4 four momentum energy component direction

[Ibix]

using seconds for time and meters for space distinguishes between time and space

How do you distinguish between time and space? What I call "time" another frame will call "a bit of time and a bit of space". Should that other frame use seconds to describe intervals in my time direction, even though it includes distance in space?

I think a sensible answer to this will conclude that you mean to distinguish between timelike and spacelike, not between time and space. And distinguishing between timelike and spacelike is what the metric does. Why, then, would you need your unit system to do it too?

The whole argument feels to me like arguing that we ought to use fathoms for vertical distances and meters for horizontal ones because you can't measure horizontal distance with a plumb line. You can, of course, measure any distance with a ruler - you just hold it pointing horizontally or vertically. Similarly you can measure intervals with a radar set - just say you know the distance and it's a light clock, or say you know the time and it's a radar set.

 

[whatif]

Why, then, would you need your unit system to do it too?

You don't.

I am used to dealing with measurements that do reflect the properties to which they are applied and I dare say that applies to many people new to relativity. It just needs to be realized that a meter of time is not the same as a meter of space. "a bit of time and a bit of space" is a mix of two different properties. Timelike and spacelike are different properties.

The whole argument feels to me like arguing that we ought to use fathoms for vertical distances and meters for horizontal ones because you can't measure horizontal distance with a plumb line.

That is not a good analogy, because it is using different units of measurement for the same property.

In my view, I am not arguing semantics.

 

[Ibix]

"a bit of time and a bit of space" is a mix of two different properties.

To you. In my frame it's just time. So is it a mix of different properties or not?

That is not a good analogy, because it is using different units of measurement for the same property

But height and width aren't the same property. You can't use a plumb line to measure width. If you use a ruler to measure height, you can't use it to measure width without rotating through 90°.

 

[m4r35n357]

Is it just me or is this thread veering away from relativity altogether?

 

[Ibix]

Is it just me or is this thread veering away from relativity altogether?

Depends on your unit system.

 

[whatif]

To you. In my frame it's just time. So is it a mix of different properties or not?

You can regard it as a mix with zero spacelike part or not a mix as you choose. If you choose the latter then it does not have to be a mix.

But height and width aren't the same property. You can't use a plumb line to measure width. If you use a ruler to measure height, you can't use it to measure width without rotating through 90°.

Timespace has one timelike part and three spacelike parts. Height and width have the same property of distance between the points of measurement, as does depth.

You seem to now be heading towards indicating that the units of measurement of timelike and spacelike parts do, indeed, relate to a specific property.

 

[whatif]

Is it just me or is this thread veering away from relativity altogether?

I will make no more contribution.

 

[PeterDonis]

It just needs to be realized that a meter of time is not the same as a meter of space.

@Ibix's comment about "timelike" and "spacelike" being more appropriate here is valid. "Time" and "space" are relative, so it makes no sense to say that a "meter of time" is always a meter of just time, since in a different frame it will, as @Ibix says, be a mixture of time and space. But whether a given spacetime interval is timelike, spacelike, or null is invariant, independent of your choice of frame. So it makes sense to say "a meter of timelike interval" is distinct from "a meter of spacelike interval". Note that that, in itself, does not mean it must be true that a meter of timelike interval is fundamentally not the same as a meter of spacelike interval; it simply means it makes sense to formulate the question and consider it (whereas it doesn't even make sense to formulate the question of whether "a meter of time" is fundamentally different from "a meter of space", since "time" and "space" have no invariant meaning).

Timespace has one timelike part and three spacelike parts.

More precisely: any orthogonal set of basis vectors in spacetime must have one timelike basis vector and three spacelike basis vectors. But there is nothing that requires you to pick an orthogonal set of basis vectors; the only requirement for basis vectors is that they have to be linearly independent, which is a much weaker condition.

Also, not all vectors in spacetime are timelike or spacelike; some are null. Does that mean spacetime has to have a "null part" as well as one timelike and three spacelike parts? How can that be when spacetime has only four dimensions?

 

[sweet springs]

ake the components (magnitudes) of the 4 momentum, 4 vector (I am assuming it is known where these equations come from):

$$p^\mu=mcu^\mu$$ where 4-velocity u is
$$u^\mu=\frac{dx^\mu}{cd\tau}$$ where tau is proper time.

It seems x^\mu, u^\mu and p^\mu are perpendicular from this relation.