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Set Planck's constant equal to 1

jacobi

Active member
May 22, 2013
58
I have an interesting 'What If' question. I understand that it was originally meant to be in jest, but I am interested to know what would happen. Here is the original joke: "There was a discussion in the math and physics departments of a university. It was about whether to allow calculators on the exams. After heated debate, the physics department decided in favor of allowing calculators because their 3 hour exam had one question: 'Describe the universe, if Planck's constant were equal to 1.'"
If Planck's constant, instead of being \(\displaystyle 6.63 \times 10^{-34}\) J s, were 1 J s, how would the universe be different?
 

Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,192
Well, one consequence is that there would be considerably more energy in the universe. The energy of a photon is given by $E=h \nu$, and so if $h$ is larger by 34 orders of magnitude, then the energy of the universe due to the presence of light would be 34 orders of magnitude greater. In other words, we would probably all burn up... unless, of course, our bodies were now (also due to the revised Planck constant) capable of handling that kind of energy without exploding. That is, unless the electromagnetic force were to increase by a similar amount, the absorption of a single photon would GREATLY increase the energy of an electron. That electron would then almost certainly break away from its nucleus. Imagine that happening en masse, and you see that your body would ionize very quickly. It would become highly positively charged, at which point you would explode.
 

topsquark

Well-known member
MHB Math Helper
Aug 30, 2012
1,123
Consider also that most equations about the quantum "world" are based on the fact that h is so small. If h were large then most quantum events would be the norm. So, for example, wave-particle duality would be common.

One of my professors made a joke that we would get an A in class if we could quantum tunnel into the final exam. If h = 1 Js you could bounce back and forth in the hallway and actually do it.

-Dan
 
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chisigma

Well-known member
Feb 13, 2012
1,704
I have an interesting 'What If' question. I understand that it was originally meant to be in jest, but I am interested to know what would happen. Here is the original joke: "There was a discussion in the math and physics departments of a university. It was about whether to allow calculators on the exams. After heated debate, the physics department decided in favor of allowing calculators because their 3 hour exam had one question: 'Describe the universe, if Planck's constant were equal to 1.'"
If Planck's constant, instead of being \(\displaystyle 6.63 \times 10^{-34}\) J s, were 1 J s, how would the universe be different?
In the usual MKS metric system is $\displaystyle h= 6.63\ 10^{- 34} \frac {k\ m^{2}}{s}$. In principle You can use a 'quantum metric system' $Q_{m} Q_{k} Q_{s}$ where is $\displaystyle h= 1\ \frac{Q_{k}\ Q_{m}^{2}}{Q_{s}}$ and in this case it would be...

$\displaystyle \frac{Q_{k}\ Q_{m}^{2}}{Q_{s}} = 6.63\ 10^{- 34} \frac {k\ m^{2}}{s}$

... and I don't know if such a metric system is very comfortable in our quotidian life (Wasntme)...

Kind regards

$\chi$ $\sigma$