What is a field?

paulb203 · 2024-11-13 23:04:56

From the Oxford Dictionary of Phyiscs (questions mine);

“A region in which a body experiences a force as a result of the presence of some other body or bodies."

Q. Do they mean region as in a certain amount of space around an object? For example, 10 metres cubed around a rubber balloon, that has a net electric charge?

“A field is thus a method of representing the way in which bodies are able to influence each other.”

Q. Calling it ‘a method of representing...’ makes me wonder if they’re backtracking on calling it ‘a region’, as if they didn't literally mean region; are they?

Bob · 2024-11-14 05:27:44

This is a new area for me so I googled it. For me the Wikipedia article (https://en.wikipedia.org/wiki/Field_(physics) makes a lot more sense than the Oxford one.

Bob

paulb203 · 2024-11-14 22:43:03

Thanks, Bob.

“An example of a scalar field is a weather map, with the surface temperature described by assigning a number to each point on the map.” Wikipedia.

The surface of what? (I’m asking rhetorically; as you said, this is a new area for you).

Because of the Oxford definition of ‘region’, and several other websites etc giving ‘region’ as the definition, I was thinking in terms of 3d space. ‘Surface’ does imply 3d, yeah?

So, the surface of..?

When we see a weather map on the telly we’re looking at regions, yeah? ‘Today it will be 10 degrees C in Liverpool.’ ‘Tomorrow it will be 6 degrees C in Blairgowrie.’ Not; 'Today it will be 10 degrees on the SURFACE of the region of Liverpool.'

Interestingly the article goes on to describe a wind as a 1 dimensional vector field.

Last edited by paulb203 (2024-11-15 22:51:43)

Bob · 2024-11-15 19:17:07

I'm catching up fast, On a weather map the region is the surface of the Earth (part of). Temperature is a scalar as it has just magnitude but not direction. Every point has a temperature so the 'field' of tempeatures matches the real world of the surface.

You can show wind simlarly but, as wind has magnitude and direction, this time it's a vector field.

Bob

paulb203 · 2024-11-15 23:11:08

Thanks, Bob.

So when we see a weather map on the TV we are looking at the various temperatures of the ground beneath our feet (the surface of the Earth) in the various regions?

From the second paragraph of the article;

"...a field occupies space, contains energy..."

I thought the field WAS the space (region). This sounds to me like it's saying a space occupies a space.

Bob · 2024-11-16 04:03:28

When an artist paints a picture it consists of layers of coloured paints on canvas. The paint is distinct from the canvas but you could say the paint occupies the canvas. The canvas is the place where the paint 'sits' (cannot think of a better word here).

The fields you have described are abstract concepts. You cannot touch the temperature values; nor can you have an isolated quantum of wind. But it's useful to think of a set of measurements superimposed on the space itself. It's the set of measurements that makes up the field.

Imagine that by some magic you could lift all the paint off the canvas so it existed separate from the canvas. That makes two objects. It's harder to imagine the same happening to the temperatures, but let's try. Somewhere in hyperspace is a set of temperatures that can be mapped back onto the surface of the Earth. It's not a concrete thing so it's harder to visualise but, if you are going to study advanced physics you'd better get used to it because I think it will happen a lot.

Bob

paulb203 · 2024-11-18 22:55:03

Thanks, Bob.

“When an artist paints a picture it consists of layers of coloured paints on canvas. The paint is distinct from the canvas but you could say the paint occupies the canvas. The canvas is the place where the paint 'sits' (cannot think of a better word here).”

Regards the one dimensional surface-of-a-region-of-the-earth weather map maybe a better analogy would be a special kind of artist who, instead of adding layers of paint to the canvas, treated it in some way (heated it?) in order to affect the colour of it, the way you have the ground beneath our feet (the canvas) and the Sun etc changing the temperature of that ‘canvas’. I hope that doesn’t sound pedantic; I’m just making the distinction between a thing that’s ALTERED and a thing that has ANOTHER THING LAYERED ON TOP OF IT.

“The fields you have described are abstract concepts.”

Why abstract? If they are indeed regions of space, with certain properties? From the article; “This has led physicists to consider electromagnetic fields to be a physical entity...”

Physical entity? Or abstract concept?

“You cannot touch the temperature values; nor can you have an isolated quantum of wind. But it's useful to think of a set of measurements superimposed on the space itself. It's the set of measurements that makes up the field.”

Ah, so you meant that the set of measurements, the numbers, symbols, etc, are the abstract concept?
But do they ‘make up the field’? Or do the merely describe it, represent it? Isn’t the field itself the region, with the particular properties?

“Imagine that by some magic you could lift all the paint off the canvas so it existed separate from the canvas. That makes two objects. It's harder to imagine the same happening to the temperatures, but let's try. Somewhere in hyperspace is a set of temperatures that can be mapped back onto the surface of the Earth.”

Interesting. But as I said above I’m thinking that a ‘heat treated’ canvas might be a better analogy. Although, having said that, I’m now wondering if somethin is actually added to the actual field (the region of space)? Is it filled with OTHER THINGS (particles or whatever)? For example when we create an electric field around a rubber balloon by rubbing it on our hair. What happens to that region of space around the balloon? Prior to the experiment it consisted of molecules of air (nitrogen, oxygen, etc), and whatever else (?). What happens to those molecules?

“It's not a concrete thing so it's harder to visualise but, if you are going to study advanced physics you'd better get used to it because I think it will happen a lot.”

I do get that a lot of this is going to be UNUSUAL, to say the least, and maybe, at times, beyond normal language. But I’m wondering if it could be helpful to push it that way as far as we can take it, if you know what I mean.

KerimF · Yesterday 03:39:58

For instance, not every scientific question has an answer. When I was learning at the university, I tried to answer the following question:
What could be the mechanism/process that lets a body detect (or be detected by) another nearby body in space? We simply see its fruit (result) only, their force of attraction.
This unknown mechanism forms a certain field (which could be called gravity for example) in the region in which the two bodies exist.

Math Is Fun Forum

#1 2024-11-13 23:04:56

What is a field?

#2 2024-11-14 05:27:44

Re: What is a field?

#3 2024-11-14 22:43:03

Re: What is a field?

#4 2024-11-15 19:17:07

Re: What is a field?

#5 2024-11-15 23:11:08

Re: What is a field?

#6 2024-11-16 04:03:28

Re: What is a field?

#7 2024-11-18 22:55:03

Re: What is a field?

#8 Yesterday 03:39:58

Re: What is a field?

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