Hey, physics guys: math notation help?

So I recently read about a scientific paper in which some physicists were able to achieve a lot more quantum entanglement at temperatures a lot higher than other people have managed.  (See here:) I was pretty sure that I wouldn't be able to understand much of this paper, but I downloaded it anyway.  (COVID lockdown craziness may or may not have played a role in this decision.)

Among the, ahem, several things that were not exactly in my wheelhouse was the following sentence: We use Bayesian statistics and spin-squeezing inequalities to show that at least 1.52(4) × 10^13 of the 5.32(12) × 10^13 participating atoms enter into singlet-type entangled states, which persist for tens of spin-thermalization times and span thousands of times the nearest-neighbor distance.

This way of writing numbers is new to me.  What do the digits in the brackets mean?  My best guess has something to do with precision, but my best guess is worth "precisely" what I paid for it.

OTOH, I'm pretty sure the Hive will know.

You ever know a kid who invented his own language, and only used it with his friends, so nobody could understand him?

Those kids grow up to be physicists.

The closest I've come to that is marking which phase something is in.  I wonder if it is conveying how many of which type of atoms are spinning a particular way?

https://en.wikipedia.org/wiki/Bayes%27_theorem

I"ll let you determine from there. Above my physics/math pay grade.

It is indeed precision. By their best calculations, they had at least 1.524x10^13, but they really can't claim that accuracy.  They are telling you they can only really claim 1.52x10^13.  It is not that the number is smaller, it is that it is less precise.

Example:  You measure your car on a scrap metal scale and they tell you your car weighs 2987 lbs.  You pull out a speaker and weigh it on a postal scale.  The speaker weighs 5 lbs 13 oz.  You can't really say your car now weighs 2981 lbs 3 oz because you did not weigh the whole car to the nearest ounce.  Your car now weighs 2981, or 2982, or maybe even 2980, but you can't claim to know down to the ounce.  Addition is easy to see; doing the same thing with a couple dozen values added, multiplied, etc., gets a little messier. 

They have very high confidence in the 1.524, but will only testify to 1.52.  They have very high confidence in the 5.3212, but they will only testify to 5.32.

Well, thank you!  That makes a lot of sense. 

(Is this the best hive, or what?)

The first thing to do is draw a free body diagram.

In reply to matthewmcl (Forum Supporter) :

Is there a confidence level that the brackets signify?  Like 80% or 90% confident in the digits? 

Streetwiseguy said:

You ever know a kid who invented his own language, and only used it with his friends, so nobody could understand him?

Those kids grow up to be physicists.

I believe it was NPR/All Things Considered that did a story about the common expression used when discussing something difficult, "Well, it's not brain surgery."

So they interviewed an imminent neurosurgeon, and he reported that they would use the equally common version, "Well, it's not rocket science."

Next, they interviewed someone from the Johnson Space Center, who informed them that under the appropriate circumstance of trying to solve a difficult problem, they  would say, "Well, it's not theoretical physics."

Naturally, they interviewed a theoretical physicist, to ask him, "Most people say that 'Its not brain surgery,' the brain surgeons say, 'Its not rocket science,' and the rocket scientists say, 'Its not theoretical physics.' What do theoretical physicists say?"

He had no answer. He'd never heard of either expression.

They live in a different world.

In reply to Floating Doc (Forum Supporter) :

and thats what we call an academic dick measuring contest.  

Hey at least it doesnt involve truck nutz. 

In reply to Apexcarver :

academic dick measuring contest.  

Is that a band name?

Floating Doc (Forum Supporter) said:

Streetwiseguy said:

You ever know a kid who invented his own language, and only used it with his friends, so nobody could understand him?

Those kids grow up to be physicists.

I believe it was NPR/All Things Considered that did a story about the common expression used when discussing something difficult, "Well, it's not brain surgery."

So they interviewed an imminent neurosurgeon, and he reported that they would use the equally common version, "Well, it's not rocket science."

Next, they interviewed someone from the Johnson Space Center, who informed them that under the appropriate circumstance of trying to solve a difficult problem, they  would say, "Well, it's not theoretical physics."

Naturally, they interviewed a theoretical physicist, to ask him, "Most people say that 'Its not brain surgery,' the brain surgeons say, 'Its not rocket science,' and the rocket scientists say, 'Its not theoretical physics.' What do theoretical physicists say?"

He had no answer. He'd never heard of either expression.

They live in a different world.

I'm not sure why, but that's very satisfying to learn, haha.

alfadriver (Forum Supporter) said:

In reply to matthewmcl (Forum Supporter) :

Is there a confidence level that the brackets signify?  Like 80% or 90% confident in the digits? 

I don't think so, but I don't work with anything using that system so I am really not sure.  All of my analysis uses XXX ± YYY or number of standard deviations.  I am in engineering, but I got a master's in teaching science (physics specifically), so that is where I learned of the parenthetical extension to significant figures.

In reply to matthewmcl (Forum Supporter) :

Thanks- I thought it was interesting that one digit was used in the first, and 2 in the second...