Uncertainty Principle

[PointOfViewGun]

The Uncertainty Principle dictates:

In quantum mechanics, the Heisenberg uncertainty principle states by precise inequalities that certain pairs of physical properties, such as position and momentum, cannot be simultaneously known to arbitrarily high precision. That is, the more precisely one property is measured, the less precisely the other can be measured.

This uncertainty arise from the inability of humans to measure the location of a certain particle. Yet, it's used in many principles to actually define physical characteristics of a certain object or event.

My question is if there is something I'm missing or simply why scientists rely on this principle so much when it only reflects our inability to observe small particles.

[Sphere]

My question is if there is something I'm missing or simply why scientists rely on this principle so much when it only reflects our inability to observe small particles.

It has nothing do with a technical limitation of observation, rather its a physical reality when dealing in quantum mechanics. It is not intuitive, but when you observe the position of a small particle to a higher degree of accuracy, the momentum becomes less knowable, i.e. has a a broader range of possibilities and vise versa. In other words no particle physically has a single value for both position and momentum at the same time. It's a little mind blowing when you realize what that means, but in quantum mechanics is a rather mundane idea.

[PointOfViewGun]

It has nothing do with a technical limitation of observation, rather its a physical reality when dealing in quantum mechanics. It is not intuitive, but when you observe the position of a small particle to a higher degree of accuracy, the momentum becomes less knowable, i.e. has a a broader range of possibilities and vise versa. In other words no particle physically has a single value for both position and momentum at the same time. It's a little mind blowing when you realize what that means, but in quantum mechanics is a rather mundane idea.

Isn't that still based on our perception though? The experiment is that the more precise you wanna know the location of a particle the shorter wavelength of photon you need to bombard the particle with and if you have shorter wavelength thus higher frequency the velocity of the particle is tempered with as you need to make two readings for that. I don't see how this means that the particle cannot have a certain location and velocity at a given moment.

[Sphere]

Wiki does an okay job of restating what I said before...

It should be emphasized that this is not meant to be a statement about a researcher's ability to measure these specific pairs of quantities. Rather, it is a statement about the system itself. That is, a system cannot be defined to have simultaneously singular values of these pairs of quantities. The principle states that a minimum exists for the product of the uncertainties in these properties that is equal to or greater than one half of the reduced Planck constant (ħ = h/2π).

The only kind of wave with a definite position is concentrated at one point, and such a wave has an indefinite wavelength (and therefore an indefinite momentum). Conversely, the only kind of wave with a definite wavelength is an infinite regular periodic oscillation over all space, which has no definite position. So in quantum mechanics, there can be no states that describe a particle with both a definite position and a definite momentum. The more precise the position, the less precise the momentum.

So in short its a property of the wave function which governs the behavior of particles. You cannot simultaneously describe a particle has having a specific position and specific momentum at the some time. And this is long before you step into the laboratory, this is with pen and paper you cannot get the wave function to spit out a definite position and a definite momentum at the same time. The certainty of one is inversely proportional to the certainty of the other.

[PointOfViewGun]

Wiki does an okay job of restating what I said before...

So in short its a property of the wave function which governs the behavior of particles. You cannot simultaneously describe a particle has having a specific position and specific momentum at the some time. And this is long before you step into the laboratory, this is with pen and paper you cannot get the wave function to spit out a definite position and a definite momentum at the same time. The certainty of one is inversely proportional to the certainty of the other.

And why would that be?

[Sphere]

And why would that be?

Because God plays dice.

[PointOfViewGun]

Because God plays dice.

What I meant is what is the evidence that makes particles not have an exact location and velocity at a given moment. I understand why it's hard for us to observe it but I don't see anything pointing to an idea that not just for our observing but in reality itself too that particles cannot have a definite location and velocity at a given time. What is the reason that two are same?

[Sphere]

have fun

http://en.wikipedia.org/wiki/Theoret...inger_equation

[Rhaegar1]

have fun

http://en.wikipedia.org/wiki/Theoret...inger_equation

Hehe, + rep.

Have fun indeed and good luck, even although I have a degree in teaching next to my (almost) master in applied physics I haven't got entirely figured out how to explain stuff like this to people with no knowledge about QM aside from how you allready explained it Sphere.

If you're really sure you want to go more in depth darklordseth, there are plenty of books that are probably doing a much better job explaining this kind of things in words and if you're interested in the mathematical part I advice introduction of quantum mechanics from Griffiths but you'll need some knowledge of differential equations and linear algebra to tackle that one.

[Sphere]

"If you think you understand quantum theory, then you don't understand quantum theory."

-Richard Feynman

That is a good way of summing up QM. There is no good way of describing the behavior a particle/wave that makes intuitive sense to us. Richard Dawkins offers an interesting hypothesis as to why this is, essentially it is because we evolved in a "middle-world", i.e. not on the scale of electrons nor the scale of stars but somewhere in between. Because of this our senses are tunned to the sizes and speeds we commonly encounter, and our brains are programed to understand intuitively things like a falling rock, or a flowing stream. However, Dawkins offers the idea that if we had evolved on the scale of electrons quantum behavior would be what is intuitive to us and things like a falling rock would seem bizarre.

[Plant]

You can measure one physical characteristic at a time. They have an exact location and velocity, but measuring one will inadvertedly affect the other. Hense, we cannot be sure of it's exact location and velocity at that moment in time.

[Jack04]

It [the uncertainty principle] can be derived reasonably simply from the wave equations which arise once you accept that all particles exhibit wave like behaviour.

[Randarkmaan]

My question is if there is something I'm missing or simply why scientists rely on this principle so much when it only reflects our inability to observe small particles.

The uncertainty (of the uncertainty principle) does not arise from human inabilty to measure small particles, or any sort of human imperfections (though that too adds uncertainties of its own). It is widely acknowledge to be a fundemental feature of nature, that is you CANNOT EVER know exactly (down to the last decimal) the velocity, the speed, the velocity, the mechanical energy, the mass, the relative position, etc, of anything in nature. Also when you try to measure for instance the velocity of a particle this reduces the accuracy with which you may measure the postition, as mentioned. The act of observation itself interferes with the particle, as it is so miniscule.

Because the uncertainty principle is seen to be a fundemental law of nature it is for instance used to theorize where dark energy (vacuum energy), through quantum fluctuations and such (spontaneous creation and annihilation of matter-antimatter particles), also it is one of the reasons why absolute zero (in temperature) seems to be unattainable.

Then again it is much more complicated than this, and I can't really boast to know everything, or indeed that much, about it.

Another important fact, which does not necessarily have to do with the uncertainty principle, is that in any measure and calculation you should note the uncertainties with which the objects were measured/calculated (for instance you could assume that if you measure something with a ruler that you may be working with an uncertainity of half a millimeter or something), because it should be emphasized that any physical process and calculation is meaningless if you don't know the uncertainties involved.

[PointOfViewGun]

have fun

http://en.wikipedia.org/wiki/Theoret...inger_equation

Hehe, + rep.

Have fun indeed and good luck, even although I have a degree in teaching next to my (almost) master in applied physics I haven't got entirely figured out how to explain stuff like this to people with no knowledge about QM aside from how you allready explained it Sphere.

If you're really sure you want to go more in depth darklordseth, there are plenty of books that are probably doing a much better job explaining this kind of things in words and if you're interested in the mathematical part I advice introduction of quantum mechanics from Griffiths but you'll need some knowledge of differential equations and linear algebra to tackle that one.

I am actually reading a book on quantum mechanics focusing mostly on black holes. The Uncertainty Principle arise from real life experiments rather than thought experiments. So most of those calculations arise from those experiments hence the principle is crippled by human's ability to measure the properties of a particle.

You can measure one physical characteristic at a time. They have an exact location and velocity, but measuring one will inadvertedly affect the other. Hense, we cannot be sure of it's exact location and velocity at that moment in time.

That only tells about our ability to measure their location and velocity but doesn't mean they do not have a definite location and velocity at a given time.

The uncertainty (of the uncertainty principle) does not arise from human inabilty to measure small particles, or any sort of human imperfections (though that too adds uncertainties of its own). It is widely acknowledge to be a fundemental feature of nature, that is you CANNOT EVER know exactly (down to the last decimal) the velocity, the speed, the velocity, the mechanical energy, the mass, the relative position, etc, of anything in nature. Also when you try to measure for instance the velocity of a particle this reduces the accuracy with which you may measure the postition, as mentioned. The act of observation itself interferes with the particle, as it is so miniscule.

Because the uncertainty principle is seen to be a fundemental law of nature it is for instance used to theorize where dark energy (vacuum energy), through quantum fluctuations and such (spontaneous creation and annihilation of matter-antimatter particles), also it is one of the reasons why absolute zero (in temperature) seems to be unattainable.

Then again it is much more complicated than this, and I can't really boast to know everything, or indeed that much, about it.

Another important fact, which does not necessarily have to do with the uncertainty principle, is that in any measure and calculation you should note the uncertainties with which the objects were measured/calculated (for instance you could assume that if you measure something with a ruler that you may be working with an uncertainity of half a millimeter or something), because it should be emphasized that any physical process and calculation is meaningless if you don't know the uncertainties involved.

Again, you're talking about the observed world while I'm trying to figure out the case of a real world. What I hear from everyone, including professors of physics, is if it's just a law that everyone accepts religiously without asking questions. Yeah, it might be well established but nowhere I've seen a well enough explanation WHY it's the way it is. They always tend to focus on HOW it is.

[Gordon Freynman]

That only tells about our ability to measure their location and velocity but doesn't mean they do not have a definite location and velocity at a given time.

If a particle had a definite velocity and location at all times then this:



wouldn't happen, instead you would only see two bands.

Yeah, it might be well established but nowhere I've seen a well enough explanation WHY it's the way it is.

You can stop looking because you're not going to find one. Right now our knowledge is simply too limited to begin answering the whys.

[PointOfViewGun]

If a particle had a definite velocity and location at all times then this:
wouldn't happen, instead you would only see two bands.

Doesn't necessarily mean that Uncertainty Principle is true. It simply explains the wave property.

You can stop looking because you're not going to find one. Right now our knowledge is simply too limited to begin answering the whys.

I don't mean why as "why we exist" but "a scientific explanation to why particles don't have exact location and velocities and what makes them behave in such a way".

[Sphere]

Again, you're talking about the observed world while I'm trying to figure out the case of a real world. What I hear from everyone, including professors of physics, is if it's just a law that everyone accepts religiously without asking questions.

Schroedinger's wave function, Heisenberg's uncertainty principle etc. were hotly contested at the time. Albert Einstein spend almost all his later years trying to develop an opposing quantum theory in which "God does not play dice", i.e. a theory which would toss out the unpleasantness of the Copenhagen Interpretation. Needless to say Einstein was unsuccessful, though it was not until 1976 that his most forceful challenge to the Uncertainty Principal, that being the Einstein–Podolsky–Rosen paradox, was disproved experimentally.

So no, the uncertainty principle is not accepted in a religious way.

[PointOfViewGun]

Schroedinger's wave function, Heisenberg's uncertainty principle etc. were hotly contested at the time. Albert Einstein spend almost all his later years trying to develop an opposing quantum theory in which "God does not play dice", i.e. a theory which would toss out the unpleasantness of the Copenhagen Interpretation. Needless to say Einstein was unsuccessful, though it was not until 1976 that his most forceful challenge to the Uncertainty Principal, that being the Einstein–Podolsky–Rosen paradox, was disproved experimentally.

So no, the uncertainty principle is not accepted in a religious way.

From a point of view of 2 centuries ago it was not known but today it's pretty much accepted religiously.

[Sphere]

From a point of view of 2 centuries ago it was not known but today it's pretty much accepted religiously.

It's accepted due to experiment and observation, if you want to call that religion theres not much I can do to stop you. It's true there are not a whole lot of experiments directly testing the Uncertainty principle, put there are a plethora which test Schroedinger's equation from which the uncertainty principle arises. But we are running into the two great problems of Quantum Theory, that is it doesn't make any sense, and that it provides the most accurate experimental predictions ever. Even Schrödinger had great qualms about the implications of it.

[PointOfViewGun]

It's accepted due to experiment and observation, if you want to call that religion theres not much I can do to stop you. It's true there are not a whole lot of experiments directly testing the Uncertainty principle, put there are a plethora which test Schroedinger's equation from which the uncertainty principle arises. But we are running into the two great problems of Quantum Theory, that is it doesn't make any sense, and that it provides the most accurate experimental predictions ever. Even Schrödinger had great qualms about the implications of it.

It's not really a matter of making sense or not. In this particular case it makes sense only if you ignore some stuff. Many physics laws or ideas are made up. This one is based on an experiment that reflects only our inability rather than reality. So the thought experiment is built upon it and the inability of the experiment to provide a different answer makes it a law for some reason. The experiment cannot produce an answer because it's not built to. It's like driving a car that can go as fast as 200 km/h and then say that no particle can move faster than 200 km/h.