Lorentz Definition and 1000 Threads

Homework Statement Show that the Lorentz force law follows from the following variational principle: S=\frac{m}{2}\int\eta_{\mu\nu}u^\mu u^\nu ds-q\int A_\mu u^\mu ds Homework Equations Definition of Field Strength Tensor Integration by Parts Chain Rule & Product Rule for Derivatives The...

For starters, there is the covariant vector (E/c, p). Dividing by the scalar invariant, h_bar/2∏, where k is the propagation vector, there is (ω/c, k). There must be a significant number of covariant objects in electromagnetism...

x'=a_{11}x+a_{12}y+a_{13}z+a_{14}t y'=a_{21}x+a_{22}y+a_{23}z+a_{24}t z'=a_{31}x+a_{32}y+a_{33}z+a_{34}t t'=a_{41}x+a_{42}y+a_{43}z+a_{44}t \vec{u}=u\vec{e}_x Coefficients a_{nm}=a_{nm}(u) Why I suppose that coefficients are function only of velocity u? Inverse relations...

I did more than one course of classical electromagnetism in college. Recently, however, after reading "How Relativity Connects Electric and Magnetic Fields" (http://galileo.phys.virginia.edu/classes/252/rel_el_mag.html) I was astounded to realize how little I knew about it! In college (if I...

Anyone help. I know I must be doing this wrong somehow Lightning hits both a tree and a pole. The spacetime coordinates for each is (x=0, t=10us) for the tree and (x=30000m, t=10us) for the pole relative to the ground. Therefore they occur simultaneously relative to the ground. A rocket comes...

Blandford & Thorne, Applications of Classical Physics: Taylor & Wheeler, Spacetime Physics: These definitions seem to be based on the notion of a "physical" or "practical" infinitesimal: a quantity too small to be detected. But how can we measure the accuracy of an imaginary detector...

Does anybody have a reference or can write out the general (so not just a boost in only one direction) Lorentz matrix in terms of rapidities?

Hi guys, Before responding to my post, please note that I am only familiar with the mathematics of nonrelativistic quantum mechanics, and don't know any quantum field theory. All I have is this vague idea that quantum field theory is the union of special relativity and quantum mechanics...

1. Homework Statement : Consider a two dimensional Minkowski space (1 spatial, 1 time dimension). What is the condition on a transformation matrix \Lambda, such that the inner product is preserved? Solve this condition in terms of the rapidity. 2. Homework Equations : Rapidity Relations...

Hallo. A question about the relationship between the formulas found using the Lorentz transform and the invariance of the space time interval. Two events A and B occur at the same time and different space locations in system S, where A and B are at rest and at distance x. The system S'...

If we get on a train and time the train’s travel over 1000 meters, we can calculate the train’s velocity; v = dx/dt But if our watch is running slow, we will measure incorrectly and think the train was going faster than it really was. v’ = dx/dt’ We know that when something moves very...

1. Problem Horizontal rod of length x traveling along the positive y-direction at velocity u. Determine the orientation of the rod in frame S', which is moving at velocity v in positive x-direction. 2. Homework Equations Lorentz Transformation for length contraction, x' =...

Can anybody help me that how to work out the direction of Lorentz Force? Should I work out from the formula? Thanks.

we all know the lorentz group is of four disconnected components about the component connected to the unit element, is it coverable with single-parameter subgroups? put it in another way are all the elements in this component of the form exp(A)? i am studying relativistic quantum...

The notation below, is consistent with Wess and Bagger's https://www.amazon.com/dp/0691025304/?tag=pfamazon01-20. Given a Majorana spinor field in 4D, written in 2-component notation as \Psi(x) = \begin{pmatrix} \psi(x) \\\\ \bar\psi(x) \end{pmatrix} , \quad (\psi_\alpha)^* =...

Homework Statement Hi everyone, in Peskin & Schroeder, P36, the derivative part of KG field is transformed as eqn (3.3). But why does the partial derivative itself not transform? Homework Equations \partial_{\mu} \phi (x) \rightarrow \partial_{\mu} ( \phi ( \Lambda^{-1} x) ) = (...

I am interested in how the Lorentz maths were derived from the Maxwell electrodynamic and field equations. But not in a struct mathemetical sense as the math is outside my range but on a simpler conceptual level. For eg. contraction seems to have relevance wrt electron electrostatic fields and...

Homework Statement I need to demonstrate the relation [\varphi(x),M^{\mu\nu}]=\matchal{L}^{\mu\nu}\varphi(x) where \mathcal{L}^{\mu\nu}\equiv \frac{\hbar}{i}(x^\mu\partial^\nu-x^\nu\partial^\mu). Homework Equations U(\Lambda)^{-1}\varphi(x)U(\Lambda) = \varphi(\Lambda^{-1}x) \Lambda =...

I am reading the definition in wiki ( nothing better at the moment) http://en.wikipedia.org/wiki/Lorentz_space It seems too vague for me, namely what they call "rearrangement function" f^{*}: f^{*}: [0, \infty) \rightarrow [0, \infty]; \\ f^{*}(t) = \inf\{\alpha \in \mathbb{R}^{+}...

There's something about the lorentz transformations which is somewhat confusing to me, and that is how to treat the "x" coordinate. Supposing I have some spaceship which is moving from Earth to some other planet located at a distance "D" (from earth) with a velocity v. Now, the spacetime...

Homework Statement The system S' moves in relation to the system S with velocity \upsilon along the -x- axis. At the time when the beginnings of the coordinate system are in the same point, clocks in both system shows t=t'=0. Which coordinates will have a reference point during the motion in...

The action for a fermion in curved spacetime is S = -\int d^4 x \sqrt{- \det(\eta^{ab} e_{a\mu}e_{b\nu})} \left[ i\overline{\psi} e^\mu_a \gamma^a D_\mu \psi + i m \overline{\psi}\psi \right] where g_{\mu\nu} = \eta^{ab} e_{a\mu} e_{b\nu} and the derivative operator acting on fermions is...

i am reading Lillian R. Lieber's book on the einstein theory of relativity and i am a bit confused on page 65. she wants to take the equations: x=x'cosθ - y'sinθ y=x'sinθ + y'cosθ and compare them to: x'=β(x-vt) t'=β(t-vx/c2) she takes c as one so: x'=β(x-vt) t'=β(t-vx) she...

I've spent a large portion of my day trying to figure this out and I figured my best answer is likely to come from here. Forgive me if I'm wildly wrong about anything, I'm somewhat basic with physics, largely due to the fact that I'm 15 and my maths is limited to a GCSE level. My dilemma is...

I've had my second class of Modern Physics and I have some "obvious" doubts that many of you certainly had, although I didn't find anything answering the first doubt on a quick google search. 1)Say I am in an inertial reference frame. I can see that any photon going around me do it at a...

Hi. My question is how the Lorentz magnetic force F=q\vec{v}\times\vec{B} is derived? Is it due to magnetic moment of charged particles? If the moving charged particle does not have magnetic moment (due to spin, so the torque on the particle is zero) how the magnetic force changes its direction...

This is related to the thread on the meaning of diffeomorphism invariance but is adressing a distinct point (at least I think so, but I may be proven wrong). As Rovelli discusses in his book, the action of the Standard Model coupled to gravity has three types of invariance: under the gauge...

In Einstein's book Relativity he provides a derivation of the LT. link here http://www.bartleby.com/173/a1.html" In step 3 he brings in constants λ and μ and now I am lost. In the equation (x'-ct') = λ(x-ct) - isn't this the same as "zero = anything X zero"? How did λ and μ get...

I am trying to establish whether the force defined by the Lorentz equation below is invariant under the Lorentz transforms: [1] F = F_E + F_B = qE + qvB In the context of this equation, [q] is moving with velocity [v] such that it is acted on by both an electric E-force and magnetic...

I am wondering about the order of operations concerning the Lorentz transformation of fields and the superposition of fields. I was given a problem: Two positively charged electrons start at the origin and then travel along the x-axis at a constant speed v in opposite directions. Calculate...

Hello, as far as I know a "fractal", by definition should manifest self-similarity or at least statistical self-similarity. This usually takes the form of scale invariance. Can anyone point out where is the self-similarity in the plots of Lorentz attractors? Thanks.

Iv just been reading a physics textbook and i feel iv completely missed something. It may help to draw a diagram and to read the thread slowly. Sorry if it is a little thick. My understanding of Special Relativity is that it allows two seemingly conflicting principles to co-exist, these being...

Homework Statement A spaceship of proper length Lp = 400 m moves past a transmitting station at a speed of v = 0.76c. At the instant that the nose of the spaceship passes the transmitter, clocks at the transmitter and in the nose of the spaceship are synchronized to t = t' = 0. The instant...

In special relativity, velocity dependent forces transform. Let us then consider frictional forces, such as drag, which are velocity dependent in the first order. Do two observers moving relative to a third body measure different frictional effects?

I'm studying General Relativity and facing several problems. We know that energy-momentum must be Lorentz invariant in locally inertial coordinates. I am not sure I understand this point clearly. What is the physics behind?

In electrodynamics, the Coulomb gauge is specified by \nabla \cdot A=0 , i.e., the 3-divergence of the 3-vector potential is zero. This condition is not Lorentz invariant, so my first question is how can something that is not Lorentz invariant be allowed in the laws of physics? My second...

My question is: why does Lorentz contraction happens? I have a understanding of this but I don't know if it's correct, so I'll tell what I understand, if I'm wrong please correct me... Suppose we have two observers A and B. If I say B is moving with respect to A then time is slower to B...

Homework Statement Q1 http://www.maths.ox.ac.uk/system/files/private/active/0/b07.2_c7.2.pdf Homework Equations The Attempt at a Solution How do I do the final bit that lead to the discrepancy and why does this occur? I have no idea where to begin.

Homework Statement Muons, which have a half-life of 2 x 10-6 s, are formed in the Earth's atmosphere at an altitude of 10 km. If they travel normal to the Earth's surface, and one half of them reach it before they decay, what is their velocity? Homework Equations Lorentz...

Einstein is commonly regarded as the primary inventor of special relativity. I'd like to trust the collective wisdom of others, but I never feel fully convinced. The argument is typically "Though people like Lorentz and Poincare have worked out most of the math it's only Einstein who realized...

If an observer O' see a body that moves with constant velocity Ux along the axis x' in a positive direction. What is the velocity VxO of body observed by O? That is all the information I have. Can you help? :blushing:

I'm having a bit of trouble understanding what exactly the lorentz force is. In this diagram here [PLAIN]http://img7.imageshack.us/img7/7065/helicinbfld.jpg I know its the force that's keeping the proton in that helicoidal trajectory so I can see its perpendicular to the direction of the...

Homework Statement Consider a particle of mass m that carries a charge q. Suppose that the particle is under the influence of both an electric field E and a magnetic field B so that the particle's trajectory is described by the path x(t) for a\leqt\leqb. Then the total force acting on the...

I was thinking that if i have for example a boost in the direction of x, then the boost should be equivalent to an hyperbolic rotation of the y and z axes in the other direction. I don't know if it's true or not. Then I want to know if somebody knows this result or why is false? I was...

Using the Lorentz transformation, at what speed relative to speed of light c must you travel so that your length along the direction of motion is seen to decrease by a factor of 2? For this speed, hwo much would your mass be increased? Please show steps, I'm confused with this question!

From this link http://en.wikipedia.org/wiki/Introduction_to_special_relativity" In the section entitled "Invariance of Length: The Euclidean Picture" the article discusses how rotations within an n-dimensional space keep length invariant. However, if you rotate and object into a higher, n+1...

I'm studying for my modern physics final and this problem is giving me trouble; Q: In a frame S, two events have spatial separation deltaX= 600m, delta y and delta z = 0, and a temporal separation deltaT= 1micro second. A second frame S' is moving along the same axis with nonzero speed v...

Homework Statement Question is E=(x,y,z) B=(x,y,z) v=(x,y,z) (in vector form) For all E,B,v find v(t) and r(t) v and r of course have their vector arrows. Homework Equations F=ma= qE + qv x B There is a hint to take second derivatives across and some terms will clear up. I was thinking more...

As I understand it, Lorentz Contraction states an object "contracts" relative to it's velocity to an observer. So at a high velocity of speed, the meter stick (carried by the object moving relative to the observer) appears to contract (to the observer) and the observer measures less distance...

Let L_w be a Lorentz transformation between to systems that coincide at t=0(paralell axes assumed) and with relative velocity w along x_1. If L_u is the Lorentz transformation when the relative velocity u is in any direcction then we have that L_u=R_2 L_w R_1 where R_2 and R_1 are sapce...