The velocity transformation formula in this case gives:$$v' = \frac{2v}{1 +\frac{v^2}{c^2}}$$Where ##v =0.9c##bensabriK said:
Do you know the velocity addition formula?bensabriK said:
You are wrong. The formula quoted by both replies is the correct formula to add any two speeds in special relativity. Why would you need a different formula for adding two speeds if one object is inside another and one outside?bensabriK said:
This requires general relativity, not special relativity. Speed is a much more complicated concept for spatially separated objects in curved spacetime. The recession speed of distant objects can exceed ##c## in this case. The speed of nearby objects cannot, though, which is the case whete SR is applicable.bensabriK said:
What are you basing this opinion on?bensabriK said:
Summing the two speeds, even with a person walking inside a train, is never exactly the right formula - the relativistic velocity addition formula topsquark gave in post #3 of this thread is always right. However, when ##u’v/c^2## is very small (as it is for walking and train speeds) the difference is small enough that we naturally use the simpler formula even though it is not exact.bensabriK said:
I am not sure why you think it would be restricted in that way. But if you do think so then you can always directly use the Lorentz transforms.bensabriK said:
It's hard to answer it. But, i can say that; if we think the universe like a baloon, then, we don't know the exact diameter of this baloon, we don't know how much the universe wide. Because it expanded with a very high speed in omni direction, not higher than light speed. But the expanding speed may be higher than lightspeed. Therefore we don't know the diameter of universe. It may larger than 13.5 *2 lightyear wide. Therefore i asked that question. The expanding speed of universe may higher than the speed of light.topsquark said:
I'm afraid this is a mishmash of misunderstandings about the expanding universe model.bensabriK said:
The expansion of the universe is not a speed. It's a speed per unit distance. About ##70 km/s## per megaparsec.bensabriK said:
If you have two masses, each moving at 0.9c in opposite direction, the separation speed would be 1.8c. However, your question asked about the speed measured from one of the masses.bensabriK said:
I usually use "separation rate" rather than "separation speed", just to keep the language that little bit more distinct.David Lewis said:
As others said, you are wrong with regard to this.bensabriK said:
Relative to what? Are they moving at speed 0.9 ##c## relative to each other?bensabriK said:
0.9 ##c##. On the other hand, if you have an observer in between the two objects (masses are not objects, mass is a property of objects) and the objects move in opposite directions at speed 0.9 ##c## relative to the observer, then an observer at rest on one of the objects will move at a speed of about 0.99 ##c## relative to the other object.bensabriK said:
No, we don't. When the speeds are small compared to ##c## we can get away with adding them as a very good approximation, but adding is not the correct way to combine the speeds.bensabriK said:
That scientists, engineers, and technicians working at thousands of places around the world every day use this as a fact of life.bensabriK said:
Yeah, don't think of the universe as a balloon. It's not anything like a balloon.bensabriK said:
The speed of separation of two masses refers to the rate at which the distance between two objects increases over time. It is essentially the relative velocity of one mass with respect to the other, in the context of them moving apart.
The speed of separation can be calculated by determining the relative velocity of the two masses. If the velocities of the two masses are \( \vec{v_1} \) and \( \vec{v_2} \), the speed of separation is given by the magnitude of the vector \( \vec{v_1} - \vec{v_2} \).
The speed of separation is affected by the initial velocities of the masses, the forces acting on them (such as gravitational, electromagnetic, or contact forces), and the masses themselves if the forces are mass-dependent. External influences like friction or drag can also play a role.
No, the speed of separation is not always constant. It can change due to varying forces acting on the masses, changes in their velocities, or interactions with other objects or fields. For example, gravitational attraction between the masses can decelerate their separation.
In collision and rebound scenarios, the speed of separation after the collision is often analyzed to understand the dynamics of the impact. The coefficient of restitution, which measures the elasticity of the collision, is defined as the ratio of the speed of separation to the speed of approach. This helps in determining how much kinetic energy is conserved or lost during the collision.