I have a ball with me and I have been observing it's position which remains constant at a place only, hence it must be largely localised, further as it remains on the same place from so long, it's velocity must be largely localised to 0 only. Now with both momentum and position know to any degree, Where is the uncertainty?? With the understanding of quantum mechanics, we must expect the "fixed" ball to have any arbitrary momentum, but that is not the case. Where am I going wrong??
121167
Let’s say you have a 3000 lb vehicle moving very slow at 1 kilometer per hour. It seems obvious that you could simultaneously determine its position and momentum at any point along the way but does the uncertainty principle still apply even here?  You should be able to calculate this at a future point. If not then why not? If so then at what point do you revert back to uncertainty?
100385
The concept of velocity is by definition the movement divided by the interval of time between initial position and final position.  If $f(t)$ is the position of a particle at time $t$; the velocity in the interval $[t_0;t_1]$ is $\dfrac{f(t_1)-f(t_0)}{t_1-t_0}$  The problem is that in a single instant there is no movement and the time is not changed; so no velocity.  I can consider $\lim_{t_1 \to t_0} \dfrac{f(t_1)-f(t_0)}{t_1-t_0}$, but mathematically it is only the limit of average velocity function and doesn't represent velocity at instant $t_0$  What are your views about this problem ?
60158
Does anyone have a (semi-)intuitive explanation of why momentum is the Fourier transform variable of position?  (By semi-intuitive I mean, I already have intuition on Fourier transform between time/frequency domains in general, but I don't see why momentum would be the Fourier transform variable of position. E.g. I'd expect it to be a derivative instead.)
43205
I'm a physics tutor for 11th and 12th grade students. I taught my students that momentum is conserved only when the net external force on the system is zero. But in the books we are following, momentum was conserved in the following cases in spite of presence of an external force:   A body (mass m1) is dropped from a tower (height h) and another body (mass m2) is projected vertically upward with initial velocity u. Find the velocities just after collision. (Gravitational force is the external force) Two bodies projected towards each other on a rough table surface, with all required parameters given asked to find the velocities after collision. (frictional force is the external force) Body explodes in mid air. Momentum is conserved before and after explosion. (Again gravitational force is the external force)   I explained to my students in all these cases though an external force is present it has negligible effect. But I'm not satisfied with my answer.  EDIT: Thank you for the comments and answer. It is clear that contribution of external force to change in momentum is negligible. Can someone do the calculation of taking change in momentum into consideration and showing that it is negligible?
25883
I could understand that the definition of a second wouldn't have an uncertainty when related to the transition of the Cs atom, so it doesn't have an error because it's an absolute reference and we measure other stuff using the physical definition of a second, like atomic clocks do.  But why doesn't the speed of light have uncertainty? Isn't the speed of light something that's measured physically?  Check out that .
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I have read the quantum mechanical model of an atom which says that path of an electron around the nucleus is uncertain due to uncertainity principle which says that it is impossible to measure both momentum and position of an electron at the same time so it is impossible for an electron to move in a well defined circular orbit.But  what if we simply do not measure the elcetron then it should move in a well defined path.So what really restrict it from moving like that?
42958
So, as your usual physics undergrad, I read Griffiths's derivation of the general   uncertainty principle. I understood it but there was no physical intuition given behind it in the book. It was basically a bunch of manipulations and inequalities used to get just the right result.  Other than "It's because of the statistical interpretation." is there a more intuitive reasoning behind uncertainty. Like commutators, behavior of particles, etc.  Thank you for the replies and as always, much obliged.
2369
Let's consider an infinite square well. In the first exited state there is a node at the middle of the well (i.e. wave function and thus probability of finding the particle is zero there). If I measure the position right now, I may find the particle on the left side of the node, and if I measure the particle after some time, I may find the particle on the right side of the node. But must  a particle on the left side to go to right side not pass through the node point? Thus the particle will spend some time at that point, so there should be some probability of finding the particle there, but the wave function is zero there, so what's wrong with the arguement? Does the particle move here to there, without passing through the space in between? But that will just violate continuity equation?
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To take an example,           Let's think of an electron which ban be in either one of two positions [...] There are two possible states of definite energy for the electron.  Each state can be described by the amplitude for the electron to be in each of the two basic positions.  In either of the definite-energy states, the magnitudes of these two amplitudes are constant in time, and the phases vary in time with the same frequency.  On the other hand, if we start the electron in one position, it will later have moved to the other, and still later will swing back to the first position.   (Feynman derives this behaviour from first principles in chapter 8-6 by solving equations for the state of an ammonia molecule, but that's a nice summary).  This sounds like the uncertainty principle - that you can know energy or position but not both.  Is it possible to derive the uncertainty principle from such an analysis?  Or is the uncertainty principle somehow axiomatic in the way this behaviour is derived?
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What is the value of momentum of particle in 1D box in state $\sin(10\pi x/a)$? My understanding Standing waves representing particle in 1D box is not an momentum eigenstate so if we measure the momentum of particle in this state we may get any value of momentum which gives a distribution whose expectation value tends to zero. Answer key In the answer key it's given that the value of momentum is 5h/a and -5h/a.If we measure the momentum for this state we may get any of these two values.But is this a wrong reasoning because if these was the case,these should mean that 5h/a and -5h/a are the eigenvalue of the following wavefunction which is clearly not. What is the correct answer?
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For an individual free particle that starts localized, the wave function packet spreads over time, so the particle becomes less localized.  Suppose now that we have a gas of those particles inside a box, and we allow them to collide (using some potential): will the wave function of each particle still spread indefinitely, or do collisions act as a source of decoherence and the wave function relocalizes again? I have heard both arguments by different colleagues, even in textbooks. Has anybody made a computer simulation that shows what would be the best picture?
69278
Suppose a sticky substance is thrown at wall. The initial momentum of the wall and substance system is only due to velocity of the substance but the final momentum is 0. Why is momentum not conserved?
29432
In Sean Carroll's book "The Big Picture," he states ():      Classical mechanics, the system of equations studied by Newton and   Laplace, isn't perfectly deterministic. There are examples of cases where a unique outcome cannot be predicted from the current state of the system. This doesn't bother most people, since cases like this are extremely rare—they are essentially infinitely unlikely among the set of all possible things a system could be doing. They are artificial and fun to think about, but not of great import to what happens in the messy world around us.   What are some of these situations he is referring to?   My first guess was something like the conceptual equivalent of a ball sitting exactly atop a hill and asking which direction it will roll. But that doesn't seem right—this would be a case where the "true" solution is that the ball wouldn't roll at all, while in reality there will always be tiny disturbances that cause the ball to roll in some direction. I don't think this is what Carroll is referring to. He seems to suggest that the "true, exact mathematical outcome" is not uniquely determined for certain classical systems.  I've heard that uniqueness theorems for solutions to differential equations don't generally apply to non-linear equations, and wonder if this may have something to do with it. Elucidation and examples would be much appreciated.
505
In many physics divulgation books I've read, this seems to be a commonly accepted point of view (I'm making this quote up, as I don't remember the exact words, but this should give you an idea):      is not a result of our lack of proper measurement tools. The fact that we can't precisely know both the position and momentum of an elementary particle is, indeed, a property of the particle itself. It is an intrinsic property of the Universe we live in.   Then this video came out:  (skip to , if you're already familiar with the uncertainty principle).  So, correct me if I'm wrong, what we may claim according to the video is:     the only way to measure an elementary particle is to make it interact with another elementary particle: it is therefore incorrect to say that an elementary particle doesn't have a well defined momentum/position before we make our measurement. We cannot access this data (momentum/position) without changing it, therefore it is correct to say that our ignorance about this data is not an intrinsic property of the Universe (but, rather, an important limit of how we can measure it).   Please tell me how can both of the highlighted paragraphs be true or how they should be corrected.
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We know that there is uncertainty principle, so question: can we ever measure wavefunction of particles? I do not think this is possible, but I am not sure. I guess that everything is probabilistic. (that's why, I believe, we have sigma level when we say we discovered some particles...)
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I just want to get an idea what  is. I know the mathematical meaning that momentum is $mv$ where $v$ is velocity. But I don't know its significance. Like I know that Acceleration is how velocity is changing with respect to time, I wanted to get feel of what momentum really is?
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My textbook and the following extract from feynman's lectures present the same idea regarding wavetrains and uncertainty in their wavelengths. Why is it that a wavetrain confined to some space has an uncertainty in its wavelength or the wave number? Is not a confined wave-train equivalent to a burst of successive pulses which can have a definite wavelength according to their origin or nature of origin.   Next, i understand that the De Broglie relation relates the uncertainty in wavelength to the uncertainty in momentum but what links the finiteness of the wave-train to the uncertainty in position?