Problem understanding Heisenberg's uncertainty principle

Question

Ok, I'm asking it, even in case of being closed and irrelevant.

It's about Heisenberg's uncertainty principle, and a very dualism of the way of information exchange in the software development world.

The problem is easy: you want to know something. In IT, we have two different ways. Either we refer to that thing, periodically, to get the information, or we ask that thing to transfer information to us on any update.

The more I read about Heisenberg's uncertainty principle, of course as a lay-person in Physics, the more I understand that it's describing a fundamental limitation in the way we can know/measure the properties of a particle, not the true nature of the particle. In other words, based on this mathematical formula our precision is not dependent upon the measuring device anymore. No matter how more precise we become, we can't find out the true value of complementary values both at the same time.

Yet what has obssessed my mind, is lingual analysis of this proposition. If we follow that model of IT, is it possible that particles someday send us their true values?

Like instead of a mom trying to find out the weight of her baby, the baby tells mom how much does he weigh. Instead of scientists trying to find out the exact position and momentom of a given particle, particles talk to scientists and tell them where they are and how much momentom do they have right in that moment (of course fictional, yet just a thought experiment).

Do I miss something in understanding Heisenberg's uncertainty principle? Can we say that just because we can't find out the true values of a given particle, it doesn't mean that true values do exist. In other words, uncertainty is not in the particle itself, but in the way we can know about it.

Uncertainty principle is a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known.

My undertanding is there is no fundamental limit to the precision of the true/real value of certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p.

Note: I can't find out my answer from these question:

Can the Heisenberg Uncertainty Principle be explained intuitively?

Heisenberg's Uncertainty Principle

Answer 1

The problem with your idea, the transmittance of the "true value" by some kind of mechanism, is that this true value does not exist. The uncertainty principle is not a statement about the impossibility of measuring something - the uncertainty principle is a statement about the nature of the possible wave functions.

You can actually see that the "eigenstates" of momentum and position in an infinite space are not properly normalisable and are thus not physically allowed wave functions. So the functions which would give us exact position and momentum are not functions which could serve as wave functions.

So if we take Quantum mechanics at face value and expect the uncertainty relation to hold in all realms of physics (which is not in any way obvious as it is usually derived for quantum mechanics, of which we know that it does not give a complete picture of the world), then we can expect for the transmittance of those "true values" never to occur because no particle can exist that has only one "true value".

Answer 2

I like Sanya's answer. I would also add two things about Heisenberg's principle of uncertainty.

1. Your question minces terms about "existence" and measurement in ways that Heisenberg sought to outline and detail in a way that was not confusing. You need to go through the actual literature pertaining to Heisenbergs work instead of perusing Wikipedia to gain your understanding of some of the most challenging fields of quantum physics. By your own admission, you are a lay-person in the realm of Physics. I certainly do not mean to be condescending but you are not going to understand quantum uncertainty by reading a Wiki or Yahoo answers after smoking a doobie.

2. a second underlying tenet of this principle are the facts that a. you change something when you measure it (albeit at a level that may be inperceptible by your equipment) and you cannot possibly produce a "reading" fast enough for it to be accurate because, in the time it took your equipment to render it's measurement, it is not longer valid because the quantum state is now different.

Answer 3

The uncertainty principle is a fundamental limit in the following way. In QM the state of a particle is described by a wave function $\psi(x)$. Let's use a one dimensional example for simplicity. It's evolution is described by the Schrödinger equation. From the wave function you can get a probability distribution for the particle over the space. The probability density the squared magnitude of the wave function, i.e. $|\psi(x)|^2$. What these Born probabilities actually mean is a partly philosophical question and I'll skip that here. So we got probabilities for the particles position. Can we get the same for its momentum? Yes we can. For that purpose we can express the wave function in momentum basis. What this means is that we take the Fourier transform of the wave function $\psi(x)$ and get $\phi(p)$. Basically this is describing $\psi(x)$ as a combination of (complex) sine waves. Now we can get a probability distribution for the momentum from squared magnitude of the wave function in the momentum basis, i.e. $|\phi(p)|^2$. How wide these probability distributions are can be characterized by variance and from the properties of the Fourier transform you can prove that the product of their variances cannot go below a certain limit.

In a certain sense, the uncertainty principle applies to anything that can be described as a combination of sine waves, not just quantum objects. If you have some kind of wave, the more localized it's in time/space, the wider range of frequencies/wavelengths it must inevitably have.

For a more concrete example, consider a laser beam. It's made of electromagnetic waves. Though laser beams can be quite narrow, the waves have lateral components which means that at sufficient distances the beam will inevitably spread out. And the narrower the beam is the wider the range of those lateral component and the faster the beam will spread out. To realize this, it's sufficient to know that light is made of electromagnetic waves and it's not necessary to consider the quantum nature of photons.

Answer 4

One of the nicest and most intuitive explanation of the Heisenberg's uncertainty principle is from Feynman, who, discussing a wave train whose length is $\Delta x$, see figure, says:

"Here we encounter a strange thing about waves; a very simple thing which has nothing to do with quantum mechanics strictly. It is something that anybody who works with waves, even if he knows no quantum mechanics, knows: namely, we cannot define a unique wavelength for a short wave train. Such a wave train does not have a definite wavelength; there is an indefiniteness in the wave number that is related to the finite length of the train."

The longer the train, the more precise the wavelength, and vice versa. This proves that there is a fundamental limit of the precision between functions that are conjugate (complementary) pairs, that is, Fourier transform of each other.