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Was Feynman Wrong?



I recently found this

talk by Richard Dawkins and was delighted to discover it contained a quote by Ricahrd Feynman who is one of the scientists who has most inspired me.


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?!


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I could be wrong, but I don't think Feynman's talking about the accuracy of the theory relative to measurement, but the accuracy of both relative to the actual Dirac number (since he talks of the accuracy of these numbers), in this case +/- 4 X 10^(-11) for measurement, and +/- 2 X 10^(-10) for the theory.


When applied to the distance analogy, this gives +/- 1.6 X 10^(-4) and +/- 7.9 X 10^(-4) respectively, which is at least the right order of magnitude (which is what a lot of scientists mean when they talk about accuracy on a small or large scale).

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I think your probably right - as you say the experimental accuracy is equivilent to 0.16mm which is close to that of a thick human hair. But the theoretical range is closer to the good old millimeter 0.79mm - now one millimeter in 4,000 kms is still pretty amazing but I think Feynman is really only giving justice to the experimental number not the theoretical one when he talks of one hairs breadth - as he was a theoretician it's a bit cheeky - you can get to a millimeter on a black board but you need an engineer to get within a hairs breadth!

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To be fair to Feynmann, the article was intended for a general audience so precise measurements for comparitive purposes would probably just interfere with what he's trying to do, that being to give a sense of scale. Compared with the distance used in the analogy, the difference between the diameter of a strand of hair and something close to a milimetre is negligible as far as trying to impress a sense of whats going on up is concerned (and it at least has some kind of rigour in that the order of magnitude is the same)!

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