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June 10

Feynman Lectures. Exercises PDF. Exercises 7-1...7-11

I have a general question. Feynman at the end of Section 7-4 describes the mechanism of tides. He says that centrifugal force balances gravitation force of the moon at the center of the earth. I assume we can prove that for moon free fall acceleration (at the distance 384 400 km) and centrifugal acceleration we can replace the earth by one point:
* for the centrifugal force:
we can divide the earth into 1 kg bricks and sum up the forces applied;
the centrifugal acceleration ω²R is linearly dependent from R , its x-projection is same for each section of the earth , its y-projections cancel each other png
during summation we see that lowering the centrifugal force on near side of the earth is just compensated by the growth at the far side of the earth. So the sum will not change if we replace all the forces by the mean force -- the force at the center.
* for the gravitation force:
for large distance from the moon (384 400 km) and for relatively small earth diameter (12 800 km) the change in the moon field (moon free fall acceleration) is almost linear (3.4×10^-5 m/sec² on near side of the earth , 3.3×10^-5 at the earth center, 3.2×10^-5 at the far side )png. Neglecting moon's field direction, the same analysis permits to change all the forces by the mean force and collect all mass of the earth in a single point.

But from such reasoning I still can't see why do the mean forces balance each other. Is it because the Earth would otherwise have come down from the orbit (no more equilibrium in rotating reference frame)? Is such reasoning correct? Username160611000000 (talk) 12:54, 10 June 2017 (UTC).

I might be misunderstanding, but I think you want the shell theorem. The idea is that a spherical shell of Earth of uniform density will orbit and attract like a point mass at its center. Note that since the Earth is not a perfect sphere or perfectly uniform in density at a given depth, your premise should not be perfectly true. Wnt (talk) 16:33, 10 June 2017 (UTC)

Feynman explains "shell theorem" later [1] . According to him a spherical body and a point with equal mass generate identical fields. But nothing is said about objects affected by that field. In this problem the moon can be thought as a point. But this does not change either the formulas or the drawings. If Feynman gives this problem in Lecture 7, then we need not "shell theorem" to explain the phenomenon. Actually the tidal effect itself shows that earth cannot be considered as a point (it can be considered as point approximately and only for collecting the force, but not for further explanation ).
So no, "shell theorem" is out of place. Username160611000000 (talk) 17:25, 10 June 2017 (UTC)

This lecture is simply applying Newtons' law of action-reaction by balancing two forces, the reactive centrifugal force (which is not to be confused with fictitious centrifugal forces that are due to rotating reference frames) and the gravitational force that are said to be acting on the masses. That is all. This is not the modern view, but it is a traditional treatment of the problem. BTW, when I was introduced to the term "centrifugal force" I understood it in the sense of the reactive centrifugal force that acts on a string (or the other mass as the case here). Strings, flywheels and spinners are always under tension due to it. To make things even more interesting, the last section of the reactive centrifugal force article points out that with the gravitational two-body case (such as that is being considered here), the reaction to the centripetal force is also a centripetal force. So there you go. I hope that helps. --Modocc (talk) 19:51, 10 June 2017 (UTC)

@Modocc: BTW, when I was introduced to the term "centrifugal force" I understood it in the sense of the reactive centrifugal force that acts on a string (or the other mass as the case here).
First, it doesn't explain then why do both forces balance in the center of the earth, and not somewhere else (according to the rules we can move a vector along an axis). Second, these forces (gravitational attraction from the moon on the earth and reactive force from the earth on the source) are applied to the different objects. Yes, we can add forces on one axis, but I'm not sure that in this case it is possible.
Username160611000000 (talk • contribs) 04:30, 11 June 2017 (UTC)

OK. Reading further, I see he says "What do we mean by “balanced”? What balances? If the moon pulls the whole earth toward it, why doesn’t the earth fall right “up” to the moon? Because the earth does the same trick as the moon, it goes in a circle around a point which is inside the earth but not at its center." So he means any system's mass center. The common mass center between the Earth's water and the rest of it is its center in this case. Both of these masses are held in place by gravity as they rotate around the Earth's center. This also means that both masses pretty much happen to trace the same orbit around the Earth-Moon barycenter, more or less. --Modocc (talk) 04:57, 11 June 2017 (UTC)

My original questions were:
1 Are the forces balanced at the center of the earth and how it could be explained?
2 If the forces are balanced at the center, then can it reason the tidal effect as consequence?
Using very accurate plotting I've found that the total effect of both forces gave a lifting acceleration over the earth intersection by the moon orbit plane PNG. The lifting acceleration is a bit smaller on the Y-axis . Image can answer question 2 ( doubtful as it seems must be not 2 high tides , but one ecliptic tide instead). But I'm still in suspense about question 1. Are my arguments at the beginning correct?
Username160611000000 (talk) 07:56, 11 June 2017 (UTC).

I had an additional question. According to [2] the typical tidal range in the open ocean = 0.6 metres. According to assumption that water pressure must be equal
ρg_lowh₀=ρg_high(h₀+0.6)
∴ g_low / g_high = 1 + 0.6/h₀.
Putting average ocean depth 3000 m we have g_low / g_high =1.0002. But according image at earth equator g_low / g_high = (9.8 - 3.4×10^-5) / (9.8 - 4.3×10^-5) = 1.000001.
Username160611000000 (talk) 11:06, 11 June 2017 (UTC)

I think you're way off track there. You seem to be assuming that water will compress in proportion to the gravity on it, but it won't. And I think you're assuming the water only gets higher and lower based on this compression or expansion from the bottom of the ocean. But this isn't how tides work - the point with tides is that the ocean surface gets tilted ever so slightly from horizontal - relative to the combined Earth-Moon gravity field, that is - and the water pours downhill. Now earth tides may indeed work that way, but that is based on compression of thousands of km of rock rather than just the ocean, and the rock can't flow much ... or can it? I just realized I have no idea how much rock can wiggle if you wiggle it ever, ever so slightly. Stuff like Young's modulus is linear.... hmmm... actually the earth tide article seems to suggest the Earth does flow on that scale, but then why so little...? Wnt (talk) 13:02, 11 June 2017 (UTC)

@Wnt: the point with tides is that the ocean surface gets tilted ever so slightly from horizontal - relative to the combined Earth-Moon gravity field, that is - and the water pours downhill. Can you prove it quickly and simply ? It seems it's correct that the liquid level is always perpendicular to the resultant acceleration. Feynman also says " If we go even further, the earth is not exactly a sphere because it is rotating, and this brings in centrifugal effects which tend to oppose gravity near the equator. It turns out that the earth should be elliptical, and we even get the right shape for the ellipse.", so he thinks we already know it. But if not pressure, then what makes the water move? E.g. there is a half-empty bottle on the table, then I put it on the side, water doesn't stay at the bottle's bottom because of unbalanced water column pressure near to the table. Username160611000000 (talk) 13:51, 12 June 2017 (UTC)

@Username160611000000: Obviously the most stable state of the water surface is perpendicular to the local gravity field. However, since the direction of this field is constantly changing (slightly), the water will inevitably lag behind ... by just the amount needed to give it the needed incentive to keep moving so that the lag doesn't increase or decrease. Wnt (talk) 15:42, 12 June 2017 (UTC)

I did not understand what you meant by "lag", but I came to the conclusion that at a liquid level other than perpendicular, there is additional free energy (weight)×(height), lect.4. Username160611000000 (talk) 20:34, 12 June 2017 (UTC)

For simplicity, suppose the Sun is eclipsed with the Moon. It goes from east to west over the ocean as the day progresses. When it is in the east, the east end of the ocean is lower, in the sense that it is deeper into the combined Earth-Moon-Sun potential energy well. And when it moves west (in an Earth-centered frame) it is then the west end of the ocean that is closer to gravitational sources, hence 'lower'. As a result, early in the day more water is east, and later some wants to go west. Except... it takes time for it to flow, and it requires force for it to flow, and there's no force to make it flow unless it is a little higher in the east than it ought to be when the sun is in the west. This makes the water lag a little bit. (Actually the effect of all that lag gets really complicated - there are high tides in some places, low in others, even the pattern of the tides can be different than in the textbook. But it all starts because the water isn't where it dreams to be at the instant.) Wnt (talk) 16:51, 13 June 2017 (UTC)

Now I understood what you meant by the word "lag". There is a lag 6 hours between the bulge and the moon-earth line. But first I must understand the bulge appearance (and height) explanation and only then consider the lag. E.g. I don't understand why is the tides effect explained by the gap of (4.51 - 4.36)×10^-5 but much bigger gap of equator point is ignored. The point on equator moves through lunar orbit plane. When the point intersects the plane, acceleration = 4.36×10^-5 , but at leftmost and rightmost positions acceleration = 3.38 ×10^-5 [3]. So gap =(4.36 - 3.38)×10^-5 . Username160611000000 (talk) 20:21, 13 June 2017 (UTC)

I'm still confused why you don't think the shell theorem is relevant. At the beginning you said that the y-components (which I assume are perpendicular to the Earth-Moon axis) cancel, and that the near and far sides "almost" average out. Well, as far as I know, the near and far sides do average out if you look at a spherical shell, taking into account that there is more of the sphere far away than close to a given point. So you're looking for it but I don't think your math will work out very easily unless you actually split up your bricks in spherical shells. Wnt (talk) 12:53, 11 June 2017 (UTC)

What do people mean by "reversing diabetes/CVD"?

Does it mean that the patient no longer has to depend on medications or be hospitalized or live with some kind of physical ailments (blindness, brain damage)? Or does it mean that the person no longer has to be restricted to diabetes-friendly food? By the way, what happens if a normal healthy person eats food made for diabetics? Is diabetic food safe for the non-diabetic? 50.4.236.254 (talk) 17:41, 10 June 2017 (UTC)

Diabetic foods are generally safe for everyone. (Caveat: some varieties may be sweetened with weird sugar substitutes that cause some digestive unpleasantness, but if so, the diabetics feel the same)

Putting type II diabetes into remission by weight loss and other therapies does happen; it's largely a matter of reversing insulin resistance. It's important to note though that diabetes is a common condition and many people, even those who don't have it, live close to the edge of it with standard Western diets. There is some evidence to suggest that even prediabetes thought not to be so bad ... is so bad. For example, prediabetics tend to prefer diet soda by taste, presumably having to do with higher blood sugar, and this study found a correlation between that and other serious problems that was not accounted for by diagnosed diabetes. Unless one goes for what seem like overblown theories about aspartame, anyway... Wnt (talk) 18:37, 10 June 2017 (UTC)

Has anybody done research on the eating habits of African, Asian, South American, and Eastern European immigrants in a Western country and whether they have the same obesity prevalence as Westerners? With obesity on the rise and so many people trying new things, just how common/prevalent is the Standard Western Diet? 50.4.236.254 (talk) 19:16, 10 June 2017 (UTC)

Not quite what you were asking but the rate among Inuit and First Nations in Canada is growing after the adoption of a western diet. See First Nations and diabetes, Inuit Type 2 diabetes gap worsens and Diabetes - First Nations & Inuit Health. CambridgeBayWeather, Uqaqtuq (talk), Sunasuttuq 00:09, 11 June 2017 (UTC)

Yes, this is a common pattern; a healthy group adopts a Western diet, then develops the same health problems as the rest of us. This shows that diet is far more important than genetics, in explaining the health differences of populations. StuRat (talk) 03:02, 12 June 2017 (UTC)

Yes. There are many studies comparing race and/or country of origin to primary comorbidities, such as hypertension, diabetes, and hyperlipidemia. The result is always the same. White people are more resistant to diseases caused by excess food and limited exercise. Blacks are the most threatened by the same excess food and limited exercise. Even within a specific disease, there is variation based on race and/or country of origin. For example, blacks accelerate from pre-hypertension to hypertension faster than whites and reach their first cardiovascular event (stroke/mi) a year earlier on average compared to whites. So, it is not simple to compare the United States (still mostly white) to a country in Africa and estimate the effect that excessive food and lack of exercise will have. Previous studies have shown that the real effects will be worse than the estimated effects. 209.149.113.5 (talk) 14:01, 12 June 2017 (UTC)

It's important to avoid assuming a Darwinian interpretation of this data, because epigenetics and in particular transgenerational epigenetics - something akin to Lamarckism, though in the shorter term - are very relevant in the case of human feast and famine. The Dutch famine of 1944–45 is one that has been studied the most - here's a sample paper. A more poetic article describes this and other famines here. So we cannot actually compare whites and blacks at the genetic level unless we make special effort to draw them from a pool with a similar history, i.e. no racial persecution since 1836. Unfortunately, that is not easy data to get. Also note that blacks have the widest genetic variation, representing all three major branches of humanity, and so black-to-black comparisons on genetic issues would probably have the best chance of yielding fruit, but you'd probably want recently mixed populations. Wnt (talk) 12:08, 13 June 2017 (UTC)

The studies I referred to, such as [4] are not genetic studies. They ask people to self assess race. In the paper for that link, those who self-identify as black accelerate to hypertension faster and reach their first stroke/mi faster than those who self-identify as white. I fully understand that political correctness is an issue when discussing race, but in this case, self-identification of race is important to aid in rapid hypertension treatment for those who self-identify as black. Waiting could be deadly. 209.149.113.5 (talk) 13:40, 13 June 2017 (UTC)

I'm not trying to be politically correct here, but scientifically correct. I understand that de facto race can be useful as an indication of various risks, sometimes for genetic reasons, sometimes for epigenetic reasons, and sometimes due to ongoing social reasons. But we don't necessarily know which, and it's important to remember that. It's also important to remember that, just as race is a poor proxy for income when a bank manager decides whether to give someone a loan, it is a poor proxy for genetic testing if there is a genetic component. Wnt (talk) 23:23, 14 June 2017 (UTC)

Grey hair

I've noticed numerous, isolated white hairs on people with otherwise dark brown or even black hair. Is the presence of such hairs, in any sense, distinct from greying, where, I believe, many more hairs have lost pigmentation, but only partially, and as such are grey rather than white?--Leon (talk) 17:53, 10 June 2017 (UTC)

“ Each individuals hair colour is determined by the particular pigment they produce (called melanin - the same stuff in your skin that makes you tan).

As the body ages this pigment (produced by the melanonocytes - cells that reside in the hair follicle) is produced less and less, until the hair is no longer coloured, and appears grey. This is unique to each individual because it is a genetic (and therefore highly heritable) trait. Because it is in no way linked to mortality there is no selection pressure against greying hair. The reason that the pigment is not longer produced is the gradual depletion of the stem-cell pool with age. This is common to many tissues, hair follicles being just one. As the 'pool' of stem cells is depleted, the melanocytes are no longer replaced as frequently, and thus less pigment is produced as we age.

” — Luke, Biology Stack Exchange

50.4.236.254 (talk) 18:16, 10 June 2017 (UTC)

I take issue with the statement "Because it is in no way linked to mortality there is no selection pressure against greying hair". A trait does not need to be linked to mortality to be subject to selection. For instance, it is quite plausible that grey hair has a negative effect on sexual attractiveness, and in that way is selected against. But one can also think of possible advantages: older looking individuals are seen as less of a threat or their opinions are more respected; this might benefit the grey haired individual directly or benefit their family members. Note that in our close relative the gorilla, the grey hair of silverbacks is clearly an adaptation concerned with signalling maturity and dominance. Note also that greying in old age seems to be a trait shared with other mammals, such as dogs. The loss of pigment in older humans might indeed just be an incidental side effect of no selective value, but my own hunches would be that it is not selectively neutral, and that it has some unrecognised positive selective value in signalling age.

Some recent discoveries about the genetics of grey hair may be of relevance to the original question: http://www.ucl.ac.uk/news/news-articles/0316/010316-first-grey-hair-gene-discovered . Jmchutchinson (talk) 19:08, 10 June 2017 (UTC)

Most humans become grey-haired only after they have reproduced, thus selective pressure against greying is minimal. Roger (Dodger67) (talk) 09:27, 11 June 2017 (UTC)

Sperm production does decline with age but not enough to make most men infertile at the age at which they would have grey hair (http://www.reproduction-online.org/content/70/1/211.long). The extent to which grey-haired men have the opportunity to mate with younger (i.e. fertile) women no doubt varies between cultures. Another important point is that the traits of post-reproductive individuals of both sexes are still subject to natural selection through their effect on the ability to care for grandchildren and other relatives (see Kin selection). Jmchutchinson (talk) 10:31, 11 June 2017 (UTC)

Star trooper man, I question your assumption that "grey hair" is due to individual hairs partially losing pigmentation with age. The article sections Human hair color#Gray and white hair and Human hair color#Aging or achromotrichia appear to corroborate my own experience (being 60) that individual hairs (ignoring bleaching by sunlight or chemicals) switch from growing with natural colour to growing white/colourless fairly quickly: the "greying" of the overall head of hair is due to an increasing proportion of white/colourless hairs amongst the still-pigmented.

In my own case, which I assume to be typical, a very few individual hairs have with age started to grow markedly darker, but so few that they do not effect the overall appearance. Up to now, I have not encountered any explanation for this latter phenomenon. {The poster formerly known as 87.81.230.195} 2.217.208.38 (talk) 09:48, 11 June 2017 (UTC)

My assumption was actually that what I described doesn't happen, that is, the person who claimed (to me) that the processes were distinct—implying that the latter process exists—was wrong. I have not observed this in people's hair.--Leon (talk) 17:53, 11 June 2017 (UTC)

Is Zaus gland considered as a lacrimal gland?

Is Zeis' gland considered as lacrimal gland? Based on this picture it seems that it is, but I'm not sure how authorized or correct it is. 93.126.88.30 (talk) 22:52, 10 June 2017 (UTC)

Judging by this abstract ( [5] ) I think not. I didn't check Sci-Hub for it, but it probably explains further. I think Zeis' gland secretes lipid while lacrimal gland secretes mostly saline solution, but I haven't looked into it enough to be sure. Tear film for the eye is really sophisticated technology at the biological level and shouldn't be underestimated. Wnt (talk) 00:28, 11 June 2017 (UTC)

Yellow mercuric oxide

When I were a lad, minor eyelid infections (styes) were treated with an ointment of "yellow mercuric oxide" (presumably mercury(II) oxide, HgO), which was sold over-the-counter. But the last time there was a need, I couldn't find the stuff. There was an ointment called Stye (trade name; we don't seem to have an article), which if memory serves used to have YMO, but it seemed to have been reduced to a lubricant with no antibacterial component.

Searching around, I find a paper that recommends it for a very particular condition, phthiriasis palpebrarum, not for styes in the usual sense. It doesn't seem to be available for pharmaceutical sale in the United States.

Presumably it was banned at some point, at least for over-the-counter sales? I didn't see anything specifically saying that, but it seems like the natural guess. When did that happen? Or was it something else, maybe product-liability concerns? --Trovatore (talk) 23:08, 10 June 2017 (UTC)

Hum. Wonder if you're so old that your birth certificate is in Latin. Banned a long time ago. See your quack Doctor. If he thinks it needs treating it will be with an antibiotic. Aspro (talk) 23:18, 10 June 2017 (UTC)

Oh, I don't have a need at the moment. I was reminded of it when clicking around in reaction to the question above, about "lacrimal glands". Do you have details on the banning, with particular attention to the United States? --Trovatore (talk) 23:23, 10 June 2017 (UTC)

Apparently this is Pagenstecher's ointment. [6] A 1990 study called it safe and effective for treatment of bacterial blepharitis of the eyelid. Apparently in 1983 the FDA published a Tentative Final Monograph banning it from over the counter use on the basis that patients might have a more serious infection, therefore must be sent to see a doctor to find out if it is only trivial. [7] As always, medicine is a racket; it's only about the money. That said, this is true for both sides, and many sorts of blepharitis often respond nicely to warm wet compresses... [8] ... the risks of mercury are probably exaggerated, but still, of various drugs unjustly banned and restricted, this one seems less indispensable than some. Wnt (talk) 00:50, 11 June 2017 (UTC)

Well, there's no longer any need for it -- antibiotics work just as well, and are safer (no need to worry about chronic toxicity). 2601:646:8E01:7E0B:E957:E363:9DD1:1743 (talk) 06:38, 11 June 2017 (UTC)

I used the original "Golden Eye Ointment" for many years after it went off the market in the UK, and found it more effective than its modern (1992) replacement and other modern OTC ointments containing dibromopropamidine isethionate, with only one or two applications needed for minor infections (though I don't doubt that a properly prescribed appropriate stronger antibiotic might be more effective, but wastes a lot of time in obtaining). I wish I hadn't thrown it out, even though it was many years out of date. There's probably more mercury poisoning risk from eating fish! Dbfirs 08:01, 11 June 2017 (UTC)

Yeah, my memory is that it worked really well. If you've ever had one of these things, you know you want it gone pronto. The reason the FDA gave, per Wnt, is unbelievably insulting. If that's the only reason, we should lobby to get it back in the stores ASAP. --Trovatore (talk) 08:42, 11 June 2017 (UTC)

Unfortunately, I don't think we'd get anywhere with the US or UK authorities. The words "contains mercury" set off warning bells for an automatic refusal these days (almost as alarming as "contains asbestos"). Is the ointment available elsewhere in the world? Can we import it? Can we make it? Sorry, don't answer that. It was not intended as a request for medical advice. Dbfirs 11:59, 11 June 2017 (UTC)

RfC Announce: Wikimedia referrer policy

In February of 2016 the Wikimedia foundation started sending information to all of the websites we link to that allow the owner of the website (or someone who hacks the website, or law enforcement with a search warrant / subpoena) to figure out what Wikipedia page the user was reading when they clicked on the external link.

The WMF is not bound by Wikipedia RfCs, but we can use an advisory-only RfC to decide what information, if any, we want to send to websites we link to and then put in a request to the WMF. I have posted such an advisory-only RfC, which may be found here:

Wikipedia:Village pump (policy)#RfC: Wikimedia referrer policy

Please comment so that we can determine the consensus of the Wikipedia community on this matter. --Guy Macon (talk) 23:28, 10 June 2017 (UTC)