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Topic: Heisenberg's Uncertainty Principle  (Read 22611 times)

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Offline Winga

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Heisenberg's Uncertainty Principle
« on: November 13, 2004, 11:19:04 PM »
(d = delta)

(dp)(dx) >= h/4 pi

1. What is the meaning of this equation?
dp is ? (change or error in momentum?)
dx is ? (change or error in position?)


e.g.
A football, mass 1kg and moves with speed 100m/s,
by de Broglie equation,

lamba (wavelength) = h / mv

lamba = 6.63 x 10-34 / 1 x 100 = 6.63 x 10-36 m

2. This wavelength is for EM wave?


p = mv = 100kgm/s

From my lecture notes, dp = p, why?

dx = h / 4(pi)(dp) = 5.3 x 10-37

3. what is the meaning of this value, 5.3 x 10-37?


Thanks!


Offline jdurg

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Re:Heisenberg's Uncertainty Principle
« Reply #1 on: November 13, 2004, 11:40:15 PM »
Okay.  Basically speaking, the Heisenberg Uncertainty principle states that you cannot know the exact position of something and the exact momentum of something because the act of observing it causes it to change position and/or momentum.  On large objects, this really isn't a big deal because the uncertainty is vanishingly small.  In the calculation you showed in your original post, you calculate the uncertainty in the position of the football (which would be in meters).  So you showed that in observing a football, you are changing its position by 5.3 x 10-37 meters.  That value is incredibly small because the size and mass of the football is huge compared to its wavelength.  Now when we get onto the scale of an electron, however, the alteration of the electron's position due to our observation is HUGE because of how tiny the electron is.  If you re-do those calculations with the wavelength and mass of an electron, your calculated uncertainty is going to be MUCH larger in comparison to the electron.
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Offline Winga

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Re:Heisenberg's Uncertainty Principle
« Reply #2 on: November 14, 2004, 12:08:49 AM »
momentum = mv = 100kgm/s (for football), is this the exact momentum or uncertainty in momentum?
And why dp is equal to this momentum?

dp dx >= h / 4 pi, when we use this equation, should we keep one of the uncertainty unchange?
That means, when calculate the uncertainty in position of football,
p dx >= h / 4 pi, is it correct?


ssssss

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Re:Heisenberg's Uncertainty Principle
« Reply #3 on: November 14, 2004, 08:25:51 AM »
(d = delta)

(dp)(dx) >= h/4 pi

1. What is the meaning of this equation?
dp is ? (change or error in momentum?)
dx is ? (change or error in position?)


e.g.
A football, mass 1kg and moves with speed 100m/s,
by de Broglie equation,

lamba (wavelength) = h / mv

lamba = 6.63 x 10-34 / 1 x 100 = 6.63 x 10-36 m

2. This wavelength is for EM wave?


p = mv = 100kgm/s

From my lecture notes, dp = p, why?

dx = h / 4(pi)(dp) = 5.3 x 10-37

3. what is the meaning of this value, 5.3 x 10-37?


Thanks!



The term dp and dx means the uncertainity in momentum and position and you can refer it as an error in the Exact value.

Now understand carefully,the De broglie wave leangth are Not the Electro magnetic waveleangths.They are the wave leangths possesed by bodies not neccesirily travelling with the Velocity of light.So the value you got refers to debroglie WL.

Finally the value 5.3x10-37 is the uncetainity in position.This means that original position of football will be somewhat less or more than this value,or you can say it as the error in the exact postion is this one.

Offline Winga

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Re:Heisenberg's Uncertainty Principle
« Reply #4 on: November 14, 2004, 09:17:37 AM »
The term dp and dx means the uncertainity in momentum and position and you can refer it as an error in the Exact value.

Now understand carefully,the De broglie wave leangth are Not the Electro magnetic waveleangths.They are the wave leangths possesed by bodies not neccesirily travelling with the Velocity of light.So the value you got refers to debroglie WL.

Finally the value 5.3x10-37 is the uncetainity in position.This means that original position of football will be somewhat less or more than this value,or you can say it as the error in the exact postion is this one.
So, can I say, in 1-Dimension, if the football travels at 100m/s from the starting point for 1s, the new position of the ball is 100 +/- 5.3x10-37m for the origin!

Offline Winga

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Re:Heisenberg's Uncertainty Principle
« Reply #5 on: November 15, 2004, 09:20:20 AM »
The wavelength of football is 6.63 x 10-36 m, how can I find its frequency?
By using frequency = c / wavelength ?

ssssss

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Re:Heisenberg's Uncertainty Principle
« Reply #6 on: November 16, 2004, 05:07:45 AM »
So, can I say, in 1-Dimension, if the football travels at 100m/s from the starting point for 1s, the new position of the ball is 100 +/- 5.3x10-37m for the origin!

This value gives the least difference of the position from the Actual value.The football will be atleast uncertain to this value,and in the 3D space around it.

ssssss

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Re:Heisenberg's Uncertainty Principle
« Reply #7 on: November 16, 2004, 05:13:01 AM »
The wavelength of football is 6.63 x 10-36 m, how can I find its frequency?
By using frequency = c / wavelength ?

The formulae you are talking about is for EM waves which travel with the speed of Light.So this formulae is not apllicable.In reality,Sir de Broglie gave the formulae for waveleagths[Lambda=h/mv].There was no formulae for De Broglie Frequency.Any way you can calculate frequency of the moving Body by Replacing the speed of the Light by its actual Velocity.The resultant Frequency will Be incalculably High.
« Last Edit: November 16, 2004, 08:26:34 AM by ssssss »

Offline Winga

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Re:Heisenberg's Uncertainty Principle
« Reply #8 on: November 16, 2004, 08:19:13 AM »
The formulae you are talking about is for EM waves which travel with the speed of Light.So this formulae is not apllicable.In reality,Sir de Broglie gave the formulae for waveleagths[Lambda=h/mv].There was no formulae for De Broglie Frequency.Any way you can calculate frequency of the moving Body by Replacing the speed of the Light by its actual Velocity.The resultant Frequency will Be incalculably low.
frequency of the football = 100m/s / 6.63 x 10-36m = 1.5 x 1037Hz

Then, can I use E = h x frequency to calculate the total energy of the football?
E = 6.63 x 10-34 x 1.5 x 1037 = 10000J

ssssss

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Re:Heisenberg's Uncertainty Principle
« Reply #9 on: November 16, 2004, 08:25:00 AM »
frequency of the football = 100m/s / 6.63 x 10-36m = 1.5 x 1037Hz

Then, can I use E = h x frequency to calculate the total energy of the football?
E = 6.63 x 10-34 x 1.5 x 1037 = 10000J



How many times,i have to tell you that Dont confuse the De Broglie waves with EM waves?You cant apply the EM waves formulaes to De broglie results.Understand?

Offline Winga

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Re:Heisenberg's Uncertainty Principle
« Reply #10 on: November 17, 2004, 10:05:23 PM »
Can I say that football has much particle property than wave property?

e- has much wave property than particle property?
(Is the motion of e- an EM wave?)

And how about photon, if we treat it as a particle, can we apply any EM wave equation on it?


Offline Winga

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Re:Heisenberg's Uncertainty Principle
« Reply #11 on: November 17, 2004, 10:07:05 PM »
Is it possible to increase the amplitude of matter(de Broglie) wave? I mean the intensity!

ssssss

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Re:Heisenberg's Uncertainty Principle
« Reply #12 on: November 18, 2004, 09:15:29 AM »

Ohhh.....Come on.Read your Books carefully.E=hv formulae of electromagnetic waves is the Energy per photon.EM waves are Photons.


You wrote,e- has much wave property than particle property?
(Is the motion of e- an EM wave?)

You cant make an Exact comparison,but you can say they are Comparable.This depends upon the mass which effects the Uncertainity and ultimately the wave like properties.

And about football,i will say the particle property of football dominates its wave property because of huge mass as compared to subatomic particle.see How small is the Uncertainity.





ssssss

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Re:Heisenberg's Uncertainty Principle
« Reply #13 on: November 18, 2004, 09:21:40 AM »
Is it possible to increase the amplitude of matter(de Broglie) wave? I mean the intensity!


Come on.Dont confuse matter Waves with EM waves.And About your Question,i think we have to bring Back the Albert Einstein or Erwin Shrodinger for answering it.

My point is that the way you are Comparing these waves with EM waves,it is Beyond the Scope of your Book,this site and Scientists too.Matter waves are very strange and compex and you cant simply derive their results Comparing EM waves and other type of waves.
« Last Edit: November 18, 2004, 09:23:37 AM by ssssss »

Offline Winga

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Re:Heisenberg's Uncertainty Principle
« Reply #14 on: November 18, 2004, 10:18:58 AM »
So, we can do nothing about the matter wave of a particle (although we can find its de Broglie wavelength)?

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