Contraction Definition and 689 Threads

Has it been shown that observed length contraction that occurs due to high relativistic speeds is any different from that that appear due to the additional time it take a signal from the trailing edge of object (as opposed to the leading edge) to reach an observer? If not, then obviously a...

Now, if I'm not mistaken, from the Lorentz transformations one derives the following equations for time dilation and length contraction, respectively: T'=gT L'=gL Where g is the gamma factor, forgive my sloppy representations, but I'm not well versed in Latex. However, the equation for...

Let Y_{1},..,Y_{k} be vector fields and let A be a tensor field of type ^{k}_{1}. Could you explain how applying k contractions to A\otimesY_{1}\otimes...Y_{k} yields A(Y_{1}...Y_{k})? Actually, could you first explain why contraction of w\otimesY is equal to w(Y)? Here, w is a 1-form and Y...

Homework Statement Two lightning bolts strike the ends of a moving boxcar (Points A and B). The boxcar has length 2d and is moving at a speed v. A stationary observes both lightning bolts hitting the boxcar simultaneously. An observer in the car, however, claims that the front (position B') of...

Ive heard that length contraction does not occur when the movement of the object is perpendicular to the observer. Is this correct? Say two identical rings were traveling at each other at relativistic speeds, whilst the observer is perpendicular to them. Ring A would see ring B contract and...

Homework Statement A rod of length L_0 moves with a speed v along the horizontal direction. The rod makes an angle of \vartheta_0 with respect to the x'-axis. (a) Show that the length of the rod as measured by a stationary observer is given by L = L_0 [1-(v/c)^{2} cos ^{2} (...

question for the Lorentz's space contraction I imagin this thought experiment: a train which travels with the speed of light is trying to enter a tunel which has absolutely the same form and dimmension like the train's shape, as if the the train goes slowly with his regular speed it will enter...

My impression was that only misinformed people argue that LQG discreteness is in conflict with Lorentz invariance. This was resolved a long time ago, i thought. Does anyone disagree? Want to talk about it? Explain something to me that I am missing? http://arxiv.org/abs/gr-qc/0205108 Reconcile...

car 2 is twice as long as car 1 when they are at rest a stationary policeman observes that car 2 is the same length as car 1 as car 2 passes car 1 going through a speed trap. car 1 is going 1/2 the speed of light I tried to solve this with L 1/sqrt(1-(1/2)^2) = 2L/sqrt(1-v^2/c^2) and...

Homework Statement Supersonic jets achieve maximum speeds of about (3 *10^-6)*c. By what percentage would observe such a jet to be contracted in length? Homework Equations The equations for these this problem would be : 1/gamma= L(proper)/Length = 1/sqrt(1-v^2/c^2) ; beta=v/c The...

Hi all, I'm teaching myself the algebraic side of tensors and I was wondering if you would be able to clarify a few things for me. I prefer to think of a tensor in the set theoretic manner as a multi-linear mapping taking several copies of a vector space and its dual space to the base...

R' is an observer from I'. A rod is in a state of rest relative to him. He measures its proper length L(0). An observer R from I measures its Lorentz contracted length L related by L=L(0)sqrt(1-vv/cc) (1). If we reverse the situation, R measuring the proper length of the rod R' measuring its...

Using the concept of length contraction and time dilation explain how is it possible to travel a distance of 1mln light years during the life of a single person? thanks for any help

Based on the Michelson Morley experiment, Lorentz proposed already length contraction as an explanation of the negative outcome of the experiment. a) Did he also propose time dilation? b) How is width contraction ruled out: is that a necessary conclusion of the Michelson Morley experiment or...

A rod. having slope m relative to the x-axis of S, moves in the x direction at speed u. what is the rod's slope in the usual second frame S'? (S is at rest realtive to S' which moves along the x direction with velocity v). well obviously the horizontal length of the rod is contracted or...

If I can explain a special relativistic effect with both Lorentz-Fitzgerald Contraction and Time Dilation, then which one is the correct answer? Because, for example in the experiment with the muons coming from the atmosphere, the explanation was Time Dilation, but we can explain it with...

Hello, I am working on the following problem and cannot figure out if I am doing the problem incorrectly or if my professor gave us the wrong answer. (I think that the former is the issue.) 1. Homework Statement [/b] To a stationary observer two frogs at opposite ends of a 100m long lake...

Here is the question -------- Give an example of a function f:[a,b] \to \mathbb{R} which is continuously differentiable and which is a strict contraction, but such that |f'(x)| = 1 for at least one value of x \in [a,b]. -------- Continuously differentiable means that the first derivative is...

Here is the question from our book: ------- Let (X,d) be a complete metric space, and let f:X\to X and g:X\to X be two strict contractions on X with contraction coefficients c and c' respectively. From the Contraction Mapping Theorem we know that f has some fixed point x_0, and g has some fixed...

Hi... I know that this question will be found little bit stupid, but unfortunatly I can't see where I made a mistake. Let's have stick with light sources on both ends. In stick's reference frame the flashes from both sources are simultaneous. In laboratory ref. frame they are not. However...

Homework Statement Two powerless rockets are on a collision course. They are moving with speeds 0.800c (ship 1) and 0.600c (ship 2) and are initially 2.25*10^12 m apart. The ships are both 50m in length as observed by a stationary observer on earth. a) what are their respective proper...

Can you have expansion without contraction?

as the sun evolved it contracted, its internal energy changing fro x to y. what's the total energy radiated, assuming luminosity is comparable with present? I understand that the rate of change of the internal energy = rate at which energy is radiated away by the star.. but i have been...

I have some questions about the relative factor: 1/'root'1-v^2/c^2 If an object moves close to the speed of light, the length contraction becomes significant. I hear this "paradox": (that was said not to be a paradox, but I didn't understand it) A train of 100 meter moves at a speed...

Homework Statement An electron travaels in an accelerator tube at a speed of 0.997 c relative to Earth. In the frame of reference of the electron, the length of the tube is 1.20 m. What is the length of the tube relative to earth? Homework Equations L = Lo / γ Textbook answer: 15.5 m...

Homework Statement The distance between the Earth and Alpha Centauri is 4.2 light years (1 light year is the distance traveled by light in one year). If astronauts could travel at v = 0.95c, then we on Earth would assume that the trip would take the astronauts 4.2 / 0.95 = 4.4 years. The...

Time dilation and length contraction are expressed by the following equations: L=L'*sqrt(1-(v^2/c^2)) T=T'/sqrt(1-(v^2/c^2)) However, according to the principle of relativity, you can't tell which is the fixed frame of reference and which the moving frame, so you can swap L and L' and T...

Hello guys. Here I am, bothering all of you again... I am having troubles proving the following: For v \in V and \omega \in \Lambda^k(V), show that if v_1,v_2,...,v_n is a basis of V with dual basis \phi_1,\phi_2,...,\phi_n then i_{v_j}(\phi_{i_1}\wedge ... \wedge \phi_{i_k})=\left\{...

consider a rod of proper length Lo located along the overlapped OX(O'X') axes of the I and I' inertial reference frames in the standard arrangement I' moving relative to I' with speed V. The rod moves with speed U relative to I and with speed U' relative to I'. The measured length of the rod is...

A short question this time : Is the gravitational length contraction an effect which acts parallel as well as perpendicular to the direction of the gravitational field ? I suppose it is not occurring perpendicular to it, but I might be wrong and I didn't find a good reference on it.

if you have a row of blocks, all touching each other in your frame, then when observed from a frame moving relative to you in the direction of the blocks will the contraction make the blocks look as if they're not touching - each one will be shorter but the total length of the row will be almost...

Relativity Two balls move with speed v along a line toward two people standing along the same line. The proper distance b/w the people is L, and the proper distance b/w the ball is γL [Note: γ is gamma]. Due to length contraction, the people measure the distance b/w the ball to be L, so the...

What does the factor that you get when you plug the length contraction and time dilation of a moving object back into the form of meters/second represent?

I stumbled on a book that seems to throw the concept of length contraction upside down to me. Maybe someone can help me here. All the books I've read to date, a popular example might be Elegant Universe, say that an object moving near the speed of light past an observer will appear...

A star is measured to be 40.0 ly from Earth, in the inertial frame in which both star and Earth are at rest. A) what would you determine this distance to be if you travveled to teh star in a spaceship moving at 1.0x10^8 m/s relative to earth. answer is 37.7 ly (calculated that, with no...

Another thing I don't understand about SR. Length contraction. As I move at near the speed of light, a stationary observer observes my length to be contracted. What exactly contracts? Is it the space between my molecules or the molecules themselves? Furthermore, if we switch perspective to...

If you have a drawing of a square (labeled ABCD starting at lower left and going clockwise) and it is first at rest in an inertial frame. When this square moves, length contraction changes its shape. In each of the following three situations the speed is the same, and the velocity is in the...

We know from experiment that time (a measure between two events) slows as we approach speed of light, but does the meter stick (a measure between two entities) then shorten as we approach speed of light ? If yes, since time stops at speed of light, then does meter stick disappear at speed of...

I have a h.w. problem that states: Explain WHY only the lengths parallel to motion shrink and why lengths perpendicular don't shrink. I know that the vector component of the velocity for an object moving in straight line would be changing. This change only occurs on the x-axis and the not...

I thought I understood SR's time dilation and length contraction. But after reading the section on "simultameity" in Tipler I am just as confused as before. Here is my source of confusion. [A] Muon Decay: S frame = frame of the earth; S' frame = frame of the muon A muon falls to Earth...

ok so i have been assinged to do a 10-12 page written lesson on the lorentz contraction, the thing is that i know very very little about it(we will assume i know nothing about it) so what i was wondering if anybody around here knew anything about it and wouldn't mind offering a hand. If there...

Does time and space dilate and or contract so that the constant of light is not violated for any observer? Thanks for your time, -Scott

Dear All, Have a small problem: Two chaps attempt to demonstrate the phenomenon of Fitzgerald-Lorentz contraction. The two meet at the centre of a fast train which is L = 500m long and traveling at a speech of u = 0.7c to synchronize their watches. One sits at the front of the train while the...

Ok I have this equations Michelson and Morley used: Delta t = t_2 - t_1 = \frac{2}{c}(\frac{{l_2 }}{{\sqrt {1 - \frac{{v^2 }}{{c^2 }}} }} - \frac{{l_1 }}{{1 - \frac{{v^2 }}{{c^2 }}}}) I need to show that if the length is contracted along the direction of motion, the result comes out to...

Special theory of relativity says that, when an object moves with a uniform velocity along its length, the length seems to be less. I believe this is the length measured from the stationary frame of reference. This is justified by Michelson-Morely experiment. What happens when the motion is in...

I am quite aware of the overwellming evidence for the math of relativity, but are we sure that the meaning (time dilation, length contraction, ect.) are true? I guess what I am saying is are there any expiroments that have proven length contraction as in the barn and pole thought expiroment?

Recently I started reading about relativity and found this flaw like thingy. I asked a friend of mine who studied physics and he came with the unsatisfying answer: 'at speeds like that everything kind of blurrs so the spearman won't crash into the door'. Is the following correct and a paradox...

If the length of an object could contract under length contraction, what about fundamental particles, like electrons, quarks, protons, etc? After all, an object is made up of a lattice/group of particles.

why Lorentz contraction transformation in the direction of motion for the problem in michelson experiment was proposed, instead of length expansion in the direction perpendicular to motion. I think that too will give the same solution. I don't know i might be crazy and silly in this argument. I...

I don't have pstricks...so I am going to use words. \text{contraction}\{ \overline{\psi}(x_1) \psi(x_1) \} My question: Propogators are usually dealing with different points...but what is the contraction of two quantities evaluated at the same point. Thanks.