omenti

a tale of two wavelengths

Just after sunset Venus and Jupiter are dancing together in the Western sky.  Venus is the brighter of the two, in fact she's the brighter than anything but the Sun and Moon.  Throughout the month of June, at least as seen from Earth, they've been getting closer and closer and tonight they'll be within about 2 degrees of each other.  On June 30^th only a third of a degree of arc separates them.

 

Believe it or not I'm going to attempt to link astronomy and 5G mobile wireless, so hang in there.

 

Astronomers measure the angular separation in degrees.  You can easily break this down - the separation between any point on the horizon and the zenith overhead is 90 degrees, halfway to the zenith is 45 degrees, the moon is about a half degree wide.  Beyond that you can use your body - your arms and fingers turn out to be fairly useful for rough measurements.  Here's what I have used since I was a teenager:

 

° Stretch your thumb and little finger as far from each other as you can. The span from tip to tip is about 25 degrees

° Do the same with your index finger and little finger. The span is about 15 degrees

° Clench your fist at arms length, and hold it with the back of your hand facing you. The width is about 10 degrees

° Hold your three middle fingers together; they span about about 5 degrees

° The width of your thumb at arm's length is about 2 degrees

° The width of your little finger at arm’s length is about 1 degree.

Depending on your  vision you may want to close an eye doing this. This even works for very tall and very short people as their arms and hands tend to scale with height.  You can measure some known objects and calibrate your hand if you want.¹  A quick calibration can be done on June 27^th or July 2^nd when Venus and Jupiter are almost exactly 2 degrees apart - see if your thumb just covers them.

 

All fine and good, but most of the objects in the sky tend to be much smaller.  The moon is about a half degree or thirty arc minutes wide.  Most of the objects you can resolve into some shape are measured in arc seconds.  Stars appear as points of light from Earth - their disks are below most resolution limits.   The angular resolution of your eye or a telescope has a theoretical limit depending on the wavelength light being imaged and diameter of the instrument's mirror or lens.  Angular resolution improves (is a smaller number) when the wavelength decreases and the diameter of the lens or the diameter of the mirror or lens increases  - at least to a point.²   Our atmosphere is turbulent causing stars to  twinkle and, through a telescope, are blurry at higher magnifications.  Astronomers rate the quality of the sky in terms of 'seeing' - the best possible angular resolution you can obtain. At Mauna Kea or La Palma spectacular nights can drop as low as 0.4 arc but normal quality at an observatory is more like 1 arcsecond.   If you were only looking for resolution, Earth based observatories could get by with mirrors well under a half meter in diameter.  But a large mirror is a light bucket - and huge mirrors collect a lot of light allowing astronomers to record extremely faint objects.³

 

The diagram shows the relative scale of some telescopes.  You'll notice a few of them have multiple mirrors in two flavors.  It is much cheaper to build several high quality small mirrors than one enormous piece of glass.  Often these are combined to tile the parabolic shape of a larger mirror.  The second flavor, interferometer telescopes,  is more exotic using widely separated mirrors.  Through some tricky optics the separate mirrors act like segments of a very large mirror.  They lack its light gathering power, but have the its resolution.   They're tricky to operate, but are a path to affordable resolution.

 

The next chart is a bit messy , but is just the angular resolution equation.  The horizontal axis is the limiting resolution in arcseconds and the vertical axis is the effective diameter of the aperture.  The red dot in the lower right is the pupil of your eye - a bit less than a centimeter in diameter when fully dilated.  The diagonal lines represent the wavelength of light.  An ideal eye looking at reddish light can resolve about 20 arcseconds.  Bluish light has a shorter wavelength and the resolution improves to about 10 arcseconds.  If we could see into the ultraviolet and beyond we could resolve smaller angles.   The blue star is the Hubble Space Telescope - it gets down to something under 0.1 arcseconds beating any Earth-based telescope without adaptive optics. 

 

We were looking West at Venus and Jupiter.  Now shift your gave South towards the spout of Sagittarius' teapot - the direction of the center of our galaxy.  Near the center is an enormous black hole.  At 4.3 million times the mass of the Sun Sagittarius A*  is approximately supermassive.  It is difficult to calculate its size, but the current limit is something smaller than about 15 times the Sun's diameter.  That may sound large, but we're about two thirds of the way out from the center of the Milky Way- 26,000 light years away.    That makes it a very small target.  So an interesting question comes up - can you take a picture of it, or more properly its accretion disk?⁴

 

There is a big problem.  The center of the Milky Way is full of dust which prevents us for seeing it in visible light.  The region is more transparent to certain radio wavelengths, but that presents a problem, At best a radio wave's wavelength is thousands of times less than visible light.  You would need a radio antenna kilometers long just to match the resolution of a one meter optical mirror.  

 

The resolution needed is about what it would take to resolve a baseball on the Moon - something around 50 micro arcseconds.  Referring to our handy chart we see this is just possible with apertures of several thousand kilometers with submillimeter wavelengths.  It turns out a variation on the trick used in multi-mirror interferometer telescopes saves the day.

 

If you record information in a passing radio wave including the precise time it was recorded and combine that with similar information from other antennas you can synthesize an effective aperture that is the distance between the antennas.  You want as many different length paths as possible, so you need to find submillimeter radio telescopes thousands of kilometers apart and and attach extremely accurate atomic clocks to create a long baseline interferometric array.  A telescope potentially the size of the Earth.  This is still a work in progress, but it is amazing astrophysics.⁵

 

Time to circle back.  Submillimeter radio waves are often absorbed by the atmosphere as well water vapor.  The telescopes are located on high mountain tops in very dry regions and at the South Pole in Antarctica.  Over the years radio astronomers have built a deep understanding of how short wavelength radio waves are absorbed.  

 

Very little communication is done above 10 GHz, but the lure is a lot of available spectrum.  One millimeter radio corresponds to 300 GHz.  Radio astronomers have done pioneering work studying how these radio waves are absorbed by the atmosphere.  Some of the 5G radio schemes are looking for such virgin territory.  Some of the problems may turn out to be good points.  Attenuation is strong at many of these frequencies, but limited range, assuming you have a high density of access points, translates into potentially huge amounts of bandwidth per radio.  We may even be able to minimize backhaul costs and perhaps route around carriers entirely.  A long shot, but maybe...

 

It is remarkable that astronomers work with such diverse wavelengths of light.  In doing so they've been early pioneers in understanding how light travels through the atmosphere.  Some of that work will allow us to image a black hole as well as to pave the way for the next generation of mobile devices.

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¹ Radians are more popular in astrophysics, but astronomers often stick with degrees.  Self calibration is just the thing for a nerdish experience.  Measure your family and see how close your measurements are.  

²  

where θ is the angular resolution (radiansr), λ is the wavelength of light, and D is the diameter of the lens' or mirror's aperture.

 ³ There are a couple of ways around the seeing limit.  One is to orbit a telescope - the effective angular resolution of the Hubble Space Telescope is only limited by its optics. The other trick is to use adaptive optics.  It is possible to measure atmospheric turbulence and correct for it in real time.  This is still fairly exotic and is mostly used on big research telescopes, but the improvement is stunning.  The VLT improves from about 1 arcsecond to as 30 to 50 arcseconds with the adaptive optics switched on.  

⁴ Matter accelerates as it falls towards a black hole radiating energy along the way.  This forms a bright accretion disk and the object that can be imaged.  

⁵ a paper here (pdf)  

leveling up

Motor vehicle deaths are currently running about 33,000 per year in the US.  While there are many ways of looking at the numbers,  perhaps the most remarkable is we find the carnage acceptable.  It is possible to simply reduce the death rate without new technology, but car performance would become unacceptable for most people.¹

 

A big hope is the autonomous vehicle. The National Transportation Safety Agency (NHTSA) has outlined five levels of technology in a 2013 research plan.   A rough summary is:

 

0  current unassisted driving c. 1990

1  Advanced Driver Assistance Systems (ADAS) like anti-lock brakes, electronic stability control, lane-keeping, etc.  Common in current cars

2  Integrated functionality like a combination of lane-keeping and adaptive cruise control.  Available in some luxury cars now.  Human monitoring and the ability to quickly intervene is necessary.

3  Self-driving in some situations like highway driving.  Human monitoring and intervention is essential.

4  Full self-driving where unmanned operation is possible.

 

These definitions are messy, but most people agree upon them as a starting point.²

 

There is a target, but how and when do we get there? What are the society and technology issues?  I'll punt on much of this (let's talk if you're interested), and just focus on a few safety issues that might provide a bit of context.

 

Level 3 cars will happen in the near future.  The capability will be an optional feature on many expensive cars although there will be limited functionality.  Highway travel on dry roads is a likely starting space.  Although speeds are higher than town driving, the problem space is much smaller most of the time.  Cars tend to stay in the same lane and relative speed differences for cars in the same lane tend to be small.  

 

Highway driving is often boring, which is ideal for a computer.   The problem is the brief moments of excitement where human intervention will be necessary.  Consider the case where the semi you're following brakes heavily and your car's computer decides it can't break in time.  A solution might be to veer to one side and pass the truck.  This requires knowing road friction, the car's performance, how to introduce torque and information on the new space you will be traveling through.  Given sophistication and the appropriate information it could find a safe path for you while not endangering others, but early on it will throw up its hands and wait for you to sort matters out.

 

In the situation above it would be useful if all of the vehicles in the area would be communicating and creating a joint plan to follow. Vehicle to vehicle communication and a potentially complex executable plan are required.  Not only will standards need to be hammered out, but many such maneuvers would require a large percentage of vehicles with at least level 3 functionality. For a long time we'll be at early level 3 where the driver must quickly take control.  As the information and computation environment becomes richer we'll move to an enhanced level 3 -- perhaps we'll talk in  terms of 3.1 or 3.4 capabilities. If you think Android system fragmentation is an issue, just wait...

 

Extra safety can be built in by having the system determine that a crash is inevitable and preparing the crash system appropriately.  It may make sense to limit speeds and speed variation to give systems better response time to allow the driver to spool up to full capability if a control hand-off is required.  We may see very strict 60mph  or slower speed limits with strong penalties to encourage all vehicles to blend into the flow.  Such tactics may be even more important with early level 4 cars and in situations where weather is involved.  

 

Security is critical and mostly missing in current prototypes.  Hacking systems could be a major attraction for a terrorist so this part has to be nearly perfect.  It could be the most difficult hurdle to full level 4 autonomy. 

 

City and suburban traffic is more challenging.  Extremely good maps and high situational awareness is required.  Low speeds would be a big help.  European traffic calmed speeds - about 20mph in many areas would be a big help.  Requiring conventional vehicles and bike riders to use GPS enabled radios - perhaps their smartphones -  to share the road with may become a requirement. 

 

Suburban self-driving is interesting for applications beyond carrying people around.  Several companies, including Amazon, are thinking about autonomous ground drones.  Lightweight electric delivery vehicles.  With appropriate planning 20 mph is just fine for such applications.  Delivery capacity is much greater than an airborne drone, costs are potentially lower and public acceptance may be greater.  Such vehicles also would create rich photographic datasets that would make autonomous travel easier for manned vehicles and, as such, they may precede city and suburban cars.

 

The level 3 to 4 transition may be difficult - so difficult that some researchers suggest skipping level 3 entirely.  Aviation experience dealing with switching from autopilots to full manual control has proven very difficult.  Current recommendations is that someone should be on the steering wheel and brakes as the vehicles begins to get in bad situation.  The system may be handling driving and giving a sensation of control and let the human take over as it the computer runs out of options.

 

Turning your seat around to chat in an autonomous car was predicted by 1960 in 1939 and 2000 in 1964 at respective World's Fairs in New York City.  It turns out the relative position of the seat, occupant, and safety equipment is a difficult engineering optimization and making even slight changes can greatly lower occupant safety (eg.  don't use an airbag in most cars if you're shorter than 5'0").  Making safety work is a huge challenge - perhaps level 4 cars in a world where most cars are level 4 will crash so little that interior safety is no longer a concern, but that is a long way from where we are now.

 

While it is very popular to talk about autonomous Uber cars, getting to robust level 4 is a long way off -  15 years before we get to anything like 5% penetration srikes me as extremely optimistic, although I wouldn't be surprised to see 20 or 30% level 3 by then.  I am assuming 'simple' issues like laws and insurance can be solved by then and that the difficult tasks like security are well understood.  Level 4 offers fascinating society and technology issues to think about, but focus on them is not understanding some larger problems.  In the meantime there is a long path to follow and much to be learned.

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¹ The kinetic energy of a car goes as the square of its velocity.  Limiting top speed could dramatically improve crash survivability as well provide more reaction time for the driver.  Some researchers suggest current safety systems in current cars would be safe for most sub 35 mph collisions.

² The plan is here (pdf)  There are some criticisms as it suggests a technology hierarchy  where each level is a superset of the previous.  Talking about level 3 and level 4 in any detail is a very complex task.  It is possible to imagine level 4 operation in some conditions that are much easier than solid level 3 in others.   Ultimately levels are probably the wrong way to look at the problem.  They are only meaningful in terms of the type of road and driving task.  Driving tasks involve hundreds of decisions rather than something simple like 'drive the car'.  Like any complex technology it is messy with a lot of qualifiers.  Hopefully this will be sorted out more meaningfully as technologies develop. my own suggestion:

° hands free

° driver not watching (eyes free)

° unmanned automatic with a network connection

° fully autonomous without network connection

° full capability/drive anywhere expertly without network connection

 

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Recipe corner

 

so good!

 

Pasta, Tomatos and Asparagus

 

Ingredients

 

° olive oil 

° 2 cloves of garlic finely sliced

° small bunch of basil finely chopped 

° one 28 oz high quality Italian plum tomatoes (until we get the real thing from the market)

° 1 bunch asparagus 

° 1 pound long flat pasta like tagliatelle

° salt and freshly ground pepper

° Parmesan cheese for serving - leave off if vegan

 

 

Technique

 

° Heat a sauce pan with a glug of olive oil to medium heat.  Sauté garlic 'til golden. Add some of the basil and tomatoes, season with a bit of salt and pepper and bring to a boil.  Cut the heat to a simmer and go about five minutes

° Snap off the woody ends of the asparagus and chop the rest.  Add it to the sauce and simmer for a short time. Remove from the heat.  Finish seasoning and add the rest of the basil.

° cook the pasta and reserve a bit of the water.  Now toss it with the sauce and  just a bit of the water.  Drizzle on an appropriate amount of olive oil and garnish with a lot of Parmesan if you like.

 

 

gain and loss

A few days of heavy rain and 83° turned the noon walk through the woods into something of a steam bath making them feel like a tropical swamp.  The soft ground and heavy winds during a thunderstorm last night felled a large white oak leaving a huge hole in the ground and a lot of broken roots.  About 30 inches at the base and 90 feet tall it contains a lot of wood.

 

Where did all of that biomass come from?

 

Most people will tell you a tree comes from the earth and water (I've asked more than a few).  I'm guessing seeing the big hole left by the oak would convince them of it.  Some may add photosynthesis, but not have a clear idea. The real answer took a few hundred years to work out.

 

Johann Baptista van Helmholt was one of the first to try and understand the process.  In the 1600s he planted a willow tree and kept track of the weight of the water and soil he had to add.  After 5 years it had had gained 164 pounds, but the weight of the soil had only decreased by about 3 ounces.  He concluded that most of the tree came from water - soil wasn't a major contributor.  Although his water conclusion was wrong, at least he had shown the tree wasn't taking on soil.

 

The answer comes from photosynthesis ..  solar energy is used to convert water and carbon dioxide into a sugar and oxygen.  The energy of the sunlight is stored in the sugar which can be burned with oxygen yielding water and carbon dioxide and heat energy.  The most important chemical reaction for life...  

 

6H₂O + 6CO₂  + light energy -> C₆H₁₂O₆ + 6O₂

 

If you do the bookkeeping involved it looks like most of the mass comes from the carbon dioxide.  Looking more deeply under the equation's hood (it turns out to be a multistep process) it can be shown most of the oxygen released comes from water and not the carbon dioxide.  About 95% of the biomass of the tree, or plants in general, comes from the air!¹  Since all of our food ultimately comes from plants, we're using quite a bit of air in a way most of us don't think about.

 

That leads to another question.  When you lose weight, where does it go?  A survey of doctors, dietitians and personal trainers had divided up as follows:

 

 

 

That turns out to be mostly wrong.

 

First consider where extra weight comes from.  Independent of what you eat, your body will try to store excess food energy in the from of triglycerides in your fat cells.  Weight loss happens when your body needs more energy that you're taking in.  Usually it taps the fat cells breaking the triglycerides into several chemicals that can be burned to provide the energy you need.²  

 

To get at where the fat goes we need to look at its oxidation - The opposite of photosynthesis and an equation something like:

 

a mixture of C, H and O + O₂ -> some CO₂ + some H₂O + energy

 

The average fatty acid (and I had to look this up:-) is has three components which approximates to:

 

C₅₅H₁₀₄O₆ + 78O₂ ->55CO₂ + 52H₂O + energy

 

Sorting out where the oxygen goes is tricky, but it can be shown that 10 kg of fat is converted to 8.4 kg of carbon dioxide and 1.6 kg of water.³ 

 

 You get rid of most of your weight, 84% of it,  by exhaling it:-)

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¹ This excludes the water normally running in the plant or tree - we're just looking at the biomass it creates.

² It can also break down muscle, but this is usually a last resort or indicative of something gone wrong.

³ BMJ journal reference

 

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A fruity pound cake - adapted from an Alton Brown recipe

 

Pound Cake

 

Ingredients

 

° 8 ounces of softened unsalted butter plus some for the pan

° 15 oz (2 cups) white cane sugar and some for the pan

° 15 oz (3 cups) AP flour

° 1 tsp baking powder

° 1/2 tsp salt

° 4 large eggs

° 1 tsp vanilla extract

° 2 cups fresh blueberries

 

Technique

 

° oven to 325° F, rack in the middle

° coat a pan with butter and sprinkle with 2 or 3 tbl of sugar - I use a traditional tube shaped bundt pan that is probably about 9" in diameter

° Whisk 10 ounces of the flour, the baking powder and salt together and set aside

° Use a mixer and cream the butter and sugar at medium speed for about five minutes.  Add the eggs one at a time, then add the vanilla extract at beat until fluffy 

° Add the dry mix to the butter/egg mixture at a low speed.  Don't over mix.

° Mix the blueberries with the remaining 5 oz of flour and shake in a bag.  Fold into the batter and pour into the bundt pan.

° Bake for about 1 hr 20 min until a thermometer is clean and shows 210°F,  

° Cool on a rack

 

 

 

the black hole that terrorized a city

Someone asked if I liked to watch horror/scifi movies.  It depends...

 

A few years ago I was trapped on a cross country flight and saw The Black Hole - one of those scripts that is so bad it is almost, but not quite, worth watching.  Check out the trailer...

 

Most special effects and animated movies take liberties with physics.  Starting with Disney many of the classic animation films created increasingly more interesting variations on physics to improve the storytelling physical worlds.  There were any number of tricks to trick the viewer to better immerse them in the story.¹

 

Special effects tend to suffer.  I'm able to enjoy films like Guardians of the Galaxy, but poor scripts and acting break the story telling and I find myself spending most of my time thinking about the physics.  

 

With that a mini-analysis of The Black Hole - (no plot is spoiled as I didn't notice one)

 

Somehow an there is an accident in a secret physics lab a hundred feet below St Louis.  Physicists have managed to create a tiny black hole that escapes and trolls around under the city coming up for buildings like the great white shark in Jaws.   At this point I'm completely out of story space and am thinking about small black holes.

 

Hmmm... about 30 meters underground and buildings on the surface are collapsing.  I'll make the assumption it is a miniature classical black hole, more on that later, and suggest that the gravitational force from it at the surface is about ten times Earth's gravity - that should be enough to flatten a building.  I could have picked other numbers, but we're just doing a little thought experiment and don't need to accurately understand how strong buildings are.  With this you can work out its mass - roughly about twenty trillionths the mass of the Earth - a bit over 100 trillion kilograms.  Now we're getting into interesting territory..

 

The event horizon of a black hole that mass is roughly a tenth of a trillionth of a meter -  about ten thousand times smaller than a hydrogen atom.²  Put it on the ground and it won't feel any resistance to any material on or in the Earth.  As soon as its created it will fall toward the center of the Earth picking up speed as it goes.  It whizzes through the center at about eight kilometers a second and starts slowing down as it heads towards a point, judging from my globe, on the surface of the Indian Ocean well off the Australian coast. Maybe it dines on a fish before reversing direction and heading back about 42 minutes later.³  Back and forth, back and forth - we have an odd sort of clock.

 

Games like this turn out to be a central part of play in physics.  You make a non-physical assumption -  assume a miniature black hole is created just under St Louis - and follow what happens using established physics.  In the process you can quickly deal with many questions and decide on those that are the best candidates for serious study.  Now that we have our black hole tic-tocking between St Louis and the Indian Ocean, let's look at smaller black holes.

 

I mentioned this was a classical black hole.  In 1974 Stephen Hawking proposed black holes can evaporate. The time required for one formed from a collapsed star is extremely long - it would take about 10⁶⁷ years for one with our Sun's mass ... approximately forever when you consider the age of the universe is 13.8 billion years.  But the rate of evaporation has a strong dependence on the black hole's mass and lighter black holes evaporate faster.   The little St Louis black hole would last about a hundred times longer than the current age of the Universe.

 

Smaller black holes can have lifetimes small even on time scales we're used to.  One with the same mass as a small car - about 1,000 kg - would evaporate in a billionth of a second and would be about 200 times as bright as the Sun.  These super tiny black holes would make a very powerful and completely impractical doomsday devices - even more impractical than antimatter.  In other words the perfect plot device for a movie.

 

I'll end with a problem for those who like to work things out.  Send mail if you'd like hints.

 

The Master from Dr Who or a slightly annoyed Vogon captain approaches the Earth with a super slicer beam that instantly makes a cut through the Earth.  What happens if the cut is through the equator and is  one centimeter wide?  What happens with a one meter cut?  How about ten meters?   Now work the problem with the same three cuts, but this time slicing from pole to pole.  How does humanity make out in each scenario?  

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¹ If you have the slightest interest in animation The Illusion of Life: Disney Animation by Olie Johnson and Frank Thomas is just wonderful.  Go for the hard cover and treasure it.  Disney did amazing groundbreaking work, and other expanded wrote new rules.   Chuck Jones created an animation for roadrunners and coyotes that is an art form.  Even today the tricksters are still at it.

² the Schwarzschild radius is proportional to mass r_s = 2GM/c².  The point is it only goes linearly with mass while the mass of a star goes as the cube of the radius - the event horizon get small very quickly as mass drops.  The Sun has an event horizon of about 3 kilometers ... far too small to contain it.  r_s for the Earth is 0.9 centimeters.  

³ 42 minutes through a frictionless tunnel is the result everyone calculates in physics 101, but that assumes the Earth's interior has a uniform density.  Recent work giving a better understanding of the Earth's density distribution cuts a few minutes off the transit time.

 

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Recipe corner

 

I grilled some asparagus and used a homemade olive based dressing.  Ideally the trick would be to layer pieces of tomato on a bed of the grilled asparagus before adding the dressing, but it isn't good tomato season (yet).  Here's the dressing...

 

Olive dressing

 

Ingredients

 

° 3 tbl finely chopped kalamata olives

° 3 tbl extra virgin olive oil - a good one pays off

° 3 tbl red wine vinegar

° 3 tbl crumbled feta (leave off if you want it to be vegan)

° 2 tbl finely chopped red onion

° 1 clove garlic - very finely chopped or grated

° 1 tbl honey

° 1 tbl dijon mustard

° 1 tsp oregano

° salt and pepper to taste

 

 

Technique:-)

 

° mix the ingredients

 

beautiful devices

well?  are you going to get one?

 

Since I have an interest in ubiquitous sensors and computation many people assumed I'd get an Apple Watch the moment it came out.  Something more interesting happened and I found myself with questions about what computation on the wrist is good for and the limits of what a wrist worn timepiece can do.  

 

First I tipped my hat to Horace and starting thinking about the jobs to be done. Beyond cheap watches are camps of those who have an interest in different devices:

° a smartwatch that mostly tells time 

° a wrist networked/computing device that happens to tell time

° a fine mechanical watch

None of these camps are right or wrong.  In addition some people will use watches to signal social class or just enjoy the design and construction of a watch.   Time keeping is central to some of these cases - particularly the mechanical watch - so it is useful to think of the  jobs they were originally hired for - when  innovations occurred and if innovation continues.

 

Navigation and event synchronization are important functions for accurate portable time pieces.  Navigation is a fundamentally important driver of technology.¹  Event synchronization became very important as the Industrial Revolution developed. There was a need to coordinate groups of people.  Town clocks and home clocks that were synchronized to the town clock were important.   The town clock would be set by the Sun's position - local noon could be determined and the clock could be adjusted regularly to good enough accuracy.  

 

Railroads presented new problems.  Every town had its own version of noon.  Tables were produced showing the time offsets for clocks in other cities.  Some stations kept clocks for each destination and hundreds of confusing charts were developed.  Scheduling was a nightmare.  Some crews would carry a half dozen clocks set for each major stop on a route.  The clocks often lacked enough accuracy making matters even worse.  

 

The solution was to standardize time.  In 1840 Great Western Railway adopted London time. Within seven years most English railroads followed and finally a rail standards body recommended using Greenwich Mean Time.  Local clocks throughout England followed, although many had two minute hands - one for local time and the other for GMT, and by about 1880 GMT was defined as the time throughout England.  Other countries followed and time zones very roughly following divisions of longitude were established. 

 

Pocket watches were reasonably accurate portable time pieces and the advent of standard time made them more practical beyond their original use on railroads. Some were  beautifully built and expensive signaling social status in addition to giving the time of day.   Wrist watches became accurate and durable enough to become important tools of military synchronization during WWI and mass production built an industry lowering prices to eventually make them a mass market item.

 

A decade before WWI a Einstein published one of his revolutionary results.  He  combined the experimental result that the speed of light was always constant with deep thinking about what the synchronization of events means and came to the conclusion that the measurement of time and that of space were not rigid.  Moving clocks would run slowly and moving objects would shorten.  Unless you could travel at a good fraction of the speed of light these  effects were small.  You would need a special clock that was much more accurate - more than a million times more accurate - than any known clock.

 

While I'm impressed by beautiful craftsmanship and design, I'm more taken with tools that allow revolutionary ideas to be discovered and verified.  I see an Apple Watch or the best conventional watches and think about their accuracy compared to what it would take to verify special relatively.  Such a watch would be impressive and more pure as a time keeping object. A regular watch does other jobs for some, but is only a time keeper for me.  

 

Consider what it would take to verify the effect of special relatively by doing a thought experiment Einstein suggested.  Place a clock in a moving vehicle and compare the time it shows to that of a clock that stays put with you.  A nice trial would be to fly a clock around the world.  Imagine an airplane going about 500 miles an hour on a 48 hour trip.  A bit of calculation shows the airborne clock would show 47.99999999999867 hours had passed. You need a wicked good clock to see the difference.

 

It turns out atomic clocks are good enough.  In October, 1971 the experiment was done by J.C. Hafele and R.E Keating.  Two Hewlett Packard atomic clocks were flew in opposite directions around the world for about $7,600 in airline tickets for the crew and "Mr Clock".   Analysis was complex as both Special and General Relativistic effects were involved.²  This was probably the least expensive new experiment involving General Relativity.

 

Portable watches won't give the required accuracy and why would you need it anyway?  Watches can be synchronized GPS signals.  They drift little enough between synchs that it is difficult to imagine a human level task they would fail at for lack of accuracy.  But people have pushed the accuracy of standalone watches -  atomic clock based watches and pocket watches have been built, but the atomic clock module they're based on isn't good enough to duplicate the 1971 flight around the world.³  

 

The Apple Watch goes beyond time keeping allowing more convenient alerts and some health monitoring and encouragement.  That isn't my use case - at least not yet.  There will be many other sensors that it will be able to receive data from - a few hours thought gave me a list of a dozen that aren't crazy.  That's where I'm hooked.  If I had the time and inclination I'd be developing one or two now, but I rest assured many others have the same thought and some will be excellent developers.⁴

 

For me the Apple Watch represents future potential.  When you see me with one consider it a signal that I've found something deeper that is beginning to get into the ubiquitous computation world.  

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¹ I touched on it here.  The subject is rich and one could write for hours.  Fortunately many others have and the history of science and technology has rich stories.

² Special Relativity for the relative motion of the clocks and General Relativity to adjust for gravitational redshift.   For the eastward flight theory predicted 144ns gained from GR, 184ns lost from SR giving 40ns lost total (+/- 23) and 59ns lost +/-10 was measured.

The atomic clocks were stock HP-5061A Cesium beam atomic clocks made in the mid 60s.  They weighed about 80 pounds each and required a separate power supply - semi-portable.

The paper is great fun. 

J.C. Hafele and R. E. Keating, Science 177, 166 (1972)

³ DARPA funded development of a miniature atomic clock for GPS denied navigation. It was commercialized by Microsemi as the Quantum SA.45s.  Very nifty and even inexpensive at about $1,500 for the module, it is useful in underwater navigation and some military applications where GPS signals are unreliable.  As atomic clocks go it isn't very accurate - not enough for testing special relativity unless you are at orbital speeds.  

There are many other  questions.  The world has standardized on an ITC time reference based on the Earth's rotation. Unfortunately this varies quite a bit, slowing down beyond tidal drag and leap seconds need to be added.  The physics and geophysics involved is amazingly rich.  We should probably move to just basing time on atomic clocks, but there is institutional pushback.

A quick note on time standards.  Coordinated Universal Time (UTC) is a standard and not a time zone.  All timing centers on Earth have agreed to synchronize their time scales with it.  There are two components of UTC -

Universal Time (UT1) is solar time and is based on the Earth's rotation.  It is adjusted several times a decade with leap seconds to adjust for unevenness in the Earth's rotation.

International Atomic Time (TAI) is a time scale that uses the output of about 200 precision atomic clocks around the world.

GMT is now a time zone.  

Steve S. notes several issues with leap seconds:

- Some NTP/GPS servers implemented the leap second 5 months early.

- Google, Amazon (others?) are implementing smeared leap seconds

- The financial community are worried (this leap second occurs on a non-holiday weekday) and its overlord the Intercontinental Exchange have announced changes in the trading schedules for June 30 due to the leap second.

- Microsoft’s Azure cloud service apparently will implement the leap second at local midnight

⁴ For the old Air Graffiti people who read this ... think iCane 2.0

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Recipe Corner

 

Lentil Fruit Salad

 

Ingredients

 

° 2 cups red lentils

° 5 scallions chopped - just the white and white-green

° 1 red bell pepper sliced

° 1 medium red onion sliced

° 1 apple diced

° 3 oranges, 2 sliced and one juiced

° 1/2 cup olive oil 

° white wine vinegar

° salt

° freshly ground black pepper

 

Technique

 

° cover the lentils with slightly salted water and bring to a boil over medium heat.  Cook until tender - 45 minutes or so.  Drain and allow to cool

° combine everything else in a large bowl and season with salt, pepper and white wine vinegar to taste

° mix in the lentils