If I am a stationary observer and the electrons are moving relative to me,then shouldn't its density increase according to special relativity and thereby create an altogether negative net charge.
Current in wire + moving charge next to wire creates magnetic force in the stationary reference frame OR electric force in the moving reference frame from special relativity due to change in charge density etc.... I think I understand this and I think it's super cool. Now here's the rub...  Current in wire + stationary charge next to wire creates no net charge. This is how nature behaves. I get it. My question is why can't I use the same special relativity logic as above, that is, current in wire cause electrons in wire to contract in accordance with special relativity so there has to be a net charge on the wire, which then acts on stationary charge next to wire.  I have been reading and reading and reading and I have come up with the following:  (1) When electrons in wire get accelerated to create current the distance between them actually expands in accordance with special relativity - something to do with bells spaceship paradox - which I am not going to pretend to understand  (2) This expansion from (1) above is exactly opposite and equal in magnitude to the contraction special relativity then causes and the expansion and contraction cancel out to keep the charge density in the wire constant and therefore no net charge on the wire  Here are my questions:  Is the explanation above correct? If so, please elaborate because i dont understand  If not correct, what is going on?  This is driving me absolutely nuts.
Why did the first Linux developers choose to implement a non-preemptive kernel? Is it to save synchronization?  As far as I know, Linux was developed in the early '90s, when PCs had a single processor. What advantage does a non-preemptive kernel give in such PCs? Why, however, the advantage is reduced by multi-core processors? Python "if X == Y and Z" syntax 1) How do I prove the following:   Let A = {6a + 4b ∈ Z : a, b ∈ Z} and B = {2a ∈ Z : a ∈ Z}. Show that A = B.  Thank you all for the help! How to force a table into page width? I have seen  and altough I face the same problem, the answer to that question is not helpful to my case.   I have large spreadsheets which are changed frequently. So, according to the solution accepted to that question, it is hard to duplicate all populated columns and it is cumbersome to edit one more cell everytime I wish to make a change on cells background colors.  Isn't there a way to sum data based on a condition regarding cell background color in Google Spreadsheets? How can the backtick character ` be included in code? I tried before to post a shell script that contained a ` character as an answer on Stack Overflow. The parser insisted on treating the backtick as formatting instead of part of code.  How can I include it? How to prove whether a matrix has rank $1$ If $u$ $∈ \mathbb R^{m \times 1}$ and $v ∈ \mathbb R^{n \times 1}$ how do you show that the $(m \times  n)$ matrix $uv^T$ has rank $1$? Would providing an example be sufficient to prove it? When a user is suspended, their account is reduced to 1 rep and all of his privileges are stripped. However, they can still join chat rooms.   This leads to various forms of possible abuse (all of which I've seen by suspended users):   Join/leave spams Expletives in profile messages Hold one sided conversations with users of the room via    Suspended users cannot be kicked, and even moderators can do very little (aside from completely removing the account, which is often overkill).  My proposal is to extend  for suspended users to one of two levels:   Prevent them from being shown in the user list at all. Strip their profile profile picture and description from the profile view visible from chat rooms (not from profile pages). Story where the main character learns to perceive time out of order from the aliens I read a story several years ago in which aliens come make first contact with Earth, and a bunch of scientists set to work trying to establish communication with them in various fields. The main character is a linguist and her team is working to try to figure out their written language, which doesn't have any sort of linear structure and can be read starting from any place.  It contains some explanation of quantum physics as an analogy for how they view time.  In the end, it turns out that the aliens don't perceive time in a linear fashion, and sort of see the future on equal terms with the past, etc. The main character learns to see time this way by studying their language, and the story is interspersed with her talking about what her child is going to do / is doing / has done.  I think I read it in a science fiction magazine but I'm not sure about this part. Why does Property Set throw StackOverflow exception? I know java and would normally put in getter/setter methods. I am interested in doing it in C# with the following code, but it throws a StackOverflow exception. What am I doing wrong?  Calling Code  c.firstName = "a";   Property Code    public String firstName; {     get     {         return firstName;     }     set     {         firstName = value;     } } Hartshorne Theorem 8.17 Importing shapefile into AutoCAD Map 3D? I'm trying to import shapefiles into a DWG using diferent layers names and during my web search I found this post. I know you did this 2 years ago but my problem is very similar and I wonder if you could help me.  Basically I've got a shapefiles of pipelines and I want to use the attribute name to sort the features into different CAD levels in teh same layer. I tried the import and although soem people say that "you can set the import to use data field" I can't see any option to do it and I'm really struggling. Any help appreciated.  I'm running on AutoCAD Map 3D 2010. How does 3-wire RTD or resistance measurement works in bridge of wheatstone? I cannot understand how 3-wire measurement will improve the resistance measurement.    They say that IF lead resistance \$ R_L \$ is the same, it will compensate. How can this happen?  If bridge is balanced (without \$ R_L \$):  \$ \frac {R_1}{R_2} = \frac {R_g}{R_3} \$  If \$ R_L \$ is added: \$ \frac {R1}{R2}= \frac {R_g+R_L}{R_3+R_L} \$  \$ \frac {R_g}{R_3} \$ is not same as \$ \frac {R_g+R_L}{R_3+R_L}\$; is this true only if \$ R_G=R_3 \$ in the beginning? So this means that \$R_L\$ does not get compensated? Dimensions of symmetric and skew-symmetric matrices As far as I can tell downvoting is mostly useless.     For questions the only people who get downvoted are lower rep users, or incredibly stupid questions    most questions that are downvoted get closed anyway which should be sufficient downvoting doesn't have too much affect on your rep anyway a negative comment is more useful and more of a push too change or delete the question  For answers downvoting is often used incorrectly as well   people commonly competitively downvote (downvoting another answer to a question that you also answered) obviously not a good behavior downvoting (and upvoting) are contagious, meaning one downvote leads to a bunch of others even though downvotes don't effect rep that much they create a negative environment, no one wants their post downvoted, on the other hand criticizing comments, I think, are far more welcome      So basically in a nutshell a downvote serves no real purpose even if a post deserves it. Flagging, closing and commenting are much more useful to everyone including the poster than downvoting so why have it.    I now see from the answers and comments that downvotes do serve a purpose and would like to retract my request. Can I use a higher rank tensor field as the metric field? What a metric should necessarily do is it should give me a way to associate a frame invariant number with a given pair of spacetime events. Now, if I use a higher rank tensor field (say, for example, a tensor field of rank 3: $g_{\mu \nu \rho}$) then also I can certainly produce a frame invariant scalar out of a given displacement $\vec{A}$ in this trivial way: $ I := g_{\mu \nu \rho} A^{\mu}A^{\nu}A^{\rho}$. Since the components of the higher rank tensor and that of the displacement vector are going to transform in a covariant and a contravariant manner respectively, the cooked up quantity is certainly a scalar.   Another crucial property, which I think has more direct physical content than the previous one, is that between two inertial frames, at least one such transformation should exist that leaves at least one metric invariant. i.e., There should exist at least one combination of transformation matrix $\displaystyle\frac{\partial{x^{\alpha}}}{\partial{x^{\mu '}}}$ and metric $g_{\alpha \beta \gamma}$ that satisfies the following equation:      $\displaystyle\frac{\partial{x^{\alpha}}}{\partial{x^{\mu '}}}\displaystyle\frac{\partial{x^{\beta}}}{\partial{x^{\nu '}}}\displaystyle\frac{\partial{x^{\gamma}}}{\partial{x^{\rho '}}} g_{\alpha \beta \gamma} - \delta_{\mu '}^{\alpha}\delta_{\nu '}^{\beta}\delta_{\rho '}^{\gamma} g_{\alpha \beta \gamma} =0$    The last thing I can think of that can put a restriction on the choice of a tensor as a metric is the existence of a possibility of finding a metric compatible symmetric connection field. Following the usual procedure of finding the expression for a metric compatible symmetric connection field, I reached following condition (unlike the case of the usual two rank metric where we get a full-fledged expression) for the connection in the terms of the metric:      $g_{\nu \rho k_1} \Gamma^{k_1}_{\mu \lambda} - g_{\lambda \mu k_2} \Gamma^{k_2}_{\rho \nu} = \displaystyle\frac{1}{2} (\partial_{\nu}g_{\rho \lambda \mu} + \partial_{\rho}g_{\lambda \mu \nu}  - \partial_{\lambda}g_{\mu \nu \rho}  - \partial_{\mu}g_{\nu \rho \lambda}) $   My question is that if it is possible to satisfy the two highlighted conditions then can we use such a 3 rank (or even higher rank tensors with similarly produced conditions) tensor fields as metric fields?   PS: This is NOT a proposal for a new home-production theory of gravity (or that of anything for that matter) but rather it is just that I am trying to understand why a two rank tensor is used in General Relativity as the metric. Thank you. Better yet, are there any Spacewalk-like software packages that work for both RedHat-based and Debian-based systems? I would like to count the number of unique selections from a column that contains multiple selections from a drop down list.  For example, column B3 contains,     Monday, Tuesday, Wednesday   The count function returns a value of 1 instead of 3 - is there any way to count the three days distinctly? Thank you!  Multiple selections from a drop down list was made possible using the VBA code from: In the sentence     What’s funny is Cat’s dry humour.   Wouldn’t it be better to put a comma after “funny”:     What’s funny, is Cat’s dry humour.   This question entails a (at the time of writing) heated discussion in the . Moved bin and other folders! How to get them back?