Special relativity Definition and 1000 Threads

Hello, please note that the following is only about special relativity, not general. Of course, if there are any things to point out that fall in general relativity, feel free to do so, but I don't know GR, so I won't understand arguments based in GR. I also am not great with a geometry-based...

It has been 2.5years since I last did any special relativity so am rather rusty on it, I have a simple time dilation problem and its making my head hurt which way around it should be. Any help much appreciated! 1. Homework Statement Bob leaves Sarah on Earth and travels in a spaceship at 0.8c...

It seems if the clocks show the same time, the rod is at rest in our frame. If clocks are out of sync, rod is in motion. The closer velocity is to that of light, the more clocks out of sync, Another question - are all these rods the SAME rod? For example you ask me - what is velocity of the rod...

Special relativity states that according to an observer at rest, a measuring stick on a moving platform will appear shorter. Would this observer still see the measuring stick as comprising of the same amount of atoms as the observer who is at rest with respect to the measuring stick? If this is...

Homework Statement Spacecraft moving at 0.6c, length 180m with someone sitting at the back. He throws a cage with a mouse towards the front also at a speed of 0.6c. A stationary observer watches. Homework Equations What is length of spacecraft from observers POV? Length according to guy...

The D'Alembert equation for the mechanical waves was written in 1750. It is not invariant under a Galilean transformation. Why nobody was shocked about this at the time? Why we had to wait more than a hundred years (Maxwell's equations) to discover that Galilean transformations are wrong...

Hi! I came out with a problem last night I wasn't able to solve: Let's assume we have a condensator with a uniform electric field E confined in its inside, lying on the z axes. Let's also assume we have a piece of a ferromagnetic object aligned with the condensator at time t = 0, on the y-axes...

My question is very simple. As far as I know, once upon a time there was the Lorentz Ether Theory. This theory admitted existence of so-called Ether as a certain preferred frame, which was undetectable because of physical contraction of moving material bodies in direction of their motion. In...

Homework Statement The aether-wind theory of the Michelson-Morley experiment was discussed in class for the special case where the arms of the interferometer (each of equal length L) are parallel and perpendicular to the wind. In this problem we consider the general case for an angular setting...

Hi guys, This is my first time posting on PF! I have a question on §3 of Einstein's paper "On the electrodynamics of moving bodies."My problem is with the following mathematical statements: Hence, if x' is chosen to be infinitesimally small, or I have just finished high school, and...

Homework Statement [/B] Homework Equations The rear clock ahead example gives vL/c^2: The Attempt at a Solution I think the solution is the same, because even if there is a time dilation due to u (downward velocity) both clocks would slow down at the same rate and so the time difference...

Hello everyone, sorry if this is a noob question; I'm just starting out with special relativity. I was wondering whether relativity of simultaneity is a direct consequence of our ability to "know" being dependent on sight (light reaching a point). If, for example, we could only judge an event...

Homework Statement Homework Equations et Em and pm be the energy and momentum of the mass m after the collision. Let p and p' be the momentum of mass M before and after the collision. From conservation of 4 momentum: \begin{bmatrix}E+m \\ p\end{bmatrix}=\begin{bmatrix}E_m+E' \\...

Hello, I want to learn QFT but I feel that my understanding of Special Relativity is not good enough. Could you please recommend to me any good relativity books to fill my gaps? My gaps are mostly conceptual. Thanks in advance!

In quantum field theory, we use the universal cover of the Lorentz group SL(2,C) instead of SO(3,1). (The reason for this is, of course, that representations of SO(3,1) aren't able to describe spin 1/2 particles.) How is the invariant speed of light enocded in SL(2,C)? This curious fact of...

Let us assume that we have inelastic collision of masses ##m_1=1## and ##m_2=k## This means ##m_2=k m_1##. (##k>>1##) ##v_1=v##, ##v_2=0##, Velocity after collision is ##v'##. Units are such that ##c=1##. Let us assume that ##v_1## is close to one. At inelastic collision we respect conservation...

I recently saw the derivation of length contraction in Special Relativity . At the end , it said x' = (x - vt) γ(gamma) x = (x' + vt') γ(gamma) Where γ(gamma) is Lorentz transformation . It is = 1/√(1- v²/c²) Then derivation continued , with expansion of x' = (x + vt)γ As t = 0 in this case...

Sorry for my ignorance... still trying to get to grips... If a lady in the middle of a moving train sends out beams to the front and back of the train. They reflect off mirrors back to her and arrive simultaneously because she can't do an experiment to give away that she is moving forward...

Hi PhysicsForum, I'm currently reading Spacetime Physics by Taylor and Wheeler and I can't wrap my head around the concept of mass in SR. In the textbook, mass is described as the magnitude of the momenergy 4-vector and is invariant no matter which inertial reference frame you choose. So does...

What in the mathematics of the derivation of special relativity limits the model to inertial frames? How is an inertial frame defined in the context of the derivation?

The de Sitter group is often used as an extension of the Poincaré group, because its a simple group and preserves, in addition to a velocity c, a length L. A natural candidate for this length scale is the Planck length. Thus it seems to make sense to think about the invariant Planck length as...

Homework Statement A particle flies along in the positive +x direction. It has a constant force F applied 30º clockwise to the x-axis. It is moving at .6 c. What is the angle of acceleration? Homework Equations a = F/(mγ3) The Attempt at a Solution [/B] I'm pretty sure I know how to do...

Homework Statement [/B] List two postulates of special relativity and then in your own words explain how these two statements are synthesized in Einstein's theory. Homework Equations 1. The laws of physics are the same in all inertial reference frames. 2. Light propagates through a vacuum...

Homework Statement $$ E = -\vec{v_{obs}} \cdot \vec{p} $$ Where ## \vec{p} ## is the four momentum, and ## \vec{v_{obs}}## the velocity of the observer. Homework EquationsThe Attempt at a Solution [/B] This was a stated result in a GR course. I look through my SR notes and find that I...

There is something about the twin paradox in special relativity that has always bothered me. One twin sets out on a journey at a large fraction of the speed of light, turns around and returns. The fact that the returning twin is the one who is younger is explained by the fact that they are the...

Homework Statement Rest length of Ship B is twice that of Ship A. Ship A travels at 0.5c relative to a "fixed" observer. Ship B travels at such a speed that the same "fixed" observer measures Length B = Length A. How fast is Ship B traveling? 2. Homework Equations [/B] All given in statement...

Homework Statement Calculate the escape velocity on the surface of the neutron star in the previous problem (##m = \frac{2}{3} \cdot 2,1 \cdot M_{\odot}##; ##R = 15km##). Hint: Basic physics. Note, however, that the escape velocity is not going to be small when compared to the speed of light...

I have a question about Special Relativity. If a person is in a rocket ship traveling at 99.999999 percent the speed of light and they are standing at the back of the ship. Will they be able to walk to the front of the ship or will inertial resistance prevent them from doing so?

Homework Statement Hi, I can't seem to understand the following formula in my professor's lecture notes: F_αβ = g_αγ*g_βδ*F^(γδ) Homework Equations Where g_αβ is the diagonal matrix in 4 dimensions with g_00 = 1 and g_11 = g_22 = g_33 = -1 and F^(γδ) is the electromagnetic tensor with c=1...

Homework Statement Two identical particles of mass m travel towards each other at speed v; they combine and form a single new particle. By employing conservation of momentum and conservation of energy, what is the mass of this new particle in Homework Equations Relativistic momentum and total...

I understand that c is the "ultimate speed" and that it is a result of the fundamental constant, the permeability of free space. But if this is a constant only to a "stationary" frame of reference, how can we accurately measure it from Earth? Since Earth is moving relative to a supposed "fixed"...

We have got some SR work to do, however we have only had 1 introductory lecture. I have a problem with one of the problems. Question: A rod of 1m parrallel to the x-axis, travels at un-relativistic speeds at 45 degrees. It passes through a slit - also parallel to the x-axis - that is 1.1 meters...

Hello! I have a question that has been bothering me since I first started learning about Special Relativity: Given only the Minskowskian metric and/OR the spacetime interval, how can one reach the conclusion that the speed of light is invariant for every observer and how can one conclude that it...

Homework Statement You are on Earth as a spaceship flies past at a speed of 0.99c relative to the earth. A high-intensity signal light on the ship blinks on and off, each pulse lasting 2.2 × 10^(−6) s, as measured on the spacecraft . Your laboratory on Earth has a length of 56.4m. How long...

From Chris' perspective Bob is traveling with 1.5*108 m/s in direction a. Angelica is also traveling with 2.4*108 m/s in direction a. From Bob's perspective Chris is traveling with 1.5*108 m/s in direction b (The opposite of x). Angelica is traveling with 1.5*108 m/s in direction a. They all...

As I understand it, the proper length, ##L## of an object is equal to the length of the space-like interval between the two space-time points labelling its endpoints, i.e. (in terms of the corresponding differentials) $$dL=\sqrt{ds^{2}}$$ (using the "mostly plus" signature). Furthermore, this is...

I thought of this 'paradox' which is somewhat similar to the twin paradox but can't be explained by a lack of symmetry etc. It is very similar to many paradoxes I have heard before of which the resolution is known (which is why I am mostly sure this can be resolved) Bob is looking through his...

This question comes from a previous years exam as practice for my upcoming. Homework Statement Two spaceships are launched from Earth, going in opposite directions. Eventually, both spaceships have a velocity of 0.75c (where c is the speed of light), each in their respective directions. A...

Homework Statement Hi, I have this problem: For motion under a pure (rest mass preserving) inverse square law force f = −αr/r3 , where α is a constant, derive the energy equation γmc2 − α/r = constant. Homework Equations E = γmc2 dE/dt = f.u for a pure force The Attempt at a Solution I...

Homework Statement In a certain inertial frame two light pulses are emitted a distance 5 km apart and separated by 5 µs. As observed from another frame, which is traveling parallel to the line joining the points where the pulses are emitted at a velocity v with respect to this frame, the pulses...

If say you have some scalar field, θ(x^u), where x^u represents the 4-vector coordinates of spacetime, and then the typical classical equation of motion, a = -∇θ, how would one go about 'generalizing' this to a relativistic version? Since F = ma, would you have to write it as d/dt (P^u)...

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...

A Moving Clock runs slow. But, If time t has elapsed in the S frame, does SR apply to a clock moving with speed u in the x-direction in the S frame, relative to the S frame? Or does SR apply only when the clock is in another reference frame S' moving in the x'-prime direction, given that...

Homework Statement In a reference system S two athletes are aligned at a distance d relative to each other on the Y axis to make a run parallel to the x axis. Two starters, one next to each athlete, shoot their guns out at slightly different times, offsetting the advantage of better athlete...

Homework Statement I really don't have a homework question just a thought. Is rest energy "maximum energy" for a particle? As to say a particle at rest has a given energy, so when it is in motion it transfers some mass energy to kinetic energy, where both the mass and kinetic energy together...

Hi, I'm a CAD student, writing a research paper for my English Comp. class on interstellar travel. I wan't to quote Einstein but can't find were he stated this exactly: Because space and time are relative, the faster you move through space the slower you move through time relative to someone...

Homework Statement System S' moves with constant speed v=(vx,0,0) respect to the system S. On the S' system a particle moves with a constant acceleration a=(ax,ay,az). What is the acceleration a'=(ax',ay',az') measured from the system S?. Homework Equations Lorentz transformation The Attempt...

I have in mind thought experiment where physicist is in elevator falling towards the Earth. Question would be if he is not allowed to look outside, how would he detect the presence of the planet? Let's not take in consideration tidal forces and assume he is taking local measurements during small...

Hello. Consider the following case: Two observers, A and B, moving relative to each other with velocity v. For B, it's A that moves (with v) and so DTb=g*DTa (where DT denotes finite time difference and g is/the Lorentz factor gamma). So, (following the same logic as in Morin's Classical...

Homework Statement http://phy240.ahepl.org/Chp1-Relativity-Serway.pdf#page=39 #32 Planet R is 25 lighthours away from Earth. It takes 25 h (according to an Earth observer) for a spacecraft to reach this planet. The clocks are synchronized at the beginning. What is the spacecraft 's time...