What is a field?

[StringJunky]

So it's another "we don't know, but this works" answer. They are mounting up.

That's the way it is in science. Scientists will never know completely but they get closer with each new model.

Edited February 4, 2017 by StringJunky

[mistermack]

That's the way it is in science. Scientists will never know completely but they get closer with each new model.

That's what I like about it. It must be boring, being god.

[StringJunky]

That's what I like about it. It must be boring, being god.

I was going to say that one needs to be omniscient to know reality as it actually is.

[Xerxes]

Where is the scale axis the the scalar constants a^k lie on, for it is not parallel to any of the existing axes x^k.

Lost me bro. The [math]\alpha^k[/math] are each scalars - numbers. What do you mean by "a scale axis" for a number? How can a number be parallel to anything

 

Do you disagree with my illustration of a tangent vector? In Mickey Mouse terms, it simply says that there exist a subset of the vector space called basis vectors such that the scalars tell you how "far" in each "direction" an individual vector "points" in the "direction" of each basis vector

[studiot]

Lost me bro. The [math]\alpha^k[/math] are each scalars - numbers. What do you mean by "a scale axis" for a number? How can a number be parallel to anything

 

Do you disagree with my illustration of a tangent vector? In Mickey Mouse terms, it simply says that there exist a subset of the vector space called basis vectors such that the scalars tell you how "far" in each "direction" an individual vector "points" in the "direction" of each basis vector

 

 

 

Lost me bro.

 

 

Yes indeed.

 

But, with respect, that is because you are only looking at what you have said, not what I have said.

 

Did you try my practical demonstration?

 

 

 

Do you disagree with my illustration of a tangent vector?

 

No, nor have I said I disagree. I fully understand what you are saying but it is not relevant. You need to go beyond that to the logical consequences of the definitions and compact notation you are using. Things often look a bit different when worked out in full for particular cases.

Mathematicians like to use compact generalizations, but Engineers have to make particular cases work.

 

 

Should I be paying special attention here as regards to your ( earlier but recent ) in a separate question?

 

http://www.scienceforums.net/topic/101620-intrinsic-curvature/page-1#entry961025

 

Are the two threads connected at this point? (irony intended )

 

Yes this is the same idea. +0.1 for remembering it

 

 

Earlier in the thread, I asked, if the magnetic force is provided by photons, why we don't see them, or detect them streaming out of a magnet.

Nobody answered that one, but I'm guessing that the answer is that they are virtual photons, discussed here:

 

So it's another "we don't know, but this works" answer. They are mounting up.

 

There are no virtual photons in Classical Physics and no the force exerted by a magnetic field is not mediated by photons.

 

Paradoxically the force can be calculated by virtual work in the Classical Physics interpretation of a magnetic field, much more simply than a more advanced treatment, which yields the same end result.

[mistermack]

There are no virtual photons in Classical Physics and no the force exerted by a magnetic field is not mediated by photons.

 

Paradoxically the force can be calculated by virtual work in the Classical Physics interpretation of a magnetic field, much more simply than a more advanced treatment, which yields the same end result.

No, but just because this is the classical physics section, doesn't mean you have to ignore quantum theory.

Note I said IF the magnetic force is provided by photons.

 

But both classical and quantum physics hypothesise some kind of virtual force carrier that can't be detected.

You can detect the force, but not what mediates it.

 

By the way, why do they say "mediates" ? Is it in the sense of acting as a medium?

[Mordred]

Studiot is using a particular methodology from the field potential as the mediator equivalent. Under those conditions the use of virtual particles isn't required.

 

All particles virtual or otherwise are simply excitations under QFT. When the excitation peaks at above a quanta you have an "Observable particle." under QFT a particle of less than

[latex]e=\frac{1}{2}\hbar w[/latex]

 

Is your virtual particle group. Anything less than the above has insufficient momentum and energy to perform action. (cannot cause motion individually.) This is what makes them undetectable. Even the best idealized detection device can detect a VP. The VP itself cannot perform sufficient action on the device. However a cloud of VP can.

 

Keep in mind a virtual photon is "off shell" it is a vector gauge boson. Which is not the same as the real photon. As per the link you provided.

 

By the way, why do they say "mediates" ? Is it in the sense of acting as a medium?

A charged field does act with medium like characteristics as the mass term itself used is a medium property.

 

QFT treats all particles as wavefunctions "excitations/fluctuations" of a given field.

 

From the link above.

 

" Virtual particles are also viewed as excitations of the underlying fields, but appear only as forces, not as detectable particles. They are "temporary" in the sense that they appear in calculations, but are not detected as single particles. Thus, in mathematical terms, they never appear as indices to the scattering matrix, which is to say, they never appear as the observable inputs and outputs of the physical process being modelled."

 

Comparing these two methods the only difference is whether to account for quantum fluctuations. Both use field potentials. As opposed to VP as pointlike objects

Edited February 4, 2017 by Mordred

[studiot]

No, but just because this is the classical physics section, doesn't mean you have to ignore quantum theory.

Note I said IF the magnetic force is provided by photons.

 

But both classical and quantum physics hypothesise some kind of virtual force carrier that can't be detected.

You can detect the force, but not what mediates it.

 

By the way, why do they say "mediates" ? Is it in the sense of acting as a medium?

 

All Physics theories are models and suitable for some purposes but not for others.

 

This subforum is about Classical Physics and the models are not suitable for QFT.

 

If you want to study Quantum Field Theory there is a sub forum provided.

 

You should be aware that models may differ in the answers/solutions they offer to particular questions and we chose the most appropriate by experimental comparison with reality.

Sometimes the models offer the same answer but one is much more computationally difficult than the other.

Would this one not then be the one of choice?

 

Here is an example:

 

An electromagnet lifts a car to the crusher.

If we model the electromagnet as a slug of ferrous metal encased in a solenoid and the car as a free slug of ferrous metal,

provide a formula for the necessary current to lift the car and the resulting magnetic field between the electromagnet and the car.

 

Now this takes a few lines using Classical Theory and I once had a debate (elsewhere) with a Doctorate in this subject who visits here occasionally.

 

He said no magnetism does not work like that and produced at least three pages of fancy more advanced mathematics to come up with the same formula!

 

So if you want to learn more about the subject, all well and good. There are several lifetimes worth of material out there.

 

But please don't try to pick off odd isolated statements to try to prove your (mis)conceptions about something.

Edited February 4, 2017 by studiot

[Xerxes]

Engineers have to make particular cases work.

Sure. And they will only work if engineers fully understand the mathematics.

 

Stalemate.

 

I am done here

Edited February 4, 2017 by Xerxes

[StringJunky]

Stalemate.

 

I am done here

Thank you for deigning come to see us.

[Xerxes]

Thank you for deigning come to see us.

Fuck off

[mistermack]

Studiot, you come across as very condescending in some of your posts. I can only assume you are reading my intentions wrong, in posting here.

 

You know perfectly well why I posed the question about photons. It's not a stupid question, it was just something I wanted to know.

Happily I found the answer myself. But thanks for your input.

[studiot]

Studiot, you come across as very condescending in some of your posts. I can only assume you are reading my intentions wrong, in posting here.

 

You know perfectly well why I posed the question about photons. It's not a stupid question, it was just something I wanted to know.

Happily I found the answer myself. But thanks for your input.

 

Not intending any condescension. I am trying to pitch my replies at an appropriate level and I seem to have hit that mark with the extract from Baden-Fuller.

 

Exchange or mediating particles form no part of classical theory, so I don't think your question was stupid at all, just off topic.

 

 

Since I have not managed to explain my contention that the field variable may require a space of additional dimensions I will try the extract method again since I have found someone else who may explain it better.

 

Here is a short extract from Beiser : Concepts of Modern Physics.

 

The author has the knack of introducing just enough Mathematics at just the right level to promote understanding without obscuring the Physics.

Not only that but the excerpt provides a bridge from classical to quantum theory that you seem to want.

Note he describes the situation for a system of particles, using position and momentum.

You should replace that by a system of values of the field variable, using appropriate phase variables for the particular field.

Note that this can incorporate the derivatives Xerxes referred to - I never denied this only meant that it is not the whole story.

 

Hopefully readers will get on better with this.

 

Edited February 5, 2017 by studiot

[mistermack]

In my original post, I just asked what a field was. We don't know seems to be the most accurate answer to that.

 

But to complicate it, we have two totally different ways of saying we don't know. And when you talk about one way, you mustn't mention the other.

 

Ok, that's all new to me, so I know more now than I did at the start. I wasn't really aware of the gulf between classical physics and quantum physics on this site. You don't get any sense of it in wikipedia articles. They usually mention both, and just say, "in classical physics this, in quantum physics that". It's all there on the same page. I just followed that example, without really thinking any more of it.

 

This is from the top of the wiki Magnetic Field page:

"Magnetic fields can be produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin.^[1][2] In special relativity, electric and magnetic fields are two interrelated aspects of a single object, called the electromagnetic tensor; the split of this tensor into electric and magnetic fields depends on the relative velocity of the observer and charge. In quantum physics, the electromagnetic field is quantized and electromagnetic interactions result from the exchange of photons."

 

It was when I read that, that I immediately wondered why we couldn't see the photons. I had to dig around quite a bit to find out that they are virtual. Mind you, the force that they produce is real enough.

You would think that if they are real enough to move goods trains, they would be real enough to see.

But obviously not.

Edited February 5, 2017 by mistermack

[MigL]

There is no 'classical physics this' and 'quantum physics that'.

 

There are classical models and quantum field models.

They are applied to the appropriate situation, to give meaningful results.

Sometimes, when the wrong model is applied, you get garbage.

Sometimes, as studiot has pointed out, you get equivalent results.

[mistermack]

 

Sometimes, when the wrong model is applied, you get garbage.

 

Example?

[MigL]

The 'original' one would be the UV catastrophy which led to Max Planck's quanta.

[mistermack]

The 'original' one would be the UV catastrophy which led to Max Planck's quanta.

That story is actually a popular myth.

[studiot]

Here is an authoritative reference on the history of Field theory (advertising suppressed)

 

Berkson : Fields of Force: The Development of a World View from Faraday to Einstein.

Original hardback 1974

 

 

 

 

Item Description: , 2015. Paperback. Book Condition: New. 234 x 156 mm. Language: English . Brand New Book ***** Print on Demand *****.This book describes the picture of reality given by Newton, and the development of the later picture of reality given by field theory. In telling this story, the author explains what problem each scientist faced, and how the process of solving them led to new discoveries. By this method he gives unique insight into the understanding of Einstein s special theory of relativity, as he explains exactly what problems led to the invention of the theory, and exactly where Einstein s solution differed from his predecessors . A similar analysis is given of the discoveries of Faraday, Maxwell, Hertz and Lorentz. The problem-oriented approach of the book, originally published in 1974, enables the reader to share in the original creative process, and in the excitement of the discoveries. It puts physics problems into new perspective and discusses the philosophical implications of the history - an illuminating account of a great episode in the history of thought

Edited February 8, 2017 by studiot

[MigL]

How is Planck's black body radiation derivation a 'popular myth' ?

 

It is a fairly straight forward classical derivation considering the density of states of radiation in thermal equilibrium inside a box, as had been done by others before him, resulting in divergence at high frequencies.

Max Planck 'fudged it' by introducing the concept of quantization, and everything worked out.

 

In QED. where the fields are treated as operators, the second quantization leads to the photon density, and the exact same results.

( I recall seeing the QED derivation a time ago but don't remember where )

 

So the 'classical' derivation of the black body distribution law gives the same results as the quantum field derivation.

[mistermack]

The first part of the popular myth is that it's spelt catastrophy.

For the second part, this is from wikepedia :

 

"

Historical inaccuracies[edit]

Many popular histories of physics, as well as a number of physics textbooks, present an incorrect version of the history of the ultraviolet catastrophe. In that version, the "catastrophe" was first noticed by Planck, who developed his formula in response. In fact Planck never concerned himself with this aspect of the problem, because he did not believe that the equipartition theorem was fundamental – his motivation for introducing "quanta" was entirely different. That Planck's proposal happened to provide a solution for it was realized only later, as stated above.^[4]Though the true sequence of events has been known to historians for many decades, the historically incorrect version persists, in part because Planck's actual motivations for the proposal of the quantum are complicated and difficult to summarize for a lay audience.^[5]"

[MigL]

OOOPS !

Typing without spell check is like driving without a seatbelt.

[mistermack]

OOOPS !

Typing without spell check is like driving without a seatbelt.

I just noticed how I spelt wikipedia !

[mistermack]

With all of the answers on this thread, I'm firstly wishing I'd been more specific in the original question, and asked what is a gravitational or electromagnetic field, since the word field gets used in different ways.

 

As to those two, what I'm getting is that a gravitational field isn't really one thing. Since it extends to infinity, we are really in billions and squillions of fields, of every bit of mass in the universe. So in theory, we are in one super-complicated field.

In practice, a lot of it is negligible, for calculation purposes, but it's still there.

We are in the Earth's gravitational field, and Earth is in the Sun's. And the Sun is in the Milky Way's field, and the Milky way is in the field of the local group and so on.

 

The picture I'm getting is of a 3D spider's web, with every bit of tension, at any point, having an effect on the shape of the rest of the web everywhere you look.

And if the spider's web was a km in diameter, it would take a finite time for any change at one end to have an effect at the other.

Which is similar to gravity effects travelling at the speed of light.

[kjelleman]

Hello Everybody. I am new to this forum. I work as professor in physics since 20 years and have taught in almost all different physics courses over the years.

I think the short question in this thread is interesting. I have myself struggled with the field concept and I have met many confused students in this respect and my teaching strategy concerning this concept is to declare that the field is a pure calculational aiding tool. It doesn't have any physical relevance. What happens ' between' two interacting objects, we have no access to, it is just speculations. Therefore physics need to be described field-free and the fields should be introduced afterwards as a model only. If you are interested in field-free physics I would like to recommend my text book:

 

https://link.springer.com/book/10.1007%2F978-3-319-13171-9

 

where part of it may be downloaded for free.

 

Best wishes,

 

Kjelleman