Quote:
Originally Posted by sjastro
Hello Markus,
I'm afraid your idea doesn't work as it cannot explain the linear relationship between distance and recession velocity.
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Hi Steven, sorry for the late reply - I've been away. Also, I've been trying to get what you're saying - I'm not particularly mathematical. So let me see if I have this right?
So you're saying my idea would not be linear as is observed in nature, but would instead be, what, logarithmic?
Quote:
Originally Posted by sjastro
The linearity can only be explained if the space between stationary objects expands rather than the objects themselves moving through space.
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Which is interesting because if spacetime expands only in the absence of matter, then you would assume that the gravitational force has limited range, or falls off in a way we don't understand, which would have implications for dark matter, one would have thought.
Quote:
Originally Posted by sjastro
If an object recedes from the observer in space at an increasing acceleration at non-relativistic velocities you get a rather messy mathematical equation of the format.
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Why non-relativistic? Isn't the whole point of the Observable universe's event horizon that it recedes from us at relativistic velocities? That's why we can never see past it?
Quote:
Originally Posted by sjastro
x=vt+(dv/dt)t^2/2!+(d^2v/dt^2)t^3/3!+(d^3v/dt^3)t^4/4!
+.......
x is the distance, v the recession velocity, t is time, (d^nv/dt^n) are the increasing higher order derivatives of velocity with respect to time.
The equation is clearly not linear for distance and recession velocity.
Regards
Steven
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So why can't we just use a = Δv / Δt if we're talking non-relativistic velocities, or a 4-vector for relativistic velocities? I'm not sure why the higher order derivatives are necessary, or why you begin by multiplying Velocity and time instead of dividing delta time by delta velocity. Sorry for my ignorance. Which acceleration equation are you using?
Best,
Markus