QM, wave , particle duality problem
- Thread starter thinking
- Start date
- Status
of course the electron is not both at the same-time
but at the same-time the electron has the qualities of both , wave and particle
I'm not sure I agree with this - in quantum mechanics the fundamental objects are not waves ever - they are quantum particles that have associated state function. That state function gives rise to the wavelike properties we observe.
Whenever you make a measurement in QM you always observe particles, not waves.
These are good points that you make about quantum particles. Am I right that you are referring to the particles of the Standard Particle Model. The fundamental particles described there are described as particles and not waves, and are described as having no internal components (that is why they qualify as fundamental). So from that perspective you are right that the composition of a fundamental object is a grouping of interacting particles. The interactions are described in a set of forces that are associated with each type of particle. The picture is of particles and forces interacting to establish the presence of mass.
But mass and energy are equivalent as Camilus pointed out so each interaction of particles and forces is addressed mathematically to prove that energy is conserved by every interaction. This is where the need for particles as waves comes into play isn't it? We observe energy as waves and see interference patterns in those waves associated with particles and so to discuss a particle in terms of energy don't you have to discuss the wave nature of the particle?
No. I'm just considering a non relativistic quantum particle.
No, we don't observe energy as waves. Are you talking about the double slit expt? The interference pattern is built up from measurements of individual particles, each of which has a probability distribution governing where it goes, and that is contained in the wavefunction.
I emphasise: Quantum mechanics is a theory of particles. Wavelike phenomena is an emergent property, not a fundamental one.
Thank you for your quick response and clarification of quantum theory and what it is.
And accepting that under the theory, "wavelike phenomena is an emergent property", how is the energy of the fundamental particle contained within the particle? How does it emerge from the particle?
And just to clarify for me the path of the "individual particles, each of which has a probability distribution governing where it goes", ... is the path that the "individual particles measured" by the two slit experiments not wavelike?
Energy is not really contained within the particle. Energy (and other things like momentum, position etc.) are properties that the particle has - and not really in an emergent way. For example, suppose you have a single particle - it has some energy. That energy is an observable of the system (the particle) and quantum mechanics has a prescription to work out what the energy is.
Observables in QM are represented by Hermitian operators and when you make a measurement of an observable you always find it is in the eigenstate of the appropriate operator. All of the information about the state of the particle, it's position, energy etc is contained in the statefunction.
The path followed by an individual particle is not a good concept in QM. If you measure it's position at some time and then measure it again some time later the particle has travelled all possible paths between point 1 and point 2. That doesn't mean to say that you could look at an intermediate state and see a mess of smeared particle everywhere - when you make a measurement you always see a well defined particle.
This all hints at an underlying structure because the particle seems to know about all of the places between points 1 and 2, and that points to the incompleteness of quantum particle mechanics. A better description of nature is quantum field theory, where the particles are not the fundamental objects. There are quantum fields which exist everywhere in spacetime and excitations of the field are called particles.
Ignoring that for a moment, if you have a double slit expt through which you send a load of identical particles all in the same state you will still see fringes on the screen. You might expect a single line where all the particles hit because they were all in the same state to begin with, but that would be wrong. The eigenstates that you measure are "selected" probabilistically. That can give the impression of a wave, even though there is no physical wave - there are only particles which behave according to their statefunction.
Thank you for taking the time to explain. QM seems pretty will defined from what you say and like any theory it doesn't have all of the answers but effectively uses the wave function to encompass all possible paths/locations. I can see possibilities where the wave function could be dealing with the spherical wave nature of the energy component of a particle. A spherical wave would be present at all points that are dealt with by the wave function. But lets not go there on this thread.
Thank you for pointing out that the path of a particle is not really the way to discuss the "presence" of a particle as it moves when talking strictly within QM. It is helpful to understand that distinction.
I'm still interested in the energy of a particle and I think I understand your earlier point about how energy is by perscription in QM. I also acknowledge your reference to quantum field theory. In QFT isn't the field, if I can use the pop phrase, the spacetime continuum? That would attribute some coupling of space and time and so I would think it comes right out of the theory of general relativity; is that right?
But I agree we might be able to ignore that to follow the energy wave for a moment.
There is always the issue of relative movement when discussing particles. I posted somewhere a thought that every particle has it own reference frame and got an affirmative response from a fellow poster whether we were right or wrong
. If that concept is true, then every particle is at rest in its own frame. But let me ask, does it have energy in its own frame while at rest or is the energy only relativistic, i.e. relative to other particles?
Thank you for pointing out that the path of a particle is not really the way to discuss the "presence" of a particle as it moves when talking strictly within QM. It is helpful to understand that distinction.
I'm still interested in the energy of a particle and I think I understand your earlier point about how energy is by perscription in QM. I also acknowledge your reference to quantum field theory. In QFT isn't the field, if I can use the pop phrase, the spacetime continuum? That would attribute some coupling of space and time and so I would think it comes right out of the theory of general relativity; is that right?
But I agree we might be able to ignore that to follow the energy wave for a moment.
There is always the issue of relative movement when discussing particles. I posted somewhere a thought that every particle has it own reference frame and got an affirmative response from a fellow poster whether we were right or wrong
. If that concept is true, then every particle is at rest in its own frame. But let me ask, does it have energy in its own frame while at rest or is the energy only relativistic, i.e. relative to other particles?
Last edited:
an idea to observe:
since we 'see' the remnant of the wave/particle exchange, such as the light we see after the exchange, then to observe the wave aspect we see the pattern of the wave and can measure the particle as if the collective of the wave is focused to point particle.
I liken the wave as the exchange over the line of sight (the range of mass exposed) where in contrast the particle is focused as being the collective of the waves energy into a fixed point. In the double slit experiment we can see the wave pattern but when reduced to one photon at a time, the same pattern reveals itself.
The idea shares that the point particle is a unit measurement of the total exposure rather than a fixed point particle. It is the measurement that confines the energy to a point particle, rather than the actual exchange itself.
A method of confirming this is by combining the wave/particles of 2 sources, and find the waves align and the point particle now are of the combined rather than the single units.
The particle is not riding a wave, but the wave (unit) as a single whole is the particle and the receptive mass, is combined (entangled). It is why the waves are localized as that mass in them wave portions has reached the threashold to re-release the energy we see (what we observe).
That is how to see the wave peaks or foam as being particles, it is at them peak points there is enough focal energy to release energy/mass (foam) from itself upon the environment. (kind of like seeing the wave patterns in the DSE)
just ideas... hope it helps
Quantum particle mechanics is incomplete because it does not include relativistic effects. The wave function (actually, the state vector, which is related to the wave function in a simple way) is the way quantum systems get described in QFT as well. The wave function is a fundamental object.
A more concrete mathematical statement; you can work out the expectation value of any operator in QM by evaluating $$\langle \hat{\mathcal{O}} \rangle = \langle \psi | \hat{\mathcal{O}} | \psi \rangle$$. In the language of wave functions this is $$\langle \hat{\mathcal{O}} \rangle = \int d^3x \psi^*(\vec{x}) \hat{\mathcal{O}} \psi (\vec{x})$$. If you want to work out the energy of a state then the appropriate operator is the Hamiltonian itself.
No. A field is something that exists at all points in spacetime but is not spacetime itself. As you note, the exception to this is the metric of GR can be considered to be a field but it doesn't lead to a consistent quantum theory.
There is always the issue of relative movement when discussing particles. I posted somewhere a thought that every particle has it own reference frame and got an affirmative response from a fellow poster whether we were right or wrong
It is true that for every particle it is possible to define a frame in which the particle is at rest. Well, it's true for particles that have a mass and as such, move at a speed less than the speed of light. For particles that are massless and move at c like photons and gluons it is not possible to define a rest frame and their speed is c in every frame.
I don’t exactly understand how the wave function is a fundamental object unless that means that for any particle movement we only have a set of probabilities to describe the location and momentum of the particle. In other words it might mean that the set of all possible locations and momentums is an object itself?
That is good. Then it seems that the rest energy of the particle is non-relativistic energy? And then I have to ask how the rest energy and the mass are characterized, i.e. what makes a particle at rest have mass and energy? I don’t mean to put you through your paces but I am trying to understand how you refer to, describe, or quantify the energy component of a rest particle that has mass.
The analogy between water waves & waves associated with quantum entities breaks down if you try to include the fact that water waves are due to vertical motion of water molecules.The following is just not valid.
Somebody once stated that quantum entities travel as waves, but arrive & depart as particles.
I'd never thought about this, but it is right. When things interact with each other, the interaction is very well understood in terms of particles. However, at "infinity" (i.e. far away from the interaction with other particles) the wave description is more accurate. In fact, a lot of quantum theory is based on the fact that this description is accurate.
pwnage. The thread starter and several socks in this thread are trying to remove that concept.
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.
This is true, but it's not because there is a physical wave. Quantum particles are always just that - particles. The wave like properties come from the wave like nature of the wave function which is a property of a system.
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" (i.e. the double slit becomes a single slit), 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!
So, at least my intuition seems to be supported by the equations. Somehow, I have to be able to understand how normal, non-relativistic quantum mechanics emerges from the description in terms of quantum fields. For this, I will have to do some more thinking, I think.
For a really cool demo, check out Mathematica.
Last edited:
These are all concepts the discoverers of these phenomena struggled with as well.
I think part of the problem is that QM can be very abstract, and science is not.
I think part of the problem is that QM can be very abstract, and science is not.
- Status