Download About the Zero Point Energy, Zero Point Mass, Zero Point

Progress In Electromagnetics Research Symposium Proceedings, Suzhou, China, Sept. 12–16, 2011
1169
About the Zero Point Energy, Zero Point Mass, Zero Point
Temperature and Zero Point Motion in the Subatomic World and
Photonics
Antonio Puccini
Department of Neurophysiology of Order of Malta, Naples, Italy
Abstract— The Heisenberg Uncertainty Principle states that no particle can be completely
motionless (since it is not possible to know two complementary parameters of e a particle at
the same time), it will at least oscillate around a plane: in this case we will talk about Zero
Point Motion. From Quantum Mechanics we learn that a real particle will never have a null
energy, but it will always have a minimum possible energy called Zero Point Energy. We also
learn from Quantum Mechanics that Absolute Zero temperature can never be reached. At this
temperature, in fact, the motion would cease and we would be able to know simultaneously the
two complementary parameters we mentioned before: the position and the momentum of the
same particle. In a number of cases, in fact, extremely low temperature have been reached, but
never touching −273, 15◦ Celsius. Thus we will talk about Zero Point Temperature.
Relativity’s Theory, on its turn, tells us that mass and energy are equivalent. Einstein, in fact, realized that scientists were wrong keeping about the mass and E as two phenomena which though
linked, were basically different. On the contrary, he understood that they had exactly equal behaviours: both expanded and contracted according to an identical factor. Under every significant
aspect, Einstein concluded mass and E were entities indistinguishable and interchangeable, and
formulated his famous formula: E = mc2 . So any particle having energy should carry a mass,
though tiny, corresponding to the energy of the examined particle divided the square of the speed
of light.
1. INTRODUCTION
We learn from Quantum Mechanics(QM) that “just as a particle will never have a null energy
(E), that is zero, but a fundamental minimal E: the Zero Point Energy (ZPE). In the same way
the particle, because of its undulation aspect, will never be able to remain completely still, that
is with a zero motion” [1]: in this case we will talk about Zero Point Motion (ZPMt). This
goes in accordance with Heisenberg’s Uncertainty Principle (HUP): it is not possible to know two
complementary parameters of a particle at the same time, such as its position (x) and momentum
(p). As it is known, the p is given by the mass (m) of the particle times its speed (v): p = m · v.
Thus, a completely motionless particle would give us simultaneously quite precise information about
its x and p which, in this case, would be zero. However, this will never be possible, this is why a
particle will never be completely still — even if it is apparently motionless, (as inside a solid) —
at least it will keep vibrating, that is it will preserve a vibrating motion, also the smallest possible.
Thus, as Chandrasekhar reminds us “there is a ZPMt which corresponds to the ZPE” [1]. Still
in accordance with HUP [2, 3], a particle will never be at a temperature of Absolute Zero. At this
temperature, in fact, the motion would cease and we would be able to know simultaneously the
two complementary parameters we mentioned before. We will talk about Zero Point Temperature
(ZPT), which can never coincide with the unreachable temperature of the Absolute Zero. In
fact extremely low temperatures have been reached, but never touching −273.15◦ Celsius. Thus,
Hawking reminds us that “the temperature is just a measurement of the mean E — or of the mean
speed — of the particles” [4]. As in the case of a particle there should not be a zero E, as we should
never reach a temperature of Absolute Zero, in the same way (also considering what Hawking and
HUP stated) a particle should never reach a zero speed, or motion. We need to consider, besides,
that the ZPE and the ZPMt are worth both for a subatomic particle and for the atom in itself.
2. DISCUSSION
We cannot forget the worries and the doubts which bothered Einstein in the first years of last
century, till he traced the fundamental concepts of Restricted Relativity. “Einstein realized that
scientists were wrong keeping thinking about the mass and the E as two phenomena which, though
linked, were basically different. Einstein understood that they had also exactly equal behaviors:
both expanded and contracted according to an identical factor. He concluded that mass and E
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PIERS Proceedings, Suzhou, China, September 12–16, 2011
were entities indistinguishable and interchangeable: as a person wearing different clothes or showing
different hairstyle. The mass and the E could be compared to the American dollars and the British
pounds: though they appeared different, they were basically the same thing, that is a kind of
exchange currency. Besides, even though the two currencies had different values, there was an
exchange rate between them, that is a formula which fixed the rate between them” [5]. Essentially
the problem the young Einstein had to face was the following: which was the formula of the rate
of exchange relating the mass and the E? Einstein managed to find the right inspiration and he
formulated mathematically the Principle of Equivalence Mass-Energy:
E = mc2
(1)
Here it is, at last, the long-desired formula of the exchange rate! Einstein’s satisfaction was big, since
the relation between Mass and Energy had revealed so easy, so elegant: since the mass and the E
were two entities interchangeable, science did not have to deal with two Principles of Conservation.
“The mass could be destroyed and transformed in E, in the same way the E could be destroyed
and transformed in mass” [5]. The Principle of Equivalence Mass-Energy are two faces of the same
coin, since they are interchangeable and since we mentioned the ZPE, why can’t we think about
a Zero Point Mass (ZPM)? After all mass and E are equivalent!. According to Planck-Einstein
equation, the E of the P is:
E =h·f
(2)
where h is the Planck’s constant, equal to 6.625 · 10−27 [erg · s] and f is the frequency of oscillation
of the P per second, which we indicate with 10n · [1/s]. We get that the E of the P is not constant,
but changes in a rate directly proportional to the f of the considered P .
Einstein explained its Equivalence Principle: “It represents the connection between inertial
mass and energy” [6]. Let’s consider, thus, which could be the inertial E of the P , that is its
minimum E, as to say its ZPE. Well, we cannot know with accuracy: it depends on the minimum
number of oscillations that a P can make in a second, that is it depends on the value of 10n . We
cannot exclude that the P is able to reach the minimum limit of one oscillation per second, that
is f = 10◦ [1/s]: nothing forbids it and HUP allows it. In this case, with reference to Eq. (2), let’s
calculate which could be the ZPE of the P :
That is:
ZPE = h · f = (6.625 · 10−27 , [erg· s]) · 10◦ [1/s]
(3)
ZPE = 6.625 · 10−27 [erg]
(4)
We have that the ZPE of the P corresponds to the value of h, which is an energetic value. In
this case we got the possible value of the minimum oscillating motion allowed to the P . Whereas,
if the minimum limit of oscillations of the P was (i.e.) 100, this value would be indicated with
102 [1/s]. In this case we would have:
E = h · f = h · 102 [1/s] = 6.625 · 10−25 [erg]
(5)
Along with Eq. (1), let’s try to calculate the value of the inertial mass of the P , which can be
indicated with the value of its minimal mass, that is with its ZPM:
ZPM = ZPE/c2
(6)
If we consider that the minimum possible value of the ZPE of the P can correspond to the one
emerging from Eq. (4), we have:
ZPM = 6.625 · 10−27 [erg]/(2.9979 · 1010 [cm/s])2
(7)
Since the erg value is expressed in [g · cm/s2 · cm], that is in [g · cm2 /s2 ], developing the (7), we
have:
ZPM = 6.625/8.9874) · 10−27−20 [g· cm2 /s2 ] · [s2 /cm2 ]
(8)
That is
That is:
ZPM = 0.7372 · 10−47 [g]
(9)
ZPM = 7.37 · 10−48 [g]
(10)
Progress In Electromagnetics Research Symposium Proceedings, Suzhou, China, Sept. 12–16, 2011
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3. CONCLUSIONS
Thus, also considering the minimum possible oscillation of the P (it twill never be able to be
completely still: HUP forbids it), and, as consequence, considering its minimum possible E (ZPE),
we get that the P has a its own inertial mass, which coincides with its ZPM [7].
It is certainly an extremely low value, yet 6= 0. Just incidentally let’s mention something about
the neutrino. The neutrino too, up until short ago, was considered massless, though having a
certain E (thus in contrast with the Mass-Energy Equivalence Principle). Later the control of its
oscillation and the well known Superkamiokande experiment permitted to consider the neutrino as
having a its own mass, though extremely small.
There is also another particle, still hypothetical, considered massless: the graviton. As we know
it is the quantum, the boson of the gravity force (GF). However the GF, as a force, subtends a E:
its force, always of attraction, so evident in galactic systems, is carried out through a E, that is
through a continuous work carried out by the graviton. Indeed the Quantum Field Theory gives
an energetic value to the graviton, just to justify the way the GF is carried out.
However, still long with the Mass-Energy Equivalence Principle, since it has been given an
energetic value to the graviton, in the same way it should correspond also an equivalent mass, the
smallest we can imagine, certainly smaller than the ZPM of the P . In fact, the ZPM should coincide
with the ZPE corresponding to the examined particle divided c2 . With regard to this Feynman
wrote: “E and mass differ only by a factor c2 which is merely a question of units, so we can say
E is mass ” [8]. In other words, the mass of any particle having E — all real particles have! —
corresponds to the specific E of the examined particle, divided the square of the speed of light in
vacuum.
We can just conclude that it is much more likely that as every physical system or every particle,
even a real boson, has a minimal quantity of E (ZPE), following the Equivalence Principle they
will have an equivalent ZPM, and preserve a ZPMt.
REFERENCES
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Cambridge University Press, Milano, 1988.
2. Heisemberg, W., Z. Phys., Vol. 43, 184–185, 1927.
3. Puccini, A., “Uncertainty principle and electromagnetc waves,” Journal of Electromagnetic
Waves and Applications, Vol. 19, No. 7, 885–890, 2005.
4. Hawking, S., A Brief History of Time, Vol. 137, 128, Bibl. Univ. Rizzoli, Milano, 1990.
5. Guillen, M., Five Equations That Changed the World, 267–269, TEA Ed., Milano, 1995.
6. Galison, P., “L’equazione del sestante,” It Must Beautiful: Great Equations of Moderne Science, 119, Il Saggiatore ed., Graham Farmelo, Milano, 2005.
7. Puccini, A., “About the restmass of photon; Session: Electromagnetic theory and design on
the optical dispersive materials, invisible cloak and photonic crystals,” PIERS Proceedings,
Marrakesh, Morocco, March 20–23, 2011.
8. Feynman, R. P., The Feynman Lectures on Physics, Vol. 3, No. 12, 1617, Zanichelli, Ed., 1989
California Institute of Technology, Bologna, 1965.