En física de partículas y cosmología física , las unidades de Planck son un conjunto de unidades de medida definidas exclusivamente en términos de cuatro constantes físicas universales , de tal manera que estas constantes físicas toman el valor numérico de 1 cuando se expresan en términos de estas unidades.
Propuestas originalmente en 1899 por el físico alemán Max Planck , estas unidades son un sistema de unidades naturales porque el origen de su definición proviene solo de las propiedades de la naturaleza y no de ninguna construcción humana . Las unidades de Planck son solo uno de varios sistemas de unidades naturales, pero las unidades de Planck no se basan en las propiedades de ningún objeto o partícula prototipo (cuya elección es inherentemente arbitraria), sino solo en las propiedades del espacio libre . Son relevantes en la investigación de teorías unificadas como la gravedad cuántica .
El término escala de Planck se refiere a cantidades de espacio, tiempo, energía y otras unidades que son similares en magnitud a las correspondientes unidades de Planck. Esta región puede caracterizarse por energías de alrededor10 19 GeV , tiempo intervalos de alrededor10 -43 s y longitudes de alrededor10 −35 m (aproximadamente, respectivamente, la energía equivalente de la masa de Planck, el tiempo de Planck y la longitud de Planck). En la escala de Planck, no se espera que se apliquen las predicciones del modelo estándar , la teoría cuántica de campos y la relatividad general , y se espera que dominen los efectos cuánticos de la gravedad . El ejemplo más conocido está representado por las condiciones en los primeros 10-43 segundos de nuestro universo después del Big Bang , hace aproximadamente 13,8 mil millones de años.
Las cuatro constantes universales que, por definición, tienen un valor numérico 1 cuando se expresan en estas unidades son:
- la velocidad de la luz en el vacío, c ,
- la constante gravitacional , G ,
- la constante de Planck reducida , ħ ,
- la constante de Boltzmann , k B .
Las unidades Planck no incorporan una dimensión electromagnética. Algunos autores optan por extender el sistema al electromagnetismo, por ejemplo, agregando la constante eléctrica ε 0 o 4 π ε 0 a esta lista. De manera similar, los autores optan por utilizar variantes del sistema que dan otros valores numéricos a una o más de las cuatro constantes anteriores.
Introducción
A cualquier sistema de medición se le puede asignar un conjunto mutuamente independiente de cantidades base y unidades base asociadas , de las cuales se pueden derivar todas las demás cantidades y unidades. En el Sistema Internacional de Unidades , por ejemplo, las cantidades base del SI incluyen la longitud con la unidad asociada del metro . En el sistema de unidades de Planck, se puede seleccionar un conjunto similar de cantidades base y unidades asociadas, en términos de los cuales se pueden expresar otras cantidades y unidades coherentes. La unidad de longitud de Planck se conoce como longitud de Planck , y la unidad de tiempo de Planck se conoce como tiempo de Planck, pero no se ha establecido que esta nomenclatura se extienda a todas las cantidades.
Todas las unidades de Planck se derivan de las constantes físicas universales dimensionales que definen el sistema, y en una convención en la que estas unidades se omiten (es decir, se tratan como si tuvieran el valor adimensional 1), estas constantes se eliminan de las ecuaciones de la física en las que aparecen. . Por ejemplo, la ley de Newton de la gravitación universal ,
se puede expresar como:
Ambas ecuaciones son dimensionalmente consistentes e igualmente válidas en cualquier sistema de cantidades, pero la segunda ecuación, con G ausente, está relacionando solo cantidades adimensionales ya que cualquier razón de dos cantidades de dimensiones similares es una cantidad adimensional. Si, por convención abreviada, se entiende que cada cantidad física es la relación correspondiente con una unidad de Planck coherente (o "expresada en unidades de Planck"), las relaciones anteriores pueden expresarse simplemente con los símbolos de cantidad física, sin escalar explícitamente por su unidad correspondiente:
Esta última ecuación (sin G ) es válida siendo F ′ , m 1 ′, m 2 ′, y r ′ las cantidades adimensionales correspondientes a las cantidades estándar, escritas, por ejemplo, F ′ ≘ F o F ′ = F / F P , pero no como una igualdad directa de cantidades. Esto puede parecer "establecer las constantes c , G , etc. en 1" si se piensa que la correspondencia de las cantidades es igual. Por esta razón, Planck u otras unidades naturales deben emplearse con cuidado. Refiriéndose a " G = c = 1 ", Paul S. Wesson escribió que, "Matemáticamente es un truco aceptable que ahorra trabajo. Físicamente representa una pérdida de información y puede generar confusión". [1]
Historia y definición
El concepto de unidades naturales se introdujo en 1881, cuando George Johnstone Stoney , al señalar que la carga eléctrica se cuantifica, derivó unidades de longitud, tiempo y masa, ahora llamadas unidades de Stoney en su honor, al normalizar G , c y la carga de electrones. , e , a 1. En 1899, un año antes del advenimiento de la teoría cuántica, Max Planck introdujo lo que más tarde se conocería como la constante de Planck. [2] [3] Al final del artículo, propuso las unidades base nombradas más tarde en su honor. Las unidades de Planck se basan en el cuanto de acción, ahora conocido generalmente como la constante de Planck, que apareció en la aproximación de Wien para la radiación del cuerpo negro . Planck subrayó la universalidad del nuevo sistema de unidades, escribiendo:
... die Möglichkeit gegeben ist, Einheiten für Länge, Masse, Zeit und Tempur aufzustellen, welche, unabhängig von speciellen Körpern oder Substanzen, ihre Bedeutung für alle Zeiten und für alle, auch außerirdische und außnchür allende la cultura » Maßeinheiten «bezeichnet werden können .
... es posible configurar unidades de longitud, masa, tiempo y temperatura, que son independientes de cuerpos o sustancias especiales, conservando necesariamente su significado para todos los tiempos y para todas las civilizaciones, incluidas las extraterrestres y no humanas, que pueden llamarse "unidades naturales de medida".
Planck consideró solo las unidades basadas en las constantes universales , , , y para llegar a unidades naturales de longitud , tiempo , masa y temperatura . [3] Sus definiciones difieren de las modernas por un factor de, porque las definiciones modernas usan en vez de . [2] [3]
Nombre | Dimensión | Expresión | Valor ( unidades SI ) |
---|---|---|---|
longitud de Planck | Longitud (L) | 1.616 255 (18) × 10 −35 m [4] | |
Masa de Planck | Masa (M) | 2.176 434 (24) × 10 −8 kg [5] | |
Tiempo de planck | Tiempo (t) | 5.391 247 (60) × 10 −44 s [6] | |
Temperatura de Planck | Temperatura (Θ) | 1.416 784 (16) × 10 32 K [7] |
A diferencia del caso del Sistema Internacional de Unidades , no existe una entidad oficial que establezca una definición de un sistema de unidades de Planck. Frank Wilczek y Barton Zwiebach definen las unidades de Planck base como las de masa, longitud y tiempo, con respecto a una unidad adicional para que la temperatura sea redundante. [8] [9] Otras tabulaciones añaden, además de una unidad de temperatura, una unidad de carga eléctrica, [10] a veces también reemplazan masa por energía al hacerlo. [11] Dependiendo de la elección del autor, esta unidad de carga viene dada por
o
La carga de Planck, así como otras unidades electromagnéticas que se pueden definir como resistencia y flujo magnético, son más difíciles de interpretar que las unidades originales de Planck y se utilizan con menos frecuencia. [12]
En unidades SI, los valores de c , h , e y k B son exactos y los valores de ε 0 y G en unidades SI, respectivamente, tienen incertidumbres relativas de1,5 × 10 −10 [13] y2,2 × 10 −5 . [14] Por lo tanto, las incertidumbres en los valores de SI de las unidades de Planck derivan casi enteramente de incertidumbre en el valor SI de G .
Unidades derivadas
En cualquier sistema de medida, las unidades para muchas cantidades físicas pueden derivarse de las unidades base. La Tabla 2 ofrece una muestra de unidades de Planck derivadas, algunas de las cuales, de hecho, rara vez se utilizan. Al igual que con las unidades base, su uso se limita principalmente a la física teórica porque la mayoría de ellas son demasiado grandes o demasiado pequeñas para un uso empírico o práctico y existen grandes incertidumbres en sus valores.
Unidad derivada de | Expresión | Approximate SI equivalent |
---|---|---|
area (L2) | 2.6121×10−70 m2 | |
volume (L3) | 4.2217×10−105 m3 | |
momentum (LMT−1) | 6.5249 kg⋅m/s | |
energy (L2MT−2) | 1.9561×109 J | |
force (LMT−2) | 1.2103×1044 N | |
density (L−3M) | 5.1550×1096 kg/m3 | |
acceleration (LT−2) | 5.5608×1051 m/s2 | |
frequency (T−1) | 1.8549×1043 s−1 |
Some Planck units, such as of time and length, are many orders of magnitude too large or too small to be of practical use, so that Planck units as a system are typically only relevant to theoretical physics. In some cases, a Planck unit may suggest a limit to a range of a physical quantity where present-day theories of physics apply.[citation needed] For example, our understanding of the Big Bang does not extend to the Planck epoch, i.e., when the universe was less than one Planck time old. Describing the universe during the Planck epoch requires a theory of quantum gravity that would incorporate quantum effects into general relativity. Such a theory does not yet exist.
Several quantities are not "extreme" in magnitude, such as the Planck mass, which is about 22 micrograms: very large in comparison with subatomic particles, and well within the mass range of living things; it may be the minimum theoretical mass of a black hole. Similarly, the related units of energy and of momentum are in the range of some everyday phenomena.
Significado
Planck units have little anthropocentric arbitrariness, but do still involve some arbitrary choices in terms of the defining constants. Unlike the metre and second, which exist as base units in the SI system for historical reasons, the Planck length and Planck time are conceptually linked at a fundamental physical level. Consequently, natural units help physicists to reframe questions. Frank Wilczek puts it succinctly:
We see that the question [posed] is not, "Why is gravity so feeble?" but rather, "Why is the proton's mass so small?" For in natural (Planck) units, the strength of gravity simply is what it is, a primary quantity, while the proton's mass is the tiny number [1/(13 quintillion)].[15]
While it is true that the electrostatic repulsive force between two protons (alone in free space) greatly exceeds the gravitational attractive force between the same two protons, this is not about the relative strengths of the two fundamental forces. From the point of view of Planck units, this is comparing apples with oranges, because mass and electric charge are incommensurable quantities. Rather, the disparity of magnitude of force is a manifestation of the fact that the charge on the protons is approximately the unit charge but the mass of the protons is far less than the unit mass.
Escala de planck
In particle physics and physical cosmology, the Planck scale is an energy scale around 1.22×1019 GeV (the Planck energy, corresponding to the energy equivalent of the Planck mass, 2.17645×10−8 kg) at which quantum effects of gravity become strong. At this scale, present descriptions and theories of sub-atomic particle interactions in terms of quantum field theory break down and become inadequate, due to the impact of the apparent non-renormalizability of gravity within current theories.
Relationship to gravity
At the Planck length scale, the strength of gravity is expected to become comparable with the other forces, and it is theorized that all the fundamental forces are unified at that scale, but the exact mechanism of this unification remains unknown. The Planck scale is therefore the point where the effects of quantum gravity can no longer be ignored in other fundamental interactions, where current calculations and approaches begin to break down, and a means to take account of its impact is necessary.[16][17]
While physicists have a fairly good understanding of the other fundamental interactions of forces on the quantum level, gravity is problematic, and cannot be integrated with quantum mechanics at very high energies using the usual framework of quantum field theory. At lesser energy levels it is usually ignored, while for energies approaching or exceeding the Planck scale, a new theory of quantum gravity is necessary. Other approaches to this problem include string theory and M-theory, loop quantum gravity, noncommutative geometry, scale relativity, causal set theory and p-adic quantum mechanics.[18]
In cosmology
In Big Bang cosmology, the Planck epoch or Planck era is the earliest stage of the Big Bang, before the time passed was equal to the Planck time, tP, or approximately 10−43 seconds.[19] There is no currently available physical theory to describe such short times, and it is not clear in what sense the concept of time is meaningful for values smaller than the Planck time. It is generally assumed that quantum effects of gravity dominate physical interactions at this time scale. At this scale, the unified force of the Standard Model is assumed to be unified with gravitation. Immeasurably hot and dense, the state of the Planck epoch was succeeded by the grand unification epoch, where gravitation is separated from the unified force of the Standard Model, in turn followed by the inflationary epoch, which ended after about 10−32 seconds (or about 1010 tP).[20]
Properties of the observable universe today expressed in Planck units:[21][22]
Property of present-day observable universe | Approximate number of Planck units | Equivalents |
---|---|---|
Age | 8.08 × 1060 tP | 4.35 × 1017 s, or 13.8 × 109 years |
Diameter | 5.4 × 1061 lP | 8.7 × 1026 m or 9.2 × 1010 light-years |
Mass | approx. 1060 mP | 3 × 1052 kg or 1.5 × 1022 solar masses (only counting stars) 1080 protons (sometimes known as the Eddington number) |
Density | 1.8 × 10−123 mP⋅lP−3 | 9.9 × 10−27 kg⋅m−3 |
Temperature | 1.9 × 10−32 TP | 2.725 K temperature of the cosmic microwave background radiation |
Cosmological constant | 2.9 × 10−122 l −2 P | 1.1 × 10−52 m−2 |
Hubble constant | 1.18 × 10−61 t −1 P | 2.2 × 10−18 s−1 or 67.8 (km/s)/Mpc |
After the measurement of the cosmological constant in 1998, estimated at 10−122 in Planck units, it was noted that this is suggestively close to the reciprocal of the age of the universe squared. Barrow and Shaw proposed a modified theory in which Λ is a field evolving in such a way that its value remains Λ ~ T−2 throughout the history of the universe.[23]
Analysis of the units
Planck time and length
The Planck length, denoted ℓP, is a unit of length defined as:
It is equal to 1.616255(18)×10−35 m,[4] where the two digits enclosed by parentheses are the estimated standard error associated with the reported numerical value.
A Planck time unit is the time required for light to travel a distance of 1 Planck length in a vacuum, which is a time interval of approximately 5.39×10−44 s.[24] All scientific experiments and human experiences occur over time scales that are many orders of magnitude longer than the Planck time,[25] making any events happening at the Planck scale undetectable with current scientific technology. As of October 2020[update], the smallest time interval uncertainty in direct measurements was on the order of 247 zeptoseconds (2.47×10−19 s).[26]
While there is currently no known way to measure time intervals on the scale of the Planck time, researchers in 2020 proposed a theoretical apparatus and experiment that, if ever realized, could be capable of being influenced by effects of time as short as 10−33 seconds, thus establishing an upper detectable limit for the quantization of a time that is roughly 20 billion times longer than the Planck time.[27][28]
Planck energy
Most Planck units are extremely small, as in the case of Planck length or Planck time, or extremely large, as in the case of Planck temperature or Planck acceleration. For comparison, the Planck energy is approximately equal to the energy stored in an automobile gas tank (57.2 L of gasoline at 34.2 MJ/L of chemical energy). The ultra-high-energy cosmic ray observed in 1991 had a measured energy of about 50 J, equivalent to about 2.5×10−8 EP.[29]
Planck unit of force
The Planck unit of force may be thought of as the derived unit of force in the Planck system if the Planck units of time, length, and mass are considered to be base units.
It is the gravitational attractive force of two bodies of 1 Planck mass each that are held 1 Planck length apart; equivalently, it is the electrostatic attractive or repulsive force of two Planck units of charges that are held 1 Planck length apart.
Various authors have argued that the Planck force is on the order of the maximum force that can be observed in nature.[30][31] However, the validity of these conjectures has been disputed.[32]
Planck momentum
The Planck momentum is equal to the Planck mass multiplied by the speed of light. Unlike most of the other Planck units, Planck momentum occurs on a human scale. By comparison, running with a five-pound object (108 × Planck mass) at an average running speed (10−8 × speed of light in a vacuum) would give the object Planck momentum. A 70 kg human moving at an average walking speed of 1.4 m/s (5.0 km/h; 3.1 mph) would have a momentum of about 15 . A baseball, which has mass 0.145 kg, travelling at 45 m/s (160 km/h; 100 mph) would have a Planck momentum.
Planck temperature
The Planck temperature of 1 (unity), equal to 1.416784(16)×1032 K,[7] is considered a fundamental limit of temperature.[33] An object with the temperature of 1.42×1032 kelvin (TP) would emit a black body radiation with a peak wavelength of 1.616×10−35 m (Planck length), where each photon and each individual collision would have the energy to create a micro black hole of Planck mass. There are no known physical models able to describe temperatures greater than or equal to TP.
Lista de ecuaciones físicas
Physical quantities that have different dimensions (such as time and length) cannot be equated even if they are numerically equal (1 second is not the same as 1 metre). In theoretical physics, however, this scruple can be set aside, by a process called nondimensionalization. Table 3 shows how the use of Planck units simplifies many fundamental equations of physics, because this gives each of the five fundamental constants, and products of them, a simple numeric value of 1. In the SI form, the units should be accounted for. In the nondimensionalized form, the units, which are now Planck units, need not be written if their use is understood.
SI form | Planck units form | |
---|---|---|
Newton's law of universal gravitation | ||
Einstein field equations in general relativity | ||
Mass–energy equivalence in special relativity | ||
Energy–momentum relation | ||
Thermal energy per particle per degree of freedom | ||
Boltzmann's entropy formula | ||
Planck–Einstein relation for energy and angular frequency | ||
Planck's law (surface intensity per unit solid angle per unit angular frequency) for black body at temperature T. | ||
Stefan–Boltzmann constant σ defined | ||
Bekenstein–Hawking black hole entropy[34] | ||
Schrödinger's equation | ||
Hamiltonian form of Schrödinger's equation | ||
Covariant form of the Dirac equation | ||
Unruh temperature | ||
Coulomb's law | ||
Maxwell's equations |
|
|
Ideal gas law | or |
Opciones alternativas de normalización
As already stated above, Planck units are derived by "normalizing" the numerical values of certain fundamental constants to 1. These normalizations are neither the only ones possible nor necessarily the best. Moreover, the choice of what factors to normalize, among the factors appearing in the fundamental equations of physics, is not evident, and the values of the Planck units are sensitive to this choice.
The factor 4π is ubiquitous in theoretical physics because the surface area of a sphere of radius r is 4πr2 in contexts having spherical symmetry in three dimensions. This, along with the concept of flux, are the basis for the inverse-square law, Gauss's law, and the divergence operator applied to flux density. For example, gravitational and electrostatic fields produced by point charges have spherical symmetry (Barrow 2002: 214–15). The 4πr2 appearing in the denominator of Coulomb's law in rationalized form, for example, follows from the flux of an electrostatic field being distributed uniformly on the surface of a sphere. Likewise for Newton's law of universal gravitation. (If space had more than three spatial dimensions, the factor 4π would be changed according to the geometry of the sphere in higher dimensions.)
Hence a substantial body of physical theory developed since Planck (1899) suggests normalizing not G but 4πG (or 8πG) to 1. Doing so would introduce a factor of 1/4π (or 1/8π) into the nondimensionalized form of the law of universal gravitation, consistent with the modern rationalized formulation of Coulomb's law in terms of the vacuum permittivity. In fact, alternative normalizations frequently preserve the factor of 1/4π in the nondimensionalized form of Coulomb's law as well, so that the nondimensionalized Maxwell's equations for electromagnetism and gravitoelectromagnetism both take the same form as those for electromagnetism in SI, which do not have any factors of 4π. When this is applied to electromagnetic constants, ε0, this unit system is called "rationalized". When applied additionally to gravitation and Planck units, these are called rationalized Planck units[35] and are seen in high-energy physics.[36]
The rationalized Planck units are defined so that .
There are several possible alternative normalizations.
Gravitational constant
In 1899, Newton's law of universal gravitation was still seen as exact, rather than as a convenient approximation holding for "small" velocities and masses (the approximate nature of Newton's law was shown following the development of general relativity in 1915). Hence Planck normalized to 1 the gravitational constant G in Newton's law. In theories emerging after 1899, G nearly always appears in formulae multiplied by 4π or a small integer multiple thereof. Hence, a choice to be made when designing a system of natural units is which, if any, instances of 4π appearing in the equations of physics are to be eliminated via the normalization.
- Normalizing 4πG to 1 (and therefore setting G = 1/4π):
- Gauss's law for gravity becomes Φg = −M (rather than Φg = −4πM in Planck units).
- Eliminates 4πG from the Poisson equation.
- Eliminates 4πG in the gravitoelectromagnetic (GEM) equations, which hold in weak gravitational fields or locally flat spacetime. These equations have the same form as Maxwell's equations (and the Lorentz force equation) of electromagnetism, with mass density replacing charge density, and with 1/4πG replacing ε0.
- Normalizes the characteristic impedance Zg of gravitational radiation in free space to 1 (normally expressed as 4πG/c).[note 1]
- Eliminates 4πG from the Bekenstein–Hawking formula (for the entropy of a black hole in terms of its mass mBH and the area of its event horizon ABH) which is simplified to SBH = πABH = (mBH)2.
- Setting 8πG = 1 (and therefore setting G = 1/8π). This would eliminate 8πG from the Einstein field equations, Einstein–Hilbert action, and the Friedmann equations, for gravitation. Planck units modified so that 8πG = 1 are known as reduced Planck units, because the Planck mass is divided by √8π. Also, the Bekenstein–Hawking formula for the entropy of a black hole simplifies to SBH = (mBH)2/2 = 2πABH.
Unidades de Planck y la escala invariable de la naturaleza
Some theorists (such as Dirac and Milne) have proposed cosmologies that conjecture that physical "constants" might actually change over time (e.g. a variable speed of light or Dirac varying-G theory). Such cosmologies have not gained mainstream acceptance and yet there is still considerable scientific interest in the possibility that physical "constants" might change, although such propositions introduce difficult questions. Perhaps the first question to address is: How would such a change make a noticeable operational difference in physical measurement or, more fundamentally, our perception of reality? If some particular physical constant had changed, how would we notice it, or how would physical reality be different? Which changed constants result in a meaningful and measurable difference in physical reality? If a physical constant that is not dimensionless, such as the speed of light, did in fact change, would we be able to notice it or measure it unambiguously? – a question examined by Michael Duff in his paper "Comment on time-variation of fundamental constants".[37][38]
George Gamow argued in his book Mr Tompkins in Wonderland that a sufficient change in a dimensionful physical constant, such as the speed of light in a vacuum, would result in obvious perceptible changes. But this idea is challenged:
[An] important lesson we learn from the way that pure numbers like α define the world is what it really means for worlds to be different. The pure number we call the fine structure constant and denote by α is a combination of the electron charge, e, the speed of light, c, and Planck's constant, h. At first we might be tempted to think that a world in which the speed of light was slower would be a different world. But this would be a mistake. If c, h, and e were all changed so that the values they have in metric (or any other) units were different when we looked them up in our tables of physical constants, but the value of α remained the same, this new world would be observationally indistinguishable from our world. The only thing that counts in the definition of worlds are the values of the dimensionless constants of Nature. If all masses were doubled in value [including the Planck mass mP ] you cannot tell because all the pure numbers defined by the ratios of any pair of masses are unchanged.
— Barrow 2002[21]
Referring to Duff's "Comment on time-variation of fundamental constants"[37] and Duff, Okun, and Veneziano's paper "Trialogue on the number of fundamental constants",[39] particularly the section entitled "The operationally indistinguishable world of Mr. Tompkins", if all physical quantities (masses and other properties of particles) were expressed in terms of Planck units, those quantities would be dimensionless numbers (mass divided by the Planck mass, length divided by the Planck length, etc.) and the only quantities that we ultimately measure in physical experiments or in our perception of reality are dimensionless numbers. When one commonly measures a length with a ruler or tape-measure, that person is actually counting tick marks on a given standard or is measuring the length relative to that given standard, which is a dimensionless value. It is no different for physical experiments, as all physical quantities are measured relative to some other like-dimensioned quantity.
We can notice a difference if some dimensionless physical quantity such as fine-structure constant, α, changes or the proton-to-electron mass ratio, mp/me, changes (atomic structures would change) but if all dimensionless physical quantities remained unchanged (this includes all possible ratios of identically dimensioned physical quantity), we cannot tell if a dimensionful quantity, such as the speed of light, c, has changed. And, indeed, the Tompkins concept becomes meaningless in our perception of reality if a dimensional quantity such as c has changed, even drastically.
If the speed of light c, were somehow suddenly cut in half and changed to 1/2c (but with the axiom that all dimensionless physical quantities remain the same), then the Planck length would increase by a factor of 2√2 from the point of view of some unaffected observer on the outside. Measured by "mortal" observers in terms of Planck units, the new speed of light would remain as 1 new Planck length per 1 new Planck time – which is no different from the old measurement. But, since by axiom, the size of atoms (approximately the Bohr radius) are related to the Planck length by an unchanging dimensionless constant of proportionality:
Then atoms would be bigger (in one dimension) by 2√2, each of us would be taller by 2√2, and so would our metre sticks be taller (and wider and thicker) by a factor of 2√2. Our perception of distance and lengths relative to the Planck length is, by axiom, an unchanging dimensionless constant.
Our clocks would tick slower by a factor of 4√2 (from the point of view of this unaffected observer on the outside) because the Planck time has increased by 4√2 but we would not know the difference (our perception of durations of time relative to the Planck time is, by axiom, an unchanging dimensionless constant). This hypothetical unaffected observer on the outside might observe that light now propagates at half the speed that it previously did (as well as all other observed velocities) but it would still travel 299792458 of our new metres in the time elapsed by one of our new seconds ( 1/2c × 4√2 ÷ 2√2 continues to equal 299792458 m/s). We would not notice any difference.
This contradicts what George Gamow writes in his book Mr. Tompkins; there, Gamow suggests that if a dimension-dependent universal constant such as c changed significantly, we would easily notice the difference. The disagreement is better thought of as the ambiguity in the phrase "changing a physical constant"; what would happen depends on whether (1) all other dimensionless constants were kept the same, or whether (2) all other dimension-dependent constants are kept the same. The second choice is a somewhat confusing possibility, since most of our units of measurement are defined in relation to the outcomes of physical experiments, and the experimental results depend on the constants. Gamow does not address this subtlety; the thought experiments he conducts in his popular works assume the second choice for "changing a physical constant". And Duff or Barrow would point out that ascribing a change in measurable reality, i.e. α, to a specific dimensional component quantity, such as c, is unjustified. The very same operational difference in measurement or perceived reality could just as well be caused by a change in h or e if α is changed and no other dimensionless constants are changed. It is only the dimensionless physical constants that ultimately matter in the definition of worlds.[37][40]
This unvarying aspect of the Planck-relative scale, or that of any other system of natural units, leads many theorists to conclude that a hypothetical change in dimensionful physical constants can only be manifest as a change in dimensionless physical constants. One such dimensionless physical constant is the fine-structure constant. There are some experimental physicists who assert they have in fact measured a change in the fine structure constant[41] and this has intensified the debate about the measurement of physical constants. According to some theorists[42] there are some very special circumstances in which changes in the fine-structure constant can be measured as a change in dimensionful physical constants. Others however reject the possibility of measuring a change in dimensionful physical constants under any circumstance.[37] The difficulty or even the impossibility of measuring changes in dimensionful physical constants has led some theorists to debate with each other whether or not a dimensionful physical constant has any practical significance at all and that in turn leads to questions about which dimensionful physical constants are meaningful.[39]
Ver también
- cGh physics
- Dimensional analysis
- Doubly special relativity
- Planck particle
- Zero-point energy
Notas
- ^ General relativity predicts that gravitational radiation propagates at the same speed as electromagnetic radiation.
Referencias
Citations
- ^ Wesson, P. S. (1980). "The application of dimensional analysis to cosmology". Space Science Reviews. 27 (2): 117. Bibcode:1980SSRv...27..109W. doi:10.1007/bf00212237. S2CID 120784299.
- ^ a b Planck (1899), p. 479.
- ^ a b c Tomilin, K. A. (1999). Natural Systems of Units. To the Centenary Anniversary of the Planck System (PDF). Proceedings Of The XXII Workshop On High Energy Physics And Field Theory. pp. 287–296.
- ^ a b "2018 CODATA Value: Planck length". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 20 May 2019.
- ^ "2018 CODATA Value: Planck mass". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 20 May 2019.
- ^ "2018 CODATA Value: Planck time". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 20 May 2019.
- ^ a b "2018 CODATA Value: Planck temperature". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 20 May 2019.
- ^ Wilczek, Frank (2005). "On Absolute Units, I: Choices". Physics Today. American Institute of Physics. 58 (10): 12–13. Bibcode:2005PhT....58j..12W. doi:10.1063/1.2138392.
- ^ Zwiebach, Barton (2004). A First Course in String Theory. Cambridge University Press. p. 54. ISBN 978-0-521-83143-7. OCLC 58568857.
- ^ Deza, Michel Marie; Deza, Elena (2016). Encyclopedia of Distances. Springer. p. 602. ISBN 978-3662528433.
- ^ Zeidler, Eberhard (2006). Quantum Field Theory I: Basics in Mathematics and Physics (PDF). Springer. p. 953. ISBN 978-3540347620.
- ^ Elert, Glenn. "Blackbody Radiation". The Physics Hypertextbook. Retrieved 22 February 2021.
- ^ "2018 CODATA Value: vacuum electric permittivity". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 20 May 2019.
- ^ "2018 CODATA Value: Newtonian constant of gravitation". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 20 May 2019.
- ^ Wilczek, Frank (2001). "Scaling Mount Planck I: A View from the Bottom". Physics Today. 54 (6): 12–13. Bibcode:2001PhT....54f..12W. doi:10.1063/1.1387576.
- ^ The Planck scale – Symmetry magazine
- ^ Can experiment access Planck-scale physics?, CERN Courier
- ^ Number Theory as the Ultimate Physical Theory, Igor V. Volovich, PDF, doi:10.1134/S2070046610010061
- ^ Staff. "Birth of the Universe". University of Oregon. Retrieved 24 September 2016. - discusses "Planck time" and "Planck era" at the very beginning of the Universe
- ^ Edward W. Kolb; Michael S. Turner (1994). The Early Universe. Basic Books. p. 447. ISBN 978-0-201-62674-2. Retrieved 10 April 2010.
- ^ a b John D. Barrow, 2002. The Constants of Nature; From Alpha to Omega – The Numbers that Encode the Deepest Secrets of the Universe. Pantheon Books. ISBN 0-375-42221-8.
- ^ Barrow, John D.; Tipler, Frank J. (1986). The Anthropic Cosmological Principle (1st ed.). Oxford University Press. ISBN 978-0-19-282147-8. LCCN 87028148.
- ^ Barrow, John D.; Shaw, Douglas J. (2011). "The value of the cosmological constant". General Relativity and Gravitation. 43 (10): 2555–2560. arXiv:1105.3105. Bibcode:2011GReGr..43.2555B. doi:10.1007/s10714-011-1199-1. S2CID 55125081.
- ^ "Planck Era" and "Planck Time"
- ^ "First Second of the Big Bang". How The Universe Works 3. 2014. Discovery Science.
- ^ "Zeptoseconds: New world record in short time measurement". Phys.org. 16 October 2020. Retrieved 16 October 2020.
- ^ Yirka, Bob (26 June 2020). "Theorists calculate upper limit for possible quantization of time". Phys.org. Retrieved 27 June 2020.
- ^ Wendel, Garrett; Martínez, Luis; Bojowald, Martin (19 June 2020). "Physical Implications of a Fundamental Period of Time". Phys. Rev. Lett. 124 (24): 241301. arXiv:2005.11572. Bibcode:2020PhRvL.124x1301W. doi:10.1103/PhysRevLett.124.241301. PMID 32639827. S2CID 218870394.
- ^ "HiRes – The High Resolution Fly's Eye Ultra High Energy Cosmic Ray Observatory". www.cosmic-ray.org. Retrieved 21 December 2016.
- ^ Venzo de Sabbata; C. Sivaram (1993). "On limiting field strengths in gravitation". Foundations of Physics Letters. 6 (6): 561–570. doi:10.1007/BF00662806. S2CID 120924238.
- ^ G. W. Gibbons (2002). "The Maximum Tension Principle in General Relativity". Foundations of Physics. 32 (12): 1891–1901. arXiv:hep-th/0210109. doi:10.1023/A:1022370717626. S2CID 118154613.
- ^ Jowsey, Aden; Visser, Matt (3 February 2021). "Counterexamples to the maximum force conjecture". arXiv:2102.01831 [gr-qc].
- ^ Nova: Absolute Hot
- ^ Also see Roger Penrose (1989) The Road to Reality. Oxford Univ. Press: 714-17. Knopf.
- ^ Sorkin, Rafael (1983). "Kaluza-Klein Monopole". Phys. Rev. Lett. 51 (2): 87–90. Bibcode:1983PhRvL..51...87S. doi:10.1103/PhysRevLett.51.87.
- ^ Rañada, Antonio F. (31 October 1995). "A Model of Topological Quantization of the Electromagnetic Field". In M. Ferrero; Alwyn van der Merwe (eds.). Fundamental Problems in Quantum Physics. p. 271. ISBN 9780792336709.
- ^ a b c d Michael Duff (2002). "Comment on time-variation of fundamental constants". arXiv:hep-th/0208093.
- ^ Michael Duff (2014). How fundamental are fundamental constants?. arXiv:1412.2040. doi:10.1080/00107514.2014.980093 (inactive 31 May 2021).CS1 maint: DOI inactive as of May 2021 (link)
- ^ a b Duff, Michael; Okun, Lev; Veneziano, Gabriele (2002). "Trialogue on the number of fundamental constants". Journal of High Energy Physics. 2002 (3): 023. arXiv:physics/0110060. Bibcode:2002JHEP...03..023D. doi:10.1088/1126-6708/2002/03/023. S2CID 15806354.
- ^ John Baez How Many Fundamental Constants Are There?
- ^ Webb, J. K.; et al. (2001). "Further evidence for cosmological evolution of the fine structure constant". Phys. Rev. Lett. 87 (9): 884. arXiv:astro-ph/0012539v3. Bibcode:2001PhRvL..87i1301W. doi:10.1103/PhysRevLett.87.091301. PMID 11531558. S2CID 40461557.
- ^ Davies, Paul C.; Davis, T. M.; Lineweaver, C. H. (2002). "Cosmology: Black Holes Constrain Varying Constants". Nature. 418 (6898): 602–3. Bibcode:2002Natur.418..602D. doi:10.1038/418602a. PMID 12167848. S2CID 1400235.
Sources
- Barrow, John D. (2002). The Constants of Nature; From Alpha to Omega – The Numbers that Encode the Deepest Secrets of the Universe. New York: Pantheon Books. ISBN 978-0-375-42221-8. Easier.
- Barrow, John D.; Tipler, Frank J. (1986). The Anthropic Cosmological Principle. Oxford: Claredon Press. ISBN 978-0-19-851949-2. Harder.
- Penrose, Roger (2005). "Section 31.1". The Road to Reality. New York: Alfred A. Knopf. ISBN 978-0-679-45443-4.
- Planck, Max (1899). "Über irreversible Strahlungsvorgänge". Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin (in German). 5: 440–480. pp. 478–80 contain the first appearance of the Planck base units other than the Planck charge, and of Planck's constant, which Planck denoted by b. a and f in this paper correspond to k and G in this entry.
- Tomilin, K. A. (1999). Natural Systems of Units: To the Centenary Anniversary of the Planck System (PDF). Proceedings Of The XXII Workshop On High Energy Physics And Field Theory. pp. 287–296. Archived from the original (PDF) on 17 June 2006.
enlaces externos
- Value of the fundamental constants, including the Planck units, as reported by the National Institute of Standards and Technology (NIST).
- "Planck Era" and "Planck Time" (up to 10−43 seconds after birth of Universe) (University of Oregon).
- The Planck scale: relativity meets quantum mechanics meets gravity from 'Einstein Light' at UNSW
- Higher-Dimensional Algebra and Planck-Scale Physics by John C. Baez
- Adler, Ronald J. (2010). "Six easy roads to the Planck scale". American Journal of Physics. 78 (9): 925–932. arXiv:1001.1205. Bibcode:2010AmJPh..78..925A. doi:10.1119/1.3439650. S2CID 55181581.
- Sivaram, C. (1 August 1986). "Evolution of the Universe through the Planck epoch". Astrophysics and Space Science. 125 (1): 189–199. Bibcode:1986Ap&SS.125..189S. doi:10.1007/BF00643984. S2CID 123344693.