My understanding of electrons is that they have no volume, eg they are point particles. If this is true, how can a point spin?
I often hear about subatomic particles having a property called "spin" but also that it doesn't actually relate to spinning about an axis like you would think. Which particles have spin? What does spin mean if not an actual spinning motion?
While studying I read about the principle of underdetermination of scientific theories. I made some researches online but I am more confused than before. I read about the Quine-Duhem holistic thesis, but I do not know if is the same as underdetermination. Using MAX in SQL Expression of ArcMap ModelBuilder If $X$ is compact and $T:X \to Y$ continuous and bijective, show that $T$ is homeomorphism. Let $X$ and $Y$ be metric spaces, $X$ compact, and $T:X \to Y$ bijective and continuous. Show that $T$ is a homeomorphism.   My attempt:  We need only show that $T^{-1}$ is continuous.  Let $M \subset Y$ be closed. Then, from the surjectiveness of $T$, there exists a $A \subset X$ such that $T(A)=M$. Since $M$ is closed, by the continuity of $T$, we must have that $A$ is closed.  Now $$T^{-1}(T(A))=T^{-1}(M)$$ i.e, $A=T^{-1}(M)$. Since $A$ and $M$ are closed, we must have that $T^{-1}$ is continuous.  My problem with this, however, is that I am not using the fact that $X$ is compact anywhere in the proof. Is there perhaps another way that I can show this, using the compactness of $X$?   Any hints will be appreciated. Adjective for someone who exaggerates emotions to get sympathy What's the word for someone who tries to get sympathy from others by exaggerating their emotions or constantly reminding them of something tragic that happened to them?  I'm looking for an adjective - no disorders or health related definitions please. I have heard rumors that you can compile documents online, and more specifically that Google has a free online compiler, but I have never been able to find any. Is there a way to compile documents online, so that I can write and compile documents even if I don't have a TeX distribution installed on my computer? How long do seasons last? In the Kittens Game, how long (in real life minutes) do seasons last? The sequence of triangular numbers is well known. Consider now the triangular numbers modulo some positive natural number $k$. That is, let $T_{n,k}$ be the remainder of dividing $T_n$ by $k$. For the regular sequence of triangular numbers, we can take as convention $T_n = T_{n, \infty}$.  Question: For all values of $k, i &lt; k$, does there exists some $n$ such that $T_{n, k} = i$ If an elephant can apply 250N force and a rabbit can apply 25N force , and if they are pulling each other , then elephant will pull with 250N force and according to newtons third law the rabbit should also pull the elephant with 250N force.then from where do the rabbit got the extra 225N i.e.(250-25=225) force??? can anyone please explain. What is the difference between convolutional neural networks and deep learning? So, Can linking verbs be used with "continuous tenses"? How do you use script variables in psql? In MS SQL Server, I create my scripts to use customizable variables:  DECLARE @somevariable int   SELECT @somevariable = -1  INSERT INTO foo VALUES ( @somevariable )   I'll then change the value of @somevariable at runtime, depending on the value that I want in the particular situation. Since it's at the top of the script it's easy to see and remember.  How do I do the same with the PostgreSQL client psql? An unfair three-sided die. An unfair three-sided die. Side $1$ will be rolled with probability $p_1$ , Side $2$ with probability $p_ 2$ and Side $3$ with probability $p_ 3$ . Find a formula for the probability that the $8^{th}$ $3$ will be rolled on the $10^{th}$ roll.  Attempt:  First 9 rolls there are 7 three's.  $$[\binom{9}{7}(p_3)^7(p_1+p_2)^2]\cdot p_3$$ $$=[84\cdot(p_3)^7(p_1+p_2)^2]\cdot p_3$$  any thoughts of this solution? I have a atmega8 that is working with 3.6V dc, I need to control some 12V relays with a not chip (7404), what is the simplest way to do this? I have connected a 12V dc to the relays, so when I connect the relays to the chip and then the atmega8, the current returns to the atmega through the not chip. Is this solution correct? There a better way to do this? For wall-sized graphics and large banners (e.g. 3m × 5m), what is an acceptable PPI for print? As I understand it 300 ppi is the typical for 'small' artworks (esp. for clean text resolution). However, for small artworks, the audience usually engages at a much closer distance. Therefore, in the interests of keeping a bitmap file down to a reasonable size, can you get away with a much-reduced PPI for a large format/banner print? Please provide me with the guidance to install oracle 11gr2 on Ubuntu 14.04. How much weigh can a torque carry? I have a servo motor with a torque of 10kgcm. My question is how much weight can it carry? I really don't understand "kgcm." Is there a way to calculate how much weight can a motor carry? Sort and count number of occurrence of lines What to do when someone other than the author changes a question to fix a substantive problem with the code See . Someone other than the OP changed the code to address a substantial problem with the it that was addressed as part of my answer. The problem was admittedly peripheral to the core question, but it was a primary differentiator between my answer and another answer submitted at the same time.  Any suggestions on what to do in this situation? Leave it be? Edit it back? Something else?  Update: I just found , from the "Related Links" section on the right, which is pretty relevant. I have to keep remembering to check there rather than just searching for answers. Texture messes up after extruding a modified plane What are recommended, general strategies to start block-cipher design and/or analysis?