Length contraction Definition and 477 Threads

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. C

    Exploring Quantum Mechanics and Length Contraction

    What if I had a double slit setup and I was shooting electrons through them. But in the rest frame the slits were to big to bring out the diffraction effect. But then suppose I move by the 2 slits at significant speed to length contract the slits to where diffraction would be eminent. Would...
  2. N

    Why does length contraction happen only in the direction of motion?

    Length contraction happens only in direction of motion. Never perpendicular to the motion. My questions are 1) Why is it so?. For an observer in the same frame, it would mean a meter scale to give 2 different results. If by some means he is able to calculate the difference won't he be able to...
  3. I

    How Does Relativistic Speed Affect Photon Wavelength Measurement?

    Homework Statement Spaceship Enterprise fires a photon torpedo at an approaching Klingon ship that has just decloaked. If the wavelength of this light beam as measured on the Enterprise is 616 nm what is the wavelength (in nm) as measured by the Klingon ship if the relative speed between the...
  4. A

    Could Non-Linear Length Contraction Resolve Relativity Paradoxes?

    hey forum, first of all, I'm a high school kid so forgive me if this is stupid. I've been thinking about relativity for some time now, and the issue with simultaneity. Einstein proposed that length contracts as you approach the speed of light. Assume for a second that a train is going...
  5. F

    Einstein's Length Contraction A problem?

    Hello, I hope you can help with my question! I am a 27 year old amateur theoretical physicist about to start a bachelor's degree in physics as a mature student... I have just been going over some bits of Einstein's theory of Special Relativity and have noticed something odd that has confused...
  6. S

    Time dilation and length contraction problem

    Homework Statement Anna is on a railroad flatcar moving at 0.6c relative to Bob. Her arm is outstretched in the dirction the flatcar moves, and in her hand is a flashbulb. According to her wristwatch, the bulb goes off at 100 ns. This even according to Bob differs by 27 ns. a) is it earlier...
  7. K

    Time dilation and length contraction in hyperbolically-curved spacetime

    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...
  8. T

    Combining time dilation and length contraction

    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...
  9. mrspeedybob

    Length contraction and the expansion of the universe.

    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...
  10. M

    Question on Michelson Morley experiment and length contraction

    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...
  11. S

    Is length contraction an actual occurrence or merely an optical illusion?

    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...
  12. S

    Calculating Velocity Using Length Contraction Formula in Relativity Theory

    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...
  13. U

    Length Contraction: Measuring Circumference of Moving Circle

    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...
  14. R

    Length Contraction of the Universe Surpassing Length of Moving Object?

    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...
  15. V

    Length Contraction and Time Dilation

    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...
  16. J

    Equations for length contraction

    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}...
  17. D

    Deriving Length Contraction From Lorentz Transform

    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...
  18. R

    Time dilation & length contraction

    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...
  19. M

    Why Does Griffiths Use Two Directions of Light in His Length Contraction Proof?

    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...
  20. M

    Length Contraction causes Time Dilation?

    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...
  21. A

    How does the length contraction work for proper length?

    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...
  22. G

    Specific relativity Length Contraction and Time dialation question

    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...
  23. N

    Time dilation and length contraction

    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...
  24. W

    Time Dilation: Does Length Contraction Apply?

    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...
  25. R

    Can Length Contraction be Proven Experimentally?

    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).
  26. P

    Length Contraction: Need Help Understanding Lorentz Transformation

    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...
  27. M

    Length contraction (no calculations)

    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...
  28. E

    Special Relativity - Time Dilation and Length Contraction

    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...
  29. A

    Deriving length contraction using Lorentz invariants

    Homework Statement Derive length contraction using Lorentz invariants. Homework Equations ds^2 = dx^2 +dy^2 + dz^2 - c^2 dt^2 The Attempt at a Solution Consider a rod parallel to the x-axis and moving with velocity v in the x-direction. We can measure the length of the rod of...
  30. K

    Time Dilation Vs. Length Contraction

    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...
  31. I

    Length contraction, light speed and a bomb

    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...
  32. E

    SR length contraction question

    A rod moves along x-axis with speed u and has length L relative to Inertial Frame S. What is its length L' relative to the other inertial S' that moves with speed v with respect to S. I know the famous length contraction formula L=L' * sqrt(1-square(v/c)) but I confuse how to include...
  33. T

    Question about length contraction

    When a moving observer views a stationary meter stick, it appears contracted. The stationary observer measures it at full length. Similarly, the stationary observer views a moving meter stick as contracted, and the moving observer views it as full length. This is conventional relativity. When a...
  34. A

    Help with time dilation and length contraction

    Homework Statement How fast must a pion be moving on average to travel 25 meters before it decays? The average lifetime, at rest, is 2.6 x 10-8s. Homework Equations \Deltat =\Deltat0/ sqrt(1 - v2/ c2) l = l0 * sqrt (1 - v2/ c2) The Attempt at a Solution I think that 2.6 x...
  35. mrspeedybob

    How would this experiment play out? Length contraction / black hole

    Bob, Ed, and Sussie are all observers, each in their own space-ship. Ed and Sussie accelerate on parallel paths to very near the speed of light. Bob sees both length contraction and an increase in mass of both Eds and Sussies ships. These effects are great enough that each ship achieves the mass...
  36. E

    Special Relativity, Length Contraction

    Homework Statement As a rocket ship moves by at 0.95c a mark is made on a stationary axis at the front end of the rocket and 9 × 10^−8 s later a mark is made on the axis at the back end. The marks are found to be 100 m apart. The rest length of the rocket is: A. 31m B. 78m C. 100m D...
  37. G

    Length Contraction Relativity Question

    Hello, I am not sure if I am doing this right or not. It seems to simple to be the right aswer, I feel I must have gone wrong somewhere. Many thanks :-) xxx Homework Statement Length Contraction Relativity Question? An aeroplane is of length L’(m) precisely when measured in its rest...
  38. N

    Exploring Einstein's Relativity: Length Contraction

    Hello, I was reading Einstein's RELATIVITY (his non-mathematical 1916 (or so) book). Having shown the Lorentz transformation formulas, i.e. t' = \gamma( t - vx/c^2) x' = \gamma(x - vt), he then talks about length contraction. He takes a meter-rod fixed in a certain coordinate system S'...
  39. W

    Special relativity and length contraction

    Homework Statement Consider a universe in which the speed of light c is equal to 100 mi/h. A lincoln continental traveling at a speed v relative to a fixed radar speed trap overtakes a Volkswagen traveling at the speed limit of 50 mi/h. The lincoln's speed is such that its length, as...
  40. T

    Time dilation or length contraction

    Hi, i asked some quesitons about this before but i need a clarification. Generally we use vertical light clocks and compare the distances taken by light and since c is constant the longer path taken by the light means a dilation in time, from here we say every other type of clcok dilates in same...
  41. B

    Length Contraction Explained Simply

    I'm having a hard time understanding length contraction. can anyone explain it to me in simple terms?
  42. R

    Length Contraction and Relativity: Muon Velocity & Gamma Factor

    http://cas.web.cern.ch/cas/Baden/PDF/Relativity.pdf on pg 16, it says that a muon traveling at a relativistic velocity towards Earth would see the distance to Earth shorted by the gamma factor... i thought the length of the muon is all that is shortened by the factor of gamma? am i wrong here? :s
  43. Y

    Question about length contraction (geometric way)

    I'm doing some independent study with a professor at my university. He has taken one GR class and he said that it was not a good experience. So we are in a sense learning together as we pursue this. We are using the book "A First Course in General Relativity" by Schultz. We are doing problem...
  44. P

    Relativity - Length Contraction

    Homework Statement A spaceship flies past a space station at 0.75c. Observers on the station measure the length of the ship to be 0.30 km. If the ship later docks alongside the station and its length is measured, what would this measured value be? Homework Equations d=d0/\gamma The...
  45. J

    Quick question - has length contraction actually been experimentally confirmed?

    Hi, I am aware that time dilation has been observed experimentally with atomic clocks on satellites etc. but after a few google searches I have not found anything about experimental confirmation of length contraction. Has this been observed at all? If so, how was it tested? thanks.
  46. C

    Length contraction and rod falling thorough a grate ?

    If i have a rod of length L at rest . And there is a hole up ahead that is L/2 and I move the rod at a velocity which will contract it to half its rest length. Will the rod fall into the grate? Well I think that from the rods point of view its still its rest length and it would appear...
  47. F

    Relativity length contraction problem

    Homework Statement A meter stick moves with speed .8c relative to frame S. What is the length observed by a person in frame S if the stick is 60 degrees to v, as measured in S? Homework Equations L=observed length l=proper length y=1/sqrt(1-B^2) L=l/yThe Attempt at a Solution Sorry, I suck at...
  48. V

    Length Contraction Euclidean Space

    Hi, Suppose a stationary frame S' is observing frame S moving with velocity v=0.866c in the x-direction, and let points (4,0),(10,0) define the ends of a rod in S, so its distance is 6, but as measured from S' contracts to 3 because of the Lorentz factor gamma. I'm unable to determine...
  49. R

    Quick length contraction question please

    Assuming 300,000 km/sec for c; I am in a spaceship which is 300 meters long traveling at 0.5c. A beam of light passes me and I want to measure how long it took to travel the length of my ship. As c is the same in all frames of reference, I would work this out as distance (300 m) divided by...
  50. S

    The Empire Strikes Back length contraction.

    Homework Statement The starships of the Solar Federation are marked with the symbol of the Federation, a circle, whereas starships of the Denebian Empire are marked with the Empire's symbol, an ellipse whose major axis is n times its minor axis (a=nb in the figure ). Homework Equations...
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