x38 y1ce we h38">
. 1
is only
for a few materials, and for 90% of materials
< 1. [14-17] show that if we consider the energy
dependence of the energy support ability in space, then
. Second, [18-20] show that if we consider the
energy dependence of the energy support ability in space,
then cold fusion can occur, and the result of experimental
observations for the cold fusion is true.
Reference [3] and Section 3 of this paper point out that
the Rutherford scattering formula, which was based on
classical mechanics, and the Mott-Gorden scattering
formula, which was based on quantum mechanics and
neglecting the energy variation of the energy support
ability in space, are the same. This fact tells us that the
energy variation of the energy support ability in space
includes quantum effect, and, therefore, it can not been
neglected. If we neglect it, then classical and quantum
mechanics give the same result.
A simple direct experimental verification on the ne-
cessity of introducing the concept of energy support abil-
ity in space is to obtain the experimental data corre-
sponding to Figure 2.
6. Conclusions
From our exact derivations and numerical calculations in
Sections 2, 3 and 4 we obtain the following conclusions.
1) It is absolutely necessary to consider the energy de-
pendences of the transition matrix element and the den-
sity of states in transition and scattering processes.
However, all the now available theories on the transition
and scattering processes do not consider these energy
dependences, and, therefore, should be revised. 2) The
general energy conservation law should be negatived in
some cases. 3) It is possible to obtain infinite energy
from space without any loss. 4) The Fermi golden rule
should be negatived in some cases because that the ap-
proximation of neglecting the energy dependence of the
energy support ability in space is reasonable only in a
few cases. 5) The transition process does not have any
connection with energy uncertainty principle. 6) The
concept on the energy support ability in space will be-
come an important new concept. 7) Section 3 points out
that the duration time of scattering between electron and
nucleus can be measured by experiment. 8) The current
standard model of cosmology, or Big Bang model, has
been receiving wider and wider attention since the dis-
covery of cosmic background radiation at 2.73 K. The
observable facts upon which the standard model is based
are, in fact, very few [10]. This paper shows that the en-
ergy support ability in space is only determined by the
structure of space, and, therefore, it can always supply
energy without any loss i.e., the energy is infinite in
cosmology. Because energy can become mass, the mass
in the cosmology is also infinite. The cosmology being
of infinite energy and mass can not collapse, should have
infinite lifetime, and the Big Bang model can not be cor-
rect. 9) The present theory to estimate the energy in
cosmology is as follows. If all the energy in cosmology
is 1, then the energy of galaxy is 4/100, the energy of
dark mass is 23/100, and the energy of dark energy is
73/100. It is obvious that this estimation is based on the
energy finiteness of cosmology. This paper concludes
that the above estimation for the energy distribution in
cosmology is wrong because the energy in cosmology is
infinite. 10) G. Amelino-Camelia [21] pointed out that
combing general relativity with quantum mechanics is
the last hundle to be overcome in the “quantum revolu-
tion”. One of the most exciting approaches to the unifi-
cation of general relativity and quantum mechanics is the
idea of a space-time that is itself quantized, for example,
replacing the space-time continuum with a collection of
isolated points. This paper shows that the energy support
ability in space depends on the structure of space.
Therefore, the energy support ability in space can be
used to judge any proposed model of space structure. 11)
B. R. Martin [13] pointed out that the observable quanti-
ties in nuclear and particle physics are cross-sections and
decay rates. However, we should note that the formulas
to calculate the two quantities are used Fermi golden rule.
This paper shows that Fermi golden rule should be nega-
tived, especially, in the calculations of cross-sections.
Therefore, many conclusions coming from the two quan-
tities might be wrong.
7. References
[1] L. I. Schiff, “Quantum Mechanics,” McGraw-Hill Book
Company, New York, 1968.
[2] W. Greiner, “Quantum Mechanics: An Introduction,” 3rd
Edition, Springer-Verlag Belin Heidelberg, New York,
[3] L. D. Landau and E. M. Lifshitz, “Quantum Mechanics:
Non-Relativistic theory,” Pergamon Press, Oxford, 1958.
[4] A. S. Davidov, “Quantum Mechanics,” 2nd Edition, Per-
gamon Press, Oxford, 1976.
[5] B. R. Desai, “Quantum Mechanics,” Cambridge Univer-
sity, Cambridge, 2010.
[6] E. R. Bittner, “Quantum Dynamics: Applications in Bio-
Copyright © 2010 SciRes. EPE
logical and Materials Systems,” Taylor and Francis/CRC
Press, New York, 2010.
[7] R. L. Liboff, “Introductory Quantum Mechanics,” Addi-
son-Wesley, New York, 2003.
[8] K. T. Hecht, “Quantum Mechanics,” Springer-Verlag,
New York, 2000.
[9] A. I. M. Rae, “Quantum Mechanics,” Taylor and Francis,
New York, 2008.
[10] E. Elbaz, “Quantum: The Quantum Theory of Particles,
Fields, and Cosmology,” Springer, New York, 1998.
[11] J. J. Sakurai and S. F. Tuan, “Modern Quantum Mechani-
cs,” Addison-Wesley, New York, 1994.
[12] S. L. Kakani and S. Kakani, “Nuclear and Particle Phy-
sics,” Anshan, Kent, 2008.
[13] B. R. Martin, “Nuclear and Particle Physics,” 2nd Edition,
John Wisley and Sons Ltd, West Eussex, 2009.
[14] F. S. Liu and C. Wen, “Dynamics of Continuous-Time
Random Walk, Fractional Time Dispersion, and Frac-
tional Exponential Time Relaxation,” Physical Review B
(Condensed Matter), Vol. 40, No. 10, 1989, pp. 7091-
[15] F. S. Liu and W. F. Chen, “A New Universal Theory of
Non-Exponential Relaxation,” Journal Physics D: App-
lied Physics, Vol. 27, No. 4, 1994, pp. 845-847.
[16] F. S. Liu, K. D. Peng and W. F. Chen, “Departure from
Fermi Golden Rule,” International Journal of Theoretical
Physics, Vol. 40, No. 11, 2001, pp. 2037-2043.
[17] F. S. Liu and W. F. Chen, “Necessity of Exact Calcula-
tion for Transition Probability,” Communications in
Theoretical Physics, Beijing, Vol. 39, No. 2, 2003, pp.
[18] F. S. Liu and W. F. Chen, “Phonon-Induced Hopping
Rate Enhancement in the Pd-D System,” Journal of Phy-
sics: Condensed Matter, Vol. 15, No. 29, 2003, pp. 4995-
[19] F. S. Liu, Y. M. Hou and W. F. Chen, “Theory of Fusion
during Acoustic Cavitation in ODC63 Liquid,” Journal
of Condensed Matter Nuclear Science, Vol. 1, No. 1, 2007,
pp. 142-147.
[20] F. S. Liu and W. F. Chen, “The Effect of Phonon-Induced
Hopping Enhancement and Exact Theory of Cold Fu-
sion,” Communications in Theoretical Physics. Vol. 23,
No. 2, 1995, pp. 241-244.
[21] G. Amelino-Camelia, “Quantums Theory’s Last Chal-
lenge,” Nature (London), Vol. 408, No. 6813, 2000, pp.