Contraction Definition and 689 Threads

Hey there, I'm having a real hard time understanding exactly how to manipulate tensors (let alone know what they actually are). I learn brilliantly from example and repetition (the understanding comes later) but the internet and my lecture notes seem to be void of any kind of worked example...

[SIZE="3"]A rod moves along x-axis with speed u and has length L relative to Inertial Frame S. What is its length L' relative to the other inertial S' that moves with speed v with respect to S. I know the famous length contraction formula L=L' * sqrt(1-square(v/c)) but I confuse how to...

When a moving observer views a stationary meter stick, it appears contracted. The stationary observer measures it at full length. Similarly, the stationary observer views a moving meter stick as contracted, and the moving observer views it as full length. This is conventional relativity. When a...

Homework Statement How fast must a pion be moving on average to travel 25 meters before it decays? The average lifetime, at rest, is 2.6 x 10-8s. Homework Equations \Deltat =\Deltat0/ sqrt(1 - v2/ c2) l = l0 * sqrt (1 - v2/ c2) The Attempt at a Solution I think that 2.6 x...

1. Homework Statement Q1) Show that a contraction transformation from V to V has a diagonal matrix representation regardless of the basis given to V (same basis in domain and range). !2) T(x1,x2,x3)=(x1,x2,x2*x3) find the kernel and range T for this transformation. 2. Homework Equations 3...

Bob, Ed, and Sussie are all observers, each in their own space-ship. Ed and Sussie accelerate on parallel paths to very near the speed of light. Bob sees both length contraction and an increase in mass of both Eds and Sussies ships. These effects are great enough that each ship achieves the mass...

Homework Statement As a rocket ship moves by at 0.95c a mark is made on a stationary axis at the front end of the rocket and 9 × 10^−8 s later a mark is made on the axis at the back end. The marks are found to be 100 m apart. The rest length of the rocket is: A. 31m B. 78m C. 100m D...

Hello, I am not sure if I am doing this right or not. It seems to simple to be the right aswer, I feel I must have gone wrong somewhere. Many thanks :-) xxx Homework Statement Length Contraction Relativity Question? An aeroplane is of length L’(m) precisely when measured in its rest...

Hello, I was reading Einstein's RELATIVITY (his non-mathematical 1916 (or so) book). Having shown the Lorentz transformation formulas, i.e. t' = \gamma( t - vx/c^2) x' = \gamma(x - vt), he then talks about length contraction. He takes a meter-rod fixed in a certain coordinate system S'...

Hi, i asked some quesitons about this before but i need a clarification. Generally we use vertical light clocks and compare the distances taken by light and since c is constant the longer path taken by the light means a dilation in time, from here we say every other type of clcok dilates in same...

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...

I'm having a hard time understanding length contraction. can anyone explain it to me in simple terms?

http://cas.web.cern.ch/cas/Baden/PDF/Relativity.pdf on pg 16, it says that a muon traveling at a relativistic velocity towards Earth would see the distance to Earth shorted by the gamma factor... i thought the length of the muon is all that is shortened by the factor of gamma? am i wrong here? :s

I'm doing some independent study with a professor at my university. He has taken one GR class and he said that it was not a good experience. So we are in a sense learning together as we pursue this. We are using the book "A First Course in General Relativity" by Schultz. We are doing problem...

Homework Statement A spaceship flies past a space station at 0.75c. Observers on the station measure the length of the ship to be 0.30 km. If the ship later docks alongside the station and its length is measured, what would this measured value be? Homework Equations d=d0/\gamma The...

Hi, I am aware that time dilation has been observed experimentally with atomic clocks on satellites etc. but after a few google searches I have not found anything about experimental confirmation of length contraction. Has this been observed at all? If so, how was it tested? thanks.

If i have a rod of length L at rest . And there is a hole up ahead that is L/2 and I move the rod at a velocity which will contract it to half its rest length. Will the rod fall into the grate? Well I think that from the rods point of view its still its rest length and it would appear...

Homework Statement A meter stick moves with speed .8c relative to frame S. What is the length observed by a person in frame S if the stick is 60 degrees to v, as measured in S? Homework Equations L=observed length l=proper length y=1/sqrt(1-B^2) L=l/yThe Attempt at a Solution Sorry, I suck at...

Hi, Suppose a stationary frame S' is observing frame S moving with velocity v=0.866c in the x-direction, and let points (4,0),(10,0) define the ends of a rod in S, so its distance is 6, but as measured from S' contracts to 3 because of the Lorentz factor gamma. I'm unable to determine...

Hi folks, This is my first post here. I hope this is the right forum for this question. I am trying to come up with a linear transform to that will take as input a vector (x, y, z) and output a vector that is scaled in the direction of another vector. For example: Suppose I...

Assuming 300,000 km/sec for c; I am in a spaceship which is 300 meters long traveling at 0.5c. A beam of light passes me and I want to measure how long it took to travel the length of my ship. As c is the same in all frames of reference, I would work this out as distance (300 m) divided by...

Homework Statement The starships of the Solar Federation are marked with the symbol of the Federation, a circle, whereas starships of the Denebian Empire are marked with the Empire's symbol, an ellipse whose major axis is n times its minor axis (a=nb in the figure ). Homework Equations...

the proper length is the length where we can measure the length, with one clock( not moving) and for someone looking at it as i moves it seems contracted.. how does this happen i do not under stand could someone explain thanks in advance Seto.

hello, how is it possible to calculate the only GRAVITATIONNAL time dilation and length contraction factor in the Kerr metric and/or the Kerr-Newman metric, for an object falling but otherwise at rest, since there is frame dragging, and the metric contains dt^2 components but also dt.dphi...

I have a curiosity. I do not have a degree in science (going to university later this year) so this should be very simple to follow. I'm looking for a refutation (preferably with words and not unnecessary equations), confirmation, maybe a link to this sort of stuff. I'm aware that as an...

Do fast moving objects in relative motion always observe length contraction regardless of their direction of travel? In every example I find the train or the rod appears to be “moving toward you.” I can’t find any thought experiments describing what happens after you pass the train and it...

So in Analysis I we explained the convergence of cos to a fixed value by Banach's contraction theorem. But is the cos a strict contraction? Is that obvious? (What is its contraction factor?)

The terms "length contraction" and "time dilation" Is there a particular reason why we say length contraction but time dilation? A Lorentz transformation \Lambda=\gamma\begin{pmatrix}1 & -v\\ -v & 1\end{pmatrix} takes \begin{pmatrix}1\\ 0\end{pmatrix} to \gamma\begin{pmatrix}1\\...

Homework Statement I've been reading a textbook on tensor analysis for a while. The book uses the conclusion of "covariant differentiation commutes with contraction" directly and I searched around and found most people just use the conclusion without proof.Homework Equations For example...

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.

By what factor would the radius parallel to the direction of travel contract for a 7 TeV proton, relative to an antiparallel 7 TeV proton, in the Large Hadron Collider?

Can length contraction be treated as a vector? E.g. Suppose I am traveling 10 degrees north of east. Will my length contraction with respect to the east direction be cos 10 times the appropriate Lorentz transformation (with respect to the direction of motion)? Thanks.

My interest surrounds the qualities and affects of gravitational length contraction (GLC). Like most other General Relativity circumstances GLC is difficult to measure because of frame of reference issues (such that a meter in space is longer than a meter on Earth but in both frames of...

Homework Statement Consider the function g : [0,∞) → R defined by g(x) = x + e−2x. Given |g(x2) − g(x1)| < |x2 − x1| for all x1, x2 ∈ [0,∞) with x1 ≠ x2. Is g a contraction on [0,∞)? Why? Homework Equations I think we are intended to use the given equation and the CMT CMT states that...

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...

Hi, i asked this before but i think i found a clearer way to define my quesiton. As i asked in the title, does length contradicts as a result of time dilation? Or time dilation and length contraction are equal? When we deal with formulas generally we use the vertical clock and derive time...

We know that the twin paradox is not a paradox since one of the twins accelerate and time passes more slowly for him relative to his twin on earth. My question is why can't we apply the same reasoning for length contraction? If one of the twin A measures the lengths of sticks in the reference...

Homework Statement Hello, Consider a rod of proper length l_{0}. Prove/Show that there is no length contraction if an observer moves perpendicular to the direction of the rod. Homework Equations l = l_{0}/\gamma where \gamma is the usual relativistic vector The Attempt at a...

Does length contraction apply only to objects, or to space as well? On the one hand, sources like this seem to imply that it applies only to objects: http://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox On the other hand, most people on this forum seem to believe it applies to space as...

hi, we all know when we derive the time dialtion formula we choose a vertical light clock, and basically since the light take a longer zig-zag path to the stationary observer, the time is dilated. That's ok but when deriving length contraction, firstly we accept time dilation for horizontal...

Length contraction is one of the main aspects of relativity. However, I have a question: When something undergoes length contraction, does it become more dense or, is the decrease in length radiated in some way? Thank you, Jake

Hello guys, Although the response of a motor unit is all-or-none, the strength of the response of the entire muscle is determined by the number of motor units activated. Nerve impulses passing down a single motor neuron will thus trigger contraction in all the muscle fibers at which the...

Let p,q : \mathbb{C} \to \mathbb{C} be defined by \begin{align*} p(z) =& z^7 + z^3 - 9z - i, \\ q(z) =& \frac{z^7 + z^3 - i}{9} \end{align*} 1. Prove that p has a zero at z_0 if and only if z_0 is a fixed point for q. If z_0 is a fixed point for q then \begin{align*} q(z_0) =...

According to SR theory, relative motion leads to -length contraction -mass inflation -time dilation. In GR theory, gravity leads to time dilation. Does it also lead to -length contraction? -mass inflation?

Question: As an object approaches C and its length contracts, does space-time contract also, causing the a larger range of the universe to become visible? I.e. if the Hubble space telescope was traveling at high velocity, would it gain access to light from more distant galaxies than it has...

I'm trying to contract a rank 4 tensor with covariant rank 2 and contravariant rank 2 with four different indices [T[ab][cd]] to get a scalar value T and I have no idea how to do it as I'm sure a or b does not equal c or d. Any help would be much appreciated.

Homework Statement A spaceship passes you at a speed of .750c. You measure its length to be 28.2 m. How long would it be when at rest? Homework Equations I think the equation that is relevant is L=L(sub0)xsqrt(1-v^2/c^2) The Attempt at a Solution L=28.2xsqrt(1-(.75^2))=18.65m...

"Does the spontaneous contraction of a cloud of gas due to gravity violate the second law of thermodynamics? In other words, does entropy decrease as a result of the gravitational contraction?" This question is posed in interesting article here...

Not sure if this is the right place for this but... I am a bit confused about taking derivatives of tensors. Let's say I have some tensors, R, S and T, and an expression like R^{abc} \nabla_a S_{bcd} T^{d}. Do I contract on the d index inside, to get an expression like R^{abc}...