What is Length contraction: Definition and 475 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. F

    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. H

    I What causes time dilation and length contraction

    This Video [Moderator's note: Unacceptable Reference removed] right here is describing a way of understanding SRs time dilation and length contraction. He tries to explain the phenomena with aether theory and argues that light does not have/is in a preferred frame of reference. So some context...
  3. C

    I Space travel question -- Does SR length contraction imply the travel time is half?

    Hello everyone, I've been learning about length contraction and started to ponder how it applies to space travel. If the Lorentz factor is 2 by traveling at .577c does that mean you would be able to get to the object in half the distance because the transformed length in your reference frame...
  4. C

    I Question about length contraction

    Hello everyone! I was researching about time dilation and I feel I have a pretty good understanding of it its very cool and fascinating, but my understanding of length contraction is fuzzy. It's not so clear why to me length contraction only happens in the direction of motion. If there is a...
  5. S

    B Does shortness from length contraction have a real physical effect?

    Do the contractions affect physics in any frame? Examples: If length contraction reduces mass in the direction of motion, and therefore reduces the total momentum. (from observer's perspective) If in the reference frame of a station, the moving train weighs less than it did when parked...
  6. Z

    I How many meter sticks are there in this length contraction reasoning?

    I have a question about the concept of length contraction. The black line from (0, 0) to (1, 0) represents a meter stick in my stationary frame, call it frame A. The blue axes represent my coordinate system with coordinates x and t. The green axes represent the coordinate system of a moving...
  7. substitute materials

    I Asymmetry in Length contraction?

    Instead of a twin paradox, let’s just consider an inbound starship approaching Earth at relativistic speed. The traveler is on a flyby mission, he will never change speed or direction. We will disagree with the traveler on how much time will have elapsed when he passes Earth. The discrepancy can...
  8. S

    B Why does length contraction occur and how does it relate to time dilation?

    Was learning about length contraction of muons that rain down from cosmic particles colliding in our upper atmosphere, and how the distance for the muon is shorter than we measure. But looking up any further info, found a number of sources describing how the muon's own length is contracting...
  9. H

    B Length Contraction: Apple Hanging from Tree & Earth

    Hello. Apologies, if this is already answered in other threads. Please redirect me, if that is the case. Imagine an apple hanging from a tree. Will there be length contraction between the apple and the earth in the frame of reference of the earth, as well as of the apple? All the best, Henrik
  10. N

    I Calculate Length Contraction for Accelerated Motion to Proxima Centauri

    Let's assume a spaceship traveling from the Earth to the Proxima Centauri with constant acceleration g = 9.81 m/s2. The ship is accelerating the first half of the trajectory and decelerating the second half. I calculated the velocity profile from the Earth reference: The travel time on...
  11. M

    B Length Contraction: Exploring the Possibility of Black Holes at High Speeds

    If I am traveling in my spacecraft at .99999999 percent the speed of light past a star, then according to the equation of length contraction a star with 4x or more solar mass would contract along the line of motion according to my frame of reference by an amount of over Length naught (8*10-E)...
  12. T

    I Time Dilation & Length Contraction: Graphically Explained

    The thread "twin paradox without math" inspired me try to find fully graphical solution of length contraction. Here is the result: Graph is 3D as I think that is ilustrative to make all in one graph, but I am sure that it is possible to do it in 2 or 3 2D slices. X and Y are spatial axes, T is...
  13. L

    I Relativistic length contraction

    Hello! I have a question. If there is a wooden rod which burns certain time, and an astronaut inside rocket lights two such rods: one oriented along the rocket's length and the other goes across the rocket, and an observer see the rocket passing by with a relativistic speed. Will the observer...
  14. S

    I An issue with length contraction

    I have read that length contraction is real and not just an illusion. However, when I compare an object at rest with an observer and the object in motion relative to another observer, I see that instead of there being a real length contraction, there is simply a difference in the part of the...
  15. E

    I Time difference caused by length contraction

    The goal is to calculate the difference in the passage of time between two ends of a cabin which is accelerating upwards due to length contraction. To help in the calculations we can consult: https://arxiv.org/pdf/1807.05338.pdf There is an old problem called the 4/3 problem which has been...
  16. DavidBalut

    I The Theoretical Minimum: Length Contraction and Time Dilation

    Hello, My name is Dave and I'm a physics major at UIUC. It looks like I will be taking the special relativity course (phys 225) this fall. I've always been fascinated by the theory so I decided to get a head start with Lenny and Art's perspective on it. My first head-scratching moment came in...
  17. Gamma Anon

    I Is the Killer Crate Paradox Resolved?

    Hi Physics Forums, I've devised a thought experiment called the "Killer Crate Paradox" to put a spotlight on an issue I'm having, with regards to understanding length contraction, specifically in instances where multiple objects are observable and they have different velocities and directions...
  18. K

    I Length contraction in General Relativity

    In GR, a free falling object when viewed by a distant observer appears to be length contracted and slows down as it approaches the event horizon of a black hole. The length contraction piece, however, seems counterintuitive. I would have thought that the leading edge of the object would...
  19. PainterGuy

    Time dilation and length contraction for a rocket

    Hi, It's not a homework but still thought to post it here as advised in the past. A rocket is going to leave Earth's surface and it is decided that a data pulse encoding emission time of pulse will be sent every second from Earth station to the rocket, and the rocket would do the same. The...
  20. wnvl2

    I Relativity paradox: rocket landing in a cylinder

    A rocket has length L with a separate head on top. The rocket lands in a cilinder on Earth with height L with speed v. From the point of view of the rocket, the cylinder undergoes a Lorentz contraction. The rocket will therefore collide with the bottom of the cilinder and damage it. From the...
  21. guyvsdcsniper

    B Check my understanding of Time Dilation and Length Contraction

    I just started learning about Special Relativity and have come upon the topics of Time dilation and Length contraction. Its a bit abstract for me and I just want to cross ref my knowledge here and see if someone can tell me if I am understanding this correctly. I've attached an excerpt of a...
  22. alexandrinushka

    B Any plausible explanation for dynamical length contraction?

    I am new here, so pardon my ignorance. First of all, I am aware of the impossibility to distinguish experimentally between SR (Special Relativity) and LET (Lorentz Ether Theory). I know there is a PF policy article on LET and the Block Universe. I must admit though that LET is more appealing...
  23. S

    I Because of length contraction, does absolute position exist?

    I know that I have heard that GR proves that there is no absolute time, so does this go for location too? If so, could it be said that particles have a superposition in position/location the same way that particles do in QM?
  24. O

    I Linear Accelerator Length Contraction

    I am trying to understand the effect of relativistic length contraction on the electron bunches in a linear accelerator. Figure B is for nonrelativistic speeds, successive cylinder lengths are progressively longer. However, wikipedia says "At speeds near the speed of light, the incremental...
  25. alan123hk

    B The Paradox of Relativity Length Contraction

    A rigid rod with length ## l_0## slides on a smooth and flat tabletop along the length at speed of ## ~\frac {\sqrt{3}}{2}c~ ##, there is a hole of width ##~l_0~##on the table. The observer who is stationary relative to the desktop thinks that the length of the rigid rod ##~ l=l_o...
  26. S

    B Is length contraction (Lorentz transformation) an illusion or real?

    My textbook (from first year university physics) says that length contraction is actually real. But how can it be real when two different observers can measure two different lengths? For example, if I am in a spaceship going close to the speed of light relative to people on Earth, they will...
  27. M

    B Distance Length Contraction at Light Speed

    I know it's not possible to travel at light speed so this is just theoretical. As I understand it at relativistic speeds the distance you need to cover to travel to a destination are length contracted. If you were traveling at light speed is the distance between you and any object ever zero?
  28. P

    Question on special relativity from "Basic Relativity"

    Summary:: Require confirmation regarding answers to a question posed by the book "Basic Relativity" by Richard A. Mould. Here is a problem which I encountered while going through Basic Relativity by Richard A. Mould- I'd like to receive a confirmation regarding the answers I've come up with to...
  29. U

    Rotation of a photograph of an object due to relativity

    I came across an interesting question in the Hartle's textbook, "An Introduction to Eisntein's General Relativity". The question is as follows: Explain why a photograph of an object moving uniformly with a speed approaching the speed of light, parallel to the plane of the film appears not...
  30. O

    I Compute Length Contraction: Is ##l=1## a Possible Model?

    Sorry, I accidentally posted this while typing it up, then when I finished typing it I found the mistake that made me come here to make this thread. I'll still write it up just to make the thread somewhat useful, and then ask my follow-up question at the end I'm picking units so the speed of...
  31. R

    I Length contraction and time dilation

    A long time ago, I was very impressed by a lecture on elementary special relativity which showed in simple math how the correct conclusion to the null results of the Michelson-Morley experiment were obtained by concluding a constant c but then adding a length contraction and time dilation. I...
  32. Kaguro

    Deriving length contraction using spacetime

    Deriving time dilation was easy: Imagine two events in frame O' at the same location. ##ds^2 = -c^2 dt'^2## The same viewed in O frame is: ##ds^2 = dx^2+dy^2 + dz^2 - c^2 dt^2## ##\Rightarrow dx^2+dy^2 + dz^2 - c^2 dt^2 = -c^2 dt'^2## ##\Rightarrow (\frac{dx}{dt})^2+(\frac{dy}{dt})^2+...
  33. greg_rack

    Special relativity (length contraction, velocity composition) problem

    First, I calculated the velocity of the object with regards to earth, which is: $$v'=\frac{V-v}{1-\frac{vV}{c^2}}=0.34c$$ Now, the problem is solved if I consider the length ##l=45m##(so by calculating the ##\gamma## factor with ##v'##) to be the proper one... but since it's measured by the...
  34. D.S.Beyer

    B SR vs GR - Visual Difference between Length Contraction

    The 2 Bowling Balls Ball(a) & Ball(b) (a) is in acceleration of 10m/s^2 (b) is in at fixed position in a gravitational field where g=10m/s^2 In both cases the observer is: - perpendicular to the vector of acceleration - distant enough to be in empty flat space Question : In an instantaneous...
  35. bq1892

    Describe the length of an electron's journey in its own frame of reference

    Lv = Lo / γ 1/γ =√(1-v^2/c^2) = √(1-0.8^2) = 0.6 Therefore Lv = Lo x 0.6 = 150 x 0.6 = 90m Therefore electron travels 90m in its own frame of reference (answer key solution) However, shouldn't the electron be assigned rest length, Lo, as its frame of reference is at rest with itself instead...
  36. Atstill77

    B Why do you need a light clock?

    what is wrong with the thought experiment below?! If I consider a light beam going straight towards an observer in motion it makes it look the moving clock ticks faster, but if you use a light clock it makes it look like the clock turns slower. What am I missing here? “Two observers convene in...
  37. J

    B Experimental Confirmation Length Contraction Velocity Addition

    What if any is the experimental confirmation for length contraction and the velocity addition formula?
  38. U

    I Length Contraction & Time Dilation: Proving It

    I have been able to prove to myself that, based on Einstein's two postulates and the the Pythagorean theorem, that time dilates. From here how do I prove that length contracts? (All of this observing a frame that is moving relative to the proper frame at uniform velocity.)
  39. T

    B On time dilation and length contraction

    Hello there.About time dilation, could we provide a derivative of time in relation to one of the coordinates of the manifold we have taking time as a function and get something as a result?Or its integral?And about time dilation we have the formula that gives it between two clocks and an...
  40. S

    B Light Clock & Length Contraction in GR

    Hi, can i use a light clock made out of mirrors a distance appart to measure whether there is length contraction in different regions of spacetime? If the clock speeds up then the distance between the mirrors decreased. If the clock slows down the distance between mirrors increased.
  41. X

    B Time Dilation & Length Contraction: Physics Explained

    So basically i know almost nothing about physics but i have this one curiosity and i hope you can help me ahah. For what i understand if you could move at the speed of light time would stop for you and you would see the whole universe age in a blink of an eye. But what if you could stand...
  42. Stephen Bulking

    Length contraction and Time dilation for LIGHT?

    Radio wave travels at the speed of light 3x10^8 (m/s) Converting the distance to meter: 1.3 x 3.1x 10^16 = 4.03x10^16m The time it takes in our Earth frame of reference is: 4.03x10^16m/3x10^8 (m/s) = 4.26 years The answer is B But wouldn't the time in light's frame of reference be 0 and it's...
  43. Flying_Dutchman

    I Length Contraction: Traveling in a Space Ship

    Suppose I'm traveling inside a spaceship at speed comparable to light between two points A and B. According to me the distance between the two points will be shortened due to length contraction. But actually my spaceship passes through every point between A and B so the distance measured by...
  44. P J Strydom

    B Length contraction and Time dilation calculation

    I was absent for a while due to personal constraints but I did keep myself busy with the Time dilation equation some member sent me a while back. I decided to set a time limit for myself to learn and understand time Dilation and length contraction, which must be before December 2020, or I will...
  45. G

    B Length Contraction Thought Experiment: Spot Mistake/Wrong Assumption

    Alice travels in a spaceship, which she measures to be L. The spaceship is moving with velocity v relatively to Bob. Alice makes a light beam traveling along the spaceship and measures the time interval it takes to go from one end to another, ΔtA. So, equation (1): L = c × ΔtA From Bob's...
  46. M

    B Help! Solving Einstein's Length Contraction Problem

    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...
  47. N

    B Clarification on Length Contraction

    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...
  48. B

    I Time Dilation, Length Contraction & Massive Bodies

    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...
  49. S

    B Length Contraction in Accelerated Frame

    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.
  50. RodolfoM

    Relativity - Time between events

    Firstly, I calculated the relative speed between the two rockets, finding v=1.6c/1.64. Then, I applied the length contraction: the length of the moving rocket will be 0.6L due to this phenomena, so the total distance traveled by one rocket, with respect to the the other, will be 1.6L. Therefore...
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