Einstein field equations

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Einstein_field_equations

General relativity
${\displaystyle G_{\mu \nu }+\mathrm{\Lambda }{g}_{\mu \nu }=\kappa T_{\mu \nu }}$

In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it.

The equations were published by Albert Einstein in 1915 in the form of a tensor equation which related the local spacetime curvature (expressed by the Einstein tensor) with the local energy, momentum and stress within that spacetime (expressed by the stress–energy tensor).

Analogously to the way that electromagnetic fields are related to the distribution of charges and currents via Maxwell's equations, the EFE relate the spacetime geometry to the distribution of mass–energy, momentum and stress, that is, they determine the metric tensor of spacetime for a given arrangement of stress–energy–momentum in the spacetime. The relationship between the metric tensor and the Einstein tensor allows the EFE to be written as a set of nonlinear partial differential equations when used in this way. The solutions of the EFE are the components of the metric tensor. The inertial trajectories of particles and radiation (geodesics) in the resulting geometry are then calculated using the geodesic equation.

As well as implying local energy–momentum conservation, the EFE reduce to Newton's law of gravitation in the limit of a weak gravitational field and velocities that are much less than the speed of light.

Exact solutions for the EFE can only be found under simplifying assumptions such as symmetry. Special classes of exact solutions are most often studied since they model many gravitational phenomena, such as rotating black holes and the expanding universe. Further simplification is achieved in approximating the spacetime as having only small deviations from flat spacetime, leading to the linearized EFE. These equations are used to study phenomena such as gravitational waves.

Mathematical form

The Einstein field equations (EFE) may be written in the form:

${\displaystyle G_{\mu \nu }+\mathrm{\Lambda }{g}_{\mu \nu }=\kappa T_{\mu \nu }}$

EFE on a wall in Leiden, Netherlands

where ${\displaystyle G_{\mu \nu }}$ is the Einstein tensor, ${\displaystyle g_{\mu \nu }}$ is the metric tensor, ${\displaystyle T_{\mu \nu }}$ is the stress–energy tensor, ${\displaystyle \mathrm{\Lambda }}$ is the cosmological constant and ${\displaystyle \kappa }$ is the Einstein gravitational constant.

The Einstein tensor is defined as

${\displaystyle G_{\mu \nu }=R_{\mu \nu }-\frac{1}{2}R{g}_{\mu \nu },}$

where ${\displaystyle R_{\mu \nu }}$ is the Ricci curvature tensor, and ${\displaystyle R}$ is the scalar curvature. This is a symmetric second-degree tensor that depends on only the metric tensor and its first and second derivatives.

The Einstein gravitational constant is defined as

${\displaystyle \kappa =\frac{8\pi G}{c^4}\approx 2.07665(5)\times {10}^{-43}{\text{N}}^{-1},}$ or ${\displaystyle \text{m/J},}$

where G is the Newtonian constant of gravitation and c is the speed of light in vacuum.

The EFE can thus also be written as

${\displaystyle R_{\mu \nu }-\frac{1}{2}R{g}_{\mu \nu }+\mathrm{\Lambda }{g}_{\mu \nu }=\kappa T_{\mu \nu }.}$

In standard units, each term on the left has units of 1/length².

The expression on the left represents the curvature of spacetime as determined by the metric; the expression on the right represents the stress–energy–momentum content of spacetime. The EFE can then be interpreted as a set of equations dictating how stress–energy–momentum determines the curvature of spacetime.

These equations, together with the geodesic equation, which dictates how freely falling matter moves through spacetime, form the core of the mathematical formulation of general relativity.

The EFE is a tensor equation relating a set of symmetric 4 × 4 tensors. Each tensor has 10 independent components. The four Bianchi identities reduce the number of independent equations from 10 to 6, leaving the metric with four gauge-fixing degrees of freedom, which correspond to the freedom to choose a coordinate system.

Although the Einstein field equations were initially formulated in the context of a four-dimensional theory, some theorists have explored their consequences in n dimensions. The equations in contexts outside of general relativity are still referred to as the Einstein field equations. The vacuum field equations (obtained when T_μν is everywhere zero) define Einstein manifolds.

The equations are more complex than they appear. Given a specified distribution of matter and energy in the form of a stress–energy tensor, the EFE are understood to be equations for the metric tensor ${\displaystyle g_{\mu \nu }}$, since both the Ricci tensor and scalar curvature depend on the metric in a complicated nonlinear manner. When fully written out, the EFE are a system of ten coupled, nonlinear, hyperbolic-elliptic partial differential equations.

Sign convention

The above form of the EFE is the standard established by Misner, Thorne, and Wheeler (MTW). The authors analyzed conventions that exist and classified these according to three signs ([S1] [S2] [S3]):

$${\displaystyle \begin{array}{rl}{g}_{\mu \nu }& =[S1]\times \mathrm{diag}(-1,+1,+1,+1)\\ {R^{\mu }}_{\alpha \beta \gamma }& =[S2]\times \left({\mathrm{\Gamma }}_{\alpha \gamma ,\beta }^{\mu }-{\mathrm{\Gamma }}_{\alpha \beta ,\gamma }^{\mu }+{\mathrm{\Gamma }}_{\sigma \beta }^{\mu }{\mathrm{\Gamma }}_{\gamma \alpha }^{\sigma }-{\mathrm{\Gamma }}_{\sigma \gamma }^{\mu }{\mathrm{\Gamma }}_{\beta \alpha }^{\sigma }\right)\\ G_{\mu \nu }& =[S3]\times \kappa T_{\mu \nu }\end{array}}$$

The third sign above is related to the choice of convention for the Ricci tensor: $${\displaystyle R_{\mu \nu }=[S2]\times [S3]\times {R^{\alpha }}_{\mu \alpha \nu }}$$

With these definitions Misner, Thorne, and Wheeler classify themselves as (+ + +), whereas Weinberg (1972) is (+ − −), Peebles (1980) and Efstathiou et al. (1990) are (− + +), Rindler (1977), Atwater (1974), Collins Martin & Squires (1989) and Peacock (1999) are (− + −).

Authors including Einstein have used a different sign in their definition for the Ricci tensor which results in the sign of the constant on the right side being negative: $${\displaystyle R_{\mu \nu }-\frac{1}{2}R{g}_{\mu \nu }-\mathrm{\Lambda }{g}_{\mu \nu }=-\kappa T_{\mu \nu }.}$$

The sign of the cosmological term would change in both these versions if the (+ − − −) metric sign convention is used rather than the MTW (− + + +) metric sign convention adopted here.

Equivalent formulations

Taking the trace with respect to the metric of both sides of the EFE one gets $${\displaystyle R-\frac{D}{2}R+D\mathrm{\Lambda }=\kappa T,}$$ where D is the spacetime dimension. Solving for R and substituting this in the original EFE, one gets the following equivalent "trace-reversed" form: $${\displaystyle R_{\mu \nu }-\frac{2}{D-2}\mathrm{\Lambda }{g}_{\mu \nu }=\kappa \left(T_{\mu \nu }-\frac{1}{D-2}T{g}_{\mu \nu }\right).}$$

In D = 4 dimensions this reduces to $${\displaystyle R_{\mu \nu }-\mathrm{\Lambda }{g}_{\mu \nu }=\kappa \left(T_{\mu \nu }-\frac{1}{2}T{g}_{\mu \nu }\right).}$$

Reversing the trace again would restore the original EFE. The trace-reversed form may be more convenient in some cases (for example, when one is interested in weak-field limit and can replace ${\displaystyle g_{\mu \nu }}$ in the expression on the right with the Minkowski metric without significant loss of accuracy).

The cosmological constant

Main article: Cosmological constant

In the Einstein field equations $${\displaystyle G_{\mu \nu }+\mathrm{\Lambda }{g}_{\mu \nu }=\kappa T_{\mu \nu },}$$ the term containing the cosmological constant Λ was absent from the version in which he originally published them. Einstein then included the term with the cosmological constant to allow for a universe that is not expanding or contracting. This effort was unsuccessful because:

• any desired steady state solution described by this equation is unstable, and
• observations by Edwin Hubble showed that our universe is expanding.

Einstein then abandoned Λ, remarking to George Gamow "that the introduction of the cosmological term was the biggest blunder of his life".

The inclusion of this term does not create inconsistencies. For many years the cosmological constant was almost universally assumed to be zero. More recent astronomical observations have shown an accelerating expansion of the universe, and to explain this a positive value of Λ is needed. The cosmological constant is negligible at the scale of a galaxy or smaller.

Einstein thought of the cosmological constant as an independent parameter, but its term in the field equation can also be moved algebraically to the other side and incorporated as part of the stress–energy tensor: $${\displaystyle T_{\mu \nu }^{(\mathrm{v}\mathrm{a}\mathrm{c})}=-\frac{\mathrm{\Lambda }}{\kappa }{g}_{\mu \nu }.}$$

This tensor describes a vacuum state with an energy density ρ_vac and isotropic pressure p_vac that are fixed constants and given by $${\displaystyle {\rho }_{\mathrm{v}\mathrm{a}\mathrm{c}}=-p_{\mathrm{v}\mathrm{a}\mathrm{c}}=\frac{\mathrm{\Lambda }}{\kappa },}$$ where it is assumed that Λ has SI unit m⁻² and κ is defined as above.

The existence of a cosmological constant is thus equivalent to the existence of a vacuum energy and a pressure of opposite sign. This has led to the terms "cosmological constant" and "vacuum energy" being used interchangeably in general relativity.

Features

Conservation of energy and momentum

General relativity is consistent with the local conservation of energy and momentum expressed as

$${\displaystyle {\mathrm{\nabla }}_{\beta }{T}^{\alpha \beta }={T^{\alpha \beta }}_{;\beta }=0.}$$

Derivation of local energy–momentum conservation

Contracting the differential Bianchi identity $${\displaystyle R_{\alpha \beta [\gamma \delta ;\epsilon ]}=0}$$ with g^αβ gives, using the fact that the metric tensor is covariantly constant, i.e. g^αβ_;γ = 0, $${\displaystyle {R^{\gamma }}_{\beta \gamma \delta ;\epsilon }+{R^{\gamma }}_{\beta \epsilon \gamma ;\delta }+{R^{\gamma }}_{\beta \delta \epsilon ;\gamma }=0}$$

The antisymmetry of the Riemann tensor allows the second term in the above expression to be rewritten:

$${\displaystyle {R^{\gamma }}_{\beta \gamma \delta ;\epsilon }-{R^{\gamma }}_{\beta \gamma \epsilon ;\delta }+{R^{\gamma }}_{\beta \delta \epsilon ;\gamma }=0}$$ which is equivalent to $${\displaystyle R_{\beta \delta ;\epsilon }-R_{\beta \epsilon ;\delta }+{R^{\gamma }}_{\beta \delta \epsilon ;\gamma }=0}$$ using the definition of the Ricci tensor.

Next, contract again with the metric $${\displaystyle g^{\beta \delta }\left(R_{\beta \delta ;\epsilon }-R_{\beta \epsilon ;\delta }+{R^{\gamma }}_{\beta \delta \epsilon ;\gamma }\right)=0}$$ to get $${\displaystyle {R^{\delta }}_{\delta ;\epsilon }-{R^{\delta }}_{\epsilon ;\delta }+{R^{\gamma \delta }}_{\delta \epsilon ;\gamma }=0}$$

The definitions of the Ricci curvature tensor and the scalar curvature then show that $${\displaystyle R_{;\epsilon }-2{R^{\gamma }}_{\epsilon ;\gamma }=0}$$ which can be rewritten as $${\displaystyle {\left({R^{\gamma }}_{\epsilon }-\frac{1}{2}{g^{\gamma }}_{\epsilon }R\right)}_{;\gamma }=0}$$

A final contraction with g^εδ gives $${\displaystyle {\left(R^{\gamma \delta }-\frac{1}{2}{g}^{\gamma \delta }R\right)}_{;\gamma }=0}$$ which by the symmetry of the bracketed term and the definition of the Einstein tensor, gives, after relabelling the indices, $${\displaystyle {G^{\alpha \beta }}_{;\beta }=0}$$

Using the EFE, this immediately gives, $${\displaystyle {\mathrm{\nabla }}_{\beta }{T}^{\alpha \beta }={T^{\alpha \beta }}_{;\beta }=0}$$

which expresses the local conservation of stress–energy. This conservation law is a physical requirement. With his field equations Einstein ensured that general relativity is consistent with this conservation condition.

Nonlinearity

The nonlinearity of the EFE distinguishes general relativity from many other fundamental physical theories. For example, Maxwell's equations of electromagnetism are linear in the electric and magnetic fields, and charge and current distributions (i.e. the sum of two solutions is also a solution); another example is Schrödinger's equation of quantum mechanics, which is linear in the wavefunction.

The correspondence principle

The EFE reduce to Newton's law of gravity by using both the weak-field approximation and the slow-motion approximation. In fact, the constant G appearing in the EFE is determined by making these two approximations.

Derivation of Newton's law of gravity

Newtonian gravitation can be written as the theory of a scalar field, Φ, which is the gravitational potential in joules per kilogram of the gravitational field g = −∇Φ, see Gauss's law for gravity $${\displaystyle {\mathrm{\nabla }}^2\mathrm{\Phi }\left(\overrightarrow{x},t\right)=4\pi G\rho \left(\overrightarrow{x},t\right)}$$ where ρ is the mass density. The orbit of a free-falling particle satisfies $${\displaystyle \ddot{\overrightarrow{x}}(t)=\overrightarrow{g}=-\mathrm{\nabla }\mathrm{\Phi }\left(\overrightarrow{x}(t),t\right).}$$

In tensor notation, these become $${\displaystyle \begin{array}{rl}{\mathrm{\Phi }}_{,ii}& =4\pi G\rho \\ \frac{d^2{x}^i}{d{t}^2}& =-{\mathrm{\Phi }}_{,i}.\end{array}}$$

In general relativity, these equations are replaced by the Einstein field equations in the trace-reversed form $${\displaystyle R_{\mu \nu }=K\left(T_{\mu \nu }-\frac{1}{2}T{g}_{\mu \nu }\right)}$$ for some constant, K, and the geodesic equation $${\displaystyle \frac{d^2{x}^{\alpha }}{d{\tau }^2}=-{\mathrm{\Gamma }}_{\beta \gamma }^{\alpha }\frac{d{x}^{\beta }}{d\tau }\frac{d{x}^{\gamma }}{d\tau }.}$$

To see how the latter reduces to the former, we assume that the test particle's velocity is approximately zero $${\displaystyle \frac{d{x}^{\beta }}{d\tau }\approx \left(\frac{dt}{d\tau },0,0,0\right)}$$ and thus $${\displaystyle \frac{d}{dt}\left(\frac{dt}{d\tau }\right)\approx 0}$$ and that the metric and its derivatives are approximately static and that the squares of deviations from the Minkowski metric are negligible. Applying these simplifying assumptions to the spatial components of the geodesic equation gives $${\displaystyle \frac{d^2{x}^i}{d{t}^2}\approx -{\mathrm{\Gamma }}_{00}^i}$$ where two factors of ⁠dt/dτ⁠ have been divided out. This will reduce to its Newtonian counterpart, provided $${\displaystyle {\mathrm{\Phi }}_{,i}\approx {\mathrm{\Gamma }}_{00}^i=\frac{1}{2}{g}^{i\alpha }\left(g_{\alpha 0,0}+g_{0\alpha ,0}-g_{00,\alpha }\right).}$$

Our assumptions force α = i and the time (0) derivatives to be zero. So this simplifies to $${\displaystyle 2{\mathrm{\Phi }}_{,i}\approx g^{ij}\left(-g_{00,j}\right)\approx -g_{00,i}}$$ which is satisfied by letting $${\displaystyle g_{00}\approx -c^2-2\mathrm{\Phi }.}$$

Turning to the Einstein equations, we only need the time-time component $${\displaystyle R_{00}=K\left(T_{00}-\frac{1}{2}T{g}_{00}\right)}$$ the low speed and static field assumptions imply that $${\displaystyle T_{\mu \nu }\approx \mathrm{diag}\left(T_{00},0,0,0\right)\approx \mathrm{diag}\left(\rho c^4,0,0,0\right).}$$

So $${\displaystyle T=g^{\alpha \beta }{T}_{\alpha \beta }\approx g^{00}{T}_{00}\approx -\frac{1}{c^2}\rho c^4=-\rho c^2}$$ and thus $${\displaystyle K\left(T_{00}-\frac{1}{2}T{g}_{00}\right)\approx K\left(\rho c^4-\frac{1}{2}\left(-\rho c^2\right)\left(-c^2\right)\right)=\frac{1}{2}K\rho c^4.}$$

From the definition of the Ricci tensor $${\displaystyle R_{00}={\mathrm{\Gamma }}_{00,\rho }^{\rho }-{\mathrm{\Gamma }}_{\rho 0,0}^{\rho }+{\mathrm{\Gamma }}_{\rho \lambda }^{\rho }{\mathrm{\Gamma }}_{00}^{\lambda }-{\mathrm{\Gamma }}_{0\lambda }^{\rho }{\mathrm{\Gamma }}_{\rho 0}^{\lambda }.}$$

Our simplifying assumptions make the squares of Γ disappear together with the time derivatives $${\displaystyle R_{00}\approx {\mathrm{\Gamma }}_{00,i}^i.}$$

Combining the above equations together $${\displaystyle {\mathrm{\Phi }}_{,ii}\approx {\mathrm{\Gamma }}_{00,i}^i\approx R_{00}=K\left(T_{00}-\frac{1}{2}T{g}_{00}\right)\approx \frac{1}{2}K\rho c^4}$$ which reduces to the Newtonian field equation provided $${\displaystyle \frac{1}{2}K\rho c^4=4\pi G\rho }$$ which will occur if $${\displaystyle K=\frac{8\pi G}{c^4}.}$$

Vacuum field equations

A Swiss commemorative coin from 1979, showing the vacuum field equations with zero cosmological constant (top).

If the energy–momentum tensor T_μν is zero in the region under consideration, then the field equations are also referred to as the vacuum field equations. By setting T_μν = 0 in the trace-reversed field equations, the vacuum field equations, also known as 'Einstein vacuum equations' (EVE), can be written as $${\displaystyle R_{\mu \nu }=0.}$$

In the case of nonzero cosmological constant, the equations are $${\displaystyle R_{\mu \nu }=\frac{\mathrm{\Lambda }}{\frac{D}{2}-1}{g}_{\mu \nu }.}$$

The solutions to the vacuum field equations are called vacuum solutions. Flat Minkowski space is the simplest example of a vacuum solution. Nontrivial examples include the Schwarzschild solution and the Kerr solution.

Manifolds with a vanishing Ricci tensor, R_μν = 0, are referred to as Ricci-flat manifolds and manifolds with a Ricci tensor proportional to the metric as Einstein manifolds.

Einstein–Maxwell equations

See also: Maxwell's equations in curved spacetime

If the energy–momentum tensor T_μν is that of an electromagnetic field in free space, i.e. if the electromagnetic stress–energy tensor $${\displaystyle T^{\alpha \beta }=-\frac{1}{{\mu }_0}\left({F^{\alpha }}^{\psi }{F_{\psi }}^{\beta }+\frac{1}{4}{g}^{\alpha \beta }{F}_{\psi \tau }{F}^{\psi \tau }\right)}$$ is used, then the Einstein field equations are called the Einstein–Maxwell equations (with cosmological constant Λ, taken to be zero in conventional relativity theory): $${\displaystyle G^{\alpha \beta }+\mathrm{\Lambda }{g}^{\alpha \beta }=\frac{\kappa }{{\mu }_0}\left({F^{\alpha }}^{\psi }{F_{\psi }}^{\beta }+\frac{1}{4}{g}^{\alpha \beta }{F}_{\psi \tau }{F}^{\psi \tau }\right).}$$

Additionally, the covariant Maxwell equations are also applicable in free space: $${\displaystyle \begin{array}{rl}{F^{\alpha \beta }}_{;\beta }& =0\\ F_{[\alpha \beta ;\gamma ]}& =\frac{1}{3}\left(F_{\alpha \beta ;\gamma }+F_{\beta \gamma ;\alpha }+F_{\gamma \alpha ;\beta }\right)=\frac{1}{3}\left(F_{\alpha \beta ,\gamma }+F_{\beta \gamma ,\alpha }+F_{\gamma \alpha ,\beta }\right)=0.\end{array}}$$ where the semicolon represents a covariant derivative, and the brackets denote anti-symmetrization. The first equation asserts that the 4-divergence of the 2-form F is zero, and the second that its exterior derivative is zero. From the latter, it follows by the Poincaré lemma that in a coordinate chart it is possible to introduce an electromagnetic field potential A_α such that $${\displaystyle F_{\alpha \beta }=A_{\alpha ;\beta }-A_{\beta ;\alpha }=A_{\alpha ,\beta }-A_{\beta ,\alpha }}$$ in which the comma denotes a partial derivative. This is often taken as equivalent to the covariant Maxwell equation from which it is derived. However, there are global solutions of the equation that may lack a globally defined potential.

Solutions

Main article: Solutions of the Einstein field equations

The solutions of the Einstein field equations are metrics of spacetime. These metrics describe the structure of the spacetime including the inertial motion of objects in the spacetime. As the field equations are non-linear, they cannot always be completely solved (i.e. without making approximations). For example, there is no known complete solution for a spacetime with two massive bodies in it (which is a theoretical model of a binary star system, for example). However, approximations are usually made in these cases. These are commonly referred to as post-Newtonian approximations. Even so, there are several cases where the field equations have been solved completely, and those are called exact solutions.

The study of exact solutions of Einstein's field equations is one of the activities of cosmology. It leads to the prediction of black holes and to different models of evolution of the universe.

One can also discover new solutions of the Einstein field equations via the method of orthonormal frames as pioneered by Ellis and MacCallum. In this approach, the Einstein field equations are reduced to a set of coupled, nonlinear, ordinary differential equations. As discussed by Hsu and Wainwright, self-similar solutions to the Einstein field equations are fixed points of the resulting dynamical system. New solutions have been discovered using these methods by LeBlanc and Kohli and Haslam.

The linearized EFE

Main article: Linearized gravity

The nonlinearity of the EFE makes finding exact solutions difficult. One way of solving the field equations is to make an approximation, namely, that far from the source(s) of gravitating matter, the gravitational field is very weak and the spacetime approximates that of Minkowski space. The metric is then written as the sum of the Minkowski metric and a term representing the deviation of the true metric from the Minkowski metric, ignoring higher-power terms. This linearization procedure can be used to investigate the phenomena of gravitational radiation.

Polynomial form

Despite the EFE as written containing the inverse of the metric tensor, they can be arranged in a form that contains the metric tensor in polynomial form and without its inverse. First, the determinant of the metric in 4 dimensions can be written $${\displaystyle det(g)=\frac{1}{24}{\epsilon }^{\alpha \beta \gamma \delta }{\epsilon }^{\kappa \lambda \mu \nu }{g}_{\alpha \kappa }{g}_{\beta \lambda }{g}_{\gamma \mu }{g}_{\delta \nu }}$$ using the Levi-Civita symbol; and the inverse of the metric in 4 dimensions can be written as: $${\displaystyle g^{\alpha \kappa }=\frac{\frac{1}{6}{\epsilon }^{\alpha \beta \gamma \delta }{\epsilon }^{\kappa \lambda \mu \nu }{g}_{\beta \lambda }{g}_{\gamma \mu }{g}_{\delta \nu }}{det(g)}.}$$

Substituting this expression of the inverse of the metric into the equations then multiplying both sides by a suitable power of det(g) to eliminate it from the denominator results in polynomial equations in the metric tensor and its first and second derivatives. The Einstein-Hilbert action from which the equations are derived can also be written in polynomial form by suitable redefinitions of the fields.

Communist terrorism

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Communist_terrorism

Communist terrorism is terrorism perpetrated by individuals or groups which adhere to communism and ideologies related to it, such as Marxism–Leninism, Maoism, and Trotskyism. Historically, communist terrorism has sometimes taken the form of state-sponsored terrorism, supported by communist nations such as the Soviet Union, China, North Korea and Kampuchea. In addition, non-state actors such as the Red Brigades, the Front Line and the Red Army Faction have also engaged in communist terrorism. These groups hope to inspire the masses to rise up and start a revolution to overthrow existing political and economic systems. This form of terrorism can sometimes be called red terrorism or left-wing terrorism.

The end of the Cold War and the dissolution of the Soviet Union have been credited with leading to a notable decline in this form of terrorism.

History

In the 1930s, the term "communist terrorism" was used by the Nazi Party in Germany as part of a propaganda campaign to spread fear of communism. The Nazis blamed communist terrorism for the Reichstag fire, which they used as an excuse to push through legislation removing personal freedom from German citizens. In the 1940s and 1950s, various Southeast Asian countries, such as the Philippines and Vietnam, witnessed the rise of communist groups engaging in terrorism. John Slocum claimed that communists in present-day Malaysia used terrorism to draw attention to their ideological beliefs, but Phillip Deery countered that the Malaysian insurgents were called communist terrorists only as part of a propaganda campaign.

In the 1960s, the Sino–Soviet split (between two communist states) led to a marked increase in terrorist activity in the region. That decade also saw various terrorist groups commencing operations in Europe, Japan, and the Americas. Yonah Alexander deemed these groups Fighting Communist Organizations (FCOs), and says they rose out of the student union movement protesting against the Vietnam War. In Western Europe, these groups' actions were known as Euroterrorism. The founders of FCOs argued that violence was necessary to achieve their goals, and that peaceful protest was both ineffective and insufficient to attain them. In the 1970s, there were an estimated 50 Marxist or Leninist groups operating in Turkey, and an estimated 225 groups operating in Italy. Groups also began operations in Ireland and the United Kingdom. These groups were deemed a major threat by NATO and the Italian, German, and British governments. Communist terrorism did not enjoy full support from all ideologically sympathetic groups. The Italian Communist Party, for example, condemned such activity.

Background

See also: Dictatorship of the proletariat

While Vladimir Lenin systematically denounced the terrorism practiced by the Socialist Revolutionaries, he also supported terror as a tool, and considered mass terror to be a strategic and efficient method for advancing revolutionary goals. According to Leon Trotsky, Lenin emphasized the absolute necessity of terror and as early as 1904, Lenin said, "The dictatorship of the proletariat is an absolutely meaningless expression without Jacobin coercion." In 1905, Lenin directed members of the St. Petersburg "Combat Committee" to commit acts of robbery, arson, and other terrorist acts.

Bolshevik banner in 1918: "Death to the Bourgeoisie and its lapdogs – Long live the Red Terror!!"

Not all scholars agree on Lenin's position towards terrorism. Joan Witte contends that he opposed the practice except when it was wielded by the party and the Red Army after 1917. She also suggests that he opposed the use of terrorism as a mindless act but endorsed its use in order to advance the communist revolution. Chaliand and Blin contend that Lenin advocated mass terror but objected to disorderly, unorganized, or petty acts of terrorism. According to Richard Drake, Lenin had abandoned any reluctance to use terrorist tactics by 1917, believing that all resistance to communist revolution should be met with maximum force. Drake contends that the terrorist intent in Lenin's program was unmistakable, as acknowledged by Trotsky in his book Terrorism and Communism: a Reply, published in 1918. In the book, Trotsky provided an elaborate justification for the use of terror, stating "The man who repudiates terrorism in principle, i.e., repudiates measures of suppression and intimidation towards determined and armed counterrevolution, must reject all ideas of the political supremacy of the working class and its revolutionary dictatorship." Trotsky's justification largely rests on a criticism of the usage of the term "terrorism" to describe all political violence on behalf of the Left, but not equally vicious political violence carried out by liberal or reactionary factions. Scholars on the Left argue that while it is a matter of historical record that communist movements did at times employ violence, the label of "terrorism" is disproportionately used in Western media sources to refer to all political violence employed by the left, while similarly violent tactics employed by the United States and its allies remain unscrutinized.

Examples

Bulgaria

The St Nedelya Church assault on 16 April 1925 was committed by a group from the Bulgarian Communist Party (BCP). They blew up the roof of the St Nedelya Church in Sofia, Bulgaria. 150 people were killed and around 500 were injured.

Cambodia

See also: Cambodian genocide

The Cambodian genocide committed by the Khmer Rouge, which led to the death of an estimated 1.7 million to 2.5 million people has been described as an act of terrorism by Joseph S. Tuman.

China

Benjamin A. Valentino has estimated that the atrocities committed by both the Nationalist government and the Chinese Communist Party during the Chinese Civil War resulted in the death of between 1.8 million and 3.5 million people between 1927 and 1949.

Indonesia

The Communist Party of Indonesia (PKI) had been engaged in what perceived as an act of terrorism during a communist rebellion in 1948, as well as the failed coup attempt in 1965. However, under the leadership of D. N. Aidit, the PKI was transformed into a legal party operating openly within the country and rejected armed struggle. The alleged coup attempt culminated in a violent anti-communist purge and a subsequent regime change into a right-wing military dictatorship following the purges.

Japan

In the late 1960s, Japanese communist Fusako Shingenobu formed the militant Japanese Red Army terrorist group. Their goal was to start a worldwide communist revolution through the use of terrorism. They committed multiple embassy attacks, airplane hijackings, bombings and taking hostages. They were responsible for the 1972 Lod Airport Massacre, in which 26 people were killed and 79 injured. In 1988, members of the JRA detonated a car bomb outside of a USO recreational facility in Naples which killed 4 Italian civilians, 1 U.S. Servicewoman, and injured 15 other people.

Members of the JRA merged with members of the Revolutionary Left Faction to form the United Red Army, which became known for the Asama-Sansō incident, a weeklong standoff with the police after the group had murdered fourteen of its own members.

Peru

Shining Path was responsible for the 1992 Tarata Bombing in the business district of Lima, Peru. The bombing killed 25 people and injured 250 others.

Shining Path was founded in 1969 by Maoist philosophy professor Abimael Guzmán as a split from the Peruvian Communist Party. In 1980 when the Peruvian government held elections for the first time in 12 years, Shining Path rejected participation instead declaring a guerilla war against the government, perpetrating "assassinations, bombings, beheadings and massacres", including the Tarata bombing and 1983 Lucanamarca massacre. Guzmán was arrested in 1992 and sentenced to life in prison on charges of aggravated terrorism and murder. Another communist terrorist group, Túpac Amaru Revolutionary Movement, gained notoriety after taking hostages at the Japanese Embassy of Peru which lead to a 126 day stand off with Peruvian authorities.

The Shining Path is regarded as a terrorist organization by Peru, Japan, the United States, the European Union, and Canada, all of whom consequently prohibit funding and other financial support to the group.

The Philippines

Main article: New People's Army

The New People's Army (NPA) founded in 1969 has been described as the third largest terrorist group operating in the Philippines. The group carried out attacks between 1987 and 1992 before entering a hiatus. Between 2000 and 2006, they carried out an additional 42 attacks. The NPA is designated as a terrorist group by The Philippines, The United States, The European Union, and New Zealand.

Rhodesia

In Rhodesia (renamed Zimbabwe in 1980), during the Bush War of the 1970s, guerrillas operating in the country were considered communist terrorists by the government. The organisations in question received war materiels and financial support from numerous communist countries, and they also received training in several of those same countries, including the Soviet Union, China and Cuba. Both guerrilla armies involved in the war—the Zimbabwe People's Revolutionary Army (ZIPRA) of the Zimbabwe African People's Union (ZAPU), and the Zimbabwe African National Liberation Army (ZANLA) attached to the Zimbabwe African National Union (ZANU)—were initially based in the Lusaka area of Zambia, so as to be within striking distance of Rhodesia. ZANU and ZANLA moved their bases to Mozambique's Tete Province around 1972, and based themselves there until the war's end in 1979. ZIPRA remained based in Zambia. In line with the Maoist ideology professed by its parent organisation, ZANU, ZANLA used Chinese Maoist tactics to great effect, politicising the rural population and hiding amongst the locals between strikes. While ZIPRA conducted similar operations to a lesser extent, most of its men made up a conventional-style army in Zambia, which was trained by Cuban and Soviet officers to eventually overtly invade Rhodesia and openly engage in combat against the Rhodesian Security Forces. This ultimately never happened.

Soviet Union

Main article: Terrorism and the Soviet Union

After the Russian Revolution in 1917, the use of terrorism to subdue people characterized the new communist regime. Historian Anna Geifman stated that this was "evident in the regime's very origins." An estimated 17,000 people died as a result of the initial campaign of violence known as the Red Terror. Lenin stated that his "Jacobian party would never reject terror, nor could it do so," referring to the Jacobian Reign of Terror of 1793–1794 as a model for the Bolshevik Red Terror. Felix Dzerzhinsky, founder of the Cheka (the Soviet secret police), widely employed terrorist tactics, especially against peasants who refused to surrender their grain to the government. Upon initiating the New Economic Policy (NEP) Lenin stated, "It is a mistake to think the NEP has put an end to terrorism. We shall return to terrorism, and it will be an economic terrorism".

South Africa

During the apartheid era in South Africa, the government under the Afrikaner National Party deemed the ANC and its military wing, Umkhonto we Sizwe, communist terrorists. As a result, a series of laws were introduced by the government, such as the Suppression of Communism Act, which defined and banned organizations and people that the government considered communist. In 1967 the government promulgated the Terrorism Act, which made terrorist acts a statutory crime and implemented indefinite detention against those who were captured.

Vietnam

Main articles: Vietnam War and Viet Cong

During World War II the communist Viet Minh fought a guerilla campaign led by Ho Chi Minh against the Japanese occupation forces and, following Japan's surrender, against the French colonial forces. This insurgency continued until 1954 as the Vietminh evolved into the Vietcong (VC), which fought against both the South Vietnamese government and American forces. These campaigns involved terrorism resulting in the deaths of thousands. Although an armistice was signed between the Viet Minh and the French forces in 1954, terrorist actions continued. Carol Winkler has written that in the 1950s, Viet Cong terrorism was rife in South Vietnam, with political leaders, provincial chiefs, teachers, nurses, doctors, and members of the military being targeted. Between 1965 and 1972, Vietcong terrorists had killed over 33,000 people and abducted a further 57,000. Terrorist actions in Saigon were described by Nghia M. Vo as "long and murderous." In these campaigns, South Vietnamese prime minister Trần Văn Hương was the target of an assassination attempt; in 1964 alone, the Vietcong carried out 19,000 attacks on civilian targets.

Infant victim of Dak Son massacre

Historian and former U.S. State Department analyst Douglas Pike has called the Massacre at Huế one of the worst communist terrorist actions of the Vietnam War. Estimates of the losses in the massacre have been cited as high as 6,000 dead. The United States Army recorded as killed "3800 killed in and around Huế, 2786 confirmed civilians massacred, 2226 civilians found in mass graves and 16 non Vietnamese civilians killed." While some historians have claimed that the majority of these deaths occurred as the result of US bombing in the fight to retake the city, the vast majority of the dead were found in mass graves outside the city. Benjamin A. Valentino has estimated a total death toll of between 45,000 and 80,000 people between 1954 and 1975 from VC terrorism.

Douglas Pike also described the Đắk Sơn massacre, in which the Vietcong used flamethrowers against civilians in Đắk Sơn, killing 252, as a terrorist act. In May 1967, Tran Van-Luy reported to the World Health Organization "that over the previous 10 years Communist terrorists had destroyed 174 dispensaries, maternity homes and hospitals." Ami Pedahzur has written that "the overall volume and lethality of Vietcong terrorism rivals or exceeds all but a handful (e.g. Algeria, Sri Lanka) of terrorist campaigns waged over the last third of the twentieth century," and that the VC used suicide terrorism as a form of propaganda of the deed. Arthur J. Dommen has written that the majority of those killed due to VC terrorism were civilians, caught in ambushes as they traveled on buses, and that the group burnt down villages and forcibly conscripted members.

Paternal age effect

From Wikipedia, the free encyclopedia

The paternal age effect is the statistical relationship between the father's age at conception and biological effects on the child. Such effects can relate to birthweight, congenital disorders, life expectancy and psychological outcomes. A 2017 review found that while severe health effects are associated with higher paternal age, the total increase in problems caused by paternal age is low. Average paternal age at birth reached a low point between 1960 and 1980 in many countries and has been increasing since then, but has not reached historically unprecedented levels. The rise in paternal age is not seen as a major public health concern.

The genetic quality of sperm, as well as its volume and motility, may decrease with age, leading the population geneticist James F. Crow to claim that the "greatest mutational health hazard to the human genome is fertile older males".

The paternal age effect was first proposed implicitly by physician Wilhelm Weinberg in 1912 and explicitly by psychiatrist Lionel Penrose in 1955. DNA-based research started more recently, in 1998, in the context of paternity testing.

Health effects

Evidence for a paternal age effect has been proposed for a number of conditions, diseases and other effects. In many of these, the statistical evidence of association is weak, and the association may be related by confounding factors or behavioural differences. Conditions proposed to show correlation with paternal age include the following:

Single-gene disorders

Advanced paternal age may be associated with a higher risk for certain single-gene disorders caused by mutations of the FGFR2, FGFR3 and RET genes. These conditions are Apert syndrome, Crouzon syndrome, Pfeiffer syndrome, achondroplasia, thanatophoric dysplasia, multiple endocrine neoplasia type 2, and multiple endocrine neoplasia type 2b. The most significant effect concerns achondroplasia (a form of dwarfism), which might occur in about 1 in 1,875 children fathered by men over 50, compared to 1 in 15,000 in the general population. However, the risk for achondroplasia is still considered clinically negligible. The FGFR genes may be particularly prone to a paternal age effect due to selfish spermatogonial selection, whereby the influence of spermatogonial mutations in older men is enhanced because cells with certain mutations have a selective advantage over other cells (see § DNA mutations).

Pregnancy effects

Several studies have reported that advanced paternal age is associated with an increased risk of miscarriage. The strength of the association differs between studies. It has been suggested that these miscarriages are caused by chromosome abnormalities in the sperm of aging men. An increased risk for stillbirth has also been suggested for pregnancies fathered by men over 45.

Birth outcomes

A systematic review published in 2010 concluded that the graph of the risk of low birthweight in infants with paternal age is "saucer-shaped" (U-shaped); that is, the highest risks occur at low and at high paternal ages. Compared with a paternal age of 25–28 years as a reference group, the odds ratio for low birthweight was approximately 1.1 at a paternal age of 20 and approximately 1.2 at a paternal age of 50. There was no association of paternal age with preterm births or with small for gestational age births.

Mental illness

Schizophrenia is associated with advanced paternal age. Some studies examining autism spectrum disorder (ASD) and advanced paternal age have demonstrated an association between the two, although there also appears to be an increase with maternal age.

In one study, the risk of bipolar disorder, particularly for early-onset disease, is J-shaped, with the lowest risk for children of 20- to 24-year-old fathers, a twofold risk for younger fathers and a threefold risk for fathers >50 years old. There is no similar relationship with maternal age. A second study also found a risk of schizophrenia in both fathers above age 50 and fathers below age 25. The risk in younger fathers was noted to affect only male children.

A 2010 study found the relationship between parental age and psychotic disorders to be stronger with maternal age than paternal age.

A 2016 review concluded that the mechanism behind the reported associations was still not clear, with evidence both for selection of individuals liable to psychiatric illness into late fatherhood and evidence for causative mutations. The mechanisms under discussion are not mutually exclusive.

A 2017 review concluded that the vast majority of studies supported a relationship between older paternal age and autism and schizophrenia but that there is less convincing and also inconsistent evidence for associations with other psychiatric illnesses.

Cancers

Paternal age may be associated with an increased risk of breast cancer, but the association is weak and there are confounding effects.

According to a 2017 review, there is consistent evidence of an increase in incidence of childhood acute lymphoblastic leukemia with paternal age. Results for associations with other childhood cancers are more mixed (e.g. retinoblastoma) or generally negative.

Diabetes mellitus

High paternal age has been suggested as a risk factor for type 1 diabetes, but research findings are inconsistent, and a clear association has not been established.

Down syndrome

It appears that a paternal-age effect might exist with respect to Down syndrome, but it is very small in comparison to the maternal-age effect.

Intelligence

A review in 2005 found a U-shaped relationship between paternal age and low intelligence quotients (IQs). The highest IQ was found at paternal ages of 25–29; fathers younger than 25 and older than 29 tended to have children with lower IQs. It also found that "at least a half dozen other studies ... have demonstrated significant associations between paternal age and human intelligence." A 2009 study examined children at 8 months, 4 years and 7 years and found that higher paternal age was associated with poorer scores in almost all neurocognitive tests used but that higher maternal age was associated with better scores on the same tests; this was a reverse effect to that observed in the 2005 review, which found that maternal age began to correlate with lower intelligence at a younger age than paternal age, however two other past studies were in agreement with the 2009 study's results. An editorial accompanying the 2009 paper emphasized the importance of controlling for socioeconomic status in studies of paternal age and intelligence. A 2010 study from Spain also found an association between advanced paternal age and intellectual disability.

On the other hand, later research concluded that previously reported negative associations might be explained by confounding factors, especially parental intelligence and education. A re-analysis of the 2009 study found that the paternal age effect could be explained by adjusting for maternal education and number of siblings. A 2012 Scottish study found no significant association between paternal age and intelligence, after adjusting what was initially an inverse-U association for both parental education and socioeconomic status as well as number of siblings. A 2013 study of half a million Swedish men adjusted for genetic confounding by comparing brothers and found no association between paternal age and offspring IQ. Another study from 2014 found an initially positive association between paternal age and offspring IQ that disappeared when adjusting for parental IQs.

Life expectancy

A 2008 paper found a U-shaped association between paternal age and the overall mortality rate in children (i.e., mortality rate up to age 18). Although the relative mortality rates were higher, the absolute numbers were low, because of the relatively low occurrence of genetic abnormality. The study has been criticized for not adjusting for maternal health, which could have a large effect on child mortality. The researchers also found a correlation between paternal age and offspring death by injury or poisoning, indicating the need to control for social and behavioral confounding factors.

In 2012, a study showed that greater age at paternity tends to increase telomere length in offspring for up to two generations. Since telomere length has effects on health and mortality, this may have effects on health and the rate of aging in these offspring. The authors speculated that this effect may provide a mechanism by which populations have some plasticity in adapting longevity to different social and ecological contexts.

Associated social and genetic characteristics

Father's age versus father's risk of death
(among French population)

Father's age at birth	Risk of father's death before child's 18th birthday
20	1.5%
25	2.2%
30	3.3%
35	5.4%
40	8.3%
45	12.1%

Parents do not decide when to reproduce randomly. This implies that paternal age effects may be confounded by social and genetic predictors of reproductive timing.

A simulation study concluded that reported paternal age effects on psychiatric disorders in the epidemiological literature are too large to be explained only by mutations. They conclude that a model in which parents with a genetic liability to psychiatric illness tend to reproduce later better explains the literature.

Later age at parenthood is also associated with a more stable family environment, with older parents being less likely to divorce or change partners. Older parents also tend to occupy a higher socio-economic position and report feeling more devoted to their children and satisfied with their family. On the other hand, the risk of the father dying before the child becomes an adult increases with paternal age.

To adjust for genetic liability, some studies compare full siblings. Additionally, or alternatively, studies statistically adjust for some or all of these confounding factors. Using sibling comparisons or adjusting for more covariates frequently changes the direction or magnitude of paternal age effects. For example, one study drawing on Finnish census data concluded that increases in offspring mortality with paternal age could be explained completely by parental loss. On the other hand, a population-based cohort study drawing on 2.6 million records from Sweden found that risk of attention deficit hyperactivity disorder was only positively associated with paternal age when comparing siblings.

Mechanisms

Several hypothesized chains of causality exist whereby increased paternal age may lead to health effects. There are different types of genome mutations, with distinct mutation mechanisms:

• DNA length mutations of repetitive DNA (such as telomeres and microsatellites), caused by cellular copying errors
• DNA point mutations, caused by cellular copying errors and also by chemical and physical insults such as radiation
• chromosome breaks and rearrangements, which can occur in the resting cell
• epigenetic changes, i.e. methylation of the DNA, which can activate or silence certain genes, and is sometimes passed down from parent to child

Telomere and microsatellite length

Telomeres are repetitive genetic sequences at both ends of each chromosome that protect the structure of the chromosome. As men age, most telomeres shorten, but sperm telomeres increase in length. The offspring of older fathers have longer telomeres in both their sperm and white blood cells. A large study showed a positive paternal, but no independent maternal age effect on telomere length. Because the study used twins, it could not compare siblings who were discordant for paternal age. It found that telomere length was 70% heritable. Regarding the mutation of microsatellite DNA, also known as short tandem repeat (STR) DNA, a survey of over 12,000 paternity-tested families shows that the microsatellite DNA mutation rate in both very young teenage fathers and in middle-aged fathers is elevated, while the mother's age has no effect.

DNA point mutations

In contrast to oogenesis, the production of sperm cells is a lifelong process. Each year after puberty, spermatogonia (precursors of the spermatozoa) divide meiotically about 23 times. By the age of 40, the spermatogonia will have undergone about 660 such divisions, compared to 200 at age 20. Copying errors might sometimes happen during the DNA replication preceding these cell divisions, which may lead to new (de novo) mutations in the sperm DNA.

The selfish spermatogonial selection hypothesis proposes that the influence of spermatogonial mutations in older men is further enhanced because cells with certain mutations have a selective advantage over other cells. Such an advantage would allow the mutated cells to increase in number through clonal expansion. In particular, mutations that affect the RAS pathway, which regulates spermatogonial proliferation, appear to offer a competitive advantage to spermatogonial cells, while also leading to diseases associated with paternal age.

DNA fragmentation

During the past two decades evidence has accumulated that pregnancy loss as well as reduced rate of success with assisted reproductive technologies is linked to impaired sperm chromosome integrity and DNA fragmentation. Advanced paternal age was shown to be associated with a significant increase in DNA fragmentation in a recent systematic review (where 17 out of the 19 studies considered showed such an association).

Epigenetic changes

DNA methylation

The production of sperm cells involves DNA methylation, an epigenetic process that regulates the expression of genes. Improper genomic imprinting and other errors sometimes occur during this process, which can affect the expression of genes related to certain disorders, increasing the offspring's susceptibility. The frequency of these errors appears to increase with age. This could explain the association between paternal age and schizophrenia.; Paternal age affects offspring's behavior, possibly via an epigenetic mechanism recruiting a transcriptional repressor REST.

Semen

A 2001 review on variation in semen quality and fertility by male age concluded that older men had lower semen volume, lower sperm motility, a decreased percent of normal sperm, as well as decreased pregnancy rates, increased time to pregnancy and increased infertility at a given point in time. When controlling for the age of the female partner, comparisons between men under 30 and men over 50 found relative decreases in pregnancy rates between 23% and 38%.

A 2014 review indicated that increasing male age is associated with declines in many semen traits, including semen volume and percentage motility. However, this review also found that sperm concentration did not decline as male age increased.

X-linked effects

Some classify the paternal age effect as one of two different types. One effect is directly related to advanced paternal age and autosomal mutations in the offspring. The other effect is an indirect effect in relation to mutations on the X chromosome which are passed to daughters who are then at risk for having sons with X-linked diseases.

History

Birth defects were acknowledged in the children of older men and women even in antiquity. In book six of Plato's Republic, Socrates states that men and women should have children in the "prime of their life" which is stated to be twenty in a woman and thirty in a man. He states that in his proposed society men should be forbidden to father children in their fifties and that the offspring of such unions should be considered "the offspring of darkness and strange lust." He suggests appropriate punishments be administered to the offenders and their offspring.

In 1912, Wilhelm Weinberg, a German physician, was the first person to hypothesize that non-inherited cases of achondroplasia could be more common in last-born children than in children born earlier to the same set of parents. Weinberg "made no distinction between paternal age, maternal age and birth order" in his hypothesis. In 1953, Krooth used the term "paternal age effect" in the context of achondroplasia, but mistakenly thought the condition represented a maternal age effect. The paternal age effect for achondroplasia was described by Lionel Penrose in 1955. At a DNA level, the paternal age effect was first reported in 1998 in routine paternity tests.

Scientific interest in paternal age effects is relevant because the average paternal age increased in countries such as the United Kingdom, Australia, and Germany, and because birth rates for fathers aged 30–54 years have risen between 1980 and 2006 in the United States. Possible reasons for the increases in average paternal age include increasing life expectancy and increasing rates of divorce and remarriage. Despite recent increases in average paternal age, however, the oldest father documented in the medical literature was born in 1840: George Isaac Hughes was 94 years old at the time of the birth of his son by his second wife, a 1935 article in the Journal of the American Medical Association stated that his fertility "has been definitely and affirmatively checked up medically," and he fathered a daughter in 1936 at age 96.

Medical assessment

The American College of Medical Genetics recommends obstetric ultrasonography at 18–20 weeks gestation in cases of advanced paternal age to evaluate fetal development, but it notes that this procedure "is unlikely to detect many of the conditions of interest." They also note that there is no standard definition of advanced paternal age; it is commonly defined as age 40 or above, but the effect increases linearly with paternal age, rather than appearing at any particular age. According to a 2006 review, any adverse effects of advanced paternal age "should be weighed up against potential social advantages for children born to older fathers who are more likely to have progressed in their career and to have achieved financial security."

Geneticist James F. Crow described mutations that have a direct visible effect on the child's health and also mutations that can be latent or have minor visible effects on the child's health; many such minor or latent mutations allow the child to reproduce, but cause more serious problems for grandchildren, great-grandchildren and later generations.