A little something from the deep recesses of my warped mind
Ok. I don't expect this to get the level of attention that the fist fight thread will, but alas I realize there are some physicists/statisticians floating around so I thought I would shoot out my question in a form most easily appreciated.
We theorize that we have a two state system (lets say one like a spin 1/2 nuclei, where there is a definitive and measurable spin up and definitive measurable spin down). How many measurements are needed to exclude the possibility of a third measurable state above a certain confidence level, lets say for the sake of argument 95% confidence.
What I am saying here is if we measure the spin of a single electron, we won't know whether this is a two state system; if we measure the spin of two electrons, we still won't know if this is a two state system etc etc. What number of measurements need to be made to assure us above a 95% confidence level that the system has only two states?
This came up because I was thinking about the mass-energy density of the universe and then what is the largest volume the universe can be divided into to obtain a well behaved distribution of local densities that average to the universes' average density and how this volume relates to the models of the shape of the universe etc and perhaps more...
All in the shower... your best thinking happens in the shower...
We theorize that we have a two state system (lets say one like a spin 1/2 nuclei, where there is a definitive and measurable spin up and definitive measurable spin down). How many measurements are needed to exclude the possibility of a third measurable state above a certain confidence level, lets say for the sake of argument 95% confidence.
What I am saying here is if we measure the spin of a single electron, we won't know whether this is a two state system; if we measure the spin of two electrons, we still won't know if this is a two state system etc etc. What number of measurements need to be made to assure us above a 95% confidence level that the system has only two states?
This came up because I was thinking about the mass-energy density of the universe and then what is the largest volume the universe can be divided into to obtain a well behaved distribution of local densities that average to the universes' average density and how this volume relates to the models of the shape of the universe etc and perhaps more...
All in the shower... your best thinking happens in the shower...
Comments
Originally posted by billybobsky
The one I grew in the basement in high school, yes, I am affraid it is...
How proud your parents must have been!
Originally posted by addabox
How proud your parents must have been!
Not as proud as my classmates...
And god damn it, if strings are mentioned once more in this thread...
BWAHAHAHAHAH!
Now I guess they should have banned me rather than just shut off posting priviledges, because kickaha and Amorph definitely aren't going to like being called to task when they thought they had it all ignored *cough* *cough* I mean under control. Just a couple o' tools.
Don't worry, as soon as my work resetting my posts is done I'll disappear forever.
Originally posted by billybobsky
[B]
We theorize that we have a two state system (lets say one like a spin 1/2 nuclei, where there is a definitive and measurable spin up and definitive measurable spin down).
Ok. Let's do a Stern-Gerlach thought experiment with a hydrogen atom containing one electron in the 1s state (ground). Keep in mind that since electrons are fermions, they may not have the same set of quantum numbers(their wave functions are antisymmetric).
How many measurements are needed to exclude the possibility of a third measurable state above a certain confidence level, lets say for the sake of argument 95% confidence.
With our Stern-Gerlach thought experiment, all we are looking for is the spatial quantization resultant from the intrinsic magnetic dipole moment as hydrogen atoms pass through a non-uniform magnetic field. Since we assume all our hydrogen is in the 1s state (we can never be sure), we can ignore orbital dipole moment/angular momentum (we know this because the rotational energy part of the Hamiltonian is zero). We should see a clear delineation by banding from a detector due to spatial quantization from the two possible 1s states for the electron. After a few hundred events from our "perfect hydrogen" (very low temperature), we should be quite confident that the experiment matches theory that there are only two possible 1s states for an electron in a hydrogen atom.
What I am saying here is if we measure the spin of a single electron, we won't know whether this is a two state system; if we measure the spin of two electrons, we still won't know if this is a two state system etc etc. What number of measurements need to be made to assure us above a 95% confidence level that the system has only two states?
I'm not sure I understand you. It all depends on the details of the experiment.
This came up because I was thinking about the mass-energy density of the universe and then what is the largest volume the universe can be divided into to obtain a well behaved distribution of local densities that average to the universes' average density and how this volume relates to the models of the shape of the universe etc and perhaps more...
Any model of the universe must account for dark energy and dark matter. Leading candidates use general relativity(or quantum gravity) with a cosmological constant, and take supersymmetry into account for dark matter.
Edit: It boils down to how much of the universe needs to be explored for us to reasonably say that we are confident in a model of the universe. Each model should have its own limit. Right now I am not sure this does anything for anyone but...
Originally posted by billybobsky
This came up because I was thinking about the mass-energy density of the universe and then what is the largest volume the universe can be divided into to obtain a well behaved distribution of local densities that average to the universes' average density and how this volume relates to the models of the shape of the universe etc and perhaps more...
Big Bang glow hints at funnel-shaped Universe
Sounds good to me...
ok, so the math certainly wasn't there, but i did draw a hypothetical picture...
anyway, "system"?!?!?
you are clearly deluded?
But that assumes the chance of coming up bellies is the same as heads or tails, 1/3. If you don't know the probability of observing that 3rd state, then you can't calculate how many observations you need to be reasonably certain it doesn't exist. If the belly side is 1x10^-100 the size of the head and tail sides, you'll need an awful lot of coin flips to observe it - but it is there all along.
(or you could just say it's like a coin flip perfectly. 99.999% of the time it's probably heads or tails, but it could, in theory, land on the edge and be neither heads or tails.)
If the universe has a predicted set of properties/rules, what is the largest you can segment the universe into that will give a well behaved distribution of all of those properties?
I am basically assuming there are some properties that are represented best in ensembles rather than assumed immutability...
And no I am not high...
Now I guess they should have banned me rather than just shut off posting priviledges, because kickaha and Amorph definitely aren't going to like being called to task when they thought they had it all ignored *cough* *cough* I mean under control. Just a couple o' tools.
Don't worry, as soon as my work resetting my posts is done I'll disappear forever.