Understanding the Uncertainty Principle in Quantum Physics: A Beginner's Guide

[vntskr]

I am a beginner to the part of quantum physics and I am not getting the ideas well enough.I am reading it on the Feynman Lectures. But the uncertainity principle does not give any hint and it does not reveal itself at all in our day to day lives.
Suppose a man starts to run at uniform velocity,say v, from t=0 and goes on,isnt it very much possible to know his position and momentum at any point of time?? Where's the uncertainity there??
Please help me out.

 

[Char. Limit]

It is possible to know (quite accurately) his position and momentum at any point in time, but never EXACTLY.

I believe the minimum possible error is:

$$\Delta p \Delta x \geq \frac{h}{4\pi}$$

In other words, the uncertainty in momentum, times the uncertainty in position, is always greater than or equal to the Planck Constant divided by 4*pi.

 

[rhenretta]

I'll throw a simple answer in here, I'm sure you'll get a more complete answer from someone with more maths skills than I.

p=mv (p = momentum, m = mass, v = velocity)

in order to find velocity, you need two samples of position at two different times.

So, let's say that you have a 50kg woman. At T=0 she is at position 0, and at T=1 second she is at a position 1 meter away. Thus, her velocity is 1 m/s, and her momentum is 50 kg*m/s... We now know her momentum, but we have a range for her position.

Consider this a placeholder answer, because I am very curious to hear what other people have to say about this. This is an explanation I worked out for myself when I had the exact same question...

 

[rhenretta]

To satisfy my own curiosity, which Feynman lectures are you reading? I'm a big fan of his :)

 

[Tac-Tics]

If I stand on a scale and see my weight is 82kg, does that mean by weight is 82kg?

Answer: No.

I probably way something more like 82.14kg. Even if I had a scientific scale and it said my weight was 82.000kg, I'd bet my house that my true weight is closer to 82.0001kg.

Nothing can be measured exactly. The best we can do is give an approximation and a tolerance. When my scale at home says 82kg, it means 82kg within an error of 1kg. The scientific scale means 82kg within an error of 0.001kg.

When you say "a man runs at velocity v", what you really mean is "a man runs at a velocity v within some reasonable error tolerance". If you're working on the back of a napkin, "reasonable error tolerance" is probably 10m/s. If you're turning in a paper for physics class, it's probably 0.001m/s.

The uncertainty principle sets a lower bound to the error tolerance in physical measurements. It says a tolerance is 0.0000001 blahs is OK, but a tolerance of 0.0000000000000000001 blahs is beyond the realm of science.

But you never notice it because a the minimum error is atomically small.

 

[DrChinese]

I am a beginner to the part of quantum physics and I am not getting the ideas well enough.I am reading it on the Feynman Lectures. But the uncertainity principle does not give any hint and it does not reveal itself at all in our day to day lives.
Suppose a man starts to run at uniform velocity,say v, from t=0 and goes on,isnt it very much possible to know his position and momentum at any point of time?? Where's the uncertainity there??
Please help me out.

Welcome to PhysicsForums, vntskr!

Yes, it is true that the Heisenberg Uncertainty Principle does not reveal itself in our day to day lives in an obvious manner. That is also true of Special Relativity and many other phenomena. This shows you how far things have advanced in the past 100 or so years.

Are you actually questioning whether the HUP is real? If you are reading the Feynman series, is there something specific you are curious about? An example about a man's P and Q is hardly a good starting point.