Set Planck's constant equal to 1

[jacobi1]

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]

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]

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

 

[chisigma]

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

$\chi$ $\sigma$

 

[CellCoree]

If Planck's constant were equal to 1 J s, it would have a significant impact on the fundamental laws of physics and the structure of the universe. Planck's constant is a crucial constant in quantum mechanics, which governs the behavior of particles at the atomic and subatomic level. It is used to calculate the energy of a photon and the wavelength of a particle, and it is also a key component in the famous equation E=mc^2.

If Planck's constant were equal to 1, it would mean that the energy of a photon would be directly proportional to its frequency, rather than being inversely proportional to its wavelength as it is currently. This would have a major effect on the behavior of light and other electromagnetic radiation, which would no longer exhibit wave-like properties. This would also have implications for the behavior of matter particles, as they would no longer behave as waves.

Furthermore, Planck's constant is also used to calculate the uncertainty principle, which states that there is a limit to how precisely we can know both the position and momentum of a particle. If Planck's constant were equal to 1, the uncertainty principle would no longer hold true, and particles could be precisely located and have a definite momentum. This would have a profound impact on the behavior of particles and the structure of matter.

Overall, if Planck's constant were equal to 1, it would fundamentally alter our understanding of the universe and the laws of physics. It is unlikely that life as we know it could exist in such a universe, as the behavior of matter and energy would be drastically different. While it is an interesting thought experiment, it is important to remember that Planck's constant is a fundamental constant of nature and cannot be changed.