The meter-second (moved from general discussion)

[zebov]

Ever since learning to integrate in high school Calculus, I've been curious as the the physical meaning of the integral of position w/ respect to time. Over the years, the topic has come up again and again in my mind, and have finally decided to put an end to my pondering; or at least let others ponder with me.

Is there any firm grasp of the concept of the meter-second already in existence? Is there a good use for this?

I have come to call the integral of position wrt time "longevity" as that seems to be the best term in my mind to describe it. From what I have been able to determine with some simple thinking is that longevity can be related to amount of energy or force placed on object in a gravitational field (ie. if you put a high amount of kinetic energy on an object, it will have a larger longevity than if you put a small amount of kinetic energy on an object).

Any thoughts on this?

[Martin]

...

Any thoughts on this?


you ask for ANY thoughts, zebov.
I assume that includes any random thoughts. So here are one or two random reactions.

The meter second is the unit needed to express this combination of fundamental constants

G h-bar/c4

Just for practice I will write the same thing in tex (if it works today)

\frac{G \hbar}{c^4}

Now this G/c4 is the coefficient in the Einstein equation, the main equation of General Relativity. Sometimes in Gen Rel the units are adjusted so that G/c4 = 1

this makes the Einstein equation look nice. If that were done, then what you are talking about, namely the unit of
G h-bar/c4, is the same as the unit of h-bar itself. That is, the unit of ACTION.

Ordinarily action is [energy x time], but setting G/c4 = 1 has the effect of identifying energy with distance...so it becomes [length x time].

h-bar is also the unit of UNCERTAINTY in the Heisenberg uncertainty relation.

But adjusting the units that way will totally get you out of the metric system. It seems like a pointless thing to do unless you have some good reason.

Now that i think more about it, I don't know of any everyday physics quantity that would be measured in meter-second. Could be something in some obscure branch of hydraulics or meteorology :-) . Did you look it up in google?

[ydoaPs]

i have been wondering about the meter second for a few weeks now as well....stupid calculus...

[zebov]

I've tried googling, but to no avail. Even had some discussion with some smart university-type grad students. I did receive a good response from Tom Mattson explaining WHY no one is particularly interested in it (because energy is based of position and velocity, and that's what we humans care about) (http://www.scienceforums.net/forums/showthread.php?t=18440). However, I'm still curious as to if there could possibly be any useful physical meaning in some branch of science.

I thought there may be some sort of connection to relativity, because it's in essence making space and time a comparable entity saying "5 meters for 1 second is the same as 1 meter for 5 seconds."

[Martin]

...

I thought there may be some sort of connection to relativity, because it's in essence making space and time a comparable entity saying "5 meters for 1 second is the same as 1 meter for 5 seconds."

you are pushing us to be creative, zebov.

I'm afraid you won't necessarily be pleased with the results:-)

probably we can't get a connection with relativity, but what about this?

the danger to a diver of nitrogen poisoning or "the bends" is proportional to the time he works under water. working 5 hours is more risky than working one hour

it is also proportional to the DEPTH he is working, work at 50 meters is 5 times more dangerous and requires 5 times more precaution when coming to the surface than working at 10 meters

so we have a integrated nitrogen burden that we calculate, say, where
if he works for FIVE HOURS AT 10 METERS that is 50 points and it is just as bad as working ONE HOUR AT 50 METERS---which also gets 50 points

after the job, the accumulated burden determines what he has to do when coming to the surface, and how soon he will be allowed to make a second dive. There are precautions that one can take like gradual surfacing, by stages, and breathing a different mixture, and so on.

Actually, zebov, I have done some SCUBA and several times we had "dive computers" on our wrists which were like FAT WRISTWATCHES and were always integrating time and depth.

After being down deep for a long time, the "dive computer" would warn us if we were coming up too fast, and it would warn us not to make a second dive that day if we had born too much Nitrogen load. It did not want us to come up too fast etc etc.

you can say it was integrating time with PRESSURE (not depth) because that is what matters. at higher pressure the nitrogen disolves into the blood more rapidly.

[JustStuit]

It could be of us as a transitional or converting unit. I don't see any practical reason for it.

[taylrl]

In theory, couldnt every physical movement be measured in meter-seconds, as we are all actually moving in 4 dimensions??

[zebov]

In theory, couldnt every physical movement be measured in meter-seconds, as we are all actually moving in 4 dimensions??

Well, every position can be expressed in terms of meter; every speed/velocity in terms of meter/second; every acceleration in terms of meter/second^2. However, one cannot determing a position from a given speed; nor can you determine a speed from a given position.

The question is, is there any application of measuring "longevity" (in meter-seconds). The post above about diving is one such application where position, velocity, or any of their derivatives are unimportant... the important thing is the "longevity" (actually, it's a pressure-time measurement, but this can be derived from the position-time measurement). Does anyone else have any valid applications of the meter-second?

[insane_alien]

if there was any use for it, it would already be used in physics and probably engineering. i'm sure that in the 300 years of calculus some physicist has asked the question.

[zebov]

Aye, that is what I thought as well; however, I wasn't able to find ANY reference to it, so I thought I'd ask around and get others' ideas. To me, this is not a dumb question, but rather and interesting idea. The answer "noone has done anything with it and I'm sure someone has tried" is not enough for me... lest nothing ever be researched and, thus, the halt of scientific development.

I very much appreciate the answers I have received, though. Esp. regarding its lack of usefullness in calculating Energy and its possible use in diving. Answers of this nature are much more informative than "i'm sure that questions been asked before, so it must not be something we should look into."