Does the Uncertainty principle " Focus on Location of Particles?"

[Iwonderaboutthings]

Taken from Wikipedia.

 

In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle known as complementary variables, such as position x and momentum p, can be known simultaneously.

 

Here is the link:

http://en.wikipedia.org/wiki/Uncertainty_principle

 

 

 

--->Although I am quite familiar with the generalization, I am wondering if.

 

 

That the uncertainty principle sounds like a mathematical attempt " with no physics involved" that tries to locate 2 positions simultaneously and or harmoniously, while using momentum and mass simultaneously <--- if that makes any sense.

 

 

I think precession may be the issue. By this I mean such as planet earth having 2 seasons at the same time.

 

However, could this uncertainty principle unknowingly have its " Translation Method" off by some factor of degree, due to fundamental limits of precision?

Edited September 23, 2013 by Iwonderaboutthings

[John Cuthber]

Does the Uncertainty principle " Focus on Location of Particles?"

No, because it also deals with the uncertainty of time and energy.

[ajb]

A general form of the uncertianty principal holds for any pair of observables such that their corresponding hermitian operators do not commute. It is a rather general statment woven into the formulation of quantum mechanics.

Edited September 23, 2013 by ajb

[swansont]

Because of the wave nature of QM, the complementary variables are Fourier transforms of each other. The uncertainty relation is present in that math.

[Iwonderaboutthings]

Because of the wave nature of QM, the complementary variables are Fourier transforms of each other. The uncertainty relation is present in that math.

Fourier transforms of each other??????????????

 

When you say "each other" does this mean one variable is used twice? In Fourier transforms?

Such that , x is used twice like " example" x = G x1 and x2, but x always has the same value G??

 

x= G and then again x = G of "each other" ????

 

 

On another note.

In the Uncertainty Principles coupled with Lorentz Transforms Special Relativity etc, does 1 mean the physical number 1 " one" or does it mean.

 

1 = c

1= pi

1= x^2

 

????

 

Here is this 1 as I am seeing it. But then we see 2 a very often number used in derivatives.

 

 

What really discourages me about science is not understanding how science equations just throws a 1 in there.

Truly 1 must be some type of squared unit per say.

 

Doesn't c = 1 second as well?????????, is this what this 1 means??????????

 

Utterly Confused on this 1 deal.

Edited September 24, 2013 by Iwonderaboutthings

[ajb]

Position and momentum are Fourier duals of each other, they can be associated with each other in a one-to-one fasion. Rather generically the derivatives of an action are conjugate variables to the variable that one is differentiating with respect to. So we have uncertianty relations for all such dual pairs.

 

I am at a loss about your question about "1". Are you getting confused about units in which we numerically set the speed of light to be 1?

 

Edited September 24, 2013 by ajb

[Iwonderaboutthings]

Position and momentum are Fourier duals of each other, they can be associated with each other in a one-to-one fasion. Rather generically the derivatives of an action are conjugate variables to the variable that one is differentiating with respect to. So we have uncertianty relations for all such dual pairs.

 

I am at a loss about your question about "1". Are you getting confused about units in which we numerically set the speed of light to be 1?

 

numerically set the speed of light to be 1 ""yes"" the units and their settings....

 

I kind of thought this to be the case but wanted to be very very sure as to the " SETTINGS OF 1"

 

So you don't minus 1 you minus the speed of light???????????

 

So as dx->0 makes more sense to me cause it would be undefined then, 1 needs to be initialized and set???????

 

So then REPLACE THE 1 IN THE UNCERTAINTY PRINCIPLE WITH C????

[ajb]

So then REPLACE THE 1 IN THE UNCERTAINTY PRINCIPLE WITH C????

No, don't do that. You can check to see if the units make sense, if not then you may have set c=1 somewhere and not realised it.

 

So we have

 

[length] [mass][length] [time]^{-1} = [length]^{2}[mass] [time]^{-1} for position times momentum.

 

Then Plancks contant is [energy] [time] = [mass] [length]^{2} [time]^{-2} [time] = [length]^{2}[mass] [time]^{-1}.

 

So the units on both sides agree. Thus there is no room for a c to be inserted which has units [length][time]^{-1} .

 

I hope that makes some sense to you.

[Iwonderaboutthings]

No, don't do that. You can check to see if the units make sense, if not then you may have set c=1 somewhere and not realised it.

 

So we have

 

[length] [mass][length] [time]^{-1} = [length]^{2}[mass] [time]^{-1} for position times momentum.

 

Then Plancks contant is [energy] [time] = [mass] [length]^{2} [time]^{-2} [time] = [length]^{2}[mass] [time]^{-1}.

 

So the units on both sides agree. Thus there is no room for a c to be inserted which has units [length][time]^{-1} .

 

I hope that makes some sense to you.

THIS MADE CRYSTAL CLEAR SENSE THANKS! !

 

Now many other things make more and more sense, I get inspired now.... TRULY APPRECIATED

[ajb]

Now many other things make more and more sense, I get inspired now.... TRULY APPRECIATED

No problem. The general matra here is if in doubt check the units.

[studiot]

Please take note that the uncertainty principle does not only apply to quantum mechanics.

There is an uncertainty principle inherent in the mathematics of classical wave theory.

 

This is the simplest reference I can find.

 

http://www.sciteclibrary.ru/eng/catalog/pages/11221.html

[Enthalpy]

"Complementary variables are Fourier transforms of each other"

 

Always? p and x yes, E and t yes... but the total angular momentum and its component along one axis?

[ajb]

You certianly have the uncertianty relation between angular position and angular momentum, these two are conjugate variables.

 

The relations you are thinking of realy boil down to relations relations between position and momentum due to the definition of angular momentum.

[Iwonderaboutthings]

Please take note that the uncertainty principle does not only apply to quantum mechanics.

There is an uncertainty principle inherent in the mathematics of classical wave theory.

 

This is the simplest reference I can find.

 

http://www.sciteclibrary.ru/eng/catalog/pages/11221.html

great article! read about 1/2 will finish the rest tomorrow thanks!

[Enthalpy]

...relation between angular position and angular momentum...

These two are linked by a Fourier transform, yes. But I believe others are not.

 

For instance the angular momentum components along x, y and z. If one is known, the others are not. I see no Fourier transform between them.

 

More must exist, in the first line those that result from angular momentum, like the magnetic momentum in x, y and z.