Summer Report 3 Red Sox Game

Went to a Red Sox game. Despite it being a Tuesday night with a pronounced threat of rain, the Sox being in last place, the opposing team being the uninspired Indians, the stands were nearly full and the fans were having a great time. Some of them even paid attention to the game, between trips to the food and drink stands. An American summertime tradition is still alive and well in Boston.

Democracy in A Small Town

 In New England towns, as opposed to cities, major decisions are made by vote at town meetings. Any resident who is a registered voter has a direct say in the matter. On Tuesday I got to see a real example of direct democracy.  Because of the rural nature of our town, about 700 year round homes spread over 40 hilly square miles,  companies such as Verizon and Comcast can't be bothered to run fiber optic cable or even DSL to most residences, and a large portion of our town is saddled with poor internet and cell service. In response to this and a few other developments, the town was considering issuing bonds to help construct a fiber optic network. Well over 300 of the town's 1200 voters showed up at the town meeting to consider the matter. Most people were pretty well convinced it would be the right thing to do and it was almost a foregone conclusion the bonding would pass. Still all who wanted to, mostly opponents to the measure,  were given the opportunity to speak, and the meeting in a crowded, hot and humid town hall went on for over 90 minutes. Since it was a bonding issue, a two thirds majority was required for passage and the measure passed easily. Regardless of he outcome it was very rewarding to see such clearcut example of democracy in action.

Summer Report 2 Ididaride

For the last several years my birthday gift to myself is to take a day off from whatever project I'm working on and go for a long bike ride. For the last two years I have been eyeing the Ididaride, a 75 mile fundraising ride run by the Adirondack Mountain Club. This year I decided to do it,.... along with about 500 other people. The ride starts in North Creek near Gore Mountain and goes mainly on state highways through Speculator and Indian Lake and back to North Creek. There was some nice scenery and a few spots with great views of the southern Adirondacks. The ride includes about 4500 feet of elevation gain. The last ten miles are a long downhill followed by a longer flat stretch along the upper Hudson River.

I was among the older riders there and I had not done a ride of over 40 miles in nearly a year and had not ridden much at all this year, so I was a little concerned that I might end up finshing late enough to cause the organizers concern. My usual strategy on these long group rides is start slow and conserve energy so I can finish a little less slow. I also enjoy passing those inexperienced riders who expend too much energy early on and fade at the end.

Well, it seems that no inexperienced riders sign up for 75 miles in the Adirondacks, so I had to content myself with not being passed too often at the end, mostly because there weren't too many folks behind me anyway. Actually I was pretty pleased, spending about six hours in the saddle and getting back long before the last riders, despite having to change out a flat about 62 miles into the ride. I think I would have been faster if I had stayed more hydrated in the first 50 miles. Five water bottles full are not enough when it hits 93 in the sun. I might do it again next year. If I do I'll take some pictures.

On the drive home I was reminded of how beautiful NY Routes 372 and 67 are. If you are ever in the area of Cambridge, New York give them a try.

Some Thoughts about the Uncertainty Principle

Here are some thoughts about a way to make the uncertainty principle more intuitive.

In classical mechanics, action is the integral over time of L [ i.e.T-V]. But let’s call integral of H [ that is  L+ 2V or simply T+V] over time as “total action” . I think that it is total action that is quantized in integral quantities of h [Planck’s constant] but I am not sure how V fits in.  I think the rest energy must be included in all this.

Do all measurements of E require some finite time and all measurements of require some finite distance? If so, can they be thought of as measurements of total action?

In some ways E= h nu is getting it backwards, or at least upside down. What does frequency mean for a particle? On the other hand looking at it as

E tau = h where tau =1/nu is more intuitive. Tau is simply the characteristic time [or period] it takes for a particle of energy E to accumulate one h worth of increase in total action.

Similarly p lambda = h indicates that a particle of momentum p must travel a distance lambda to accumulate one h of increase in total action.

If total action is truly quantized, then there is no measurable change until total action changes by h.

 Heisenberg’s uncertainty principal can be explained as follows: Suppose one measures the change in total action over a time interval, t,  less than tau. Say sometime during that interval, t,  the total action changes by one h.  The only things you know are that sometime during t total action changed by h. From this you conclude that E could be as high as h/t. On the other hand if you think about it a bit you realize that your interval t could have started after a large fraction of tau had passed since the last increase in total action by h, so that most of the accumulation of energy time leading to an addition of h in total action occurred prior to your beginning your measurement. Therefore the energy could be much lower( near zero?). Thus you are uncertain about E by h/t.

Now suppose your measurement takes place over a period, t’,  several times tau, lets say  t’ = 7 tau for example. Depending on exactly when you begin your measurement vis a vis  when a period begins [ i.e. the time when the last increase in total action by h occurred prior to the measurement]  you will measure either 6 h or 7h as the change in total action. So you know the energy is between 6h/t’ and 7h/t’  but since t’ is 7 x t , you have reduced your uncertainty by a factor of 7.

Similarly, for momentum if you measure the particle’s total action over a length , L, shorter than lambda , you may detect a change in total action of h. Then you can conclude that the momentum may be as high as h/L. However, most of the accumulation of momentum times distance since the last change in total action may have occurred in the particle path before your measurement, so p could be much lower (near zero?) so your uncertainty in p is h/L. IF you measure over L’ = 7 lambda  you will measure between 6h and 7h change in total action, and the uncertainty becomes h/L’ or 1/7 of h/L.

Summer Report 1 Trip to Britain

It's been a very busy summer. We were in Britain starting June 23 and returning July 16 with our nearby neighbors. We visited Salisbury and it's famous cathedral; spent a few hours in Gloucester; three days in the Shopshire towns of Church Stretton and Ludlow; seven days on a canal boat; a few hours in  Chester; six days in the Scottish Highlands and a morning in Oxford.

 The Cathedral in Salisbury with it's 400 foot tall spire

 My wife and our neighbors above the carding mill valley in Shropshire

 The Carding Mill Valley, a truly lovely place.

 My wife and my neighbor did all the steering. He did all the tricky bits.

  A bank in Whitchurch.

 The aqueducts that carry the canal above steep sided valleys were a highlight of the trip. Built around 1800, the canal were out done by railroads about 40 years later. The higher structure carries a railroad. Both still in use about 200 years after they were built. Not much we do today will last that long.

 The breakfast club waiting for toast.

The view from the Ferry from Oban to the Isle of Mull. The flat topped mountain in the far distance is Ben Nevis, the highest mountain in the United Kingdom. While only 4400 feet high the base is near sea level so it;'s a pretty good walk. My neighbor and I had to to walk through a couple of snow fields on our way to the top. Not bad for a low mountain in July.

 A couple of views from Pitlochry, a town on the southern edge of the highlands.

Weather could have been better in Scotland, but still a great trip.

More on scouting

The new boys in our troop spent two days at a Council run camporee and had a great time. The event was well organized and there was plenty to do, more than any one could do in fact. The only downside was that  many units were not there, probably because they did not kow how much fun they wwould be missing, and probably more so, because of the overwhelming time commitments demanded by sports.

Among the many activities, the boys learned to build a small bridge with no rope or fasteners and got to throw hatchets at targets ( pieces of logs).

Physics: Action and Wave Function

I believe action, S,  is defined as integral of KE - PE over time or integral L over time. There appears to be an intimate relationship between the wave function and the action. A sample wave function can be A exp[(-h/i)S(omega t -kx)] or something similar. A function of this type satisfies Schroedinger's equation in that the second spatial derivative  gives KE and the first time derivative gives total E as long as E =hbar [ Plancks constant /2 pi] omega.

Since the probability of a system being in a state is proportional to the wave function* dot  wavefunction, the question is why the probability density is related so closely to the action. L can be thought of as two times the work input from the field into the particles KE in going from some reference point to the current position. 

Visit to Basking Ridge

I'll be in Basking Ridge on Thursday 6/18. If interested in getting together, send me a comment with your email address.

BACK INTO SCOUTING

Our boy scout troop in Ashfield had dwindled down to two scouts. We now have four or five new members and a few of us adult leaders are working to revitalize the troop.

Spent the last weekend in a training program to refresh my knowledge about being a scout leader. It was very gratifying to see that about thirty adults from rural Massachusetts were willing to spend a weekend learning how to help boys develop into useful young men. I was impressed with the friendliness, ability, and dedication of just about everyone there.

Not So Random Thought

When woodworking an instant of inattention or clumsiness can undo days of careful workmanship.

Five minutes of binge eating can undo a week of discipline.

 A few moments of hate or anger can wipe out years of care and love.

Physics Non Progress Report

Been doing a lot of reading of papers written at the inception of quantum mechanics from a collection " Sources of Quantum Mechanics, published by Dover. It leads off with a paper by Einstein concerning how the proper spectrum of radiation from a gas in thermal equilibrium can be derived from quantum absorption and emission. Right now I am in the midst of a paper by Bohr which seems to be an attempt to relate quantum emissions to classical electrodynamics/mechanics of charged oscillators. Trying to relate the classical emissions expected from charged oscillators to emissions, and absorption of quanta from transitions between the quantized "stationary" energy states is a tall order. I expect to have to read this paper more than once to see if Bohr achieves anything like this. I need to get through this and a few more papers before reaching Heisenberg's major paper on some of the fundamental "principles" of quantum mechanics. Wish me luck, I'll need it.

A Bit of an Obituary for a Small Creature

Yesterday our 20 year old cat died. She was officially my son's cat but she lived with us for the last nearly four years. She was quirky and  at first pretty anti-social, but after several months of adjustment she became very affectionate. Whenever she could, she would spend time in our laps or sleeping on us.

She argued with her drinking fountain,  made loud outbursts in the middle of the night, shouted for us to come upstairs and keep her company, needed special food, and lot's of attention, including frequent cleaning of the aforementioned water fountain. However all this was an okay price to pay for her warm affection, her loud purring, and the appreciation she showed for any attention we gave her. Life is simpler and quieter around here. I do miss her.

Miscellaneous Mid April Report

Haven't posted much lately because not too much blog worthy to report and our internet service makes posting painful. Not much snow or precipitation of any kind for the last several weeks. We are having a reasonably early melt out of the snow and the lack of precipitation is holding any flooding to very low levels.

Visited some family in North Carolina in march. Good to see some nice folks.

On the flights back and forth I got to see some of the development around Pittsburgh and Raleigh. It looks like sprawl is still in season, despite all its ills. More reliance on automobiles for everything, nothing within walking distance, kids needing appointments to find other kids to play with, large lots that only the landscapers get to see or use, etc.

Our local scout troop is in a rebuilding mode and we got a nice outing in, using snow shoes and a sledge, while the snow was still deep and firm.

A small project

I recently completed a present for my cousin's fiftieth birthday. I turned a pair of mahogany candlesticks for her, making use of some of what I learned making the night stands. I then decided to make a case for the candlesticks, the globes to be mounted in the candles sticks (wood and burning candles are not a great combination) and the candles. The case ended up taking more time than the candlesticks.  My hand cut half blind dovetail technique can still use more practice.

Here are some pictures.