Matter Is Binary

 

For those of you who are literal minded, this is a metaphor.

Metric Meters And Seconds

The speed of light is, by the current definition of the meter, 299,792,458 m/s. The second, in turn, is currently defined in terms of the rate of radioactive decay of a certain isotope of an unstable atom. Specifically:

The second [...] is defined by taking the fixed numerical value of the caesium frequency, Δν_Cs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9192631770 when expressed in the unit Hz, which is equal to s⁻¹.

The second was originally based upon 60 seconds per minute, 60 minutes per hour, 24 hours per day on Earth. The new definitions, however, are independent of the properties of planet Earth.

Meanwhile: 

The metre was originally defined in 1791 by the French National Assembly as one ten-millionth of the distance from the equator to the North Pole along a great circle, so the Earth's polar circumference is approximately 40000 km. . . . today Earth's polar circumference measures 40007.863 km, a change of 0.022% from the original value of exactly 40000 km, which also includes improvements in the accuracy of measuring the circumference.

If the original definition of the meter from 1791 had been carried through to the currently accurately measured distance from the North Pole to the Equator, then the speed of light would have been: 299,858,412.340 76 m/s, about 0.05% less than the nice round number of 300,000,000 m/s.

It would have be nice if the definition of the meter could have been changed to make the speed of light 300,000,000 m/s (which would be a meter that is is 0.0691806666667% longer than the current definition), or better yet, 100,000,000 new meters/s which would be 33333.3333 old mm per per new meter (about 13.12 Imperial inches). But the speed of light wasn't possible to measure until the length of the meter had been established to high precision, and the slight adjustments to precision metric measurements weren't deemed worth the numerological convenience by the time that the speed of light started to be used to define the meter.

A 300,000,000 m/s speed of light would slightly increase the size of the kilogram (by a fraction of a gram) which was originally based upon the mass of 1000 cubic centimeters of water at room temperature at sea level air pressure.

It would also slightly tweak the electromagnetic units that were originally based upon interactions that are a function of the meter.

Incidentally, the Imperial system of length measurement is defined in terms of the metric system, with one Imperial inch equal to exactly 25.4 mm, and all other Imperial length measurements flowing from that definition.

The Tesla Cybertruck And Industry Standards

Telsa has finally starting selling its weird modernist looking, stainless steel, bullet proof cybertruck. A tweet at X explains another thing about the new model that is a landmark change in automative electronics standards:

Techies are obsessed with Cybertruck's 48 volt architecture. 12 volt has been the standard for over 50 years, though a 1965 VW bug actually had a 6 volt system. . . . 

The reality is that the car industry has been moving toward 48V for the last decade. But it's a difficult transition. Part of the reason is that we've moved from MECHANICAL linkages to ELECTRONIC. Things like the air conditioner, power steering, and power brakes tapped into the main engine mechnically. Power brakes, for example, were powered by the vacuum generatedby the engine. Even the original Tesla Model S didn't have electronic brakes -- it had an electronic device generate a vaccuum, which then powered normal brakes. 

Nowadays, everything is electronic, not just in electric cars, but in traditional gasoline cars as well. Lower voltage means power needs to be delivered by thicker copper cables, which now becomes a major expense for the car, as well as an extra hundred pounds of weight to carry around. 

Increasing the DC voltage to 48V from 12V reduces the the copper thickness by exactly 4 (Ohms Law), reducing the cost and weight of copper by 75%. 

Specifically, one of the things driving the change is "Power over Ethernet". I know what you are thinking, WTF is Ethernet doing in a car??? 

Here's the deal. There are cameras throughout the car now that need to send hi-def video from the edges of the car to the central computer. This far exceeds the bandwidth of old technologies so they are using gigabite Ethernet these days. They've developed a special wiring standard that needs only a single pair of copper wires for both transmit and receive ("Single Pair Ethernet"). They've also developed enough technology to use that same pair to transmit power. These cameras use several watts of power, so would otherwise need additional cables for power. Single-pair Ethernet carrying power thus solves a ton of requirements for car makers. The desired voltage of such systems is 48 volts. 

The same revolution is happening for consumers, by the way. The USB C Power Delivery standard maxes out at 48 volts when you try to power your laptop at 240 watts. Power = volts times current, and USB cables support a maximum of 5 amps of current. 

48 volts is where government regulators have decided that DC electronics are "safe" from electrocuting people. Getting much beyond that introduces a whole new level of government interference and regulations. 

Thus, 48 volts is probably going to be the standard for cars, Ethernet, and USB for the next hundred years. 

Tesla's Cybertruck is making the jump early. . . .  it's likely going to result in a lot of recalls as Tesla makes fixes. But that's okay for a low-volume, new product. What Tesla doesn't want is to change to 48 volts in a Model Y and suddenly have to do a recall of a million vehicles. Cybertruck is a good test platforms to get it working. Presumably, we'll next see it in the higher end Models S/X, and then eventually in the Models 3/Y.

More Efficient Chemical Engineering Coming Soon?

A general principle to make more efficient catalysts could have great economic implications. 

In an advance they consider a breakthrough in computational chemistry research, chemical engineers have developed model of how catalytic reactions work at the atomic scale. This understanding could allow engineers and chemists to develop more efficient catalysts and tune industrial processes -- potentially with enormous energy savings, given that 90% of the products we encounter in our lives are produced, at least partially, via catalysis.

From Science Daily citing Lang Xu, et al., "Formation of active sites on transition metals through reaction-driven migration of surface atoms." 380 (6640) Science 70 (2023) DOI: 10.1126/science.add0089

Not Big Enough?

NASA confirmed that a 1000-pound meteor entered the atmosphere on February 15.

According to NASA, the meteor was seen at around 5:23 p.m. near McAllen, Texas. The meteor's speed was about 27,000 miles per hour, and it had the same amount of energy as 8 tons of TNT.

Although meteorites tend to hit Earth’s atmosphere at high speeds, they slow as they travel through the atmosphere, breaking into small fragments before hitting the ground. Meteorites cool rapidly and generally are not a risk to the public.

There were no reports of injury or property damage.

From here.

Now, if the meteorite had only been say, 50,000 short tons (about half the size of an aircraft carrier), with 800 kilotons of TNT impact, maybe it could have done the damage to Texas that it deserves, without doing much harm to the rest of the world, the evil part of me muses.

Don't Solve For The Equilibrium

One of the classic catch phrases of both economics and physics is "solve for the equilibrium". It is easier, mathematically and simpler, in  principle, to solve a problem with formulas in which everything has to balance out, than it is to solve a problem and predict a result where everything is out of equilibrium.

But, in the 21st century, we are in a context in which most questions worth asking in the social sciences involves circumstances that are further from an equilibrium state than at almost any other time in human history.

Technology, the fundamentals and system self-interactions that drive economics, the climate, the ecological balance of nature, parenting, dating, marriage, gender, racial identities, the way the political system works, military realities, and more are in intense flux.

Only a handful of political regimes anywhere in the world are more than five generations old. The first powered fixed wing aircraft flew four generations ago in 1903, commercial aircraft entered wide use about a generation later, and two generations later a man had walked on the Moon. Internal combustion engine vehicles fueled with refined petroleum became predominant by 1908 and will probably be a minority of vehicles on the road by 130 years later - the vast majority of non-transportation uses of petroleum have already largely been phased out (except heavy heating oil in a few regions, electricity generation in Hawaii and Alaska, lubricants, plastics, and fertilizers). General Relativity and quantum mechanics are less than four generations old, and when they were invented, Armies still had horse cavalry. Most of the national boundaries in the Middle East were drawn shortly after World War II. 

Jews started to return to Israel in the 1920s, after by tradition, about 1850 years in the diaspora, and the State of Israel came into being in 1948. Hebrew was an exclusively a liturgical language and a language used by religious scholars from about 200 CE to 1880 CE, was spoken by a community of about 34,000 people during World War I, and did not start to become a widespread living first language until the 1920s in the British Mandate in Palestine and first became a national language in 1948, about two generations after it started to be revived, when Israel became an independent state (at which point about 80% of Jews spoke it as a first language, and 15% spoke it as a second language).

The home that I live in was built less than a hundred years ago, in 1925 with coal fired steam heat boiler made popular by then recent global Spanish flu pandemic, had a door in the kitchen wall to receive ice deliveries, had a garage sized for a Model T, had galvanized steel pipes, didn't have electricity until it was added in later renovations, and was in a neighborhood that got its start as a streetcar suburb of Denver called "South Denver" before it was annexed by the City of Denver. Coal is now used predominantly to generate electricity in large power plants, in which it has a rapidly decreasing market share, and for "coke" in the steel production process.

Soviet style communism lasted less than 75 years in Europe, where it no longer exists. Many countries in East Asia and Southeast Asia still have nominally communist political systems (none of which are yet 75 years old), but their economies have adopted so many market economy reforms that their economies aren't really communist anymore. These nominally communist regimes are still authoritarian one-party states, but collective ownership of the means of production, and distribution of the fruits of production according to need, is a Marxist pipe dream that Asian regimes that are nominally communist have largely abandoned.

Around the time that my parents were born, the Great Depression wasn't over yet, the airship industry was collapsing, most of Africa and Asia was governed by European colonial powers, the Communists were just an upstart political party in China, and the Soviet Union was alive and well. My in-laws were born during World War II and experienced the Korean War in ways that put their lives at risk. The farm my father grew up on used a horse for farm labor when he was a child. The entire nuclear dimension of military affairs came into being at a time when my parents could read about it in the newspaper, as did the political regimes in Europe, Asia, and Africa. 

When my parents started high school, Latin was a mandatory subject for every college bound high school student and public schools in the South were still segregated by race as a matter of law. All Roman Catholics in the world conducted their church services in Latin at a time when my parents had both finished their undergraduate educations. My parents were first generation college students who earned PhDs. Co-ed dorms didn't exist when my parents were in college. At the time my father served in the Army, it was just in the process of desegregating. 

Long term mortgages and employment based health insurance were first widely used in my parent's lifetimes. My father-in-law was one of the first doctors to use radiology machines more sophisticated than X-Rays and his parents were first generation Christians. 

Over the course of my parents lives, the Republican party went from being a liberal leaning Northern party to a conservative party of the South and rural America. At my father's first job as a professor in Atlanta, Georgia, many of his students had spent at least some of their school years in segregated schools, and some of their African-American friends had first been able to vote in a Presidential election just four years before they arrived in Georgia as a consequence of the Voting Rights Act of 1965. 

My father was on the committee that organized the first Earth Day. My parents were peers of Elvis Presley and disliked the Beatles and pretty much all other kinds of rock musics, well into their 30s, when rock music started to become predominant. Big band music, more than one sub-genres of jazz music, rock music, and the music of "crooners", like Frank Sinatra featured on the Lawrence Welk show on TV, all came into being during their lifetimes before I was born.

Most of the hydroelectric, geothermal, and nuclear power plants in the world were built during my parents lifetimes before I was born, or when I was a child. The vast majority of the wind, solar, tidal power and natural gas fueled power plants powering the electrical grid in the world has come online in my lifetime, and a majority of the wind, solar and tidal power powering the electrical grid in the world has been added during my children's lifetimes.

Polio afflicted tens of thousands of people a year in the United States until after my parents were finished with college; there were ten cases of polio that originated in the United States in the first decade of my life, and there has only been one case of polio from any source in the United States in the last twenty-nine years, which was this year. The concept of autoimmune diseases as a coherently class of ailments was developed after my parents had graduated from college (and after my aunt was first diagnosed with M.S. an autoimmune disease whose true cause has only been ascertained in the last few years).

When I was born, most cars ran on leaded gasoline, most physics and engineering calculations were still done with slide rules, computers took up whole rooms, the primary method of putting information into a computer was a punchcard, formulas in physics journal articles were written by hand, and many rural areas were still served by "party line" telephone service. Early computers (in my lifetime) with the power of my cell phone would have taken the same amount of electricity to operate as a skyscraper. Computer processor power and memory has increased exponentially, and has seen power consumption decrease exponentially, for my entire life. The core components of the Standard Model of Particle Physics were invented in my lifetime. "No fault" divorce, legal recognition for LGBT rights, females making up more than low single digit percentages of lawyers and doctors and professors, the modern concept of attention deficit disorder, the generalized concept of post-traumatic stress disorder, widespread use of statins to control cholesterol, widespread use of student loans for higher education, and the modern environmental movement all came into existence, for all practical purposes, in my lifetime. Obesity rates for both children and adults in the U.S. have roughly tripled from their long term historical norms to current levels during my lifetime. 

The first time I met someone who was openly gay was in college, which is also the first time that I used the Internet, and the first time I'd encountered Muslims face to face, and the first time I'd eaten tofu. The Soviet Union ceased to exist when I was in college. Crime rates hit all time highs around the time that I was in college and have since declined to half century lows. Divorce rates which were once low across the board soared to record highs during my lifetime, then experienced a class divide with divorce rates for college educated couples plummeting and divorce rates for couples without any college educations reaching levels never before seen that continue to rise checked only by couples not bothering to get married when living together and having children at all.

MTV came and went in my lifetime, as did disco, New Wave, eight track tapes, cassette tapes, videodisks, compact disks (CDs), DVDs, and analog broadcast television. Broadcast satellite TV and radio came into wide commercial use in my lifetime and I doubt that either will still be in wide commercial use when I die. Rap and Hip hop were invented in my lifetime and remain vibrant. The proportion of Americans who identify as non-religious has increased by a factor of ten in my lifetime. 

Commercial supersonic aircraft came into being and then ceased to exist in my lifetime, and will renter the market again in a few years.

"Smart bombs", guided missiles, stealth aircraft, and unmanned military drones all entered regular military use in my lifetime.  Amphibious assaults, air to air combat between fighter aircraft in "dog fights", ship to ship battles, submarine to ship battles, ship to submarine battles, and the use of nuclear weapons in war, have become vanishingly rare or non-existent in my lifetime.

The death penalty in the United States was abolished nationally, and then reinstated on a much more restricted basis, in my lifetime. Abortion was first constitutionally protected after my brother and I were born, and has now been denied constitutional protection in my lifetime. Marital rape was criminalized, and domestic violence  and acquaintance rape first began to be taken very seriously by the criminal law in my lifetime, and gay sex between consenting adults was legalized by becoming constitutionally protected in the United States in my lifetime. Serious drunk driving penalties and major reductions in tobacco use both arose in my lifetime.

At my first job as a summer law clerk with a law firm, lawyers were not allowed to use computers or typewriters, we had to dictate everything that we didn't write longhand, leaving typing for a large and almost entirely female corps of secretaries who knew how to use typewriters and early word processors (even though the youngest lawyer in the firm and the law clerks knew how to do so themselves). Legal research, including checking cases to make sure that they had not been overruled or narrowed by subsequent cases, was done almost entirely with dead tree books, because computerized legal research while it existed, was very expensive per minute or per search. At the end of each day, a recent high school graduate would rush to hand deliver all of the firm's court filings to the local court clerk before the office closed at five p.m., and to mail copies of those documents before five p.m. at the local post office that this courier had spent all afternoon photocopying to every party of record in the case and the court with an extra copy to be pinned down with metal clamps in a hard copy paper pleadings file. Lawyers needed to finish their dictations and final handwritten revisions to court documents by three or four o'clock in the afternoon, to allow time for them to be typed by the secretaries, photocopied, delivered to the court clerk, and mailed, before the hard five o'clock deadlines for doing so. All court hearings were held in person.

Now those jobs are gone. All lawyers except men in their sixties or older type their own first drafts of court documents subject to only light editing and proofreading by staff (younger lawyers do their own advanced typesetting as well, while older ones rely on secretaries or paralegals for these formatting tasks), after personally researching cases and statutes online, and then they either personally, or with one paralegal serving several lawyers, e-file the documents to the court and to all other parties in the case by midnight deadlines, often without the final draft ever being printed or manually signed or filed. The client gets an email copy and often there is no paper pleadings file in a case at all. Many non-evidentiary court hearings like status conferences and pre-trial conferences are conducted remotely, as are many mediation sessions (something that also was rare back then, but now is required in almost every case).

Back in the day, many court documents needed to be notarized, in person, with a red ink stamp with a raised embossed seal. Now, the documents that used to be notarized are just signed by the client or witness in pen under penalty of perjury, scanned, and emailed to the lawyer for filing. 

As a result, modern law firms are profoundly more top heavy than they used to be in most kinds of law practices, and lawyers no longer work "banker's hours."

Mass produced electric cars were reinvented in my children's lifetime. I have never owned a car that wasn't made by a Japanese or Korean car company since my children were born. We haven't had broadcast television service at any time in my children's lives. We ended our cable TV service before they started middle school. We discontinued our landline telephone service before my children were in high school. My wife was pregnant with my oldest child when the Euro came into being and about a dozen European national currencies ceased to exist. My children were alive when cryptocurrencies came into being and when same sex marriages were legalized. The Department of Homeland Security, the TSA, the "no fly list", security checkpoints with shoe removal, and limits on carrying liquids arose after my oldest child was born. The U.S. has been a party to low intensity "small" wars for essentially all of my children's lifetimes. The privately enforceable constitutional right to bear arms was first recognized in my children's lifetimes. Lockdown drills at school, in response to numerous mass school shootings, have replaced in my children's generation the duck and cover drills of the Cold War era.

My children don't really remember ever living without the Internet or cell phones. Some of my children's high school textbooks were delivered on electronic tablets and they had homework assignments in high school that included typing mathematical formulas using LaTex computer typesetting. COVID, of course, arose during my children's lifetime. We are still a couple of years away from the U.S. getting its first truly high speed rail line, long after they have become common in Europe and China.

This recitation of historical events reminiscent of Billy Joel's song, "We Didn't Start The Fire" and a few subsequent imitations of its structure, may be a bit excessive and familiar. But, in this post, my real point is that everyone alive today, and our parents, and our grandparents, and even a generation or two beyond them, have never known a time when science, technology, economics, international affairs, culture, and law weren't in periods of breakneck change. 

Austrian-born economist Joseph Schumpeter, who is most famous for his Marxist inspired characterization of dynamic capitalist economies in the long run as a process of "creative destruction", particularly in his 1942 book Capitalism, Socialism and Democracy, was one of my favorite economists in college. This was because he had a realistic description and astute understanding of the essential features of the big picture of the workings of modern capitalism, when other economists so frequently seemed to lose sight of the forest for the trees attempting to devise simple, theory driven mathematical models of the economy.

It is easy to fall into the trap of thinking about the present as if this is the way that the world has always been and always will be, and one of the most important lessons I learned as a history minor in college was just how untrue that assumption was over far shorter time frames than I ever would have guessed otherwise.

But, solving for an equilibrium in the social sciences that can't be reached in the very short term of a fewer minutes to a few decades, at most, is irrelevant and often counterproductive. 

Change, and not equilibrium, has been the long standing norm for all of living history and all of the oral history and recollections of the vast majority of living people alive today. 

Forcing yourself to almost always consider dynamic models in the social sciences and in predicting the future of technology, is far harder and far less certain than trying to solve for an equilibrium predicted by your theories based upon the present. But, at least doing so avoids the near certainty that any attempt to solve for the equilibrium for any significant period of time will be wrong.

Prospects For Interstellar Travel Without Breaking The Laws Of Physics

If humanity can refrain from driving itself to extinction, it could send small probes to the nearest star in the foreseeable future, and could send a small village of people there on a one way trip that could be completed in a human lifetime within a few centuries. These are the boundaries of "hard" science fiction.

The key concept is to use lasers from near Earth to supply the space craft with power so that the space craft can have less fuel per payload on board, which in turn means it takes less energy to get the lighter craft relative to payload size up to marginally relativistic speeds.

Breakthrough Starshot is an initiative to explore the Centauri system using laser-accelerated sailcraft. Earlier work produced a point design for a 0.2 c mission carrying 1 g of payload. 

The present work widens the design space to missions having 0.1 mg to 100 kt payload and 0.0001-0.99 c (6-60,000 au/yr) cruise velocity. Also, the beam director may now draw up to 5 GW of power directly from the grid to augment the power drawn from its energy storage system. Augmenting stored energy with grid power shrinks beam director capital cost by 1-5 orders of magnitude. 

The wider design space encompasses new possibilities: 

A 0.1 mg microbiome accelerated to 0.01 c in only 2 min by a beam director that expends $6k worth of energy. 

A 10 kg Solar system cubesat accelerated to 0.001 c (60 au/yr) by a $600M beam director that expends $60M worth of energy per mission. 

A progression from cost-optimized point designs to whole performance maps has been made possible by replacing numerical trajectory integration with closed-form equations. Consequently, the system model now computes 1-2 orders of magnitude more point designs per unit time than before. Resulting maps reveal several different solution regimes that are characterized by their performance-limiting constraints. 

The performance maps also reveal a family of missions that accelerate at Earth gravity. The heaviest such mission is a 2 km diameter 100 kt vessel (equivalent to 225 International Space Stations) that is accelerated for 23 days to achieve 0.07 c, reaching the Centauri system within a human lifetime. While unthinkable at this time, the required 340 PW peak radiated power (twice terrestrial insolation) might be generated by space solar power or fusion within a few centuries. 

Regardless, it is now possible to contemplate such a mission as a laser-accelerated sailcraft.

Kevin L. G. Parkin, "Cost-Optimal System Performance Maps for Laser-Accelerated Sailcraft" arXiv:2205.13138 (May 26, 2022).

My Geographic Identity

Even a predominantly geographic personal identification is not a singular thing. It has many levels of resolution. And, this list does not even consider that people have associations with places that they work, places where they work out, places that they used to live, and places that they feel connected to because they have family and friends there.

* My side of the bed (perhaps sixteen square feet).

* My room in my house (a couple hundred square feet or so). Some art in my room (my photographs):

* My home (about 1/15th of an acre a.k.a. 2,887 square feet), also my subdivision lots.

* The area where my "immediate neighbors" live (about 5 acres), also my subdivision shown below via the City and County of Denver.

* My neighborhood (about 2000 acres a.k.a. about a one mile radius from my home a.k.a. about 3 square miles) defined as the area within easy walking distance of my home. Also overlapping areas from smaller to larger in area including my precinct, my census tract, the officially defined West Washington Park neighborhood (further divided into Byers and West Washington Park proper), the greater combined Washington Park and West Washington Park neighborhood, my zip code (3.5 square miles), my "home school attendance zones" within the school district for elementary school, middle school and high school respectively, my state house district, and my city council district.

A church in my neighborhood (my photo):

A bar near my neighborhood (my photo):

* My larger region within or near the city that I live in (about 30-50 square miles), either central Denver or Southeast Denver depending upon how you divide up the city, also my recycling pickup zone, my Denver School Board district, my state senate district, my RTD i.e. regional transportation district director district, the portion of the city that was formerly the city of South Denver, the portion of the city that was formerly in Arapahoe County, and the survey Township and Range in which I live (about 36 square miles).

* The City and County proper of Denver where I live (155 square miles), which is contiguous with the school district and state judicial district in which I live. Also, my Congressional District which is almost, but not perfectly contiguous with the City and County of Denver, which is also a district for the election of state school board and CU Regent candidates (189.62 square miles).

* The Denver metropolitan area where I live, i.e. Denver, Adams, Arapahoe, Broomfield, Jefferson, Boulder and Douglas counties (4,482 square miles). Also regional governmental areas (DRCOG i.e. the Denver regional council of governments, RTD i.e. the Regional Transportation District (2,342 square miles), SCFD i.e. the Scientific and Cultural Facilities District, and the Mile High stadium district), my allegiances to various professional sports franchises that represent the Denver area, such as the Broncos, Avalanche, Nuggets, Rockies, Rapids and Outlaws, and the telephone area codes associated with my metropolitan area (303) and (720).

* The larger regions of the state where I live (perhaps 18,000-45,000 square miles), i.e. the Front Range and the I-25 corridor. Also, the South Platte River basin (24,300 square miles which is located in parts of three States: Colorado (79 percent of the basin), Nebraska (15 percent of the basin), and Wyoming (6 percent of the basin)). The South Platte River basin is shown below via the U.S. Geological Survey:

* The State of Colorado where I live (104,185 square miles).

* The Mountain West states consisting of eight states (855,767 square miles). Also, the Mountain Time Zone.

* The Western United States (1,751,206 square miles).

* The United States of America (3.797 million square miles).

* North America  (9.54 million square miles).

* The Americas (16.43 million square miles).

* The Earth (196.9 million square miles of surface area). Photo taken by Apollo 17:

* The Solar System (roughly a 175 billion mile diameter disk a.k.a. about 11 light hours, with about 600-800 million square miles of solid surface area). The solar system, as far out as Neptune, to scale:

The surface area map below is from xkcd via a Creative Commons license.

Fun facts: Former planet Pluto has a similar amount of surface area to the continent of Australia. Africa has a similar amount of land area to the Moon. The surface of Venus bears the closest resemblance to Christian descriptions of hell.

* The Local Interstellar Cloud, a.k.a. Local Fluff, is the interstellar cloud roughly 30 light-years across through which the Solar System is moving (image below via Wikipedia).

* The Local Bubble (a.k.a. Local Cavity), which is a relative cavity in the interstellar medium of the Orion Arm in the Milky Way galaxy. It contains the Local Interstellar Cloud, which contains the Solar System. It is at least 300 light years across (shown below via Wikipedia, the dot in the middle with text attached to it is our sun).

* The Orion Arm (a.k.a. the Orion-Cygnus Arm) of the galaxy where the solar system is located, about half-way between the center of the Milky Way galaxy and the furtherest extent of this arm within it. It is about 3,500 light years wide and about 10,000 light years long.

* The Milky Way galaxy (roughly a 105,700 light years in diameter disk with about 100 billion stars and a supermassive black hole at the center) (an edge on view of the Milky Way from Earth and Earth orbit compiled from multiple images via Wikipedia is below).

* Our "local group" of galaxies (roughly 10 million light years in diameter including about 30-50 galaxies) (via Wikipedia with the Milky Way depicted as the center):

* The Universe (roughly a 28 billion light years in diameter sphere at the moment). The image below is approximately linear in years (except for the first few moments which are smaller than they appear) and has roughly logarithmic dimensions in two dimensional diameter representing the three dimensions of space which are roughly symmetric. The scientific consensus regarding this image starts to break down in the area all of the way at the beginning labeled "inflation" (which cosmologists who support some version of the inflation hypothesis say lasted for less than a second), but everything beyond the first hour or so after the Big Bang (depicted as a flash of light) does have solid, consensus support except that there is some dispute regarding the true exact cause of what is labeled as "dark energy accelerated expansion."

N.B. We have no real idea "where" within the universe we are located spatially relative to any helpful big picture landmarks. The observable universe is basically homogeneous subject to a very, very subtle large scale cellular filamentary structure that extends as far as we can see in distance which is also back in time, in every direction. 

It doesn't even really make sense to talk about a "center" of the universe because observable space itself has expanded from a space definitely smaller than the solar system and quite plausibly smaller than a basketball at the beginning of the Big Bang to what exists today. All space in existence today maps back in time to this tiny immediate Big Bang vicinity area that set the initial conditions for everything. Thus, not only has the stardust that makes up our planet moved around within space; the space itself within which that movement took place has been massively stretched out.

Space-time itself is also bent by gravity. Topologically, at the largest observable scale space-time in the present day is almost, but not quite perfectly, topologically flat. It has an overall slight curvature in four dimensions that is analogous to the curvature of the surface of a three dimensional sphere that is called de Sitter space. This is unfortunate, because we have all sorts of wonderful mathematics to describe anti-de Sitter space which is analogous to the curvature of a hyperbolic plane in three dimensions, but the math needed to describe a universe like our own is much harder than less beautiful. 

Truly topologically flat space-time that observes special relativity (i.e. with no bending of space-time caused by gravity) is called Minkowski space. It turns out that the large scale curvature of the Universe is so slight, and the curvature induced by the gravity of large objects is also modest away from black holes, neutron stars and other very massive and very dense objects (i.e. away from strong gravitational fields), that the far more mathematically easy to deal with Minkowski space is used as a working approximation of the topology of space-time for even extremely high precision physics applications at short distance scales like quantum physics, and for the estimating for practical purposes effects of gravity at the fringes of galaxies, galactic clusters, or small systems of nearby galaxies, which in general relativity is only slightly different from Newtonian gravity (except that gravity bends light as well as influencing the trajectories of matter in space).

Cutting Edge Educational Technology In Mathematics And Theoretical Physics

Coverage of the important topic of blackboards is to be found here. To those ill-informed sorts who think that blackboards are the past, whiteboards or some other technology the future, I’ll point out the following. When I came to Columbia back in 1989, there was a recently installed modest-sized whiteboard in the math department common room. Everyone hated it, and after many years it was replaced by a similar-sized blackboard. Last year, in a renovation of the lounge, that blackboard was replaced by a better one, and one whole wall of the room was replaced by a floor-to-ceiling blackboard. A year or so ago, a newly renovated Theory Center was unveiled here in the Physics department: floor-to-ceiling, wall-to-wall blackboards. That’s the future, the whiteboard is the past.

From Not Even Wrong

Incidentally, the linked material notes that chemists, unlike mathematicians and physicists, prefer whiteboards.

Quote of the Day

What's the speed of dark?

- Fortune Cookie

A Platonic Nerd Love Story

One day in the spring of 2013, for instance, as he sat in the Queen’s Gallery at Buckingham Palace awaiting the annual Order of Merit luncheon with Elizabeth II, Sir Michael made a match for his lifelong friend and colleague, Sir Roger Penrose, the great mathematical physicist.

Penrose had been trying to develop his “twistor” theory, a path toward quantum gravity that’s been in the works for nearly 50 years. “I had a way of doing it which meant going out to infinity,” Penrose said, “and trying to solve a problem out there, and then coming back again.” He thought there must be a simpler way. And right then and there Atiyah put his finger on it, suggesting Penrose make use of a type of “noncommutative algebra.”

“I thought, ‘Oh, my God,’” Penrose said. “Because I knew there was this noncommutative algebra which had been sitting there all this time in twistor theory. But I hadn’t thought of using it in this particular way. Some people might have just said, ‘That won’t work.’ But Michael could immediately see that there was a way in which you could make it work, and exactly the right thing to do.” Given the venue where Atiyah made the suggestion, Penrose dubbed his improved idea “palatial twistor theory.”

Nerds are capable of feeling that rapture that others find in romance. The triggers are just a little different (from Quanta magazine via Not Even Wrong).

Scientific Proof of the Flying Spaghetti Monster's Existence

Pastafarians rejoice! Australian astronomers have validated your faith scientifically.

Invisible structures shaped like noodles, lasagne sheets or hazelnuts could be floating around in our Galaxy radically challenging our understanding of gas conditions in the Milky Way.

From here.

Could you tell the difference between hazelnuts and meatballs in a fuzzy telescope image?

The "hazelnuts" may really be meatballs that are being misdescribed.

The structures are known as "dark noodles", by analogy to dark matter and dark energy, because, obviously, matter, energy and noodles are the three fundamental states of the stuff that makes up the universe.

Physics GRE Scores Don't Predict Success In Astronomy

A study of the Physics GRE exam scores of successful post-docs tends to show that your Physics GRE score is irrelevant to your success in an astronomy program.  By implication, it may be a poor tool to regulating admissions to graduate programs in astronomy.

A Conjecture On The Purpose Of Academia

My conjecture is this:

Academia exists to protect society from the risks associated with having too many geniuses making decisions in our lives in the worlds of business and politics.  The most dangerous geniuses of all are safely sealed away from the real world in posts as professors of theoretical physics. (Once upon a time they would have been made professors of theology and philosophy.)

Nuclear Power v. Hydrocarbons

There is a stunning difference in fuel volume between nuclear power and chemical power.

Tachyonic Judges Found On Second Circuit Court of Appeals

At How Appealing, we have a report of tachyonic appellate judges:

We all get some dates wrong when the year changes, and sometimes they lead to amusing results. Today's decision from the Second Circuit, for example, was argued December 13, 2012, and decided on January 6, 2012. Must be a new record! . . . Not surprisingly, this extreme example of judicial efficiency is attributed to Judge "Per Curiam."

("Per Curiam" is Latin for "by the Court" and is the default author of an opinion of a multi-judge panel when no one judge claims authorship of the opinion. This authorship is common used in brief, unanimous opinions that summarily dispose of a case that are written by law clerks, opinions that are so bare bones that nothing that distinguishes from judge's ideas or writing style from another's, or when there are substantial contributions from multiple judges in a more collaborative than usual process and it is desirable for the legitimacy of the courts to show a united front.)

Feynman On Big Numbers

There are 10^11 stars in the galaxy. That used to be a huge number. But it's only a hundred billion. It's less than the national deficit! We used to call them astronomical numbers. Now we should call them economical numbers.

- Richard Feynman (from here).

General Relativity Still Works Perfectly

[I]n 2007 the Gravity Probe B team confirmed one prediction of general relativity. According to Einstein, the Earth’s gravity warps spacetime like a bowling ball on a trampoline. This geodetic effect was measured with an error of about 1 percent. [The theoretical prediction for the geodetic effect in this experiment from general relativity was 6.61 arcseconds (1.84x10-3 degrees) per year.]

The much-smaller frame-dragging effect from the Earth’s rotation, though, remained hidden in the noisy data. Theory predicted frame-dragging should change the orientation of the spinning spheres by only 39 milliarcseconds per year, about the width of a human hair seen from 400 meters.

After NASA pulled the plug in 2008, private funding arranged by an executive at Capital One Financial and the royal family of Saudi Arabia bought some extra time to clean up the data. . . . The results of this painstaking analysis, scheduled for publication in an upcoming Physical Review Letters, reconfirm the geodetic effect with an error of about 0.2 percent [about 12 milliarcseconds]. Gravity Probe B puts the frame-dragging effect at 37 milliarcseconds with an error of about 19 percent [about 6 milliarcseconds], far from the original goal of 1 percent precision.

From Science News.

An experiment with the LAGEOS satellites whose results were published in Nature in 2004 had already confirmed the frame dragging effect with an error of 10 percent, but the independent replication of this result still has value. The team that achieved that result hope to improve their precision to 1% with a satellite launched this year.

Suffice it to say that the results are accurate enough, and the track record of general relativity's predictions in this domain (weak field, low speed), are good enough that nobody is betting that these predictions will be disproved. The experimental results are within 0.4 sigma of the theoretical prediction, well within the range of what would be expected from experimental error and not a result of cherry picking given that the result has been experimentally tested only twice.

The dark energy effects which have been observed to date can be incorporated completely into the equations of general relativity simply by setting the appropriate value for the cosmological constant, although there are alternative explanations as well. The uncertainty in this constant is currently about 3.3%.

The gravitational constant "G" remains one of the least accurately determined fundamental constants of physics, primarily because it is hard to precisely measure the gravitational effects of masses amenable to laboratory measurement since the gravitational impact of laboratory sized masses is so weak. It is 6.67428 x 10^-11 Newtons (meters/kilogram)^2
with a relative standard uncertainty 1 part in ten thousand. This latest estimate from 2007 is an improvement by a factor of roughly one hundred over an error factor of about 1.3% as of 1798.

Gravitational time dilation effects have been measured directly with atomic clocks in Colorado within the last year and have been precisely as predicted by General Relativity.

Some of the missing pieces of an experimental confirmation of all aspects of general relativity include the direct observation of gravitational waves, although there are strong indirect indications that they exist as predicted.

More seriously, there is not a consensus explanation for "cosmological inflation" (i.e. much faster than cosmological constant rate expansion of the universe during the time from 10^−36 seconds after the Big Bang to sometime between 10^−33 and 10^−32 seconds after the Big Bang). Still, a glitch this tiny, for that short of a time period, 14 billion or so years ago, isn't exactly a glaring flaw. The Big Bang theory still provides a simple, consistent explanation from that time forward, and there are all sorts of uncertainties, some of which may never be possible to resolve, about the extremely early cosmology of the universe.

Also, there is some reason to believe that singularities aren't as singular as they appear in classical general relativity equations at a quantum level.

The only observations from astronomy that do not fit the equations of general relativity, which was proposed in 1916 by Albert Einstein, and the directly observed distributions of matter, within the realm of experimental accuracy, are those attributed to dark matter, most commonly via a cold dark matter paradigm.

The main problem with this theory is that a dark matter particle that would be a fit for the model has never been observed directly. Indeed, experimental results about the potential mass of such a particle so far this year are contradictory. DAMA and COGENT experiments seem to show annual variation in the frequency of events attributed to a dark matter particle proposal in the mass range of about 7 GeV/c^2, something seemingly ruled out by other dark matter detection experiments, one of which used the same material in its detector as COGENT.

Another problem is that a naive cold dark matter model do not fit the observed data, because that model produces the wrong dark matter distribution to predict the effects expected (cuspy halos), an insufficient number of dwarf galaxies, and incorrect amounts of angular momentum in galaxies. Efforts to determine the amount of ordinary matter in the universe also make estimates of the right amount of dark matter error prone. There was a major underestimate of the amount of ordinary matter in elliptical galaxies that was just discovered in the last year, and there is still little clarity regarding the aggregate mass of neutrinos in the universe, because the average mass of an individual neutrino isn't very precisely established. Various efforts have been made to solve these problems, but no one consensus resolution has solved all of them yet.

According to one person I've heard explain why gravitational effects of dark matter can't be observed at the solar system level: “The density of the solar system is much bigger than the density of our galaxy, and dark matter gives 1-5 times the density of our galaxy. Utterly irrelevant in the solar system[.]”

Alternatives to dark matter such as Modified Newtonian Gravity aka MOND (TeVeS in a relativistic variant) have been proposed and work at the galactic scale, but still need some dark matter of some kind to explain how galactic clusters behave (possibly simply massive neutrinos, however), and have not provided a good explanation for the behavior of the "bullet cluster" collision. But, efforts to validate this hypothesis have shown that a simple equation with just a couple of constants (that calls for gravity to fall off at 1/r rather than 1/r^2 below a critical value for gravitational field strength) can accurately predict all dark matter driven phenomena at the galactic scale in all types of galaxies (including some whose behavior was predicted before it was measured), so any dark matter theory that works must accurately reproduce this relationship at this scale.

The bullet cluster observation also places the tighest limits to date on the cross-section of interaction of dark matter, which in inextricably intertwined in experimental practice in most cases with dark matter particle mass. This isn't wonderful for the cold dark matter model because it "rules out most of the [cross-section of interaction constant] range invoked to explain inconsistencies between the standard collisionless cold dark matter model and observations."

One of the main effects of the experimental confirmation provided by Gravity B and other general relativity testing experiments has been to tightly constrain the extent to which any quantum gravity theory that does not reduce exactly to general relativity can deviate from it.

Light Higgs Rumor

An internal paper at the ATLAS project set the world on fire on Friday when it showed signs at the four standard deviation of a possible Higgs-like particle with a mass of about 115 GeV, which is right where a lot of people think it ought to show up in the data. Previous studies have shown "bumps" of almost two standard deviations at the same mass but haven't been able to provide convincing proof that the data are more than a statistical fluke.

Skepticism abounds, however, because the magnitude of the effect in the diphoton channel observed is much larger than anyone had predicted. This could be a sign that something is wrong with the analysis in the as yet not peer reviewed paper, or could be evidence of not only a Higgs but also of at least a fourth generation of fundamental particles beyond the three known to exist (something that neutrino data has already hinted might be the case). For technical reasons, a prediction that there is at least a fourth generation of fundamental particle would still provide almost no information about its mass.

Alternately, there could be a 115 GeV mass particle that is not a Higgs. The properties that can be inferred from the data in this paper tend to favor a scalar particle, like a Higgs, but do not distinguish it from other possibilities.

For SUSY and string theory fans, a 115 GeV Higgs is great confirmation of what they expect, but a fourth or greater generation of fundamental particles could throw a serious wrench in their theories.

WIMPs Very Weakly Interacting Or Not So Massive

Sean at Cosmic Variance summarizes the latest findings of the Xenon 100 experiment's effort to directly observe dark matter better than any other account that I've seen so far.

What Is Dark Matter?

Dark matter is a hypothetical collection of non-luminous, non-baryonic matter particles that can explain why objects we observe with telescopes don't behave the way that they would if matter were distributed proportionately to the matter we can see with telescopes and only gravity as we understand it with Newton's law and General Relativity, governed them.  Plain vanilla ordinary matter doesn't behave in ways that could explain all the the dark matter that we infer exists from the way that objects in our telescopes behave.

There are various proposals for what kind of particle dark matter might be, with WIMPs (weakly interacting massive particles) being among the most popular. 

The First Round of Xenon 100 Results

Xenon 100 was an experiment designed to directly detect WIMPS, but so far, it hasn't seen any.  Instead, it has ruled out a large swath of properties that hypothetical WIMPs could have that would have caused them to be detected by this experiment.

Here we see the usual 2-dimensional dark matter parameter space: mass of the particle is along the horizontal axis, while its cross-section with ordinary matter is along the vertical axis. Anything above the blue lines is now excluded. . . . That grey blob in the bottom right is a set of predictions from a restricted class of supersymmetric models (taking into account recent LHC limits).

The closer you get to the bottom of the chart, the more weakly interacting a particle is (a bit like a neutrino which is also very weakly interacting).  The closer you get to the left of the chart, the less mass it has.

The chart shows that a massive particle must be very weakly interacting to fit the data, while a very light particle could still be reasonably strongly interacting, given the experimental data.  CoGeNT and DAMA were experiments looking for fairly light, somewhat strongly interacting dark matter particles.  Xenon 100 covered a much larger range to potential dark matter particles.

The kind of SUSY motivated WIMP proposed by Buckmueller, et al. with a mass on the order of 150-250 GeV and very lower levels of interaction with normal matter is not ruled out by Xenon 100, nor are more strongly interacting particles with masses of under 6 GeV.  But, the Buckmueller proposal will be threatened as the Xenon 100 data set gets larger over the next year or two.

The Difficulties and Attractions of Lower Mass WIMPs

The lighter a proposed WIMP is, the harder it is to come up with a particle creation theory that explains how there could be so many of them in the universe, despite the fact that we haven't observed them yet.  The lighter a particle is, the more prone it is to be created in a high energy particle accelerator experiment.  Yet, already observed weakly interacting particles, like the three types of neutrinos known to exist, with their currently estimated masses, produced in the ways that we are aware that they can be produced, don't seem to be large enough to account for the quantity of dark matter that astronomy tells us should be out there if gravity works the way that we think that it does.

We have observed lots of ordinary standard model particles with masses in the range from 0.0005 GeV to 91 GeV (the electron, the up quark, the down quark, the muon, strange quark, charm quark, the tau, bottom quark, the W particle, and the Z particle), and in a few cases we have observed a particle that is strongly interacting and strongly theoretically motivated, the top quark, with a mass of about 168-192 GeV.  Thus, while it wouldn't be impossible for a weakly interacting light dark matter particle to be missed, that particle would have to have some pretty unusual properties to escape even indirect detection as a result of missing matter in high energy particle physics experiments that have been conducted so far.  So, detecting a not all that weakly interacting light dark matter particle with a mass of less than 10 GeV or so, is less plausible that the chart would suggest.  We have no reason to think that any particle of that type that is electro-magnetically charged or interacts with the strong nuclear force exists and we have good reason to be highly skeptical that any particle of that type heavier than a tau neutrino that interacts with the weak nuclear force exists.

A discovery like that would be a bit like discovering a new species of insect in Washington Park.  Not impossible if you looked at it in some way that nobody had previously considered, but unlikely given how carefully and regularly that plot of real estate has been examined, sometimes by people with considerable expertise who admittedly weren't really looking for it in particular.

The most strongly theoretically motivated hypothetical particle with properties that would fit the light end of the mass range is the "sterile neutrino" (a heavish neutrino that differs from ordinary neutrinos in that it doesn't interact with the weak nuclear force as regular neutrinos do, perhaps because it is "right handed").  The latest conference on neutrino physics provided indications from a couple of lines of evidence that there might actually be more than the three known flavours of neutrino in existence (perhaps four or five), boosting the attractiveness of this kind of dark matter candidate.  But, none of the hints that there are more kinds of neutrinos out there so far are definitive enough to proclaim that they have been discovered.

None of the experiments in place to directly observe dark matter could detect a weakly interacting dark matter particle that is this light, and has properties that have caused it to evade detection so far in high energy physics experiements.  This kind of particle will become one of the most likely dark matter candidate by process of elimination if the Xenon 100 experiment fails to find any sign of heavier WIMPS before it is ended.

Heavy SUSY WIMPs Considered

The alternative of a heavy SUSY dark matter particle is attractive because SUSY predicts lots of additional particles, the lightest of which would be expected to be stable, and some of which wouldn't be strongly interacting with ordinary matter.  One of the more common proposals for a lightest supersymmetric particle is called the neutralino, by SUSY predictions are rather fuzzy about the precise masses of the particles it predicts, even though it predicts their other properties very exactly.  Several other SUSY predicted particles are also candidates for a lightest supersymmetric particle.  A heavy SUSY dark matter particle is also attractive because if it is heavy enough, current experiments wouldn't have detected it enough because they didn't have enough energy to create one or observe its indirect effects.

Both the large hadron collider (LHC) and Xenon 100 have a good chance of finding a heavy SUSY dark matter particle of the kind suggested by Buckmueller, et al. in the next few years if one is out there to be found.  If no particle is observed in the hypothesized mass and cross-section range in the next few years in these two experiments, SUSY itself becomes harder and harder to justify as an experimentally plausible extension of the Standard Model, because some of the phenomena that SUSY exists to make neater and tidier are mass scale dependent, yet also have to be heavier than anything that we've produced in high energy physics experiements so far so as not to contradict existing experimental data.

A heavy SUSY WIMP so close to being discovered or disproved, in part, because it would be similar in mass to the long sought after Higgs boson that the LHC was designed to discover (although probably a bit heavier).  Metaphorically, this means that it is on the fringe of a part of the universe upon which we are shining the brightest spotlight that humanity has ever had to look for something else that should be in the same vicinity.

SUSY is just a theory motivated by the ugliness of the Standard Model, but the Higgs boson is something we currently assume to make the Standard Model, which we used every day to make detailed and superaccurate predictions work.  It is the only missing piece of an already tremendously successful theory of physics.

If a SUSY WIMP isn't found, we have to conjure up some other way source of dark matter effects and have to give more credibility to the possiblity that the laws of physics are fundamentally ugly and arbitrary.  If a Higgs isn't found, we have to rewrite the laws of physics we use today.  We should have much better answers to both of those questions before my tweens go to college.