We continue our series of excerpts (and discussion) from the outstanding survey paper by George F. R. Ellis, Issues in the Philosophy of Cosmology.
The physical explanatory power of inflation in terms of structure formation, supported by the observational data on the fluctuation spectra, is spectacular. For most physicists, this trumps the lack of identification and experimental verification of the underlying physics. Inflation provides a causal model that brings a wider range of phenomena into what can be explained by cosmology, rather than just assuming the initial data had a specific restricted form. Explaining flatness (Ω0 ≅ 1 as predicted by inflation) and homogeneity reinforces the case, even though these are philosophical rather than physical problems (they do not contradict any physical law; things could just have been that way). However claims on the basis of this model as to what happens very far outside the visual horizon (as in the chaotic inflationary theory) results from prioritizing theory over the possibility of observational and experimental testing. It will never be possible to prove these claims are correct.
Inflation is one compelling approach to explaining the structure we see in the universe today. It is not necessarily the only one, but it currently has the most support. Basically, a tiny fraction of a second after the Big Bang, the universe expanded dramatically. Around 10-36 seconds after the Big Bang the universe had a diameter on the order of 1.2 × 10-27 meters. To put that size in perspective, the diameter of a proton is between 0.84-0.87 × 10−15 meters. So, when inflation began, the entire universe had a diameter almost a trillion times smaller than a single proton! 10-34 seconds later when the inflationary period was coming to an end, the size of the universe was a little over half the distance to Alpha Centauri!
The basic underlying cosmological questions are:
(1) Why do the laws of physics have the form they do? Issues arise such as what makes particular laws work? For example, what guarantees the behaviour of a proton, the pull of gravity? What makes one set of physical laws ‘fly’ rather than another? If for example one bases a theory of cosmology on string theory, then who or what decided that quantum gravity would have a nature well described by string theory? If one considers all possibilities, considering string theory alone amounts to a considerable restriction.
(2) Why do boundary conditions have the form they do? The key point here is, how are specific contingent choices made between the various possibilities, for example whether there was an origin to the universe or not.
(3) Why do any laws of physics at all exist? This relates to unsolved issues concerning the nature of the laws of physics: are they descriptive or prescriptive? Is the nature of matter really mathematically based in some sense, or does it just happen that its behaviour can be described in a mathematical way?
(4) Why does anything exist? This profound existential question is a mystery whatever approach we take.
The answer to such questions may be beyond the limits of experimental science, or even beyond the limits of our intellect. Maybe, even, these questions are as meaningless as “What lies north of the north pole?1” because of our limited intellect. Many would claim that because there appears to be limits to what science or human intellect can presently explain, that this constitutes evidence for the existence of God. It does not. Let’s just leave it as we don’t know.
Finally, the adventurous also include in these questions the more profound forms of the contentious Anthropic question:
(5) Why does the universe allow the existence of intelligent life?
This is of somewhat different character than the others and largely rests on them but is important enough to generate considerable debate in its own right.
Well, a seemingly flippant answer to this question is we wouldn’t be here if it didn’t, but that begs the question. Perhaps intelligent life is the mechanism by which the universe becomes self-aware, or is this just wishful thinking? In the end, I am willing to admit that there may be some higher power in the universe—in the scientific pantheist and humanist sense—but I will stop short of calling that “God” in any usual sense of the term.
The status of all these questions is philosophical rather than scientific, for they cannot be resolved purely scientifically. How many of them—if any—should we consider in our construction of and assessments of cosmological theories?
Perhaps the limitations of science (and, therefore, cosmology) is more a manifestation of the limitations of our human intellect than any constraint on the universe itself.
One option is to decide to treat cosmology in a strictly scientific way, excluding all the above questions, because they cannot be solved scientifically. One ends up with a solid technical subject that by definition excludes such philosophical issues. This is a consistent and logically viable option. This logically unassailable position however has little explanatory power; thus most tend to reject it.
Let’s call this physical cosmology.
The second option is to decide that these questions are of such interest and importance that one will tackle some or all of them, even if that leads one outside the strictly scientific arena. If we try to explain the origin of the universe itself, these philosophical choices become dominant precisely because the experimental and observational limits on the theory are weak; this can be seen by viewing the variety of such proposals that are at present on the market.
And let’s call this metaphysical cosmology.
1Attributed to Stephen Hawking
Ellis, G. F. R. 2006, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
Ryden, Barbara. 2003. Introduction to Cosmology. San Francisco: Addison Wesley.
We are all going to miss Stephen Hawking. His incredible intellect, and his even more remarkable determination to make something of himself despite a terrible affliction, has been a universal inspiration all over the world. Stephen Hawking was the individual equivalent of the Apollo lunar program. He raised the bar when almost everyone else we see nowadays is lowering it. He succeeded against all the odds.
Now would be a good time to watch (or rewatch) five extraordinary documentaries and films about Stephen Hawking and his ideas.
Edmund Weiss (1837-1917) and many astronomers since have called asteroids “vermin of the sky”, but since October 4, 1957 another “species” of sky vermin made their debut: artificial satellites. In the process of video recording stars for possible asteroid occultations, I frequently see satellites passing through my ~¼° field of view.
I’ve put together a video montage of satellites I’ve recorded between June 21, 2017 and October 20, 2017. The component events are presented chronologically as follows:
10-20-2017 (2 satellites)
You’ll notice that sometimes the satellite crosses the field as a moving “dash”. That’s because sometimes I used longer exposure times to record a fainter target star.
In general, the slower the satellite is moving across the field, the higher is its orbit around the Earth. One must also consider how much of the satellite’s orbital motion is along your line of sight to the satellite. In the following video clip, you’ll see a slow-moving “tumbler” satellite moving from right to left across the top of the field.
179462 (2002 AJ202)
On January 10th of this year, I figured out how to identify satellites crossing the telescope field of view using the amazing program Guide 9.1, which I use for all my observatory research work. On March 4th, I was hoping to be the first to record the asteroid 3706 Sinnott passing in front of a star. This asteroid is named after Sky & Telescope Senior Editor Roger Sinnott, whom I had the good fortune to work with in writing the article “A Roll-Down-Roof Observatory” in the May 1993 issue of Sky & Telescope, p. 90. Roger is amazing. He took an article that I had written and edited it in a way that only lightly touched my original text yet ended up saying what I wanted to say even better than I was able to say it myself. The mark of a great editor! Anyway, I’m sure Roger remembers me and I was looking forward to giving him the news that I had observed the first stellar occultation by “his” asteroid. Alas, it was not to be, because, as so often happens, the too-faint-to-be-seen asteroid passed either above or below the target star. The consolation prize, however, was recording a third stage Long March Chinese rocket booster (CZ-3B R/B; NORAD 43004U; International # 17069D) passing through the field. This rocket launched on November 5, 2017, and added two satellites to China’s Beidou positioning network. As you can see in the light curve below, the rotation period of the rocket booster is a bit longer than the 19 seconds of usable video I had.
Once in a great while, I record a telescopic meteor. Here are two.
Hughes, D. W. & Marsden, B. G. 2007, J. Astron. Hist. Heritage, 10, 21
Fermilab is a name well known to all physicists. When I was an astrophysics undergraduate student at Iowa State University in Ames, Iowa in the mid-to-late 1970s, I remember that several members of our large high energy physics group made frequent trips to Fermilab, including Bill Kernan and Alex Firestone. At the time, it was the best place in the world to do high energy physics. What is high energy physics? Basically, it is the creation and study of new and normally unseen elementary particles formed by colliding subatomic particles into one another at very high velocities (kinetic energies).
On Sunday, March 4, a group of us from the Iowa County Astronomers met up at Fermilab for an afternoon tour of this amazing facility. We were all grateful that John Heasley had organized the tour, and that Lynda Schweikert photo-documented our visit.
Our afternoon began with an engaging talk by Jim Annis, Senior Scientist with the Experimental Astrophysics Group: “Kilonova-2017: The birth of multi-messenger astronomy using gravitational waves, x-rays, optical, infrared and radio waves to see and hear neutron stars”. Here he is showing a computer simulation of an orbiting pair of neutron stars coalescing, an event first observed by the LIGO and Virgo gravitational wave detectors on 17 August 2017 (GW170817), and subsequently studied across the entire electromagnetic spectrum.
One of the amazing factinos I remember from his talk: even though neutrinos were not directly detected from the GW170817 event, the matter in colliding neutron stars is so dense that neutrinos push material outwards in what is called a neutrino wind. Yes, these are the same neutrinos that could pass through a light year of solid lead and only have a 50% chance of being absorbed or deflected, and pass through your body at the rate of 100 trillion every second with nary a notice.
Even though CERN has now eclipsed Fermilab as the world’s highest-energy particle physics laboratory, Fermilab is making a new name for itself as the world’s premier facility for producing and studying neutrinos. This is a fitting tribute to Enrico Fermi (1901-1954)—after whom Fermilab is named—as Fermi coined (or at least popularized) the term “neutrino” for these elusive particles in July 1932.
Basic research is so important to the advancement of human knowledge, and funding it generally requires public/government funding because practical benefits are often years or decades away; therefore such work is seldom taken up by businesses interested in short term profit. However, as our tour guide informed us, the equipment and technology that has to be developed to do the basic research often leads to practical applications in other fields on a much shorter time frame.
Thoughts Inspired by Leon Lederman: A Footnote
I had the great privilege in October 2004 of attending a talk given by Leon Lederman (1922-), winner of the 1988 Nobel Prize in Physics and director emeritus of Fermilab. I listened intently and took a lot of notes, but what I remember best besides his charm and engaging speaking style was his idea for restructuring high school science education. The growing scientific illiteracy in American society, and the growth of dogmatic religious doctrine, is alarming. Lederman advocates that all U.S. high school students should be required to take a conceptual physics & astronomy course in 9th grade, chemistry in 10th grade, and biology in 11th grade. Then, in 12th grade, students with a strong interest in science would take one or more advanced science courses.
Teaching conceptual physics (and astronomy) first would better develop scientific thinking skills and lay a better groundwork for chemistry, which in turn would lay a better groundwork for biology. Whether or not a student chooses a career in science, our future prosperity as a society depends, in large part, on citizens being well-informed about science & technology matters that affect all of our lives. We also need to be well-equipped to assimilate new information as it comes along.
It is in this context that I was delighted to read Leon Lederman’s commentary, “Science education and the future of humankind” as the last article in the first biweekly issue of Science News (April 21, 2008). He writes:
Can we modify our educational system so that all high school graduates emerge with a science way of thinking? Let me try to be more specific. Consider Galileo’s great discovery (immortalized as Newton’s First Law): “An isolated body will continue its state of motion forever.” What could be more counterintuitive? The creative act was to realize that our experience is irrelevant because in our normal experience, objects are never isolated—balls stop rolling, horses must pull carts to continue the motion. However, Galileo’s deeper intuition suspected simplicity in the law governing moving bodies, and his insightful surmise was that if one could isolate the body, it would indeed continue moving forever. Galileo and his followers for the past 400 years have demonstrated how scientists must construct new intuitions in order to know how the world works.
I’d like to take Lederman’s comments one step further. Whether it be science, politics, economics, philosophy, or religion, we must realize that most ignorance is learned. We all have blind spots you could drive a truck through. Our perceptions masquerade as truth but sometimes upon closer inspection prove to be faulty. Therefore, we must learn to question everything, accepting only those tenets that survive careful, ongoing scrutiny. We must learn to reject, unlearn if you will, old intuitions and beliefs that are harmful to others or that have outlived their usefulness in the world. We must develop new intuitions, even though at first they might seem counterintuitive, that are well supported by facts and that emphasize the greater good. We must, all of us, construct new intuitions in order to make our world a better place—for everyone.
IAU Commission F1 (Meteors, Meteorites, and Interplanetary Dust) officially approved some terms and definitions in meteor astronomy last year. This is a revision of the terms and definitions that were approved in 1961. Meteor astronomy knowledge has grown by leaps and bounds since then.
A solid natural object of a size roughly1 between 30 micrometers and 1 meter moving in, or coming from, interplanetary space
The light and associated physical phenomena (heat, shock, ionization) which results from the high speed entry of a solid object from space into a gaseous atmosphere
Any natural solid object that survived the meteor phase in a gaseous atmosphere without being completely vaporized
1“Roughly”, because the 1 meter size limit is not a physical boundary; it is set by agreement. There is a continuous population of bodies both smaller and larger than 1 meter. Bodies larger than 1 meter tend to be dominated by asteroidal debris, rather than debris from comets. “Roughly”, also because the 30 micrometer size limit is not a physical boundary; it is set by agreement. There is a continuous population of bodies both smaller and larger than 30 micrometers. Bodies smaller than 30 micrometers, however, tend to radiate heat away well and not vaporize during an atmospheric entry.
“Small dust particles do not give rise to the meteor phenomenon when they enter planetary atmospheres. Being heated below the melting point, they sediment to the ground more or less unaffected.”
“When collected in the atmosphere, they are called interplanetary dust particles (IDPs). When in interplanetary space, they are simply called dust particles. The term micrometeoroid is discouraged.”
Looking at the definition for meteorite above, what about meteoroids that reach the surface of a world with little or no atmosphere, such as the Moon? The IAU Commission has a less-than-satisfying answer (to this writer, at least).
“Foreign objects on the surfaces of atmosphereless bodies are not called meteorites (i.e. there is no meteorite without a meteor). They can be called impact debris.”
What’s the harm in calling any meteoroid that reaches the surface of a planetary body (planet, moon, asteroid, etc.) a meteorite? To me, “impact debris” implies material pre-existing on the planetary body that is excavated by an impact event.
“In the context of meteor observations, any object causing a meteor can be termed a meteoroid, irrespective of size.”
“A meteoroid in the atmosphere becomes a meteorite after the ablation stops and the object continues on dark flight to the ground.”
“A meteorite smaller than 1 millimeter can be called a micrometeorite. Micrometeorites do not have the typical structure of a fresh meteorite—unaffected interior and fusion crust.”
“Meteor stream is a group of meteoroids which have similar orbits and a common origin. Meteor shower is a group of meteors produced by meteoroids of the same meteoroid stream.”
Finely divided solid matter, with particle sizes in general smaller than meteoroids, moving in, or coming from, interplanetary space.
“Dust in the solar system is observed e.g. as the zodiacal dust cloud, including zodiacal dust bands, and cometary dust tails. In such contexts the term ‘dust’ is not reserved for solid matter smaller than about 30 micron; the zodiacal dust cloud and cometary dust trails contain larger particles that can also be called meteoroids.”
For consistency with the rest of the document, micron in the above paragraph should be micrometers.
Solid matter that has condensed in a gaseous atmosphere from material vaporized during the meteor phase.
“The size of meteoric smoke particles (MSPs) is typically in the sub-100 nm range.”
“Meteors can occur on any planet or moon having a sufficiently dense atmosphere.”
“A meteor brighter than absolute visual magnitude (distance of 100 km) -4 is also termed a bolide or a fireball.”
The fireball definition makes sense, but it was always my understanding that a bolide is accompanied (later) by audible sound and is thus much rarer.
“A meteor brighter than absolute visual magnitude -17 is also called a superbolide.”
“Meteor train is light or ionization left along the trajectory of the meteor after the meteor has passed.”
“Small (typically micron-size) non-vaporized remnants of ablating meteoroids can be called meteoritic dust. They can be observed e.g. as dust trails in the atmosphere after the passage of a bolide.”
Again, for consistency with the rest of the document, micron-size in the above paragraph should be micrometer-size.
“The radiation phenomenon accompanying a direct meteoroid hit of the surface of a body without an atmosphere is not called a meteor but an impact flash.”
The following excerpts are from the 1911 and 1925 editions of A Text-Book of Physics by Louis Bevier Spinney, Professor of Physics and Illuminating Engineering at Iowa State College (now Iowa State University) in Ames, Iowa.
From the 1911 edition…
516. The intensity of illumination of any surface is defined as the ratio of the light received by the surface to the area of the surface upon which the light falls. A unit of intensity which is oftentimes employed is known as the foot candle, and is defined as the intensity of illumination which would be present upon a screen placed at a distance of one foot from a standard candle. The meter candle is a unit of intensity which is employed to some extent.
The table below gives a number of values of illumination such as are commonly observed, the intensity of illumination being expressed in foot candles.
Suitable for drafting table . . . . . 5 to 10
Suitable for library table . . . . . . 3 to 4
Suitable for reading table . . . . . . 1 to 2
Required for street lighting . . . . . 0.05 to 0.60
Moonlight (full moon) . . . . . . . 0.025 to 0.03
And from the 1925 edition…
532. The eye has a remarkable power of adaptation. In strong light the pupil contracts and in weak light expands, so that we are able to use our eyes throughout a range of illumination which is really quite astonishing. However, the continued use of the eyes under conditions of unfavorable illumination causes discomfort, fatigue, and even permanent injury. Experiment and experience show that eye comfort, efficiency, and health considerations demand for each kind of eye work a certain minimum illumination. Some of these illumination values taken from tables recently compiled are given below.
Streets . . . . . . . . . . . . . . 1/20 to 1/4
Living rooms; Halls and passageways . . 1 to 2
Auditoriums; Stairways and exits;
Machine shops, rough work . . . . . . 2 to 5
Classrooms; Laboratories; Offices;
Libraries; Machine shops, close work . . 5 to 10
Engraving; Fine repairing work; Drafting;
Sewing and weaving, dark goods . . . . 10 to 20
By comparing the 1911 and 1925 data with the illumination levels recommended today by IESNA, we can see that recommended light levels for streetlighting have increased anywhere from 40% to 380% since 1925. A cynic might say that we need more light than our ancestors did to see well at night. As you may have noticed, light levels have been steadily creeping upward, everywhere, over the last few decades.
Recommended Illumination Levels for Streetlighting
Year Minimum Average Maximum
1911 0.05 ??? 0.60
1925 0.05 0.25 ???
1996 0.07 1.20 ???
Have you ever noticed how well you can see at night when the full moon is lighting the ground? The full moon provides surprisingly adequate non-glaring and uniform illumination at just 0.03 footcandles! For inspiration, take a look at the following text from an Ames, Iowa city ordinance, dated July 8, 1895:
“The said grantees shall keep said lamps in good condition and repair, and have the same lighted every night in the year from dark until midnight, and from 5:00 a.m. until daylight, except such moonlight nights or fractions of the same as are not obscured by clouds, and as afford sufficient natural light to light the streets of said city.”
This was originally published as IDA Information Sheet 114 in November 1996, and authored by David Oesper.
Under the direction of Friedrich Argelander (1799-1875), astronomers at the Bonn Observatory spent seven years (1852 to 1859) measuring the positions and magnitudes of roughly 324,000 stars, one star at a time. This phenomenal work resulted in the Bonner Durchmusterung (BD) catalog and atlas, which included stars down to approximately magnitude 9.5 and is a tribute to the foresight of Argelander and the diligence of his small staff. The Bonner Durchmusterung was the last star catalog to be produced without the benefit of photography, and it is certainly the most comprehensive of the pre-photographic atlases.
Back in 2007, Alan MacRobert stated (Sky & Telescope, July 2007, p. 59), “Someday machines will measure the brightness of every star in the sky to some amazingly deep magnitude many times a night, and blind software will compile and analyze light curves automatically.” No doubt, he is correct, but he does add that this has not happened yet, despite years of pregnant expectations.
But we are getting closer to that day, with the Large Synoptic Survey Telescope (LSST) scheduled to come online in 2022 and many other similar survey instruments in the pipeline or already operational. That is one reason as an amateur astronomer with limited resources (including time) I focus on observing the occultation of stars by asteroids and trans-Neptunian objects. It is one of the few areas where an amateur observational astronomer can provide location-dependent observations. You are either in the shadow path or you are not. Though truth be told I would rather be studying exoplanets, we can only do what we have the resources to do—regardless of talent or potential.
History is full of examples of skills and techniques made obsolete almost overnight by new technologies (or a different point of view), but what is seldom recorded is the sense of desolation and indeed mortality experienced by those unfortunate enough to live to see that their highly-developed skills are no longer wanted or needed. As my meteor-watching friend Paul Martsching has said, “It is good we don’t live forever: we are a product of our times.” He realizes full well that someday automated systems will count every meteor above the horizon far better and more completely than any visual meteor observer can, but for many years he has carefully recorded meteor activity many nights a year. The data he collects will always be relevant as part of the historical record, at least, and the sheer joy of being out under the stars and away from light pollution can never be replaced by a computer. To us, astronomy is something much deeper than what can be delivered through a computer screen.
We are a product of our times, and as we approach the twilight (or autumn) of our lives we don’t necessarily feel compelled to embrace every new thing that comes along. Peace.
From the standpoint of daily life, however, there is one thing we do know: that we are here for the sake of each other—above all for those upon whose smile and well-being our own happiness depends, and also for the countless unknown souls with whose fate we are connected by a bond of sympathy. Many times a day I realize how much my own outer and inner life is built upon the labors of my fellow men, both living and dead, and how earnestly I must exert myself in order to give in return as much as I have received. – Albert Einstein (1879-1955)
A vacuum is not nothing. It is only a region of three-dimensional space that is entirely devoid of matter, entirely devoid of particles.
The best laboratory vacuum contains about 25 particles (molecules, atoms) per cubic centimeter (cm3).
The atmosphere on the surface of the Moon (if you can call it that) contains a lot more particles than the best laboratory vacuum: about 40,000 particles per cm3. This extremely tenuous lunar atmosphere is mostly made up of the “noble” gases argon, helium, and neon.
The vacuum of interplanetary space contains about 11 particles per cm3.
The vacuum of interstellar space contains about 1 particle per cm3.
The vacuum of intergalactic space contains about 10-6 particles per cm3. That’s just 10 particles per cubic meter of space.
But what if we could remove all of the particles in a parcel of space? And somehow shield that empty parcel of space from any external electromagnetic fields? What would we have then?
It appears that even completely empty space has some inherent energy associated with it. The vacuum is constantly “seething” with electromagnetic waves of all possible wavelengths, popping into and out of existence on unimaginably short time scales—allowed by Heisenberg’s energy-time uncertainly principle. These “quantum flourishes” may be a intrinsic property of space—as is dark energy. Dark matter, on the other hand, is some weird form of matter that exists within space, exerting gravitational influence but not interacting with normal matter or electromagnetic waves in any other way.
Is there any evidence of this vacuum energy, or is it all theoretical? There are at least three phenomena that point to the intrinsic energy of empty space. (1) The Casimir effect; (2) Spontaneous emission; and (3) The Lamb shift.
The Casimir effect
Take two uncharged conductive plates and put them very close to each other, just a few nanometers apart. Only the shortest wavelengths will be able to exist between the plates, but all wavelengths will exist on the other side of the two plates. Under normal circumstances, this will cause a net force or pressure that pushes the two plates towards one another.
An example of spontaneous emission is an electron transitioning from an excited state to the ground state, emitting a photon. What causes this transition to occur when it does?
The Lamb shift
The Lamb shift is a tiny shift in the energy levels of electrons in hydrogen and other atoms that can’t be explained without considering the interaction of the atom with “empty” space.
If I had to pick a favorite symphony—and that would be difficult to do as I love so many—then it would have to be Symphony No. 1 by Johannes Brahms. Though he completed it in 1876 at the age of 43, he had been working on it for something like 21 years. He was a consummate perfectionist, and it shows.
The Madison Symphony Orchestra performed this extraordinary work this past weekend as the second half of a really fine program featuring Alban Gerhardt playing the Walton Cello Concerto, and Rossini’s Overture to Semiramide. We are so very fortunate to have an orchestra of this caliber in southern Wisconsin, and music director John DeMain is a treasure. I am a season subscriber, of course, and attend all the concerts except for the Christmas program in December.
I cannot get through a performance of the Brahms First Symphony without being moved to tears, and Sunday’s excellent performance by the MSO was no exception. The final section of the second movement (Andante sostenuto) features an incredibly beautiful violin solo, gorgeously played by concertmaster Naha Greenholtz. The fourth and final movement (Adagio — Più andante — Allegro non troppo, ma con brio — Più allegro) is pure ecstasy. Just when you think the symphony is drawing to a conclusion, it launches into another, even more remarkable, section. And that happens more than once. The modulating transition to the coda in measures 367-390 (about 15:42 to 16:24 into the movement, two minutes before the end) for me is one of the most exciting sections of the entire work.
I once asked my friend and accomplished horn player John Wunderlin—who is similarly deeply moved by orchestral music—how he keeps from choking up during the most moving passages he plays. “Fear of messing up” he said, half jokingly and half serious. Part of the discipline that any professional musician must have is maintaining composure during even the most moving and beautiful sections. I don’t think I could do it. But I did once see a teary-eyed violinist in the orchestra at the conclusion of a work. Want to know what that work was? It was the Symphony No. 1 by Johannes Brahms.
The Fourth Symphony of Dmitri Shostakovich (1906-1975) was completed in May 1936, but had to be withdrawn before it was performed due to the withering criticism and scrutiny Shostakovich was at the time receiving from Joseph Stalin and his increasingly repressive government. This symphony did not receive its first public performance until 1961. To get a sense of the enormous difficulties Shostakovich had to endure under the Soviet regime—and the extraordinary music of one of the 20th century’s most gifted composers, and indeed the last great symphonist—I highly recommend Robert Greenberg’s eight-part video course, Great Masters: Shostakovich – His Life and Music.
The Fourth Symphony is certainly not one of Shostakovich’s more accessible works, but I want to draw your attention to the remarkable, ethereal conclusion of this symphony that few have ever heard.
My entire Shostakovich collection was lost in the Memorial Day weekend 2015 Houston flood, and I’m gradually trying to replace it. I am currently listening to all fifteen Shostakovich symphonies in an excellent box set, conducted by Mstislav Rostropovich (1927-2007). Rostropovich was a close friend of Shostakovich.
Here is the final 4m45s of the third and final movement (Largo — Allegro) of the Symphony No. 4 in C minor, op. 43, by Dmitri Shostakovich, performed by the National Symphony Orchestra conducted by Mstislav Rostropovich. Turn up the volume—after the first couple of seconds, it is all very quiet. Enjoy!