Is scale a 5th dimension?

[gib65]

This is just a thought, and I'm wondering if it makes sense to anyone else.

 

Can scale be considered a 5th dimension? Before the concept of spacetime became mainstream, we thought of space as consisting of 3 interwoven dimensions and time as another separate dimension. But with spacetime, we end up thinking of time as a 4th dimension that is interwoven with the 3 spatial dimensions, meaning essentially that the only difference between space and time is how we experience them.

 

Now the more I think about it, the more I see the same being applicable to scale - that is the dimension along which we place the size of things. So, for example, we say that planets, solar systems, and galaxies are at the end of the scale we label as "large" whereas atoms, electrons, and quarks are at the end of the scale we label as "small". Is this a 5th dimension? It is interwoven with time and space - that is, for any value of scale (any size), that same value can be talked about at any point in space and at any point in time.

 

Of course, one might say that scale is nothing more than a certain interval of space - that is, distance, area, or volume. So scale is essentially a specific way of talking about space. But the same could be said of time. That is, time is just a specific way of talking about how things move through space. In other words, time is just what you get when things take on different values with respect to their spatial positions. But we still talk about time as a 4th dimension. Why not scale?

 

What do others think?

[GutZ]

wow ok let me give this one a shot. I am going to write down some definitions.

 

Dimension

 

Physics. A physical property, such as mass, length, time, or a combination thereof, regarded as a fundamental measure or as one of a set of fundamental measures of a physical quantity: Velocity has the dimensions of length divided by time.

 

Scale

 

A system of ordered marks at fixed intervals used as a reference standard in measurement: a ruler with scales in inches and centimeters.

 

 

I guess by definition it's not. Dimension being a fundamental measurement of physics, where as scale is a simplification/standardization of the 3 direction based dimensions. Even though "time" is interwoven with the other 3, its still it's own entity.

 

It might be it's own entity down the road when more is found out about the origin of the universe, I can't picture it though, it would be very hard to explain. Plus things do work differently on different scales, that could just be proportionality differences right?

 

Well, I tried.

[the tree]

We label stuff as large/small depending how much of each dimension it takes up, usualy not including the temporal one.

[swansont]

Scale isn't orthogonal to the first four dimensions. So, no.

[gib65]

Well, I'm not so sure about this idea myself, but let me see if I can defend it a little.

 

"Ordered marks" is one way to define scale, but it isn't the only way. You could define scale as distance: how much distance a certain object spans from each of its most extreme points. This is indeed how much of each dimension it takes up, as The Tree said, but as I said in my first post, time is like this too. Time could be reduced to space: it is the space taken up by the distance that the object moves through. Of course, an object's spatial locations does not explain how it actually moves through space - this gets at the fact that time is "it's own entity" as GutZ pointed out - that is, you need to think of time as a separate phenomenon in order to explain motion. But I think the same could be done with respect to scale: you need to take scale into account in order to explain how an object like a rock could be identical with the collection of atoms that constitute the rock.

 

Swansont - I need to know what you mean by "orthogonal" please?

[swansont]

Swansont - I need to know what you mean by "orthogonal" please?

 

A more generalized expression of what we call perpendicular, in two dimensions.

 

x, y and z, for example, are mutually perpendicular in Cartesian coordinates. A dot product will result in zero; there is no way I can express one coordinate by multiplying a different coordinate by a scalar. (I can't change y simply by changing my x coordinate)

 

However, if your scale is mm vs km, I can get there simply by multiplying by 10⁶, which is just a number, i.e. a scalar.

[gib65]

Ah, so let me see if I understand: in order for something to be a dimension in the true sense of the word, it has to be able to change independently of any other dimensions involved, and likewise for those other dimensions. So, for example, you can talk about a point in space being exactly the same point at many different times. It's the same point at 12:00, 2:00, 4:00, and so on. Likewise for time - you can talk about a certain time, like 12:00, being the same time regardless of where you are in space.

 

But it's not so for scale, is it? You might be able to talk about the same scale at different times and points in space, and you can talk about different scales existing at the same time, but you can't talk about different scales at the same points in space. When something gets larger or smaller, it necessarily spans and greater or less amount of space.

 

That's it! My idea crumbles!

[J.C.MacSwell]

Scale isn't orthogonal to the first four dimensions. So, no.

 

Wouldn't that rule out time also? It isn't orthogonal to the first three. (although it is often pictured that way)

[swansont]

Wouldn't that rule out time also? It isn't orthogonal to the first three. (although it is often pictured that way)

 

 

In curved spacetime the rules change somewhat, from what I understand, but in flat spacetime they are orthogonal. The Lorentz transformation matrix being diagonal shows that.