Is the maximum possible measurable velocity = 2c

Question

What is the maximum velocity that can be measured between two objects? Is $2c$ the correct answer?

Two photons (A & B) are emitted simultaneously from my position; photon A going north and photon B south. Both photons are traveling in opposite directions such that a single straight line can be drawn through A, B, and our position.

Given:

1. Photon A is moving north with a velocity $v = c$

2. Photon B is moving south with a velocity $v = c$

3. The rate of increase of the distance between A and B, expressed as a velocity, is $v = 2c$

Therefore, the maximum possible measurable velocity between two objects = $2c$

Answer 1

Consider two objects approaching each other, along a line through both objects, with speed $u_1$ and $u_2$ respectively in some inertial frame of reference (IRF).

The distance between the two objects, decreases at the rate of $u_1 + u_2$; this is the closing speed. Note that this speed is not a relative velocity and so the relativistic velocity addition formula does not apply.

Thus, for massive objects, this closing speed can approach arbitrarily close to $2c$.

However, from the perspective of either object, the relative velocity of the other object is less than $c$ since the relativistic velocity addition formula applies.

In summary, the rate of decrease of the distance between two objects, as measured in some IRF, is not the speed of any object and thus, is not limited to $c$ or less. But, since the relative speed of any object cannot exceed $c$ (as far as we know), the closing speed cannot exceed $2c$.

Answer 2

This is really a plain old Special Relativity question about addition of velocities. The guy in the middle gave object 1 a velocity $-v_1$ and object $2$ a velocity $v_2$. When you ask for the relative velocity between the two objects, you mean as observed from sitting on one of the objects (say object 1). In this case, you see the guy in the middle receding from you with $v_1$. In his frame he throws object $2$ with $v_2$. You see the special relativistic addition of $v_1$ and $v_2$ which is always less than $c$. $$ \lambda_1 = \tanh^{-1}\left(\frac{v_1}{c}\right) $$ $$ \lambda_2 = \tanh^{-1}\left(\frac{v_2}{c}\right) $$ $$ \frac{v}{c}=\tanh\left(\lambda_1+\lambda_2\right) $$ For fun, this is shown using Lorentz Boost parameters which are additive when the velocities are in the same direction. The maximum tanh can become is $1$. Therefore $c$ is the maximum possible relative velocity, not $2c$.

Answer 3

The velocity a body can show is $5c$ which can be obtained by going at $0.5^{1/2}c$ i.e one divided root two $c$. Going at more or less velocity causes you to show less velocity in the real world or the actual reference frame so max relative velocity is $0.5+0.5=1c$.

Answer 4

Two objects/photons moving at c in opposite direction, the distance will increase at 2c for a "stationary" observer in between them.

But They can not see or communicate with one another. Therefore, their relative speed is immeasurable.

Suppose, they start with c, they will instantaneously disappear for each other.