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. A

    The 'mechanism' of length contraction

    Let's suppose that we have a rod which is 2 meters long in its rest frame. Its rest length can be defined as a set of points which do not occupy the same place, measured in a frame which is at rest with the rod as a whole. Now if we travel relative to the rod, it gets length contracted, I...
  2. A

    Are length contraction and time dilation conventions?

    Since many authors call simultaneity between events a convention, and that under the specific set of rules we may choose a convention or a coordinate system relative to an IRF (or non-inertial) to describe space time, I wonder what's the relation between this and the effects of length...
  3. S

    How Does Length Contraction Affect Markings on a Moving Conveyor Belt?

    Homework Statement A relativistic conveyor belt is moving at speed 0.5c relative to frame S.Two observers standing beside the belt, 10 ft apart as measured in S, arrange that each will paint a mark on the belt at exactly the same instant (as measured in S). How far apart will the marks...
  4. A

    Time dilation, length contraction and relative simultaneity on Earth

    The three main effects of SR occur in inertial frames and change the description of space-time relative to a particular observer. My question here is how do these effects occur on Earth, since we know that motion on Earth is non-inertial. I know that we travel at small speeds and that we can't...
  5. A

    Is Virtual Length Contraction Influenced by Changes in Refractive Index?

    What should it be, {sin(ωt-\frac{k}{n}x)} or {sin(ωt-nkx)}? I am contemplating this with respect to the proper waveform in a medium, following specific rules, particularly when it comes to the dispersion relation and ultimately what this would mean in the context of the Lorentz transformations...
  6. S

    Confusion about time dilation and length contraction

    Hi all, I tried searching for this but failed to find an answer to my question. I am having an issue with properly interpreting the equations for time dilation and length contraction. Let's assume that I am standing still and a train is passing by next to me (moving with uniform velocity). Let...
  7. O

    Derive length contraction formula given a two system experiment.

    Homework Statement Show that the experiment depicted in Figure 2.11 and discussed in the text leads directly to the derivation of length contraction. Figure 2.11: Homework Equations d=v*t Requested result: L=L0\sqrt{1-\frac{v^2}{c^2}} The Attempt at a Solution In K the...
  8. M

    Time Dilation and Length Contraction

    I had a quick question about Time Dilation and Length Contraction. Are the two just different ways of measuring/describing the same effect? Or rather they both follow as a consequence from one another? i.e. I can find how much a length is contracted by finding the dilated time interval and...
  9. maajdl

    Why no electric field from a current in a wire? Length contraction.

    I found a funny video on youtube, but I am not totally convinced by the argument. It says that a pure magnetic field caused by a current in a wire can lead to a combined electric + magnetic field in a moving frame. It explains more or less convincingly that this can be understood as a...
  10. T

    Do the distance between two objects contract in length contraction

    Imagine two asteroids which are separed by 1Ly distance. They are in uniform velocity (.9c) with respect to an observe in space. So from the observers point of view (rest frame), does the distance between the asteroids (ie. 1Ly) appear contracted?
  11. Superposed_Cat

    Length Contraction oes the object or travel distance shrink?

    Length Contraction:Does the object or travel distance shrink? I had always thought that length contraction meant that the object itself shrunk but I stumbled across an article where they said "Because of length contraction the photon doesn't travel any distance at all. Which is it? Any help...
  12. T

    Length contraction clarification

    Consider two iron rods of about 10 metres separated by 10 metre. They are in series position and not connected in anyway. If the rods are passing nearby an observe with a velocity of 90% speed of light, then what would he observe? 1) does the separation between the rods (ie 10m) undergo length...
  13. T

    Do length contraction affects accelerating objects?

    Suppose I'm standing on Earth and i see an iron rod accelerating through space with a rate of 1m/s^2. Will it undergo length contraction after reaching a speed nearly to the c? Will there be any deformations to a spinning disk?
  14. F

    How does this affect the length contraction paradox?

    Hi, As is well known, Relativity claims that a rod of a given proper length will appear length contracted when measured by a moving observer. Now consider a rod of length L and observer initially at rest relatively to it, with one end of the rod at the observer's coordinate x1(0) and the...
  15. B

    Problem caused by length contraction and relativity and personal expla

    The problem has been shown in the picture. Because of relativity, both the guys on the ground and on the vehicle would observe length contraction. So the destination of the guy on the vehicle---the galaxy, would be more closed to him. If the vehicle is replaced with the light, which means the...
  16. Z

    Perspective on Relativity and Length Contraction

    Hello All, I like to think that I have a decent background in physics and related material, but I confuse myself quite easily on, well, everything. I guess I think about it too much, really. So feel free to give complex answers and I will do my best to follow along accordingly. Anyways, here...
  17. R

    Trying to reconcile Lorentz Transformation and Length Contraction

    Suppose I am in a stationary frame of reference S and there is a lamp post at a distance X from my origin in the positive X direction. Say you move at a velocity V along that axis and the distance of the lamp post in your frame of reference S' is X'. Then by Lorentz transformation equation X'...
  18. F

    Need help with time dilation and length contraction.

    Can anyone help me with this thought experiment. I have a spaceship moving at very close to the speed of light. Inside are the captain and two crew members. The captain is positioned at the front of the spaceship with a clock and a light. One crew member is positioned at the back of the...
  19. C

    Question about symmetry of length contraction

    Say we have two inertial observers Bob and Alice moving relative to each other at a significant fraction of the speed of light c (say 0.5c). Bob is moving to the left relative to Alice and Alice to the right relative to Bob. When their origins cross, a pulse of light is emitted to the right...
  20. S

    Time dilation and length contraction

    can both time dilation and length contraction occur for the same observer? i don't think it is possible since then c=reduced length/increased time which is impossible(since c is constant)... Am i wrong?
  21. Crazymechanic

    Force on a particle , length contraction

    Okay because my previous post of similar kind was I guess rather too full of thought experiments and ideas that nobody actually responded to it except for one user then I will try to explain the same thing here only much simpler. A few situations. so there is this site...
  22. M

    The Physics of Length Contraction of physical objects and distances

    I've been trying for a long time to get an answer to the question, "What is the physics or mechanical explanation of contracting physical objects and the distances between them?" I understand that the phenomenon is theorized to depend on different observations from different frames of reference...
  23. M

    Confused about length contraction

    Hello, I am a bit confused about the length contraction formula. The formula is : l=lo*sqrt(1-u^2/c^2), where lo is the distance measured in a frame at rest with the moving object. Now I was looking at a problem where a spacecraft just as it touches the finish line (event 1) a message from...
  24. D

    Does Length Contraction Occur in All Directions for a Speeding Object?

    If an object were to approach the speed of light, its length, as measured by an observer, would become shorter and shorter. But what about the view of the speeding object? If the object is approaching the speed light, then would the world surrounding it appear to be shorter as well? I say...
  25. N

    Bell's Spaceship Paradox and Length Contraction

    Can someone please clarify for me whether length contraction in special relativity is considered a physical effect (a contraction of a cohesive material) or a kinematic effect (applied to the space the material occupies)? I've been thinking about Bell's Spaceship Paradox this week and realized...
  26. D

    Understanding Length Contraction in Relativity: Explained and Analyzed

    As I've just recently started studying relativity, I need some help with these basic concepts. So this thread is about length contraction. Can somebody explain the effects of it, since I've already found out some things, like the existence of the invariant proper lenght, the fact that...
  27. ash64449

    Is this simple derivation of length contraction and time dilation corr

    well,i found this article and i find it simple to understand. But is this article totally correct? Here is the link:http://m.sparknotes.com/physics/specialrelativity/kinematics/section2.rhtml
  28. Saxby

    Length contraction of two spaceships

    Homework Statement Two space ships, each a hundred metres long when measured at rest, travel toward each other with a speed of 0.85c relative to the Earth. Homework Equations λ = 1 / √1 - (v2/c2) x' = λ(x - vt) L' = L / λ The Attempt at a Solution Well to be honest i may be...
  29. P

    Length Contraction and Time Dilation in Special Relativity

    Hi all, Page 94 of Special relativity by AP French has a worked out example that puzzled me. This is the example: Frame S’ has a speed v=0.6c relative to S. Clocks are adjusted so that t=t’=0 at x=x’=0. Two events occur. Event 1 occurs at x1=10m, t1=2E-7s (y1=0, z1=0). Event 2 occurs...
  30. A

    Time dilation and length contraction

    I've recently been thinking more about special relativity, and while I understand the Lorentz factor and how to apply it to find correct solutions, I'm still stuck on the link between the effects of length contraction and time dilation, are they permutation of the same thing from different...
  31. A

    Time dilation and length contraction

    I've recently been thinking more about special relativity, and while I understand the Lorentz factor and how to apply it to find correct solutions, I'm still stuck on the link between the effects of length contraction and time dilation, are they permutation of the same thing from different...
  32. N

    Gravitational Length Contraction

    I understand the concepts of time dilation and length contraction in SR. I also understand the concept of time dilation in a gravitational field. But what about length contraction in a gravitational field? Is there such a thing and can it be derived from the Schwarzschild metric?
  33. coktail

    Length contraction occurs infront of AND behind you?

    If I am moving through space, things in front of me contract in the direction parallel to my movement. Does this also occur to objects behind me? For example, I look behind me, would things be contracted? As always, thanks.
  34. P

    Length contraction on charged wire

    Lets say we have an infinite charged wire with a line charge \lambda on it. Now when I move with respect to this wire the E field will increase do to length contraction. And there will also be a B field that we could calculate with ampere's law. But the increased E would make it seem...
  35. V

    Radial length contraction = mass anisotropy?

    Mach's principle is considered falls by many because mass anisotropy would not be consistent with the Huges-Drever experiments, which showed the isotropy of nuclear resonance. However, anisotropy appears as well in GR in the form of radial length contraction, which can be interpreted as increase...
  36. coktail

    Length contraction of space with multiple reference frames

    My understanding is that as I move, from my FoR all objects and space itself (according to Einstein) contract along the direction of my movement. This length contraction occurs for all space and objects in front of me for an infinite distance. Furthermore, relative motion is relative, and the...
  37. V

    Time dilation and length contraction

    I am confused about these two concupiscences of the consistency of light. One of my books/notes says that time dilation and length contraction do not happen at the same time because they are 'the same thing' which kind of makes sense but the other says "when we reach relativistic velocities both...
  38. D

    Length contraction problem of right angled triangle

    http://https://www.physicsforums.com/attachment.php?attachmentid=56297&stc=1&d=1362318192 problem:- The situation is shown in attachment. the right angled frame of rods (in stationary ) is moving at speed v perpendicular to its hypotenuse. according to length contraction the corresponding...
  39. S

    Arguments Against Existence of Isotropic Length Contraction/Expansion

    according to special relativity theory, any object that has relative velocity also has lorenz- contraction L' = L0 *sqrt (1-(v/c^2)) it sounds odd that this is only kind of length contraction known to exist. why there are no other kind of length expansions or contractions, or are them...
  40. D

    Proving length contraction exists

    Homework Statement Hey All; I am trying to follow along with the following example in my book, but I am getting lost somewhere. "We can perform another gedanken experiment to arrive at the same result (showing that length contraction is described as L=Lo/γ; this time we lay the meterstick...
  41. A

    Time Dilation & Length Contraction, Further Thoughts

    This is a very common topic especially regarding the apparent slowing down of time, the twins paradox etc. I have come across the figures for a muon and the relativistic effects that allow it to reach the Earth's surface despite its very short life. The relevant transforms show length...
  42. A

    Length Contraction vs. Distance Contraction

    Consider observer A at rest, seeing observer B traveling in a rocket at high speed towards a star C. Star C is at rest w.r.t. A. A in his frame sees B's rocket to be length contracted. B considers his distance to C to be shorter than (contracted) compared to what A sees. I seem to be...
  43. 7

    Length contraction and Minkowski diagram

    Hello, in my other topic members on the forum helped me to understand time dilation by using Minkowski spacetime diagram. Now i would also need some assistance with explaining length contraction in Minkowski spacetime diagram. I have observer Žiga in his frame ##x,ct## and observer Ranja...
  44. P

    Question about length contraction

    I am on a spacecraft as it makes a journey between two planets. I use a lightpulse to measure the distance before I set off, I then accelerate to a speed that is close to the speed of light and measure the distance again. I find that the distance when I am stationary (relative to the planets)...
  45. B

    Will Relativity Determine the Outcome of a Spaceship Explosion?

    Hi Consider a spaceship at rest in space, this ship is equipped with a bomb connected to two rings. Once the rings connected to each other, the bomb explodes making the ship also explodes. The proper distance between the rings is one meter. Now consider a conducting rod of proper length one...
  46. J

    Using length contraction to push a bomb trigger

    Inspired by Aziza's question i came up with a similar, seemingly puzzling question. Imagine a space-platform with a big cylinder on it. The cylinder has a hole drilled in, with a bomb-button at the end of the hole, which would trigger a bomb destroying the whole galaxy. A terrorist is on that...
  47. U

    Length Contraction Ether wind

    Length Contraction "Ether wind" Homework Statement Due to the ether wind, anything that moves along it is "contracted". The Attempt at a Solution Taking L1 to be contracted length, (L1)2 = (L1x)2 + (L1Y)2 = (L10,X/γ)2 + (L10,Y)2But what they wrote is the opposite..
  48. A

    Bohr radius and length contraction

    from wikipedia - "The Bohr radius is a physical constant, approximately equal to the most probable distance between the proton and electron in a hydrogen atom in its ground state." in Planck units bohr radius (a0) = (mp/me).(1/\alpha).(lp) the 1st 2 terms of the RHS of the equation are...
  49. coktail

    Relativistic mass, time dilation, length contraction, and traveling near c

    A spaceship with an arbitrarily large quantity of fuel cells departs Earth and accelerates away from it with a fixed trajectory until it reaches .9c. It continues to accelerate, but never reaches c because that is impossible for any object with mass. From the frame of reference of the crew...
  50. coktail

    Length contraction of distant objects/space, etc

    If I am moving through space at a velocity that is a significant fraction of c, are all objects ahead of me in my path contracted in the direction of my travel for an infinite distance? In other words, are planets and stars from right in front of me to the edge of the known universe contracted...
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