Poll: A little math problem
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I have no idea what this principle of sufficient causation is that you mention, but this is simple physics that is easily calculable by any junior year undergrad or first year graduate physics student. Nothing freaky about it. In fact, dealing with light is the easy stuff.Cheeze_Pavilion post=18.73797.860423 said:
Now if you want freaky, try dealing with identical particle mixed states. There you find that the particles suffer an identity crisis. Particle1 actually will not be able to decide if it is particle1 or particle2, and particle2 will have the same trouble.
In this case with the polarizations, we are using the wave nature of the light. Explaining the truth of the wave-particle duality of nature is...hard. Really, really, freaking hard. And even harder to make real sense of it. You begin to understand it in a back-of-the-mind intuition, but it's impossible to really convey the true reality of it to anyone who is not well experienced with the math and machinery of quantum mechanics(I tried explaining eigenstates and eigenvalues to a friend of mine once. Got about half-way before he asked me to just stop). It seems easy at first to just say that it means things act like a particle and a wave. But, it's not until you start really truly thinking about it that you discover you don't really know what that truly means. We just know how to calculate it.Lukeje post=18.73797.860435 said:
This is just probablity. These questions are often counter-intuitive.Fud post=18.73797.809286 said:
Two beagles, we know that at least one is male. The possible combinations:
MM
FF
MF
FM
So we know that FF is out leaving us with:
MM
FM
MF
So the chance that the other is a male is 1/3 and that the other is a female is 2/3.
Before you go saying that I'm wrong etc. I have a degree in mathematics and studied statistics all the way through
.This question is just a tricky way of asking what's the ratio between MM and MF/FM, but if you don't believe me, here's some c++ code to simulate it yourself:
#include
using namespace std;
#include // prototypes for rand and srand
using std::rand;
using std::srand;
#include // time for seeding rand
using std::time;
inline int coinflip()
{
return rand()%2; //returns either 0 or 1 (heads or tails)
}
int main(int argc, char *argv[])
{
int n=1000000; //sample size for simulation
int coinFlipValue[2];
int results[2];
results[0]=0;
results[1]=0;
srand( static_cast( time( 0 ) ) );
for(int i=0; i<n; i++)
{
coinFlipValue[0]=0; // so past values don't affect current results
coinFlipValue[1]=0; // we simply clear the values
coinFlipValue[coinflip()]++; //flip coin 1
coinFlipValue[coinflip()]++; //flip coin 2
// cout << coinFlipValue[0] << endl << coinFlipValue[1] << endl;
// cout << coinflip() << endl;
if(coinFlipValue[0]) //conditional that says "if at least 1 of them is heads"
{
if(1<coinFlipValue[0]) //conditional that says "if both are heads"
{
results[0]++;
}
else //if they're not both heads, than up the tails count instead
{
results[1]++;
}
}
}
cout << "# of heads: " << results[0] << endl;
cout << "# of tails: " << results[1] << endl;
system("PAUSE");
return EXIT_SUCCESS;
}
#include
using namespace std;
#include // prototypes for rand and srand
using std::rand;
using std::srand;
#include // time for seeding rand
using std::time;
inline int coinflip()
{
return rand()%2; //returns either 0 or 1 (heads or tails)
}
int main(int argc, char *argv[])
{
int n=1000000; //sample size for simulation
int coinFlipValue[2];
int results[2];
results[0]=0;
results[1]=0;
srand( static_cast( time( 0 ) ) );
for(int i=0; i<n; i++)
{
coinFlipValue[0]=0; // so past values don't affect current results
coinFlipValue[1]=0; // we simply clear the values
coinFlipValue[coinflip()]++; //flip coin 1
coinFlipValue[coinflip()]++; //flip coin 2
// cout << coinFlipValue[0] << endl << coinFlipValue[1] << endl;
// cout << coinflip() << endl;
if(coinFlipValue[0]) //conditional that says "if at least 1 of them is heads"
{
if(1<coinFlipValue[0]) //conditional that says "if both are heads"
{
results[0]++;
}
else //if they're not both heads, than up the tails count instead
{
results[1]++;
}
}
}
cout << "# of heads: " << results[0] << endl;
cout << "# of tails: " << results[1] << endl;
system("PAUSE");
return EXIT_SUCCESS;
}
So, is this the idea? After the light passes through the horizontal filter, the light's polarization is known as horizontal. Therefore none will pass through the vertical filter. But if there is a 45 degree filter after the horizontal filter, the light that passes through will be of unknown polarization, even though it was previously all known to be horizontal, since light passing through a 45 degree filter could be either horizontal or vertical. Therefore, some of the light will pass through the vertical filter. 50 percent of light through the horizontal filter, 25 percent through the 45 degree filter, and 12.5 percent through the final, vertical filter, I'd guess.geizr post=18.73797.861422 said:
Yeah, the 45 degree filter would have to be between, since it essentially scrambles the polarizations by destroying what knowledge you had of them. Not logical, of course, but that's quantum mechanics.
You have the basic idea with just one misstep in understanding. The 45-degree filter doesn't make the light have unknown polarization; it makes the light have a 45-degree polarization. However, the 45-degree polarization is split equally between vertical and horizontal polarizations. So, in that sense it does destroy information about the polarization coming out of the horizontal filter, just as the last vertical filter destroys the information about the 45-degree filter.Samirat said:
Like I said, I've always found this a fun trick to demonstrate to people whenever I go to a 3D movie that uses the polarized lenses(which most good ones do), instead of the red/blue lenses(it doesn't work with those cause they are not polarized).
That's one of the main problems with the higher level physics. You can calculate the stuff, but it's hella hard to understand what it really means. It takes many years of experience to gain that insight, and there are aspects that you may never gain that insight with(such as wave-particle duality).Lukeje said:
Err, google "two coins probability" or something.Cheeze_Pavilion said:
This text [http://books.google.com/books?id=L6IWgaCuilwC&pg=PA14&lpg=PA14&dq=two+coins+probability&source=bl&ots=yzBvncg2JA&sig=agzX9UzzqBDkmHuhheVo7Tg40_Q&hl=en&ei=2tK8ScjRD8G0twfyseX2Cw&sa=X&oi=book_result&resnum=1&ct=result] may be helpful.
-- Alex
