Contraction Definition and 708 Threads

As object separate with a receding velocity proportional to the distance, it would seem appropriate to think that objects and space itself, which are located at a distance sufficiently far away (and beyond) to were recession velocities are large enough that Lorentz length contraction effects...

I have a question which I've found very difficult to Google. The easiest way to frame it I can think of is this: Given a cylinder moving lengthwise by an observer at some significant fraction of C, with the forward half of the cylinder (relative to the direction of motion) painted red, and the...

I have to admit that my "best" math days are long gone. That said, I wonder if anyone can help me? I'm stuck in part 1 of Einstein's book on 'Relativity, The Special & General Theory: The behaviour of measuring rods & clocks in motion', specifically on the second equation : √(1-v^2/c^2) used to...

While writing out the Dyson series due to the time ordering above I encountered the two expressions $$T(\mathcal{L}_{int}(x))\quad \text{and}\quad T(\mathcal{L}_{int}(x)\mathcal{L}_{int}(y))$$ I was able to write out the first term in terms of contractions using Wick's theorem and then finally...

The rule for length contraction seems to be inconsistent with the lorentz transformations for distance. The rule for length contraction is: ## x = \gamma x ^\prime ## and ## x ^\prime = \frac {1} {\gamma} x ## But the lorentz transformations for distance are ## x = \gamma x ^\prime + \gamma vt...

For instance, if a stream of muons were released from a box near a massive object and traveled on a straight path slowly (at a non-relativistic velocity) away from that object, a faraway observer would notice that the particles would take longer to decay than a muon typically would in empty...

I was wondering, would there be a length contraction (or expansion) in the z and y axis' if an object was accelerating in x axis? I know that in special relativity there is no deformation in the y and z axis' if the object is moving in the x axis. I was looking a this paper for clarification.

Comparing high precision atomic clocks, one flying in a airplane and one on the ground had demonstrated permanent time dilation presumably due to special relativity (speed) and/or general relativity (gravity) . While similar experiment with a ruler would demonstrate length contraction only...

I’m not a physicist but let’s say hypothetically ;we have the Millennium Falcon. It’s FTL hyperdrive can go Class 0.5 past lightspeed. Then we have an X-wing which has a Class 1 past lightspeed drive. This is all from the lore. MF is 0.5 and X Wing is 1 but MF is faster. Anyway even though the...

If I'm computing $$\mathcal{T} \langle 0 | \prod_i^Ne^{\imath \beta_i \phi(x_i)} | 0\rangle $$ where the contractions at the same spacetime point are ignored, can I simply insert a complete set of states (product now outside of expression) between each exponential to give $$\mathcal{T}...

I've managed to stump myself in attempting to answer a member on another forum. He is attempting to demonstrate length contraction using two electrons a known distance apart and moving at a known velocity.My thought experiment is based on his proposal; that's why I've chosen the components I...

Space/time is relative. What is the expansion relative to? Is there a reference point of no expansion to make a comparison? Accelerated contraction would appear to be expansion by an observer looking back in time so how can we be certain that the universe is expanding instead of collapsing at...

Two astronauts, Neil and Michael, visit a solid not revolving planet. They mount a jet engine on this planet to get it turning around its axis. Before starting the engine they put three dots on the surface with the help of an isosceles triangle, which measures 1 by 1 meter. Two dots are placed...

Richard Feynmann, in His lectures on Physics, Vol I, chapter 28. Gives an expression for calculating the E and B field of a moving point charge based on retarded radius; eg: Knowledge of where the charge was at the time when the field was being formed. The Equation was originally derived by...

If the table (with the mirrors, beamsplitter, etc.) is rotated 90 degrees, one arm will get shorter (due to lengthcontraction) because its longitudinal speed goes from zero to 30 km/s (our speed around the sun) and the other arm will get longer as its speed goes from 30 km/s to zero. So with a...

I had posted a similar question on another forum but didn't get much of a discussion. I'm interested to know what people here think. So consider a spaceship midway between stars A and B and initially at rest in the reference frame of the stars. The ship then accelerates away from A to some...

Homework Statement A spaceship of proper length L is moving with respect to the ground with speed v. As measured on the ground, how much time does a light signal need to get from the front to the end of the spaceship. Homework Equations L'=L/γ t'=tγ The Attempt at a Solution The right answer...

Hi all. I have a question about something Nima Arkani-Hamed said in his lecture on space-time about space contraction near light speed. I included a link to the lecture at the point where he refers to contraction of two space ships with a 'cable' between them, they are accelerating towards the...

Homework Statement https://imgur.com/a/OLPyMfK Homework Equations F=ma W=F*d W=T2 - T1The Attempt at a Solution For part A i figured it must be E because that is the only one that goes to 0 as the hit says. but nothing about this problem makes any sense to me. Where it says "You notice...

Hello, I am struggling to see why for a fermionic field $\psi$, one has the time ordered contraction $<0|T(\psi(x)\psi(y))|0>$. Could someone offer an outline/hints to see this please? Thanks!

Hello everyone and apologize if my questions seem a bit off, please have patience with me. I want to have the following, rather simple, thought experiment. Let's say that we have a moving object O with the proper length L, when at rest. Let's say that object O starts moving at 0.9c (90% the...

Is it possible to derive the Lorentz transformation from time dilation and length contraction? If so, how should I start? I know how to derive it while considering 4 scenarios finding values of A, B,D,E in x'=Ax+Bt t'=Dx+Et and the transformation is: x'=(x-vt)/sqrt(1-v^2/c^2)...

Hello all. I am having some small trouble with applying the lorentz transformations to calculate lorentz contraction. Here's what I did: Let O be the rest system and O' be the system moving with velocity v w.r.t O along x axis. Consider a rod lying in the O' system with ends x1' and x2'...

1. Homework Statement [/B] This is a problem that was in my Physics HW. Two powerless rockets are on a collision course. The rockets are moving with speeds of 0.800c and 0.600c and are initially ## 2.52 × 10^{12} ## m apart as measured by Liz, an Earth observer, as shown in Figure P1.59. Both...

I have seen in SR that regular time and regular distance is equal to slower time and less distance because of length contraction. Say a person on Earth sees a ship moving towards it. This reference frame has regular time and regular length and it views the ship's reference frame as having slower...

What affect does the phenomenon of "length contraction" have on the shape (e.g. spherical, rugby ball, barbell, donut) of protons accelerated to 0.999999991 c in the LHC?

Hello, I do not fully understand nature of Lorentz contraction. Is it bona fide effect or not? https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment The article says: “This allows a more elegant and intuitive explanation of the Michelson-Morley null result. In a comoving frame...

Hello! If we have a 1m stick (as measured in its stationary reference frame, call it S) and we (S') move with a high enough velocity, we can make the length of the stick in our frame as small as we want. So for high enough velocities, the stick will appear so small in our frame, S', that it will...

You and two identical spaceships are all at rest with respect to each other. You note that the two engines start up at the same time, and the thrust curve and acceleration profile of both spaceships are identical. As the ships pick up speed, would you measure the ships to be shorter than their...

Hi all, I'm doing undergraduate research this summer, and a few times I've been told to calculate a term with the following form: ∈abcdpaqbkcsd, where p,q,k and s are four vectors (four-momentum, spin, etc). Now I know this ends up calculating exactly like a 4x4 determinant, I'm just not quite...

Homework Statement The proper length of spaceship A is 60.0m and the proper length of spaceship B is 120.0m. The proper mass of spaceship A is 15000 kg. An observer on Earth watches the two spaceships fly past at a constant speed and determines that they have the same length. If the speed of...

Hi, I was browsing the internet for interactive simulations illustrating special relativity concepts. It seems to me that those in this http://kcvs.ca/concrete/visualizations/special-relativity are mostly nice and clear, although not very "chrome-friendly" (I have to use firefox to play their...

Does space contract when one observes the space from the frame which is moving with relativistic velocity?

1. Homework Statement Why does the non-relative simultaneous frame have an additional term of ##v \Delta t## along with the contracted length ## L ## for ## \Delta x ##? 2. Homework Equations ## L + v \Delta t = \Delta x ## ---- (1) ## \Delta x = \gamma \Delta x' = \gamma L_{\star} ## ----...

I'm reading Weinberg's QFT volume 1. At the end of section 2.4 he is deriving the Inonu-Wigner contraction where he reduces the Poincaré group to the Euclidean one by taking the low velocity limit. In analyzing how the operators depend on velocity there are some I understand and some I don't. I...

Hey! :o We have the function $f(x)=x^5-\frac{5}{16}$. I have approximated the root of that function using three steps of Newton's method with initla value $x_0=\frac{1}{2}$ : \begin{align*}x_1&=x_0-\frac{f(x_0)}{f'(x_0)}\approx \frac{7}{5} \\ x_2&=x_1-\frac{f(x_1)}{f'(x_1)} \approx...

Homework Statement Find the length of a meter stick if in the laboratory frame it is angled at 60 degrees relative to the direction of motion, and it is traveling at .8 c. I have calculated gamma to be 1.667 Homework Equations Lorentz transformations The Attempt at a Solution a' = l' cos(x)...

In special relativity, an object moving at higher speed experiences time dilation, length contraction, and mass increase, compared to an object moving at slower speed. In general relativity, for an object in stronger gravitational field (i.e., with higher acceleration due to gravity), time runs...

Homework Statement A graduate student discovers that an elementary particle produced in his experiment travels 0.250 mm through the lab at a speed of 0.950c before it decays (becomes another particle). What is the lifetime of the particle measured in its rest frame (proper lifetime). A) 8.77 x...

Hello I am new here and I am just Junior college student. So please use simpler terms. I need to know that does relativity work for mediums like air and water. I mean the equations of time dilation and length contraction, do they work for other mediums. If so shall I take C as the speed of light...

Does the “space twin” benefit from length contraction as well as time dilation? In Einstein’s thought experiment, let one of twins travel to a galaxy known to be 10 light years from Earth at a speed of sixty percent of light speed (0.6c). Were it not for time dilation the one-way trip would...

Homework Statement Explain how it is possible to perform a contraction of the tensor ##T^{\beta \gamma}_{\delta \epsilon}## in order to produce a scalar T Homework EquationsThe Attempt at a Solution $$T^{\beta \gamma}_{\delta \epsilon}T_{\beta \gamma}^{\delta \epsilon}=T$$ Not sure if that is...

When a test charge stands next to a wire, there are coulomb forces between the test charge and the protons of the wire. 1: When the test charge starts to move, the Coulomb forces stays the same, because distances from test charge to protons stay the same. There is no magnetism in this case...

Hi people, me bother yo again! I understand that relativity theory length contraction is the explanation of magnetics fields. See the image: https://dl.dropboxusercontent.com/s/vuy69jhig3kni3n/densidadcargasencorriente.jpg?dl=0 1) In the S system, if q is moving at the same velocity than the...

Homework Statement Anna and Bob are both born just as Anna's spaceship passes Earth at 0.9c. According to Bob on Earth, Planet Z is a fixed 30 ly away. As Anna passes Planet Z on her continuing outward journey, what will be (a) Bob's age according to Bob, (b) Bob's age according to Anna, (c)...

Hi Is this analysis right A spaceship is traveling at a steady speed V in the direction shown. Inside the spaceship is a simple clock of length L and consisting of a light source at “a” and a mirror at “b”. The light leaves “a”, bounces off the mirror at “b” and goes back to “a”, which counts...

Homework Statement I've been given the Bianchi identity in the form ##\nabla _{\kappa} R^{\mu}_{\nu\rho\sigma} + \nabla _{\rho} R^{\mu}_{\nu\sigma \kappa} + \nabla _{\sigma} R^{\mu}_{\nu\kappa\rho} =0##Homework EquationsThe Attempt at a Solution In order to get from this to the Einstein...

Suppose we have a spinning disk with a very fast spin, an observer in the center, and an observer on the edge. Suppose that the observer on the edge measures the circumference of the spinning disk. (1) Now, the observer on the edge at a given instant will be moving at a faster speed than the...

I've heard that Planck length is the smallest length ever! but if something that his length is equal to Planck length and moving by speed dv which is infinitesimal change in speed or higher than that , then according to special relativity his length must be equal to L'=L \sqrt1-v^2/c^2 which...