**Ask a monkey a physics question thread**

[Juked07]

I suspect these are related:

1. Please characterize the effort that a helicopter expends to hover in place. Work is force dotted with distance, but distance here is 0, so it seems the usual physics quantification of work yields 0, which I find highly unsatisfactory. Perhaps impulse is relevant, but we don't typically use impulse to characterize effort and it has strangeness of it's own. Please explain.

2. Characterize the effort that a cyclist expends to climb a hill with constant gradient theta at two constant speeds, s1 and s2 where s2 > s1, assuming there is no energy lost to friction or air resistance. The force required at the two speeds is equal (only need to overcome another constant force, gravity, in both cases), so the total impulse over some time period t is equal. Yet at speed s2 the cyclist has clearly accomplished more than at speed s1. But work doesn't seem a fair measure either -- the impulse applied was the same!

[MadMojoMonkey]

If spacetime is not a material substance, how can it make MASSIVE objects, which tend not to accelerate due to their inertia, move?
2 - If gravity is not a force, why does an object put in rest relative to the earth accelerate toward it?
3 - If the earth mass curved ONLY space, than an object put at rest relative to the earth would continue at rest relative to it. But this is not what happens, so the earth mass also curves TIME. How does this curved time make things to accelerate?
4 - What did you find more difficult, to answer these general relativity questions or playing heads up against me in Stars?
Thanks

Disclaimer: I am not trained in GR. I took emphasis on QM during my undergrad. I have a smattering of knowledge about certain relativistic phenomena, but I have never learned the math behind a full GR calculation.

I think I've touched on all the major concepts (as I understand them) in prior posts in this thread. In short, it's mass that warps space-time and the warps in space-time interact with each other. Space-time can flow in this manner. The notion that space-time isn't "material" is irrelevant. An electric or magnetic field is not a "material" thing, but it obviously interacts with charged particles.

This paragraph is pure unconfirmed speculation on my part:
If you take Einstein's "Magic Elevator" thought experiment and reform everything to be an object near the Earth's surface, then it seems that the object appears to be falling, but it's really sitting still in moving space-time. In this picture, a gravity well is a kind of space-time Hoover, that sucks in the surrounding space. (I doubt this is a very good description, but it's something I thought about while reading Einstein's Relativity.)

1 - 3) University of Illinois' answer to your copy/pasted questions.

4) GR is way harder than poker.
I'd gladly exchange my candid analysis of your play during that session (for the same) in PM's or another thread.

[MadMojoMonkey]

Do galaxies form around black holes only?

All evidence currently suggests this is the case. Unfortunately, the evidence is pretty slim and slow to come in. It requires very sensitive instruments to observe our own galactic core, much less that of another galaxy.

The major issue is that in order to observe the center of a galaxy, you have to see past the rest of it. It's all the same stuff, so it's difficult to filter out the "noise".

Other effects, like gravitational lensing also show evidence for black holes.

A 6 1/2 minute video from 60 symbols that shows the evidence for the Milky Way's black hole(skip to 5:00 if that's all you're interested in).

[MadMojoMonkey]

1. Please characterize the effort that a helicopter expends to hover in place. Work is force dotted with distance, but distance here is 0, so it seems the usual physics quantification of work yields 0, which I find highly unsatisfactory. Perhaps impulse is relevant, but we don't typically use impulse to characterize effort and it has strangeness of it's own. Please explain.

Newton's Laws tell us that an object will accelerate if and only if the vector sum of forces on the object is non-zero.

In order to remain hovering (not accelerating), the helicopter must experience a vector sum of forces which is equal to 0 N. We know that gravity can be accurately modeled as a force in this circumstance. That force must be countered with an equal and opposite force to maintain a net force of 0 N.

In order to create this countering force, the helicopter does work to spin the rotors. The rotors have cross sections that are airfoils. When the air flows around the rotors, a pressure differential is created, with low pressure on top, and high pressure on the bottom. This creates lift, a force in opposition to gravity.


Consider a hovering rocket. It is stationary, so the work it experiences is 0 J. However, the gasses expelled from its jet experience a force as they are accelerated out the nozzle. The work done on the fuel creates the force which counters the force of gravity on the rocket.

Bear in mind that, in either case, a whole lot of energy is dissipated through friction, noise, heat, rotations in the air molecules, and linear momentum that is not directed in opposition to gravity.

2. Characterize the effort that a cyclist expends to climb a hill with constant gradient theta at two constant speeds, s1 and s2 where s2 > s1, assuming there is no energy lost to friction or air resistance. The force required at the two speeds is equal (only need to overcome another constant force, gravity, in both cases), so the total impulse over some time period t is equal. Yet at speed s2 the cyclist has clearly accomplished more than at speed s1. But work doesn't seem a fair measure either -- the impulse applied was the same!

Force per unit distance would be the same. So, as you pointed out, the energy (measured as impulse; J = Nm) would be the same.
However, the energy per unit time would be different.
Recall that power is energy/time (W = J/s). Moving at s2 would be consuming more power than moving at s1.

Revision: Oops, complete fail on my part. Impulse is NOT Fd (force x distance), it's Ft (force x time), and is NOT a measure of energy.

In your example, the force per distance is the same in both cases. The impulse delivered over a given time is, too. Since one rate traverses more distance than the other in the same time, it requires more energy in the same time. Since the acceleration is 0 m/s^2 in both cases, the net force on the cyclist must be 0 N, so the impulse is then 0 Ns.

Other than that, .

[Pelion]

Since one rate traverses more distance than the other in the same time, it requires more force in the same time, meaning greater impulse.

Other than that, my analysis holds.

I don't understand what you mean here. If you resolve gravity into the directions parallel and perpendicular to the slope then you will find out what force is needed (propulsion) for constant speed. This gravitational force should not be speed dependent. With no friction, the required propulsion force should also not be speed dependent.

The way I would look at this is that with speed constant, you are increasing gravitational potential energy (mass x g x height). Cyclist 2 will increase height faster than cyclist 1, so he will convert weetabix energy into potential energy faster. If he moves twice as fast then he uses energy twice as fast.

[MadMojoMonkey]

These are not the droids you're looking for.

[Renton]

This is probably a stupidly basic question but:

Are freezing/boiling points of substances completely hard numbers? By that I mean, can water in liquid form exist below 0 degrees celsius, or likewise can it exist at above 100?

I'm aware that running water cannot freeze as easily as standing water, but is that because the movement of the water raises the temperature or what?

[NightGizmo]

This is probably a stupidly basic question but:

Are freezing/boiling points of substances completely hard numbers? By that I mean, can water in liquid form exist below 0 degrees celsius, or likewise can it exist at above 100?

I'm aware that running water cannot freeze as easily as standing water, but is that because the movement of the water raises the temperature or what?

The freezing/boiling points are not absolute, they also depend some factors. It's been a while since chemistry, but you can change those temperatures by dissolving other materials (like salt, which is why it is used to de-ice roads -- it lowers the freezing point and raises the boiling point). Pressure also affects those numbers -- that's why there are different directions for cooking at high altitudes (the boiling point is lower due to the reduced air pressure).

[MadMojoMonkey]

Temperature, pressure and density are intrinsically linked. If you know 2 of them, you can calculate the third. If you know 2 of them, and you have an appropriate chart or table, you can look up the phase(s) of matter.

The easiest way to talk about it here is in terms of pressure and temperature. I'm ignoring density in this post.
It's like describing a circuit in terms of Volts and Ohms, but not the Amps. The circuit is still completely described.

I'll be using atmospheres for pressure. 1 atm is the mean air pressure at sea level.
1 atm = 14.7 psi = 760 mmHg = 101.325 kPa

Are freezing/boiling points of substances completely hard numbers? By that I mean, can water in liquid form exist below 0 degrees celsius, or likewise can it exist at above 100?

For a given pressure, these temperatures are hard numbers. Like NG said, impurities in the water will subtly change the numbers. Still, for a given substance, the thermodynamic behavior is deterministic.

Water can exist at temperatures below 0 C or above 100 C if the pressure is greater than 1 atm.

Here's a useful graph, called a P-T diagram, for water. This shows pretty much everything you're asking and more for this question.

Notice that a horizontal line across the upper portion of the graph shows exactly what you're asking.

There's also a cool phenomenon at 0.006 atm and 0.01 C where water can exist equally as steam, water or ice. This is called the triple point of water.

The top-right portion of the graph, beyond the 'C' (critical point) water becomes a supercritical fluid, where there are not distinct liquid and gas phases.

Here's a link to an article that says the coldest water can exist without becoming ice is -48 C. I scanned it quickly and didn't see any mention of what pressure they had it.

I'm aware that running water cannot freeze as easily as standing water, but is that because the movement of the water raises the temperature or what?

This one is really tough, actually. It's a very complicated system with a ton of variables.
While geothermal heating can play a part, water flowing in mountain streams and rivers can definitely get below -2 C. So it's not necessary that the water is above 0 C.

I could only find partial explanations over and over again in my search.

Part of the reason it doesn't freeze is that the Hydrogen bonds that form between water molecules when it freezes are quite weak. The turbulence in the flowing water can break apart newly formed Hydrogen bonds, and effectively lower the freezing point of the flowing water.

Another part is that the water requires a nucleation site to begin crystallization. This partly explains why rivers freeze at the banks first.

Thermal energy is lost to evaporation on the surface of the flow, which partly explains why rivers freeze on top first. That frozen layer acts as an insulation layer against further evaporation, which partly explains why a river that is frozen over is still flowing beneath the ice.

Ice forms in hail storms under very turbulent conditions, though. Waterfalls do freeze.

[CoccoBill]

Water is cool. No pun intended.

[jackvance]

How do you solve this using the chain rule? I believe it is of the format g(t)'*g(t)^p but not sure what next.

I'm a bit unsure if the exponent -2 should be positive +2, but the solution should be the logistic function, I'm interested in the intermediate steps because my calculus is so rusty.

[Pelion]

I do find myself wondering if this should be renamed the "ask Monkey to do your homework" thread .

[MadMojoMonkey]

I was constantly losing points on this kind of problem for not changing the limits of integration on substitution steps, but it shouldn't matter since everything gets un-substituted by the end. Also, I looked up the logistic function and verified that I got the correct answer.

That's just MS Word's equation editor, and yes, this is how I do math problems when I have to show the work to anyone but myself. I am quite slow at math, and my handwriting is atrocious, so it's a win-win.

[Savy]

Wolframalpha says



Which is a much nicer way of writing it

[jackvance]

I was going through the mathematical biostatistics course on coursera for fun :P. My homework would be preparing doctorate abstracts.

edit: Thanks MMM, I like how you wrote it out. I was getting almost all of the quiz answers right except these annoying integrals. Need to practice it again.

[MadMojoMonkey]

I was getting almost all of the quiz answers right except these annoying integrals. Need to practice it again.

I wouldn't have learned how to solve integrals if not for Wolphram|Alpha.

I heartily suggest making friends with this site. If you create an account, it will show you each step in the solution, so you can see how to get through substitution steps, chain rule, and integration by parts.

[jackvance]

I "know" how to do this from my engineer studies but it's coming from very far. That site looks very interesting, I'll check it out tomorrow (one of my flaws is I like too much to just write stuff out on paper). Enough study for today, if my poker tourneys end it's party time :P. Btw I watched the courses from the first two weeks of Mathematical Biostatistics today, can recommend this course greatly, it goes very deep into the fundamentals of statistics to give you a thorough understanding. For anyone interested.

[MadMojoMonkey]

For the record, I didn't use the chain rule, I used integration by substitution. It's really just picking nits about terminology. The chain rule is a method of solving derivatives. Integration by substitution is the same process, but in the integral form.

[jackvance]

Yes the chain rule is normally for derivatives but the professor of this class gave a short explanation that went something like "this is of the format g(t)'*g(t)^p so we use the chain rule and easily see that it is (solution)". How you solve it here through substitution is the correct way of course.

[eugmac]

My dad's an engineer (working in the automotive industry) and all through school he would berate me for not being able to do math homework of any sort (insert asian dad meme or whatever), until we started with calculus. He looked over my shoulder and said "Calculus! Never mind about that crap. You'll never need it. Your uncle working with nuclear plants needs to worry about that sort of thing..." and refused to help me lol.

[eugmac]

Oh which brings me to my nerdy uncle who works in nuclear energy. When my mother (his sister) died, he came over from Japan to Canada to stay with us for a while. We offered him my room for him to stay in and I moved to the basement. I'm eating my breakfast one day minding my own business and he comes up to me with one of my math notebooks with calculus crap in it (he went through my school work, wtf!) and pointed out a more elegant way of solving a problem. Like "see how you can skip like 6 steps if you just [bunches of stuff I don't follow, at all]." Meanwhile I'm like, I'm trying to eat my breakfast, dude.... Random memory.

[a500lbgorilla]

My question is: what is it that this is? https://www.simonsfoundation.org/qua...antum-physics/

Also, how come they can get press coverage like this and not even have a paper out?

"“Both are hard-wired in the usual way we think about things,” said Nima Arkani-Hamed, a professor of physics at the Institute for Advanced Study in Princeton, N.J., and the lead author of the new work, which he is presenting in talks and in a forthcoming paper. “Both are suspect.”"

Unless this is it ---> http://arxiv.org/abs/1212.5605

[MadMojoMonkey]

This is way over my head, both mathematically and in terms of what that math is describing, specifically the 'superpartner particles'.

I haven't even heard of the technique that makes Feynman diagrams seem like the long way to do it.

This description sounds promising, but string theory has sounded promising for decades, with no tangible verifiable predictions. As such, I think a healthy dose of skepticism is in order while the data, if any, comes in.

It also sounds like they've started from some rather confining assumptions (which is common), and the theory needs to be developed to see how robust it is in a broader context (also quite common).


What can they mean here?
"But the new amplituhedron research suggests space-time, and therefore dimensions, may be illusory anyway."

That does not sound like physics... or mathematics for that matter. It sounds like Savy told them to say that, just to troll me.

(much respect, Savy )

[Savy]

You never heard of stuff like that before MMM? I obviously dunno a huge amount behind how solid they are as theories or even how much it applies here tbh, but you must have heard of like holographic universes and the like before.

[MadMojoMonkey]

You never heard of stuff like that before MMM? I obviously dunno a huge amount behind how solid they are as theories or even how much it applies here tbh, but you must have heard of like holographic universes and the like before.

Yes, I've heard of them, but they're of no physical relevance... yet. They are based on complicated, unfounded assumptions and describe unobserved objects. Where the theories agree with the Standard Model of Particle Physics, they are correct, but they do not overlap entirely with the Standard Model. Also, they do not make predictions that can be tested beyond what the Standard Model predicts.

What this means is that string theories are not incorporated into the Standard Model, because they do no add to or clarify the Standard Model. No string theory has yet to yield a significant contribution to our understanding of reality as we observe it.


As such, I don't spend a lot of time digging deeply into string theories. Many people, much smarter and more educated than me, have spent their lives working on string theory, and to no avail, other than to eliminate possibilities... which is good in its own right. Proving something can't be the answer, or putting limits on the form of the answer, is sometimes a vital step in determining the answer.

My point is that I, personally, focus more on practical, tested theories and their applications. As such, I'm not very fluent in the language of string theory. Also, as pertains to this topic specifically, this is PhD level stuff. I'm struggling to keep up with an undergraduate degree.

[Savy]

Ye a post I was going to make was about how it's kind of getting a bit philosophical about whether we can actually ever begin to truly understand the universe or whether we just literally don't even begin to understand (and maybe aren't even capable) what's actually going on and we are just good at creating models which seem to have use. It's pretty mental the applications we can find for theories which aren't even close to being complete.

One thing I will say though is I've known far too many people who are very good at Maths who think Maths has some deep lying fundamental part of nature, kind of like it's something that was always going to be found. Not that it's just a model that we have built up that seems to work and from my limited knowledge of this area of Maths is actually something that we've found that is always going to be incomplete.

[MadMojoMonkey]

There is something inherently beautiful about mathematics that becomes more and more profound the more I study it. I mean... what is a number? It seems to me that a number is just a human-invented label for something. Just a placeholder to describe something abstract.

All of mathematics stems from 2 simple assumptions:
1) Lets assume that the number 1 means what we all think it means. Let's assume that the idea of a 'single', 'solitary' thing is a practical thing to assume, and attach a symbol to this notion of 'unity'.
(Note how all I did there was write a bunch of synonyms for 1, without really defining it. Find me another way to do it, I challenge you. This, in itself is a beautiful thing, no? Doesn't it say something profound that we all understand this thing, but really can't define it without being redundant?)

2) Now let's have a generator function, such that whenever we give it input, it outputs a number that is greater by exactly 1.
f(x) = x + 1
(Note, we inadvertently invented addition in the process. Oops.)

I'm simplifying it a (shockingly tiny) bit, but that's the foundation of all mathematics. Everything else just spills out from those seemingly obviously trivial assumptions. So far, we've only defined 1,2,3,... but all of the decimals and fractions and rules of arithmetic and algebra just come spinning out of there, with a little application of logic.

Logic is the most powerful tool of math. Math and logic are somehow intrinsically linked. I find that beautiful as well.


Your friend may be referring to Goedel's incompleteness theorems:
"The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (e.g., a computer program, but it could be any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency."
-wikipedia

What that means is that it has been mathematically proven that no finite number of mathematical theories can yield a mathematically complete set of mathematical truths. There will always be more true statements to be made, no matter how robust our understanding of mathematics ever becomes.

I.e., it is absolutely proven that humans have invented/discovered something that can never be fully understood... not just by humans, but by any conceivable finite intelligence. I find this to be remarkably beautiful, too.

[rpm]

my question is on what grounds do you claim mathematics to be inherently beautiful? my general perspective is that nothing can be inherently beautiful, but if there did exist such a thing as inherent beauty, mathematics would have the least amount of it on the planet. ok now i'm starting to sound like a troll but i am genuinely curious about this connection you are making between "beauty" and "solving problems with numbers"

[MadMojoMonkey]

I don't want to derail this thread too far, but I am happy to explain myself. I did start it, after all.

First of all, I'm not talking about "solving problems with numbers". I'm talking about the interconnectedness of elaborate systems of interactions of numbers which blooms from the most simple and seemingly obvious assumptions with only applying a bit of logic. I'm talking about the fact that no matter how much we understand this idea called mathematics, we know that there will always be more to know. I'm talking about the fact that for some unknown reason, we can use these symbols to describe and understand our world and our bodies (*sigh* by creating and solving problems with numbers).

As for my use of inherent, I mean that it's a quality that seems to just be there. I don't propose there's an equation that quantifies beauty or any proof of its location. Which brings me to beauty. I don't propose there's a way to define beauty. I think appreciation of beauty is an emotional response, and that what is beautiful to one person may not be beautiful to another.

So all I'm saying really, is that I find emotional satisfaction in the complex interconnectedness of numbers. I find it wholly gratifying to be able to "predict the future" using numbers. By which I mean, of course, plot trajectories, calculate probabilities and whatnot... not the whole clairvoyance thing, obv. I mean it in the sense of, "I predict if we build this rocket and point it that way, we can play golf on the moon."

I mean... without mathematics, we wouldn't understand Quantum Mechanics at all. We wouldn't have cell phones, or touchscreen, or GPS, or microwave ovens... We got those things from our (well some dedicated person's) understanding of how to use math to describe something, and use that description to make a new thing.

I find it beautiful and truly awesome that from 1,2,3,... we get those things. I can't convince you to agree, but that's what I mean.

[a500lbgorilla]

I like to think of Math as the world we created when we said, "what if there was only logic?"

We take a few inspired steps here and there from the real world, create a 1 when it seems to be useful, claim parallel lines never cross because they don't really seem like they should, and follow every conclusion to its next conclusion.

[surviva316]

my question is on what grounds do you claim mathematics to be inherently beautiful? my general perspective is that nothing can be inherently beautiful, but if there did exist such a thing as inherent beauty, mathematics would have the least amount of it on the planet. ok now i'm starting to sound like a troll but i am genuinely curious about this connection you are making between "beauty" and "solving problems with numbers"

Not to derail a derail, but I think you mean intrinsic. I can't imagine you're skeptical that inherent goods don't exist. If you're talking about intrinsic, then I'm right there with you. I don't really understand what the fuck intrinsic good/bad even means, and I imagine it's just a holdover from simplistic theistic worldviews where there exists good vs evil that are independent of perspective.

Anyway, I think MMM could make a very good case for math having an inherent "beauty". In fact, I'll go as far as to say that something that lies at the heart of our physical world, and also potentially defines the limits of epistemology certainly seems to have some kind of intrinsicness to it, but I just don't really understand what the fuck good and bad mean outside of instrumental terms, so I wouldn't call it an intrinsic good.

[Pelion]

my question is on what grounds do you claim mathematics to be inherently beautiful? my general perspective is that nothing can be inherently beautiful, but if there did exist such a thing as inherent beauty, mathematics would have the least amount of it on the planet. ok now i'm starting to sound like a troll but i am genuinely curious about this connection you are making between "beauty" and "solving problems with numbers"

Math also does this

http://www.misterx.ca/Mandelbrot_Set...WALLPAPER.html

[MadMojoMonkey]

Nobody mentioned good or bad, outside the context of 'good at math', or 'good step in solving a problem', aside from you, sur. Also, I had to google the difference between inherent and intrinsic, and it's a fine line. Anyway, I already defined what I meant in the 3rd paragraph of #179.

It was my own fault for waxing poetic on the subject of the beauty of math. We can certainly agree that the question, "What is beauty?" is not a scientific question, and certainly not suitable for a physics thread.

Thank you for the positive thoughts. I really could go on for hours.


On the topic of the aplituhedron, here's a link to Nima Arkani-Hamed speaking this year at SUSY.
Full disclosure, this is way over my head, and I imagine that you will all hate me if I don't warn you:
Even though he speaks American, I did feel like I was listening to a foreign language for an hour while he was enthusiastically gesturing at lines on a screen.

That link is from a rather long forum post I found on physics.stackexchange about the amplituhedron which discussed the significance of the object. The author certainly seemed to know what he was talking about.

Apparently, it's still describing things that are a couple of steps below string theory thus far... so you know... don't get your hopes up any time soon for a revolution in physics. This new object has still got to describe the proposed objects that underlie string theory, which itself is not a physically accepted theory for reasons I've stated ITT.

[rpm]

Nice response, apologies for the mini derail

[surviva316]

Nobody mentioned good or bad, outside the context of 'good at math', or 'good step in solving a problem', aside from you, sur. Also, I had to google the difference between inherent and intrinsic, and it's a fine line. Anyway, I already defined what I meant in the 3rd paragraph of #179.

It was my own fault for waxing poetic on the subject of the beauty of math. We can certainly agree that the question, "What is beauty?" is not a scientific question, and certainly not suitable for a physics thread.

Thank you for the positive thoughts. I really could go on for hours.

I'm content to end the derail, but just a couple of clarifying points:

1) I never meant "good at math" or any of that either. Sorry for whatever I might have said that caused the confusion (I just edited my post for language because Christ it was messy).

2) I Googled "difference between inherent and intrinsic" just to see what you were getting, and good God everything is so WTF terrible, except for the Wikipedia hit on Intrinsic Value (Ethics). I guess the takeaway is that in most everyday exchanges of language or in an English class, they're basically the same thing and if we have to distinguish between the two then we'll just throw out random bullshit theories. But as far as a philosophical discussion on ethics or aesthetics, they're closer to opposites because one refers to instrumental value (something that's only good in so far as it lends to something else that is good) and the other to intrinsic value (something is an end in itself).

3) I wasn't nitpicking you so much because your use of the word inherent seems perfectly fine. In fact that 3rd paragraph you point out is like the perfect distinction between inherent and intrinsic aesthetic value (ie: beauty for the purposes of this convo). It has qualities that are inextricable from its essence (it's there for everyone to see and experience in the same way), but the value is not intrinsic (ie: "appreciation of beauty is an emotional response, and that what is beautiful to one person may not be beautiful to another").

Anyway, sorry I engaged with that more than I meant to in a clarifying points post, but oh well, I'll shut up now.

[ChipEaterMan]

My dad's an engineer (working in the automotive industry) and all through school he would berate me for not being able to do math homework of any sort (insert asian dad meme or whatever), until we started with calculus. He looked over my shoulder and said "Calculus! Never mind about that crap. You'll never need it. Your uncle working with nuclear plants needs to worry about that sort of thing..." and refused to help me lol.

Oh which brings me to my nerdy uncle who works in nuclear energy. When my mother (his sister) died, he came over from Japan to Canada to stay with us for a while. We offered him my room for him to stay in and I moved to the basement. I'm eating my breakfast one day minding my own business and he comes up to me with one of my math notebooks with calculus crap in it (he went through my school work, wtf!) and pointed out a more elegant way of solving a problem. Like "see how you can skip like 6 steps if you just [bunches of stuff I don't follow, at all]." Meanwhile I'm like, I'm trying to eat my breakfast, dude.... Random memory.

[jackvance]

Explain the spin of the toilets in relation to distance to the equator.

[MadMojoMonkey]

There is no relation. It's an urban myth. The water will spin whatever way the jets at the top are pointing.


Wait... the spin of toilets? ... The toilets themselves?

They revolve at 1 revolution per day at any latitude.

The spin is the same as the spin of the Earth.

[jackvance]

So simpsons lied to us?!

[a500lbgorilla]

[jackvance]

Sooo

Q: Explain the spin of [water in] the toilets in relation to distance to the equator.

A: There is no relation. It's an urban myth. The water will spin whatever way the jets at the top are pointing.

There actually *is* an influence on the spin of water in the toilet bowl, the coriolis effect, which is a force that makes water spin clockwise in the southern hemisphere and counterclockwise in the northern hemisphere. The distance to the equator has no effect in itself, because coriolis forces are linear with the rotation speed (1/day=very slow) and the mass.

It's typically not observable in such tiny spots as it is overshadowed by other factors (the way the jets are pointing as you said) but there is an effect.

[MadMojoMonkey]

So if you already knew the answer, then why did you ask the question?*

Yes, you are correct, but the other factors are so prevalent that the Coriolis Effect is not relevant. The no-slip boundary condition of Fluid Dynamics overpowers the Coriolis Force for most containers.

By far the most influential factor is the geometry of the drain point. If you imagine a hemispheric bowl, with the drain not exactly at the bottom, or normal to the bowl's surface, then there will be an induced rotation.

Assuming we have an appropriate bowl/drain to eliminate that issue (I.e. NOT a toilet):
The net angular momentum near the drain at the moment the plug is released plays the most prevalent role. The thermal motions of the molecules will have random localized rotations, which will create the initial conditions for the rotation direction at the moment the plug is pulled. Once the plug is pulled, there is an amplification of the initial rotation as the fluid drains away in a spiral, leaving a low-pressure spiral that self-perpetuates until the bowl drains.

Factors such as the geometry of the container are relevant in the non-hemispheric case.



*Just state the effect as something cool and attach a question if you like.

P.S. I find the whole "gotcha" type question line to be non-conducive to open, intellectual conversation. If I mis-read your intent, then I apologize for the assumption.

[jackvance]

It wasn't like that at all man, it was a genuine question in my drunken mind at the time, now I just looked it up.

[MadMojoMonkey]

I am sorry I took it the wrong way.

[Galapogos]

This thread should become the stump the physics monkey thread. That reaction to jackvance's question was entertaining.

[wufwugy]

I'm gonna butt my junk in here and say there can be no unified field theory because there is no ultimate foundation or ultimate sense. The best we can ever say is "it works because it works". The place of no rules is the foundation of rules

[MadMojoMonkey]

I think I agree with you.

Science is very good at describing what is going on, but no good at explaining why it's going on.

[MadMojoMonkey]

All electrons are identical.

Are they? I remember asking my chemistry professor: "Is a hydrogen electron, which the atom shares with oxygen to make h2o, a general electron or a hydrogen-specific one?" And he said hydrogen-specific. So if what he told me is true, wouldn't that mean all electrons aren't the same?

Electrons are indistinguishable from each other. I'm not sure exactly how you phrased the question or the exact answer, so it's tricky to know exactly what your professor meant. Chemists and Physicists understand things in different contexts, and use similar terminology in subtly different ways.

My guess as to why a chemist would say that:
In a sense, the electron that is bound to the Hydrogen atom is not an electron bound to the Oxygen atom. The quantum state of the electron in the Hydrogen atom is what holds the nucleus in the bond. Otherwise, the electron would just ionize off of the Hydrogen nucleus onto the Oxygen nucleus, and the Hydrogen nucleus would not be bound in the water molecule.

What a physicist would say, and a chemist would not argue with:
In another sense, it is indeterminate exactly which electron is bound to the Hydrogen atom. Once the molecular bond is formed, the electrons are in a bound state, and it is only clear that 1 is the Oxygen electron and 1 is the Hydrogen electron, but not which is which.

There is no measurable property of any electron which is distinct from any other electron.

[MadMojoMonkey]

There is no measurable property of any electron which is distinct from any other electron.

This is poorly stated. Clearly the quantum state, position/momentum, etc. can be different for different identical particles. The particles are the same in the sense of identical electric charge, mass, and other intrinsic properties.

[wufwugy]

That makes loads of sense, and I didn't think his response made perfect sense in the first place. If it did, there would probably be a periodic table of electrons instead of just elements

[MadMojoMonkey]

That makes loads of sense, and I didn't think his response made perfect sense in the first place. If it did, there would probably be a periodic table of electrons instead of just elements

There is a table of fundamental particles, but it's not periodic.

[Savy]

Out of interest do you not think it's strange that all protons are the same, all electrons etc etc. Is there literally 0 scope for them to be different? Or could there still room for their to be tiny differences between them that we just aren't currently aware of?

And do we ever find more exotic particles taking the same roll in a larger atom even if just for a brief period of time? I'm pretty sure I remember that you can add muons to certain things in place of electrons but this is all ages ago and it was never very deeply discussed.

[MadMojoMonkey]

Out of interest do you not think it's strange that all protons are the same, all electrons etc etc. Is there literally 0 scope for them to be different? Or could there still room for their to be tiny differences between them that we just aren't currently aware of?

I don't think it's strange now... I can't remember if I thought it was strange the first time I heard it.


The next paragraph talks about color in a completely non-intuitive sense. Particles are too small to have a color, as you and I experience color. Physicists notices this obscure quality in quarks and didn't know how to talk about it, so they used color, which is handy for a couple of reasons I wont get into. The bottom line is that this is "quantum color" and not visual color.

Protons are weird... I don't want to talk about their same-ness, because I'm not trained in Quantum chromodynamics. They ARE the same, but they are also always in a state of flux, due to the quarks exchanging color when they express forces on each other. There is always 1 green quark, 1 red quark, and 1 blue quark, but since the Proton is made of 2 Up quarks and 1 Down Quark, it is not necessarily the case for 2 'identical' protons that their Down quark is the same color.


There is always the possibility that any scientific statement is wrong. Science isn't concerned with 'truth' so much as 'observable predictability'. There is always room for new information to alter current statements.

There’s no a priori reason that fundamental particles have to be fundamental. We don’t know for certain that electrons (or any particles) are fundamental.

Quantum Electrodynamics (the most precise theory ever measured) says an electron-like particle (i.e. a particle of spin-1/2) is fundamental. Half-spin particles are the fundamental excitations of the field, according to Quantum Electrodynamics.

And do we ever find more exotic particles taking the same roll in a larger atom even if just for a brief period of time? I'm pretty sure I remember that you can add muons to certain things in place of electrons but this is all ages ago and it was never very deeply discussed.

Absolutely, but they are unstable.

You (well someone) can replace the electron in Hydrogen with a Muon, since they have identical charge. However, the Muon is less stable than an electron (which is fundamental and therefore completely stable), and will eventually decay into other particles. This ionizes the Hydrogen atom, leaving only its nucleus, which is just a proton.

Anti-Hydrogen atoms have been made, which consist of an anti-proton and a positron. These are as stable as a 'regular' Hydrogen, but still difficult to maintain. Since the positron will annihilate with any electron it encounters, it is difficult to contain it.

You can wiki "Exotic Atoms" for some more descriptions.

[MadMojoMonkey]

Physics and pooping: how to prevent back-splash.

Poop Splash Elimination

Best part is at 3:20
Little girl: Are you potty training big people?
Adult: Yes.

[jackvance]

I'm gonna butt my junk in here and say there can be no unified field theory because there is no ultimate foundation or ultimate sense. The best we can ever say is "it works because it works". The place of no rules is the foundation of rules

I believe it exists. We just have to find a representational system that can explain everything. The essence should be really simple.

[wufwugy]

Well that's an even harder proposition. A sensible foundation existing is one thing, but thinking that humans can know it is something else. That may not be unlike being stuck inside something and trying to explain what it looks like from the outside.

[MadMojoMonkey]

Yeah, I decided to weight Wuf's 2nd sentence for my previous response. I don't think there's any reason a physicist should think that the Unified Field Theory, UFT, or Theory Of Everything, TOE, is an impractical goal. I do believe that these theories will be solved.

Also, there's no need to include 'essence' or 'ultimate sense' in physics at this point. Furthermore, I can't say there's no such thing as gods or magic, but so far, everything that was once explained by either divine intervention or magic has turned out to be better explained by something that is neither divine intervention nor magic. So I feel pretty confident that these ideas are not needed to explain the structure and development of the universe.

Still, science isn't interested in what is 'true'. I feel that is the greatest misunderstanding in the world as pertains to science. Science is interested in what's consistent, not what is true. It's a subtle, but important distinction. The idea of a 'scientific truth' is an absolute misnomer.

So if what Wuf is saying is, "Even the best scientific theory can't be true," well, I agree with that as well.

[Pelion]

However, the Muon is less stable than an electron (which is fundamental and therefore completely stable)...

But Muons are also fundamental particles (and electrons are not always completely stable)

[wufwugy]

Well my original point was an extension of the fact that the smaller things we find, the more smaller things we need to find. It's possible we could just reach a point of no capability to find that smaller thing, or that the smaller thing is no thing at all. It's not intuitive, but if I had to guess at what the foundation of all things is, it's nothing

[MadMojoMonkey]

But Muons are also fundamental particles (and electrons are not always completely stable)

Excellent catch, what a screw-up on my part.

... working on where I got that notion, and what the best description is...

EDIT: I had it in my head that a Muon was a Meson, or 2-quark structure. It was once called a Mu meson, but later found to be a lepton. So that's why I thought it was unstable... but even that much is a brain fart, apparently. It is true that Muons and Tauons are both fundamental particles and unstable.

They are called fundamental particles because when their structure is probed, it shows no internal pieces. It can still decay because QM is tricky as anything and so long as conservation laws are maintained, anything can change into anything else.

[MadMojoMonkey]

Well my original point was an extension of the fact that the smaller things we find, the more smaller things we need to find.

Yep. It goes both ways. The bigger things we find, the bigger things we need to find. This goes back to describing the outside of the universe from the inside. (That sentence presupposes an outside to the universe, of which there is no physical evidence.)

One of the troubles with the Standard Model as pertains to the laws of physics being 'the same everywhere in the universe' is that these laws were based on the assumption that the universe is 'essentially homogeneous from some scale'. There is data which suggests that this is not the case, though.

A 10 minute vid about the Largest Structure in the Universe, which explains this a bit better than I do.

It's possible we could just reach a point of no capability to find that smaller thing, or that the smaller thing is no thing at all.

This is exactly where particle physics is limited in some ways. In order to probe something very small, you need a particle with very high energy. The LHC at CERN does exactly that. It accelerates protons so they have incredible amounts of kinetic energy, then slam that proton into something... probing it.

I've heard, but I don't recall where, that a bigger particle accelerator that is a significant step above the one at CERN, would need to be the size of Pluto's orbit. So, even though it's theoretically possible, there may be practical limits to creating a controlled environment.

It's not intuitive, but if I had to guess at what the foundation of all things is, it's nothing

Write that paper, do the experiments and prove your hypothesis. Instant Nobel Prize in Physics!

[MadMojoMonkey]

This is so cool. I was just clicking links and found this one. I'd never heard of Prince Rupert's Drop before this, but it's a damn cool little structure.

It's created by dropping molten glass into cool water. It hardens into a tadpole form with a long twisting tail. You can hit the thick part of the glass with a hammer, and it wont break. However, if you even slightly nick the tail, it explodes.

Watch it explode @ 130,000 FPS.

Mystery of Prince Rupert's Drop at 130,000 fps

[jackvance]

Yeah, I decided to weight Wuf's 2nd sentence for my previous response. I don't think there's any reason a physicist should think that the Unified Field Theory, UFT, or Theory Of Everything, TOE, is an impractical goal. I do believe that these theories will be solved.

Also, there's no need to include 'essence' or 'ultimate sense' in physics at this point. Furthermore, I can't say there's no such thing as gods or magic, but so far, everything that was once explained by either divine intervention or magic has turned out to be better explained by something that is neither divine intervention nor magic. So I feel pretty confident that these ideas are not needed to explain the structure and development of the universe.

Still, science isn't interested in what is 'true'. I feel that is the greatest misunderstanding in the world as pertains to science. Science is interested in what's consistent, not what is true. It's a subtle, but important distinction.

A bit vague. We want theories to be quantitative (measurable) and have predictive value.

[abelardx]

Will we ever have tokamaks/cold fusion so we can move into space with our own energy sources? Like in the SF book Schismatrix by Bruce Sterling? Did you read that? I really want to move into space but of course we'll need energy.

[daviddem]

Cold fusion is most likely a load of bullsh*t.
http://en.wikipedia.org/wiki/Cold_fusion

What's much more exciting is that we are on the way to having energy efficient fusion reactors (meaning they can produce significantly more energy than they need to consume for their own functioning). These reactors can produce energy from water...
http://en.wikipedia.org/wiki/ITER

[jackvance]

Cold fusion apparently does work. An italian i forgot his name made a cold fusion reactor a few months ago and it was peer reviewed and ok'd from the scientific community. Someone at the university of a russian friend of mine bought one of his reactors ($30k it costs apparently) and my friend even went to check it out it seems to really work.

[a500lbgorilla]

Can you get pics of it from the Ruskie?

[Pascal]

Why does stuff still smell even like 3 days later (like curry on a plate)? Doesn't the smell disappear into the air? Where is the smell coming from

[abelardx]

Why does stuff still smell even like 3 days later (like curry on a plate)? Doesn't the smell disappear into the air? Where is the smell coming from

Smell is mollycules.

[MadMojoMonkey]

Will we ever have tokamaks/cold fusion so we can move into space with our own energy sources? Like in the SF book Schismatrix by Bruce Sterling?

As daviddem pointed out. There is every good reason to believe that what is called cold fusion in Sci-Fi books is based on fraudulent claims made in the late 1980's.

Did you read that?

I have not.

I really want to move into space but of course we'll need energy.

Energy in space is not a problem. The energy required to get there is the problem.

If there was a more efficient way to accelerate stuff through the Earth's atmosphere, and we could put a nuclear reactor in space, then we'd basically have as much power as we were willing to produce. The bonus is that nuclear waste is a lot safer when there's not a planet's gravity holding that waste close to humans.

If it weren't going to pollute the entire planet with radiological fallout, we could have build a space ship big enough to lift a city and truly engage in long-term space travel back in the 1960's. All you have to do is make a gigantic shock absorber/radiation shield and start setting of nuclear explosions behind it. It was called Project Orion.

[MadMojoMonkey]

Cold fusion apparently does work. An italian i forgot his name made a cold fusion reactor a few months ago and it was peer reviewed and ok'd from the scientific community. Someone at the university of a russian friend of mine bought one of his reactors ($30k it costs apparently) and my friend even went to check it out it seems to really work.

Links, please.

[Pelion]

This is so cool. I was just clicking links and found this one. I'd never heard of Prince Rupert's Drop before this, but it's a damn cool little structure.

It's created by dropping molten glass into cool water. It hardens into a tadpole form with a long twisting tail. You can hit the thick part of the glass with a hammer, and it wont break. However, if you even slightly nick the tail, it explodes.

Watch it explode @ 130,000 FPS.

Mystery of Prince Rupert's Drop at 130,000 fps

Thats pretty awesome. Never seen that before - and the explanation is pretty neat too.

[a500lbgorilla]

I'm pretty sure the thing keeping Project Orion from taking off was a treaty to not detonate nukes in space and not necessarily the logistics of detonating nukes in space.

edit: "Danger to human life was not a reason given for shelving the project – those included lack of mission requirement (no-one in the US Government could think of any reason to put thousands of tons of payload into orbit), the decision to focus on rockets (for the Moon mission) and, ultimately, the signing of the Partial Test Ban Treaty in 1963. The danger to electronic systems on the ground (from electromagnetic pulse) was not considered to be significant from the sub-kiloton blasts proposed since solid-state integrated circuits were not in general use at the time."

[MadMojoMonkey]

Why does stuff still smell even like 3 days later (like curry on a plate)? Doesn't the smell disappear into the air? Where is the smell coming from

The human sense of smell is sensitive to several parts per billion. Which means that only a few molecules of 'stink' per every billion molecules of air can be smelled by an average human's sense of smell. Microscopic particles can remain suspended in the air for a surprisingly long time. Dust from the Sahara makes its way to South America.

Even after you wash something, most anti-bacterial soaps /sanitizers claim to kill 99.99% of germs. So that leaves about 1 part per ten thousand... which is a over a thousand times more than necessary for the average person's nose to smell.


P.S. smell disappear

[chemist]

This is so cool. I was just clicking links and found this one. I'd never heard of Prince Rupert's Drop before this, but it's a damn cool little structure.

It's created by dropping molten glass into cool water. It hardens into a tadpole form with a long twisting tail. You can hit the thick part of the glass with a hammer, and it wont break. However, if you even slightly nick the tail, it explodes.

Watch it explode @ 130,000 FPS.

Mystery of Prince Rupert's Drop at 130,000 fps

That was cool, thanks for the link.
Shame King Charles and his friends didn't have high speed cameras, it is so much better in slow motion.

So why does it have the opposite effect on steel?
Dropping it in cold water and quenching it strengthens it and makes it less likely to shatter.