Contraction Definition and 689 Threads

For the universe to be totally flat, and not just asymptotically closer to being flat as the universe expands, wouldn't there have to be pockets of hyperbolically-curved spacetime? In either case, I still would like to know how one expresses time dilation and length contraction in hyperbolic...

So, I am having trouble understanding how time dilation and length contraction in special relativity merge together and describe space-time. I guess the best way to ask this question is to pose a question, which i know how to answer mathematically, but I would like to discuss some thoughts about...

Start with the following 3 statements... 1. If I were traveling through the cosmos at high velocity relative to the CMB I should observe the distances between stars and galaxies to be length contracted in the direction of my motion, but not in directions perpendicular to my travel. 2. The...

Homework Statement A Rocket Moves away from the Earth at a speed of (3/5)c. When a clock on the rocket says that one hour has elapsed, the rocket sends a signal back to the earth. (A). According to clocks on the earth, when was the signal sent? (B). According tot eh Clocks on the earth, how...

hello people... i have a doubt regarding Lorentz length contraction... according to what he described, the length of a body measured in a moving frame appears shorter as compared to the one taken by an observer at rest...if a train moving with uniform relativistic velocity , is thought of...

I have started with the space-time metric in a weak gravitational field (with the assumption of low velocity): ds^2=-(1+2\phi)dt^2+(1-2\phi)(dx^2+dy^2+dz^2) Where \phi<<1 is the gravitational potential. Using the standard form for the Christoffel symbols have found: \Gamma^0_{00}=\phi_{,0}...

I'm a lay person who is interested in developing a better understanding of science in general, as well as specific theories. I'm just wondering if someone would be able to help me understand how Length contraction explains the null set of the Michelson Morley experiment? Hopefully this...

Regarding the observer riding on the middle of the train sees the light strike first the fwd first and then the aft. Will it be safe to say that for the observer to see the light strikes them both at the same time to adjust the tail of the train by shortening the train so that light can arrive...

Hey guys it's me again! I'm now asking you 2 question, I'm sure you'll be helpful as usual! 1) changing basis- changing tensors ok, the law of transformation of a (let's make this simple) 02 tensor is g_{\mu '\nu '}=\frac{\partial x^\alpha}{\partial {x^{\mu}}'}\frac{\partial x^\beta}{\partial...

Hi guys, If I use the definition of the scalar complex field as the combination of two scalar real fields, I can get \phi (x) = \int \frac{d^3 p}{(2\pi )^3} \frac{1}{\sqrt{2p_0}} [ \hat a _{\vec{p}} e^{-ip.x} + \hat b _{\vec{p}}^{\dagger } e^{ip.x}] which I can rewrite in terms of...

Hey there. I've been searching the internet on volume contraction with water and methaol mixture. Although I have found a little bit of infomation I don't know why it happens. I found it quite intriguing that mixing 50ml of water and 50ml of Methanol =/= 100ml of liquid. In fact there is a 4%...

Hi guys, this is my first post/thread, so I'd like to start with an easy one:rolleyes: I've searched the web and I wasn't able to find a satisfying proof of the fact that Lorentz contraction is NOT applied to the dimensions, that are not parallel to the direction of motion (e.g...

Terrell Revisited: "The Invisibility of the Lorentz Contraction" I recently posted this response to a general question of how Special Relativity worked. G H Wells Jr pointed out that and [SIZE="5"]Terrell's Argument Both of these are important issues to take into account...

hi Just wondering if someone can clarify for me whether it is merely the length of a moving object that appears contracted to a stationary observer, or whether it is also the distance between the moving object and other objects in its direction of motion that appears contracted. Or is the...

Hello everyone. I was thinking about length contraction in Special Relativity last night. I looked up information on the internet, and from what I understand, length contrtaction has never been measured (I'm not completely sure if I simply failed to find information to the contrary). So my...

Homework Statement A spaceship moves past you at speed v. You measure the ship to be 300 m long, whereas an astronaut on the ship measures a length of 445 m. Find v. The Attempt at a Solution I tried to substitute my numbers into L1=Lsqrt(1/(v^2/c^2)) and keep getting a negative wrong answer...

If a circular disk rotates about its centre, what will happen to its geometry. Since a spinning disk has velocity gradients, different regions of the disk must contract by different proportions. For example, a uniformly moving body undergoes length contraction and its new geometry is easily...

It is written that when the gas of the protostar is completely ionized, it stops contraction and it gets into hydrostatic equilibrium. I don't understand why?

As I understand it, there is no length contraction in the direction perpendicular to the motion being described. So if I were to observe a circle moving along a line (not rostating) and I were to measure the radius in te direction parallel to the motion, I would observe a contracted radius, and...

Simple thought experiment I read and would like to hear what others think will the result will be: Let two spaceships A and B accelerate along a straight line. Observer C does not accelerate. The accelerations, as judged by C, are constant for both ships. Each ship is equipped with a...

A spaceship is of length 1000 meters (to the observer standing in the spaceship). It is traveling so close to the speed of light that to the observer in the spaceship, the 'length' of the universe has contracted to 900 meters. Q1: If I am the observer in the spaceship, what do I think the front...

The canonical symplectic form on T^*M is the exterior derivative of the tautological 1-form: \omega=d\alpha where \alpha_p(X):=p(d\pi(X)) is the tautological 1-form. Let Y \in T_pT^*M a vertical vector, that is d\pi(Y)=0. It's trivial to prove using canonical coordinates that for...

In my class we were doing examples with a current carrying wire and if we moved with a speed v we would see length contraction. And because of this the moving line charge would go up in value and we would see an Electric field. And then we did the same for a solenoid but he said we need to...

Let's say I want to calculate the Ricci tensor, R_{bd}, in terms of the contractions of the Riemann tensor, {R^a}_{bcd}. There are two definitions of the Riemann tensor I have, one where the a is lowered and one where it is not, as above. To change between the two all that I have ever seen...

Length Contraction and Time Dilation Gamma= 1/sqrt(1-v^2/c^2) = 2 (Assumed) We have L=L’/Gamma…………………………………….1 And dT= dT’ * Gamma ………………………………2 Let primed frame is that of Bob and unprimed that of Dave. Let us define identity as an equation in which values on both...

So I was bored and decided to find some simple equations to deal with relativistic geometric edges and angles at an angle to the direction of movement. L=L_0\sqrt{(\frac{\cos(\Delta\theta_0)}{\gamma})^2+(1-\cos(\Delta\theta_0)^2)^2}...

Q: if you travel closer to c, will you see length(distance) contraction between andromeda and earth?

Homework Statement From Lorentz Transform, x^{\prime} = \gamma (x - vt) From textbooks and wikipedia, L_0 = x'_2 - x'_1 = \gamma (x_2 - x_1 ) Where x_1 and x_2 = L Thus, \L_0 = \gamma L Question is this: If i take the same method and us the Inverse Lorentz transform, i seem to...

Hi guys and girls. Need some assistance with these problems, not the hardest examples, but I need some help on the way. Homework Statement 1. An astronaut travels at 0.9c across our galaxy, which is 100 000 light years in diameter. How long time will it take (according to the...

Okay so I have: Eqn1) Tij=\rhouiuj-phij = \rhouiuj-p(gij-uiuj) Where Tij is the energy-momentum tensor, being approximated as a fluid with \rho as the energy density and p as the pressure in the medium. My problem: Eqn2) Trace(T) = Tii = gijTij = \rho-3p My attempt: Tr(T) = Tii...

Hi all, I'm trying to follow through some of my notes of a GR course. The notes are working towards a specific expression and the following line appears: R^{\alpha \beta}_{\gamma \delta ; \mu} + R^{\alpha \beta}_{\delta \mu ; \gamma} + R^{\alpha \beta}_{\mu \gamma ; \delta}=0 Which by...

In Griffiths book (Intro to Electrodynamics, page 489) he uses one simple gedanken experiment with train, lamp and mirror, to prove the length contraction \Delta x'=\gamma \Delta x. My question is why he uses two directions of light and not just only one? For example, when we use, for observer...

I had a big epic discussion on another board after someone stated that "if I were to travel to Betelgeuse at a sufficient velocity I would reduce the distance between myself and Betelgeuse until it is say, 2 light years, which means I would only experience 2 years or so during my journey", this...

Well.. Proper length ,from my understanding, is the minimum distance between 2 events in any frame. Then, how does the length contraction work? suppose someone from other inertial frame try to measure the length.. The length will be contracted to L/gamma..shorter than proper length...

Special relativity Length Contraction and Time dilation question Homework Statement Planet X is 18 Light Years from earth, A spaceship moving towards the Earth at a speed of 0.82C (Measured from Planet X) fires a series of 1.2 cm long and 2.1 gram mass (as measured by the pilot) projectiles...

The example I have read to show time dilation is that of a light clock on a train. Two mirrors are one metre apart. Light is beamed from the first mirror to the second. An observer on the train sees that it takes the amount of time for light to travel 1m for the light to reach the second mirror...

Can someone please clear this up for me? Lets say the distance of Point A from Earth is 10.4 light years. Some spacecraft is traveling 0.95c. So. The person in the spacecraft will see Earth contract but Earth will see the spacecraft contract in length too. The thing I'm confused on is...

I wish I could calculate the contraction: gabgab I wish someone could show me how to get n! Unfortunately, I find it difficult, for I am not familiar with Tensor Algebra ... My wrong way to calculate it: gabgab= gabgba (since gab is symmetric) = δaa = 1Why is it wrong?

Suppose I am standing on the Earth surface and observing a rockhet of very high speed then i will see the length the rocket contracted and abserver on the rocket will also see my length contracted(I am not sure about it)in the direction of motion. Is the same case takes place with time...

Is length contraction an assumption which is verified experimentally or can it be proved? If it can be proved, how to prove it graphically? By proof, I do not mean demonstrate. I just want to prove length1=length2 * (gamma).

Hello! need some help with length contraction. So according to lorentz transformation we got I don't know how to put symbols so ill use Y as gamma since they look alike :) dx' = Y dx - u Y dt So proper length refers to the frame where dt = 0 since u are measuring the ends at the...

Greetings everyone, I understand the derivation of the Lorentz transformations, and have not had trouble applying the concepts and the math to most elementary SR problems. However, something occurred to me recently which I have been unable to resolve. Let’s say there are two tennis balls...

i am wondering when i read about planets or solar systems that are like 1million lightyears away, those that take into account length contraction, because if the light is traveling at the speed of light then the distance it has to go will contract. also another (possibly) stupid question...

Hi, I have been looking at hoop stresses and the information I have found hasn't been all that useful to me as I am having a hard time converting the thermal contraction of a system into a pressure for the equation (stress=a+b/r^2). This is the thick walled hoop equation The disc is a few...

Homework Statement I have a two part question where one has to solve for a velocity to make a moving clock run half the rate as one at rest. Then the second part is what velocity would an object have to move in order to make its length halved. Homework Equations t'=t\gamma...

Hi I am trying to solve this problem. I will present my solution though I couldn't get the tension right. At 40 Celsius , there is no tension in the wire. When the wires are cooled , they contract and the tension increases. But the tensile stress, which is force per unit area, will remain...

I'm having a major mental block to special relativity - i understand it the principle of it but seem to be struggling with time dilation and lenth contraction. I've spent a while thinking that time dilation and length contraction happen both togethor like you can't get one without the other...

Homework Statement We have the application h: (C[0,1], R) --> (C[0,1], R), defined by h(f(x)) = \[\int_0^x cos(f(t))/2\, dt \] Prove that h is a contraction. Homework Equations Need to prove there exists k, 0<k<1 s.t. sup_(x in [0,1]) \left|\int_0^x (cos(f(t)) - cos(g(t)))/2\, dt...

Homework Statement Let f be a function defined on all of R and assume there is a constant c such that 0<c<1 and |f(x)-f(y)<c|c-y| a) Show f is continuous on all of R b)Pick some point y1 in R and construct the sequence (y1,f(y1),f(f(y1)),...) In general if y_(n+1)=f(yn) show that the...

This was probably asked some time ago. It involves a paradox of relativity and I hope someone can answer it for me: Imagine a solid cylinder (call this the plunger) with a bar welded to one end making a T. The plunger fits just perfectly into a hollowed cylinder of the same length, and the...