# What is Lorentz contraction: Definition and 82 Discussions

Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. It is also known as Lorentz contraction or Lorentz–FitzGerald contraction (after Hendrik Lorentz and George Francis FitzGerald) and is usually only noticeable at a substantial fraction of the speed of light. Length contraction is only in the direction in which the body is travelling. For standard objects, this effect is negligible at everyday speeds, and can be ignored for all regular purposes, only becoming significant as the object approaches the speed of light relative to the observer.

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1. ### Confused by Lorentz transformation equation

TL;DR Summary: Solving a problem regarding a train going past a station using length contraction and the Lorentzian transformation. I'll dive straight in. I encountered a problem where there is a train travelling at 0.6c going past a station, length 500 m when measured by an observer at rest...
2. ### I Lorentz Contraction & Twin Paradox

The twin paradox is connected to the special relativity but I wonder simply if one might construct the paradox (or something very similar) based on the Lorentz’ (and FitzGerald) work alone? Several ingredients in the paradox, time dilation and Lorentz contraction, are often mentioned with...
3. ### I Newton's Gravity & Lorentz Contraction: Is Modification Needed?

Newton's gravity depends on the euclidean distance between two masses. Two comoving frames will have different values of length between masses so the forces will be different in two frames. Is it enough to prove that the gravity rule has to be modified?
4. ### B Why Aren’t ALL SR Effects Cumulative?

Why aren’t all the SR effects cumulative like Time Dilation? Why should the Space dimensional effect become null when v—>0 while the Time dimension does not revert back to the 2 frames being in sync if Space and Time are treated on an equal footing. Clearly, Space and Time are not treated on an...
5. ### Lorentz contraction and Spacetime diagram

Hello, i can't understand how does the author found this expression relating ##x_{c}## and v. I already tried by a lot of geometrical ways, knowing that the tangent of the angle between the dotted line and the x-axis should be v, but the results are illogical. Could you help me? I am start to...
6. ### [Special Relativity] - Finding the Proper Length at Rest in Frame S'

Currently, the only part of the textbook question that is completely throwing me off is "an angle of ##l=\sqrt{2}c##". If I am not mistaken, how am I suppose to interpret that as an angle and calculate for the answers of (a) and (b) accordingly? As for my attempted solution process of this...
7. ### I Does the expanding Universe follow Lorentz contraction?

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...
8. ### B Question About Lorentz Contraction: Red vs Blue?

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...
9. ### I Solving Lorentz Contraction Question: What went Wrong?

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'...
10. ### I Difference between an electromagnetic field and a photon?

So I'm kind of confused. The way I understand it, an electromagnetic field is just a regular electric field viewed from a relativistic point of view, meaning that since we see the charges moving relative to us, we feel like the particles and the fields created by them come closer together (I...
11. ### B Is Lorentz Contraction Bona Fide or Just A "Perspective"?

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...
12. ### B Planck Length and Lorentz Contraction

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...
13. ### [SR] Relativistic runner and two relativistinc trains....

Homework Statement A train of length L moves at speed 4c/5 eastward, and a train of length 3L moves at speed 3c/5 westward. How fast must someone run along the ground if he is to coincide with both the fronts-passing-each-other and backs-passingeach-other events? Homework Equations Velocity...
14. ### B Muon Time Dilation: Earth vs Muon Perspective

From the reference frame of the earth, the distance between the surface of the Earth and the muon is longer, but the muon survives because time for the muon is slowed down. From the reference frame of the muon, the time experienced by the muon is not slowed down but the muon survives because...
15. ### I Relativity Paradox w/ Charged Spheres

There is a similar thought experiment I imagined to help me begin to understand the Bell's spaceship paradox: Consider two positively charged spheres, placed side-by-side inside a frame S' with a string stretched to the point where it balances the repulsive electrostatic force between them. For...
16. ### B Entangled particles and lorentz contraction?

can lorentz contraction be measured via quantum entanglement with one of the entangled particles moving near the speed of light? would the particle in motion be affected by lorentz contraction? if so, would the particle at rest follow suit and appear affected?
17. ### I Symmetry of Liénard-Wiechert Potentials

According to responses at: http://physics.stackexchange.com/questions/93390/field-of-moving-charge-lorentzlienard-wiechert The Lorentz contraction of the electric field of a charge with uniform velocity is supposed to be symmetric across the plane pi/2 radians from the velocity vector of the...
18. ### B Is Lorentz contraction explained by space time diagram ?

Is there a way to explain Lorentz contraction on space-time diagrams ? I cannot find a way by myself. Your teaching will be appreciated.
19. ### I Lorentz derivation of length contraction in electrodynamics

Here is a quote from this website: My question is: is this derivation of length contraction considered to be sound and correct today? Are they treated in modern textbooks?
20. ### I Subbing Planck length into length contraction equation?

I was wondering if it is possible to work out the maximum amount of energy an object with mass can have using the length contraction equation (i.e. "actual" length divided by Lorentz factor). The way I thought of doing this was by rearranging e = mc^2 to get c^2 = e/m. Then, substitute e/m into...
21. ### I Why Can't Lorentz Boosts be Used for Length Contraction?

Let's say you have a rod that is 10 meters long. Observer O sees the ends of the rod at (t=0, x=0), and (t=0, x=10). Observer O' moves at speed v = 0.8c relative to O. What is the length of the rod in O's perspective? Using the length contraction formula L' = γL, we find that O' sees the rod as...
22. ### I Length contraction: Is it permanent?

Lorentz contraction problem: By Bertrand Boucquillon Components of the problem: - Bob (observer) - 2 identical rods that both measure 1 meter. Let's call them rod X and rod Y - Point A - Point B Scenario (step by step): 1) Bob is at point A, and is at rest with both rods in his hands 2) Bob...
23. ### Is Lorentz Contraction Specious for Photon Traversal Time?

bcrowell wrote: "Lorentz contraction doesn't describe what we see. When we see things, that's an optical measurement. Relativistic optics is a whole separate subject. Lorentz contraction describes the results of the kind of elaborate surveying process that we have to undertake in order to lay...
24. ### Derive Lorentz Transformations w/ Special Relativity

Hope this derivation helps someone!
25. ### Relativistic motion of the bullet

1. A distant camera is taking an image of a bullet of proper length l_0 and velocity v. The bullet is moving on a straight line which is parallel to the ruler (a bit behind the bullet, when it is watched from the camera). An angle between the velocity vector and the line that connects the camera...
26. ### Length contraction at an angle

Hi, My question concerns the following problem from chapter 4 of Special Relativity by A.P. French. A statement of the problem: 4-15 A flash of light is emitted at point O and is later reabsorbed at point P. In frame S, the line OP has a length l and makes an angle θ with the x axis. In a...
27. ### Lorentz Contraction: How Fast Can Objects Travel?

I just got to know about this concept, "Lorentz contraction". It says The size(measure) of objects decrease as we approach the speed of light(I think, I'm right!). If this is true, then the size of our sun should be slightly smaller, as the Earth races around the sun, at a speed of one-tenth of...
28. ### How To Understand This Lorentz Transform?

Prof Ramamurti Shankar has this Youtube video 'Introduction to Relativity' at And in it he derives the Lorentz Transforms something like this, at about 58 minutes into it. |------------------------- t ----------------------| time |-----ut---------------|---------- x' -------------|...
29. ### Rindler Horizon and Lorentz contraction

Hello, Onhttp://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html website it says in the section "below the rocket, something strange is happening" that the distance of an object which passes the accelerating observer never increases -c2/α. I think this means, that the Rindler Horizon...
30. ### Lorentz Contraction and Energy

I already know the solution to this problem, but I'm not sure exactly why it works out the way it does, so I'm looking for an explanation. Homework Statement A particle accelerator accelerates electrons at 40 GeV in a pipe 2 miles (3218.69 metres) long, but only a few cm wide. How long is the...
31. ### Lorentz contraction and Time dilation (Special relativity)

A quick question. It's been a long time since I had anything to do with special relativity, so I really can't remember much. But last night I was thinking about the "proof" of special relativity with the case of muons. So basically: Muons are created when particles hit the atmosphere. They...
32. ### Deriving Lorentz contraction from Michelson-Morley experiment

In order for the light to take the same amount of time for both paths in the interferometer, simple geometry implies that the ratio between length and width will have to decrease. A straightforward derivation gives L/W=Sqrt(1-v^2/c^2) where the velocity v is in the direction of the length...
33. ### Problem analyzing rod-slot 2-D Lorentz contraction paradox

I have encountered a difficulty which arises from my attempt to combine non collinear Lorentz transformations in analyzing the following problem: A thin rod is cut from a metal plate leaving a slot of exactly the same size. The two are separated and set in motion thus: the rod lies along x...
34. ### Lorentz contraction in circular particle accelerators

My question is essentially a variation of the Ehrenfest paradox in SR. But hopefully with some experimental data. In the LHC, for example, a fixed number of particle bunches with some length are injected into the main ring. Now, as the velocity of the particles increases, the bunches would be...
35. ### Detailed working out Lorentz contraction from the Lorentz transform

We have a few posters struggling with this, I thought I'd post a step by step guide, to see if it would help. That seems easier than trying to untangle the confused threads we have. We'll see if it works... Setup and notation: We have a rocket, which has a front and a back. We have a...
36. ### Franklin, Lorentz contraction, Bell's spaceships, and

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...
37. ### Lorentz Contraction of Moving Line of Charge

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...
38. ### Lorentz Contraction ?s and Implication

Unfortunately, my knowledge on this is limited to wiki which I trust is relatively correct but I would like to clear up some ambiguity. (I don't mind technical but please back it up with a general explanation since I am completely new to this. The general explanations I value more.) Wiki...
39. ### Lorentz contraction in the Quantum realm

Special Relativity states that a ruler flying by at near the speed of light will appear to be shortened as observed by a stationary observer in the lab frame. This is, of course, exactly what happens to macroscopic objects. The question is how far can we push this into microscopic realm...
40. ### De broglie wavelength and lorentz contraction

Am I correct in thinking that the quantum mechanical de broglie wavelength explains relativity's contraction of matter? because lambda = h/p, as the velocity of say a proton increases, the momentum also increases, and the wavelength should get smaller because lim p-->infinity of h/p = 0. At very...
41. ### Lorentz contraction and gravitational field

Here's a scenario: A rod shaped object 1m in diameter and 300m in length is moving through space at a velocity of .999994444429013c (picked that velocity arbitrarily for the 300:1 length contraction). The Lorentz factor is 300 for this problem. So the equation to figure length contraction is...
42. ### Hypothetical implication of Lorentz contraction

Would it be possible for a truck, measuring 5ft tall when stationary, to pass under a 4ft barrier by accelerating towards the speed of light? If so what would a spectator see if standing next to the barrier, would the spectator see the truck shrink? What would you see of the barrier from the...
43. ### Question on Lorentz contraction and size of pancakes

Question on Lorentz contraction and size of "pancakes" I have read that nucleons (protons in particular) appear to look like flattened "pancakes" hitting each other due to the lorentz contraction when crashed together at high speeds. Do any of the colliders give a hint at the "size" of the...
44. ### Lorentz Contraction: Gaining Mass & Shrinking

Hi all, modern physics student here. If the Lorentz contraction occurs at relativistic speeds, how does it gain mass yet get shorter? The best I can think of is that it has to depend in which reference frame one is in at the time. Does anyone know any useful links where I can read about this?
45. ### Lorentz Contraction/ Simultan Problem

Hi all, this is not a HW problem but one I made up myself, (so you won't find it in any txtbooks or solutions etc.). It also is much more advanced than for someone on the physics HW site, as I can see, so I thought it best to put here. I'm having trouble working out simultaneity and Lorentz...
46. ### Relativity (lorentz contraction)

Homework Statement As measured by an observer on earth, a spacecraft runway has a length of 3.6km. What is the length of the runway as measured by the pilot of a spacecraft flying directly over the runway at a speed 4.00 x10^7 m/s relative to the earth?Homework Equations L= Lnot/γThe...
47. ### Lorentz contraction in other dimensions?

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...
48. ### Terrell Revisited: The Invisibility of the Lorentz Contraction

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 Terrell's Argument Both of these are important issues to take into account. However, they do...
49. ### Lorentz Contraction Physical Reality

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...
50. ### What would actually be observed during Lorentz contraction?

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...