Re: [math-fun] how many decimal places exist in the mass of an electron (& other such things)?
There's a bit of a problem in gathering together a million-electron blob: they repel one another like crazy. In fact, the amount of energy require to confine them is significant in the m=E/c^2 sense. It might be easier to estimate the mass of an electron & an anti-electron by colliding them together & measuring the energy. At 01:46 PM 11/23/2013, Warren D Smith wrote:
If you try to measure the mass m of an electron, some experimental error DELTAm, and the energy-time uncertainty principle combined with the finite lifetime of the universe (at least so far...) causes a limit on the accuracy of m.
So one could argue, the mass of the electron is inherently unknowable and undefined to more than a certain number of decimal places.
Except, somebody could measure the mass of a million-electron blob to try to dodge that limitation.
So anyhow... what are the inherent limits on how many decimal places can exist in such quantities (any further would have no meaning) and if so, estimate them. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
Physicists spend a great deal of time and effort on understanding the errors in any physical measurement. A particle physics PhD involves about 2 years of classes, 2 years of slave labor, 1 year of measurement and then 3 years of error analysis. This is no joke. Since particle physics is an inherently statistical field, particle physicists are experts at error analysis. http://pdg.lbl.gov/2013/listings/rpp2013-list-electron.pdf On Sat, Nov 23, 2013 at 4:05 PM, Henry Baker <hbaker1@pipeline.com> wrote:
There's a bit of a problem in gathering together a million-electron blob: they repel one another like crazy. In fact, the amount of energy require to confine them is significant in the m=E/c^2 sense.
It might be easier to estimate the mass of an electron & an anti-electron by colliding them together & measuring the energy.
At 01:46 PM 11/23/2013, Warren D Smith wrote:
If you try to measure the mass m of an electron, some experimental error DELTAm, and the energy-time uncertainty principle combined with the finite lifetime of the universe (at least so far...) causes a limit on the accuracy of m.
So one could argue, the mass of the electron is inherently unknowable and undefined to more than a certain number of decimal places.
Except, somebody could measure the mass of a million-electron blob to try to dodge that limitation.
So anyhow... what are the inherent limits on how many decimal places can exist in such quantities (any further would have no meaning) and if so, estimate them. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
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This is my chance to ask: When a physicist writes a measurement like 548.57990943 ± 0.00000023, does the number after the ± represent the standard deviation (root-mean-squared error), or something else? Thanks, Dan On 2013-11-23, at 7:57 PM, Rowan Hamilton wrote:
Physicists spend a great deal of time and effort on understanding the errors in any physical measurement. A particle physics PhD involves about 2 years of classes, 2 years of slave labor, 1 year of measurement and then 3 years of error analysis. This is no joke. Since particle physics is an inherently statistical field, particle physicists are experts at error analysis.
It means a great deal more than that. There are statistical errors (usually calculated assuming a Poisson distribution) but there are also systematic errors, which are very complicated to study. The systematic errors come from many sources, some of which may be correlated. It is necessary to understand these systematic errors in a linear algebra sense. You need to think of the solution space a manifold, and the errors live in a tangent space near the measurement point. Correlated errors represent non-orthogonal basis vectors in this tangent space. If you have removed all correlations from your errors, then you have an orthogonal basis for your tangent space, and then you can add your errors in quadrature and be sure that you have an accurate error analysis. I spent years studying this in great detail in grad school. On Sat, Nov 23, 2013 at 8:34 PM, Dan Asimov <dasimov@earthlink.net> wrote:
This is my chance to ask: When a physicist writes a measurement like
548.57990943 ± 0.00000023,
does the number after the ± represent the standard deviation (root-mean-squared error), or something else?
Thanks,
Dan
On 2013-11-23, at 7:57 PM, Rowan Hamilton wrote:
Physicists spend a great deal of time and effort on understanding the errors in any physical measurement. A particle physics PhD involves about 2 years of classes, 2 years of slave labor, 1 year of measurement and then 3 years of error analysis. This is no joke. Since particle physics is an inherently statistical field, particle physicists are experts at error analysis.
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I just want to know what the number after the ± means. --Dan On 2013-11-23, at 10:16 PM, Rowan Hamilton wrote:
It means a great deal more than that. There are statistical errors (usually calculated assuming a Poisson distribution) but there are also systematic errors, which are very complicated to study. The systematic errors come from many sources, some of which may be correlated. It is necessary to understand these systematic errors in a linear algebra sense. You need to think of the solution space a manifold, and the errors live in a tangent space near the measurement point. Correlated errors represent non-orthogonal basis vectors in this tangent space. If you have removed all correlations from your errors, then you have an orthogonal basis for your tangent space, and then you can add your errors in quadrature and be sure that you have an accurate error analysis. I spent years studying this in great detail in grad school.
On Sat, Nov 23, 2013 at 8:34 PM, Dan Asimov <dasimov@earthlink.net> wrote:
This is my chance to ask: When a physicist writes a measurement like
548.57990943 ± 0.00000023,
does the number after the ± represent the standard deviation (root-mean-squared error), or something else?
Hello, just to point out that the value of the third magnetic moment of the electron is : Li4(1/2). Best regards, Simon Plouffe
If it's in a table it should tell you what it means. In a paper think it is usually three standard deviations, but NIST tables quote the std dev and relative uncertainty (std dev/mean value). Brent On 11/24/2013 4:05 AM, Dan Asimov wrote:
I just want to know what the number after the ± means.
--Dan
On 2013-11-23, at 10:16 PM, Rowan Hamilton wrote:
It means a great deal more than that. There are statistical errors (usually calculated assuming a Poisson distribution) but there are also systematic errors, which are very complicated to study. The systematic errors come from many sources, some of which may be correlated. It is necessary to understand these systematic errors in a linear algebra sense. You need to think of the solution space a manifold, and the errors live in a tangent space near the measurement point. Correlated errors represent non-orthogonal basis vectors in this tangent space. If you have removed all correlations from your errors, then you have an orthogonal basis for your tangent space, and then you can add your errors in quadrature and be sure that you have an accurate error analysis. I spent years studying this in great detail in grad school.
On Sat, Nov 23, 2013 at 8:34 PM, Dan Asimov <dasimov@earthlink.net> wrote:
This is my chance to ask: When a physicist writes a measurement like
548.57990943 ± 0.00000023,
does the number after the ± represent the standard deviation (root-mean-squared error), or something else?
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Nobody so far has addressed Warren's actual question, which seems to raise the problem of how well it is ultimately possible to even define such physical constants. A more conveniently macroscopic example is the length of a day. Variations in the earth's orbit limit the accuracy to which the length of individual days can be treated as a constant. Averaging over an entire year (itself subject to smaller variations) permits greater accuracy, but involves redefining the meaning of "day" in a more sophisticated fashion. Digging further down encounters alarming philosophical questions concerning (for example) the definition of measurement, and the universe within which it is legitimate to take an average --- over a sufficiently long period, the "day" is progressively lengthening. Fred Lunnon On 11/24/13, meekerdb <meekerdb@verizon.net> wrote:
If it's in a table it should tell you what it means. In a paper think it is usually three standard deviations, but NIST tables quote the std dev and relative uncertainty (std dev/mean value).
Brent
On 11/24/2013 4:05 AM, Dan Asimov wrote:
I just want to know what the number after the ± means.
--Dan
On 2013-11-23, at 10:16 PM, Rowan Hamilton wrote:
It means a great deal more than that. There are statistical errors (usually calculated assuming a Poisson distribution) but there are also systematic errors, which are very complicated to study. The systematic errors come from many sources, some of which may be correlated. It is necessary to understand these systematic errors in a linear algebra sense. You need to think of the solution space a manifold, and the errors live in a tangent space near the measurement point. Correlated errors represent non-orthogonal basis vectors in this tangent space. If you have removed all correlations from your errors, then you have an orthogonal basis for your tangent space, and then you can add your errors in quadrature and be sure that you have an accurate error analysis. I spent years studying this in great detail in grad school.
On Sat, Nov 23, 2013 at 8:34 PM, Dan Asimov <dasimov@earthlink.net> wrote:
This is my chance to ask: When a physicist writes a measurement like
548.57990943 ± 0.00000023,
does the number after the ± represent the standard deviation (root-mean-squared error), or something else?
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The default assumption is that our knowledge of the measurement result can be described by a Bayesian posterior which is a Gaussian with the stated mean and standard deviation. -- Gene
________________________________ From: Dan Asimov <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Saturday, November 23, 2013 8:34 PM Subject: Re: [math-fun] how many decimal places exist in the mass of an electron (& other such things)?
This is my chance to ask: When a physicist writes a measurement like
548.57990943 ± 0.00000023,
does the number after the ± represent the standard deviation (root-mean-squared error), or something else?
Thanks,
Dan
On 2013-11-23, at 7:57 PM, Rowan Hamilton wrote:
Physicists spend a great deal of time and effort on understanding the errors in any physical measurement. A particle physics PhD involves about 2 years of classes, 2 years of slave labor, 1 year of measurement and then 3 years of error analysis. This is no joke. Since particle physics is an inherently statistical field, particle physicists are experts at error analysis.
participants (7)
-
Dan Asimov -
Eugene Salamin -
Fred Lunnon -
Henry Baker -
meekerdb -
Rowan Hamilton -
Simon Plouffe