Contraction Definition and 708 Threads

Since many authors call simultaneity between events a convention, and that under the specific set of rules we may choose a convention or a coordinate system relative to an IRF (or non-inertial) to describe space time, I wonder what's the relation between this and the effects of length...

If a spaceship travels a distance of one light year as measured from Earth in one year's time as measured from the spaceship what is the relative velocity for earth-ship. Also how far did the pilot travel according to the pilot and how long was the trip according to an earth-clock? I found...

Homework Statement A relativistic conveyor belt is moving at speed 0.5c relative to frame S.Two observers standing beside the belt, 10 ft apart as measured in S, arrange that each will paint a mark on the belt at exactly the same instant (as measured in S). How far apart will the marks...

Homework Statement Consider the metric space (R^{n}, d_{∞}), where if \underline{x}=(x_{1}, x_{2}, x_{3},...,x_{n}) and \underline{y}=(y_{1}, y_{2}, y_{3},...,y_{n}) we define d_{∞}(\underline{x},\underline{y}) = max_{i=1,2,3...,n} |x_{i} - y_{i}| Assume that (R^{n}, d_{∞}) is...

how do i prove that this function is a contraction map? f(x)=⟨(1/9)cos(x1+sin(x2)),(1/6)arctan(x1+x2)⟩; x1=⟨0,−1⟩.i wantd to use the matrix form of the jacobian i said x(1)' = -1÷9sin(x_1 +sinx_2) ∙ (x'_1 + cos_2) x(2)' = 1÷(6(1+ (x_1 + x_2)^2) ∙ x'_1 + x'_2 I don't know how to put this...

I am given this function $f(x)=\langle (1/9) \cos(x_1+ \sin(x_2)) , (1/6) \arctan(x_1+ x_2) \rangle$ where $x_1= \langle 0,-1 \rangle$. may I please get hints on how to prove that this function is a contraction map

The three main effects of SR occur in inertial frames and change the description of space-time relative to a particular observer. My question here is how do these effects occur on Earth, since we know that motion on Earth is non-inertial. I know that we travel at small speeds and that we can't...

if you given a function f from R^2 to R^2 f(x)=<f_1(x),f_2(x)>, x in R^2 with f_1 and f_2 from R^2 to R being differentiable on R. if there is contants K_1 and K_2 greater than or equal to 0 so the 2-norm of (gradient f_1(x)) is less than or equal to K_1 and 2-norm of (gradient f_2(x)) is...

Franklin, "Lorentz contraction, Bell's spaceships, and ..." In the discussion of a new FAQ entry on the Bell spaceship paradox, the following paper came up: Jerrold Franklin, "Lorentz contraction, Bell's spaceships, and rigid body motion in special relativity," Eur. J. Phys. 31 (2010) 291...

What should it be, {sin(ωt-\frac{k}{n}x)} or {sin(ωt-nkx)}? I am contemplating this with respect to the proper waveform in a medium, following specific rules, particularly when it comes to the dispersion relation and ultimately what this would mean in the context of the Lorentz transformations...

Hi all, I tried searching for this but failed to find an answer to my question. I am having an issue with properly interpreting the equations for time dilation and length contraction. Let's assume that I am standing still and a train is passing by next to me (moving with uniform velocity). Let...

Homework Statement Show that the experiment depicted in Figure 2.11 and discussed in the text leads directly to the derivation of length contraction. Figure 2.11: Homework Equations d=v*t Requested result: L=L0\sqrt{1-\frac{v^2}{c^2}} The Attempt at a Solution In K the...

Prove the Contraction Mapping Theorem. Let ##(X,d)## be a complete metric space and ##g : X \rightarrow X## be a map such that ##\forall x,y \in X, d(g(x), g(y)) \le \lambda d(x,y)## for some ##0<\lambda < 1##.Then ##g## has a unique fixed point ##x^* \in X ##, and it attracts everything, i.e...

I had a quick question about Time Dilation and Length Contraction. Are the two just different ways of measuring/describing the same effect? Or rather they both follow as a consequence from one another? i.e. I can find how much a length is contracted by finding the dilated time interval and...

I found a funny video on youtube, but I am not totally convinced by the argument. It says that a pure magnetic field caused by a current in a wire can lead to a combined electric + magnetic field in a moving frame. It explains more or less convincingly that this can be understood as a...

Imagine two asteroids which are separed by 1Ly distance. They are in uniform velocity (.9c) with respect to an observe in space. So from the observers point of view (rest frame), does the distance between the asteroids (ie. 1Ly) appear contracted?

At the bottom of page 708 in Dummit and Foote (Chapter 15, Section 15.4 Localization) we find the definition of the extension and contraction of ideals. The notation is similar to I^e and I^c except that the superscripts e and c occur before the I. Can someone please help me with the latex...

Homework Statement A meter stick moves parallel to its length with speed v = 0.6c relative to you. a. Compute the length of the stick measured by you. b. How long does it take for the stick to pass you? Homework Equations t = to*γ L = Lo/γ The Attempt at a Solution Part a was...

Homework Statement You are exploring a newly discovered planet when a colleague contracts a deadly alien virus. Left untreated, it will probably kill him in 5 days, but the nearest medical station is 10 light-days away! How can you get him there in time? Homework Equations Δtp=L/v...

I am currently designing a convergent nozzle for use in experiments and wanted to check something: Will the pressure and density of the flow always expand to ambient (following the isentropic relations) when it reaches the nozzle exit regardless of nozzle contraction ratio and length? Any...

I would like some information concerning GR and the dimensional contraction of a standard rod due to gravity. As the potential energy per unit mass decreases as one approaches the center of a planet, time dilates and therefore, space needs to contract, relative to one in deep space. I’ve seen...

Homework Statement Water flows at room temperature in a horizontal pipe with mean velocity of 1 m/s. Then a sudden contraction of the pipe changes the diameter to half the upstreams diameter (##\frac{D_1}{D_2} = 2##). What is the pressure drop (##p_1 - p_2##) from a point (1) upstream of...

Hello Everyone, I came here with a question and hope you can shed some light. We know that Ricci tensor which is a contraction of Riemann tensor contains a subset of information as contained by Riemann tensor. In 3-D infact they contain the same information. I was wondering is it always...

Length Contraction:Does the object or travel distance shrink? I had always thought that length contraction meant that the object itself shrunk but I stumbled across an article where they said "Because of length contraction the photon doesn't travel any distance at all. Which is it? Any help...

Consider two iron rods of about 10 metres separated by 10 metre. They are in series position and not connected in anyway. If the rods are passing nearby an observe with a velocity of 90% speed of light, then what would he observe? 1) does the separation between the rods (ie 10m) undergo length...

Suppose I'm standing on Earth and i see an iron rod accelerating through space with a rate of 1m/s^2. Will it undergo length contraction after reaching a speed nearly to the c? Will there be any deformations to a spinning disk?

Hi, As is well known, Relativity claims that a rod of a given proper length will appear length contracted when measured by a moving observer. Now consider a rod of length L and observer initially at rest relatively to it, with one end of the rod at the observer's coordinate x1(0) and the...

The problem has been shown in the picture. Because of relativity, both the guys on the ground and on the vehicle would observe length contraction. So the destination of the guy on the vehicle---the galaxy, would be more closed to him. If the vehicle is replaced with the light, which means the...

Homework Statement . Let ##X## be a complete metric space and let ##T:X \to X## such that there exists ##n \in \mathbb N##: ##T^n## is a contraction. Prove that there is a unique ##x \in X## such that ##T(x)=x##. The attempt at a solution. Sorry but I am completely lost with this exercise...

Hello All, I like to think that I have a decent background in physics and related material, but I confuse myself quite easily on, well, everything. I guess I think about it too much, really. So feel free to give complex answers and I will do my best to follow along accordingly. Anyways, here...

Suppose I am in a stationary frame of reference S and there is a lamp post at a distance X from my origin in the positive X direction. Say you move at a velocity V along that axis and the distance of the lamp post in your frame of reference S' is X'. Then by Lorentz transformation equation X'...

Homework Statement A point charge +q rests halfway between two steady streams of positive charge of equal charge per unit length λ, moving opposite directions and each at c/3 relative to the point charge. With equal electric forces on the point charge, it would remain at rest. Consider the...

Can anyone help me with this thought experiment. I have a spaceship moving at very close to the speed of light. Inside are the captain and two crew members. The captain is positioned at the front of the spaceship with a clock and a light. One crew member is positioned at the back of the...

Say we have two inertial observers Bob and Alice moving relative to each other at a significant fraction of the speed of light c (say 0.5c). Bob is moving to the left relative to Alice and Alice to the right relative to Bob. When their origins cross, a pulse of light is emitted to the right...

can both time dilation and length contraction occur for the same observer? i don't think it is possible since then c=reduced length/increased time which is impossible(since c is constant)... Am i wrong?

All but one of the tensor operations can be defined without reference to either coordinates or a basis. This can be done for instance by defining a ##(^m_n)## tensor over vector space ##V## as a multi-linear function from ##V^m(V^*)^n## to the background field ##F##. This allows us to define...

Okay because my previous post of similar kind was I guess rather too full of thought experiments and ideas that nobody actually responded to it except for one user then I will try to explain the same thing here only much simpler. A few situations. so there is this site...

I'm starting to doubt about something: In 4 dimension, what value has δ^{λ}_{μ} in following equation: ημ\nuη\nuλ = δ^{λ}_{μ} is it 4 or 1? and IF it's 1, what is the difference that this equation: ημσημσ = 4?

Hi all! I've got a short question concerning a minor notational issue about tensor contraction I've run across recently. Let A be an antisymmetric (0,2)-tensor and S a symmetric (2,0)-tensor. Then their total contraction is zero: C_1^1C_2^2\,A \otimes S=0. As a proof one simply computes...

I've been trying for a long time to get an answer to the question, "What is the physics or mechanical explanation of contracting physical objects and the distances between them?" I understand that the phenomenon is theorized to depend on different observations from different frames of reference...

Hello, I am a bit confused about the length contraction formula. The formula is : l=lo*sqrt(1-u^2/c^2), where lo is the distance measured in a frame at rest with the moving object. Now I was looking at a problem where a spacecraft just as it touches the finish line (event 1) a message from...

Hi everyone! I have some problems with indices in general relativity. I am now working with the classic textbook by S. Weinberg and in eq. (4.7.4) we find...

If an object were to approach the speed of light, its length, as measured by an observer, would become shorter and shorter. But what about the view of the speeding object? If the object is approaching the speed light, then would the world surrounding it appear to be shorter as well? I say...

Can someone please clarify for me whether length contraction in special relativity is considered a physical effect (a contraction of a cohesive material) or a kinematic effect (applied to the space the material occupies)? I've been thinking about Bell's Spaceship Paradox this week and realized...

Hello All: I am working on a function given as f(x) = 10/x + (1/20)x^2 for x such that 0≤x≤10. What can be said about the contraction mapping property of f(x)=x? If it is not a contraction map, is there any way to make modifications on the function or the interval and prove a contraction mapping...

As I've just recently started studying relativity, I need some help with these basic concepts. So this thread is about length contraction. Can somebody explain the effects of it, since I've already found out some things, like the existence of the invariant proper lenght, the fact that...

Here is a link to the question: Prove that a contraction T on a metric space is a continuous mapping? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Find an interval [a, b] for which the Contraction Mapping Theorem guarantees convergence to the positive fixed point or verify that there is no such interval. Homework Equations x = g(x) = \frac{14}{13} - \frac{x^{3}}{13} The Attempt at a Solution I know...

well,i found this article and i find it simple to understand. But is this article totally correct? Here is the link:http://m.sparknotes.com/physics/specialrelativity/kinematics/section2.rhtml

Homework Statement Two space ships, each a hundred metres long when measured at rest, travel toward each other with a speed of 0.85c relative to the Earth. Homework Equations λ = 1 / √1 - (v2/c2) x' = λ(x - vt) L' = L / λ The Attempt at a Solution Well to be honest i may be...