What is a field?

[Mordred]

What all fields describes is a distribution of whatever objects/events/coordinates etc you are describing.

 

This is true in relativity as well. Your describing geometric freefall (in essence mass) distribution.

 

Universe spacetime curvature (expansion history due to thermodynamic relations) in essence temp/pressure distribution.

 

Thats all a field is, a means to make mathematical sense of any distribution usually under a coordinate system but coordinates are not a requirement. ie tensors.

 

GR maps freefall motion a geodesic/ Worldline is a type of mathematical treatment describing the freefall motion between two events at each coordinate.

 

This relationship is the curved part. Spacetime curvature does not mean spacetime is its own substance. Its simply describing specified relations into a coordinate system.

Non ontologically ,does a moving electron or proton set up a magnetic field and does that field require an environment composed of

other EM fields to have effect?

 

Is there such a thing as a diagram of the field set up by one moving "elemental" EM charge (such as an electron or a proton ,I surmize)

An electron can both interact with other multiparticle fields as well as have its own field. This however doesn't mean the field is contained of some substance. The last example is describing the possible interaction range with geometry

 

Ie a single electron has infinite range in which it can potentially interact with another electron. The field strength may be zero but the possibility of interaction is still present. Once that single electron interacts the field becomes charged.

 

Note the field is still present whether charged or not. (A field being the abstract system being described under geometry)

 

[Latex]\frac {1}{2}|V\phi\rangle(x,t)[/latex] here is your single electron in field treatment. Remember QFT treats all particles as field excitations. The field in this case being comprised of potential oscillations [latex]\phi [/latex] x in this case is a complex variable

[latex]x=(x_1,x_2,x_3)= (x,y,z)[/latex]

 

The reason behind the last nomenclature is that the last equation is describing potential interaction strength between any two points. So we only need to identify any other point and draw a line between those two points. This line becomes x

 

In QFT a scalar field defined as

[latex]\phi (x,t)[/latex] x is still the three dimensional complex variable I described above. So we can see from this last equation I am simply mapping the oscillator potentials under geometry.

 

If we take the above a non interacting free field in QFT treatment that is identical to your Minkowskii metric is

 

[latex]V\phi=\frac{1}{2}m^2\phi^2 [/latex]

 

where m is your mass term, the fraction is your harmonic oscillator (Heiesnburg uncertianty) V is volume

Edited February 1, 2017 by Mordred

[Xerxes]

As far as gravity goes, there seems to be confusion. A warping of space time? OK, but that seems to definitely assume a physical structure of space time, rather than nothing.

Why are you assuming that "spacetime is nothing"? Why shouldn't spacetime have a structure?

 

In truth, your question has a venerable history; having ditched the so-called aether, Einstein,following his introduction of a tensor field description of gravitation, wondered exactly the same thing.

 

He concluded, in his case, as e.g. Laplace had done long before him that fields exist even in the absence of a gravitational source.

 

In the case of a scalar theory of gravitation, this statement takes the rather simple form of [math]\nabla^2 \phi =0[/math], where [math]\phi[/math] is the scalar field and [math]\nabla^2 \phi= \nabla\cdot(\nabla \phi)[/math] i.e. the divergence of the gradient of the scalar field.

 

In the field theory of gravitation, this reads [math]R_{\mu \nu}=0[/math] i.e. in the absence of a source spacetime is not curved.

 

But note this crucial point - curvature [math]R_{\mu \nu}[/math] is derived from a second order partial differential of the metric field [math]g_{\mu \nu}[/math], which mandates, by the property of second order derivatives, ONLY that if [math]R_{\mu \nu}=0[/math] that the field [math]g_{\mu \nu}= \text{constant}[/math].

 

In other words, space is ALWAYS "filled" by the metric field. Einstein called this a form of aether

 

Likewise for the electromagnetic field

Edited February 1, 2017 by Xerxes

[StringJunky]

In other words, space is ALWAYS "filled" by the metric field. Einstein called this a form of aether

 

Likewise for the electromagnetic field

But is it just a template with co-ordinates that can alter their position depending on the phenomena and energies present?

Edited February 1, 2017 by StringJunky

[Mordred]

if you include the energy/momentum tensor. Which follows from the full EFE.

Edited February 1, 2017 by Mordred

[studiot]

Ok, but it's pretty obvious that I'm asking what the field describes. I made that clear.

I don't buy the comment that science doesn't study what things are, only how they behave. The study of the Sun didn't just discover how it behaved. The most important discoveries were about what they Sun actually WAS.

 

I'm not trying to introduce ontological mystery to the debate.

Studiot, you say you answered the question. You didn't. You said a field was a catalogue of values of a variable.

It's the nature of the variable that I was inquiring about, and that was pretty clear in the OP.

ie , what is that variable, in seemingly empty space?

 

I'm getting the feeling that the answer is " I don't know " and that's fair enough.

As far as gravity goes, there seems to be confusion. A warping of space time? OK, but that seems to definitely assume a physical structure of space time, rather than nothing. Or is the variable a particle that is passing between bodies?

 

I asked the same question about a magnetic field. Is it a different kind of warping of space time, or the result of photons being constantly passed through the field?

 

Actually I did, and what's more I told you that there are many different (types of) Fields with equally many different types of properties and that the properties are controlled by the field variable.

 

Note you did not mention this field variable, I did.

 

And yes, if you were not so determined to try to force the answers into some preconceived but inappropriate form we could certainly have a productive discussion.

 

I could tell you that magnetic fields, electric fields and gravitational fields have a fundamental difference.

 

I could note that neither magnets, nor currents are 'fields' themselves but are physical entities capable of interacting with a suitable field.

 

Do you know which of these is a conservative fields and which a non conservative field - I have already introduced conservative and non conservative fields as a fundamental property?

 

I could say look at a flowing river and note that if we place an 'arrow' at every point we get a 'direction field' which will tell us which way the water flows at every point.

We could improve that by placing a vector which tells us both the strength and direction of the flow.

 

I could say that the record of temperatures at every point in a body constitutes a temperature field, which will tell us which way the heat will flow, but doesn't refer to any mysterious 'lines of force'.

 

Or I could say the same of a record of reagent concentrations in a mixture and note the concentration gradient field.

 

 

I could also observe that one common usage of the word is not what is meant in science.

A field is not the (physical) stage upon which a particular activity takes place.

This usage is very common for instance the field of play for a game, the field of battle, a field of poppies etc, all of which have physical embodiment and may be specially prepared in some way for the intended action.

I wonder, perhaps, if you aren't trying to make the scientific usage conform to this notion?

[Xerxes]

But is it just a template with co-ordinates that can alter their position depending on the phenomena and energies present?

Is what just a template.....?

 

Coordinates do not "alter their position", whatever that means. Let me try to explain.

 

A manifold - for that is what spacetime is - is equipped at every point with a unique set of coordinates that completely describe the position of all events at that point.

 

In "moving" these events to a new point, then a new set of coordinates must (according to co-variant or gauge theories) must describe the same events.

 

This is the reason that coordinate transformations play such a prominent role in field theories - you need to know how coordinates change as you "move" from on point to another.

 

Having established that, using the differential calculus, then you can forget about coordinates and get on with your life.

[geordief]

 

A manifold - for that is what spacetime is - is equipped at every point with a unique set of coordinates that completely describe the position of all events at that point.

 

Do you mean (should you have written?) "A manifold - for that is what spacetime is - is equipped at every point with a unique set of coordinates that completely describe the position of all events with respect to that point." ?

[Nedcim]

Mistermack: science descibes how things behave, not what they are.

There are many fields in science that deal with form and structure. If the form and structure does not define what something is then what would you use to define it?

[StringJunky]

Deleted

 

There are many fields in science that deal with form and structure. If the form and structure does not define what something is then what would you use to define it?

Behaviour. Define the structure or form of a photon or electron. They are excitations in a field.

 

I should have said physics describes behaviour.

Edited February 2, 2017 by StringJunky

[Mordred]

Myself I would use the word relations. Just cuz I see some weird posts coming from the word behavior.

 

lol too much time reading speculations forum

[studiot]

There are many fields in science that deal with form and structure. If the form and structure does not define what something is then what would you use to define it?

 

One thing that comes out of Green's / Gauss' theorems as a surprise to many is the fact that ie form and structure for many physical phenomena, in the interior of a bounded region, can be completely defined by knowledge of what is happening on the surface.

 

The Boundary Element Method can often achieve great computation efficiency in replacing the Finite Element Method because of this.

[mistermack]

So does the gravitational field of every object extend right around the Universe?

Or does it stop when it's effect drops below one "quantum" of gravity?

[Strange]

The question is what it IS.

 

 

In general science can't answer that question. Outside of metaphysics and religion, nothing can answer that question.

[mistermack]

 

 

In general science can't answer that question. Outside of metaphysics and religion, nothing can answer that question.

I disagree. There are levels of answering.

Take my example of the Sun. People used to think it was a disk that moved across heaven. Then they found it is a globe, and we moved, not it. Then they discovered it was lit by nuclear fusion. Then they measured it's composition. And deduced it's age.

These are all things that tell you about what it is. There is still a long way to go, but they are all part of the answer.

[Strange]

I disagree. There are levels of answering.

 

 

So we agree. But there always comes a point where the question can't be answered.

[mistermack]

 

 

So we agree. But there always comes a point where the question can't be answered.

Yes, we agree, but I would say that most physics questions are at the point where we can still go further than we are at the moment.

We have the problem of dark energy. People can see what it does, but they still are trying to find out what it IS.

Not necessarily what it fundamentally is. But any progress is better than nothing.

[geordief]

So does the gravitational field of every object extend right around the Universe?

Or does it stop when it's effect drops below one "quantum" of gravity?

Anyone have an answer to this?

 

Do all particles ("objects" a better word?) that have interacted remain forever connected in some way -and also in a gravitational way?

Edited February 2, 2017 by geordief

[Mordred]

The gravitational force has infinite range but its strength falls off at 1/r^2. At some range the interaction strength will be insufficient to cause kinematic motion. Range will vary according to the masses involved.

Edited February 2, 2017 by Mordred

[mistermack]

The gravitational force has infinite range but its strength falls off at 1/r^2. At some range the interaction strength will be insufficient to cause kinematic motion. Range will vary according to the masses involved.

I'm not sure I agree totally agree. I don't think "cause" is the right word. Affect is maybe better?

My head isn't all that big. But it's part of the Earth, which gives the Sun a wobble.

All parts of the Earth must be taking part in that?

And the Sun gives the Milky Way a minute wobble. All parts of the Solar System must be helping? You can't exclude my head from that, surely?

And the Milky Way interacts with a local group and so on.

So my head makes a negligible, but non-zero contribution to how the Universe moves, I would have thought.

[Mordred]

Affect vs cause hrrm lets leave that to philosophy.

 

All mass including your head contribute under the sum of mass. Though I have no idea how much mass your head has lol. You can use Newtons gravitational law to calculate how much influence it would have over a given radius. You will find its contribution would be considered neglibible.

Edited February 2, 2017 by Mordred

[Strange]

So does the gravitational field of every object extend right around the Universe?

Or does it stop when it's effect drops below one "quantum" of gravity?

We don't currently have a theory of quantum gravity so it never stops (in principle - as Mordred says, it ceases to have any practical effect st some point).

[mistermack]

Affect vs cause hrrm lets leave that to philosophy.

 

No, what I meant was, everything's already moving. (In all frames apart from one) So it's not a question of causing something to move, it a question of affecting it's existing motion.

[Mordred]

Correct not that its important but cause also includes inertial change

[mistermack]

If every bit of mass has a field that extends to every part of the Universe, is it in a similar way that all roads lead to Rome? Or all phones are connected to the White House?

In other words, the field is just a reflection of the object's connection to the fabric of space time?

[Xerxes]

Although I am aware this discussion as drifted away from most things that interest me, for accuracy, let me correct myself. I said

A manifold - for that is what spacetime is - is equipped at every point with a unique set of coordinates that completely describe the position of all events at that point.

This is false for the types of manifold that are useful in applications. These are the so-called "connected" manifolds, which have no "holes" or "gaps". This means that for any such manifold [math]M[/math] and any point [math]m \in M[/math] there exist at least two associated coordinate systems. Call them [math]x^1,x^2,.....,x^n[/math] and [math]\overline{x}^1, \overline{x}^2,....,\overline{x}^n[/math]. So my self-quote above is not generally true

 

Then in relativistic applications - in fact in general - since the single point [math]m \in M[/math] is assumed to have some sort of "reality", there must exist a functional relationship between these two sets of coordinates.

 

This is called a coordinate transformation.

 

More abstractly.....for a manifold with the so-called Hausdorff property*, it makes little sense to distinguish between the point [math]m \in M[/math] and the coordinates [math]x^1, x^2, ....,x^n[/math]. In other words, the point IS the coordinate set.

 

*Roughly speaking, the Hausdorff property says that if, for any 2 points [math]p,\,\,q \in M[/math], it is impossible to assign distinct coordinates, we must assume that [math]p=q[/math]