General relativity tells us that as you get closer to a mass clocks run a bit more slowly. The effect can be observed on Earth with precise clocks at different distances from the center of the Earth and is pronounced enough that you have to correct for it to get the precise timing signals from GPS satellites right.
It follows that time runs more slowly at the center of a mass like the Earth. Apparently Feynman mentioned that, over the life of the Earth, the center of the Earth would be a day or two younger than its surface. The calculation is quite easy and one might expect it assigned as an undergrad physics problem.
It turns out that when you do a back of the envelop calculation you get about a year and a half. Feynman may have made a simple mistake or perhaps he was incorrectly quoted - apparently he never wrote the result down. I was unaware of his result, but I would have probably accepted it even though I had worked it out for distances from the earth (tall buildings, mountains, orbiting satellites).
The paper paper works out the result at the level of an undergrad physics class.
The young center of the Earth
U.I. Uggerhøj,1 R.E. Mikkelsen,1 and J. Faye2
1Department of Physics and Astronomy, Aarhus University, Denmark 2Department of Media, Cognition and Communication, University of Copenhagen, Denmark (Dated: April 20, 2016)
We treat, as an illustrative example of gravitational time dilation in relativity, the observation that the center of the Earth is younger than the surface by an appreciable amount. Richard Feynman first made this insightful point and presented an estimate of the size of the effect in a talk; a transcription was later published in which the time difference is quoted as ’one or two days’. However, a back- of-the-envelope calculation shows that the result is in fact a few years. In this paper we present this estimate alongside a more elaborate analysis yielding a difference of two and a half years. The aim is to provide a fairly complete solution to the relativity of the ’aging’ of an object due to differences in the gravitational potential. This solution - accessible at the undergraduate level - can be used for educational purposes, as an example in the classroom. Finally, we also briefly discuss why exchanging ’years’ for ’days’ - which in retrospect is a quite simple, but significant, mistake - has been repeated seemingly uncritically, albeit in a few cases only. The pedagogical value of this discussion is to show students that any number or observation, no matter who brought it forward, must be critically examined.
At the turn of the nineteenth century, Aaron Burr, who would later become the third Vice-President of the United States, secured a charter and millions of dollars in financing to establish the Manhattan Company, which promised to tap clean drinking water for New York City. Instead, Burr and his associates cut costs by drawing water from a putrid pond just south of what is now Canal Street and redirected the remaining money to found a bank (now called JPMorgan Chase). The city’s contaminated water supply contributed to two major outbreaks of cholera, a disease that causes vomiting, diarrhea, and dehydration so extreme that patients can lose ten per cent of their body weight in less than a day.
The audience of THE HUXLEY FILE, then, is educated people of whatever culture (THH was translated into Chinese and Japanese, as well as into European languages Hungarian, Russian, Italian, German, French, Spanish, and Italian), especially high school and college teachers who can select and present for their students sections from THE HUXLEY FILE to enrich, liberalize, and vitalize courses in at least these fields: (1) education, (2) biology, (3) anthropology, (4) philosophy, (5) religion, (6) social studies, and (7) style. Though these categories are designed to help understand Huxley's contributions, it's important to note that he was not a strict disciplinarian–a river of text, essay or letter, could and often did flow with relevant material on all of these and other tributaries as well. Huxley's popularization adventures resulted in what he called "fugitive pieces," many of them written when he was assailed by insomnia, and most of them constituting Collected Essays ; but since he was a professional biologist, an ample supply of his Scientific Memoirs is offered, though most of those pieces would not be understood or appreciated by most of us lay people.
Just how do you navigate in open waters without a compass when it is cloudy? Sunstones have been proposed. In theory you can use polarization of the available light and combine that information with a sundial to figure out where the Sun is.
Several researchers have tried to duplicate this over the years with poor results. Another attempt appear in the Royal Society Open Science journal. They find it is sort of possible with very clear cordierite crystals with tourmaline crystals being the next choice. It is still very iffy.
Adjustment errors of sunstones in the rst step of sky-polarimetric Viking navigation: studies with dichroic cordierite/ tourmaline and birefringent calcite crystals
Dénes Száz1, Alexandra Farkas1,2, Miklós Blahó1, András Barta1,3, Ádám Egri1,2,3, Balázs Kretzer1, Tibor Hegedüs4, Zoltán Jäger4 and Gábor Horváth1
1Environmental Optics Laboratory, Department of Biological Physics, Physical Institute, Eötvös University, Pázmány sétány 1, Budapest 1117, Hungary 2 Danube Research Institute, MTA Centre for Ecological Research, Karolina út 29–31, Budapest 1113, Hungary 3Estrato Research and Development Ltd, Nemetvolgyi ut 91/c, Budapest 1124, Hungary 4Astronomical Observatory of Baja, University of Szeged, Pf. 766, Baja 6500, Hungary
According to an old but still unproven theory, Viking navigators analysed the skylight polarization with dichroic cordierite or tourmaline, or birefringent calcite sunstones in cloudy/foggy weather. Combining these sunstones with their sun-dial, they could determine the position of the occluded sun, from which the geographical northern direction could be guessed. In psychophysical laboratory experiments, we studied the accuracy of the first step of this sky-polarimetric Viking navigation. We measured the adjustment error e of rotatable cordierite, tourmaline and calcite crystals when the task was to determine the direction of polarization of white light as a function of the degree of linear polarization p. From the obtained error functions e(p), the thresholds p* above which the first step can still function (i.e. when the intensity change seen through the rotating analyser can be sensed) were derived. Cordierite is about twice as reliable as tourmaline. Calcite sunstones have smaller adjustment errors if the navigator looks for that orientation of the crystal where the intensity difference between the two spots seen in the crystal is maximal, rather than minimal. For higher p (greater than pcrit) of incident light, the adjustment errors of calcite are larger than those of the dichroic cordierite (pcrit=20%) and tourmaline (pcrit=45%), while for lower p (less than pcrit) calcite usually has lower adjustment errors than dichroic sunstones. We showed that real calcite crystals are not as ideal sunstones as it was believed earlier, because they usually contain scratches, impurities and crystal defects which increase considerably their adjustment errors. Thus, cordierite and tourmaline can also be at least as good sunstones as calcite. Using the psychophysical e(p) functions and the patterns of the degree of skylight polarization measured by full-sky imaging polarimetry, we computed how accurately the northern direction can be determined with the use of the Viking sun-dial under 10 different sky conditions at 61° latitude, which was one of the main Viking sailing routes. According to our expermiments, under clear skies, using calcite or cordierite or tourmaline sunstones, Viking sailors could navigate with net orientation errors |Σmax|≤3°. Under overcast conditions, their net navigation error depends on the sunstone type: |Σmax(calcite)|≤6° , |Σmax(cordierite)|≤10° and |Σmax(tourmaline)|≤17°∘
Trembley’s first thought was that he had discovered a completely new species. This would turn out to be untrue, as these tiny animals had already been identified by van Leeuwenhoek. The name van Leeuwenhoek gave them was “polyps,” though they would eventually be commonly known as hydras. They were strange creatures, to say the least. Beneath the lens of a microscope, they looked like a cross of a snail, an octopus, and a plant. As Trembley tried to learn more about the little creatures, he cut some of them in half. He was shocked to see that both halves continued to live. He wondered whether he was just witnessing residual movement akin to a severed lizard’s tail. Then something amazing happened. Each half polyp gradually began to regenerate the portions of its body that it had lost. Amazingly, the two halves became two separate creatures.
Trembley sent a summary of his results and a sample of the freshwater polyps to a well-known naturalist in Paris, René-Antoine Ferchault de Réaumur, an important skeptic of the doctrine of preformation who had written an influential paper about the regeneration of crayfish claws. Réaumur repeated Trembley’s steps, cutting the odd specimens into sections. He, too, watched in wonder as the little creatures he had split formed into entirely new creatures. “I could hardly believe my eyes,” he later wrote. “It is a fact that I am not accustomed to seeing after having seen it again hundreds and hundreds of times.” When he presented a demonstration to the Paris Academy of Sciences later that year, the official report on the event compared it to “the story of the Phoenix that is reborn from its ashes,” and asked witnesses to draw their own conclusions “on the generation of animals . . . and perhaps on even higher matters.”
I stumbled across a paper by the English chemist Robert Boyle
A New Frigorifick Experiment Shewing, How a Considerable Degree of Cold May be Suddenly Produced without the Help of Snow, Ice, Haile, Wind, or Niter, and That at Any Time of the Year
Frigorifick - what a wonderful word! Apparently coined by Boyle, it referred to chemicals that were part of endothermic reactions removing heat making something cooler. A modernized spelling would be frigorific.