Velocity and recessive velocity

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Velocity refers to the speed of an object, which cannot exceed the speed of light, while recessive velocity describes an object moving away from an observer, often in the context of the universe's expansion. The expansion of space itself allows for recessive velocities that can exceed the speed of light, unlike the movement of objects through space. Relativity asserts that the speed of light is constant across all reference frames, complicating perceptions of relative motion. Observers moving at high speeds may perceive light traveling at the speed of light, but all velocities are ultimately relative. Understanding these concepts clarifies the distinction between motion through space and the expansion of space itself.
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What is the difference between velocity and recessive velocity. I read that with velocity, an object may not past the speed of light; but with recessive velocity, an object may past the speed of light.
 
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There's no difference. "Recessive velocity" or "velocity of recession" just refers to the velocity of some object moving away from the observer. The opposite would be "approaching velocity" or "velocity of approach", for example.

The speed of light is a limit on the speed of an object in space, whether an object is coming towards you or going away. However, maybe you are thinking of the expansion of the universe, in which space itself expands, carrying objects such as galaxies along with it. The expansion of space, as opposed to the movement of objects in space, is not limited by the speed of light.
 
thanks James R. Yeah I was thinking of the expansion. I also have another problem. Well, according to relativity (I think) the speed of light is the same for all reference points. So, imagine if you willl, that you are a particle of light. You are traveling in a straight line from point A to B and another particle of light is traveling parallel and in the same direction as you. According to relativity, wouldn't the second particle of light be traveling ~3*10^8 meters per second relative to you? Wouldn't this happen if the object was traveling parallel yet in the opposite direction as well? ..:( I don't think I understand relativity very well..
 
You can't really look at things from the point of view of a particle of light. From that particle's perspective, the size of the universe would be zero, for a start.

If you consider your scenario from the point of view of a person traveling at 99.9999% the speed of light, then you would indeed see the light particle traveling the same direction as you as going at 3*10^8 metres per second, as usual.
 
At this point might I clarify that the crux of this is that all velocity is relative. There is no such thing as absolute velocity according to Relativity and every situation must be considered by the relative velocities of objects with reference to one another. In this sense, recession velocity would be the velocity with which an object moves away from the observer's specific point in space. Recession in this context just means 'moving away from'.

Hope that helps.
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...

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