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. U

    Velocity addition formula for multiple velocities within each other

    I am having a problem coming up with an empirical formula for multiple objects moving with the same speed relative to each one up. I.e. there is a cart moving with speed u relative to me, and inside it is a cart moving speed u relative to the cart is inside it. and inside that cart is a cart...
  2. D

    How Fast is C Moving Relative to B?

    Homework Statement relative to A, B is moving towards A at a speed of 0.4c. Farther out C is moving towards A at a speed of 0.5c. all motion is along the x-axis how fast is C moving relative to B? Homework Equations U = (U' + V) / 1+ VU'/c^2 The Attempt at a Solution...
  3. W

    Resultant Gamma after Einstein velocity addition

    Hello. Let's say that I am in a frame in which I see a rocket traveling at v. This rocket then fires a projectile forward with velocity u in its rest frame. I can find u' easily enough using the Einstein velocity addition formula. However, I recall seeing a version of the formula that uses...
  4. G

    Velocity addition expressed as gamma

    if object A is moving with gamma=x in one direction and object B is moving with gamma=y in the opposite direction then what is the gamma factor for object A as it would be calculated by object B? I know the velocity addition rule for relativity but I can't find anything on the net about...
  5. Y

    Velocity addition ain't what it used to be

    In special relativity, the velocity-addition for colinear velocities u and v is given by (u+v)/(1+uv/c^2), but for non-colinear velocities the formula is more complicated and is not symmetric in u and v. But since the reciprocal velocity of v is -v then the reciprocal of (u+v) should be -(u+v)...
  6. kreil

    Can Relativistic Velocity Addition Ensure Speeds Stay Within Limits?

    Homework Statement Show that the addition of velocities implies the following: - If | \vec V | < c in one inertial frame, then | \vec V | < c in any inertial frame - If | \vec V | > c in one inertial frame, then | \vec V | > c in any inertial frameHomework Equations V^{x'}=\frac{V^x...
  7. stevmg

    Exploring the Invariable Speed of Light: Einstein's Velocity Addition Formula

    Using drudkh's example cited above and using Einstein's velocity addition formula, closure speed between a particle moving to the right at v and light coming from the right and moving left at c would still be c. Why? Let's use v as the velocity of the particle expressed as a fraction of c...
  8. T

    Observed speed of light [actually about relativistic velocity addition]

    I apologize if this is a repost, my original post didn't seem to take. If you accelerate a particle to 99% the speed of light and accelerate another particle to 99% the speed of light directly into the path of the first would this not create the observed effect from either particle that the...
  9. F

    What is the Einstein Velocity Addition Formula and How Does It Work?

    http://hyperphysics.phy-astr.gsu.edu/Hbase/relativ/einvel.html#c1 ok, so I'm looking at this, and i see that where c = speed of light if ship A is moving at .7c to the right ===> <=== and ship B moving .7c to the left and they are both on the same line and about to collide, at...
  10. O

    What is the Speed of Ship A as Observed from Ship B?

    Homework Statement Nevermind, got it. Two spaceships approach the Earth from opposite directions. According to an observer on the Earth, ship A is moving at a speed of 0.753c and ship B at a speed of 0.851c. What is the speed of ship A as observed from ship B? Of ship B as observed from ship...
  11. E

    Special Relativity Velocity Addition: Vector or Axis?

    I know how to add speed in special relativity. v=\frac{u+v'}{1-\frac{uv'}{c^2}} Is this a vector thus velocity? Or does this only apply to objects traveling on the same axis? Judging from the way it's derived, I really think that it only applies to objects on the same axis. What if I want...
  12. B

    How Fast Are Proton and Antiproton Moving Towards Each Other?

    Homework Statement A proton and an antiproton are moving toward each other in a head-on collision. If each has a speed of 0.8c with respect to the collision point, how fast are they moving with respect to each other? Homework Equations Ux = [U'x + V] / [1 + (v/c^2) Ux'] The...
  13. O

    Does the presence of B change the velocity of C with respect to A?

    Let's say there are two observers A and C. C is moving .5c with respect to A. If we introduce a third observer which we will call B and B is moving at .2c with respect to A and is moving in the same direction as C and is inbetween A and C, and we now apply the velocity addition formula we get...
  14. C

    A question on velocity addition

    Consider frame S1 and another frame S2 moving with a velocity v with respect to S1 along +X direction. Consider a photon comes in -X direction. Velocity of photon in S1 is c.I would like to find the velocity of light in S2 from S1 without forgetting length contraction and time dilation as...
  15. A

    Coming to terms with the velocity addition formula

    I have two rockets, one in point A and another in point B, I'm going to crash one against the other, twice, and I will be observing safely from my laboratory at C, which is right in the middle between A and B. The first time the experiment takes place, I see both rockets rushing forward to...
  16. E

    Einstein velocity addition rule

    Car 1 is traveling at 3/4c. Car 2 in behind Car 1 is traveling at 1/2c. Car2 fires a bullet that travels at 1/3 c. OK. In order to determine whether the bullet reaches Car 1 or not we need to use Einsteins velocity addition rule and determine whether the relative velocity of the bullet...
  17. B

    Velocity Addition in MG and Light Scenarios

    Consider a scenario which involves a stationary machine gun (MG) and a moving target T. MG emits successive bullets at constant time intervals t(e) which hit the moving target at constant time intervals t(r). The bullets move with velocity U and the target with velocity V. The first bullet...
  18. M

    Velocity Addition: Solving the Mystery

    I'm trying to figure this problem out, and think it's not that hard, but am having trouble acquiring the answer. Here is the problem: You and a friend decide to "hitch" a ride in the mailcar of a train heading to Green Bay (due north). Halfway there, your friend asks you for a sandwich out...
  19. S

    Using the Galilean transformation and classical velocity addition

    My problem is this: Let's say momentum is conserved in all frames... An observer on the ground observes two paticles with masses m1 and m2 and finds upon measurement that momentum is conserved. Use classical velocity addition to prove that momentum is conserved if the observer is on a train...
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