In three dimensions, massive objectsmay appear to be stationary, or moving. But cannot move at the speed of light.
Massless particles move at and only at the speed of light.
Tachyons…with negative complex mass…move at velocities above c to theoretically infinite speed at zero energy.
If I understand it correctly, observing from four dimensions, ALL objects are actually moving at c: slow or stationary objects move very little in the space direction, but still move forward throught time at c.
Tachyons are just the opposite: they move forward through time relatively little, but are free to move through space.
As a particle moves closer and closer to the speed of light, it’s mass increases and time slows down.
I think this is analogous to indeterminancy in quantum mechanics: the more you are moving in space, the less you are moving in time.
Massless luxons essentially straddle the light speed barrier in space and time simultaneously.
During the Big Rip
eventually ALL objects are flying away from each other at c.
Would this indicate that the time dimension is shrinking to nothing, leaving c to propagat in space only?
The analogy is inexact at best; the relationship between motion in space and movement through time is governed very explicitly and completely by the Lorentz transformation on a Minkowski space, which is linear if the properties of that space are homogenous (an underlying assumption of Special Relativity). Indeterminancy, on the other hand, is based on the notion that you cannot know or measure the exact state of a system; that you can only know the system stochastically to within certain bounds. Admittedly, those bounds necessarily get larger with an increasing time period, but that’s about as far as the analogy goes. Indeterminacy has nothing to do with the relationship between movement in space and in time except when you get into relativistic quantum field theory, which goes back to Special Relativity.
I’m not even sure exactly what to make of these statements. Massless particles do move at c, which means that they don’t experience/move through time from their own perspective. The accelerating expansion of spacetime does mean that the apparent motion of objects increases with distance and time, eventuallly achieving and even exceeding c (as currently occurs at the cosmic event horizon, 46 billion light years or so distant), but that doesn’t mean that the objects are literally in motion or experiencing acceleration, but rather that the space between them is expanding. Special Relativity is perfectly fine with this (as long as it occurs evenly in any relatively flat volume of spacetime) and it doesn’t result in any contraction of time to an infinitesmal, though any information transmitted from one object to another will have to take an increasingly longer path and thus greater time, and (in the case of electromagnetic carrier bosons, i.e. photons) be shifted in frequency toward the red end of the spectrum, eventually disappearing. At that point, distance in terms of space or time are meaningless, just like measuring the literal radius of a black hole.
I’m not sure that answered your question, or indeed, exactly what your question is, but there you go.
Only very vaguely. Much better analogies are available in plain ordinary experience. If I stand a meterstick vertically on the floor, then I could say that it’s 100 cm tall. If I tilt it to the side a bit, I might instead say that it’s 80 cm tall, and 60 cm across. But the actual inherent length of the stick is still 100 cm.
Also, the only reason that people say that the mass of an object increases as it approaches c is that they’re assuming that the formula for momentum is always p = mv. But it makes all of the calculations in relativity much simpler to instead just say that the mass is constant, and p = mgammav, or p = mu, where u = gamma*v.
As for your main question, there are already things in the Universe for which the distance between them is increasing at a rate greater than c. To say they’re moving at a speed of greater than c relative to each other, though, you’d need an inertial reference frame that encompassed both objects, and that’s just not possible in an expanding universe. The difference between the current situation and a Big Rip is just that right now, such objects are very far apart, but in a Big Rip, the distance at which this would occur would get arbitrarily small.