# Was Feynman Wrong?

I recently found this

Feynman in his lecture QED: The Strange Theory of Light and Matter was discussing just how accurate quantum theory was. He said:

Just to give you an idea of how the theory has been put through the wringer, I'll give you some recent numbers: experiments have Dirac's number at 1.00115965221 (with an uncertainty of about 4 in the last digit); the theory puts it at 1.00115965246 (with an uncertainty of about five times as much). To give you a feeling for the accuracy of these numbers, it comes out something like this: If you were to measure the distance from Los Angeles to New York to this accuracy, it would be exact to the thickness of a human hair.

I had known that some scientist had used an analogy of great distance to get some idea of the amazing accuracy of a scientific prediction; I'd read about it years and years ago, but had forgotten the exact details (I thought the distance was between London and New York!). I'm really glad that I now know that the original source was Feynman!

I do think it is trully amazing - just think about that for a second - many hundreds of people have worked together and created simple mathematical abstractions which can be written down in a scientific paper or on a black board and argued about and which describe the real world to such an incredible amount of detail. What a feat!

But after reading this my fact-checking brain wanted to do the calculations to confirm what he'd written - and the results surprised me so I thought I'd post them here to check whether I've made a mistake!

The best guess of Dirac's Number produced from theory is 0.00000000025 units bigger than the best guess from actually measuring it. IE the theoretical number is bigger by about one part in 4,000,000,000.

Now the distance between New York and Los Angeles is about 3932.8 km.

Measuring it to that accuracy is to find the figure to a range of about 982.06 microns. Which is absolutely tiny - but it isn't as small as the thickness of a human hair. 982 microns is about a millimeter - a human hair is roughly one tenth of a millimeter.

It looks like Feynman was out by a factor of ten!!!

I think there is something hugely wonderfully ironic about all this.

Either I'm wrong - more than likely.

Or Feynman is wrong.

But sloppy, mistake making fallible humanity has been able to collaborate and measure a property of the universe (which most of us have no idea about) to a level of detail that is literally mind boggling. We have also been able to come up with a model which explains that part of the universe to a comparable level of detail and we've been able to show they agree to that mindbogglingly accurate extent.

Practically it really doesn't matter if the accuracy is one millimeter in the distance between New York and Los Angeles, or one hair - but science does care and wants to continue to ever refine it down.

There will definitely be mistakes as that refinement continues, but science mercilessly looks for mistakes and corrects them.

So am I correct to correct Feynman's mistake, or is the mistake mine?

I'm not sure - but I'll put my result out there to be queried. Trust but verify said Reagan.

That is what I did to Feynman's quote - can someone do the same for me?!

## 3 Comments

## Recommended Comments