question about the uncertainty principle

[swansont]

Yeah I figured as much. Sometimes rigor is good' date=' sometimes not. Depends.

 

Let me ask you this, do you personally know how to derive the uncertainty principle from wave analysis? It was in a book of mine, but I confess I didn't follow the argument.[/quote']

 

The conjugate-variable wave functions are fourier transforms of each other.

[Johnny5]

The conjugate-variable wave functions are fourier transforms of each other.

 

That's not what I mean. There was a picture in the book, I think of beats, and then some kind of reasoning, using k, and w.

[Johnny5]

If you want to discuss Fourier transforms with me, I'm up for it. But it's that picture which was used in the derivation that I'm most concerned about, because I never understood how they arrived at the uncertainty principle from the picture.

[ydoaPs]

Can you explain your question more please?

 

ok, gravity is the warping of space. energy/mass is what warps the space. how do you find the uncertainty of said warp in a certain area? i would assume you start by finding the uncertainty of energy. where do you go from there?

[Johnny5]

ok, gravity is the warping of space. energy/mass is what warps the space. how do you find the uncertainty of said warp in a certain area? i would assume you start by finding the uncertainty of energy. where do you go from there?

 

I thought you meant something like that.

 

I'm not convinced that gravity warps space, so I am not the one to answer that.

[ydoaPs]

1)it doesn't matter if you are convinced or not. i just want to know how to do it.

2)what do you think gravity is?

[Johnny5]

Originally Posted by yourdadonapogos

ok, gravity is the warping of space. energy/mass is what warps the space. how do you find the uncertainty of said warp in a certain area? i would assume you start by finding the uncertainty of energy. where do you go from there?

I thought you meant something like that.

 

I'm not convinced that gravity warps space, so I am not the one to answer that.

 

1)it doesn't matter if you are convinced or not. i just want to know how to do it.

2)what do you think gravity is?

 

Your exact question is "how do you find the uncertainty of curvature of space in some region of space?".

 

I told you I don't know how to answer it.

But to give you some math to look at' date=' and have criticized, I can do this:

 

[b']Time/energy uncertainty relation[/b]

 

[math] \Delta E \Delta t \underline > \frac{\hbar}{2} [/math]

 

I've not derived the relation, perhaps someone else can.

 

At any rate, you can let E denote the relativistic energy of something, and t denotes the time coordinate of some frame of reference.

 

Let E = Mc^2. Then we have this:

 

[math] \Delta Mc^2 \Delta t \underline > \frac{\hbar}{2} [/math]

 

And of course c is a temporal constant of nature (it's certaintly nonzero), hence we can divide both sides of the statement above, to obtain the following new statement, which will have the same truth value as the previous one:

 

[math] \Delta M \Delta t \underline > \frac{\hbar}{2c^2} [/math]

 

I would translate this as follows: "The product of the uncertainty in the inertia of some object, multiplied by the uncertainty in the time coordinate of the reference frame in which that object is having its inertia measured, is greater than or equal to Planck's constant of nature, divided by two c squared, where c has been defined to be a speed of 299792458 meters per second.

The relation I just obtained, is a very peculiar one, and I don't see how to answer your question using it. I shall try something else.

 

Position/momentum uncertainty relation

 

[math] \Delta x \Delta p \underline > \frac{\hbar}{2} [/math]

 

In the statement above, x denotes the position of the center of inertia of something, and p denotes the momentum of that object in some reference frame. Classically, the momentum p of an object, is defined to be the product of that things inertia m, and its speed v in a frame.

 

So we have:

 

[math] \Delta x \Delta (Mv) \underline > \frac{\hbar}{2} [/math]

 

For something whose (nonzero) mass is constant in time (and can have no measured uncertainty), we can do this:

 

[math] M \Delta x \Delta v \underline > \frac{\hbar}{2} [/math]

 

Dividing both sides by M, we have:

 

[math] \Delta x \Delta v \underline > \frac{\hbar}{2M} [/math]

 

Let the center of inertia, of the object of mass M be constrained to be moving on the positive x axis for some reason. Then the instantaneous speed v, of the center of mass of this thing, can be written as:

 

[math] v = \frac{dx}{dt} [/MATH]

 

So we now have this:

 

[math] \Delta x \Delta (\frac{dx}{dt} ) \underline > \frac{\hbar}{2M} [/math]

 

Now, consider what the Delta symbol above is.

 

The uncertainty of a mathematical quantity Q is defined as follows:

 

[math] \Delta Q = <Q^2> - <Q>^2 [/math]

 

Where <Q> is the expectation value of Q, for example.

 

Now, you need to know whether Q is a continuous variable, or a discrete variable, because you are going to need either a probability mass function, or a probability distribution function to go any further.

 

Of course we can go further if we make certain assumptions, using the wavefunction of quantum mechanics, but this question is far from being answered.

 

What I wanted to do was eliminate uncertainty of time, by mixing the two uncertainty principles together. They are really just coming from the same set of assumptions anyways, so that you could do that.

 

I will stop here for now.

 

Oh for what its worth, if the body was moving in a straight line at a constant speed, your math would take you in one direction.

 

If the particles path were curved, it would take you in another.

 

As for the reason the path is curved, there is where you would insert the idea that the space is curved.

 

 

Proper analysis is going to take you into probability theory, and you will encounter many questions whose answer you don't know.

[ydoaPs]

I told you I don't know how to answer it.

not really. u just said that u weren't convinced that gravity warps space.

[ydoaPs]

ok, magnetic field. is it [math]\Delta{\phi}\Delta{B}{\geq}\frac{\hbar}{2}[/math], or is flux not the same thing as the rate of change of magnatude of the field?

 

with position v momentum, is the most accurately you can know the position a sphere with a radius of half the wavelenth or a diameter of half the wavelength.

[unknow force]

hmmm......,numbers and equations... forget that, the uncertainly concept is based in the wave propieties of the particles, if you take away particle energy (to know the momentum) this increase the wave behavior (position uncertainly), with lower energy levels, bigger the wave length -reducing the frecuency-, you can understand this better with an experiment,

 

you "throw" an particle -electron- inside an pasive magnetic coil (momentum measure) pointing in an "target" (position measure), now if you want to take an measure of the momentum you use the coil, but actually you take particle energy, so this increase the wave lenght and will not very precise to hit the target, but if you want an better position certainly (to hit the target) you must not interactue with the electron (but also without any information of the real energy)

 

btw, there is any relation with the increase of frecuency in high energized particles and the reduce of relative lenght in relativistics effects?? (near c speed) i have disscused that with friends, y want to see your opinions guys.

[Chatha]

Uncertainty principle

 

place a gum on a car tire and set it at high speed. You can calculate its speed but you will find it hard to locate the gum on the tire, at the same time if you manage to locate the gum you will be hard pressed to know what exact speed its going. Kind of like taking a picture of a speeding car. The principle, along with the entire copahegen interpretation emphasizes the inhibitions on accuracy.