Special relativity Definition and 1000 Threads

Homework Statement A rod of length L0 moves with a speed v along the horizontal direction. The rod makes an angle of θ0 with respect to the x'-axis. (a) Show that the length of the rod as measured by a stationary observer is given by L = L0*√[1-(v2/c2)cos2θ0] (b) Show that the angle that the...

Homework Statement A photon beam is incident on a proton target (at rest). Particle X (and nothing else) with rest mass M=1.232GeV/c2 is then produced. Use m_p =0.938GeV/c2 as the proton mass. a) What is the energy of the photon beam, in terms of GeV? b) What is the momentum of the moving...

Homework Statement For a fast moving particle, its momentum and energy are frequently easier to measure than its velocity. a) Show that the factor of beta (as defined by β=v/c), can also be determined by measuring the ratio of relativistic momentum (p) and total energy (E). b) Sketch...

Homework Statement Two events occur in an inertial system K as follows. Event 1: x1 = a, t1 = 2a/c, y1 = 0, z1 = 0 Event 2: x2 = 2.6a, t2 = 1.9a/c, y2 = 0, z2 = 0 What is the velocity of the frame K' in which these events appear to occur at the same time? Express the velocity vector using...

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 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...

Homework Statement I have encountered a problem in Sean Carroll's GR book, exercise 1.1 Consider an inertial frame S with coordinates ##~x^μ = (t, x, y ,z)~##, and a frame S' with coordinates ##x^{μ'}## related to S by a boost with velocity parameter ##v## along the y-axis. Imagine we have a...

Hey there, I have two questions - the first is about an approximation of a central gravitational force on a particle (of small mass) based on special relativity, and the second is about the legitimacy of a Lagrangian I'm using to calculate the motion of a particle in the Schwarzschild metric...

Homework Statement Plane harmonic waves of 1/p, 1/q, 1/r and 1/s are travelling, respectively, in the directions of the (non-unit) vectors (1,1,1), (1,-1,-1), (-1,1,-1) and (-1,-1,1). Show that there exists an inertial coordinate system in which they have the same frequency if and only if...

Homework Statement Imagine two motorcycle gang leaders racing at relativistic speeds along perpendicular paths from the local pool hall, as shown in Figure 1.21. How fast does pack leader Beta recede over Alpha’s right shoulder as seen by Alpha? Solution Figure 1.21 shows the situation as seen...

Homework Statement Unstable particles cannot live very long. Their mean life time t is defined by N(t) = N0e−t/τ , i.e., after a time of t, the number of particles left is N0/e. (For muons, τ=2.2µs.) Due to time dilation and length contraction, unstable particles can still travel far if their...

Homework Statement Unstable particles cannot live very long. Their mean life time t is defined by N(t) = N0e−t/τ , i.e., after a time of t, the number of particles left is N0/e. (For muons, τ=2.2µs.) Due to time dilation and length contraction, unstable particles can still travel far if their...

In the way I was taught about special relativity, time dilation is like the fundamental building block from which you derive things like relativistic mass and length contraction. So it has always struck me as quite odd, that the derivation of time dilation (in some sense the basis of special...

Homework Statement A 35 m long rocket is receding at 0.6c. From the point of view of a stationary observer, how long does it take for light to travel (a) from the bottom of the rocket to the top and (b) from the top to the bottom? Homework Equations t = d/v L = L0 / gamma The Attempt at a...

Homework Statement A particle moving at 0.95c travels 10 m, as measured by a stationary observer, and then disappears. How long did the particle live (a) from the point of view of the observer and (b) from the point of view of the particle? Homework Equations t = d/v d = d0/gamma The Attempt...

Homework Statement A nova is the sudden, brief brightening of a star. Suppose Earth astronomers see two novas occur simultaneously, one in the constellation Lyra. Both nova are the same distance from Earth, ## 2.5 \times 10^3 [cy]##, and are in exactly opposite direction from Earth. Observers...

For quite a long time now I'm having some trouble to bridge the gap between two different approaches to Special Relativity. The first approach is the traditional one. It is the approach that Einstein presented in his paper and that is taught in most of the basic textbooks. In this approach...

Homework Statement The last of the human race are leaving the earth, after a total nuclear destruction, to reach the only known planet suitable for lives, 2 million light years away from earth. They are traveling on the spaceship ARK, capable of close to speed of light. There is only enough...

[Note from mentor: this thread was originally posted in a non-homework forum, therefore it does not use the homework template.] I have been given an equation for the relativistic doppler effect but I'm struggling to see this as a function and then give a first order Taylor expansion. Any help...

Maxwell's equations reveal an interdependency between electric and magnetic fields, inasmuch as a time varying magnetic field generates a rotating electric field and vice versa. Furthermore, the equations predict that even in the absence of any sources one can have self propagating electric and...

Hello I have a question about how time effects velocity:So we have a car on Earth traveling 200m with 5 seconds we get that car moves 40m/s and 40x3600=144000 and 144000:1000=144km/h so car on Earth travels 144km/h now let's consider a that there is observer on spacecraft traveling 0.5c...

Hello, If anyone could help me with the prerequitisetes for an undergraduate General Relativity and Cosmology course I will enroll into, It will be much appreciated. The syllabus is the following(sorry for the rough translation): -Review of Special Relativity -Spacetime in GR -Geodesics...

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. 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...

I have been reading these notes on Rindler coordinates for an accelerated observer. In Rindler coordinates, the hyperbolic motion of the observer is expressed through the coordinate transformation $$t=a^{-1}e^{a{{\xi}}}\sinh a{\eta}\\ {}x=a^{-1}e^{a{{\xi}}}\cosh a{\eta}.$$On a space-time...

I was wondering if it is possible to work out the maximum amount of energy an object with mass can have using the length contraction equation (i.e. "actual" length divided by Lorentz factor). The way I thought of doing this was by rearranging e = mc^2 to get c^2 = e/m. Then, substitute e/m into...

I'm trying to understand something about relativity that doesn't seem to add up. I will extend Einstein's carriage example to incorporate 4 clocks. At the beginning all these clocks are running at the same time when they are together. I put two of the clocks far away from each other (100 km...

Bill_K submitted a new PF Insights post https://www.physicsforums.com/insights/precession-special-general-relativity/ https://www.physicsforums.com/insights/precession-special-general-relativity/

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...

If a photon were trapped between two perfect mirrors perpendicular to its axis of motion, and they were gradually brought together until they were touching, so that the distance between their faces was 0m, would the photon be "trapped" between the mirrors? Without space in which to move, how...

Can one shed light on the velocity of the photon through the fourth dimension x4 using limits? To begin with, please study the mathematics from Brian Greene’s book An Elegant Universe. The upshot is that the faster an object moves through space, the slower it moves through the fourth...

Let's say I have a Space craft traveling at 1% of speed of light and at rest speed it has an thrust of 600 kN with Specific impulse at 1.000.000s. We know we can calculate the relatavistic mass of the vessel with Einstein Special Relativity : γ = 1 / (1 - v2 / c2 )0.5 = 1.00005. Now the...

My impression always was that when you describe a problem in special relativity, you are already implicitly taking into account the light that would need to travel for some person to theoretically "see" a special relativistic phenomenon. I was confronted recently in another thread that this...

What is the velocity of the photon through the fourth dimension x4? Photons are real, physical entities. The fourth dimension is a real, physical entity. Therefore, photons must have a relationship with the fourth dimension. They must have some velocity relative to it. What is the velocity...

There are a few fundamental questions I wanted to ask about related to special relativity: 1) Firstly, is there an intuitive explanation for length contraction and why lengths are relative? For example, the fact motion is relative is intuitive. E.g. someone sitting inside a train moving 60...

Hello, I was wondering if anyone knows about the the book "The Geometry of Spacetime: An Introduction to Special and General Relativity" by Callahan and what their opinions are. Thanks!

I've read that one of the primary motivations for the need for QFT is that quantum mechanics cannot account for particle creation/annihilation, however special relativity "predicts" that such phenomena are possible (clearly they have been observed experimentally, but I'm going for a heuristic...

Dear PF Forum, I've been wondering about how on Earth (and I do mean it, from earth :smile:) that we know there's a galaxy 20 billions light away. Considering that https://en.wikipedia.org/wiki/Age_of_the_universe is 13.8 billions years old. But before I'm asking about Supernova Ia and Hubble...

Hello, I have often heard special relativity was not too difficult to study. I was wondering as a 6th former what knowledge is needed to do so and if it was even possible at my level. If yes does anyone suggest any good books or websites? I am searching for a more in depth mathematical...

Einstein's relativity of simultaneity & quantum measurement paradox. Suppose a rocket traveling close to the velocity of light which emits a single photon from its midpoint at point A, illustrated below. The rocket is equipped with a single detector drawn in green at the front of the rocket...

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...

Homework Statement Consider an inertial frame S with coordinates ##x^μ = (t, x, y ,z)##, and a frame S' with coordinates ##x^{μ'}## 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 x' = -y'. From the point of view of...

Homework Statement Two inertial frames S and S' are in standard configuration, the frame S' is moving along the x-axis of S with velocity v. In S' a straight rod parallel to the x' axis moves in the y' direction with velocity u. Show that in S the rod is inclined to the x-axis at an angle ##-...

Hello again, I would like to know what your opinions about this book. As I have figured out, there are a lot of great GR books out there, but this very rarely gets any mention in forums like this. Why is this? Its got pretty good reviews at amazon and goodreads. Thanks in advance!

I have heard/read that Carroll's Spacetime and Geometry: An Introduction to General Relativity is one of the best books on General Relativity but its price is insanely high! Does anybody know any place which sells it at a lower price than, say, Amazon? If not, what are other books that cover...

Homework Statement A photon of frequency ν is reflected without change of frequency from a mirror, with an angle of incidence θ. Calculate the momentum transferred to the mirror. Homework Equations E= hν Conservation of four-momentum The Attempt at a Solution If the mirror is in the x-y...

Something that has been bothering me for a while is this question. As seen from this Minkowski diagram,http://imgur.com/GkBN2HQ , the angle between x and x' is equally big as the angle between ct and ct'. I really can't seem to figure out why this is, although I think it has to do with the...

I've read in various places that magnetism can be explained in terms of the effects of special relativity. However, all of the explanations of this only mentioned the case of current flowing in a wire. Can special relativity explain the magnetism of free flowing electrons and other moving...

In Galilean Relativity, laws of mechanics are invariant across frames. In all the frames they are the same. So, in Dynamics and Relativity by W.D.McComb, it is written that this implies you cannot perform any experiment in an inertial frame that can tell whether an inertial frame is moving or...

I was bored, so I decided to derive the special relativity formulae. I drew the following diagram of a light clock: In order to find t, I did sinθ=d/ct Which gives tsinθ=d/c Which gives t=d/csinθ If v = 0, vt = 0, and θ = 90 sin90 = 1 t = d/csinθ = d/c We call this t0If v is greater than 0, vt...