Demonstration that vibrating basic particles constitute non-vibrating individuals

I am a dilettante in physics; I ask for pardon for my confusion-causing (if any) terminology usage, and also for my imprecise choice of question tags.

I know that basic particles of any individual stopping vibrating contradicts Heisenberg's uncertainty principle, so the particles must whenever vibrate. Then how could basic particles constitute a seemingly non-vibrating individual? Is it a natural limitation of human eyesight or ...? Is there any scientific explanation for it?

A demonstration not using analogy or common sense is seeking after.

• Maybe you are using a translating program? Your question does not make sence. Are you talking about the wave particle duality? – anna v Jul 7 '14 at 5:58
• Oh, sorry about that. Indeed I am not using any translating program~ Uh, allow me to re-present my question: how could I at the same time not vibrate with my basic constituents vibrating? I see not an apparent reason – Megadeth Jul 7 '14 at 6:04
• Much appreciated. It seems that I have not had the right to vote up; otherwise I will vote up for gratitude. – Megadeth Jul 7 '14 at 8:38

It is certainly true that as I type this the atoms in my fingers are vibrating, and so are the atoms in my keyboard. Yet I can still type. There are several reasons we don't perceive any vibration.

Firstly, the vibrational frequencies are around $10^{12}$ to $10^{14}$Hz, that's from a trillion times a second to 100 trillion times a second. Since we can't even see the 50Hz refresh on our TV screens it shouldn't be any surprise that at such high frequencies we can't detect any vibration of the atoms in us.

Secondly the vibrations are all in random directions, so on average they balance each other out. On average we aren't vibrating.

Lastly, and this is really the important point, atoms are quantum objects. We tend to visualise a vibrating atom as a little ball flying to and fro on the end of a spring but this isn't a good description of what a vibrating atom looks like. The vibration means the wavefunction of the atom spreads out, so in effect it just becomes a little blurry. Since this blurriness is on a scale of around 0.1 nm it is completely undetectable in everday life.

• Thank you all so much! So, if I am not mistaken, the limitation of human eyesight renders me to perceive no vibration, just like a playing movie renders me to detect no discontinuities. – Megadeth Jul 7 '14 at 8:35

Heisenberg uncertainty principle said that: (according to me)

• We cannot at the same time "know" (or measure) the momentum and the position of a particle.

How can we know? How can we define the momentum and the position of a particle? There are many difficulties describing the quantum world by the normal language, because the normal language is created only to describe what we can see, feel directly. Sadly, the quantum world is not as simple as the macro world here. There is no particle (as a ball or a bullet) and there is no wave (as sound wave or water wave) in the micro length. There are just states of physics, which can give us predictions about the measurements we can take.

Then to translate the quantum physics language to more classical language, we must use some analogy of the states to, sometimes, particles and sometimes, waves. The description is therefore not always exactly true or understood in normal sense.

You seem to be posing a question about the nature of the Wave-Particle Duality. If you're asking how can a particle be a non "vibrating" particle and a vibrating wave at the same time, then the answer is as follows:

With the Wave-Particle duality, we can view the same subatomic particles that we can apply point particle mechanics to as probability densities. These Probability density functions have wavelike nature. The function is explicitly called the Wavefunction and is typically denoted by $\psi (\vec{x},t)$ and the probability density is $|\psi (\vec{x},t)|^2$. Solutions to the Equations of Motion for quantum potentials ( the Schrödinger Equation ) yield equations of motion analogous to the classical harmonic oscillator.

Even though say, an electron, is a point-like particle that at some point in time has a position with a degree of measurable certainty, we can still view the particle in terms of the derived mathematical construct of wave mechanics. In this manner, one can technically vibrating and not vibrating. It all depends on which framework you chose to utilize in analyzing a system of particles.