# Is there a better way of writing speeds very close to c?

Any discussion on, say, interstellar travel, seems to rapidly devolve into repeating the word “nine” many times.

Is there a better way?

All I can think is saying “99 point, followed by ten nines, percent” or “within 1x10^-7 of a percent of the speed of light”.

I guess if you can talk in terms of percent you could also just use an absolute value, e.g. “a billion trillionth part slower than the speed of light”?

This is similar to purity notation for laboratory gases: a gas that is 99.999% pure is said to be “five nines pure.”

I’ve never heard a discussion of interstellar travel that references speeds very close to (but less than) c. Real interstellar travel is going to happen at speeds far less than c, and science-fiction interstellar travel always seems to happen at large multiples of c.

High-energy particle physics, OTOH, does make reference to values very close to (but less than) c. The Oh-My-God particle was said to be traveling at 99.99999999999999999999951% of the speed of light, or about 23 nines. That article expresses the speed of the particle in a variety of ways in an attempt to get the reader to grasp how ridiculous this particle was, mostly by comparing its kinetic energy to more familiar levels - but the fact that the 99.999… notation is there suggests that when it comes to reporting the speed, there really isn’t a better notation.

It is also used to denote system reliability. I once worked on an air traffic control system with critical functions that were required to have “six nines” of reliability, which translates to unscheduled downtime of about 2 seconds per month.

Consider the following table
.9 --> 2.3
.99 --> 7.1
.999 --> 22.4
.9999 --> 70.7
.99999 --> 223.6
.999999 --> 707.1
.99999999 --> 7071
… where the final line means "an object traveling at 99.999999% of the speed of light has mass-energy equal to 7071 times its rest mass. The number “7071” seems easier to say and grok than “99.999999%.” I’ve no idea if this approach is in common use, nor if my phrasing is correct.

You could use rapidity, which is basically the arctanh(v/c). So five nines would be about 6.

Ah thanks, this is the kind of thing I was looking for.

This doesn’t necessarily follow though. There are many contexts where there is very neat, specific language that scientists and mathematicians use, but for the general public very awkward constructions must be used, because authors cannot assume prior knowledge.

In the case of 99.999… it rapidly stops having any intuitive meaning after the first couple of 9s and we may as well be saying “really really really really really close to c”.
If it’s the best we have then fair enough though. But it doesn’t add a lot to pop sci discussions IMO.

I’d go with citing the Lorentz Factor value.

Can you give me some examples of what pop sci discussions need this?

This is great, thanks

In astronomy, you can measure the redshift (relative difference between the observed and emitted wavelengths) of a given object. Often this will be related to its relative motion via the relativistic Doppler effect.

You’re welcome!

I’m not surprised that the function I described has a name.

If you then divided this by an extra factor of beta (or leave it as is for speeds close to c where beta is close to 1), you get a non-SciFi based warp factor. That can be interepreted as the number of times the speed of light you are travel according to subjective time.

So if you travel one light year at “warp factor” 365. You will age about 1 subjective day.

OK, was anyone else expected a discussion about words per minute around the cursive letter C?

[sub]ok, just me then[/sub]

Yeah, listing the gamma (what septimus described and Francis Vaughan linked to) is the standard approach. Scientists almost never actually use the string-of-nines form, except in writing for the general public who doesn’t know what gamma is.

He said very close to c.

Obviously, the intended topic was not getting your b’s and d’s mixed up when you’re writing them really fast.

I actually expected a rather dumb discussion about writing code that is as fast as c. I’m glad to see that it was actually something not dumb. – and I’ve learned something, I didn’t know ‘rapidity’ was a thing.

The notation doesn’t just use nines. Or at least when we talk about metal purity or filtration efficiency, it doesn’t. 0.9997 can be written 3N7 and 0.99999446 is 5N446.