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. ibkev

    B Length Contraction: Real Compressive Forces?

    I'd like to get some conceptual clarification on whether or not length contraction is only apparent to an observer or if it's physically real in the sense that the object under contraction would experience compressive forces? My thinking on this has been along the lines of: I know that time...
  2. Pushoam

    Length contraction -- numerical problem

    Homework Statement Homework EquationsThe Attempt at a Solution a) t' = l0/c b) ct1 = l0 /ϒ - vt1 t1 = l0 /ϒ(c + v) c) t2 = l0 / (ϒ v) Is this correct?
  3. Pushoam

    Length contraction numerical problem

    Homework Statement Homework Equations 1) k.e. = (1/2)mv2, non- relatvistic 2)K.E. = m0 c2 (ϒ -1), relativistic 3) L=L0/ϒ , Length contraction The Attempt at a Solution (A) Taking 1019 eV to be the kinetic energy of the proton, Non- relativistic calculation (1/2)mv2 = 1019 eV = 1.6 v =...
  4. Pushoam

    I Derivation of length contraction

    Problem : To measure length of a scale Rest frame : The frame w.r.t. which scale is at rest Moving frame : The frame w.r.t. which the scale is moving with speed v along +ve x-axis In rest frame ,the positions of the two ends of the scale are (measured simultaneously ) x1 and x2. So length L =...
  5. A

    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...
  6. Ranvir

    B Why is interstellar travel so hopelessly difficult?

    So, I have been thinking about TRAPPIST-1 and how far away that system is from us. It is 40ly away from Earth, according to our frame of reference. This is often put in a way that makes one think that even at speeds close to that of light, it will take almost 40 years to get there. The muons in...
  7. D

    Relativity With velocity of objects moving in different fram

    Homework Statement i)A police spaceship P is chasing another spaceship A. Both ships have velocities βP = βA = 3c/5 as measured along the x-axis in the Solar System reference frame O. The police ship is a distance L = 1 light-second (i.e. the distance traveled by light in one second) behind...
  8. L

    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?
  9. peroAlex

    Special Relativity: Length Contraction Problem

    Hello! I have a small problem with a task professor gave us. I tried many options (you will see below) but I cannot seem to get the right solution. Any advice or guideline how to solve this would be really helpful. In advance I thank you for helping me. Homework Statement Our professor of...
  10. S

    B Length Contraction & Time Dilation: Relative Velocity Impact?

    So an object moving close to the speed of light will be length contracted. Does that mean the distance it covers also contracts in length? From the traveling object's point of view it's surrounding's would contract as he sees them moving along. In these scenarios wouldn't velocity be a...
  11. Divy Jain

    I Interactive Minkowski Diagram Tool

    I've made a Interative Minkowski Diagram Tool, http://divykjain.github.io/IMD You can add events, connect events and add world lines. Lorentz transformation for moving frames also present. I've added support for frame velocities equal or greater than light speeds(but the animations are a mess...
  12. ElPimiento

    Puzzled by an equation for relativistic time difference....

    Homework Statement Suppose that A', B', and C' are at rest in frame S', which moves with respect to S at speed v in the +x direction. Let B' be located exactly midway between A' and C'. At t' = 0, a light flash occurs at B' and expands outward as a spherical wave. (A', B', and C' are all on...
  13. Pouyan

    Distance and Time for a Moving Muon

    Homework Statement A muon is created in the atmosphere 3 km above Earth's surface, heading downward at speed 0.98c. It survives 2.2 * 10-6s in its own frame of reference before decaying. Relativistitically, according to the muon, what is the distance from the point in the atmosphere where the...
  14. G

    B A supplementary length contraction question

    Sorry community, I know I have another outstanding relativity question but something else is currently troubling me. What got me thinking was the question of muons moving towards earth. Now according to their half lives very few of them should make it through 12Km of atmosphere... ANALYSIS...
  15. G

    B Time dilation and length contraction question

    Hi All, Bob and Alice are both 21. I'm imagining a scenario where Alice starts on a journey at 0.8c towards a distant planet. Bob (stays still) says this planet is 16 light years away and that it takes Alice 16/0.8 = 20 years to get there (so Bob is 41 years old when Alice gets there). So Bob...
  16. F

    I Length Contraction & Time Dilation Beyond Planck Scale: Correct?

    If an object was traveling fast enough relative to an observer such that it's length is contracted down to the Planck scale (as with time), I would imagine that any further increase in speed would result in no more observable relativistic effects? Please correct me if I'm wrong.
  17. J

    I Solving Length Contraction Paradox

    Hello there, Suppose there are two inertial frames of reference ##S## and ##S'## with coordinates ##(x,ct)## and ##(x',ct')## such that ##S'## is moving relative to ##S## with velocity ##v##. Suppose ##v>0##, that implies ##\gamma >1##. We know that a Lorentz boost is given by: $$ x' = \gamma...
  18. Inderjeet

    B Length Contraction equation derivation

    I recently saw the derivation of length contraction in Special Relativity . At the end , it said x' = (x - vt) γ(gamma) x = (x' + vt') γ(gamma) Where γ(gamma) is Lorentz transformation . It is = 1/√(1- v²/c²) Then derivation continued , with expansion of x' = (x + vt)γ As t = 0 in this case...
  19. Axidecimal

    V=? for Relativistic Mass,length contraction & time dilation

    Homework Statement Velocity Equations for Relativistic Mass,length contraction and time dilation. I was able to figure out one. This is not for homework. I want to learn these equations for future reference. Homework Equations The Attempt at a Solution Length Contraction : v = c...
  20. F

    I Length contraction vs expansion

    I'm coming across a contradiction that I can't resolve. Two points on the ground are separated by 30km. If you're in a moving frame at velocity +v relative to the ground and you view those two points on the ground, would those two points be greater or less than 30km apart? At first, I thought it...
  21. L

    Length Contraction of spaceships

    Homework Statement Two identical spaceships are under construction. The constructed length of each spaceship is 1.5 km. After being launched, spaceship A moves away from Earth at a constant velocity (speed is 0.850c) with respect to the earth. Spaceship B follows in the same direction at a...
  22. K

    Lorentz Transformation, Time Dilation, Length Contraction

    Homework Statement [/B] A spaceship is approaching Earth from the far side of the sun. The Earth and sun are 8 light minutes apart and the ship is traveling at .8c. Two events are indisputable. 1) the ship is at the sun 2) the ship is at the earth. Assume that the Earth and sun are at rest...
  23. M

    Length contraction and time dilation from Lorentz S

    I'm trying to understand special relativity well enough to explain it to others, ANY others, including myself. I am trying to use Robert Resnick's Introduction to Special Relativity to inform my thinking. In introducing length contraction, he introduces L' as the length measured by an observer...
  24. Sentosa

    I How Does Length Contraction Affect Train Wheel Rotation at Near Light Speeds?

    There's a section in my astronomy book on relativity. The image shows a train traveling at a slow speed and a second image of the train approaching the speed of light. The text says the second train is length contracted, but only in the horizontal direction. In the vertical direction the train...
  25. Babbeus

    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?
  26. Zahidur

    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...
  27. P

    1A caused by half the charge density at twice the velocity

    In the situation consisting of a steady current of 1A in an arbitrary closed path, what would the consequences be for the electric field if the drift velocity was non-uniform along the path due to non-uniform carrier density? This would be a case of a "uniform" 1 amp, but where the charge...
  28. A

    I Why can't you use Simultaneity when doing Length Contraction

    Suppose that frame O' moves at speed v = 0.6c relative to frame O. A rod with two balls is attached to its ends is 10 meters long in its rest frame, O'. Length contraction will tell you that in frame O, the rod is 8 meters long. But aren't the two balls at the ends "events"? They are clearly...
  29. Einstein's Cat

    B Planck's Length, Length Contraction?

    Would Planck's length be subject to length contraction if an object hypothetically of the length had a velocity near c? I suspect that it won't becuase Planck's length is defined by the invariant, physical constants of G, c and the reduced Planck's constant. Thus, Planck's length would not be...
  30. Daleri Mc Rileda

    B How Far Is It To The Center Of The Milky Way/Tootsie Pop?

    With length contraction being ever increased while approaching the mass of a black hole singularity, how does one measure the distance to the virtual infinite contracting frames of reference of time and space /distance of the singularity? Related question : How can one measure the size of a...
  31. G

    I Minkowski diagrams without scales on axes

    Hi. I have seen quite a lot of demonstrations of time dilation and length contraction that used standard Minkowski diagrams WITHOUT any scales on the axes at all. If I understand them correctly they seem to directly compare lengths, which would imply (I think) that the scaling on the ##ct/x##...
  32. R

    B Some basic questions about length contraction in SR

    Imagine there are two space ships, Ship A and Ship B. Ship A sees Ship B traveling at 0.865c towards him. (And of course vice versa) From Ship A's FOR there is a marker 9,000,000 km away which is at rest wrt Ship A. The marker, Ship A and the path of Ship B therefore form a straight line. When...
  33. Einstein's Cat

    B Exploring Length Contraction in Higher Dimensions: A Scientific Inquiry

    Please excuse any stupidity, but I'm under the impression that objects that travel "along" 3- dimensional" space (therefore the objects are three dimensional) with velocity v are subject to length contraction. However would objects of 3+ dimensions and with velocity v still be subject to length...
  34. KaleLetendre

    I Calculating Radius and Mass of Disc for Velocity 0.75C

    Imagine a disc witch has a radius of R=1000m and a mass M=1000kg, this disc sits on an cube that is considered static it has no velocity in any direction whatsoever. There is a light clock with the length L=17.45240644m (approximately the same as the arc length for 1 degree on the disc θ=1)...
  35. Vidar Martinsen

    I Consequences of length contraction

    If you are in a space ship, traveling near light speed, will length contraction enable you to se astronomical events lightyears away, before it is possible to see them from earth? This because the distance is shorter for you in the spaceship and light speed is constant. Example: A star 100 ly...
  36. Stephanus

    B Torch Contraction Problem in SR: A and B Observe Differently

    Dear PF Forum, There's a problem in SR that I cannot solve (or understand) This is, I think, a well known SR problem. The picture is telling the problem itself. A and B and C are in the same frame (let's call it ABC frame) D and E are in the same frame (DE) wrt DE D stays and E stays above...
  37. F

    B Length contraction vs Space time

    Does length contraction means the contraction of space time?
  38. M

    B "Length contraction" prior to observation/measurement

    Since special relativity insists that length is not invariant but rather depends on the frame of reference from which an object or distance is observed... and since the cosmos is many billions of years older than any possible observer, then objects and the distances between them must exist...
  39. Jonathan Densil

    B Using Lorentz Transformations vs Time Dilation/Length Contraction

    Hey guys, In what circumstance or scenario would you use Lorentz transformations as a opposed to time dilation or length contraction? The reason that I ask this is because in all of the problems that I have worked with, the observer is always stationary relative to the event. For example, if...
  40. S

    I What Actually is Length Contraction?

    When I first learned special relativity it was on an elementary level. I was told that "space itself" contracts in a moving reference frame. Now I am studying electrodynamics out of Griffiths. I just read the derivation of the Lienard-Wiechert potential and the fields for a moving charge...
  41. P

    How Long Does a Relativistic Journey to a Star 65 Light-Years Away Take?

    Homework Statement Suppose you decide to travel to a star 65 light-years away at a speed that tells you the distance is only 25 light-years. How many years would it take you to make the trip? Homework Equations ∆t=∆t0/(√ (1−v2/c2 )) / ∆t0 = ∆t √(1−v2/c2) L=L0√ (1−v2/c2) The Attempt at a...
  42. S

    I Length Contraction: Lorentz vs Einstein Explained

    I read that: "Length contraction is caused because moving objects bend space. And that is the difference between Lorentz's and Einstein's length contraction concepts. Lorentz thought length contraction really occurs but Einstein thought that length contraction is a consequence of bending space...
  43. J

    Trying to understand length contraction

    I have a very basic question about the relativity of simultaneity (damn that's a mouth full). So basically rule no. 1 would be that it's all relative right? In the example of the ladder thought experiment it's shown that because of "Lorentz length contraction" a ladder which is bigger than a...
  44. K

    Length Contraction: Does It Really Occur?

    (Sorry my bad English). I'd like to know if a body traveling near the speed of light really experiences a length contraction or if it SEEMS to be contracted for an observer in a inertial frame.
  45. mrsmitten

    Length Contraction & Simultaneity: Train-and-Platform Experiment

    I was reading about (The train-and-platform thought experiment) from https://en.wikipedia.org/wiki/Relativity_of_simultaneity and was wondering a couple of things. 1.) Would the observer on the train agree with the stationary observer that event A and B happen at the same place in the stationary...
  46. A

    How Does Special Relativity Affect Uncle Joe's Appearance at High Speed?

    Homework Statement After year of over-eating and no exercise, Uncle Joe's is overweight, with a waist 50cm wide. He's also out of shape and can only hold his breath for 20 seconds. Worse, he can only jump 20cm high. But at his high-school reunion, he'd like to fool his old friends who haven;t...
  47. B

    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...
  48. Julian102

    What is the relative area of a rectangular field?

    Homework Statement If the area of a rectangular field has length of 110 m and 80 m.If a spaceship is traveling with 0.9c velocity along the diagonal of the field.Then what is the area of the field seen by the astronaut in the spaceship? Homework Equations L=L(initial) Root over (1- (v/c)^2)...
  49. J

    Relativity - Length Contraction Problem

    Homework Statement You are watching a race between two space ships who pass you moving at different constant speeds. In your reference frame, both ships are the same length while moving. It takes the first ship 26.8 minutes to get to the finish line a distance 14 light-minutes away. It takes...
  50. kablion

    Why does length contraction solve this? (2 Lightclocks)

    Hey, I'm currently working on an explanation of the special Relativity. Now I'm at the point of explaining length contraction, but I don't understand why the following example is a reason for length contraction to exist: Imagine we have two Lightclocks in a fast moving Rocket. Lightclock 1...
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