Browsed the web for a bit and was unable to find much information on this topic.
I am slightly confused as to how so many ducks can exist with such similar ways of life. Gadwall, mallard, teal species, pintails, etc. Greater & lesser scaups, ringnecks, redheads, canvasbacks, buffleheads, etc. Different scoter and eider species. What are the differences in the niches that these ducks occupy? They all seem to fall into the categories of dabblers, divers, and sea ducks. How is there so much speciation in each category and how do they not outcompete other similar species?
I understand how different warblers and kinglets, that are otherwise very similar, forage in different parts of the tree all at once, and have observed it. But I've seen several dabblers and several divers all in the same place, seemingly eating the same food. Maybe I am at a loss because when ducks feed it is typically out of sight (underwater), and thus outside the realm of observation?
For those not clear, the competitive exclusion principle, also known as Gause's law of competitive exclusion or simply "Gause's law", states that two or more species competing for the exact same resources cannot coexist under the same conditions if all/other ecological factors remain constant. This is because if one species has even a slight edge, then it will muscle out the other species/species in the area. Obviously, there has to be a way around this, because we see environments with many species competing for the same resources all the time. One way around this is through "Niche Partitioning". To give an example of this, cottonwood trees can be grown in a fairly wide variety of areas. I have one growing in my yard. In nature however, you just about only see them along rivers. This is because the habitat it grows best in is along rivers. When it is growing near water, it is able to outcompete other species trying to grow in the same habitat. However, it is not as strong of a competitor away from rivers, so it is out competed by other species.
The problem for me is, I can't see how this explains what is happening when trees are occupying virtually the same environment. For example, in the mountains where I live, I can go hiking and see two species of tree, Box Elder and Cottonwood growing along rivers next to each other. How is one not out competing the other? Another example in the mountains where I live, I can see two trees, Engelmann Spruce and Alpine Fir growing next to each other in the same forest, with the same aspect, with (what appears to be at least) the same level of access to water and soil type/quality. And what about in the Amazon rainforest where in a few hectares you can find a few hundred species of tree? I want to know what environmental factors could the species I have mentioned be taking advantage of to avoid direct competition? I understand that predator mediated competition could explain part of this, but it doesn't seem like an entirely adequate explanation. I am an aspiring ecologist and have been thinking about this for a little while. Any help answering this question would be nice.
Edit: Thanks everyone who has answered so far. If anyone else has any extra input, the mountains I am referring to is the Wasatch range in Utah.
Let's say I observe a photon. How would I know that's not, for instance, ten photons in the same state? Once two particles are in the same state, is there some mechanism by which they can diverge?
Is it verifiable by experiments or is it a way to explain what happens given no other explaination is present, this isn't meant is a rude way. I genuinely don't understand
https://en.m.wikipedia.org/wiki/Exchange_interaction
One of my teachers asked the question and I wanna know how it is related in the atomic level. Answers are much appreciated.
I did some googling, and soon realized that i cannot find a decent explanation for light refraction. So what interaction between light and matter causes this behavior? (Given bosons dont obey the pauli exclusion principle, which was my first intuition before i quickly realized this fact and was dumbstruck that i couldnt explain to myself such a rudimentary phenomena)
Hello
The problem is in the picture below.
Any sort of help is very much appreciated :D
Thank you in advance!
https://preview.redd.it/xgcvx7xbex081.png?width=942&format=png&auto=webp&s=ac73f720d4549c7fef687f7349b4f9c448115af8
I was studying quantum statistical mechanics when my professor talked about many-particle systems, making us see (in a not too detailed way) what the Pauli exclusion principle consists of. As far as I understand the fact is the following: no 2 fermions can occupy the same eigenstate of the Hamiltonian that describes them, so for example if we consider a helium atom and suppose we do not know that spin exists then we would expect to find one electron per energy level, however there is spin and, since the spin state of the electron lives in C^2, we can expect at most 2 electrons per energy level with antiparallel spin. However if we consider 2 helium atoms, it is possible to find all 4 electrons in the same energy level and therefore the same spin in pairs ... why don't they occupy the same state? Why does the Pauli principle not apply? Obviously I'm the one who doesn't understand something, but what?
Probably stupid sorry.
Here is a mythological PDF document that floats around the internet, and discusses competitive 1500m training over 74 pages. It's an interesting read, and covers training principles for middle distance running, so is still relevant to those who don't race over 1500m.
Who is Joe Rubio?
Former two-time US Olympic Marathons trial qualifier (1992, 1996), and has been a coach at the HOKA ONE ONE Aggies Running Club since 1999. Founded Running Warehouse (I never understood why runningwarehouse.com hosted the PDF document... now I do).
Further reading about Joe: 2008 Interview with Rubio
Target audience:
The manual is intended for the "competitive post collegiate middle distance runner, who has recently completed their college eligibility". Rubio further qualifies that the runner in question should be experienced (4-8 years of racing and training at a competitive level), and that it is not for beginners.
As such, the macrocycles of the program are based around the college/professional racing season (winter, cross country, racing season), but also keeps in mind a multi-year timeline for improvement.
The mileage of the program generally targets 65-70 mi for females, 75-80 mi for males.
Training overview:
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Training initially focuses on developing aerobic capacity (VO2max), and develops it to highest level possible for season (4-6 months, with 5k and 10k pace workouts); then anaerobic condition through tempo runs (at HM pace) and long runs faster than recovery pace (slightly slower than marathon race pace 70-75% of VO2max).
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Rubio explains that the effect leads to the runner attaining "the fitness of a competitive 5k runner", before then periodising the final 8-12 weeks for racing through anaerobic capacity work (intervals at 400m, 800m, and 1500m paces). Rubio states any significant gains from such speed work only stem from the aerobic distance development that precedes it.
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The role of leg speed in the 1500m is also emphasised by Rubio. Effectively, to run fast in the 1500m, a runner must be able to have the functional leg speed to match. Regular speed enhancement workouts across the year also serve to improve efficiency. These vary from near all out sprint bursts of 5 seconds, to 5-10 se
So, I've always been fascinated by quantum physics and just recently started looking into it to try to understand and learn about it, but I'm a little confused about this principle.
To my understanding of the Pauli Exclusion Principle, it states that no two fermions can exist in the same space at the same time (the structure of a proton/neutron) so it was discovered that quarks have spin, +/-1/2. So there could be a +1/2 x, -1/2 x, +/- 1/2 y and make a proton or neutron. It was later discovered that there are particles comprised of 3 of the same quark (i.e., omega minus particle). So it was then concluded that quarks also have colors, meaning that in the cases of the uuu, ddd, sss particles, these could exist without contradicting the Pauli Exclusion Principle. My question is, how did they discover that these quarks have charges and colors? Could the answer not just be that the Pauli Exclusion Principle isn't true and 3 of the same exact quarks can coexist?
Obviously, there are very smart people who come up with these theories/concepts, so I don't believe that I discovered some loophole, I'm just trying to fully understand this.
Okay. So i have a VERY rudimentary understanding of this. From what I understand, swapping the position of two fermions will reverse the sign of the wavefunction, but swapping the position of two bosons won't. The consequence of this is that the probability of two fermions having the exact same quantum state is zero (i.e. the exclusion principle). Because that doesn't happen for bosons, things like photons for example CAN occupy the same quantum state as each other.
But then I've heard people say things like some isotopes of helium are bosons.
How does that make sense?? Helium clearly obeys the exclusion principle.
I've obviously misunderstood something here somewhere.
You've cast the dye Russell.....once there has been a turd in the punch bowl, it's not easy getting the stench out of it.
Im gonna be honest, I'm not the smartest. Just a young high schooler that is curious with the world of science. A VERY long train of thought led me to fermions and bosons and now I ask this question which much curiosity. If I said something wrong or phrased something wrong please correct me. Thank you in advance!
Recently I took up self-studying probability using Sheldon Ross' A First Course in Probability when I came across some questions that got my friends confused and I didn't know how to explain the concept properly. Namely, when do we use the inclusion-exclusion principle instead of calculating the probability directly. Here is the example that started this question:
https://preview.redd.it/2xbot93xsob61.png?width=1252&format=png&auto=webp&s=8eeb764d5ef396c7810e9743d127501cf773deba
My friend's first instinct was to simply multiply the probabilities that no person gets their hat, something like for person 1: (n-1)/n, for person 2: (n-2)/(n-1), which when all multiplied together:
(n-1)/n * (n-2)/(n-1) * ... * 2/3 * 1/2 = 1/n
However the book offers an alternate solution that when compared for say, n=5, does not yield the same result:
https://preview.redd.it/rl8hatuktob61.png?width=1254&format=png&auto=webp&s=b7a4aecf13fd54f40499a38310c9fb740183bd47
https://preview.redd.it/cp7zvwsktob61.png?width=1257&format=png&auto=webp&s=d376d57f23a51a4029bd03cbceceb8e2f2824000
https://preview.redd.it/w1lsfpsktob61.png?width=1216&format=png&auto=webp&s=bf0fc882640482e5660e05852cfeeae1dd360781
So then my question is, although I understand the intuition and it makes sense, I have no good reason to say why my friend's approach shouldn't be able to work either. Is there a rule of thumb we can adhere to to understand when to use one approach vs the other?
Paraphrasing Caroll my own understanding was based on his lecture that it deals with how protons and neutrons and many other particles are either up,up,down or up,down,down right? It deals with this right? I could have googled an answer, but I would rather have someone versed in this break it down!
In the derivations I've seen, Pauli's principle is -in principle - independent of the distance between the particles. And I can't wrap my head around why this doesn't seem to be the case in real life situations
In the Holographic Universe conjecture, the information content of the universe has a upper cap which is given by the surface area of our cosmological horizon. Can it be that the Pauli exclusion principle is fundamentally an “Information” problem as in having two fermions in the same quantum states will require more information to be embedded in the surface of the horizon than it is possible?
Does Pauli exclusion principle apply for molecules too?
