What is the uncertainty of a physics lab? What does uncertainty mean? Let's say I'm measuring a height of where the ball is on the ramp and let go of the ball and the ball hits the ground and we use our eyes to see how far the ball lands from the ramp next to another ruler.
4 answers
lands before the ball bounces off
If you are into modern physics, there is a low but finite possibility of anything. In fact you might not be there where you think you are at all. Luckily you usually are on the same side of the wall you were before you did not move.
Look here maybe:
http://en.wikipedia.org/wiki/Uncertainty_principle
particularly the wave probability stuff.
http://en.wikipedia.org/wiki/Uncertainty_principle
particularly the wave probability stuff.
According to the de Broglie hypothesis, every object in the universe is a wave, a situation which gives rise to this phenomenon. The position of the particle is described by a wave function \Psi(x,t). The time-independent wave function of a single-moded plane wave of wavenumber k0 or momentum p0 is
\psi(x) \propto e^{ik_0 x} = e^{ip_0 x/\hbar} ~.
The Born rule states that this should be interpreted as a probability density function in the sense that the probability of finding the particle between a and b is
\operatorname P [a \leq X \leq b] = \int_a^b |\psi(x)|^2 \, \mathrm{d}x ~.
In the case of the single-moded plane wave, |\psi(x)|^2 is a uniform distribution. In other words, the particle position is extremely uncertain in the sense that it could be essentially anywhere along the wave packet. Consider a wave function that is a sum of many waves, however, we may write this as
\psi(x) \propto \sum_{n} A_n e^{i p_n x/\hbar}~,
\psi(x) \propto e^{ik_0 x} = e^{ip_0 x/\hbar} ~.
The Born rule states that this should be interpreted as a probability density function in the sense that the probability of finding the particle between a and b is
\operatorname P [a \leq X \leq b] = \int_a^b |\psi(x)|^2 \, \mathrm{d}x ~.
In the case of the single-moded plane wave, |\psi(x)|^2 is a uniform distribution. In other words, the particle position is extremely uncertain in the sense that it could be essentially anywhere along the wave packet. Consider a wave function that is a sum of many waves, however, we may write this as
\psi(x) \propto \sum_{n} A_n e^{i p_n x/\hbar}~,
1 answer