steevey

Planck units like the mass and length come up all over the place in modern physics---they are not the only system, there are other convenient special purpose units, but they are worth getting familiar with.

 

Using the google calculator we can take a kind of almost experimental approach to planck units, explore, build up our concepts, try them out. It is easy---a few posts will show what I mean. So here's a brief tutorial.

 

1. get to know hbar (Planck's constant)

Think of hbar as being the product of amounts of energy and time. Check that by typing things like this into google

 

hbar/minute

hbar/year

 

It will give you answers in energy terms----small amounts of energy.

If you like BTU or calories or foot pounds you can always ask for the answer in those terms

 

hbar/hour in foot pounds

 

Personally I am most comfortable with ordinary metric units like second meter joule newton, but I want to emphasize that the google calculator works with a wide range of units and will give you answers in pretty much any units you happen to like. It knows how to convert and it does what you tell it.

 

2. Think of hbar as the product of (typically small) amounts of force x distance x time.

 

Try pulling hbar apart using the calculator. Take hbar, pull out some length, then pull out some time

 

(hbar/inch)/day

 

It will always turn out to be a force. Let's have the answer come out in pounds of force:

 

(hbar/inch)/day in pounds

 

(hbar/foot)/hour in pounds

 

Try putting the blue thing into google and see.

 

More later

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Merged post follows:

Consecutive posts merged

 

This is the second post of this tutorial. The title of the post is

Your first planck unit--the Force :-D

 

1. Try putting this into google

 

c^4/G

 

Again, to emphasize that there's no metric bias, put this in

 

c^4/G in pounds

 

c^4/G is a natural amount of force. It's the Planck force. Remember it.

 

2. Besides the Planck force we don't have very much we have to remember. You already pulled apart hbar and you know it is made up of

force x length x time

 

Well what other natural constant do you know that involves length and time?

c

c is length/time

So what happens if you multiply

force x length x time together with length/time? You get force x area.

 

So let's try that. Multiply hbar*c and check to see if it is the product of some force with some area. The way we check is we put this in google:

 

hbar*c/square inch

 

That is, we multiply hbar and c together and then divide out any amount of area we please, square foot, square meter, square inch, square mile whatever. If hbar*c is the hidden product of some force with some area, then if we divide out some area we should get a force.

 

Just to show we're not biased let's get it in pounds

 

hbar*c/square inch in pounds

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Merged post follows:

Consecutive posts merged

This is the third post in this short tutorial. The title of the post is

Your second planck unit---the Area

 

OK we picked apart hbar a little and we know it acts like it's made of a bit of force multiplied by other stuff.

 

And we teased apart hbar*c some and we know it acts like it is a force x area quantity... made of a small amount of force multiplied by some area.

 

And we know c^4/G is a force. It is a natural amount of force that doesn't involve any man-made units like inch or hour or foot etc.

 

So let's divide hbar*c by that natural force and see what we get.

 

Put this into google

 

hbar*c/(c^4/G)

 

or even better put this in

 

hbar*c/(c^4/G) in square inches

 

That is a natural amoung of area that doesn't depend on man-made stuff like joules kilograms etc. It's expressed in square inches, OK, but that doesn't matter, you could choose any unit of area to express it in---square yards, square millimeters... The quantity of area itself is natural.

 

And if you took highschool algebra you probably noticed that something could be simplified by canceling a c.

 

hbar/(c^3/G) in square foot

 

And we can make it look nicer by flipping the G up

 

hbar*G/c^3 in square miles

 

Your third Planck unit---the Length.

 

Try this in google

 

sqrt (hbar*G/c^3 ) in miles

I know that some scientists say the universe is moving along increments of Planck time, but Planck time is just the shortest amount of time that matters in our current physics, why would scientists think its the shortest amount of time possible? Couldn't something have happened in the creation of the universe that took less than a unit of Planck time?

They way I see it, 1/0 (in terms of physics) would equal infinity, and the evidence for that would be that the universe's volume (not visible matter, but rather just the fabric of space itself) is infinite because when you apply a wave function equation to when the universe was just a single point, the distance is 0 because a point is a 0 dimensional sphere (weird huh?). And even if that is somehow flawed which I think it is, but not by much, you still have to consider the entanglement between two particles renders distance meaningless. No matter how great the distance is between two components of a system of entangled particles, either of the two will respond instantly to a change in the properties of another, but how could that be true unless the true distance between all objects in the universe is actually 0 and everything is still somehow the same thing? In mathematics, you would have to be able to do this

4*2=8

8/2=4

8/4=2

which you can't do with infinity (or all real numbers), but mathematics isn't the universe, it's simply a way to recognize the components of the universe in terms of numeric values. Never in nature is something actually going "well lets see, 1 + 1 = 2". What happens is, you have two apples, all with their own atoms, which have separate distance (according to modern physics), and all your doing is bringing them closer together and saying "now I have two", but the universe doesn't recognize ( I had 1 then I added 1, now I have 2) in any way. The math is something that we just made up. In terms of the universe, it's just a cluster of atoms being brought closer together, and the evidence for that is that the apples' gravitation fields have a greater effect on each other, however the apples aren't fused together. The apples are not counted as one system, and if they were, that would be a violation of quantum mechanics because if you can measure the two apples in some way to quantify the information, that means you'd have to be collapsing the wave function, which means the two apples aren't actually one system. Math can easily describe things, but it isn't necessarily actually those things. Thats why I can have an equation for how the price of an item in a shop increases with the amount of that item bought, and yet neither the shop nor the item have to exist. There are still rules and things that govern how things happen, but that's why we have physics and science.