[paul cotter (OP)]

Suppose I was travelling in a vehicle at a speed od 0.9c. My apparent speed, in my frame would be 2.3c(if I have got my math right!). I thought this would be defined as a rapidity of 2.3c but some recent comments cast doubt on this. Am I right or wrong?

[A-wal]

Suppose I was travelling in a vehicle at a speed od 0.9c. My apparent speed, in my frame would be 2.3c(if I have got my math right!).

Why?  Your speed relative to what? Your apparent speed is always < c, unless you use a coordinate system that you've accelerated out of after you've accelerated out of it.

[Halc]

What is the correct term for a speed apparently greater that c?

Still called speed, distance over time.  For instance, the red dot that you cat chases, or a Moire pattern, are examples of things that can easily move faster than c.

Suppose I was travelling in a vehicle at a speed od 0.9c. My apparent speed, in my frame would be 2.3c(if I have got my math right!).

No.  You apparent speed in your own frame is by definition zero.

For instance, in the inertial frame of some muon in the upper atmosphere, you are traveling in a vehicle at about 0.97c, but in your own frame, your apparent speed is zero.

I thought this would be defined as a rapidity of 2.3c

OK, rapidity (or celerity) would be 2.3, meaning that if there were markers every light-second apart, stationary in the frame relative to which you are moving at 0.9c, you'd see those markers go by at a rate of 2.3 per second, but each marker would be moving at 0.9c relative to you.  They go by quicker only because they're 1/2.3 light seconds apart in your frame.  This isn't a speed since nothing is moving faster than c.

As for recent comments, what, by A-wal?  Can't read most of it in absence of Tex, and he apparently has an aversion to hyperbolic functions and an aversion to finding fault in posts with which he apparently disagrees.

Sorry that this comments below are from a different topics, but I don't want to contribute too much to topics that seems to be attempting obfuscation.

(1) there is no time contraction in SR.

Sort of. It's just called time dilation, which is a coordinate effect, not a physical one.

(2) an inertial frame of reference is one without acceleration.

The frame is not an accelerating one, yes, but objects can still accelerate withing an inertial frame.

(3) it is possible to accelerate uniformly and stay v<c. I think a move to "new theories" is on the cards,

Indefinite uniform coordinate acceleration is impossible, but indefinite uniform proper acceleration is always possible.

There must be a simple formula to calculate the time dilation by the acceleration.  This seems to be a way to know who is correct.

Of course there is, T = (2(√(c^2/(c^2−v^2))))((vx)/c^2)

In the topic where this comment originated, I gave several examples of constant acceleration with negligible dilation, and examples of different accelerations that gave identical dilation.

Meanwhile, the formula posted makes no mention at all of acceleration, only speed, making it a function of speed, not of acceleration at all.

Given that the clock on my wall is effectively constantly accelerating at about 9.8 m/s/s I'd have thought this was a well studied question with a well known answer.

This is indeed an example of continuous (but not uniform) proper acceleration, but it isn't framed in an inertial frame except locally.  It isn't uniform since the direction vector changes, but that would not be true at say the North pole, so the comment is valid in that sense.  Yes, in deep space, a constantly linear accelerating clock will tick at one second per second in its own frame. This is not news, it being true regardless of the motion of the clock.

[paul cotter (OP)]

Thanks Halc, and no problem with the additional stuff. One final question, which is the most appropriate for that apparent speed of 2.3c, rapidity or celerity(a term I am not familiar with)?

[A-wal]

One final question, which is the most appropriate for that apparent speed of 2.3c

That is not your apparent speed! Your apparent speed is 1.9c. As I said...

Your apparent speed is always < c, unless you use a coordinate system that you've accelerated out of after you've accelerated out of it.

That's exactly what you're doing.

[Halc]

Thanks Halc, and no problem with the additional stuff. One final question, which is the most appropriate for that apparent speed of 2.3c, rapidity or celerity(a term I am not familiar with)?

I've been corrected on this since I've called it rapidity in the past, but celerity is the correct term, being γv , or (gamma.v), while rapidity is arctanh(v), which is similar.  Celerity is coordinate distance (relative to one frame) per proper time of a clock not stationary in that frame.  Rapidity is more geometric, a hyperbolic rotation, angle of Lorentz boost.

That is not your apparent speed! Your apparent speed is 1.9c. As I said...

As I said, one's own apparent speed is always zero.  Perhaps Earth (or wherever you started) is moving at 0.9c, but that's it's apparent speed,  not yours.

[A-wal]

As I said, one's own apparent speed is always zero.  Perhaps Earth (or wherever you started) is moving at 0.9c, but that's it's apparent speed,  not yours.

Pedantic overload! No it's not their their speed or yours, it's your speed relative to each other. Saying it's their speed relative to you is no more correct than saying it's your speed relative to them.