# Planck;s constant

1. Mar 16, 2006

### the iron maiden

hi, i have an essay question which entitles " what if planck;s constant was 6.63x10^30, how would this change the world? prove your reasoning mathematically. "

all i can think of as a starting point is blackbodies and the equation E=hf.

any help would be apprectiated.
cheers.

2. Mar 16, 2006

### vanesch

Staff Emeritus
You would first have to say how the other constants, like the lightspeed, the mass of the electron and so on would alter. But let us assume that we keep the lightspeed and the mass of the electron constant. In that case, you've just re-defined the units "second" and "meter", and kept the universe the way it is.

The reason is that the planck constant gives you a definition of what means 1 J s = 1 kg m^2/ s: it says essentially that 1 kg m^2/ s is 4 pi / 6.6 10^(-34) = 1.9 10^34 times the spin angular momentum of an electron.

Lightspeed essentially says that 1 m/s = 1/2.99 10^8 = 3.34 10^(-9) times the velocity of light.

The electron mass essentially says that 1 kg = 1/9.109 10^(-31) = 1.098 10^30 times the mass of an electron.

Let's define the new units kg', m' and s'

If we say now that Planck's constant equals 6.63x10^30, then this means that 1 kg' m'^2 /s' = 4 pi/ 6.63 10^30 = 1.9 10^(-30) times the spin angular momentum of an electron.

Keeping lightspeed, it means that 1 m'/s' = 1/2.99 10^8 = 3.34 10^(-9) the speed of light.

Keeping the electron mass means that 1 kg' = 1/9.109 10^(-31) = 1.098 10^30 times the mass of an electron.

Now, you can say that you want to KEEP 1 kg = 1 kg', 1m = 1m' and 1s = 1s'. However, each unit is defined in a particular way, as a certain number of times a physical quantity. By keeping the mass of the electron, we've used the mass of the electron as our definition of the unit kg.
The lightspeed is just a definition of the ratio of the unit of length over the unit of time: if we keep it numerically the same, both units are now in fixed relation. In the same way, the planck constant relates the combination of the unit of mass, of length (square) and of time so that it is a certain number times the angular momentum of the electron. All this means that if we change that number, we've just changed the unit of length (and, because of the fixed ratio (lightspeed!), the unit of time).

In fact, 1 kg = 1 kg', and 1m' = 6.6 10^(-34)/6.63 10^30 = 10^(-64) m
and 1s' = 10^(-64)s

cheers,
Patrick.

3. Mar 16, 2006

### jf117

An easy way of thinking to it is the exact opposite to the arguments used to
prove that our world would be exclusively governed by classical laws if
$\hbar\rightarrow 0$. When Planck's constant becomes very big, then
all physical laws will tend to become quantum laws. In such a case we would
have a world exclusively governed by quantum physics, with everything
proceeding through quantum jumps.

J

Last edited: Mar 16, 2006
4. Mar 16, 2006

### vanesch

Staff Emeritus
Depends how big you are now ! If it turns out that you're of the order of 10^64 meters now, then nothing would essentially change... (that was my point)

The "limit h->0" is a very tricky one, especially if you're working in natural units where h = 1...

5. Mar 17, 2006

### coolguy

the constants in physics are due to the way the physical world behaves.if a constant changes may be we would have a situation where some constants used in equations are replaced by some other ones.that could create a interesting situation.if two constants in an equation are being replaced by constants that bear a similar relation as the previous,some phenomenon would not change.need to think deeper on this.

6. Mar 17, 2006

### jf117

Actually, making $\hbar$ that big would mean making the rest of the world (us) very small, not big.

I agree with you that these are tricky arguments, but then the whole topic's theme is quite tricky.

J

7. Mar 17, 2006

### Perturbation

Are you the same guy that posted this in the Myspace physics forums? If so, what Patrick is saying is what I, Dave, was trying to say there.

8. Mar 17, 2006

### vanesch

Staff Emeritus
The point I was trying to make, was, that if you "change" a dimensionful constant, you're actually changing the unit system, and not the physics. The only way to change the physics is by changing *dimensionless* constants.

Why do I say that ? Because "units" are conventions, which are expressed as a function of certain physical phenomena. A physical constant (with dimensions) is a certain number times a physical phenomenon which determines a "natural" measure of the dimension of the constant, and as such, serves to DEFINE what we mean by our units.
Look at the definition of the second:
"The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom."

So the physical phenomenon is this radiation of the caesium atom, and we multiply it with an arbitrary number to obtain a certain unit which we call "second".

Once we do that, you cannot anymore say: what happens, for instance, if the duration of the period of the cesium atom changes such that we only have 4032 periods in a second, of course, because BY DEFINITION the second contains 9192631770 of these periods.

In the same way, the lightspeed fixes the unit of distance to the unit of time. You cannot ask what would happen if the lightspeed changes !

Now, for the moment, Planck's constant has not been used as a fundamental defining quantity, but it would enter it soon: read up on the proposed fundamental definitions of the kilogram (which are not yet official!): http://en.wikipedia.org/wiki/Kilogram

One of the proposed definitions is:
Planck's constant will then be like lightspeed:
"The kilogram is the mass of a body at rest whose equivalent energy corresponds to a frequency of exactly [(299792458)^2/6626069311] × 10^43 Hz."

So if you change Planck's constant, you simply change the definition of the kilogram. If you define the kilogram differently, changing Planck's constant might show up somewhere else in the definition of the unit system.

These issues are very tricky. Again, the only thing that makes physical sense is to change *dimensionless* quantities. For instance, change the fine structure constant alpha. The reason for that is that we could work in natural Planck units where h = 1, c = 1, G = 1. All of physics can be expressed that way, and there it doesn't make sense to ask what will happen when h changes value!

9. Mar 17, 2006

### jf117

I'm not the same guy that "Perturbation" refers to.
By the way, I perfectly understand your point, and I basically agree with you.
But I think the spirit of the proposed topic was something like: "If, at the moment in history when it was introduced, we had discovered that Planck's constant were larger or smaller than its known value, what effect would the laws of Quantum Mechanics have had on our knowledge of Nature?" Then it makes sense to speculate on transition rates, atomic sizes, etc, all things where $\hbar$ enters one way or the other. Of course we live in a world where Planck's constant has the value we know, but, from a logical point of view, it makes sense to speculate on things, had we found a different value.

J

10. Mar 17, 2006

### vanesch

Staff Emeritus
I think that is then better re-formulated into: what if we were beings that lived for about 30 seconds, had a mass of about 10^(-25) kg and measured 25 nanometers from the top of our head to our feet, how would we perceive the world ? If we had been such beings, we would have defined our "length" unit of the order of 25 nanometers, our time unit of the order of a few microseconds and our mass unit of the order of the mass of an electron. We'd then have a big Planck's constant in our units, and one could ask as of how the world would be perceived. This is actually a very good exercise in "interpretation of quantum theory" stuff! Because for these creatures, it DOES make a difference whether there is a projection or not. According to many views, we WOULDN'T see 'waves' all over the place, but we'd probably see a much "noisier" classical physics.

In fact, the "measurement problem" becomes much more accute for such a being.

I'd like to make the point that "going to little men" and "changing the value of h" are equivalent. For instance, if h is big, then the hydrogen atom is very big (Bohr radius = hbar/m c alpha) - at least if alpha, c and m remain constant!

Now, if a hydrogen atom is very big, and I'm made up of hydrogen atoms, then I'm also a very big dude. And I'll choose my conventional unit of length very big...
So if, in THAT world, with big hydrogen atoms, I'd like to look at how people OUR size look upon things, then that's the same as asking how little men look upon things in OUR world.

Last edited: Mar 17, 2006
11. Mar 17, 2006

### jf117

I agree.
J

12. Mar 17, 2006

Staff Emeritus
How would Merriam's relational view appear to these little people (Planckiputians?). Recall that in his approach the measured system and the environment measure each other's lengths and times as transformed to preserve the constancy of h, analogous to the way inertial frrames with a velocity between them are related by Lorentz transforms.

Last edited: Mar 17, 2006
13. Mar 17, 2006

### jf117

What is this "Merriam's relational view"?
J

14. Mar 18, 2006

Staff Emeritus
Paul Merriam has recently proposed an approach to quantum reality based on a relational principle.

See his paper Quantum Relativty: Physical Laws Must be Invariant Over Quantum Systems; http://www.arxiv.org/abs/quant-ph/0506228.

From the abstract:

15. Jun 8, 2008

### a.a

How would changeing the constant change light speed and the mass of an electron?
:S

16. Jul 16, 2008

### exponent137

I were not read answer, I hope that I do not repeat.
If we change c for factor 10^-4 or G for factor 10^4 or m of all particles for factor 10^2, the effect would be the same, as we change h for factor 10^4.
Regards