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. S

    Can a pole traveling at 0.88c fit inside a 2 light year long garage?

    before I start, I should say that I'm a layman and as such will probably say something which sounds quite stupid to the rest of you. I will clarify anything that needs clarifying Ok, so we have A - a 2 light year long garage with two doors that can swing open and closed B - a 4 light year...
  2. E

    Electron and positron length contraction q.

    Homework Statement In the stanford linear accelerator, electrons and positrons are fired at each other at 50Gev. In the lab, each electron and positron beam is 1cm long. (a) how long is each bundle in its frame? (b) what is the proper length of the accelerator for a bundle to have both its...
  3. K

    Explaining Length Contraction with the Light Clock Argument

    We're just learning special relativity in class and my lecturer uses the light clock argument (two moving clocks - one parallel and one perpendicular) to explain length contraction. I didn't quite get one thing about it. My notes say the light beam reflects at different times (i.e. they have...
  4. P

    Help about length contraction and spacewarps

    I have two problems that I got confused with and I am not sure if I am doing right Homework Statement 1) The starship ENTERPRISE 1200m long when at rest. How long would it seem to be to someone watching the ship pass by them at 0.75c? Homework Equations length contraction \Delta...
  5. Ookke

    Length contraction compression and Schwarzschild radius

    We could imagine a rod moving fast enough to compress it within its own Schwarzschild radius. Should it collapse into a black hole? Or is the rod's own reference frame, where it isn't compressed, the one that makes decisions here?
  6. E

    SR's Length Contraction and Time Dilation

    If an observer rotates a four dimensional object, the lengths of the object would change to the observer. If that same observer walks backwards, the lengths of the object will also appear to change from his frame. In fact, if either the observer or the object rotates or moves in any way, it will...
  7. P

    Basic question on length contraction.

    good night, this is not actually a homework question, this is just plain curiosity. we've written a basic problem on length contraction and tried to resolve it ourselves. we just want to know if the concept of the problem is right. Homework Statement a body of length L=20m travels...
  8. K

    Is relativistic effect of length contraction physically real ?

    Is relativistic effect of length contraction physically "real"? Is Lorentz contraction a real contraction? For example, if one tries to accelerate a solid body, does its contraction require an extra input of energy to squeeze the atoms of the body closer together? Will this extra energy go into...
  9. F

    In what direction does length contraction occur?

    Consider a train traveling at a relativistic velocity, with three observers. One inside the train, and two outside the train traveling at different velocities with respect to it. Say there is a finish line of sorts at a certain point. All observers will agree when the train reaches the line...
  10. I

    Length Contraction: Calculate Observed Length w/o and w/ Theory of Relativity

    A stick of 1m in length travels at v = 1/2 c along its axis away from the observer. Question 1: Show that the observer perceives the length of the stick to be shorter without theory of relativity. Calculate the length as perceived by him if he calculates it by the difference in length...
  11. F

    Solving the Paradox of Length Contraction on a Train

    There's one of the paradoxes with SR that I've never actually seen an answer for. There is a man on a train traveling at a velocity where length contraction starts to matter. Say, .3c. There are some dirty bandits that have rigged up a trap door system in a mountain up ahead on the tracks...
  12. B

    Length contraction and time dilaton

    Please let me know if length contraction could be derived without using synchronized clocks. Thanks in advance.
  13. A

    How can length contraction of a rod be measured?

    Here is a simple question. How can an observer measure length (or length contraction) of a cylindrical Iron rod, when it is moving with a relative velocity v with respect to the observer? The reason to ask is not to inquire the math about it, but if the rod is moving say in x direction, from...
  14. J

    Another length contraction paradox

    This is similar to the pole and barn paradox, but different enough that I'm not quite confident in my answer: A train and tunnel have the same length when at rest relative to each other. The train approaches the tunnel with constant velocity. An engineer on the train places rockets on the...
  15. Q

    Help: Length Contraction and changing Frames

    [SOLVED] Help: Length Contraction and changing Frames Hi i have been learning about length contraction and i thought i understand how it works until i was given this question. A very fast train of proper length Lo rushes through a station which has a plaform of length L(<Lo). According to...
  16. T

    Length contraction v. time dilation

    Bear with me. I am a lawyer, not a physicist... I understand how the light clock demonstrates time dilation with special relativity. I think I understand length contraction. Here is my question: at relativistic speeds, why does length contraction not affect the distance traveled by the light...
  17. A

    A question regarding length contraction

    I am not a physics student (my background is that of an engineer + MBA) but have read a lot about relativity and have built up a fair level of understanding. I just thought up a situation regarding Lorentz contraction that has kind of confused my understanding of the same. Consider the...
  18. B

    Time Dilation to Length Contraction

    So I have been trying to wrap my head around time dilation and length contraction... It is all good until i come to the point to derive length contraction from time dilation... So we have \gamma \Delta \tau = \Delta t \gamma L = L_0 So now from my lecture notes i have an observer...
  19. C

    Problems on Length contraction

    Problems on "Length contraction" Homework Statement This is a problem in my text. The idea is that a bar is moving with a high speed (say 0.5c) relative to us. We now want to know what will be the length appeared to us if the bar is parallel, perpendicular and 60 degrees tilted. And we are...
  20. B

    Deriving Length Contraction: Is There Another Way?

    Textbooks I know derive the formula that accounts for the time dilation by measuring simultaneously the space coordinates of a moving rod. Is there another way to derive it?
  21. I

    Exploring Length Contraction and Light Rays in Frame O: Analysis and Discrepancy

    A rod of length 2l is at rest in frame O' with co-ords (x',y',z')=(±l,λ,0) Observer O moves at speed u along the x axis. The first part of the question is just to derive the length contraction - fine, O measures the length as 2l / γ The next part has me stuck: "Show that, at t = 0...
  22. B

    Force propagation and length contraction

    Consider some material object, more or less rigid, with two ends, A and B, like A---B It is at rest at a point in time t_0 in my reference frame. Now I kick it a bit, i.e. I apply some force for a limited amount of time at A in the direction of B. After the kick, the whole object has a...
  23. G

    Time dilation, length contraction

    Has it been shown that observed length contraction that occurs due to high relativistic speeds is any different from that that appear due to the additional time it take a signal from the trailing edge of object (as opposed to the leading edge) to reach an observer? If not, then obviously a...
  24. N

    On the Notations of Length Contraction and Time Dilation

    Now, if I'm not mistaken, from the Lorentz transformations one derives the following equations for time dilation and length contraction, respectively: T'=gT L'=gL Where g is the gamma factor, forgive my sloppy representations, but I'm not well versed in Latex. However, the equation for...
  25. V

    Solving Physics Problem Involving Time Dilation and Length Contraction

    Homework Statement Two lightning bolts strike the ends of a moving boxcar (Points A and B). The boxcar has length 2d and is moving at a speed v. A stationary observes both lightning bolts hitting the boxcar simultaneously. An observer in the car, however, claims that the front (position B') of...
  26. D

    Special relativity & length contraction

    Ive heard that length contraction does not occur when the movement of the object is perpendicular to the observer. Is this correct? Say two identical rings were traveling at each other at relativistic speeds, whilst the observer is perpendicular to them. Ring A would see ring B contract and...
  27. S

    Modern Physics: Length Contraction

    Homework Statement A rod of length L_0 moves with a speed v along the horizontal direction. The rod makes an angle of \vartheta_0 with respect to the x'-axis. (a) Show that the length of the rod as measured by a stationary observer is given by L = L_0 [1-(v/c)^{2} cos ^{2} (...
  28. E

    What is the velocity of car 2 when car 1 is going 1/2 the speed of light?

    car 2 is twice as long as car 1 when they are at rest a stationary policeman observes that car 2 is the same length as car 1 as car 2 passes car 1 going through a speed trap. car 1 is going 1/2 the speed of light I tried to solve this with L 1/sqrt(1-(1/2)^2) = 2L/sqrt(1-v^2/c^2) and...
  29. B

    Length contraction from two inertial frames

    R' is an observer from I'. A rod is in a state of rest relative to him. He measures its proper length L(0). An observer R from I measures its Lorentz contracted length L related by L=L(0)sqrt(1-vv/cc) (1). If we reverse the situation, R measuring the proper length of the rod R' measuring its...
  30. M

    Length contraction & time dilation

    Using the concept of length contraction and time dilation explain how is it possible to travel a distance of 1mln light years during the life of a single person? thanks for any help
  31. C

    What is causing confusion in the concept of length contraction?

    Hello, I am working on the following problem and cannot figure out if I am doing the problem incorrectly or if my professor gave us the wrong answer. (I think that the former is the issue.) 1. Homework Statement [/b] To a stationary observer two frogs at opposite ends of a 100m long lake...
  32. D

    Length Contraction: Understanding the Paradox of a 100m Train in a 40m Tunnel

    I have some questions about the relative factor: 1/'root'1-v^2/c^2 If an object moves close to the speed of light, the length contraction becomes significant. I hear this "paradox": (that was said not to be a paradox, but I didn't understand it) A train of 100 meter moves at a speed...
  33. B

    Length Contraction in Relativity

    Homework Statement An electron travaels in an accelerator tube at a speed of 0.997 c relative to Earth. In the frame of reference of the electron, the length of the tube is 1.20 m. What is the length of the tube relative to earth? Homework Equations L = Lo / γ Textbook answer: 15.5 m...
  34. D

    Relativity : On length contraction

    Homework Statement The distance between the Earth and Alpha Centauri is 4.2 light years (1 light year is the distance traveled by light in one year). If astronauts could travel at v = 0.95c, then we on Earth would assume that the trip would take the astronauts 4.2 / 0.95 = 4.4 years. The...
  35. N

    Length Contraction, Time Dilation and The Principle of Relativity

    Time dilation and length contraction are expressed by the following equations: L=L'*sqrt(1-(v^2/c^2)) T=T'/sqrt(1-(v^2/c^2)) However, according to the principle of relativity, you can't tell which is the fixed frame of reference and which the moving frame, so you can swap L and L' and T...
  36. B

    Length contraction and wave length transformation

    consider a rod of proper length Lo located along the overlapped OX(O'X') axes of the I and I' inertial reference frames in the standard arrangement I' moving relative to I' with speed V. The rod moves with speed U relative to I and with speed U' relative to I'. The measured length of the rod is...
  37. N

    Gravitational length contraction

    A short question this time : Is the gravitational length contraction an effect which acts parallel as well as perpendicular to the direction of the gravitational field ? I suppose it is not occurring perpendicular to it, but I might be wrong and I didn't find a good reference on it.
  38. daniel_i_l

    Length Contraction: Row of Blocks & Rods

    if you have a row of blocks, all touching each other in your frame, then when observed from a frame moving relative to you in the direction of the blocks will the contraction make the blocks look as if they're not touching - each one will be shorter but the total length of the row will be almost...
  39. T

    Relativity: Explaining Length Contraction from γL to L

    Relativity Two balls move with speed v along a line toward two people standing along the same line. The proper distance b/w the people is L, and the proper distance b/w the ball is γL [Note: γ is gamma]. Due to length contraction, the people measure the distance b/w the ball to be L, so the...
  40. petm1

    Speed of Moving Object: Exploring Length Contraction & Time Dilation

    What does the factor that you get when you plug the length contraction and time dilation of a moving object back into the form of meters/second represent?
  41. D

    The true nature of length contraction

    I stumbled on a book that seems to throw the concept of length contraction upside down to me. Maybe someone can help me here. All the books I've read to date, a popular example might be Elegant Universe, say that an object moving near the speed of light past an observer will appear...
  42. M

    Calculating Distance and Time for Traveling to a Star at 1.0x10^8 m/s

    A star is measured to be 40.0 ly from Earth, in the inertial frame in which both star and Earth are at rest. A) what would you determine this distance to be if you travveled to teh star in a spaceship moving at 1.0x10^8 m/s relative to earth. answer is 37.7 ly (calculated that, with no...
  43. S

    Exploring Length Contraction in Special Relativity

    Another thing I don't understand about SR. Length contraction. As I move at near the speed of light, a stationary observer observes my length to be contracted. What exactly contracts? Is it the space between my molecules or the molecules themselves? Furthermore, if we switch perspective to...
  44. E

    Length contraction of a square

    If you have a drawing of a square (labeled ABCD starting at lower left and going clockwise) and it is first at rest in an inertial frame. When this square moves, length contraction changes its shape. In each of the following three situations the speed is the same, and the velocity is in the...
  45. G

    Why Does Length Contraction Affect Only Dimensions Parallel to Motion?

    I have a h.w. problem that states: Explain WHY only the lengths parallel to motion shrink and why lengths perpendicular don't shrink. I know that the vector component of the velocity for an object moving in straight line would be changing. This change only occurs on the x-axis and the not...
  46. L

    Length Contraction, which way is it?

    I thought I understood SR's time dilation and length contraction. But after reading the section on "simultameity" in Tipler I am just as confused as before. Here is my source of confusion. [A] Muon Decay: S frame = frame of the earth; S' frame = frame of the muon A muon falls to Earth...
  47. K

    Length contraction and special relativity

    Special theory of relativity says that, when an object moves with a uniform velocity along its length, the length seems to be less. I believe this is the length measured from the stationary frame of reference. This is justified by Michelson-Morely experiment. What happens when the motion is in...
  48. W

    Are Experiments Proving Length Contraction?

    I am quite aware of the overwellming evidence for the math of relativity, but are we sure that the meaning (time dilation, length contraction, ect.) are true? I guess what I am saying is are there any expiroments that have proven length contraction as in the barn and pole thought expiroment?
  49. J

    Understanding the Length Contraction Paradox in Special Relativity

    Recently I started reading about relativity and found this flaw like thingy. I asked a friend of mine who studied physics and he came with the unsatisfying answer: 'at speeds like that everything kind of blurrs so the spearman won't crash into the door'. Is the following correct and a paradox...
  50. T

    Length Contraction: Can Fundamental Particles Contract?

    If the length of an object could contract under length contraction, what about fundamental particles, like electrons, quarks, protons, etc? After all, an object is made up of a lattice/group of particles.
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