# I If fields fill all of space, how do they have room to move?

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1. Mar 25, 2016

### Pjpic

If fields fill all of space, how do they have room to move? Those tile games we had as kids always required one empty space to slide the tile into.

2. Mar 25, 2016

### Staff: Mentor

Fields aren't matter. They aren't solid. They don't have to take up space to fill it and they can overlap.

3. Mar 25, 2016

### Staff: Mentor

They don't move. For example, the E field has a magnitude and a direction at each point in space, and that magnitude and direction can change over time, but it does not have a velocity at any point.

4. Mar 25, 2016

### Pjpic

How can something change if there's no empty space (room to grow you might say)? I must be missing a basic idea.

5. Mar 25, 2016

### Staff: Mentor

I have no idea what would possibly give you the idea that empty space is necessary for change to occur. It seems like such a bizarre connection, how can you possibly justify it?

6. Mar 25, 2016

### Pjpic

If you have 12 eggs you can't change the arrangement in the carton, but if you only have 11 (one empty space) you can arrange the eggs in 12 different ways.

7. Mar 25, 2016

### Staff: Mentor

So what? Changing the arrangement is obviously not the only thing that could change. You could change an egg's temperature or pressure or color or hardness or smoothness or shape or any number of other changes that would be changes without requiring empty space and would be possible with all 12 eggs in place. The idea that the only possible change is change which requires empty space is so wrong I don't know where to begin.

Changing the value of a field is not like changing the arrangement of eggs. I cannot see any reason for thinking that it should be.

8. Mar 25, 2016

### Staff: Mentor

Suppose a certain point in space has, at a certain time, an electric field E = 10 V/m northward, and a nearby point has E = 0 at the same time; then a bit later, the first point has E = 5 V/m northward and the second point has E = 10 V/m northward. This doesn't mean the 10 V/m has literally "moved" from the first point to the second point. The field has simply changed its value at both points.

9. Mar 25, 2016

### Pjpic

Are these points the dimensionless points I've read about? And they can have values of any size (except infinite)?

10. Mar 25, 2016

### Staff: Mentor

In classical field theory, yes.

11. Mar 25, 2016

### phyzguy

One example of a field that I've found people have an easier time of visualizing is temperature. Imagine the temperature at every point in space. This is a scalar field. Clearly the temperature can be defined at every point in space, so there are no "empty points" where the temperature is not defined. But clearly the temperature can change in many ways. It can get hotter everywhere, colder everywhere, or hotter in some places and colder in others. No movement is required for these changes to occur. Vector fields like the electric field are the same idea, but instead of one number at every point in space, there are three numbers at every point in space.

12. Mar 27, 2016

### Staff: Mentor

One of my local TV stations includes on its animated weather maps, arrows representing wind speed and direction. The arrows are arranged in a square grid of fixed locations. As time elapses, the arrows grow and shrink to reflect changes in speed (magnitude), and pivot around to point in different directions, but they do not move from their fixed locations. Any vector field, e.g. the electric and magnetic fields, can be represented in the same way. In each case the grid represents only a sample of possible locations. The field actually exists everywhere, and you can imagine "filling in" the spaces between arrows with more and more arrows, spaced closer and closer together.

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