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.