## fredag 7 mars 2014

### Absurdity of Small Planck Constant, Length and Time

Absurdity of modern physics as quantum foam and strings of Planck length.

Starting from Planck's (reduced) constant $\bar h\approx 10^{-34}$, the Planck length $l_p$ and Planck time $t_p$ are defined by
• $l_p =\sqrt{\frac{\bar hG}{c^3}}\approx 1.6\times 10^{-35}\, m$,
• $t_p = \sqrt{\frac{\bar hG}{c^5}}\approx 5.3\times 10^{−44} s$,
where $G$ is the gravitational constant and $c$ the speed of light. Wikipedia tells us the following limits of modern physics:
• The Planck length is about $10^{-20}$ times the diameter of a proton, and thus is exceedingly small.
• The Planck length sets the fundamental limits on the accuracy length measurement.
• Planck time is the time it would take a photon traveling at the speed of light to cross a distance equal to one Planck length
• Theoretically, this is the smallest time measurement that will ever be possible, roughly $10^{−43}$ seconds.
The relation of the Planck length to the size of the proton is about the same as the diameter of golf ball to the size of a galaxy.

Planck length and time is the scale of string theory. The goal of string theory is to explain the origin of gravitation with a change of scale of $10^{60}$, and to explain the origin of the Universe starting from Big Bang at time $10^{-43}$.

All this absurdity comes from an absurdly small Planck's constant $h = 6.626\times 10^{-34}$. To see clearly see the absurdity, recall that Planck's constant enters Planck's radiation law
• $R_\nu (T)=\gamma\nu^2T\times \theta(\nu ,T)$,
where $R_\nu (T)$ is radiated energy per unit frequency, surface area, viewing angle and second, $\gamma =\frac{2k}{c^2}$ where $k = 1.3806488\times 10^{-23} m^2 kg/s^2 K$ is Boltzmann's constant and $c$ the speed of light in $m/s$, $T$ is temperature in Kelvin $K$, only in the high-frequency cut-off factor
• $\theta (\nu ,T)=\frac{\alpha}{e^\alpha -1}$,
• $\alpha=\frac{h\nu}{kT}$,
where $\theta (\nu ,T)\approx 1$ for $\alpha < 1$ and  $\theta (\nu ,T)\approx 0$ for $\alpha > 10$. In other words, the relevant quantity in Planck's law is not the absurdly small $h$, but instead
• $\hat h\equiv\frac{h}{k}= 4.8\times 10^{-11}$,
which is to be compared with $\frac{T}{\nu}$ and thus with the dependence on $\nu$ connects to atomistic dimensions. The relevant Planck constant $\hat h\approx 10^{-10}$ thus has a physical meaning, while the conventional Planck constant $h\approx 10^{-33}$ can only represent fiction.

The idea of a quantum of energy as a smallest possible quantity (as well as particle) is absurd. The idea of a quantum of energy which is absurdly small, is doubly absurd.

#### 30 kommentarer:

1. You write,

h = 6.626 * 10^-34.

That is nonsensical, you need to attach units, Js to be precise. So that tells us that Planck's constant is small in SI units.

Units are something relative, and that we use SI units needs to be related to the fact that they are convenient for measure things on scales that are close to our own experience. This of course doesn't tell us anything about what is the natural scale.

It must be better to turn the question around. Instead of asking why the Planck constant is so small, why are our SI units so large?

It is of course natural to think about fundamental units as units where h ~ 1 (h_bar = 1 is the most convenient one).

Further you need to take under considerations that the Planck constant, related to experiments, is not only appearing at the atomic scale, it also appears at the subatomic scale, so your reasoning is a bit flawed when relating the constant to the atomic scale only.

That it appears at the atomic scale is not that surprising. Think about it, Planck's constant appears in the fine structure constant that is a measure of the strength of electromagnetic interaction, so that it appears in setting the atomic scale (the Bohr radius) is not surprising at all.

2. If you don't think that a Planck length 20 orders of magnitude smaller than the proton is absurd, then you must be ready to accept anything.

3. I don't really see the relevance of the comparison.

There's nothing really interesting with the magnitude of the Planck scale more than that it is less than the smallest known structure (the electron). The scale is just a measure of where there is no point in making a distinction between two points.

Besides that, there is nothing much to believe in. The constants used to form the Planck scale are nothing that can be decided by theory, they are empirical by nature and turned out to combine to something ~10⁻35m. What is this to argue about?

4. To clarify my confusion about the mystery you propose.

If you don't think that a Planck length 20 orders of magnitude smaller than the proton is absurd

What absurdities does this lead to, in your opinion? You need to provide something concrete here, otherwise you words are just empty rhetorics. Don't you agree?

For you this is absurd I guess. Why?

5. your answers to legitimate questions are always straight to the point and never focused on the person asking them. godd job claes!

6. Real physics must be reasonable. This basic requirement has been lost in the mysteries of infinitely small small packets of energy as quanta with dimension Joulesecond which cannot be a measure of a physical quantity.

The energies are not infinitely small, the energies are given by

E = \hbar * \nu.

Using a \hbar = 6.5e-16 eVs and the spectrum of visible light 430-790 THz, gives typical energies in the range of 0.27-0.51 eV, and that is not infinitely small, that is even big enough to overcome the band gap in some semiconductors.

As was implied above, the SI system is not a good system to be used in situations like this, just because that we, at the macroscopic level, is so darn big compared to the microscopic to nano level.

8. I see a small mistake in my post...

\hbar is of course just h when working with frequencies.

So \hbar should be shifted to h. But that only increases the energies so no harm done...

9. No I care about dimensions and notice that Joulesecond as the dimension of Planck's constant h is strange as physical quantity. My view is that h/k with dimension Ksecond acts as threshold value for T/f with f frequency and as such does not refer to a physical quantity like mass, length, time, energy.

10. Two things.

First.
You wrote:
Real physics must be reasonable. This basic requirement has been lost in the mysteries of infinitely small small packets of energy as quanta with dimension Joulesecond which cannot be a measure of a physical quantity.

...Small small packets of energy as quanta with dimension Joulesecond...

That is a gross negligence of units. The energy unit in this case is preferably eV, and the energy quanta is not small on this scale for reasonable frequencies. Do you disagree to this? I did show above that they are of order unity...

Second.
What I originally meant with neglecting units was first aimed at you writing things like

h = 6.626e-34

which makes no sense at all.

h = 6.626e-34 Js

does make perfect sense on the other hand.

11. What physical quantity is measured in Joulesecond? Or Joulemeter?

12. Well, on the top of my head, angular momentum...

13. Helicity would also qualify

14. And spin of course...

15. Action is a physical quantity that is measured in Js.

16. You can construct mathematically quanties of any dimensions, but the real question is what physics they represent. The equations of motion represent equilibrium of forces and as such have a physical meaning. To express the equations as stationarity of action is mathematics and not physics, because physics can care about equilibrium of forces but not stationarity or minimality of action, because action does not have a physical representation. Action is an integral of energy and while energy can be stored e.g. kinetic energy, an integral of energy is not stored physically. To understand physics it is important to separate mathematics
from physical reality. At least this is what I am trying to do, but not everybody is thinking this way.

17. How about angular momentum, helicity and spin?

18. The question is if physics can represent these quantities by storing them in physical terms, or if they are only quantities defined by a mathematician writing symbols on a piece of paper?

19. Is angular momentum then non-physical in your opinion? A mathematical construction?

20. Angular momentum L = r x p of dimension mass x length^2/time or Js depends on the choice of origin and thus on the eye of the observer and is not a quantity that is physical in the sense that an object itself stores L in the same way it can store kinetic energy of dimension mass x length^2/time^2 or J.

22. Who in the audience of that lecture is deciding how the wheel spins then?
If the angular momentum only is a mathematical construction dependent on the observer?

23. What is conserved without forcing is kinetic energy not angular momentum. When an ice scater speeds up rotation by pulling arms to the body, work is done and the kinetic energy increases under a fiction that angular momentum is conserved. A rotating body can store kinetic energy but not angular momentum.

24. The wheel does not care about angular momentum, it just spins under precession with angular momentum turning around. The teacher teaches about angular momentum because it contains mathematics which the teacher masters while students get impressed but confused.

25. Is linear momentum non-physical?

26. Newton's 2nd law expresses conservation of linear momentum mv and like mass and energy which are also conserved, has a physical reality. But the absolute value of linear momentum depends on the choice of coordinate system, while changes are independent of coordinate system. This means that there is an unphysical coordinate system dependence of linear momentum, but modulo this dependence linear momentum is a real physical quantity.

27. But in Newtonian mechanics the kinetic energy is frame dependent (mass isn't though).

Say you are watching two cars (mass m) collide head on at 10m/s each.

The energy in the observing system is then,
m(10)^2/2 + m(10)^2/2 = 100 * m [J].

In one of the cars,
m*(0)^2/2 + m(20)^2/2 = 400 * m [J].

Does this mean that kinetic energy is non-physical?

28. For a single car there is an ambiguity in velocity (up to a constant). For two cars there is no ambiguity in their relative velocity and that is what counts in a collision, and a collision is a real physical event with real change of momentum, and kinetic energy.

29. kinetic energy is a scalar. angular momentum is a vector. the experiment performed by lewin shows is that there is a vectorial quantity that is conserved.

30. Would that be the center of mass frame...?