1.When we measure meters, we measure distance. When we measure square meters, we measure area.

 

There is a difference between distance and area: these are different concepts representing 2 different aspects of the physical world.

 

2.When we measure seconds, we measure time. When we measure square seconds, we measure...what?

 

Are there 2 times orthogonal to each other, like the meters oriented in orthogonal directions?

 

And if yes (or if no), what are square seconds representing?

You don't have square seconds, you have seconds squared. In the example of squaring a speed, which has units of distance squared, it does not represent an area. We draw the distinction between meters squared and square meters — the latter tells us it's an area. In an example of acceleration, sec^2 appears as a rate of change of a rate of change (of position), but it's still seconds squared, not square seconds.

 

(You also a similar concept with N-m for torque. You never express it as Joules, even though a Joule has units of N-m. Torque is not energy.)

What are meters squared then ?

 

It can't be a distance.

 

Similarly, what are seconds squared?

Acceleration as opposed to just velocity which is m/s

What are meters squared then ?

 

It can't be a distance.

 

Similarly, what are seconds squared?

 

m^2 is a distance multiplied by a distance. Similarly s^2 is time multiplied by time. Units don't necessarily give you contextual information.

m^2 is a distance multiplied by a distance.

I call that an area.

 

Similarly s^2 is time multiplied by time.

what is this?

 

Units don't necessarily give you contextual information.

hmm. Shouldn't it?

Do we encounter square mass, for example?

I call that an area.

 

Area is a two dimensional measure involving lengths.Do you call it an area when a length in one dimension is multiplied by a length in the same dimension?

 

For example: [taken from http://www.school-fo...work_energy.htm]

The definition of work is that it equals force times the distance traveled while that force is being applied or

 

 

W = Fd

 

where (for example) F = ma,

and a is the acceleration or change in velocity in meters per second-squared (m/s²).

 

 

So the acceleration involves a measure of length along one dimension, and work involves length along that same dimension, and W ends up with a squared length.

These equations work in one spatial dimension. What would the "area" be?

Edited December 29, 201114 yr by md65536

Area is a two dimensional measure involving lengths.Do you call it an area when a length in one dimension is multiplied by a length in the same dimension?

 

For example: [taken from http://www.school-fo...work_energy.htm]

The definition of work is that it equals force times the distance traveled while that force is being applied or

 

 

W = Fd

 

where (for example) F = ma,

and a is the acceleration or change in velocity in meters per second-squared (m/s²).

 

 

So the acceleration involves a measure of length along one dimension, and work involves length along that same dimension, and W ends up with a squared length.

These equations work in one spatial dimension. What would the "area" be?

You made a point.

It should be written as per second(m/s) not s^2.

s^2 implies multi universes.

Edited December 29, 201114 yr by derek w

It should be written as per second(m/s) not s^2.

s^2 implies multi universes.

???

10 seconds in 10 different universes =10^2=100 seconds.

derek you lost me.

We are in speculations but the OP was not intended to discuss about multiple universes.

It was simply a question about units in basic physics.

hmm. Shouldn't it?

 

No. I already gave an example of torque vs energy.

Sorry Michel but,you asked the question "when we measure square seconds we measure what"?

I was simply giving a suggestion of what square seconds would be.

yeh,sorry Michel I was not having a go at you,I was having a go at the way acceleration is expressed as m/s^2.It gives no indication of how much time is spent accelerating.

Where as m/s x t.where t = the amount of time spent accelerating makes more sense to me.

e.g. an acceleration of 10 metres per second for 10 seconds.Just seems more meaningful.

 

Therefore I agree with your question "when we are measuring square seconds we are measuring what?"

 

 

yeh,sorry Michel I was not having a go at you,I was having a go at the way acceleration is expressed as m/s^2.It gives no indication of how much time is spent accelerating.

Where as m/s x t.where t = the amount of time spent accelerating makes more sense to me.

e.g. an acceleration of 10 metres per second for 10 seconds.Just seems more meaningful.

 

Therefore I agree with your question "when we are measuring square seconds we are measuring what?"

A rate of change by second. That is time twice, thus s^2.

But we refuse 2 dimensions of time. We say there is only one time. But then, if there is only one time, what are s^2?

 

As an analogy, it is like having m^4 in an equation.

A rate of change by second. That is time twice, thus s^2.

But we refuse 2 dimensions of time. We say there is only one time. But then, if there is only one time, what are s^2?

 

As an analogy, it is like having m^4 in an equation.

 

A fourth-order process will depend on terms raised to the fourth power. Not common, perhaps, but they exist.

 

Black hole lifetime from Hawing radiation depends on m^3

The Stefan-Boltzmann law depends on T^4

Planck's radiation law depends on wavelength^5

Dipole-dipole interactions depend on r^6 (because dipoles fall of as r^3, with higher-order multipoles on even larger exponents)

 

Units don't give the information you seem to think they do.

Sorry for the interuption, but in reading the OP I got the impression that the question was about square seconds not seconds^2. Square meters would still be the measurement of an area, but what would square seconds? I thought this was the question that michael123456 posed. If there is some demension to time that can be applied to square seconds? As applying area somehow to time.

Edited December 30, 201114 yr by JustinW

Great discussion of units, and unit cancellation at xkcd's "What If" http://what-if.xkcd.com/11/

Great discussion of units, and unit cancellation at xkcd's "What If" http://what-if.xkcd.com/11/

 

Interesting.

I thought it was amusing.

!

Moderator Note

The tangent on relativity has been split off http://www.scienceforums.net/topic/69186-relativity/

Gravitational potential depends on the inverse distance from a body such as the moon; gravitational force on the inverse square; tidal force on the inverse cube; and the difference in tidal force between the side nearest the moon and the side furthest, depends on the inverse fourth power of distance.

 

Gravitational potentials are measured in units of m²/s², forces in terms of m/s². Extending that logic, tidal force ought to be measured in /s², and difference in tidal force in /ms². More evidence that physicists choice of units are rather dodgy.

You don't choose the dimensions that go into units. That is dictated by the phenomenon under investigation.