QM, wave , particle duality problem

[Bishadi]

post 35 is a gem

I could be wrong, so let's sort this out. This is how I understand it, so please tell me if I'm wrong!

When we talk about interactions, we should understand "states" as excitations of quantum fields. Scattering amplitudes are normally described in terms of well-defined set of "out" and "in" states (the S matrix tells you how they interact). These out and in states are written in terms of plane waves, "at infinity". These plane waves appear in the Fourier expansion of the field, with the ladder operators acting as Fourier coefficients. So asymptotically the field is only described in terms of its Fourier expansion, so I don't understand why I shouldn't think of this as just a plane wave.

Interactions (i.e. the whole edifice of perturbation theory/effective field theory) is built on the fact that states can be "localized" (in some sense) near a specific point in space and time. (Local means that the center of mass energy is much less than the largest scale in the problem.) This suggests that, near an interaction zone, the particle description is more fitting. While the decomposition of a field into it's Fourier modes is still legitimate, it is not clear to me how to understand the interaction between particles as an interaction between individual modes of the field. I think that it may be that the equations of motion become non-linear, and it is just not possible to solve for a scattering amplitude. I know this is the case for a general phi-4 theory.

So this is the dichotomy, and we can look at various physical phenomena to see how well we understand them. For example, consider electrons going through a multiple slit experiment. Let the slit separation be d, and the distance to the screen be L. As long as the slit separation is not too big, and not too small, you see a diffraction pattern. "Too big" means that the slit separation has to be much smaller than the distance from the screen. "Too small" is set by the dimensions in the problem. So, for example, the only dimensionful quantity in QED is the electron mass, which corresponds to a length scale of about 1/10000 the Bohr radius (I think). This means that as long as the slit separation is much bigger than the Bohr radius (which is about 5 nm?), the electrons will act as a wave. As soon as the slit separation gets close to the "classical electron radius" (which isn't really possible), I think the electron should behave as a particle, again.

On the one hand, you'd expect the system to be "more quantum" as you probe shorter distance scales. But what I have just proved is that the system becomes "more classical" as we probe smaller scales. The result of the double slit experiment is that

$$n\lambda = \frac{xd}{L}$$

so as d gets smaller and smaller, while holding $$\lambda$$ fixed, the separation of the fringes (x) goes to infinity, and you only see the central peak. Likewise, as d gets bigger and bigger, the fringes start to overlap, and again you only see the central peak!

I am comforted by the fact that there are some equations which support my intuition, but still this is a bit of an awkward result. Hopefully someone can show me where I'm wrong.

Wow!

another great post

a method of identifying that your intuition has merit is to move the slit, closer and further from its optimum wave revealing point. Notice the densities change. (not just coherance) Then bring in a second source of wave/particles and watch the effects, once again these will show your intuition is pretty good.

It is upon the exchange with mass, the appearance of particle phenomenon shows itself, but to use different mediums of mass (elemental structure), then find the particles (released) changes with the mass; see photoelectric effect or even notice the color changes.

great thread

and ben you are better than you realize (thanks)

 

[quantum_wave]

Not really. It seems to me that you're trying to imply that things are made of "quantum waves" but it's not the case. You have to remember that any measurement you make of a particle will always see a particle. The wavelike properties that come out of quantum mechanics are consequences of the statistical nature of measurement. Classically you can think of a particle that has position, momentum energy etc as properties. In quantum mechanics the particle properties are replaced by the wave function from which you can extract the classical properties of the system.



From the point of view of quantum mechanics the mass of the particle is simply a parameter that appears in the Schrodinger equation:

$$\left(-\frac{\hbar^2}{2m} \nabla^2 + V(\vec{x}) \right) \psi (\vec{x}) = E \psi (\vec{x})$$

As you can see, $$m \to 0$$ is not a good limit to take so Schrodinger particles are always massive.

I suspect you're thinking in terms of special relativity and from that point of view, again, mass is just a parameter that appears in the equations

$$E^2 = (mc^2)^2 + (pc)^2$$

Here when the particle is at rest, p = 0 and you get the familiar $$E = mc^2$$. When m = 0 you get another familiar formula $$E =pc$$ which is simply the de Broglie relation. Note here that the rest energy of a particle is simply it's mass, and your notion that the rest energy is "not relativistic" is correct, if worded in a confusing way. A better way to say it is the mass of the particle is the same when viewed from any inertial frame.

If you want to know what particles have mass then you'll have to study the Higgs mechanism. That is a hard topic that I don't know an awful lot about, but I suspect Ben or AN will be able to explain it if they want.

Thank you again for you thoughtful and helpful responses to my questions.

I want to address what you say about my implying that things are made of “quantum waves” without going astray of the rules of the forum. The “quantum” in my name “quantum wave” is not the same usage as the “quantum” in the term “quantum mechanics”. The quantum part of my name “quantum wave” refers to the tiniest meaningful amount of energy, and which is associated with a force called quantum action. These are ideas that don’t directly relate to any current science theory. So if you gather that my line of questioning here is to imply that my ideas are part of or could be an amendment to quantum mechanics, then I am not implying that.

My follow up questions are to learn what I can about what we know of the nature of mass and energy and to see where you think the energy resides, i.e. what is the characteristic of particles that their energy component can be attributed to. I haven’t tried to introduce my ideas about that in this forum and apologize for any such implication.

It is my belief that we don’t know what causes mass, and I understand enough to know that science hopes to find evidence of the Higgs mechanism in order to confirm the theory of the cause of mass.

 

[thinking]

Thank you again for you thoughtful and helpful responses to my questions.

I want to address what you say about my implying that things are made of “quantum waves” without going astray of the rules of the forum. The “quantum” in my name “quantum wave” is not the same usage as the “quantum” in the term “quantum mechanics”. The quantum part of my name “quantum wave” refers to the tiniest meaningful amount of energy, and which is associated with a force called quantum action. These are ideas that don’t directly relate to any current science theory. So if you gather that my line of questioning here is to imply that my ideas are part of or could be an amendment to quantum mechanics, then I am not implying that.

My follow up questions are to learn what I can about what we know of the nature of mass and energy and to see where you think the energy resides, i.e. what is the characteristic of particles that their energy component can be attributed to. I haven’t tried to introduce my ideas about that in this forum and apologize for any such implication.

It is my belief that we don’t know what causes mass, and I understand enough to know that science hopes to find evidence of the Higgs mechanism in order to confirm the theory of the cause of mass.

quantum_wave

for me the starter of this thread

feel free to go where you'd like here

no worries

thinking

 

[quantum_wave]

quantum_wave

for me the starter of this thread

feel free to go where you'd like here

no worries

thinking

Thank you thinking but I have mentioned my ideas in my threads and I always welcome you and the community to evaluate and criticise them there.

 

[thinking]

It is my belief that we don’t know what causes mass, and I understand enough to know that science hopes to find evidence of the Higgs mechanism in order to confirm the theory of the cause of mass.

quantum wave



isn't mass a culmination of lower energy states , less energetic of Plasmic energy states ( which is based on proton and electron energy ) which allows interactions of then particles and therefore the formation of chemical elements ?

 

[BenTheMan]

isn't mass a culmination of lower energy states , less energetic of Plasmic energy states ( which is based on proton and electron energy ) which allows interactions of then particles and therefore the formation of chemical elements ?

No.

 

[thinking]

No.

Originally Posted by thinking
isn't mass a culmination of lower energy states , less energetic of Plasmic energy states ( which is based on proton and electron energy ) which allows interactions of then particles and therefore the formation of chemical elements ?

no why ?

 

[BenTheMan]

Where did you come up with that explanation?

 

[thinking]

Where did you come up with that explanation?

what does it matter ?

 

[BenTheMan]

Because it doesn't make any sense

 

[thinking]

Because it doesn't make any sense

okay , why ?

 

[BenTheMan]

I don't even know where to start. What do you think your statement means?

 

[thinking]

I don't even know where to start. What do you think your statement means?

okay think of it this way

would any particle(s) at the speed of light have any chance to combine into any chemical elements ?

 

[James R]

Just answer the question, thinking.

 

[thinking]

Just answer the question, thinking.

I will

if you tell me what question it is that I'm suppose to answer , specifically

 

[James R]

thinking:

Your statement (in case you've already forgotten):

isn't mass a culmination of lower energy states , less energetic of Plasmic energy states ( which is based on proton and electron energy ) which allows interactions of then particles and therefore the formation of chemical elements ?

Question for you:

What do you think your statement means?

So?

 

[thinking]

thinking:

Your statement (in case you've already forgotten):

Originally Posted by thinking
isn't mass a culmination of lower energy states , less energetic of Plasmic energy states ( which is based on proton and electron energy ) which allows interactions of then particles and therefore the formation of chemical elements ?

I just wanted to clear about your referrence as to what statement?

Question for you:

Originally Posted by BenTheMan
What do you think your statement means?

So?

that Plasmic energies or specifically Cosmic Plasmas are extremely energetic

and that as Plasmic energy looses their energy , that the protons and electrons are able to combine into fundamental chemical elements

objections ?

 

[James R]

that Plasmic energies or specifically Cosmic Plasmas are extremely energetic

What's a Plasmic energy?

What is a Cosmic Plasma, and why is it so energetic?

and that as Plasmic energy looses their energy , that the protons and electrons are able to combine into fundamental chemical elements

How does a plasmic energy lose its energy, exactly?

How does losing a plasmic energy allow protons and electrons to be able to combine into fundamental chemical elements?

objections ?

I think your statement is meaningless.

 

[thinking]

objections ?

I think your statement is meaningless.

oh... no doubt

but you can't tell me why

 

[James R]

thinking:

I note that, once again, you failed to answer any of the questions put to you.

You're trolling.

Thread closed.