time is curved, then the path of light is curved as well.  On May 29, 1919, British astronomer Arthur Eddington led an expedition to measure a star’s position near the Sun during a solar eclipse. Einstein’s theory predicted a deflection of 1.75 seconds of arc as opposed to Newton’s Law predicting the deflection at 0.875 seconds of arc. The measurements came in at 1.98 and 1.61 seconds of arc. These measurements are within the range of 30 seconds of arc error allowed for observational uncertainties and proved light was deflected by the Sun’s gravity well. Both the London Times and the New York Times reported the story and Einstein quickly became, by far, the most famous scientist of the era.

Negative photo of 1919 eclipse, Credit: Royal Society of London/Dyson, Eddington, Davidson
The Sun’s gravity well deflects starlight. Credit: ESA

The Cosmological Constant

The General Theory of Relativity yields a field equation which takes the following form: (Ruv)-1/2 (guv) R = (8)(π)Tuv – Λ(guv)

The subscripts in the equation are indications of what are called stress tensors. This enables mathematicians to express a complex set of equations in a compact form. You can think of this as a mathematical version of a zip file. This equation explains how matter and energy ( Tuv) curves space-time [(Ruv)-1/2 (guv)]. Now, I won’t go into the gory details of this equation. In fact, Einstein himself needed help with the complexities of the mathematics when he derived it. What is important about this equation is it predicts the universe must be either contracting or expanding as matter will deform space-time.

Einstein was not satisfied with this result. At the time, the universe was considered to be a permanent unchanging entity. What Einstein did to correct this was to add the constant Λ in the right side of the equation. This constant changes the equation providing a stable universe offsetting the effects of gravity on space-time. During the 1920’s, Georges Lemaitre argued the cosmological constant was not required and the universe could expand after originating from a primeval atom. Lemaitre used relativity to formulate what would later be called the Big Bang theory.  Edwin Hubble (whom the Hubble Space Telescope was named after) discovered that all the galaxies in the universe were receding from each other. The universe was expanding! Relativity, in its original form, had predicted this result. Einstein would later admit his addition of the cosmological constant was an error.

New knowledge contradictory to our preconceived ideas can form a disequilibrium in our minds that can take time to sort out . Even Albert Einstein, who did as much as anybody to revolutionize physics, suffered once from an inability to overcome a preconceived idea. In this case, he believed the universe was static. It is something we all must guard against. In science, we must let the evidence point us to a conclusion and not allow a preconceived conclusion allow us to define the evidence. It should be noted that once the evidence of the Big Bang arrived, Einstein came around as a supporter of the theory rather than sticking with an outdated idea of the universe. As I speak of preconceived ideas, most would assume when Einstein was awarded the Nobel Prize in 1921, it would have been for relativity. However, he won the Nobel Prize for his explanation of the photoelectric effect.

If you want to read more about Einstein and Relativity

The following sources I highly recommend for anybody who desires a greater understanding of the theory of relativity.

Issacson, W., (2007) Einstein. New York, Simon and Schuster.

A very readable biography of Einstein includes non-mathematical overviews of Einstein’s work.  I found this book very enlightening describing the educational and life experiences that enabled Einstein to make breakthroughs where others failed.

Guttfreund, H. & Renn, J., (2015).  The Road to Relativity.  Princeton, Princeton University Press.

This book contains Einstein’s original manuscript for the theory of general relativity with a page by page interpretation for the public.  It also has an excellent historical background on how Einstein developed the theory.

Einstein, A., Relativity:  The General and Special Theory.

Want to learn about relativity directly from the source?  This is Albert Einstein’s attempt to describe the theory to the public.  The book can be purchased in the usual online outlets but is also in the public domain and can be read online for free, for example, here.

Lambourne, R., (2010). Relativity, Gravitation, and Cosmology. Cambridge University Press.

If you are seeking a textbook to get started on relativity, this is the best treatment I have seen. It will walk you through the algebra of special relativity to the tensors of general relativity. The text has many problems to work through to obtain a solid understanding of the subject. Lambourne has in the past taught a short course in relativity at Oxford’s Department for Continuing Education open to the public. Sounds like a good way to spend a week in the summer.

*Image atop post is the gravitational lensing of a galaxy by another galaxy in front. Typically, such lensing can result in two or more images of an object but if the alignment is just right, it will form a ring structure. Gravitational lensing was predicted by Einstein in 1915. Credit: ESA/NASA/Hubble

Evidence for the Big Bang

The evolution of the world can be compared to a display of fireworks that has just ended, some few red wisps, ashes, and smoke. Standing on a cooled cinder, we see the slow fading of the suns, and we try to recall the vanished brilliance of the origin of the worlds.” – Fr. Georges Lemaitre

Since the ancient astronomers, humans have wondered about the origins of the universe.  For most of history, mythology filled the void in our knowledge.  Then with Issac Newton, scientists began to assume the universe was infinite in both time and space.  The concept of a universe that had a discrete origin was considered religious and not scientific.  During the 20th century, dramatic advancements in both theory and observation provided a definitive explanation how the universe originated and evolved.  Most people I talk to, especially in America, are under the impression the Big Bang is just a theory without any evidence.  Nothing could be further from the truth.  In fact, every time you drink a glass of water, you are drinking the remnants of the Big Bang.

In 1916, Einstein published his general theory of relativity.  Rather than viewing gravity as an attractive force between bodies of mass, relativity describes gravity as mass bending the fabric of space-time.  Think of a flat trampoline with nothing on it.  If you roll a marble across the trampoline, it moves in a straight path.  Now put a bowling ball on the trampoline, the marble’s path is deflected by the bend in the trampoline.  This is analogous to the Sun bending space-time deflecting the paths of planets.  Once Einstein finished up on relativity, he endeavored to build models of the universe with his new theory.  These models produced one puzzling feature.

The equations describing the universe with relativity produced the term dr/dt.  The radius of the universe could expand or contract as time progresses.  If you introduced matter into the model, gravity would cause space-time and the universe itself to contract.  That didn’t seem to reflect reality, and Einstein was still operating with the Newtonian notion of an infinite, unchanging universe.  To check the contraction of the universe, Einstein included a cosmological constant to relativity to offset the force of gravity precisely.  By doing this, Einstein missed out on one of the great predictions made by his theory.

Balancing forces are not unheard of in nature.  In a star like the Sun, the inward force of gravity is offset by the outward force of gas as it moves from high pressure in the core to lower pressure regions towards the surface.  This is referred to as hydrostatic equilibrium and prevents the Sun from collapsing upon itself via gravity to form a black hole.  Einstein’s cosmological constant served the same purpose by preventing the universe as a whole from collapsing into a black hole via gravity.  However, during the 1920’s, a Catholic priest who was also a mathematician and astrophysicist, would provide a radical new model to approach this problem.

Georges Lemaitre had a knack for being where the action was.  As a Belgian artillery officer, Lemaitre witnessed the first German gas attack at Ypres in 1916.  Lemaitre was spared as the wind swept the gas towards the French sector.  After the war, Lemaitre would both enter the priesthood and receive PhD’s in mathematics and astronomy.  The math background provided Lemaitre with the ability to study and work on relativity theory.  The astronomy background put Lemaitre in contact with Arthur Eddington and Harlow Shapley, two of the most prominent astronomers of the time.  This would give Lemaitre a key edge in understanding both current theory and observational evidence.

It’s hard to imagine, but less than 100 years ago it was thought the Milky Way was the whole of the universe.  A new telescope, the 100-inch at Mt. Wilson, would provide the resolution power required to discern stars in other galaxies previously thought to be spiral clouds within the Milky Way.  One type of star, Cepheid variables, whose period of brightness correlates with its luminosity, provided a standard candle to measure galactic distances.  It was Edwin Hubble at Mt. Wilson who made this discovery.  Besides greatly expanding the size of the known universe, Hubble’s work unveiled another key aspect of space.

Edwin Hubble, Albert Einstein, & Fr. Georges Lemaitre. Credit: American Institute of Physics.

When stars and galaxies recede from Earth, their wavelengths of light are stretched out and move towards the red end of the spectrum.  This is akin to the sound of a car moving away from you.  Sound waves are stretched longer resulting in a lower pitch.  What Hubble’s work revealed was galaxies were moving away from each other.  Hubble was cautious in providing a rational for this.  However, Fr. Lemaitre had the answer.  It wasn’t so much galaxies were moving away as space was expanding between the galaxies as allowed by relativity theory.  Lemaitre also analyzed Hubble’s data to determine that the more distant a galaxy was, the greater its velocity moving away from us.  Lemaitre published this result in an obscure Belgian journal.  Hubble would independently publish the same result a few years later and received credit for what is now known as Hubble’s law.  This law equates recessional velocity to a constant (also named after Hubble) times distance.

As space is expanding between each object and in each direction, the recession velocity is greater the more distant an object is. Credit: OpenStax Astronomy/CC 4.0.

It would require more resolving power to determine the final value of the Hubble constant.  In fact, it took Hubble’s namesake, the Hubble Space Telescope to pin down the value which also provides the age of the universe.

Hubble’s original plot of recession velocity vs distance. The more distant a galaxy, the faster it is moving away from us. This is indicative of an expanding universe. Credit: doi: 10.1073/pnas.15.3.168 PNAS March 15, 1929 vol. 15 no. 3 168-173

In the meantime, the debate on the origin of the universe still needed to be settled.  Lemaitre favored a discrete beginning to the universe that evolved throughout its history.  Specifically, Lemaitre felt vacuum energy would cause the expansion of the universe to accelerate in time and thus, kept Einstein’s cosmological constant, albeit with a different value to speed up the expansion.  Einstein disagreed and thought the cosmological constant was no longer required.  By 1931, Einstein conceded the universe was expanding, but not accelerating as Lemaitre thought.  A decade later, the most serious challenge to the Big Bang theory emerged.

The label Big Bang was pinned on Lemaitre’s theory derisively by Fred Hoyle of Cambridge, who devised the Steady State theory.  This theory postulated an expanding universe, but the expansion was generated by the creation of new hydrogen.  Hoyle scored points with the discovery that stellar nucleosynthesis created the elements from carbon to iron via fusion processes.  Although Hoyle proved the Big Bang was not required to form these heavy elements, he still could not provide an answer to how hydrogen was created.  It would take some modifications to the Big Bang model to challenge Hoyle’s Steady State model.

Fred Hoyle and Fr. Georges Lemaitre. Credit: St. Edmond’s College/University of Cambridge.

During the 1940’s, George Gamow proposed a hot Big Bang as opposed to the cold Big Bang of Georges Lemaitre.  In Gamow’s model, the temperature of the universe reaches 1032 K during the first second of existence.  Gamow was utilizing advancements in quantum mechanics made after Lemaitre proposed his original Big Bang model.  Gamow’s model had the advantage over Hoyle’s Steady State model as it could explain the creation of hydrogen and most of the helium in the universe.  The hot Big Bang model had one additional advantage, it predicted the existence of a background microwave radiation emanating from all points in the sky and with a blackbody spectrum.

A blackbody is a theoretical construct.  It is an opaque object that absorbs all radiation (hence, it is black) and remits it as thermal radiation.  The key here is to emit blackbody radiation, an object has to be dense and hot.  A steady state universe would not emit blackbody radiation whereas a big bang universe would in its early stages.  During the first 380,000 years of its existence, a big bang universe would be a small, hot, and opaque.  By the time this radiation reached Earth some 13 billion years later, the expansion of the universe would stretch out these radiation wavelengths into the microwave range.  This stretching would correlate to a cooling of the blackbody radiation somewhere between 0 and 5 K or just 5 degrees above absolute zero.  Detection of this radiation, called the Cosmic Microwave Background (CMB) would resolve the Big Bang vs. Steady State debate.

In 1964, Arno Penzias and Robert Wilson were using the 20-foot horn antenna at Bell Labs to detect extra-galactic radio sources.  Regardless of where the antenna was pointed, they received noise correlating to a temperature of 2.7 K.  Cosmology was still a small, somewhat insular field separate from the rest of astronomy.  Penzias and Wilson did not know how to interpret this noise and made several attempts to rid themselves of it, including two weeks cleaning out pigeon droppings from the horn antenna.  Finally, they placed a call to Princeton University where they reached Robert Dicke, who had been building his own horn antenna to detect the CMB.  When the call ended, Dicke turned to his team and said:

“Boys, we’ve been scooped”

Actually, the first time the CMB was detected was in 1941 by Andrew McKeller but the theory to explain what caused it was not in place and the finding went forgotten.  Penzias and Wilson published their discovery simultaneously with Robert Dicke providing the theory explaining this was proof that the young universe was in a hot, dense, state after its origin.  Georges Lemaitre was told of the confirmation of the Big Bang a week before he passed away.  Penzias and Wilson were awarded the Nobel in 1978.  Back at Cambridge, Fred Hoyle refused to concede the Steady State theory was falsified until his death in 2001.  Some believe this refusal, among other things, cost Hoyle the Nobel in 1983 when it was awarded for the discovery of nucleosynthesis.  Hoyle was passed in favor of his junior investigator, Willy Fowler.

It would take 25 more years before another mystery of the CMB was solved.  The noise received by Penzias and Wilson was uniform in all directions.  For the stars and galaxies to form, some regions of the CMB had to be cooler than others.  This was not a failure on Penzias and Wilson’s part, but better equipment with higher resolution capabilities were required to detect the minute temperature differences.  In 1989, the COBE probe, headed by George Smoot, set out to map these differences in the CMB.  The mission produced the image below.  The blue regions are 0.00003 K cooler than the red regions, just cold enough for the first stars and galaxies to form.  This map is a representation of the universe when it was 380,000 years old.

The oval represents a 3-D spherical map of the universe projected into 2-D by cutting from one pole to the other. Credit: NASA

Could we peer even farther into the universe’s past?  Unfortunately, no.  The universe did not become transparent until it was 380,000 years old, when it cooled down sufficiently for light photons to pass unabated without colliding into densely packed particles.  It’s similar to seeing the surface of a cloud and not beyond.

The first nine minutes of the COBE probe produced a spectrum of the CMB.  The data was plotted against the predicted results of a blackbody spectrum.  The results are below:

Credit: Mather et al. Astrophys. J. Lett. , 354:L37ÐL40, May 1990

The data points are a perfect match for the prediction.  In fact, the CMB represents the most perfect blackbody spectrum observed.  The universe was in a hot, dense state after its creation.

The late 1990’s would add another twist to the expansion of the universe.  Two teams, one based in Berkeley and the other at Harvard, set out to measure the rate of expansion throughout the history of the universe.  It was expected that over time, the inward pull of gravity would slow the rate of expansion.  And this is what relativity would predict once the cosmological constant was pulled out, or technically speaking, equal to zero.  The two teams set about their task by measuring Type Ia supernovae.

Like Cepheid variables, Type Ia supernovae are standard candles.  They result when a white dwarf siphons off enough mass from a neighboring star to reach the size of 1.4 Suns.  Once this happens, a supernova occurs and as these transpire at the same mass point, their luminosity can be used to calibrate distance and in turn, the history of the universe.  A galaxy 1 billion light years away takes 1 billion years for its light to reach Earth.  A galaxy 8 billion light years away takes 8 billion years for its light to reach Earth.  Peering farther into the universe allows us to peer farther back in time as well.

What the two teams found sent shock waves throughout the world of astronomy.

The first 10 billion years of universe went as expected, gravity slowed the expansion.  After that, the expansion accelerated.  The unknown force pushing out the universe was dubbed dark energy.  This puts the cosmological constant back into play.  The key difference instead of operating from an incorrect assumption of a static universe, data can be used to find a correct value that would model an increasingly expanding universe.  Georges Lemaitre’s intuition on the cosmological constant had been correct.  While the exact nature of dark energy needs to be worked out, it does appear to be a property of space itself.  That is, the larger the universe is, the more dark energy exists to push it out at a faster rate.

Besides detecting the CMB, cosmologists spent the better part of the last century calculating the Hubble constant.  The value of this constant determines the rate of expansion and provides us with the age of the universe.  The original value derived by Hubble in the 1920’s gave an age for the universe that was younger than the age of the Earth.  Obviously, this did not make sense and was one reason scientists were slow to accept the Big Bang theory.  However, it was clear the universe was expanding and what was needed was better technology affording more precise observations.  By the time I was an undergrad in the 1980’s, the age of the universe was estimated between 10-20 billion years.

When the Hubble Space Telescope was launched in 1990, a set of key projects were earmarked for priority during the early years of the mission.  Appropriately enough, pinning down the Hubble constant was one of these projects.  With its high resolution able to measure the red shift of distant quasars and Cepheid variables, the Hubble was able to pin down the age of the universe at 13.7 billion years.  This result has been confirmed by the subsequent WMAP and Planck missions.

The story of the Big Bang is not complete.  There is the lithium problem. The Big Bang model predicts three times the amount of lithium as is observed in the universe.  And there is inflation.  In the first moments of the universe’s existence, the universe was small enough for quantum fluctuations to expand it greatly.  Multiple models exist explaining how this inflation occurred and this needs to be resolved.  This would determine how the universe is observed to be flat rather than curved and why one side of the universe is the same temperature as the other when they are too far apart to have been in contact.  An exponential expansion of the universe during its first moments of existence would solve that.

NASA’s WMAP mission measured the average angular distance between CMB fluctuations. One degree is flat, 0.5 degrees open, 1.5 degrees closed. The measurement came in flat at 1 degree consistent with inflation theory. Credit: NASA/WMAP

Then there is the theory of everything.  In his 1966 PhD thesis, Stephen Hawking demonstrated that if you reverse time in the Big Bang model, akin to running a movie projector in reverse, the universe is reduced to a singularity at the beginning.  A singularity has a radius of zero, an infinite gravity well and infinite density.  Once the universe has a radius less than 1.6 x 10–35 meter, a quantum theory of gravity is required to describe the universe at this state as relativity does not work on this scale.

When discussing these problems with Big Bang skeptics, the tendency is to reply with a gotcha moment.  However, this is just scientists being honest about their models.  And if you think you have an alternative to the Big Bang, you’ll need to explain the CMB blackbody spectrum, which can only be produced by a universe in a hot dense state.  And you’ll need to explain the observed expansion of the universe.  It’s not enough to point out the issues with a model, you’ll need to replicate what it gets right.  While there are some kinks to work out, the Big Bang appears to be here to stay.

You don’t need access to an observatory or a NASA mission to experience the remnants of the Big Bang.  Every glass of water you drink includes hydrogen created during the Big Bang.  And if you tune your television to an empty channel, part of the static you see is noise from the CMB.  The Big Bang theory and the observational evidence that backs it up is one of the landmark scientific achievements of the 20th century, and should be acknowledged as such.

*Image atop post is a timeline of the evolution of the universe.  Credit:  NASA/WMAP Science Team.

The March of Time

Time is a mystery to physicists.  The Newtonian notion of absolute time, that is, all clocks run at the same rate, was demolished by Einstein’s relativity theory.  Despite the fact that we know clocks in different reference frames can run at different rates, we don’t know what exactly time is.  Does time run continuously or in discrete packets?  Can one travel backwards in time?  Why don’t the laws of physics tell us what time is?  An intriguing book, Now by Richard Muller, gives us some paths to seek these answers.

During the Victorian age, time was considered a constant for everyone.  A conductor’s watch on the way to London would run at the same rate as the station master’s clock.  Perhaps this is why Big Ben is the perfect symbol for that era.  Einstein proved this notion wrong.  The conductor’s pocket watch will run slower than the motionless station master’s clock.  Given the speeds we travel, the difference is too small to discern.  Einstein’s genius was to follow a theory to its natural conclusion and not allowing false intuition to lead him astray.  Clocks run slower the faster you go.  Gravity also slows the rate of time.  Once you hit the speed of light, or enter the infinitely deep gravity well of a black hole, time stands still.

The question remained, why does time always flow forward?  The most common response to that has been quoting the 2nd law of thermodynamics.  This is the only law in physics that suggests a flow of time.  It states that entropy of the universe always increases with time.  More specifically, a closed system, one which energy cannot enter or leave, must become more disordered over time.  An open system, like the Earth which receives a constant stream of energy from the Sun, can experience a decrease in entropy and an increase in ordered states.  The universe, as far as we know, is a closed system.  This argument was first advanced by Arthur Eddington, but Richard Muller proceeds to poke some holes in it.

Eddington was one of the most accomplished astronomers of the early 20th Century.  One of the first to grasp Einstein’s relativity theory, Eddington led an expedition to the island of Príncipe off the west coast of Africa to observe the solar eclipse of 1919.  Eddington was able to measure the bending of starlight by the Sun as predicted by Einstein.  Once this result was reported by the media, Einstein became the most famous scientist in the world.  Eddington was also what we would call today a populizer of science.  His hypothesis that entropy mandates the flow of time was published in his book The Nature of the Physical World, written in a manner for the general public to enjoy.

However, as Muller notes, clocks do not run slower in local regimes where entropy is decreasing.  A recent experiment verified that, at least on a quantum level, heat can run from a cold to warmer object.  This is a violation of the 2nd law of thermodynamics where energy runs from hot to cold objects.  Some of the news articles on this experiment also claim this has reversed the arrow of time.  Muller considers entropy and time to be two separate concepts.  Rather than rely on entropy, Muller’s hypothesis on time is tied into one of the most asked questions I receive from my students.

When going over the Big Bang, I am often asked what existed before then?  The answer is…nothing.  Space did not exist before the Big Bang.  And neither did time.  Muller speculates that just as space is being created with the expansion of the universe, so is time.  And it is this expansion that gives us the flow of time and a sense of now.  Unlike Eddington’s entropy argument, Muller provides a means of falsifying his theory.

The idea of falsifying a theory might seem odd as we are taught in grade school that experiments prove a theory right.  That’s not quite correct.  As Richard Feynman would say, we don’t prove a theory correct, only that it is not wrong.  Newton’s law of gravity was not wrong for a couple of centuries.  It predicts the motion of most celestial objects quite well.  By the late 1800’s, observations came in that Newton’s laws could not predict, specifically the precession of Mercury’s orbit.  Einstein’s relativity theory provided accurate predictions in two areas Newton could not, when an object is near a large gravity well like the Sun and when an object moves at velocities near the speed of light.

When Einstein realized his theory predicted Mercury’s orbit correctly, he was so excited he suffered from heart palpitations.  For a hundred years, Einstein’s theory has been proven not wrong.  It may take a unification of quantum mechanics and relativity to change that.

Muller speculates that as dark energy is accelerating the expansion of the universe, it must also accelerate time.  That is, time runs faster now than in the past.  To detect this, we must look at galaxies at least 8 billion light years away and make highly precise measurements of their red shifts.  Any excess in the red shift not predicted by space expansion would be caused by time expansion.  At this time, we do not have instruments to make this precise a measurement.  It’s not unusual for theory to race ahead of experimental ability.  After all, it took one hundred years to prove gravitational waves predicted by Einstein actually exist.

Is there any way to falsify relativity or quantum mechanics? To date, both have held up to rigorous testing.  One possibility is the simultaneous collapse of the quantum probability curve upon observation.  With the Copenhagen interpretation of quantum mechanics, atomic particles exist in all possible states along a probability curve.  Once observed, the probability curve collapses instantaneously to its exact state.  As Muller notes, this is in direct odds with relativity where nothing, not even information, can exceed the speed of light.  Perhaps, this can provide a crack in the theory that can lead to a unification of the physics of atoms and of large-scale objects.

Muller’s exploration of time delves into other topics, often Star Trek related. In the case of the transporter, Muller questions if the person assembled at the other end is the same person or a duplicate with the original destroyed.  I thought this was interesting as it follows the plot of James Blish’s one off Star Trek novel Spock Must Die.  Published in 1970, the opening chapter involves a rec room conversation between Scotty and Dr. McCoy, where McCoy frets over the possibility he is no longer his original self.  That is, the transporter destroyed the original McCoy the first time he used it and constructed a replicate each time afterward.  Scotty is nonplussed – “a difference that makes no difference is no difference.”

Would it make a difference?

As Muller notes, our bodies are mostly made of different atoms and cells than it was years ago, yet we maintain our sense of self.  The only thing that does change is the sense of now.  So, when I bought Spock Must Die in the mid-70’s, the body of atoms that searched through department and stationery store bookshelves, is markedly different than the body of atoms that purchased Now online.  In that sense, I am a replicate of my childhood self.  Yet, throughout that whole time, my mind has maintained a continuous state of consciousness.

That brings me back to an argument made in a college philosophy class.  If you take a boat, and replace each plank of wood over time, is it still the original boat?  Boats do not experience the sensation of time, it takes a mind to do that.  The brain, in some regions, does replace neurons throughout life and this may lead to memory loss.  For other regions, it appears not to replicate.  This may explain our continuity of consciousness, but as many a journal article has ended, more research is required in this area.

In the same philosophy class, our professor discussed how we lack access to each other’s state of consciousness.  Unless we could perform a mind meld a la Mr. Spock, our life experience and sense of time is locked up within each individual.  So, is time a matter that can be solved by physics alone?  Or does in require an interdisciplinary approach?  My instinct is that time is a problem for physics to solve.  We require eyes to see light and the mind to interpret it, but the electromagnetic waves that create light was solved by physics.  Until some evidence based results come in, we’ll have to keep an open mind. Many a time instincts have led a scientist astray.  How will this story end?

I honestly don’t know.  Only time will tell.

*Image atop post is a Munich clock store.  Credit:  Gregory Pijanowski

Relativity and Planet of the Apes

“Seen from out here, everything seems different, time bends, space is boundless, it squashes a man’s ego.” –  Charlton Heston in The Planet of the Apes on the relativistic effects of traveling near the speed of light.

The Statue of Liberty just celebrated its 130th birthday which reminded me of the famous ending of the original Planet of the Apes.  For me, the beginning of this movie is important as it was the first time I had encountered the concept of relativity and time travel.  That is, time will move more slowly for a person in motion than for a person who is stationary.  This effect is not noticeable with the slow velocities in which we travel on Earth but becomes more pronounced when moving towards the speed of light.  And give Planet of the Apes credit, it gets it right, unlike say Star Trek, which often takes a cavalier attitude towards relativity for dramatic purposes.  The video below is the beginning two minutes where this plot device is introduced.

One caveat here, even during the height of the Mad Men era, NASA did not allow smoking during its missions.  The scientist mentioned, Dr. Hasslien, is a fictitious character.  The chronometer puts the ship year at 1972 but the Earth year at 2673.  By the time the ship lands, it is the year 3978.

So how does this premise work?  We can start by looking at Einstein’s time dilation equation:

Δt’ = Δt/[1 – (v2/c2)]1/2  where:

Δt’ = time elapsed on Earth

Δt = time elapsed on spacecraft

v = velocity of spacecraft

The exponent of 1/2 is another way of saying square root.

c = speed of light (3 x 108 m/s or 186,282 miles per second)

When an object is stationary (v = 0) the denominator on the right side equals one.  Thus, Δt’ = Δt and both clocks run at the same rate.  As v approaches c, the term v2/c2 approaches 1.  This increases the value of the right side of the equation meaning Δt’ must increase to keep both sides of the equation equal.  Lets take a look at a couple of examples.

The velocity of the International Space Station is about 5 miles per second or 8000 m/s.  What is the time dilation effect of an astronaut who spends a year aboard the station?

Δt = one year or 3.15 x 107 seconds

v = 8000 m/s

Plugging into the equation gives:

Δt’ = 3.15 x 107 s/[1 – (8000 m/s)2/(3 x 108 m/s)2]1/2

Δt’ = 3.15 x 107 s/[1 -(6.4 x 107 m2/s2/9.0 x 1016 m2/s2)]1/2

Before the final calculation, a couple things to note.  You have to standardize your dimensions before calculating.  In physics, this usually means converting to meters/kilograms/seconds.  Not doing this is a common mistake for students taking their first physics course.  Also, the term m2/s2 cancels out leaving us with only seconds in the answer.  Since we are measuring time, checking dimensions will make sure you are on the right track. So, the answer is:

Δt’ = 3.15 x 107 s/[1 -(7.11 x 10-10)]1/2

Δt’ = 3.15 x 107 s (0.99999999964)

Δt’ = 31499999.99 s

So on Earth, our clocks advanced 31,500,000 seconds and the astronauts in orbit clocks advanced 31,499,999.99 seconds, so the ISS astronaut would have aged about 1/100 of a second less than us on Earth.*  What would happen if you were to spend a year traveling at  99% the speed of light?  Here, we can use fraction of light speed in the equation as the dimensions will drop out.

Δt’ = 3.15 x 107 s/[1 – (0.98c/1c)]1/2  0.98 being 0.99 squared.

Δt’ = 3.15 x 107 s/(0.02)1/2

Δt’ = 3.15 x 107 s/(0.141)

Δt’= 223,404,255 s or 7.1 years

If we up the speed to 99.9% of light speed, Δt’ becomes 22.3 years.  To get the time dilation effect seen in Planet of the Apes you would need to travel about 99.99999% of light speed.  The graph below shows the time dilation effect with changing velocity.

Credit: Wiki Commons
Credit: Wiki Commons

You’ll note the time dilation effect does not show up significantly until you reach 40% of light speed or about 75,000 miles per second.  That speed would get you to the Moon in 3 seconds.  The effect has an upper bound at the speed of light.  That is, the time dilation effect approaches infinity as velocity nears light speed.  In fact, once you hit the speed of light, your clock would stand still.  And there’s no going back.  The time travel possibility is a one way ticket forward as going faster than light speed is required to move backwards in time.  In Einstein’s universe, nothing can travel faster than light speed.  The reason for this is mass increases when velocity increases.

Newton’s second law states that force is equal to mass times acceleration.  The assumption here is that mass is constant and thus, all the force results in accelerating an object.  Einstein discovered that as an object approaches light speed, mass is not constant and approaches infinity.  The equation to determine mass with velocity is as follows:

m = m0/[(1 – v2/c2)]1/2

m0 = rest mass

m = mass in motion

When velocity is 0, m = m0.  To apply this to the Planet of the Apes scenario, lets assume the mass of the space vehicle is the same as the Apollo command/service module at 15,000 kg (33,000 lbs).  If we accelerate to 99.99999% of light speed, its mass would increase to 33.5 million kg (74,000,000 lbs) or about 12 Saturn V rockets.  At this point, more force gets decreasing returns in velocity as the spacecraft’s mass increases and becomes more difficult to push.

The term (1 – v2/c2)1/2  is referred to as the Lorentz transformation and is frequently seen in special relativity equations.  For shorthand, is is often symbolized by γ.  Besides time and mass, length is also impacted by velocity and contracts as an object approaches light speed.  The Hyperphysics website has some nifty relativity calculators you can check out here.

Our first attempts to reach another star will not be in large starships such as the U.S.S. Enterprise of Star Trek fame.  More than likely, it will be in a fleet of tiny spacecraft such as proposed by Stephen Hawking for Operation Starshot.  Using nanotechnology, the goal is to send thousands of 20 gram (about 0.7 oz.) probes to our nearest interstellar neighbor Alpha Centauri.  Light sail technology would propel these vessels to 20% of light speed.  At this rate, the mass of each probe would only increase from 20 to 20.4 grams.  Even if velocity reached 80% of light speed, the mass increase would only be to a manageable 32 grams.  Having thousands of smaller probes rather than one large craft increases the odds that the mission reaches its final destination even if some get damaged along the way.

To sum it all up, the faster you move through space, the slower you move through time.  Also, motion brings about an increase in mass.  Both these effects do not become pronounced until you reach 40% light speed, which does not happen to us here on Earth.  Time stands still at the speed of light and mass approaches infinity as you close in on light speed.  This makes human travel to the stars very problematic.  Of course, in The Planet of the Apes, the crew basically made a round trip to Earth.  Charlton Heston discovers that when happening across the ruins of Lady Liberty.

Never did understand why all those apes speaking perfect English did not clue him in to that beforehand.

*If we were to delve into general relativity, gravity slows clocks the same as velocity does as seen in Interstellar.  This means being on a planet surface with greater gravity slows your clock compared to someone in orbit.  This offsets the velocity time dilation for astronauts in orbit.  Factoring the two, astronauts age about a millionth of a second less than us here on Earth.

**Photo atop post is the chronometer on Heston’s spacecraft.  Credit: 20 Century Fox.

The Education of Albert Einstein

Most historic figures have myths attached to them and certainly Albert Einstein is no exception.  Among them, Einstein failed math in high school and did his famous work on relativity in “splendid isolation”.  After reading Walter Isaacson’s biography on Einstein, one can see the social influences that shaped Einstein in his early years and how it enabled him to make advances in physics that others could not.  And much of that is rooted in modern educational theory.

Jean Piaget’s research on child development concluded there are four stages of development.  The final transition usually occurs around age eleven when a child moves from a concrete understanding of the world to an ability to solve abstract and hypothetical problems.  The age this transition occurs can vary with each individual and also with the subject matter.  Contrary to the struggling student myth, Einstein began thinking in abstract terms at a very early age.  A compass given to Einstein at age five demonstrates this.  Rather than thinking of the compass in concrete terms, that is, a mechanical device that points north, Einstein conjectured on the invisible magnetic field that caused the compass to always point north.  And this trend continued in Einstein’s early life.

During the 1930’s, a Ripley’s Believe It or Not! column stated Einstein failed math in high school and has remained part of the Einstein lore.  Truth is, Einstein had learned calculus by age 15.  And physics?  Einstein was at a college level by age 11.  How did this myth begin?  More than likely from Einstein’s days as a student in Germany’s authoritarian educational system.  Einstein thought little of rote learning, and was not afraid to make his teachers aware of that.  In today’s parlance, that bit of acting out probably gave the impression of a troubled student.  So what was it in Einstein’s background that allowed him to advance so quickly in his studies?

The second pillar of modern educational theory is Lev Vygotsky’s theory of learning by social interaction.  Part of that theory is the concept of the zone of proximal development.  Here, a student is placed in contact with a more skilled partner to help master a subject.  In Einstein’s case, his parents provided the first zone of proximal development.  Hermann Einstein, Albert’s father, partnered with his brother Jakob building electric generators and lighting.  This surrounded Albert with a technical/scientific background from the get-go not unlike, say, Bill Belichick growing up in a household with a football coach as a father.  Pauline, Albert’s mother, was a pianist and Albert would play the violin most of his life to catch a break from physics.

Einstein plays the violin during the charity concert in the New Synagogue, Berlin, January 29, 1930. Credit: Institute of Czech Literature, Czech Academy of Science.

At age 10, Einstein was introduced into another zone of proximal development in the person of Max Talmud, a 21-year-old medical student who had dinner with the Einsteins weekly.  Talmud introduced Einstein to many subjects including geometry and Kant’s Critique of Pure Reason.  Talmud’s greatest gift to Einstein may have been Aaron Bernstein’s 21 volume People’s Book on Natural Science.  Bernstein encouraged constructive learning techniques, in particular, thought experiments such as what it would be like to ride along a light beam.  These thought experiments played a crucial role in Einstein’s relativity breakthroughs and his attempt to describe the theory to the public in his book, Relativity:  The Special and General Theory.

As one might imagine, Einstein raced out of Talmud’s zone of proximal development in short order.  Not unlike the first time a student realizes they have raced ahead intellectually of their teacher.  Nonetheless, Talmud served as a rich pipeline of learning resources for Einstein.  In some sense, Talmud was Einstein’s version of the internet without all the negative distractions.  This resource enabled Einstein to think in ways that provided insights to solve problems other physicists were not able to.  Young Albert Einstein also possessed a fierce streak of individuality.

Self-identity is typically formed during high school years, but can be delayed beyond college.  By all indications, Einstein’s self-identity was molded by his family and his ethnicity.  Of the four general parenting characteristics, the Einsteins would fall into authoritative (not to be confused with authoritarian).  This engaged parenting style typically endows a child with high self-esteem and confidence, which certainly Albert Einstein possessed.  As a Jew in Germany, Einstein was an outsider in German society (as Isaacson notes, only 2% of Munich’s population was Jewish) and this reinforced Einstein’s contempt for the German authoritative educational system.  The Swiss educational system was another story.

Aarau, Switzerland. Credit: Roland Zumbuhl/Wiki Commons

Fed up with Germany, Einstein moved to Switzerland at age 16 and spent a year at the Aarau Cantonal School.  This school favored a constructionist educational philosophy where students build their own knowledge rather than simply accepting what was told to them by an authority figure.  Part of the instructional technique at Aarau included an emphasis on visualization of mathematical concepts based on the ideas of Johann Heinrich Pestalozzi who also valued student individuality.  Einstein thrived at Aarau and its visualization techniques played a significant role in Einstein’s breakthroughs in relativity.

Einstein’s Aarau transcript. Grade scale is 1-6 with 6 being best grade. Credit: Wiki Commons. Translation can be found at: https://commons.wikimedia.org/wiki/File:Albert_Einstein%27s_exam_of_maturity_grades_(color2).jpg

However, Einstein’s professional academic career did get off to a slow start.  In fact, he was working at a Swiss patent office in 1905 when he published four landmark papers on special relativity, mass-energy equivalence (E = mc2) the photoelectric effect (proving light acts as particles as well as waves) and Brownian motion (which established the existence of atoms).  Einstein’s anti-authoritarianism during his college years at Zurich Polytechnic rubbed some of his professors the wrong way and he had difficulty obtaining good references.  This has led to the myth of Einstein working in “splendid isolation” during this time.  And in a sense, Einstein was isolated from the heavy hitters in physics.  However, this may have been a godsend as those heavy hitters made discoveries that pointed towards relativity, but lacked the creativity Einstein possessed to put all the pieces together.  In pursuit of this, Einstein found one more learning social component in Zurich.

The Olympia Academy founders Conrad Habicht, Maurice Solovine, and Albert Einstein. Credit: Wiki Commons/Emil Vollenweider und Sohn

Had Einstein been discussing the current problems of physics in academia after the turn of the century, he would have been hamstrung by the Newtonian concept of absolute time.  That is, clocks run at the same pace for every observer in the universe.  Einstein and a group of friends formed what they jokingly dubbed the Olympia Academy.  Of the many topics discussed during these weekly sessions were David Hume’s and Ernst Mach’s rejection of absolute time.  This skepticism of Newtonian absolute time is the linchpin of special relativity, which states the speed of light is constant to all observers in the universe and time is variable as a function of velocity (times moves more slowly the faster you go, reaching a standstill at the speed of light).  Special relativity also put the universal speed limit at light speed leading to general relativity, which redefined gravity as curvatures in space-time which ripple throughout the universe at the speed of light and not instantaneously via Newton’s gravitational fields.

So is there anything we can apply from Einstein’s education?

To begin, don’t expect your students to become Einstein – the human race is lucky to experience such a genius once a century.  Great disasters are usually the result of many little things going wrong, great successes require many little things going right.  Replicating Einstein’s education will not likely produce another Einstein anymore than putting a hockey stick in a child’s hand will make him a Wayne Gretzky.  But to continue the sport’s analogy, Red Auerbach expressed a coaching philosophy that his job was to help his players reach their differing levels of maximum potential.  To illustrate, I am the same height as Larry Bird and Magic Johnson, but my maximum potential as a basketball player is significantly lower.  Rather than concern myself with that, with proper instruction, I should focus on reaching my personal potential level.

For example, if a student is struggling putting the ball in the hoop, rather than give a wedgie George Costanza style, have the player perform a thought experiment Albert Einstein style.  Instead of traveling with a light beam, imagine moving along with a basketball headed for the rim.  Take two scenarios, a shot with a low arc and one with a high arc.  How does the hoop appear as you are headed with the ball towards it?  The ball with the high arc “sees” more area in the hoop to enter, increasing the odds of making two points.  It  might not make the child into Larry Bird, but will move forward into reaching their full basketball potential wherever that may fall.

Techniques such as this allows a student to internally construct knowledge and not simply take a teacher’s word for it.  And student’s can apply these techniques in other subjects.  Also, the social component of learning cannot be ignored.  Ridiculing, instead of providing instruction, for a poor performing student causes social isolation not only in that class, but can cascade throughout the educational experience.  All the educational resources in the world cannot help a student who is socially isolated.  And likewise, lack of community resources in the educational system can thwart good instruction.  Teaching someone to fish may keep them well fed, but it only works if they actually have a fishing rod to use.

To maximize a student’s potential a rich social experience is required where ideas are passed back and forth as well as contact with more experienced learners.  This does not stop after childhood.  As the great economist Alfred Marshall noted, inexperienced workers are more productive when teamed with more experienced workers.  This is also why industries tend to form geographic clusters such as Silicon Valley.  In fact, despite his disdain for Germany, Einstein moved to Berlin in 1914 as that was the center of physics on the continent.  The diaspora of Jewish scientists, including Einstein, in the 1930’s had the opposite effect of diminishing Germany’s physics research.  Also, adequate resources must be available to apply what is learned.  Can a student without computer resources expect to function well in today’s society?  Finally, do not burden the student with unrealistic expectations.  Focus on what the student can do, not what they cannot do, and use that as a base to build upon to reach their own level of maximum potential.

*Image on top of post is Einstein presenting a lecture at American Association for the Advancement of Science in Pittsburgh on December 28, 1934.  Credit:  AP/Public Domain.

Science and Authoritarianism

With authoritarianism making headway in both Europe and America, it might be instructive to take a look back at what has historically happened to scientists and their supporting institutions when democracy wanes.  Here, I’ll take a look at Nazi Germany.  This might tempt some to invoke Godwin’s law as this is the extreme case study.  However, the Freedom Party of Austria has its roots in the Nazi party while Greece’s Golden Dawn party employs an altered swastika for its emblem inviting the comparison.  In America, the rise of Donald Trump trends more towards the celebrity cult/buffoonery of Gabriele d’Annunzio/Benito Mussolini, but the same can not be said of his most strident Twitter followers.  We’ll focus on the three most prominent German scientists of the era, Albert Einstein, Max Planck, and Wernher von Braun.

The Refugee

Over a decade before Hitler rose to power, Albert Einstein became the most famous scientist in the world during 1919 when the Eddington expedition provided experimental confirmation of general relativity.  Einstein’s troubles in Germany started only a couple of years later as Philipp Lenard and Johannes Stark, Nobel Prize winners in their own right, began to wage an anti-Semitic campaign against Einstein.  Lenard was a fine experimental physicist, but had been left behind in the modern physics revolution.  Stark also had difficulty comprehending the mathematics of the new physics.  Unable to critique relativity on its merits, both referred to modern theoretical physics as “Jewish science” and eventually espoused what was referred to as Deutsche Physik or Aryan Physics.  This politicization of science discarded modern physics and was intended to ride the wave of Nazi power.

Events in Germany came to a head as Hitler became Chancellor in January of 1933.  Shortly afterwards, Jews were forbidden to hold university or research positions.  Einstein had been in Belgium during early 1933 with the intention of returning to Germany.  However, as the situation deteriorated (Einstein’s house had been raided and sailboat confiscated), Einstein appeared at the German consulate and renounced his German citizenship (Einstein was still a Swiss citizen) and resigned his position at the Prussian Academy of Sciences, the same academy where he announced his final general relativity theory in 1916.  During the summer of 1933, while still in Belgium, word was put out that a $5,000 bounty had been placed on Einstein’s life.

On October 3rd, four days before he left Europe never to return, Einstein gave a speech at the Royal Albert Hall.

During the speech, Einstein asked, “How can we save mankind and its spiritual acquisitions of which we are the heirs? How can we save Europe from a new disaster?”  The eventual answer, of course, was at a cost of millions of lives.

After arriving in America, Einstein took up a job offer at Princeton where he had remained until his death in 1955.  Einstein worked to get other unemployed German Jewish physicists jobs in America.  In all, over a thousand Jewish scientists relocated to America including  several Nobel prize winners.  This represented a significant shift in intellectual and innovative resources from Europe to America.  In 1939, Einstein wrote a letter to President Roosevelt warning about the potential for Nazi Germany to produce an atomic bomb.  Many top refugee scientists worked on the Manhattan Project, whose final result would have been used against Germany had it not surrendered a couple months before the first atomic test.

The essential lesson here is that Einstein’s enormous talent did not spare him from Nazi persecution.  Purging or banning an ethnic group, besides the obvious ethical considerations, results in an intellectual drain.  Segregating an ethnic group from educational resources presents a loss of potential economic growth, which is why ideologues need to resort to ethnic stereotyping to deflect attention from the negative by-products of their policies.  Einstein, to his last days, spoke out for civil rights, lectured at black colleges, and was rewarded for his efforts with an 1,800 page FBI file.

As a pacifist, Einstein deeply regretted the letter that started the Manhattan Project.  As a scientist, to this day, his work has held up to every rigorous test experimental physicists have thrown up against it.  Relativity theory has provided us with the Big Bang, black holes, time dilation, and gravitational waves.  Einstein will be long remembered while those who chose the expedient path of supporting Nazism have had their scientific legacy tarnished greatly.  Not everyone in the German scientific establishment jumped aboard the Nazi bandwagon, some tried to mitigate the effects of Nazism by working within the system.

The Statesman

When Hitler ascended to power, Max Planck was president of the Kaiser Wilhelm Society.  Planck had revolutionized physics in 1900 by discovering energy was emitted in discrete packages dubbed quanta.  This would kick-start the quantum mechanics breakthroughs in the decades to follow.  Planck was among the first to recognize the significance of Einstein’s work in 1905 on special relativity, and as editor of the journal Annalen der Physik, published Einstein’s work.  It was Planck, as dean of Berlin University, who opened up a professorship for Einstein in 1913.  It was here that Einstein finished up his work on general relativity.

Max Planck. Credit: Bain News Service/Library of Congress

Max Planck was born in 1858 and his life arced with Germany’s rise from a patchwork of unorganized states to unification as a single nation in 1871, eventually to  rival the British Empire as a European power.  Conservative in temperament, Planck was inclined to be apolitical publicly.  However, Planck was a firm believer in advancing German science and loyalty to the German state.  In May 1933, as Einstein was severing his ties to Germany, Planck announced at the Kaiser Wilhelm Society annual meeting that:

“The Kaiser Wilhelm Society for the Advancement of the Sciences begs leaves to the tender reverential greetings to the Chancellor and its solemn pledge that German science is also ready to cooperate joyously in the reconstruction of the new national state.” 

In reality, Planck thought the Nazi party would moderate its views once in power (sound familiar?) and personally endeavored to continue the high standard of German research.  That did not happen, of course.  Planck met with Hitler personally in 1933 hoping to moderate his policy to stem the exodus of Jewish scientists from Germany.  The meeting ended with a Hitler rant that science would have to suffer.  Not surprising, as that is how discussions with hopeless ideologues tend to go.  At the annual Kaiser Wilhelm Society meeting in 1934, Planck noted while the society was devoted to science in service of the fatherland, pure research was suffering as a result of Nazi policies.  By 1935, Planck openly defied Hitler and attended the funeral service for Fritz Haber, who had been in exile from Germany.

It is difficult to maintain a functional operation when the overall organization is dysfunctional.  Eventually the dam breaks, and the dysfunctionalty takes control.  Planck in 1933 was also playing the role of the extreme centrist, blaming both Nazi and Jewish cultures equally for the situation in Germany.  In this one can see the danger in not recognizing an asymmetric authoritarian movement.  By 1936, Planck had openly stated that intelligence counts more in science than race.  But despite Planck’s efforts, the purging of highly talented Jewish scientists had been complete.  In 1937, Planck retired as president of the society, but not without offering the parting shot that scientific work required opposition to prove its merit, something Nazi supported science would not permit.

Planck’s experience offers the cautionary tale that an authoritative movement must be defeated before it obtains the keys to governance.  There was no reasoning to be had with Hitler in 1933 and access to power offered no motivation for Nazis to moderate their policies towards Jews.  By the end of World War II, Planck’s Berlin house had been destroyed in an Allied air raid, and he lost his son who was put to death for his participation in the plot to kill Hitler.  Planck had previously lost another son in World War I during the battle of Verdun.

Eight days after the surrender of Germany in 1945, at the age of 87, Planck resumed his role as president of the Kaiser Wilhelm Society.  After Planck had passed away in 1947, the Kaiser Wilhelm Society was renamed the Max Planck Institute.  Under a democratic Germany, the institute has produced 18 Nobel prize winners and over 13,000 scientific publications annually.  ESA’s Planck mission measured the cosmic microwave background radiation – the remnants of the Big Bang.  The spectrum of this radiation is that of a blackbody, the same type Planck studied to determine that energy is emitted in packages.  Blackbody spectra are emitted by objects in a hot, dense state, meaning that was the state of the universe when it was 380,000 years old.  Planck’s legacy has enabled us to understand the nature of the electron and the origins of the universe.

In 2007, the Max Planck Institute completed a ten-year study on the history of the Kaiser Wilhelm Society during Hitler’s reign.  The report acknowledged, especially after Planck’s departure in 1937, unethical scientific research during that period.  It was not just party hacks involved in this behavior, some of the most talented scientists engaged in projects that degraded their reputations.

The Opportunist

On July 20, 1969, Neil Armstrong and Buzz Aldrin became the first humans to walk on the lunar surface.  It was the culmination of a decade’s worth of work and $150 billion (2016 dollars) to beat the Soviet Union to the Moon.  At the head of the Saturn V design team was Wernher von Braun, who was director of the Marshall Space Flight Center in Huntsville, Alabama.  During the post World War II era, von Braun was the leading public advocate of space exploration.  In many ways, von Braun was the Carl Sagan or Neil deGrasse Tyson of his era.  Unlike Sagan or deGrasse Tyson, von Braun’s reputation originated on the backs of slave labor.

In some regards, von Braun was similar to Planck in that he was not a Nazi ideologue.  He was loyal to Germany as a nation, but his main focus, obsession really, was space exploration and rocketry.  His childhood dream was to go to Mars, but as Hitler rose to power, only military rocket research was permitted.  During the early 1930’s, von Braun received a government research grant that permitted him to complete his PhD ahead of schedule.  Unlike Planck, he joined the Nazi party in 1937 to advance his career.

Wernher von Braun (in civilian cloths) at the Peenemünde Army Research Center where the V-2 was developed. March 21, 1941. Credit: Wiki Commons/German Federal Archives.

During World War II, von Braun headed up the German V-2 program.  While the V-2 killed 9,000 in its attacks, some 12,000 slave laborers were killed in the V-2 Mittelwerk production plant.  The facility was adjacent to the Dora-Nordhausen concentration camp which supplied the labor.  While von Braun was not stationed near the plant, he did visit it and was aware of the deaths at the plant.  The V-2 program was not enough to stave off the eventual defeat of Germany in 1945.  Von Braun planned to escape to America as he felt that would provide him the best opportunity to advance his career.  Along with about 1,600 other scientists and engineers, von Braun was shepherded to America as valuable assets for the upcoming Cold War against the Soviet Union in a program code named Operation Paperclip.

Von Braun became famous to the American public during the 1950’s.  In 1952, von Braun played a key role in a influential series of articles in Collier’s magazine.  These articles presented to the public a peek at how future space missions to the Moon and Mars as well as a space station might look like.  In 1955, von Braun started work on a series of television programs for Disney promoting space exploration.  A sample of which is below:

Von Braun was a true visionary of space exploration.  It is difficult to reconcile a man who worked for both Adolf Hitler and Walt Disney.  My first lesson on space exploration was an article written by von Braun for the 1969 World Book Encyclopedia.  When NASA was founded in 1958, it got to choose the pick of the litter from the existing military rocket programs, and that was von Braun’s army team.  The rest is history and cemented von Braun as the face of America’s space program.

Von Braun passed away in 1977, about a decade before Operation Paperclip was investigated by the Justice Department.  While von Braun’s work on the V-2 project was common knowledge, his membership in the SS was not well known to the public until 1985.  Arthur Rudolph, whose contributions were crucial to the development of the Saturn V, was also the operations manager at Mittelwerk.  Rudolph was deported in 1984.  Kurt Debus, the first director of the Kennedy Space Center and an ideological Nazi during the war, avoided the investigation by passing away in 1983.  How would have von Braun fared if probed by the Justice Department?

Wherner von Braun and Kurt Debus, roll out of Saturn V, May 26, 1966. Credit: NASA

Von Braun’s supporters point out that he would have been executed had he opposed the working conditions at Mittelwerk.  No doubt, that is the case.  In fact, von Braun was arrested by the SS in 1944 for carelessly opining that the war was a lost cause and the future of rocketry would be space exploration.  However, this is a variation of the I was following orders routine, and von Braun was too high up in the food chain to use that as a passable defense.  Clearly, von Braun had charted his own course in the Nazi apparatus.  It is difficult to imagine a rigorous investigation ending well for von Braun.

What can we take from all this?  Under an oppressive authoritarian regime, you can leave the country, try to maintain institutional integrity within the system, or advance your career regardless of personal debasement.  If you want to leave, you’ll have more difficulty than Einstein securing a visa and a job.  If Max Planck could not preserve the integrity of the Kaiser Wilhelm Society, what are the chances you’ll be able to where you are situated?  As for careerism, if landing a man on the Moon is not enough to cleanse questionable past associations, do you really think you could pull that off?

The easiest solution is simply to reject authoritarianism before it takes power.  Democracy is far easier to sustain by pushing for needed reforms than it is to re-institute it after it falls.  Authoritarianism typically ends in chaos, war in the case of Germany and Japan in 1945 and Syria today, economic in the case of the Soviet Union in the 1990’s or Venezuela today.  Regardless how you navigate your path through it, don’t think you will get out unscathed one way or another.

*Photo at top of post:  Nazi Germany’s loss is America’s gain. Albert Einstein receives from Judge Phillip Forman his certificate of American citizenship.  October 1, 1940.  Credit:  Al Aumuller/Library of Congress.

Beware of Outliers

As we currently digest the run-up to the 2016 presidential election, it can be expected that the candidates will present exaggerated claims to promote their agenda.  Often, these claims are abetted by less than objective press outlets.  Now, that’s not supposed to be the press corps job obviously, but it is what it is.  How do we discern fact from exaggeration?  One way to do that is to be on the lookout for the use of outliers to promote falsities.  So what exactly is an outlier?  Merriam-Webster defines it as follows:

A statistical observation that is markedly different in value from the others of the sample.

The Wolfram MathWorld website adds:

Usually, the presence of an outlier indicates some sort of problem. This can be a case which does not fit the model under study, or an error in measurement.

The most simple case of an outlier is a single data point that strays greatly from an overall trend.  An example of this is the United States jobs report from September 1983.

bls
Credit: Bureau of Labor Statistics

In September 1983, the Bureau of Labor Statistics announced a net gain of 1.1 million new jobs.  As you can tell from the graph above, it is the only month since 1980 that has gained 1 million jobs.  And why would we care about a jobs report from three decades ago?  It is often used to promote the stimulus of the Reagan tax cuts.  When you see an outlier such as this being used to support an argument, you should be wary.  As it turned out, there is a simpler explanation for this that has nothing to do, pro or con, with Reagan’s economic policy.  See the job loss immediately preceding September 1983?  In August 1983, there was a net loss of 308,000 jobs.  This was caused by the strike of 650,000 AT&T workers who returned to work the following month.

If you eliminate the statistical noise of the striking workers from both months, you have a gain of over 300,000 jobs in August 1983, and 400,000 jobs in September 1983.  Those are still impressive numbers and require no need for the use of an outlier to exaggerate.  However, it has to be noted, it was the monetary policy of the Fed Chair Paul Volcker, rather than the fiscal policy of the Reagan administration that was the main driver of the economy then.  Volcker pushed the Fed Funds rate as high as 19% in 1981 to choke off inflation causing the recession.  When the Fed eased up on interest rates, the economy rebounded quickly as is the normal response as predicted by standard economic models.  So we really can’t credit Reagan for the recovery, or blame him for the 1981-82 recession, either.  It’s highly suspect to use an outlier to support an argument, it’s even more suspect to assume a correlation.

To present a proper argument, your data has to fit a model consistently.  In this case, the argument is tax cuts alone are the dominant driver determining job creation in the economy.  That argument is clearly falsified in the data above as the 1993 tax increases were followed by a sustained period of job creation in the mid-late 1990’s.  And that is precisely why supporters of the tax cuts equals job creation argument have to rely on an outlier to make their case.  It’s a false argument intended to rely on the fact that, unless one is a trained economist, you are not likely to be aware of what occurred in a monthly jobs report over three decades ago.  Clearly, a more sophisticated model with multiple inputs are required to predict an economy’s ability to create jobs.

When dealing with an outlier, you have to explore whether it is a measurement error, and if not, can it be accounted for with existing models.  If it cannot, you’ll need to determine what type of modification is required to make your model explain it.  In science, the classic case is the orbit of Mercury.  Newton’s Laws do not accurately predict this orbit.  Mercury’s perihelion precesses at a rate of 43 arc seconds per century greater than predicted by Newton’s Laws.  Precession of planetary orbits are caused by the gravitational influence of the other planets.  The orbital precession of the planets besides Mercury are correctly predicted by Newton’s laws.  Explaining this outlier was a key problem for astronomers in the late 1800’s.

At first, astronomers attempted to analyze this outlier within the confines of the Newtonian model.  The most prominent of these solutions was the proposal that a planet, whose orbit resided inside of Mercury’s, perturbed the orbit of Mercury in a manner that explained the extra precession.  This proposed planet was dubbed Vulcan, after the Roman god of fire.  Several attempts were made to observe this planet during solar eclipses and predicted transits of the Sun with no success.  In 1909, William W. Campbell of the Lick Observatory stated no such planet existed and declared the matter closed.  At the same time, Albert Einstein was working on a new model of gravity that would accurately predict the orbit of Mercury.

Vulcan’s Forge by Diego Velázquez, 1630. Apollo pays Vulcan a visit. Instead of having a real planet named after him, Vulcan settled for one of the most famous planets in science fiction.  Credit: Museo del Prado, Madrid.

The general theory of relativity describes the motion of matter in two areas that Newton could not.  That is, when located near a large gravity well such as the Sun or moving at a velocity close to the speed of light.  In all other cases, the solutions of Newton and Einstein match.  Einstein understood that if his new theory could predict the orbit of Mercury, this would pass a key test for his work.  On November 18, 1915, Einstein presented his successful calculation of Mercury’s orbit to the Prussian Academy of Sciences.  This outlier was finally understood and a new theory of gravity was required to do it.  Nearly 100 years later, another outlier was discovered that could have challenged Einstein’s theory.

Relativity puts a velocity limit in the universe at the speed of light.  A measurement of a particle traveling faster than this would, as the orbit of Mercury did to Newton, require a modification to Einstein’s work.  In 2011, a team of physicists announced they had recorded a neutrino with a velocity faster than the speed of light.  The OPERA (Oscillation Project with Emulsion-tRacking Apparatus) team could not find any evidence for a measurement error.  Understanding the ramifications of this conclusion, OPERA asked for outside help in verifying this result.  As it turned out, a loose fiber optic cable caused a delay in firing the neutrinos.  This delay resulted in the measurement error.  Once the cable was repaired, OPERA measured the neutrinos at its proper velocity in accordance with Einstein’s theory.

While the OPERA situation was concluding, another outlier was beginning to gain headlines.  This being the increase in the annual sea ice in Antarctica, seemingly contradicting the claim by climate scientists that global temperatures are on the rise.  Is it possible to reconcile this observation within the confines of a model of global warming?  What has to understood is this measurement is an outlier that cannot be extrapolated globally.  It only pertains to sea ice surrounding the Antarctica continent.

Glaciers on the land mass of Antarctica continue to recede, along with mountain ranges across the globe and in the Arctic as well.  Clearly something interesting is happening in Antarctica, but it is regional in nature and does not overturn current climate change models.  At least, none of the arguments I’ve seen using this phenomenon to rebut global warming models have provided an alternative model that also explains why glaciers are receding on a global scale.

Outliers are found in business as well.  Most notably, carelessly taking an outlier and incorporating it as a statistical average in a forecasting model is dangerous.  Lets take a look at the history of housing prices.

Credit: St. Louis Federal Reserve.
Credit: St. Louis Federal Reserve.

In the period from 2004-06, housing prices climbed over 25% per year.  This was clearly a historic outlier and yet, many assumed this was the new normal and underwrote mortgages and derivative products as such.  An example of this would be balloon mortgages, where it was assumed the homeowner could refinance the large balloon payment at the end of the note with newly acquired equity in the property as a result of rapid appreciation.  Instead, the crash in property values left these homeowners owing more than the property was worth causing high rates of defaults.  Often, the use of outliers for business purposes are justified with slogans such as this is a new era, or the new prosperity.  It turns out to be just another bubble.  Slogans are never enough to justify using an outlier as an average in a model and never be swayed by any outside noise demanding you accept an outlier as the new normal.  Intimidation in the workplace played no small role in the real estate bubble, and if you are a business major, you’ll need to prepare yourself against such a scenario.

If you are a student and have an outlier in your data set, what should you do?  Ask your teachers to start with.  Often outliers have a very simple explanation, such as the 1983 jobs report, that will not interfere with the overall data set.  Look at the long range history of your data.  In the case of economic bubbles, you will note a similar pattern, the “this time is different” syndrome.  Only to eventually find out this time was not different.  More often than not, an outlier can be explained as an anomaly within a current working model.  And if that is not the case, you’ll need to build a new model to explain the data in a manner that predicts the outlier, but also replicates the accurate predictions of the previous model.  It’s a tall order, but that is how science progresses.

*Image on top of post is record Antarctic sea ice from 2014.  This is an outlier as ice levels around the globe recede as temperatures warm.  Credit:  NASA’s Scientific Visualization Studio/Cindy Starr.

Science’s First Rough Draft

It has often been said that newspapers are “history’s first rough draft.”  The same is true of science.  One could argue that journals fill the role, but historically, the vast majority of the public reads of scientific discoveries and/or events in the newspaper.  It is quite interesting to see how these events were interpreted at the time without the benefit of hindsight.  The New York Times online archive dates back to the paper’s origins in the 1850’s and represent a rich source of historical material that can be used in the class or for personal research.  Here are some historical articles pertaining to astronomy and physics.

Auroral Phenomena – September 5, 1851.  This article describes the aftermath of the Carrington Event, the most powerful magnetic storm in recorded history.  The aurora was seen across America and telegraph operators could still send messages even after disconnecting the batteries.  Below, NASA presents a computer model of the 1859 magnetic storm.

Glowing After – Sunset Skies – December 1, 1883.  Three months after the Krakatoa eruption, the skies around the world appeared deep red after sunset as a result of aerosols ejected into the atmosphere.  The cause of these sunsets were not known at the time – the article never refers to the Krakatoa eruption.

A Comet Visible by Daylight – September 20, 1882.  The Great Comet of 1882, considered the brightest comet of the past 1,000 years, is visible during the day.  The image atop this post is this comet.  In 2015, the Rosetta mission became the first to attempt a landing on a comet.

The Roentgen Discovery – February 7, 1896.  The discovery of x-rays and possible applications in the medical field.  A century later, astronomers would use the orbiting Chandra X-Ray Observatory to discover the universe to be a violent place.

Wireless Signals Across the Ocean – December 15, 1901.  Guglielmo Marconi receives radio signals in Newfoundland from London to open the era of mass communication.  Decades later, astronomers use radio telescopes to discover pulsars and peer into the center of the galaxy.

The Greatest Telescope in the World – January 27, 1907.  Plans to build a 100-inch telescope on the summit of Mt. Wilson in California.  Opened in 1917, this telescope is where Edwin Hubble discovered the universe was expanding.

Mt. Wilson 100-inch telescope. Credit: Gregory Pijanowski
Mt. Wilson 100-inch telescope. Credit: Gregory Pijanowski

Comet Gazers See Flashes –  May 19, 1910.  Report on Earth passing through tail of Halley’s Comet.  The comet tail was 100 degrees long and 10 degrees wide in the sky.  Whatever was seen that night, comet tails are much too tenuous to cause flashes in the atmosphere.

Lights All Askew in the Heavens – November 10, 1919.  Eddington Expedition proves Einstein’s General Relativity theory correct by measuring the bending of starlight during a total solar eclipse.  Relativity has passed every test since, including the recent observation of gravity waves.

Ninth Planet Discovered on Edge of Solar System – March 14, 1930.  Pluto is discovered.  Since reclassified as a dwarf planet, the New Horizons mission gave us the first close up images of Pluto in 2015.

Nebula Velocities Support Einstein – June 12, 1931.  Edwin Hubble discovers the expansion of the universe as predicted by Einstein’s relativity theory.  Actually, Einstein was originally skeptical the universe could expand.  It was Fr. Georges Lemaitre, Catholic priest and physicist, who proposed what was later called the Big Bang theory.  The word nebula in the title refers to what we now call galaxies.

Lemaitre Follows Two Paths to Truth – February 19, 1933.  Fr. Georges Lemaitre does not find a conflict between science and religion.  Einstein and Lemaitre, “Have a profound respect and admiration for each other”.  Article quotes Einstein as stating, “This is the most beautiful and satisfactory explanation of creation to which I have ever listened” regarding Lemaitre’s Big Bang theory.

Fr. Georges Lemaitre (center) and Albert Einstein, January 10, 1933. To the left is Robert Millikan who was the first to measure the charge of an electron. Credit: California Institute of Technology.

Bohr and Einstein at Odds – July 28, 1935.  The conflict between relativity and quantum mechanics.  The quest to unify the theory of relativity, which governs large objects, and quantum mechanics, which explains physics on an atomic scale, continues to this day.

Science and the Bomb – August 7, 1945.  One day after Hiroshima, nuclear fission as a weapon and the implications for humanity are explained.

Palomar Observers Dazzled in First Use of 200-inch Lens – June 5, 1948.  Delayed by World War II for five years, Mt. Palomar Observatory finally opens for business.

Palomar
Mt. Palomar 200-inch telescope. Largest in the world from 1948-97. Credit: Gregory Pijanowski

Radio Telescope to Expose Space – June 19, 1959.  Navy to build largest radio telescope in West Virginia.  The current radio observatory in Green Bank, WV is surrounded by a 13,000 square mile (slightly larger than the state of Maryland) radio quiet zone, meaning no cell phones, radio, or microwave ovens.

New Clues to the Size of the Universe – March 26, 1963.  The brightest objects in the universe, dubbed quasars, are discovered.  Located over 10 billion light years away, these objects are so bright some astronomers thought they must reside within the Milky Way.  However, further research would prove quasars to be the most distant objects observed by humans.

Signals Imply a Big Bang Universe – May 21, 1965.  The discovery of the cosmic microwave background radiation (CMB) proves the universe was born in a hot, dense state aka the Big Bang.  The CMB was most recently mapped by the ESA Planck mission.  The map shows the state of the universe when it was 380,000 years old.

*Image on top of post is the Great Comet of 1882 from the Cape of Good Hope.  Credit:  David Gill.

Gravitational Waves – A New Window to the Universe

Some 1.3 billion years ago, as plant life was making its first appearance on Earth, two black holes 29 and 36 times the mass of our Sun, collided.  The result of this collision was a single black hole 62 times the mass of the Sun.  The remaining mass, equal to three Suns, was expelled as energy.  This energy created a ripple in the space-time fabric referred to as gravitational waves.  These waves, which emanated from the colliding black holes like pond waves formed by a rock tossed into it, were detected by the LIGO team on September 14, 2015.  The announcement made today, culminates a 100 year effort by physicists to confirm Albert Einstein’s prediction of gravitational waves.

What are gravitational waves?

Issac Newton’s theory postulates that gravity acts as an instantaneous force throughout the universe.  That is, the gravitational force from the Sun, Earth, even your body, is felt immediately on every other body everywhere.  As Einstein worked up his theory of relativity, he knew there was a problem with this.  According to relativity, there is a firm speed limit in the universe, this limit being the speed of light.  As nothing, whether it is matter or energy, could travel faster than this, it would not be possible for the effect of gravity to travel faster than light as well.  Clearly, a new way of explaining gravity was required.

Einstein found this explanation in the form of gravitational waves.  If there was to be some sort of perturbation in the Sun’s gravitational field, we would not sense it right away on Earth.  Instead, the disturbance would radiate from the Sun at the speed of light in the form of gravitational waves.  It takes light eight minutes to reach Earth.  Thus, a time lag of eight minutes would occur before we would feel the gravitational disturbance on Earth.  In the same manner, there was a 1.3 billion year lag to detect the gravitational waves from colliding black holes located 1.3 billion light years away.  Had Newton’s theory of gravity been correct, the gravitational effect of the colliding black holes, however faint, would have reached Earth instantly 1.3 billion years ago rather than last September.

I want to emphasize that Newton’s theory of gravity works in most situations.  Newton’s predictions deviate from Einstein’s predictions in two key situations.  One is when a body is located very close to a large mass, such as Mercury is to the Sun.  The other is when a body is traveling near the speed of light.  In other situations, Newton’s and Einstein’s equations yield the same result.  In fact, NASA engineers will use Newton’s version of gravity when they can as it is easier to work with than relativity.  The Apollo program, for example, sent humans to the Moon using Newton as a guide.  Replicating Newton’s results where they are accurate was a key stepping stone for Einstein when devising relativity theory.

Another key stepping stone for relativity was making successful predictions where Newton could not.  One such example is the orbit of Mercury.  The perihelion (spot closest the Sun) of Mercury’s orbit advances 43 seconds of arc per century (43/3600th of a degree) more than predicted by Newton.  This advance is visualized in exaggerated form below.

Credit: Wikipedia/Rainer Zenz

When Einstein found out that his theory’s solutions predicted Mercury’s orbit perfectly, he was so excited he experienced heart palpitations.  As opposed to being a force, general relativity views gravity as a bending of space-time.

Earth bends space-time. Credit: NASA

As an object bends the space around it, another object will travel along the path of that curvature.  Also, electromagnetic radiation such as light will follow the curvature as well.  If an object accelerates, as when happens when black holes are colliding, it will generate ripples in space time.  And it is these ripples that LIGO detected.

A 3-D visualization of gravitational waves generated by colliding black holes. Credit: Henze, NASA

The universe is not very pliable and it took a tremendous amount of energy to create these waves which are very small, only 1/1000th the size of a atomic nucleus.  How much energy?  Matter in the amount of 3 solar masses was converted into energy in the collision.  Using Einstein’s famous equation:

E = mc2

E = 3(1.99 x 1030 kg)(3.0 x 108 m/s)2

E = 1.79 x 1039 J  where J = Joules

The Hiroshima atomic bomb released about 1014 J of energy.  This means the black hole collision detected by LIGO released 1.79 x 1025 times the amount of energy as the 1945 atomic bomb.  When you see the amount of energy involved, and how small the gravitational waves detected were, its easy to understand how difficult it is to observe these waves.  In fact, Einstein was doubtful gravitational waves could ever be detected as they are so faint.  The announcement today is a result of an effort started in the 1980’s to build the LIGO facility.

LIGO’s two gravitational wave detectors. Credit : LIGO

In 1992, the NSF granted funding for the LIGO project to commence.  It consists of two facilities, one in Livingston, LA, and the other in Hanford, WA.  As a sidenote, Hanford was the site of a key plutonium production plant during the Manhattan project.  Each facility has two 4 km tubes where a laser is sent through.  The mirrors in the interferometer are calibrated so when the two light beams reach their final destination, they cancel each other out so no light is recorded at the photodetector.  This is known as destructive interference and is pictured below.

Credit: NASA

If a gravity wave passes through LIGO, the ripple in space-time moves the mirrors just enough to cause the laser to captured by the photodetector.  This movement is much too slight to be felt by humans and thus the need for sophisticated equipment to catch it.

Credit: LIGO

LIGO has been operational since 2002.  During its first run, no gravitational waves were detected.  LIGO underwent a recent $220 million overhaul to increase its sensitivity.  As mentioned in the press conference today, LIGO is only at a third of its final expected resolution capability.  This bodes very well for more discoveries at LIGO over the next decade.  In all, LIGO has cost $650 million since its inception in 1992.  That is 1/10th the cost to rebuild the San Francisco-Oakland Bay Bridge.  This discovery has the potential to open a new window of observation for astronomers.

To the general public, astronomy for the most part means the classic image of an astronomer peering through an optical telescope or the famous imagery from the Hubble Space Telescope.  What is not as well known are telescopes that observe other forms of radiation.  This includes Earth-bound radio telescopes and space telescopes such as the infrared Spitzer Space Telescope and the Chandra X-ray Observatory.  Why bother with these other forms of radiation?  Think of it this way, imagine a tower located a mile away on a foggy day.  The tower has both a light beacon and radio transmitter.  The fog blocks out the light, making it invisible.  However, if you have a radio receiver, you’ll be able to pick up the radio transmission as fog is transparent to radio waves.  In this manner, astronomers use different types of radiation to detect objects not visible in the optical range.

Besides the continuing upgrade at LIGO, there are future gravitational wave observatories anticipated in India, Japan, and it is hoped, in space.  Today’s result overcomes the most important hurdle.  When LIGO was funded, many scientists were skeptical it could actually detect gravitational waves.  Now that we know it can be done, that clears a major obstacle for funding.  The opening of the radio window allowed the discoveries of pulsars and the cosmic microwave background radiation.  The x-ray window allowed us to view accretion disks around black holes.  The next decade should provide us with additional surprises about the universe as the gravitational wave window opens up.

Credit: LIGO

Above is the LIGO gravitational wave detection result announced today.  The strain is the distance space-time was stretched during the event.  At 10-21 m this is, as mentioned before, about 1/1000th the size of an atomic nucleus.  What gives the LIGO team confidence this is not a false detection as the one produced by the BICEP team two years ago is the gravitational wave was detected by both the Livingston and Hanford observatories.  You’ll also note how closely the observed wave matches with the predicted wave.  The hallmark of progress in science is when theoretical prediction matches observation.  If Einstein were around to see this, I suspect he may have had heart palpitations just as when he found a match between relativity and the orbit of Mercury 100 years ago.

*Image on top of post displays how the colliding black holes produced the gravitational waves discovered by LIGO.  Credit:  Credit: LIGO, NSF, Aurore Simonnet (Sonoma State U.)

Elementary Einstein

While I was in grade school, a teacher wrote the equation E = mc2 on the board and flatly stated, “less than ten people in the world understand this equation.”  In retrospect, that really seems an odd statement to make about a rather simple algebraic equation.  However, it did speak to mystique relativity has among even the educated public.  Nonetheless, this classic equation, which demonstrates the equivalency between matter and energy, is perhaps the easiest aspect of relativity theory to understand.

Relativity typically deals with phenomena that we do not experience in our day to day lives.  In the case of special relativity, most of its esoteric quality deals with objects as they approach the speed of light that represents the highest velocity possible.  As an object approaches this upper bound, it’s clock runs slower compared to stationary observers and its mass approaches infinity.  The fastest speed we approach for most of us is when we fly a jet airliner at about 700 mph.  While that seems fast, it is only 0.000001 the speed of light, much too slow for relativistic effects to be noticed.  Thus, relativity has a strong counter-intuitive sense for us.

That alone does not explain relativity’s fearsome reputation as expressed by my teacher some forty years ago.  Some of that reputation can be attributed to how the media reported the experimental confirmation of general relativity during after the eclipse of 1919.  General relativity provides a more comprehensive theory of gravity than Newton’s Laws.  During the eclipse, astronomers were able to measure the Sun’s gravity bend light, something not predicted by Newton but is by general relativity.  The New York Times reported that:

“When he (Einstein) offered his last important work to the publishers he warned them that there were not more than twelve persons in the whole world who would understand it.”

That was referring to general relativity, which is very complex mathematically and was only four years old in 1919.  It is understandable for those not trained in modern physics to conflate special and general relativity.  Add to that the equation E = mc2  was most famously associated with Einstein and you got the perception it could not be understood unless you were a physicist.  As we will see below, that perception is most assuredly false.

To begin with, lets start with a hypothetical situation where mass can be completely converted to energy.  A science fiction example of this is the transporter in Star Trek that converts a person to energy, transmits that energy at another location, then reconverts the energy back into matter in the form of that person.  How much energy is present during the transmission stage?  Einstein’s famous equation gives us the answer.

Lets say Mr. Spock is about 200 pounds.  Converted to kilograms that comes out to 90 kg.  The speed of light is 3.0 x 108 m/s.  The mass-energy equation gives us:

E = (90 kg)(3.0 x 108 m/s)2

E = 8.1 x 1018 kg*m2/s2

The term kg*m2/s2 is a unit of energy called a Joule (J).  So as Mr. Spock is beaming down to the planet surface, his body is converted to 8.1 x 1018 J of energy.  Exactly how much energy is that?  Well, the average amount of energy consumed in the United States each month is 8.33 x 1018 J.  That’s right, if you converted your body to energy, it would almost provide enough to power the United States for an entire month.  As you can see, a small amount of matter has a whole lot of energy contained with it.

However, most nuclear fission and fusion processes convert a small fraction of matter to energy.  For example, lets take a look at the fusion process that powers the Sun.  It’s a three step process where four hydrogen atoms are fused to form a single helium atom.  The four hydrogen atoms have four protons in their nuclei whereas the final helium atom has two neutrons and two protons in its nucleus.  A proton becomes a neutron by releasing a positron and a neutrino, thus a neutron has slightly less mass than a proton.  In the solar fusion cycle, this mass is converted to energy.

The mass of four hydrogen atoms is 6.693 x 10-27 kg and the mass of the final helium atom is 6.645 x 10-27 kg with a difference between the two being 0.048 x 10-27  kg.  How much energy is that?  Using the famous Einstein equation:

E = (0.048 x 10-27 kg)(3 x 108 m/s)2 

E = 4.3 x 10-12 J

By itself, that might seem like a small amount of energy.  However, the Sun converts some four million tons of mass into energy each second for a total of 4 × 1026 watts (one watt = one J/s).  Worry not, although average sized for a star, the Sun is still pretty big.  In fact, it constitutes over 99% of the mass of the Solar System.  The Sun will burn up less than 1% of its mass during its lifetime before becoming a planetary nebula some five billion years from now.

Albert Einstein, 1904.

Einstein published this equation in 1905, what would later be called his Annus Mirabilis (Miracle Year).  During this year, Einstein would publish four groundbreaking papers along with his doctoral dissertation.  These papers would describe the photoelectric effect (how light acts as a particle as well as a wave-a key foundation of quantum mechanics), Brownian motion (heat in a fluid is caused by atomic vibrations-helped establish atoms as building blocks of matter), special relativity, and finally, the mass-energy equivalence.  Ironically, it was the photoelectric effect and not relativity that was cited when Einstein was awarded the Noble Prize in 1921.

Information traveled a lot slower back then, and the fame that awaited Einstein was more than ten years away.  The major news story that year would be the conclusion of the war between Russia and Japan as well as the election of Theodore Roosevelt to another term as president.  The New York Times would not mention Einstein at all in 1905.  Even in 1919, when Einstein became a famous public figures, some were mystified at the attention.  The astronomer W.J.S. Lockyer stated that Einstein’s ideas “do not personally concern ordinary human beings; only astronomers are affected.”  As we now know, the public was ahead of the curve in discerning the importance of Einstein’s work.

And that interest remains today.  Yet, there is very little opportunity for students to take a formal course in relativity (or quantum mechanics) unless they are college science majors.  Does the mathematics of relativity make it prohibitive for non-science majors to study relativity?  It shouldn’t.  A graduate level course in electromagnetism contains higher order mathematics that is very complex.  Yet, that does not stop us from presenting the concepts of magnetic fields and electrical circuits in grade school.  As educators, we should strive to do the same for relativity.  And I can’t think of a better place to start than that famous equation E = mc2.

*Photo on top of post is sunset at Sturgeon Point 20 mile south of Buffalo.  The light photons recorded in this image were produced via a nuclear fusion reaction in the Sun’s core that occurred 1 million years ago when only 18,500 humans lived on Earth.  Once the photons were released at the Sun’s surface, it took only an additional eight minutes to end their journey on Earth in my camera.  Photo:  Gregory Pijanowski