Lorentz Definition and 1000 Threads

In the representation theory of Lorentz transformations, the words Clifford algebra and Dirac algebra are used interchangeably. However, there is a distinction between the two. Indeed, the Dirac algebra is the particular Clifford algebra ##Cl_{4}({\bf{C}})\equiv Cl_{1,3}({\bf{C}})## with a basis...

Homework Statement For a plane, monochromatic wave, define the width of a wavefront to be the distance between two points on a given wavefront at a given instant in time in some reference frame. Show that this width is the same in all frames using 4-vectors and in-variants. Homework...

Homework Statement Hi everybody! I am struggling with an old exam problem, could someone maybe help me out to figure it out? Here is how it goes: A rod with resistance ##R = 0.1 \Omega## lays over two parallel tracks (resistance ##\approx 0 \Omega##, ##l=10##cm). A battery is connected...

Hi, I have trouble understanding why the following relations hold true. Given the Minkowski metric \eta_{\alpha\beta}=diag(1,-1,-1,-1) and the line segment ds^2 = dx^2+dy^2+dz^2, then how can i see that this line segment is equal to ds^2 = \eta_{\alpha\beta}dx^\alpha dx^\beta . Further, we...

Homework Statement For an event occurring at (x,t), consider the quantity I = x^2 - (ct)^2 Find a simple expression for this in the S' frame: I' = x'^2 - (ct')^2 How are I and I' related, and why is this noteworthy? The Attempt at a Solution So the question is under "Lorentz Transformation"...

Homework Statement Show that the Lorentz Force Law, \frac{dp^{\nu}}{d \tau} = -q U_{\mu} F^{\mu \nu}, is consistent with P^\mu P_\mu= -m^2. Here U is the 4-velocity, F is the Electromagnetic Tensor, and p is the 4-momentum. (Minkowski Space) Homework Equations As stated above. The Attempt at...

I have some confusion about the Lorentz force. First of all, I found that there are two equations for the Lorentz force: one of them is F = qE + qv × B , and the other one is just F = qv × B . What's the difference between them and how do you know which one to use? My other question is: Is the...

Homework Statement [/B] A spaceship is approaching Earth from the far side of the sun. The Earth and sun are 8 light minutes apart and the ship is traveling at .8c. Two events are indisputable. 1) the ship is at the sun 2) the ship is at the earth. Assume that the Earth and sun are at rest...

I'm trying to understand special relativity well enough to explain it to others, ANY others, including myself. I am trying to use Robert Resnick's Introduction to Special Relativity to inform my thinking. In introducing length contraction, he introduces L' as the length measured by an observer...

Generally we use the left hand rule - (if index finger shows velocity, middle finger shows magnetic field, the thumb points towards force). Recently I also came across a left hand rule for lorentz force- Using your right-hand: point your index finger in the direction of the charge's velocity, v...

Homework Statement A rocket is traveling toward a galaxy with speed v. a) If NASA says that distance from Earth to the galaxy is d, what is the distance d' from Earth to the galaxy according to the astronauts? b) The astronauts experience a travel time to the galaxy t' and NASA records the...

Homework Statement I'm asked to prove that Et - p⋅r = E't' - p'⋅r' Homework Equations t = γ (t' + ux') x = γ (x' + ut') y = y' z = z' E = γ (E' + up'x) px = γ (p'x + uE') py = p'y pz = p'z The Attempt at a Solution Im still trying to figure out 4 vectors. I get close to the solution but I...

Homework Statement Synchronized clocks A and B are at rest in our frame of reference a distance 2 light minutes apart. Clock C passes A at a speed of c*4/5 bound for B, when both A and C read t =0 in our frame. a) What time does C read when it reaches B? b) How far apart are A and B in C's...

Homework Statement Perform a Taylor Series expansion for γ in powers of β^2, keeping only the third terms (ie. powers up to β^4). We are assuming at β < 1. Homework Equations γ = (1-β^2)^(-1/2) The Attempt at a Solution I have no background in math so I do not know how to do Taylor expansion...

Homework Statement Suppose given an electric field \vec{E} and a magnetic field \vec{B} in some inertial frame. Determine the conditions under which there exists a Lorentz transformation to another inertial frame in which \vec{E} || \vec{B} Homework Equations If we give a Lorentz boost along...

<Moderator note: moved from technical forums, so no template> Problem: Two trains (A and B) are moving along parallel tracks at different speeds. A person sitting on train A looks out the window and sees two things happen: a firecracker explodes right outside his window, and, exactly 1.0...

While Minkowski space and Euclidean space both have identically zero curvature tensors it seems that a flat Lorentz manifold in general, may not admit a flat Riemannian metric. Such a manifold is the quotient of Minkowski space by the action of a properly discontinuous group of Lorentz...

Hello everyone, There is something that has been bugging me for a long time about the meaning of Lorentz Transformations when looked at in the context of tensor analysis. I will try to be as clear as possible while at the same time remaining faithful to the train of thought that brought me...

Hi. This question most probably shows my lack of understanding on the topic: why are scalar fields Lorentz invariant? Imagine a field T(x) [x is a vector; I just don't know how to write it, sorry] that tells us the temperature in each point of a room. We make a rotation in the room and now...

Hi. First, excuse my English. In my lecture notes on classical electrodynamics, we are introduced to the Lorentz transformations: a system S' moves relative to a system S with positive veloticy v in the x-axis (meassured in S), spatial axis are parallel, origin of times t and t' coincide...

Here is a quote from this website: My question is: is this derivation of length contraction considered to be sound and correct today? Are they treated in modern textbooks?

So I am constructing an analogy between the self replicating fracturing effect on thin films and the path of a charged particle. (Qualitatively, several cracks have similar shapes to charged particle motion) I won't go into the details of the fracture mechanics, so I will only use E+M...

1. Two long trains pass each other head on with a relative speed of 0.97c. Bob, the driver of the first train notices that it takes 5.8 secs to pass the entire second train. How long do people on the second train say it takes for Bob to go by their train? 2. t = t0/(1-v2/c2)1/23. I understand...

In a standard problem of an electron released from the negative plate in an E field between 2 parallel plates in which the velocity must be determined why can the Lorentz transformation be used (involving v^2/c^2) when the electron is undergoing acceleration and there is nothing in the...

As I understand it, since space-time is modeled as a four dimensional manifold it is natural to consider 4 vectors to describe physical quantities that have a direction associated with them, since we require that physics should be independent of inertial frame and so we should describe it in...

I'm trying to understand the relativistically spinning disk within the framework of SR (if that is even possible). I thought to first simplify the problem by considering a spinning ring/annulus, but I don't know if my analysis is correct. I imagined a spinning ring of radius R, spinning at an...

Ok so... It's been a while since I first saw this problematic scenario and I want to know how to deal with it. The question arises in the context of special relativity. Suppose 2 objects moving at the same speed. The floor is the rest frame 'A' and the front object is the moving frame 'B'. The...

Does the lorentz fitzgerald contraction hypothesis contradicts the classical motion of rigid body? I am not sure but i think it doesn't contradicts the classical motion of rigid body.

Hi. I read that the Lorentz invariance Minkowski norm of the four-momentum $$E^2-c^2\cdot \mathbf{p}^2=m^2\cdot c^4$$ has no analogue in Newtonian physics. But what about $$E-\frac{\mathbf{p}^2}{2m}=0\quad ?$$ It might look trivial by the definition of kinetic energy, but it's still a relation...

Someone posted this link to a paper I really appreciated. http://www.hindawi.com/journals/physri/2015/895134/ But doesn’t the author have the wrong sign on the relative velocity in his Lorentz Transform associated with his figure 2b? And if so, doesn’t that reverse his conclusion that “leading...

Homework Statement A relativistic proton is traveling next to a stream of negatively charged particles that are traveling at the same velocity as the proton. I'm to find the force on the proton by transforming the field from the negative stream to a stationary lab frame. Homework Equations f=...

Homework Statement Show that an infinitesimal boost by v^j along the x^j-axis is given by the Lorentz transformation \Lambda^{\mu}_{\nu} = \begin{pmatrix} 1 & v^1 & v^2 & v^3\\ v^1 & 1 & 0 & 0\\ v^2 & 0 & 1 & 0\\ v^3 & 0 & 0 & 1 \end{pmatrix} Show that an infinitesimal rotation by theta^j...

They seem to defy the most fundamental principle of SR. The first postulate/equivalence principle. According to wikipedia, we get Lorentz boost (x direction) and slightly different formulas for the inverse Lorentz boost "This "trick" of simply reversing the direction of relative velocity...

Let's say you have a rod that is 10 meters long. Observer O sees the ends of the rod at (t=0, x=0), and (t=0, x=10). Observer O' moves at speed v = 0.8c relative to O. What is the length of the rod in O's perspective? Using the length contraction formula L' = γL, we find that O' sees the rod as...

Homework Statement I am meant to show that the following equation is manifestly Lorentz invariant: $$\frac{dp^{\mu}}{d\tau}=\frac{q}{mc}F^{\mu\nu}p_{\nu}$$ Homework Equations I am given that ##F^{\mu\nu}## is a tensor of rank two. The Attempt at a Solution I was thinking about doing a Lorents...

Homework Statement 1. Homework Statement [/B] Prove the potential energy of interaction between an electric charge ##q## moving with velocity ##\vec{v}## and an electromagnetic field with potentials ##V## and ##\vec{A}## is given by ##U = qV-q \vec{v} \cdot \vec{A}## Homework Equations...

Homework Statement Using the tensor transformation law applied to ##F_{\mu\nu}##, show how the electric and magnetic field ##3##-vectors ##\textbf{E}## and ##\textbf{B}## transform under (a) a rotation about the ##y##-axis, (b) a boost along the ##z##-axis. Homework Equations The Attempt at...

Hi, I was wondering what Lorenz Factors are. Can someone give me a simple definition?

Homework Statement Spaceship A of length 30m travels at 0.6c past spaceship B. Clocks in frame S' of spaceship A and S of spaceship B are synchronised within their respective frames of reference and are set to zero, so that t' = t = 0 at the instant the front of spaceship A passes the rear of...

Homework Statement Three events, ##A##, ##B##, ##C##, are seen by observer ##\mathcal{O}## to occur in the order ##ABC##. Another observer, ##\mathcal{\bar{O}}##, sees the events to occur in the order ##CBA##. Is it possible that a third observer sees the events in the order ##ACB##? Support...

Homework Statement Consider the infinitesimal form of the Lorentz tranformation: ##x^{\mu} \rightarrow x^{\mu}+{\omega^{\mu}}_{\nu}x^{\nu}##. Show that a scalar field transforms as ##\phi(x) \rightarrow \phi'(x) = \phi(x)-{\omega^{\mu}}_{\nu}x^{\nu}\partial_{\mu}\phi(x)## and hence show that...

Homework Statement [/B] A Lorentz transformation ##x^{\mu} \rightarrow x'^{\mu} = {\Lambda^{\mu}}_{\nu}x^{\nu}## is such that it preserves the Minkowski metric ##\eta_{\mu\nu}##, meaning that ##\eta_{\mu\nu}x^{\mu}x^{\nu}=\eta_{\mu\nu}x'^{\mu}x'^{\nu}## for all ##x##. Show that this implies...

Homework Statement Consider an inertial frame ##S## with coordinates ##x^{\mu}=(t,x,y,z)##, and a frame ##S'## with coordinates ##x^{\mu'}## related to ##S## by a boost with velocity parameter ##v## along the ##y##-axis. Imagine we have a wall at rest in ##S'##, lying along the line...

Is it proved experimentally that the Planck constant is invariant in the moving system? If that experiment exists, would you show me that in detail?

I would like to prove the Lorentz invariance of the Klein-Gordon equation by proving the invariance of the action ##\mathcal{S} = \int d^{4}x\ \mathcal{L}_{KG}## under a Lorentz tranformation. I would like to do this by first proving the Lorentz invariance of the ##\mathcal{L}_{KG}## and then...

Homework Statement 1. Show directly that if ##\varphi(x)## satisfies the Klein-Gordon equation, then ##\varphi(\Lambda^{-1}x)## also satisfies this equation for any Lorentz transformation ##\Lambda##. 2. Show that ##\mathcal{L}_{Maxwell}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}## is invariant under...

We have that \Lambda^{\mu}_{\nu} = \frac{1}{2}Tr(\overline{\sigma}^{\mu}A\sigma^{\nu}A^{\dagger}) I would like to make sense of the statement that this is a homomorphism because the correspondence above is preserved under multiplication. Can someone clarify how I could see this?

Hello! Got a bit of an issue with thew two above mentioned equations about time. From the Lorentz transformation t' = [t - (vx)/c^2]/lorentz factor, we get that the time read by a moving observer for an event in the stationary observer's frame of reference will always be slower (longer) because...

Homework Statement Show that the isotropy and homogeneity of space-time and equivalence of different inertial frames (first postulate of relativity) require that the most general transformation between the space-time coordinates (x, y, z, t) and (x', y', z', t') is the linear transformation...

<<Moderators note: Discussion split from: https://www.physicsforums.com/threads/motivation-for-the-introduction-of-spacetime.866669/>> You think the violation of Bell's inequality is not a serious challenge? You have to give up realism as well as causality if you want to defend the...