Is  problem still unresolved? I've heard from my electrodynamics class that solving the equation of motion with Abraham-Lorentz term causes either pre-acceleration or runaway solution. Have we found a way to obtain a solution that is neither pre-accelerating nor run away?
121403
Allow me to preface this by stating that I am a high school student interested in physics and self-studying using a variety of resources, both on- and off-line, primarily GSU's HyperPhysics website, Halliday &amp; Resnick's Fundamentals of Physics, Taylor's Classical Mechanics, and ultimately the Feynman lectures (mirrored by Caltech). Hopefully this gives somewhat of a feel of my level of physics understanding so as to avoid any answers that fly far above my head.  As I've understood from previous reading of electromagnetism (for example, in Halliday), a point charge is not affected by its own electromagnetic field. Unfortunately, as I recently read in the Feynman lecture on electromagnetism, :     For those purists who know more (the professors who happen to be reading this), we should add that when we say that () is a complete expression of the knowledge of electrodynamics, we are not being entirely accurate. There was a problem that was not quite solved at the end of the 19th century. When we try to calculate the field from all the charges including the charge itself that we want the field to act on, we get into trouble trying to find the distance, for example, of a charge from itself, and dividing something by that distance, which is zero. The problem of how to handle the part of this field which is generated by the very charge on which we want the field to act is not yet solved today. So we leave it there; we do not have a complete solution to that puzzle yet, and so we shall avoid the puzzle for as long as we can.   At first I figured I must've misunderstood, but upon rereading, it's clear Feynman states the that electromagnetic field due to a point charge does, in fact, influence said charge; I inferred this "self-force" must be somewhat negligible for Halliday to assert otherwise. What stood out to me was that Feynman states this problem had not yet been solved.  I suppose my first major question is simply, has this problem been solved yet? After a bit of research I came across the  which appears to refer exactly to this "problem of self-force". As the article states the formula is entirely in the domain of classical physics and a quick Google search indicates it was derived by Abraham and Lorentz in 1903-4, why is it that Feynman state the problem was still unsolved in 1963? Has it been solved in the classical case but not in QED?   Lastly, despite the Wikipedia article , is this problem of self-force present with other forces (e.g. gravity)? I believe it does state that standard renormalization methods fail in the case of GR and thus the problem is still present classically, though it does mention that non-classical theories of gravity purportedly solve the issue. Why is there not a similar Abraham-Lorentz-esque force possible in GR -- is there an underlying fundamental reason? Due to the relative weakness of gravity, can these self-force effects be ignored safely in practice?  I apologize for the long post size and appreciate any help I can receive. I only hope my post isn't too broad or vague!
37580
It's a question of a some time ago test, I've found a way to solve the problem using calculus, but always I've thought that exist a solution with algebra and geometry.  Thank you for your time.
36921
The other day, I was listening to  on the Lagrangian for a charged particle in an electromagnetic field, and at one point in the video, the lecturer mentions that we can add any total time derivative of a function $f(q, t)$ to the Lagrangian without altering its equations of motion.   This is nothing new to me, and I understand it fully, but shortly afterwards (approximately two minutes after the linked starting point), he goes on to say that you can, in fact, add a total time derivative of a function $f(q, \dot{q}, t)$, given certain conditions. This definitely surprised me, and I would love to know more about it, but the lecturer quickly moves on, so my question is as follows: under what conditions can one add the total time derivative of a function which depends on the particle's generalized velocities in addition to its generalized coordinates and time without affecting the particle's equations of motion?
113522
Please refer to my school textbook pg48 (of the book, and not the pdf counter) here:   My doubt is in this context: (right side column)  $a = dv/dt = v dv/dx$  then integrating $v$ with respect to $dv$, and $a$ with respect to $dx$.  Now, when we integrate $a$, either we say it is a constant, and give $a\times(x-x_o)$ as a result of the integration, or we say it is not constant, and is a function of time, in which case, it can not be integrated like this. But the book integrates it like this, and then it is written:     The advantage of this method is that it can be used for motion with non-uniform acceleration also.   Can you please explain how it can be used with non uniform acceleration while it has been assumed while integrating that $a$ is constant? And moreover, does this line seem to apply to only this derivation, or does it apply to other two before it as well?
31787
I've heard that special relativity makes the concept of magnetic fields irrelevant, replacing them with relativistic effects between charges moving in different velocity frames. Is this true? If so, how does this work?
13841
What was the improvement that Maxwell did to the  and why?  I understand that he combined the main equations so that you could get a wave equation for the vectors of $\bf E$ and $\bf B$ but is there anything else?
60483
Suppose an electron is created somehow in the universe -- through particle-pair production or what have you. Suppose it is stationary so that electrodynamics (and specifically propagating electromagnetic waves) is unavailable for explanation. Certainly distance charges will feel Coulomb's force, but how quickly?   I'm wondering if, since electromagnetism is manifestly relativistic (Lorentz rather than Galilean invariant) we can use that to always move to a frame where the electron is travelling and then claim that there are in fact EM waves? I don't know.
5422
What is the reason for the observation that across the board fields in physics are generally governed by second order (partial) differential equations?    If someone on the street would flat out ask me that question, then I'd probably mumble something about physicists wanting to be able to use the Lagrangian approach. And to allow a positive rotation and translation invariant energy term, which allows for local propagation, you need something like $-\phi\Delta\phi$.  I assume the answer goes in this direction, but I can't really justify why more complex terms in the Lagrangian are not allowed or why higher orders are a physical problem. Even if these require more initial data, I don't see the a priori problem.  Furthermore you could come up with quantities in the spirit of $F\wedge F$ and $F \wedge *F$ and okay yes... maybe any made up scalar just doesn't describe physics or misses valuable symmetries. On there other hand in the whole renormalization business, they seem to be allowed to use lots and lots of terms in their Lagrangians. And if I understand correctly, supersymmetry theory is basically a method of introducing new Lagrangian densities too.   Do we know the limit for making up these objects? What is the fundamental justification for order two?
103254
I was told that Lorentz' force is given by   $${\bf F}=  q{\bf v} \times {\bf B}.$$  But I have read that it is given by $${\bf F}=  \frac{q}{c}{\bf v} \times {\bf B}.$$  Why have these two relations different forms if they represent the same force? Thanks for any help!
6953
Could someone please provide an explanation for the origin of ? (Ideally someone who I have been speaking with on the h-bar)  Any advanced maths beyond basic calculus will most probably leave me at a loss, though I do not mind a challenge! Please assume little prior knowledge, as over the past few days I have discovered that much of my understanding surrounding the process as virtual particle pairs is completely wrong.
93624
How do you prove that the time for two objects traveling towards each other at relativistic velocities is still d/(v1+v2).  Answer seems to have something to do with velocity addition but I'm stumped...
32545
I know this may seem a weird question, but it always bothers me. My physics book (Resnick,Halliday,Walker), and also various sites never say anything beyond acceleration.   But when a moving body is being acted by a variable force , its acceleration will definitely change: it will either increase or decrease. Then there will be rate of change of acceleration with respect to time. So, why don't books mention this? What is the cause for not measuring $\frac{d\vec{a}}{dt}$ ? If it exists, what is the use of it?
68789
For example if the force on a particle is of the form $ \mathbf F = \mathbf F(\mathbf r, \dot{\mathbf r}, \ddot{\mathbf r}, \dddot{\mathbf r}) $, then the equation of motion would be a third order differential equation, what will require us to know the initial conditions $ \mathbf r(0), \dot{\mathbf r}(0), \ddot{\mathbf r}(0) $ in order to get the exact solution.  EDIT: As akhmeteliless mentioned the Abraham–Lorentz force is an example for such force. But, how such force is possible if the Lagrangian contains only the coordinates and their first time derivatives? Shoudn't the equations of motion be second order differential equations?
75625
I find differential equations in physics to be quite challenging so I'm looking for a book to help me master them.  I'm familiar with solving ordinary differential equations via seperation of variables but haven't really gone much further than that.  I was thinking about buying this:   However I'm open to recommendations on books that are specifically targeted to physics, or will help me in general to solve any differential equation.
44008
We consider in Lorentz spacetime, $(x^0,x^1,x^2,x^3)=(t,x,y,z)$, choose the unit of time such that $c=1$.   Given a four vector $A_\mu$, and let the Lagrangian  $$L(x^i,\dot x^i,t)=-m\sqrt{1-\dot x_i\dot x^i}+qA_0+qA_i\dot x^i,\tag{1}$$ where we use Einstein's convention for summation. (See  with electron charge $q=-e$.)    By the Euler-Lagrange equation $$\frac{d}{dt}\frac{\partial L}{\partial\dot x^i}-\frac{\partial L}{\partial x^i}=0\tag{2}$$ we can get three equations, and if we use the fact that  $$\frac{d}{d\tau}=\frac{1}{\sqrt{1-\dot x_i\dot x^i}}\frac{d}{dt}\tag{3}$$  then these equations are, for $i=1,2,3$ $$m\frac{d^2x^i}{d\tau^2}=q(\frac{\partial A_\mu}{\partial x^i}-\frac{\partial A_i}{\partial x^\mu})\frac{dx^\mu}{d\tau}\tag{4}$$  My question follows, can we obtain a fourth equation which is just letting $i=0$?   The  says that this fourth equation is from the property that the action is invariant under Lorentz transformation. But I think this is not very convincing. I tried to view the first three equations as two four vectors having three equation space components, but I do not think this fact can lead to the equality for the last time component.  References:   L. Susskind, .
89751
The usual Lorentz force expression I am familiar with is this:  $$\vec F=q(\vec E+\vec v \times \vec B)$$  I have seen some other versions lately that include an extra factor $1/c$:  $$\vec F=q\left(\vec E+ \frac{1}{c} \vec v \times \vec B\right)$$  What is this $c$ and how is it included? I guess other parameters in the expression are also different from the top expression for this to fit?  Example of a text snippet where I have run across this extra parameter:
55748
Does anybody know how to solve the following differntial equation?  $$w^2\cdot r+\frac{dw}{dt}\cdot r+\frac{dr}{dt}\cdot w=3g$$  where w and r are a function of time so $w(t)$ and $r(t)$. $g$ is a constant  EDIT: This equation came from a thought problem of mine which I will now explain since I still do not know how to approach the problem.  Basically I want to design a spiral track in which a vehicle will accelerate. However the total acceleration needs to be constant.   The vehicle will have 2 acceleration components, a radial component ($a_r$) and a change in speed component ($a_s$). Since we want constant acceleration: $a_r + a_s = constant$  From circular motion we know that $a_r = \omega ^2 r$ where $r$ is the radius, and $\omega$    Further we know that $v=\omega*r$, therefore: $a_s=\frac{d}{dt}(\omega r)$  For constant acceleration $a_{total} = a_r + a_s = \omega ^2 r + \frac{d}{dt}(\omega r) =constant$  Further usefull information: Length of the track covered at a certain time $l=v*t=\omega r t$  With all this the radius will be a function of time, $r(t)$ and the angular velocity will be a function of time, $\omega (t)$  Boundary conditions: $r(0)  = 0$ $\omega (0) = 0$  Now I would like to find a possible set of solutions to create a track by implementing end boundary conditions that i choose e.g. $v(t_{end})=100 [m/s]$ and $l(t_{end})=5000 [m]$  Here is a diagram for clarity: