Hi Imad,

What do you mean by "physical meaning"? Why is a wave function any less physical than a velocity vector? Surely, all you need are rules for interpreting what these objects mean in the context of physical experiments?

Best regards,

David

Hi Imad,

What do you mean by "physical meaning"? Why is a wave function any less physical than a velocity vector? Surely, all you need are rules for interpreting what these objects mean in the context of physical experiments?

Best regards,

David

Hi David

When you solve Schrodinger equation and obtain the wave function, can you think of this wave function as a " real" physical entity?

I can not tell you, what a wave function is - only how to calculate it and what it can do for you once you have got it.

Hi Imad,

I suppose when you look for any "physical meaning" you mean "something that may be measured". But look, there are many instancies which cannot be directly measured. For example - Flow or Velocity or any another derivative which can be valued only as averaged values. Lagrange function, potential energy and so on are intergals over measured forcies and also some approximations need to be applied. Another words, "physical meaning" in such a sence have only Lengh, Time, Mass and others initial Units. Therefore I think your question is somewhat scholastic, i.e. it has no physical meaning :-)

Best regards

Hi Vladimir,

I'm afraid Time is not physical.

Electric field and Lagrangian are physical, i. e. measurable quantities. Schrodinger Wave function is not physical since it is complex in general and is not directly measurable.

Regards,

Rajat.

Hi Vladimir

Please, have a look at page 61, end of 1st paragraph, in David Griffiths,3rd edition, introduction to electrodynamics.

Let me briefly explain the concept of a wave function.

In subatomic range (10^{-8} CM), classical mechanics

cannot predict trajectories of particles. Particles themselves

behave in dual (matter/wave) manner. In that atomic length scale,

one does not solve force equations of Newtonian mechanics,

rather, one formulates a wave equation which depends on the

potential term. That is essentially the potential energy of

the particle whose trajectory has to be known. Suppose

the particle in undergoing simple harmonic motion, then

we apply corresponding potential energy and solve Schrodinger

wave equation which is essentially a second order

partial differential equation. To solve this problem you

have to apply the method of separation of variables.

Solving this differential equation you get

a function which depends on space and time coordinates.

This function is a complex scalar function which is single valued.

By mod-squaring this complex function you get another

scalar function depending on space and time coordinates.

You can show that now this gives you the probability of

finding the particle at that given point at that given time.

Thus the trajectories are no longer determined uniquely

but the trajectory has become probabilistic in the

subatomic range.

Dear Rajat and Imad,

I just refer you to David's answer. What is the reson to name something as "physical" or not? Let it be any oblect that is interesting for physicists :)

Hi Vladimir,

David's right. It is measurability and interpretation that render the quantity physical or unphysical. Time is measurable but is not physical. Therefore, velocity etc. strictly speaking will not be physical, but mixed quantities. Please see other questions relating to the nature of time on RG. Assuming, as we do naively, that time is physical, velocity, energy, lagrangian etc all can be called physical.

The wave function is probabilistic and hence is dual in nature. It is subjective belief based on objective frequencies. In this sense even psi-mod-squared which we interpret as physical will not be physical, but will have a dual nature. Please see my article on RG-- "Are all Probabilities fundamentally Quantum Mechanical?"

Regards,

Rajat

The Lagrangian function is not measurable, in fact is is not unique. On the other hand, the phase of the wavefunction is known to satisfy an analogue of the Hamilton-Jacobi equation so this gives the Action functional a physical meaning. The phase of the wavefunction gives rise to interference effects so it is (in a limited sense) observable.

As to the physical meaning of the electric field... a strong enough electric field can kill you, so it is definitely physical.

Hi Imad,

Physical meaning of electric field is quite straightforward classically.

It is just the force per unit charge, which is a measurable quantity.

At the quantum level, we cannot measure it directly inside an atom.

What is exactly is your question regarding the electric field ? If we

take a test charge and make a 3-D map of `FORCE ON THAT

TEST CHARGE' at each point of the 3 dimensional space, then

the resulting map in a function of (x,y,z) coordinates, and then

we write it as a vector field.

for instance:

H = EE+BB: Energy of the el.-mg. field

L = EE-BB: Lagrangian: infinitesimal probagator

|n): wavefunction of the field, in oscillator representation

Hi Imad,

Finally the Largangian, it is not something which is

measurable. Consider the simplest system with

just one particle. This particle will have a kinetic energy

and a potential energy at each point of 3D space. If

you subtract out the potential energy from kinetic

energy at each point in space then you get an infinite

set of numbers. One number is assigned per point.

This is a scalar function or a scalar field. This is

the Lagrangian function for the simplest one particle

system. Advantage of Lagrangian formulation is that

it is easy to solve a problem in relatively difficult

coordinate systems such as the spherical polar

system. Im am not sure whether you are looking for

such answers. Please give your feedback.

Dear Biswajoy Brahmachari

Please, have a look at the attached paragraph related to electric field, and after we settle that we come to Lagrange (David Griffiths, introduction to electrodynamics, 3rd edition ) .

Also, Please have a look at the following paragraph sent to me from my friend Dr, Lama Sakhnini

( I found this in one of the websites, I like it, read!!!

The electric field isn't real. It's just something some guy (Michael Faraday) made up to make it easier to think about the universe. Unfortunately, when students hear something was made up, they automatically see that something as something they have to think about and learn. They see it as something difficult. No one ever thinks about the alternatives. What if the electric field had never been invented? What would life be like without it? The answer to that is "horribly different", because the field was the gift that Michael Faraday gave to the rest of us. The field makes it easier to think about the universe. When it's easier to think about the universe, it's easier to work with the universe and use its laws to make stuff. What a horrible inconvenience for the rest of us. What a frightening world we live in, where arbitrary decisions are made, and students find themselves tormented with ideas that work. The electric field is a really important idea about something that doesn't "really" exist.)

Hi Imad,

Have you come across the Wheeler-Feynman absorber theory? If not, you might find it interesting (you'll find it on Wikipedia). One of the aspects of this theory is that there is no electromagnetic field as such, there are only charged particles directly interacting with one another. This works in classical physics, but quantum physics seems to need the electromagnetic field.

Best regards,

David

I Ii Imad,

strong electric fields E come from electric CURRENTS j,

rot E = - dB/dt, rot H = j: then delta E = dj/dt

and exactly this FIELD - of a bolt - may even kill you!

by the way, how about the gravitational field?

Ohm's Law? U = IR, so E is not - gradU?

with no E, follows no j, B, I, U, R, ... no nothing.

this is called solipsism, an acceptable philosophy.

eventually you may have a look into Jackson, Classical E-dynamics.

Do mathematical equations define the concepts we use when we think about what those equations represent? When teaching science we usually use the concepts to 'explain' the equations. However useful this is, the concepts do not come from the equations and the two do not have to match up.

A mathematical equation can represent many different concepts we can use to think about how things work. If this were not the case, then changing a physical theory would necessarily require us to change the mathematical equations.

However, there are many times we change our theories, yet the equations remain valid (though potentially in a more limited sphere of influence than before). Newton's theory of gravitation has been 'upgraded' with a new theory - yet the equations of Newton remain valid today (within limits defined by the 'new' GR theory).

The quote referred to by Ahmed states this well. An Electric Field is a concept we use to understand the world. We can understand equations about electricity, determined through experiments on reality, using this concept. However the equations do not require this concept to be valid. What we call an Electric Field might be understandable - and fit the equations - using a fluid concept of electricity - an Electric Fluid. The equations are the same in either case.

Considering a different perspective: Will our current concept of an Electric Field remain valid forever into the future? The equations might remain valid (within limits), yet a completely different theory could (and likely will) evolve.

As an hypothetical example: We have defined a 'gravitational field' as being a 'field' of force pulling objects toward a mass. By convention and our current understanding, this is a 'pulling' force 'field' directed toward the center of the mass. However, Einstein's equivalence principle states that, standing in an elevator, we cannot determine if we are stationary in a gravitational field 'pulling' us down, or being pushed upwards in the elevator.

The difference is a sign reversal of the equation, however the difference in concept is much more significant. What if 'gravity' really is the mass pushing upward on us and not our current 'pulling' force? There might not be a need for the concept of a 'gravitational field', if the earth 'pushes' up on us. The equation doesn't care, but our theories sure do.

Imad,

There are several views - a good place to begin would be the book 'The Wave Function' , edited by Alyssa Ney and David Albert.

See especially Chapters 3 & 4 on 'Wave Function Realism', which deal with your question

You may find below useful;

https://www.researchgate.net/publication/261562344_A_Qualitative_Interpretation_of_Lagrangian_-_A_Proposition_-?ev=prf_pub

"A Qualitative Interpretation of Lagrangian - A Proposition -"

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