Would a particle at the edge of the universe have an infinite amplitude

[clearwater304]

First off let me state that I'm just a mechanical engineering student, so I'm not too savvy when it comes to quantum physics, but my teacher was talking about this equation in class and it reminded me about infinite wavelengths near the egde of the universe and the event horizon on a black hole.

The equation my teacher mentioned.

A=±F/√[(1-Ω²/w_n²)² +[(cw_n/k)(Ω/w_n)]²]

Which basically states without dampening a particle will approach its natural frequency giving it an infinite amplitude.

Take this into consideration with gravitational redshift, you have a downhill region (inside black hole), an uphill region (outside of black hole), and a region at the top of the hill (event horizon).

Redshift relates to z=(observed wavelength-wavelength at emmision)/(wavelength at emmision)

So if you can get the wavelength at emission equal to zero, you can get an infinite redshift.

http://en.wikipedia.org/wiki/Gravitational_redshift

My understanding is a particle with an infinite wavelength would have no oscillation. If all particles in this region have no oscillation there would be no dampening. If there's no dampening, the particles would approach an infinite amplitude. But if this is true, wouldn't it violate the conservation of energy?

 

[mfb]

Which cosmology model does the teacher assume, when he talks about an "edge of the universe"?
Classical quantum physics at an event horizon? That looks a bit suspicious.

The formula looks a bit like a driven oscillator, but what drives it and what is "the natural frequency of a particle"? And what is the physical meaning of this amplitude in this context?

It seems that your teacher uses some stuff I have never heard about. While it might be possible that I missed it during the whole university, I would be surprised if it is something mechanical engineering students learn there.
Or maybe I am just confused, or the post does not reflect what the teacher said, or something else (there are always other options).

 

[Bill_K]

The equation my teacher mentioned.

A=±F/√[(1-Ω2/wn2)2 +[(cwn/k)(Ω/wn)]2]

Which basically states without dampening a particle will approach its natural frequency giving it an infinite amplitude.

clearwater304, The equation you quote is for the amplitude of a driven harmonic oscillator. I'm sure your teacher said nothing about the edge of the universe or event horizons. All the rest is simply your own imagination.

 

[clearwater304]

It didn't have anything to do with cosmology, it was just a Intermediate Dynamics class. I assumed the equation was related to a simple harmonic oscillator, which I assumed was the basis for determining the energy of a particle.

I realized earlier that the particles natural frequency would have been reduced to zero as well, so the amplitude would be zero. But I guess the question would be, does the particle have zero energy.

 

[Demystifier]

If there's no dampening, the particles would approach an infinite amplitude. But if this is true, wouldn't it violate the conservation of energy?

Without dampening, an oscillator can get a large amplitude only if there is a large external source of energy. Whatever this source is, the increase of oscillator energy is compensated with the decrease of source energy, so that the total energy is conserved.

This, indeed, is elementary understanding of energy conservation which even a mechanical engineering student should have. It has nothing to do with quantum physics, relativity, red shift, or edge of the universe.

 

[clearwater304]

Good point Demystifier, I completely forgot about the real case scenerios where the external frequency had to match the natural frequency to increase the energy.

I used to be a physics student but I switched my junior year. In modern physics, we covered energy levels of particles and quantum tunneling. When I saw this equation in Intermediate Dynamics, I remembered the energy levels of particles are based on simple harmonic oscilators. That and I've read a lot of stuff about what happens at the event horizon of a black hole. Idk, maybe you can't have a completely undamped area in space, even at the event horizon of a black hole.