misster y
May19-05, 05:42 PM
Hello,
this is a part of an article (www.webcom.com/musics/mass.pdf (http://www.webcom.com/musics/mass.pdf)) I have wrote:
From the definitions of Planck units of length and time is deduced a correspondence between mass and time equal to m=@'t, where @' is a constant that has force dimension. The similarity of this equation with the equation l=ct could allows us to extrapolate a possible physical meaning of this correspondence: the energy of light is vibration of space-time with a constant force and maximum for all observers. A possible equation of the amplitude of curvature of vibration of the space based on the frequency and the constants G, h and c is proposed.
Definition: System SL of units:
unit of lenght = second-light
Some relation between magnitudes in SL and SI (International System) are: (4)
l'=l/c (lenght)
t'=t (time)
m'=m (mass)
v'=v/c (speed)
a'=a/c (acceleratión)
F'=F/c (force)
E'=E/c^{2} (energy)
G'=G/c^{3} (constant of gravitation)
Once situated in system SL we will see that we easily arrive to a peculiar correspondence between space, time and mass:
In SL the length, time and mass of Planck takes the following values:
l_{p}'=t_{p}=\sqrt{\hbar'G'}
m_{p}=\sqrt{\hbar'/G'}$
where we easily deduce:
t_{p}/m_{p}=G'
(Planck constant disappears!)
that is to say,
l_{p}'=t_{p}=G'm_{p}
This equality defines a relation between the units of Planck; however, because we are speaking solely of a correspondence (with a physical meaning to be determined) and because we can multiply each side of the equation by any same number without the equality is modified (any length and any time can be obtained from Planck units l'=xl_{p}' or t=xt_{p}) we can generalize this correspondence as:
l'=t=G'm\;\;\;\;\;\;\;\;(5)
and, adding (3)
l'=t=G'm=G'E'\;\;\;\;\;\;\;\;(6)
Up to here we have solely a correspondence between length, time, mass and energy. But, what physical meaning can have these equalities?
Another relation between space and mass can be found in the formula of the radius of Schwarzschild, that in SL takes the form, very similar to (5):
r'=2G'm\;\;\;\;\;\;\;\;(7)
and in general relativity we found the relation between the curvature of the space produced by a mass-energy system, by means of the metric tensor G and the tensor energy-moment T
G_{\alpha\beta}=8\Pi G T_{\alpha\beta}\;\;\;\;\;\;\;\;(8)
the parallelism of the equations (5) and (6) with the equations (7) and (8) does us to suspect a possible physical meaning of (5) and (6): the affectation of the space due to a mass m or an energy E
But the equation (5) can also be seen from another point of view:
if we define @'=1/G'
we obtain
m=@'t\;\;\;\;\;\;\;\;(9)\;\;\;\;or \;\;\;E'=@'t
that takes the form of the well-known equation (1) of which we have spoken in the beginning (of the article) but with m instead of l and with another constant:
l=ct \;\;\;\;\;\;\;\;(1)
m=@'t\;\;\;\;\;\;\;\;(9)
We could speculate extrapolating the physical properties of the equation (1) to the new dimensions of (9):
See that @' has dimensions of force (MT^{-1} in SL) (see Appendix 1). We could say, extrapolating the meaning of the constant c in the equation (1), that there is a constant force @' in the universe, being the same one for all the observers, and that is the maximum force possible.
Let us convert @' to SI units (International System units)
F_{max}'=@'=1/G'
replacing the relations between SL and SI showed in (4):
F_{max}/c=\frac{1}{G/c^{3}}
@=F_{max}=c^{4}/G
That is to say, we obtain as maximum force --equal for all the observers-- the force of Planck c^{4}/G
@' is the force of Planck in SL units @'=@/c. The relation (9) between m and t becomes in SI:
m=@'t=\frac{@}{c}t=\frac{c^{3}}{G}t\;\;\;\;\;\;\;\;(9b)
Our proposal, as we will see in the following section, is that this maximum force would be pronounced not only in the black holes --like it could be seen by the similarity of (5) with the formula of the radius of Schwarzschild (7)-- but that is the habitual form whereupon the force produced by the original energy of any luminous source modifies the space-time, doing it to vibrate, producing waves of ``space-time'' (something similar to gravitational waves) that transport the information of the original electromagnetic waves.
The equations (1), (6) and (9) say to us, in addition, that the matter-energy is not inserted independently within a space-time, but that the space-time is pronounced (for any observer) through the matter-energy. That is to say, extending what we have said at the beginning of the article respect the equation l=ct, a space-time without matter-energy cannot exist and viceversa. The matter-energy is a manifestation of the space-time through @' (E'=m=@'t=@'l').
what do you think?
see the complete article in: (partially translated:)
(www.webcom.com/musics/mass.pdf (http://www.webcom.com/musics/mass.pdf))
in spanish:
(www.webcom.com/musics/masa.pdf (http://www.webcom.com/musics/masa.pdf))
the original in catalan:
(www.webcom.com/musics/massa.pdf (http://www.webcom.com/musics/massa.pdf))
Appendix1: The dimensions length and time as cycles of the light
(resume)
If we consider the dimensions of length and time as cycles of light (as they are oficially defined), we could group these dimensions with the C symbol (C=L=T) (Cycles of light)
Then we could separate the main physical dimensions in three groups according to the exponent of C (1, 0 or -1):
Group A (C^{1}):
C \equiv Length, time
MC \equiv Planck constant h
Group B (C^{0}):
(C^{0} \equiv Speed)
M \equiv Mass, energy, moment, work
Group C (C^{-1}):
C^{-1} \equiv Acceleration, frequency
MC^{-1} \equiv Force, power, 1/G
All these dimensions can be divided or be multiplied by the dimension speed, in concrete the speed of the light c, without its dimension be altered:
As particular cases:
1/G, c/G, c^{2}/G, c^{3}/G, c^{4}/G, etc... have the same dimension (force)
m, mv, mc, mc^{2}, mc^{3}, etc... have the same dimension (energy)
this is a part of an article (www.webcom.com/musics/mass.pdf (http://www.webcom.com/musics/mass.pdf)) I have wrote:
From the definitions of Planck units of length and time is deduced a correspondence between mass and time equal to m=@'t, where @' is a constant that has force dimension. The similarity of this equation with the equation l=ct could allows us to extrapolate a possible physical meaning of this correspondence: the energy of light is vibration of space-time with a constant force and maximum for all observers. A possible equation of the amplitude of curvature of vibration of the space based on the frequency and the constants G, h and c is proposed.
Definition: System SL of units:
unit of lenght = second-light
Some relation between magnitudes in SL and SI (International System) are: (4)
l'=l/c (lenght)
t'=t (time)
m'=m (mass)
v'=v/c (speed)
a'=a/c (acceleratión)
F'=F/c (force)
E'=E/c^{2} (energy)
G'=G/c^{3} (constant of gravitation)
Once situated in system SL we will see that we easily arrive to a peculiar correspondence between space, time and mass:
In SL the length, time and mass of Planck takes the following values:
l_{p}'=t_{p}=\sqrt{\hbar'G'}
m_{p}=\sqrt{\hbar'/G'}$
where we easily deduce:
t_{p}/m_{p}=G'
(Planck constant disappears!)
that is to say,
l_{p}'=t_{p}=G'm_{p}
This equality defines a relation between the units of Planck; however, because we are speaking solely of a correspondence (with a physical meaning to be determined) and because we can multiply each side of the equation by any same number without the equality is modified (any length and any time can be obtained from Planck units l'=xl_{p}' or t=xt_{p}) we can generalize this correspondence as:
l'=t=G'm\;\;\;\;\;\;\;\;(5)
and, adding (3)
l'=t=G'm=G'E'\;\;\;\;\;\;\;\;(6)
Up to here we have solely a correspondence between length, time, mass and energy. But, what physical meaning can have these equalities?
Another relation between space and mass can be found in the formula of the radius of Schwarzschild, that in SL takes the form, very similar to (5):
r'=2G'm\;\;\;\;\;\;\;\;(7)
and in general relativity we found the relation between the curvature of the space produced by a mass-energy system, by means of the metric tensor G and the tensor energy-moment T
G_{\alpha\beta}=8\Pi G T_{\alpha\beta}\;\;\;\;\;\;\;\;(8)
the parallelism of the equations (5) and (6) with the equations (7) and (8) does us to suspect a possible physical meaning of (5) and (6): the affectation of the space due to a mass m or an energy E
But the equation (5) can also be seen from another point of view:
if we define @'=1/G'
we obtain
m=@'t\;\;\;\;\;\;\;\;(9)\;\;\;\;or \;\;\;E'=@'t
that takes the form of the well-known equation (1) of which we have spoken in the beginning (of the article) but with m instead of l and with another constant:
l=ct \;\;\;\;\;\;\;\;(1)
m=@'t\;\;\;\;\;\;\;\;(9)
We could speculate extrapolating the physical properties of the equation (1) to the new dimensions of (9):
See that @' has dimensions of force (MT^{-1} in SL) (see Appendix 1). We could say, extrapolating the meaning of the constant c in the equation (1), that there is a constant force @' in the universe, being the same one for all the observers, and that is the maximum force possible.
Let us convert @' to SI units (International System units)
F_{max}'=@'=1/G'
replacing the relations between SL and SI showed in (4):
F_{max}/c=\frac{1}{G/c^{3}}
@=F_{max}=c^{4}/G
That is to say, we obtain as maximum force --equal for all the observers-- the force of Planck c^{4}/G
@' is the force of Planck in SL units @'=@/c. The relation (9) between m and t becomes in SI:
m=@'t=\frac{@}{c}t=\frac{c^{3}}{G}t\;\;\;\;\;\;\;\;(9b)
Our proposal, as we will see in the following section, is that this maximum force would be pronounced not only in the black holes --like it could be seen by the similarity of (5) with the formula of the radius of Schwarzschild (7)-- but that is the habitual form whereupon the force produced by the original energy of any luminous source modifies the space-time, doing it to vibrate, producing waves of ``space-time'' (something similar to gravitational waves) that transport the information of the original electromagnetic waves.
The equations (1), (6) and (9) say to us, in addition, that the matter-energy is not inserted independently within a space-time, but that the space-time is pronounced (for any observer) through the matter-energy. That is to say, extending what we have said at the beginning of the article respect the equation l=ct, a space-time without matter-energy cannot exist and viceversa. The matter-energy is a manifestation of the space-time through @' (E'=m=@'t=@'l').
what do you think?
see the complete article in: (partially translated:)
(www.webcom.com/musics/mass.pdf (http://www.webcom.com/musics/mass.pdf))
in spanish:
(www.webcom.com/musics/masa.pdf (http://www.webcom.com/musics/masa.pdf))
the original in catalan:
(www.webcom.com/musics/massa.pdf (http://www.webcom.com/musics/massa.pdf))
Appendix1: The dimensions length and time as cycles of the light
(resume)
If we consider the dimensions of length and time as cycles of light (as they are oficially defined), we could group these dimensions with the C symbol (C=L=T) (Cycles of light)
Then we could separate the main physical dimensions in three groups according to the exponent of C (1, 0 or -1):
Group A (C^{1}):
C \equiv Length, time
MC \equiv Planck constant h
Group B (C^{0}):
(C^{0} \equiv Speed)
M \equiv Mass, energy, moment, work
Group C (C^{-1}):
C^{-1} \equiv Acceleration, frequency
MC^{-1} \equiv Force, power, 1/G
All these dimensions can be divided or be multiplied by the dimension speed, in concrete the speed of the light c, without its dimension be altered:
As particular cases:
1/G, c/G, c^{2}/G, c^{3}/G, c^{4}/G, etc... have the same dimension (force)
m, mv, mc, mc^{2}, mc^{3}, etc... have the same dimension (energy)