Velocity addition Definition and 69 Threads

In relativistic physics, a velocity-addition formula is a three-dimensional equation that relates the velocities of objects in different reference frames. Such formulas apply to successive Lorentz transformations, so they also relate different frames. Accompanying velocity addition is a kinematic effect known as Thomas precession, whereby successive non-collinear Lorentz boosts become equivalent to the composition of a rotation of the coordinate system and a boost.
Standard applications of velocity-addition formulas include the Doppler shift, Doppler navigation, the aberration of light, and the dragging of light in moving water observed in the 1851 Fizeau experiment.The notation employs u as velocity of a body within a Lorentz frame S, and v as velocity of a second frame S′, as measured in S, and u′ as the transformed velocity of the body within the second frame.

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  1. M

    B Relativistic Velocity Addition: Is c Ever Exceeded?

    I was watching this video by Brian Green about relativistic velocity addition when he said something at the end that I wondered about. https://www.britannica.com/video/222286/Your-Daily-Equation-07-Relativistic-Velocity-Combination It was along the lines of the formula will always result in...
  2. Sagittarius A-Star

    I Only Minkowski or Galilei from Commutative Velocity Composition

    The LT can be derived from the first postulate of SR, assuming linearity an that velocity composition is commutative, and that GT can be excluded: ##t' \neq t##. Definition of the constant velocity ##v##: ##x' = 0 \Rightarrow x-vt=0\ \ \ \ \ \ ##(1) With assumed linearity follows for the...
  3. P

    I Velocity addition via k-calculus

    We had a thread a while ago where a poster was particularly interested in the SR rule of velocity addition. And in that thread, I suggested a better foundation was the k-calculus approach, with a reference to Bondi's treatment in "Relativity and Common Sense". Here I would like to show how to...
  4. lindberg

    I Applying Velocity Addition in Rotating Frame: Is It Correct?

    From the top of my head, I would say that yes, the very moment our clocks are aligned, and the two bullets are launched it is perfectly ok to use the relativistic velocity addition formula to determine the speed of the bullets from my reference frame. But the more the disk keeps rotating, the...
  5. lindberg

    I Relativistic Velocity Addition: Calculating Electron Speed

    If we imagine launching an electron wave in a reference frame S with speed v, should someone viewing the electron from frame S1, which is in inertial motion referring to S, use the relativistic velocity addition to calculate the speed of the electron?
  6. R

    Understanding Velocity Addition Laws for People on Train & Ground

    I kind of just made up the questions. I realize this is a basic question but my knowledge of physics is very limited.q1 answer v_left_ball = v_left_ball - v_train v_right_ball = v_right_ball + v_train q2 answer To get the speed from Bob's frame I would use v_Bob = v_Bob + v_Alice To get the...
  7. Kairos

    B Misuse of Velocity Addition: Troubleshooting

    Something seems wrong with my use of velocity addition: A fly of rest mass ## m_{0} ## in your reference frame (say a platform) is posed in a train passing with a velocity ## v ## relative to the platform. The fly mass is now for you ## m_{1} = m_{0} \gamma(v) ##. Now in the train the fly is...
  8. J

    Lorentz Velocity Addition Problem

    So for the formula, u'=u/(δ(1-(uv)/c^2) u=2.06E8 and v=0. I am only looking at the y components here. Since v=0 it really becomes u'=u/δ or u'= u*sqrt(1-(u^2)/c^2)). Anyways when I plug this in I am getting 1.49E8 when the answer should be 0.951E8. Am I not using the correct formula here?
  9. V

    How Does the Angle Theta Affect the Velocity Calculation in String Problems?

    The way I tried to solve it is by using following reasoning. The inclined part of the string will each have a speed of U m/s. So the point P just above mass M where the inclined strings meet is being moved up by each inclined string at ##U \cos {\theta} ##. Therefore, the speed of the point P...
  10. G

    Einstein velocity addition solving for v

  11. P

    Velocity addition formula in X and Y axes (Relativity)

    The problem: Visualising the problem (My question is with regards to this): Why is the above set-up correct? In the above diagram, S would be moving at velocity -v relative to S', instead of v. Is this because the question says "speed v", and so we can set the direction as such? Why would the...
  12. J

    B Velocity Addn Paradox: SR Postulate Explained

    Velocity addition paradox: In observer A's frame, observers B and C move away from him at the speed of light c, B to the left and C to the right. In B's, frame A and C are both moving away from him at c, i.e. at the same speed. In both A's and C's frames they are moving at different speeds...
  13. Kairos

    I Velocity Addition and Doppler Effect: Explained

    The Doppler effect of light corresponds to the classical Doppler effect corrected by time dilation, but the first one is obtained with classical velocity additions (c+v at the front of the source and c-v at the back) whereas velocity addition of special relativity gives c at the front and c at...
  14. J

    B Experimental Confirmation Length Contraction Velocity Addition

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

    I Special Relativity and Velocity

    I can't seem to wrap my head around it: if an object is moving at speed v in frame S, and its observed to move at speed v' in S', what is the relationship?
  16. DaveC426913

    B Velocity Addition: Unraveling the Mystery

    I keep getting into these discussions and finding out they are not as simple as I thought. Or at least, my math is rusty. Scenario A: Two ships are each receding from Earth at .9c in opposite directions. Since these are velocities, they should have opposite signs. That can't be right, since...
  17. IgorIGP

    B Special case of relativistic velocity addition law

    Hi gentlemen. My model is simple. Imagine, I watch a body which approaches me with velocity of w which value I can measure . I know that this a body has velocity v in a some reference system which aproaches me with same velocity of v. This velocity needs to be calculated (I can not mesure it)...
  18. N

    Solve velocity addition problems using 4-vector

    I used the two equations above to solve for u_x and u_y and got u = 0.987c, where u_parallel = u_x and u_perpen = u_y. I wonder if I can use velocity four-vectors to solve this problem. Modify η'μ = Λμνην so we can use it for velocity addition?
  19. M

    I Velocity Addition: Angled Motion Explained

    Any ideas?
  20. N

    B Velocity Addition Q: Ball Thrown from Moving Ship?

    Suppose a spaceship is flying past me, an observer on earth, at .86c. A traveler on the ship has a ball which is attached to a string which is 100 feet long in the ship frame. The traveler grabs the string and throws the ball out of the front window of the ship at a speed of 100 feet per second...
  21. CDL

    Einstein Velocity Addition for a Moving Charge in a Wire

    Homework Statement I am reading through Griffiths' Electrodynamics, and I have come to the scenario in the Relativity chapter where in an inertial reference frame ##S##, we have a wire, with positive charges (linear density ##\lambda##) moving to the right at speed ##v##, and negative charges...
  22. Hamza Abbasi

    How Fast Does Spaceship A Move Relative to Spaceship B?

    Homework Statement Two spaceships pass each other. Spaceship A moves relative to nearby planet at velocity v1 , while spaceship B moves at velocity v2 relative to the planet . How fast does spaceship A moves relative to spaceship B. Homework Equations Velocity Transformation : v* =...
  23. M

    I Velocity difference not preserved in special relativity

    Consider single line motion. If an observer sees two objects, and one is seen moving say 50 m/s faster than the other, will all other observers measure the same velocity difference? The answer seems to be 'No' from the velocity addition formula of special relativity? Thus same velocity...
  24. S

    I Velocity addition and conservation of the energy

    Hello everyone, For some time I'm a little bit confused about (at the first view) a very simple question, which is about the conversation of the energy of moving objects (in terms of special relativity). As an example let's talk about firearms. If the mass of the gun M1 is infinitely higher...
  25. D

    I Velocity Addition Formula: u_y > c?

    If a frame S' moves with velocity v in x direction wrt S, and you have v = 0.5c, u_x' = -0.9c and u_y' = 0.9c then it seems you find that u_y = 1.417c, greater than c. The relevant formula is: u_y = u_y'/(gamma * [1+v u_x' / c^2]) Apologies for formatting. Details: gamma = 1/sqrt(1-v^2/c^2)...
  26. I

    I Velocity Addition & Relativity of Simultaneity

    I have some issues understanding the following thought experiment: Suppose you are standing still, and two balls are moving towards you from opposite direction. From your own reference frame, Ball A is ##10^5## m away from you, moving towards you from the left with speed ##0.8c##, and Ball B is...
  27. O

    I Velocity Addition Example: Morin's Confusing Use of Equation

    Ok, so here's another example Morin did in his book: Ok, so the thing that confuses me is when he used the velocity addition equation: Note:4c/5 and 3c/5 are their speeds relative to the ground. Where v2 is the velocity of the S' frame, and v1 is the velocity of the object moving in the...
  28. Stephanus

    B Hubble flow and velocity addition

    Dear PF Forum, I've been wondering about this thing. The universe's radius is 46 gly. But a galaxy in 13.8 gly from us cannot be seen because it travels faster than the speed of light. So is there a galaxy in, say, 30 billions light years away from us? But before that, I'd like to know about...
  29. G

    I Velocity Addition: Physical Meaning of Non-Singularity at c?

    Hi. In the derivation of the relativistic formula for adding velocities, the Lorentz factor drops out. Mathematically, the formula works for inertial frames with relative velocity c and even gives an answer to Einstein's famous question about what happens if you drive at the speed of light and...
  30. C

    What is the path of a ball thrown between two children in a moving car?

    Homework Statement LOOKING AT PART (c) The ball is traveling at velocity c/√2. The car is traveling at velocity c/√2. Ball is thrown up through the sun roof or something I don't know. Homework Equations The Attempt at a Solution I don't know how to think about this in 3D. I've done parts (a)...
  31. M

    Is There Enough Information to Solve the Relativistic Velocity Addition Problem?

    Homework Statement Two asteroids are approaching one another moving with the same speed speed as measured from a stationary observer on Europa. Their relative speed is 0.5c. Find the speed of one of asteroids relative to Europa. I understand how relativistic velocity addition works but am not...
  32. DiracPool

    Bob's Relativistic Velocity Addition: 0.9c for Alice & Charlie

    My name is Bob. I'm floating in deep space and I have these two powerful cannons that shoot my friends Alice and Charlie in opposite directions to me, one to the left and one to the right. I shoot each out at 0.9c. As I look to the left, I see that Alice is flying away from me at 0.9c. Then...
  33. P

    Generalized velocity addition and aberration formulas

    Not sure if this will be of interest to others, but, as an exercise, I decided to derive formulas for SR velocity addition for any angular relationship, and similar aberration of angle for any object speed and direction and observer relative velocity - using pure algebra/geometry. That is, no...
  34. J

    Addition of Velocities Special Relativity Problem

    [Mentor's note: this post does not use the homework template because it was originally posted in a non-homework forum.] ----------------------------- A ship (attached to reference frame S') is passing us (standing in reference frame S) with velocity v= 0.933c. A proton is fired at speed...
  35. T

    Velocity Addition for Orthogonal Boosts in SR

    Hi, is there any general formula to find out the final velocity w, happened by a boost in x direction forst and then to y direction? I could find the boost matrices for both and I know it's not purely another boost, rather a boost and a rotation, but I am really confused which formula to use...
  36. Quarlep

    Einstein Velocity Addition for Relative Speed Calculation

    Lets suppose we used Einstein Velocity Addition equation and we found a result this is the same for every observer isn't it ?
  37. N

    Is Absolute Space and Time Really Absolute?

    Imagine two space ships each with thrusters that can accelerate them .1c or .3c almost instantly. The velocity addition formula indicates that if one spaceship applied the .1c thruster 3 times then if c is estimated to be 300,000,000 m/s the velocity of the ship after the accelerations the ship...
  38. M

    Three Reference Frame Relativity Problem - Velocity Addition or Proper Lengths

    Homework Statement Anna and Bob have identical meter sticks. Anna an observer on Earth, sees Bob traveling in a spaceship at 0.5c away from her. Bob leaves his spaceship in an escape pod, moving away from Earth and the spaceship at 0.1c with respect to the spaceship. How long is Bob's meter...
  39. DiracPool

    Relativistic velocity addition

    I feel I understand relativistic velocity addition fairly well. However, the way I usually see it modeled is with two travelers moving in the same direction. Bob is in a spaceship traveling at 0.6c and shines his flashlight in the direction of travel. An inertial observer, Alice, relative to...
  40. A

    Relativistic velocity addition and signs

    Hello all, I have just covered a very brief module on special relativity as a part of my physics course. I have also done some extra reading mostly; Morrin's Classical Mechanics. While I found the book really illuminating in some aspects, I still feel that regardless of how hard I try there is...
  41. W

    Velocity Addition: Solving Minkowski Space with Metric Techniques

    Hi all. I'm taking a course in GR and trying to get my intuition and mathematical techniques up to speed. I've been trying to derive the velocity addition formula in Minkowski space, but for some reason I can't do it. Here's what I have: I'll use the Minkowski metric of signature...
  42. D

    Special Relativity: Velocity Addition

    Homework Statement Two objects fly toward you, one from the east with speed u, and the other from the west with speed v. Is it correct that their relative speed, as measured by you, is v+u? Or should you use the velocity addition formula, V=(u+v)/(1+uv/c2)? Is it possible for their relative...
  43. M

    Velocity addition formula question

    In the Galilean formula u=u'+v, the velocities are bold so we know they're vectors, so for instance if u'=(a,b), and v=(c,d), we say that u=(a+c,b+d). But, in SR u=(u'+v)/(1+vu'/c2), none of the velocities are shown in bold, at least not not the way I saw it written. So, if we used the same two...
  44. S

    Non-parallel Relativistic Velocity Addition

    Homework Statement (d) A spaceship moves with velocity (4/5)c relative to Earth. The astronaut throws his empty beer bottle out the window with velocity (3/5)c relative to the ship in the sideways direction. What is the velocity of the bottle (magnitude and direction) relative to the Earth (i)...
  45. J

    What Is the Velocity of a Probe Released from a Moving Spaceship?

    Homework Statement A spaceship moves with a velocity 0.75c xhat with respect to the earth. The ship releases a probe with a velocity 0.75c yhat relative to the ship. What is the velocity of the probe as viewed on earth, magnitude and direction? Homework Equations The velocity-addition...
  46. D

    Why am I getting this relativity velocity addition problem wrong?

    Homework Statement A spacecraft S2 is capable of firing a missile which can travel 0.98c. S2 is escaping from S1 at a speed of 0.95c when it fires a missile towards S1. part A) According to the pilot of S2, what speed does the missile approach S1? Part B) according to pilot of S1, what...
  47. R

    Velocity Addition in Special Relativity

    Hi All, Pardon me if this question looks so silly. Trying to understand velocity addition in special relativity. Say velocity components as measured in stationary frame of reference S are u, v, w in x, y, Z directions respectively and those in moving frame S' are u', v', w' in x', y', z'...
  48. D

    How to derive the velocity addition formula

    Homework Statement Derive the formula v= (v'+u)/(1+v'u/c^2) the velcoty addition formula using the below formulas? Homework Equations 1. vt1=L+ut1 2. (proper time)=(proper length)/v'+(proper length)/c 3. ct2=L-ut2 4. (dilated time)= (proper time)/(sqrt(1-v^2/c^2)) 5. L=(proper...
  49. C

    Electrons - Relativistic velocity addition

    electrons -- Relativistic velocity addition... Homework Statement an observer measures the velocity of two electrons, finding one with a speed c/2 in the x direction and the other c/2 in the y direction. what is the relative speed of the two electrons. Homework Equations The...
  50. V

    Special relativity - A problem on velocity addition (several increments)

    Homework Statement A spaceship, at rest in a certain reference frame S, is given a speed increment of 0.50c. Relative to its new rest frame, it is then given a further 0.50c increment. This process is continued until its speed with respect to its original frame S exceeds 0.999c. How many...
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