**6. The meaning and existence of Planck's constant h** [Ragazas 2010c]

Planck's constant *h* is a fundamental universal constant of Physics. And although we can experimentally determine its value to great precision, the reason for its existence and what it really means is still a mystery. Quantum Mechanics has adapted it in its mathematical formalism. But QM does not explain the meaning of *h* or prove why it must exist. Why does the Universe need *h* and *energy quanta?* Why does the mathematical formalism of QM so accurately reflect physical phenomena and predict these with great precision? Ask any physicists and uniformly the answer is "that's how the Universe works". The units of *h* are in *energy-time* and the conventional interpretation of *h* is as a *quantum of action*. We interpret *h* as *the minimal accumulation of energy* that can be manifested. Certainly the units of *h* agree with such interpretation. Based on our results above we provide an explanation for the existence of Planck's constant -- what it means and how it comes about. We show that the existence of *Planck's constant* is not necessary for the Universe to exist but rather *h* exists by Mathematical necessity and inner consistency of our system of measurements.

Using *eta* we defined in **Section 5.0** above the *temperature of radiation* as being proportional to the ratio of *eta/time*. To obtain a *temperature scale*, however, we need to fix *eta* as a standard for measurement. We show below that the fixed *eta* that determines the Kelvin *temperature scale* is Planck's constant *h*.

In The Interaction of Measurement [Ragazas 2010h] we argue that direct measurement of a physical quantity *E t*( ) involves a physical interaction between the *source* and the *sensor*. For measurement to occur an interval of time *t* must have lapsed and an incremental amount *E* of the quantity will be absorbed by the *sensor*. This happens when there is an *equilibrium* between the *source* and the *sensor*. At *equilibrium*, the 'average quantity *Eav* from the source' will equal to the 'average quantity *Eav* at the sensor'. *Nothing in our observable World can exist without time, when the entity 'is' in equilibrium with its environment and its 'presence' can be observed and measured.* Furthermore as we showed above in **Section 3.0** the *interaction of measurement* is described by *Planck's Formula.* 

The Thermodynamics *in* Planck's Law 705

*Characterization 4*. Interestingly, this quantity is essentially *thermodynamic entropy*, since

. Thus entropy is *additive over time.* Since

as the *evolution rate* of the system (both positive or negative), entropy is a measure of the *amount of evolution* of the system over a duration of time *t* . Such connection between *entropy* as *amount of evolution* and *time* makes eminent intuitive sense, since *time* is generally thought in terms of *change*. But, of course, this is *physical time* and not some mathematical

Note that in the above, *entropy* can be both positive or negative depending on the *evolution* 

Photoelectric emission has typically been characterized by the following experimental facts

1. For a given metal surface and frequency of incident radiation, the rate at which photoelectrons are emitted (the photoelectric current) is directly proportional to the

2. The energy of the emitted photoelectron is independent of the intensity of the incident

3. For a given metal, there exists a certain minimum frequency of incident radiation below which no photoelectrons are emitted. This frequency is called the threshold frequency.

4. The time lag between the incidence of radiation and the emission of photoelectrons is

radiation by the metal surface. The combined rate locally at the surface will then be

. If we let Planck's constant *h* be the *accumulation of energy* for an electron, the

*<sup>e</sup> e <sup>E</sup> E h n*

 

The radiation energy at a point on the surface can be represented by

, we get the *photoelectric current <sup>I</sup>* ,

will then be *ne <sup>h</sup>*

, then by *Characterization 1* we'll have that

(10)

*instantaneously*. Physical time is really *duration t* (or dt) and not *instantiation t s* .

**8. The photoelectric effect without photons** [Ragazas 2010k]

light but depends on the frequency of the incident light.

radiation of an incident light on a metal surface and let

*E*0 is the intensity of radiation of the incident light. If we let

 

> 

*Explanation of the Photoelectric Effect without the Photon Hypothesis:* Let

 . That the *duration of time t* is positive, we argue, is postulated by *The Second Law of Thermodynamics*. It is amazing that the most fundamental of all physical quantities *time* has no fundamental Basic Law pertaining to its nature. We argue *the Basic Law pertaining to time*  **is** *The Second Law of Thermodynamics.* Thus, a more revealing rewording of this Law should state that *all physical processes take some positive duration of time to occur.* Nothing happens

be the rate of absorption of this

<sup>0</sup> ( ) *<sup>t</sup> Et Ee* , where

be the *accumulation of energy*

and the energy of an

be the rate of

 .

can be thought

*E kT av* , and so *<sup>E</sup> S kt*

*rate*  *T*

abstract parameter as in *spacetime continuum*.

*(some of which can be disputed, as noted)*:

intensity of the incident light.

very small, less than 10-9 second.

locally at the surface over a time pulse

electron *Ee* will be given by

Since

 

number of electrons *ne* over the pulse of time

 0 0 <sup>0</sup> *<sup>u</sup> <sup>e</sup>* <sup>1</sup> *E e du E*

*(see below)* 

 *E* 

From the mathematical equivalence (5) above we see that can be *any* value and *e* 1 <sup>T</sup> will be invariant and will continue to equal to *<sup>E</sup>*<sup>0</sup> . We can in essence (Fig. 3*)*  'reduce' the formula 0 1 *E e* <sup>T</sup> by reducing the value of and so the value of *Eav* T will correspondingly adjust, and visa versa. Thus we see that and T go *handin-hand* to maintain <sup>0</sup> 1 *E e* <sup>T</sup> invariant. And though the mathematical equivalence (5) above allows these values to be anything, the calibrations of these quantities in Physics require their value to be specific. Thus, for *h* (Planck's constant) and *k* (Boltzmann's constant), we get T *T* (Kelvin temperature) (see Fig. 3). Or, conversely, if we start with T *T* and set the arbitrary constant *k* , then this will force *h* . Thus we see that *Planck's constant h , Boltzmann's constant k , and Kelvin temperature T* are so defined and calibrated to fit Planck's Formula. Simply stated, when *h* , T*<sup>h</sup> T* .

*Conclusion: Physical theory provides a conceptual lens through which we 'see' the world. And based on this theoretical framework we get a measurement methodology. Planck's constant h is just that 'theoretical focal point' beyond which we cannot 'see' the world through our theoretical lens. Planck's constant h is the minimal eta that can be 'seen' in our measurements. Kelvin temperature scale requires the measurement standard eta to be h.* 

*Planck's Formula is a mathematical identity that describes the interaction of measurement. It is invariant with time, accumulation of energy or amount of energy absorbed. Planck's constant exists because of the time-invariance of this mathematical identity. The calibration of Boltzmann's constant k and Kelvin temperature T , with kT being the average energy, determine the specific value of Planck's constant h .* 

### **7. Entropy and the second law of thermodynamics** [Ragazas 2010b]

The quantity *av E E* that appears in our *Planck's Law* formulation (3) is *'additive over time'*. This

is so because under the assumption that *Planck's Formula* is *exact* we have that *av <sup>E</sup> <sup>t</sup> E* , by

<sup>T</sup> will be invariant and will continue to equal to *<sup>E</sup>*<sup>0</sup> . We can in essence (Fig. 3*)* 

<sup>T</sup> invariant. And though the mathematical equivalence (5)

*h* (Planck's constant) and

*T* (Kelvin temperature) (see Fig. 3). Or, conversely, if we start with

<sup>T</sup> , <sup>1</sup>

*k* , then this will force

<sup>T</sup> by reducing the value of

above allows these values to be anything, the calibrations of these quantities in Physics

*Planck's constant h , Boltzmann's constant k , and Kelvin temperature T* are so defined and

 , *E av* 

*Conclusion: Physical theory provides a conceptual lens through which we 'see' the world. And based on this theoretical framework we get a measurement methodology. Planck's constant h is just that 'theoretical focal point' beyond which we cannot 'see' the world through our theoretical lens. Planck's constant h is the minimal eta that can be 'seen' in our measurements. Kelvin temperature scale* 

*Planck's Formula is a mathematical identity that describes the interaction of measurement. It is invariant with time, accumulation of energy or amount of energy absorbed. Planck's constant exists because of the time-invariance of this mathematical identity. The calibration of Boltzmann's constant k and Kelvin temperature T , with kT being the average energy, determine the specific value of* 

that appears in our *Planck's Law* formulation (3) is *'additive over time'*. This

**7. Entropy and the second law of thermodynamics** [Ragazas 2010b]

is so because under the assumption that *Planck's Formula* is *exact* we have that

*h* , T*<sup>h</sup> T* .

 and T

*<sup>t</sup> Et E e*

> *av <sup>E</sup> <sup>t</sup>*

, by

*E*

 

 <sup>T</sup> , ( ) <sup>0</sup>

can be *any* value and

and so the value of

*k* (Boltzmann's

*h* . Thus we see that

go *hand-*

From the mathematical equivalence (5) above we see that

1

*E*

*e* 

*E*

require their value to be specific. Thus, for

*T* and set the arbitrary constant

*e* 

calibrated to fit Planck's Formula. Simply stated, when

1 1

 

<sup>T</sup> , *<sup>E</sup>*

1

will correspondingly adjust, and visa versa. Thus we see that

*e* 1 

*Eav* T

T

Fig. 3. 0

*<sup>E</sup> <sup>E</sup> E E*

*Planck's constant h .* 

*av E E*

The quantity

*av <sup>e</sup> <sup>e</sup>*

*requires the measurement standard eta to be h.* 

'reduce' the formula 0

*in-hand* to maintain <sup>0</sup>

constant), we get T

*Characterization 4*. Interestingly, this quantity is essentially *thermodynamic entropy*, since *E kT av* , and so *<sup>E</sup> S kt T* . Thus entropy is *additive over time.* Since can be thought

as the *evolution rate* of the system (both positive or negative), entropy is a measure of the *amount of evolution* of the system over a duration of time *t* . Such connection between *entropy* as *amount of evolution* and *time* makes eminent intuitive sense, since *time* is generally thought in terms of *change*. But, of course, this is *physical time* and not some mathematical abstract parameter as in *spacetime continuum*.

Note that in the above, *entropy* can be both positive or negative depending on the *evolution rate* . That the *duration of time t* is positive, we argue, is postulated by *The Second Law of Thermodynamics*. It is amazing that the most fundamental of all physical quantities *time* has no fundamental Basic Law pertaining to its nature. We argue *the Basic Law pertaining to time*  **is** *The Second Law of Thermodynamics.* Thus, a more revealing rewording of this Law should state that *all physical processes take some positive duration of time to occur.* Nothing happens *instantaneously*. Physical time is really *duration t* (or dt) and not *instantiation t s* .
