Work (physics)

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Work
A baseball pitcher does positive work on the ball by applying a force to it over the distance it moves while in his grip.

In science, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force strength and the distance traveled. A force is said to do positive work if it has a component in the direction of the displacement of the point of application. A force does negative work if it has a component opposite to the direction of the displacement at the point of application of the force.

For example, when a ball is held above the ground and then dropped, the work done by the gravitational force on the ball as it falls is positive, and is equal to the weight of the ball (a force) multiplied by the distance to the ground (a displacement). If the ball is thrown upwards, the work done by the gravitational force is negative, and is equal to the weight multiplied by the displacement in the upwards direction.

Both force and displacement are vectors. The work done is given by the dot product of the two vectors, where the result is a scalar. When the force F is constant and the angle θ between the force and the displacement s is also constant, then the work done is given by: $${\displaystyle W=Fs\cos \theta }$$

If the force is variable, then work is given by the line integral:

${\displaystyle W=\int \overrightarrow{F}\cdot d\overrightarrow{s}}$

where ${\displaystyle d\overrightarrow{s}}$ is the tiny change in displacement vector.

Work is a scalar quantity, so it has only magnitude and no direction. Work transfers energy from one place to another, or one form to another. The SI unit of work is the joule (J), the same unit as for energy.

History

The ancient Greek understanding of physics was limited to the statics of simple machines (the balance of forces), and did not include dynamics or the concept of work. During the Renaissance the dynamics of the Mechanical Powers, as the simple machines were called, began to be studied from the standpoint of how far they could lift a load, in addition to the force they could apply, leading eventually to the new concept of mechanical work. The complete dynamic theory of simple machines was worked out by Italian scientist Galileo Galilei in 1600 in Le Meccaniche (On Mechanics), in which he showed the underlying mathematical similarity of the machines as force amplifiers. He was the first to explain that simple machines do not create energy, only transform it.

Early concepts of work

Although work was not formally used until 1826, similar concepts existed before then. Early names for the same concept included moment of activity, quantity of action, latent live force, dynamic effect, efficiency, and even force. In 1637, the French philosopher René Descartes wrote:

Lifting 100 lb one foot twice over is the same as lifting 200 lb one foot, or 100 lb two feet.

— René Descartes, Letter to Huygens

In 1686, the German philosopher Gottfried Leibniz wrote:

The same force ["work" in modern terms] is necessary to raise body A of 1 pound (libra) to a height of 4 yards (ulnae), as is necessary to raise body B of 4 pounds to a height of 1 yard.

— Gottfried Leibniz, Brevis demonstratio

In 1759, John Smeaton described a quantity that he called "power" "to signify the exertion of strength, gravitation, impulse, or pressure, as to produce motion." Smeaton continues that this quantity can be calculated if "the weight raised is multiplied by the height to which it can be raised in a given time," making this definition remarkably similar to Coriolis's.

Etymology

According to the 1957 physics textbook by Max Jammer, the term work was introduced in 1826 by the French mathematician Gaspard-Gustave Coriolis as "weight lifted through a height", which is based on the use of early steam engines to lift buckets of water out of flooded ore mines. According to Rene Dugas, French engineer and historian, it is to Solomon of Caux "that we owe the term work in the sense that it is used in mechanics now".

Units

The SI unit of work is the joule (J), named after English physicist James Prescott Joule (1818-1889), which is defined as the work required to exert a force of one newton through a displacement of one metre.

The dimensionally equivalent newton-metre (N⋅m) is sometimes used as the measuring unit for work, but this can be confused with the measurement unit of torque. Usage of N⋅m is discouraged by the SI authority, since it can lead to confusion as to whether the quantity expressed in newton-metres is a torque measurement, or a measurement of work.

Another unit for work is the foot-pound, which comes from the English system of measurement. As the unit name suggests, it is the product of pounds for the unit of force and feet for the unit of displacement. One joule is equivalent to 0.07376 ft-lbs.

Non-SI units of work include the newton-metre, erg, the foot-pound, the foot-poundal, the kilowatt hour, the litre-atmosphere, and the horsepower-hour. Due to work having the same physical dimension as heat, occasionally measurement units typically reserved for heat or energy content, such as therm, BTU and calorie, are used as a measuring unit.

Work and energy

The work W done by a constant force of magnitude F on a point that moves a displacement s in a straight line in the direction of the force is the product $${\displaystyle W=\overrightarrow{F}\cdot \overrightarrow{s}}$$

For example, if a force of 10 newtons (F = 10 N) acts along a point that travels 2 metres (s = 2 m), then W = Fs = (10 N) (2 m) = 20 J. This is approximately the work done lifting a 1 kg object from ground level to over a person's head against the force of gravity.

The work is doubled either by lifting twice the weight the same distance or by lifting the same weight twice the distance.

Work is closely related to energy. Energy shares the same unit of measurement with work (Joules) because the energy from the object doing work is transferred to the other objects it interacts with when work is being done. The work–energy principle states that an increase in the kinetic energy of a rigid body is caused by an equal amount of positive work done on the body by the resultant force acting on that body. Conversely, a decrease in kinetic energy is caused by an equal amount of negative work done by the resultant force. Thus, if the net work is positive, then the particle's kinetic energy increases by the amount of the work. If the net work done is negative, then the particle's kinetic energy decreases by the amount of work.

From Newton's second law, it can be shown that work on a free (no fields), rigid (no internal degrees of freedom) body, is equal to the change in kinetic energy E_k corresponding to the linear velocity and angular velocity of that body, $${\displaystyle W=\mathrm{\Delta }{E}_{\text{k}}.}$$ The work of forces generated by a potential function is known as potential energy and the forces are said to be conservative. Therefore, work on an object that is merely displaced in a conservative force field, without change in velocity or rotation, is equal to minus the change of potential energy E_p of the object, $${\displaystyle W=-\mathrm{\Delta }{E}_{\text{p}}.}$$ These formulas show that work is the energy associated with the action of a force, so work subsequently possesses the physical dimensions, and units, of energy. The work/energy principles discussed here are identical to electric work/energy principles.

Constraint forces

Constraint forces determine the object's displacement in the system, limiting it within a range. For example, in the case of a slope plus gravity, the object is stuck to the slope and, when attached to a taut string, it cannot move in an outwards direction to make the string any 'tauter'. It eliminates all displacements in that direction, that is, the velocity in the direction of the constraint is limited to 0, so that the constraint forces do not perform work on the system.

For a mechanical system, constraint forces eliminate movement in directions that characterize the constraint. Thus the virtual work done by the forces of constraint is zero, a result which is only true if friction forces are excluded.

Fixed, frictionless constraint forces do not perform work on the system, as the angle between the motion and the constraint forces is always 90°. Examples of workless constraints are: rigid interconnections between particles, sliding motion on a frictionless surface, and rolling contact without slipping.

For example, in a pulley system like the Atwood machine, the internal forces on the rope and at the supporting pulley do no work on the system. Therefore, work need only be computed for the gravitational forces acting on the bodies. Another example is the centripetal force exerted inwards by a string on a ball in uniform circular motion sideways constrains the ball to circular motion restricting its movement away from the centre of the circle. This force does zero work because it is perpendicular to the velocity of the ball.

The magnetic force on a charged particle is F = qv × B, where q is the charge, v is the velocity of the particle, and B is the magnetic field. The result of a cross product is always perpendicular to both of the original vectors, so F ⊥ v. The dot product of two perpendicular vectors is always zero, so the work W = F ⋅ v = 0, and the magnetic force does not do work. It can change the direction of motion but never change the speed.

Mathematical calculation

For moving objects, the quantity of work/time (power) is integrated along the trajectory of the point of application of the force. Thus, at any instant, the rate of the work done by a force (measured in joules/second, or watts) is the scalar product of the force (a vector), and the velocity vector of the point of application. This scalar product of force and velocity is known as instantaneous power. Just as velocities may be integrated over time to obtain a total distance, by the fundamental theorem of calculus, the total work along a path is similarly the time-integral of instantaneous power applied along the trajectory of the point of application.

Work is the result of a force on a point that follows a curve X, with a velocity v, at each instant. The small amount of work δW that occurs over an instant of time dt is calculated as $${\displaystyle \delta W=\mathbf{F}\cdot d\mathbf{s}=\mathbf{F}\cdot \mathbf{v}dt}$$ where the F ⋅ v is the power over the instant dt. The sum of these small amounts of work over the trajectory of the point yields the work, $${\displaystyle W={\int }_{t_1}^{t_2}\mathbf{F}\cdot \mathbf{v}dt={\int }_{t_1}^{t_2}\mathbf{F}\cdot \frac{d\mathbf{s}}{dt}dt={\int }_C\mathbf{F}\cdot d\mathbf{s},}$$ where C is the trajectory from x(t₁) to x(t₂). This integral is computed along the trajectory of the particle, and is therefore said to be path dependent.

If the force is always directed along this line, and the magnitude of the force is F, then this integral simplifies to $${\displaystyle W={\int }_{C}Fds}$$ where s is displacement along the line. If F is constant, in addition to being directed along the line, then the integral simplifies further to $${\displaystyle W={\int }_{C}Fds=F{\int }_{C}ds=Fs}$$ where s is the displacement of the point along the line.

This calculation can be generalized for a constant force that is not directed along the line, followed by the particle. In this case the dot product F ⋅ ds = F cos θ ds, where θ is the angle between the force vector and the direction of movement, that is $${\displaystyle W={\int }_C\mathbf{F}\cdot d\mathbf{s}=Fs\cos \theta .}$$

When a force component is perpendicular to the displacement of the object (such as when a body moves in a circular path under a central force), no work is done, since the cosine of 90° is zero. Thus, no work can be performed by gravity on a planet with a circular orbit (this is ideal, as all orbits are slightly elliptical). Also, no work is done on a body moving circularly at a constant speed while constrained by mechanical force, such as moving at constant speed in a frictionless ideal centrifuge.

Work done by a variable force

Calculating the work as "force times straight path segment" would only apply in the most simple of circumstances, as noted above. If force is changing, or if the body is moving along a curved path, possibly rotating and not necessarily rigid, then only the path of the application point of the force is relevant for the work done, and only the component of the force parallel to the application point velocity is doing work (positive work when in the same direction, and negative when in the opposite direction of the velocity). This component of force can be described by the scalar quantity called scalar tangential component (F cos(θ), where θ is the angle between the force and the velocity). And then the most general definition of work can be formulated as follows:

Area under the curve gives work done by F(x).

Work done by a variable force is the line integral of its scalar tangential component along the path of its application point.

If the force varies (e.g. compressing a spring) we need to use calculus to find the work done. If the force as a variable of x is given by F(x), then the work done by the force along the x-axis from x₁ to x₂ is:

$${\displaystyle W=\underset{\mathrm{\Delta }\mathbf{x}\to 0}{lim}\sum _{x_1}^{x_2}\mathbf{F}\mathbf{(}\mathbf{x}\mathbf{)}\mathrm{\Delta }\mathbf{x}={\int }_{x_1}^{x_2}\mathbf{F}\mathbf{(}\mathbf{x}\mathbf{)}d\mathbf{x}.}$$

Thus, the work done for a variable force can be expressed as a definite integral of force over displacement.

If the displacement as a variable of time is given by ∆x(t), then work done by the variable force from t₁ to t₂ is:

$${\displaystyle W={\int }_{t_1}^{t_2}\mathbf{F}(t)\cdot \mathbf{v}(t)dt={\int }_{t_1}^{t_2}P(t)dt.}$$

Thus, the work done for a variable force can be expressed as a definite integral of power over time.

Torque and rotation

A force couple results from equal and opposite forces, acting on two different points of a rigid body. The sum (resultant) of these forces may cancel, but their effect on the body is the couple or torque T. The work of the torque is calculated as $${\displaystyle \delta W=\mathbf{T}\cdot \mathit{\omega }dt,}$$ where the T ⋅ ω is the power over the instant dt. The sum of these small amounts of work over the trajectory of the rigid body yields the work, $${\displaystyle W={\int }_{t_1}^{t_2}\mathbf{T}\cdot \mathit{\omega }dt.}$$ This integral is computed along the trajectory of the rigid body with an angular velocity ω that varies with time, and is therefore said to be path dependent.

If the angular velocity vector maintains a constant direction, then it takes the form, $${\displaystyle \mathit{\omega }=\dot{\varphi }\mathbf{S},}$$ where ${\displaystyle \varphi }$ is the angle of rotation about the constant unit vector S. In this case, the work of the torque becomes, $${\displaystyle W={\int }_{t_1}^{t_2}\mathbf{T}\cdot \mathit{\omega }dt={\int }_{t_1}^{t_2}\mathbf{T}\cdot \mathbf{S}\frac{d\varphi }{dt}dt={\int }_C\mathbf{T}\cdot \mathbf{S}d\varphi ,}$$ where C is the trajectory from ${\displaystyle \varphi (t_1)}$ to ${\displaystyle \varphi (t_2)}$. This integral depends on the rotational trajectory ${\displaystyle \varphi (t)}$, and is therefore path-dependent.

If the torque ${\displaystyle \tau }$ is aligned with the angular velocity vector so that, $${\displaystyle \mathbf{T}=\tau \mathbf{S},}$$ and both the torque and angular velocity are constant, then the work takes the form, $${\displaystyle W={\int }_{t_1}^{t_2}\tau \dot{\varphi }dt=\tau ({\varphi }_2-{\varphi }_1).}$$

A force of constant magnitude and perpendicular to the lever arm

This result can be understood more simply by considering the torque as arising from a force of constant magnitude F, being applied perpendicularly to a lever arm at a distance ${\displaystyle r}$, as shown in the figure. This force will act through the distance along the circular arc ${\displaystyle l=s=r\varphi }$, so the work done is $${\displaystyle W=Fs=Fr\varphi .}$$ Introduce the torque τ = Fr, to obtain $${\displaystyle W=Fr\varphi =\tau \varphi ,}$$ as presented above.

Notice that only the component of torque in the direction of the angular velocity vector contributes to the work.

Work and potential energy

The scalar product of a force F and the velocity v of its point of application defines the power input to a system at an instant of time. Integration of this power over the trajectory of the point of application, C = x(t), defines the work input to the system by the force.

Path dependence

Therefore, the work done by a force F on an object that travels along a curve C is given by the line integral: $${\displaystyle W={\int }_C\mathbf{F}\cdot d\mathbf{x}={\int }_{t_1}^{t_2}\mathbf{F}\cdot \mathbf{v}dt,}$$ where dx(t) defines the trajectory C and v is the velocity along this trajectory. In general this integral requires that the path along which the velocity is defined, so the evaluation of work is said to be path dependent.

The time derivative of the integral for work yields the instantaneous power, $${\displaystyle \frac{dW}{dt}=P(t)=\mathbf{F}\cdot \mathbf{v}.}$$

Path independence

If the work for an applied force is independent of the path, then the work done by the force, by the gradient theorem, defines a potential function which is evaluated at the start and end of the trajectory of the point of application. This means that there is a potential function U(x), that can be evaluated at the two points x(t₁) and x(t₂) to obtain the work over any trajectory between these two points. It is tradition to define this function with a negative sign so that positive work is a reduction in the potential, that is $${\displaystyle W={\int }_C\mathbf{F}\cdot d\mathbf{x}={\int }_{\mathbf{x}(t_1)}^{\mathbf{x}(t_2)}\mathbf{F}\cdot d\mathbf{x}=U(\mathbf{x}(t_1))-U(\mathbf{x}(t_2)).}$$

The function U(x) is called the potential energy associated with the applied force. The force derived from such a potential function is said to be conservative. Examples of forces that have potential energies are gravity and spring forces.

In this case, the gradient of work yields $${\displaystyle \mathrm{\nabla }W=-\mathrm{\nabla }U=-\left(\frac{\mathrm{\partial }U}{\mathrm{\partial }x},\frac{\mathrm{\partial }U}{\mathrm{\partial }y},\frac{\mathrm{\partial }U}{\mathrm{\partial }z}\right)=\mathbf{F},}$$ and the force F is said to be "derivable from a potential."

Because the potential U defines a force F at every point x in space, the set of forces is called a force field. The power applied to a body by a force field is obtained from the gradient of the work, or potential, in the direction of the velocity V of the body, that is $${\displaystyle P(t)=-\mathrm{\nabla }U\cdot \mathbf{v}=\mathbf{F}\cdot \mathbf{v}.}$$

Work by gravity

Gravity F = mg does work W = mgh along any descending path

In the absence of other forces, gravity results in a constant downward acceleration of every freely moving object. Near Earth's surface the acceleration due to gravity is g = 9.8 m⋅s⁻² and the gravitational force on an object of mass m is F_g = mg. It is convenient to imagine this gravitational force concentrated at the center of mass of the object.

If an object with weight mg is displaced upwards or downwards a vertical distance y₂ − y₁, the work W done on the object is: $${\displaystyle W=F_g(y_2-y_1)=F_g\mathrm{\Delta }y=mg\mathrm{\Delta }y}$$ where F_g is weight (pounds in imperial units, and newtons in SI units), and Δy is the change in height y. Notice that the work done by gravity depends only on the vertical movement of the object. The presence of friction does not affect the work done on the object by its weight.

In space

The force of gravity exerted by a mass M on another mass m is given by $${\displaystyle \mathbf{F}=-\frac{GMm}{r^2}\hat{\mathbf{r}}=-\frac{GMm}{r^3}\mathbf{r},}$$ where r is the position vector from M to m and r̂ is the unit vector in the direction of r.

Let the mass m move at the velocity v; then the work of gravity on this mass as it moves from position r(t₁) to r(t₂) is given by $${\displaystyle W=-{\int }_{\mathbf{r}(t_1)}^{\mathbf{r}(t_2)}\frac{GMm}{r^3}\mathbf{r}\cdot d\mathbf{r}=-{\int }_{t_1}^{t_2}\frac{GMm}{r^3}\mathbf{r}\cdot \mathbf{v}dt.}$$ Notice that the position and velocity of the mass m are given by $${\displaystyle \mathbf{r}=r{\mathbf{e}}_r,\mathbf{v}=\frac{d\mathbf{r}}{dt}=\dot{r}{\mathbf{e}}_r+r\dot{\theta }{\mathbf{e}}_t,}$$ where e_r and e_t are the radial and tangential unit vectors directed relative to the vector from M to m, and we use the fact that ${\displaystyle d{\mathbf{e}}_r/dt=\dot{\theta }{\mathbf{e}}_t.}$ Use this to simplify the formula for work of gravity to, $${\displaystyle W=-{\int }_{t_1}^{t_2}\frac{GmM}{r^3}(r{\mathbf{e}}_r)\cdot \left(\dot{r}{\mathbf{e}}_r+r\dot{\theta }{\mathbf{e}}_t\right)dt=-{\int }_{t_1}^{t_2}\frac{GmM}{r^3}r\dot{r}dt=\frac{GMm}{r(t_2)}-\frac{GMm}{r(t_1)}.}$$ This calculation uses the fact that $${\displaystyle \frac{d}{dt}{r}^{-1}=-r^{-2}\dot{r}=-\frac{\dot{r}}{r^2}.}$$ The function $${\displaystyle U=-\frac{GMm}{r},}$$ is the gravitational potential function, also known as gravitational potential energy. The negative sign follows the convention that work is gained from a loss of potential energy.

Work by a spring

Forces in springs assembled in parallel

Consider a spring that exerts a horizontal force F = (−kx, 0, 0) that is proportional to its deflection in the x direction independent of how a body moves. The work of this spring on a body moving along the space with the curve X(t) = (x(t), y(t), z(t)), is calculated using its velocity, v = (v_x, v_y, v_z), to obtain $${\displaystyle W={\int }_0^t\mathbf{F}\cdot \mathbf{v}dt=-{\int }_0^{t}kx{v}_{x}dt=-\frac{1}{2}k{x}^2.}$$ For convenience, consider contact with the spring occurs at t = 0, then the integral of the product of the distance x and the x-velocity, xv_xdt, over time t is ⁠1/2⁠x². The work is the product of the distance times the spring force, which is also dependent on distance; hence the x² result.

Work by a gas

The work ${\displaystyle W}$ done by a body of gas on its surroundings is: $${\displaystyle W={\int }_a^{b}PdV}$$ where P is pressure, V is volume, and a and b are initial and final volumes.

Work–energy principle

The principle of work and kinetic energy (also known as the work–energy principle) states that the work done by all forces acting on a particle (the work of the resultant force) equals the change in the kinetic energy of the particle. That is, the work W done by the resultant force on a particle equals the change in the particle's kinetic energy ${\displaystyle E_{\text{k}}}$, $${\displaystyle W=\mathrm{\Delta }{E}_{\text{k}}=\frac{1}{2}m{v}_2^2-\frac{1}{2}m{v}_1^2}$$ where ${\displaystyle v_1}$ and ${\displaystyle v_2}$ are the speeds of the particle before and after the work is done, and m is its mass.

The derivation of the work–energy principle begins with Newton's second law of motion and the resultant force on a particle. Computation of the scalar product of the force with the velocity of the particle evaluates the instantaneous power added to the system. (Constraints define the direction of movement of the particle by ensuring there is no component of velocity in the direction of the constraint force. This also means the constraint forces do not add to the instantaneous power.) The time integral of this scalar equation yields work from the instantaneous power, and kinetic energy from the scalar product of acceleration with velocity. The fact that the work–energy principle eliminates the constraint forces underlies Lagrangian mechanics.

This section focuses on the work–energy principle as it applies to particle dynamics. In more general systems work can change the potential energy of a mechanical device, the thermal energy in a thermal system, or the electrical energy in an electrical device. Work transfers energy from one place to another or one form to another.

Derivation for a particle moving along a straight line

In the case the resultant force F is constant in both magnitude and direction, and parallel to the velocity of the particle, the particle is moving with constant acceleration a along a straight line. The relation between the net force and the acceleration is given by the equation F = ma (Newton's second law), and the particle displacement s can be expressed by the equation $${\displaystyle s=\frac{v_2^2-v_1^2}{2a}}$$ which follows from ${\displaystyle v_2^2=v_1^2+2as}$ (see Equations of motion).

The work of the net force is calculated as the product of its magnitude and the particle displacement. Substituting the above equations, one obtains: $${\displaystyle W=Fs=mas=ma\frac{v_2^2-v_1^2}{2a}=\frac{1}{2}m{v}_2^2-\frac{1}{2}m{v}_1^2=\mathrm{\Delta }{E}_{\text{k}}}$$

Other derivation: $${\displaystyle W=Fs=mas=m\frac{v_2^2-v_1^2}{2s}s=\frac{1}{2}m{v}_2^2-\frac{1}{2}m{v}_1^2=\mathrm{\Delta }{E}_{\text{k}}}$$

In the general case of rectilinear motion, when the net force F is not constant in magnitude, but is constant in direction, and parallel to the velocity of the particle, the work must be integrated along the path of the particle: $${\displaystyle W={\int }_{t_1}^{t_2}\mathbf{F}\cdot \mathbf{v}dt={\int }_{t_1}^{t_2}Fvdt={\int }_{t_1}^{t_2}mavdt=m{\int }_{t_1}^{t_2}v\frac{dv}{dt}dt=m{\int }_{v_1}^{v_2}vdv=\frac{1}{2}m\left(v_2^2-v_1^2\right).}$$

General derivation of the work–energy principle for a particle

For any net force acting on a particle moving along any curvilinear path, it can be demonstrated that its work equals the change in the kinetic energy of the particle by a simple derivation analogous to the equation above. It is known as the work–energy principle: $${\displaystyle W={\int }_{t_1}^{t_2}\mathbf{F}\cdot \mathbf{v}dt=m{\int }_{t_1}^{t_2}\mathbf{a}\cdot \mathbf{v}dt=\frac{m}{2}{\int }_{t_1}^{t_2}\frac{d{v}^2}{dt}dt=\frac{m}{2}{\int }_{v_1^2}^{v_2^2}d{v}^2=\frac{m{v}_2^2}{2}-\frac{m{v}_1^2}{2}=\mathrm{\Delta }{E}_{\text{k}}}$$

The identity $\mathbf{a}\cdot \mathbf{v}=\frac{1}{2}\frac{d{v}^2}{dt}$ requires some algebra. From the identity $v^2=\mathbf{v}\cdot \mathbf{v}$ and definition $\mathbf{a}=\frac{d\mathbf{v}}{dt}$ it follows $${\displaystyle \frac{d{v}^2}{dt}=\frac{d(\mathbf{v}\cdot \mathbf{v})}{dt}=\frac{d\mathbf{v}}{dt}\cdot \mathbf{v}+\mathbf{v}\cdot \frac{d\mathbf{v}}{dt}=2\frac{d\mathbf{v}}{dt}\cdot \mathbf{v}=2\mathbf{a}\cdot \mathbf{v}.}$$

The remaining part of the above derivation is just simple calculus, same as in the preceding rectilinear case.

Derivation for a particle in constrained movement

In particle dynamics, a formula equating work applied to a system to its change in kinetic energy is obtained as a first integral of Newton's second law of motion. It is useful to notice that the resultant force used in Newton's laws can be separated into forces that are applied to the particle and forces imposed by constraints on the movement of the particle. Remarkably, the work of a constraint force is zero, therefore only the work of the applied forces need be considered in the work–energy principle.

To see this, consider a particle P that follows the trajectory X(t) with a force F acting on it. Isolate the particle from its environment to expose constraint forces R, then Newton's Law takes the form $${\displaystyle \mathbf{F}+\mathbf{R}=m\ddot{\mathbf{X}},}$$ where m is the mass of the particle.

Vector formulation

Note that n dots above a vector indicates its nth time derivative. The scalar product of each side of Newton's law with the velocity vector yields $${\displaystyle \mathbf{F}\cdot \dot{\mathbf{X}}=m\ddot{\mathbf{X}}\cdot \dot{\mathbf{X}},}$$ because the constraint forces are perpendicular to the particle velocity. Integrate this equation along its trajectory from the point X(t₁) to the point X(t₂) to obtain $${\displaystyle {\int }_{t_1}^{t_2}\mathbf{F}\cdot \dot{\mathbf{X}}dt=m{\int }_{t_1}^{t_2}\ddot{\mathbf{X}}\cdot \dot{\mathbf{X}}dt.}$$

The left side of this equation is the work of the applied force as it acts on the particle along the trajectory from time t₁ to time t₂. This can also be written as $${\displaystyle W={\int }_{t_1}^{t_2}\mathbf{F}\cdot \dot{\mathbf{X}}dt={\int }_{\mathbf{X}(t_1)}^{\mathbf{X}(t_2)}\mathbf{F}\cdot d\mathbf{X}.}$$ This integral is computed along the trajectory X(t) of the particle and is therefore path dependent.

The right side of the first integral of Newton's equations can be simplified using the following identity $${\displaystyle \frac{1}{2}\frac{d}{dt}(\dot{\mathbf{X}}\cdot \dot{\mathbf{X}})=\ddot{\mathbf{X}}\cdot \dot{\mathbf{X}},}$$ (see product rule for derivation). Now it is integrated explicitly to obtain the change in kinetic energy, $${\displaystyle \mathrm{\Delta }K=m{\int }_{t_1}^{t_2}\ddot{\mathbf{X}}\cdot \dot{\mathbf{X}}dt=\frac{m}{2}{\int }_{t_1}^{t_2}\frac{d}{dt}(\dot{\mathbf{X}}\cdot \dot{\mathbf{X}})dt=\frac{m}{2}\dot{\mathbf{X}}\cdot \dot{\mathbf{X}}(t_2)-\frac{m}{2}\dot{\mathbf{X}}\cdot \dot{\mathbf{X}}(t_1)=\frac{1}{2}m\mathrm{\Delta }{\mathbf{v}}^2,}$$ where the kinetic energy of the particle is defined by the scalar quantity, $${\displaystyle K=\frac{m}{2}\dot{\mathbf{X}}\cdot \dot{\mathbf{X}}=\frac{1}{2}m{\mathbf{v}}^2}$$

Tangential and normal components

It is useful to resolve the velocity and acceleration vectors into tangential and normal components along the trajectory X(t), such that $${\displaystyle \dot{\mathbf{X}}=v\mathbf{T}\text{and}\ddot{\mathbf{X}}=\dot{v}\mathbf{T}+v^2\kappa \mathbf{N},}$$ where $${\displaystyle v=|\dot{\mathbf{X}}|=\sqrt{\dot{\mathbf{X}}\cdot \dot{\mathbf{X}}}.}$$ Then, the scalar product of velocity with acceleration in Newton's second law takes the form $${\displaystyle \mathrm{\Delta }K=m{\int }_{t_1}^{t_2}\dot{v}vdt=\frac{m}{2}{\int }_{t_1}^{t_2}\frac{d}{dt}{v}^{2}dt=\frac{m}{2}{v}^2(t_2)-\frac{m}{2}{v}^2(t_1),}$$ where the kinetic energy of the particle is defined by the scalar quantity, $${\displaystyle K=\frac{m}{2}{v}^2=\frac{m}{2}\dot{\mathbf{X}}\cdot \dot{\mathbf{X}}.}$$

The result is the work–energy principle for particle dynamics, $${\displaystyle W=\mathrm{\Delta }K.}$$ This derivation can be generalized to arbitrary rigid body systems.

Moving in a straight line (skid to a stop)

Consider the case of a vehicle moving along a straight horizontal trajectory under the action of a driving force and gravity that sum to F. The constraint forces between the vehicle and the road define R, and we have $${\displaystyle \mathbf{F}+\mathbf{R}=m\ddot{\mathbf{X}}.}$$ For convenience let the trajectory be along the X-axis, so X = (d, 0) and the velocity is V = (v, 0), then R ⋅ V = 0, and F ⋅ V = F_xv, where F_x is the component of F along the X-axis, so $${\displaystyle F_{x}v=m\dot{v}v.}$$ Integration of both sides yields $${\displaystyle {\int }_{t_1}^{t_2}{F}_{x}vdt=\frac{m}{2}{v}^2(t_2)-\frac{m}{2}{v}^2(t_1).}$$ If F_x is constant along the trajectory, then the integral of velocity is distance, so $${\displaystyle F_x(d(t_2)-d(t_1))=\frac{m}{2}{v}^2(t_2)-\frac{m}{2}{v}^2(t_1).}$$

As an example consider a car skidding to a stop, where k is the coefficient of friction and W is the weight of the car. Then the force along the trajectory is F_x = −kW. The velocity v of the car can be determined from the length s of the skid using the work–energy principle, $${\displaystyle kWs=\frac{W}{2g}{v}^2,\text{or}v=\sqrt{2ksg}.}$$ This formula uses the fact that the mass of the vehicle is m = W/g.

Lotus type 119B gravity racer at Lotus 60th celebration

Gravity racing championship in Campos Novos, Santa Catarina, Brazil, 8 September 2010

Coasting down an inclined surface (gravity racing)

Consider the case of a vehicle that starts at rest and coasts down an inclined surface (such as mountain road), the work–energy principle helps compute the minimum distance that the vehicle travels to reach a velocity V, of say 60 mph (88 fps). Rolling resistance and air drag will slow the vehicle down so the actual distance will be greater than if these forces are neglected.

Let the trajectory of the vehicle following the road be X(t) which is a curve in three-dimensional space. The force acting on the vehicle that pushes it down the road is the constant force of gravity F = (0, 0, W), while the force of the road on the vehicle is the constraint force R. Newton's second law yields, $${\displaystyle \mathbf{F}+\mathbf{R}=m\ddot{\mathbf{X}}.}$$ The scalar product of this equation with the velocity, V = (v_x, v_y, v_z), yields $${\displaystyle W{v}_z=m\dot{V}V,}$$ where V is the magnitude of V. The constraint forces between the vehicle and the road cancel from this equation because R ⋅ V = 0, which means they do no work. Integrate both sides to obtain $${\displaystyle {\int }_{t_1}^{t_2}W{v}_{z}dt=\frac{m}{2}{V}^2(t_2)-\frac{m}{2}{V}^2(t_1).}$$ The weight force W is constant along the trajectory and the integral of the vertical velocity is the vertical distance, therefore, $${\displaystyle W\mathrm{\Delta }z=\frac{m}{2}{V}^2.}$$ Recall that V(t₁)=0. Notice that this result does not depend on the shape of the road followed by the vehicle.

In order to determine the distance along the road assume the downgrade is 6%, which is a steep road. This means the altitude decreases 6 feet for every 100 feet traveled—for angles this small the sin and tan functions are approximately equal. Therefore, the distance s in feet down a 6% grade to reach the velocity V is at least $${\displaystyle s=\frac{\mathrm{\Delta }z}{0.06}=8.3\frac{V^2}{g},\text{or}s=8.3\frac{{88}^2}{32.2}\approx 2000\mathrm{f}\mathrm{t}.}$$ This formula uses the fact that the weight of the vehicle is W = mg.

Work of forces acting on a rigid body

The work of forces acting at various points on a single rigid body can be calculated from the work of a resultant force and torque. To see this, let the forces F₁, F₂, ..., F_n act on the points X₁, X₂, ..., X_n in a rigid body.

The trajectories of X_i, i = 1, ..., n are defined by the movement of the rigid body. This movement is given by the set of rotations [A(t)] and the trajectory d(t) of a reference point in the body. Let the coordinates x_i i = 1, ..., n define these points in the moving rigid body's reference frame M, so that the trajectories traced in the fixed frame F are given by $${\displaystyle {\mathbf{X}}_i(t)=[A(t)]{\mathbf{x}}_i+\mathbf{d}(t)i=1,\dots ,n.}$$

The velocity of the points X_i along their trajectories are $${\displaystyle {\mathbf{V}}_i=\mathit{\omega }\times ({\mathbf{X}}_i-\mathbf{d})+\dot{\mathbf{d}},}$$ where ω is the angular velocity vector obtained from the skew symmetric matrix $${\displaystyle [\mathrm{\Omega }]=\dot{A}{A}^{\mathsf{T}},}$$ known as the angular velocity matrix.

The small amount of work by the forces over the small displacements δr_i can be determined by approximating the displacement by δr = vδt so $${\displaystyle \delta W={\mathbf{F}}_1\cdot {\mathbf{V}}_1\delta t+{\mathbf{F}}_2\cdot {\mathbf{V}}_2\delta t+\dots +{\mathbf{F}}_n\cdot {\mathbf{V}}_n\delta t}$$ or $${\displaystyle \delta W=\sum _{i=1}^n{\mathbf{F}}_i\cdot (\mathit{\omega }\times ({\mathbf{X}}_i-\mathbf{d})+\dot{\mathbf{d}})\delta t.}$$

This formula can be rewritten to obtain $${\displaystyle \delta W=\left(\sum _{i=1}^n{\mathbf{F}}_i\right)\cdot \dot{\mathbf{d}}\delta t+\left(\sum _{i=1}^n\left({\mathbf{X}}_i-\mathbf{d}\right)\times {\mathbf{F}}_i\right)\cdot \mathit{\omega }\delta t=\left(\mathbf{F}\cdot \dot{\mathbf{d}}+\mathbf{T}\cdot \mathit{\omega }\right)\delta t,}$$ where F and T are the resultant force and torque applied at the reference point d of the moving frame M in the rigid body.

New Atheism

From Wikipedia, the free encyclopedia

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

The term New Atheism describes the positions of some atheist academics, writers, scientists, and philosophers of the 20th and 21st centuries. New Atheism advocates the view that superstition, religion, and irrationalism should not be tolerated. Instead, they advocate the antitheist view that the various forms of theism should be criticised, countered, examined, and challenged by rational argument, especially when they exert strong influence on the broader society, such as in government, education, and politics. Critics have characterised New Atheism as "secular fundamentalism" or "fundamentalist atheism". Major figures of New Atheism include Richard Dawkins, Sam Harris, Christopher Hitchens, and Daniel Dennett, collectively referred to as the "Four Horsemen" of the movement.

History

The secular humanist Paul Kurtz (1925–2012), founder of the Center for Inquiry, is often regarded as a forerunner to the New Atheism movement. The 2004 publication of The End of Faith: Religion, Terror, and the Future of Reason by Sam Harris, a bestseller in the United States, was joined over the next couple years by a series of popular best-sellers by atheist authors. Harris was motivated by the events of 11 September 2001, for which he blamed Islam, while also directly criticizing Christianity and Judaism. Two years later, Harris followed up with Letter to a Christian Nation, which was a severe criticism of Christianity. Also in 2006, following his television documentary series The Root of All Evil?, Richard Dawkins published The God Delusion, which was on the New York Times best-seller list for 51 weeks.

In 2010, Tom Flynn (1955–2021), then editor of Free Inquiry, stated that the only thing new about "New Atheism" was the wider publication of atheist material by big-name publishers, books that appeared on bestseller lists and were read by millions. Mitchell Landsberg, covering a gathering held by the Council for Secular Humanism in 2010, said that religious skeptics in attendance were at odds between "new atheists" who preferred to "encourage open confrontation with the devout" and "accommodationists" who preferred "a subtler, more tactical approach." Kurtz was ousted from the Center for Inquiry in the late 2000's. This was in part due to a perception that Kurtz was "on the mellower end of the spectrum" according to Flynn.

In November 2015, The New Republic published an article entitled "Is the New Atheism dead?" In 2016, the atheist and evolutionary biologist David Sloan Wilson wrote: "The world appears to be tiring of the New Atheism movement." In 2017, PZ Myers, who formerly considered himself a new atheist, publicly renounced the New Atheism movement. The book The Four Horsemen: The Conversation That Sparked an Atheist Revolution was released in 2019.

Legacy

In a January 2019 retrospective article, Steven Poole of The Guardian observed: "For some, New Atheism was never about God at all, but just a topical subgenre of the rightwing backlash against the supposedly suffocating atmosphere of 'political correctness'." In November 2019, Scott Alexander argued that New Atheism did not disappear as a political movement but instead turned to social justice as a new cause to fight for.

In an April 2021 interview, Natalie Wynn, a left-wing YouTuber who runs the channel ContraPoints, commented: "The alt-right, the manosphere, incels, even the so-called SJW Internet and LeftTube all have a genetic ancestor in New Atheism." In a June 2021 retrospective article, Émile P. Torres of Salon argued that prominent figures in the New Atheist movement had aligned themselves with the far-right.

In a June 2022 retrospective article, Sebastian Milbank of The Critic stated that, as a movement, "New Atheism has fractured and lost its original spirit", that "much of what New Atheism embodied has now migrated rightwards", and that "another portion has moved leftwards, embodied by the 'I Fucking Love Science' woke nerd of today." Following the conversion of writer Ayaan Hirsi Ali to Christianity in 2023, the columnist Sarah Jones wrote in New York magazine that the New Atheism movement was in "terminal decline".

Prominent figures

Key figures associated with New Atheism include Richard Dawkins, Sam Harris, Christopher Hitchens, Daniel Dennett, and Ayaan Hirsi Ali.

"Four Horsemen"

The "Four Horsemen of the New Atheism": Richard Dawkins (b. 1941), Christopher Hitchens (1949–2011), Daniel Dennett (1942–2024), and Sam Harris (b. 1967).

On 30 September 2007, Dawkins, Harris, Hitchens, and Dennett met at Hitchens' residence in Washington, D.C., for a private two-hour unmoderated round table discussion. The event was videotaped and titled "The Four Horsemen". During "The God Debate" in 2010 with Hitchens versus Dinesh D'Souza, the group was collectively referred to as the "Four Horsemen of the Non-Apocalypse", an allusion to the biblical Four Horsemen of the Apocalypse from the Book of Revelation. The four have been described by critics as "evangelical atheists".

Harris wrote several bestselling non-fiction books including The End of Faith, Letter to a Christian Nation, The Moral Landscape, and Waking Up, along with two shorter works (initially published as e-books) Free Will and Lying. Dawkins, the author of The God Delusion, and director of a Channel 4 television documentary titled The Root of All Evil?, is the founder of the Richard Dawkins Foundation for Reason and Science. He wrote: "I don't object to the horseman label, by the way. I'm less keen on 'new atheist': it isn't clear to me how we differ from old atheists."

Hitchens, the author of God Is Not Great, was named among the "Top 100 Public Intellectuals" by Foreign Policy and Prospect magazines. He served on the advisory board of the Secular Coalition for America. In 2010, Hitchens published his memoir Hitch-22 (a nickname provided by close personal friend Salman Rushdie, whom Hitchens always supported during and following The Satanic Verses controversy). Shortly after its publication, he was diagnosed with esophageal cancer, which led to his death in December 2011. Before his death, Hitchens published a collection of essays and articles in his book Arguably; a short edition, Mortality, was published posthumously in 2012. These publications and numerous public appearances provided Hitchens with a platform to remain an astute atheist during his illness, even speaking specifically on the culture of deathbed conversions and condemning attempts to convert the terminally ill, which he opposed as "bad taste".

Dennett was the author of Darwin's Dangerous Idea and Breaking the Spell. He had been a vocal supporter of The Clergy Project, an organization that provides support for clergy in the US who no longer believe in God and cannot fully participate in their communities any longer. He was also a member of the Secular Coalition for America advisory board, and a member of the Committee for Skeptical Inquiry, as well as an outspoken supporter of the Brights movement. He did research into clerics who are secretly atheists and how they rationalize their works. He found what he called a "don't ask, don't tell" conspiracy because believers did not want to hear of loss of faith. This made unbelieving preachers feel isolated, but they did not want to lose their jobs and church-supplied lodgings. Generally, they consoled themselves with the belief that they were doing good in their pastoral roles by providing comfort and required ritual. The research, with Linda LaScola, was further extended to include other denominations and non-Christian clerics. The research and stories Dennett and LaScola accumulated during this project were published in their 2013 co-authored book, Caught in the Pulpit: Leaving Belief Behind.

"Plus one horse-woman"

Main article: Ayaan Hirsi Ali

Ayaan Hirsi Ali (born 1969)

Ayaan Hirsi Ali was a central figure of New Atheism until she announced her conversion to Christianity in November 2023. Hirsi Ali, originally scheduled to attend the 2007 meeting, later appeared with Dawkins, Dennett, and Harris at the 2012 Global Atheist Convention, where she was referred to as the "plus one horse-woman" by Dawkins. Robyn Blumner, CEO of the Center for Inquiry, described Hirsi Ali as the "Fifth" horseman.

Hirsi Ali was born in Mogadishu, Somalia, fleeing in 1992 to the Netherlands in order to escape an arranged marriage. She became involved in Dutch politics, rejected faith, and became vocal in opposing Islamic ideology, especially concerning women, as exemplified by her books Infidel and The Caged Virgin.

Hirsi Ali was later involved in the production of the film Submission, for which her friend Theo van Gogh was murdered with a death threat to Hirsi Ali pinned to his chest. This event resulted in Hirsi Ali's hiding and later emigrating to the United States, where she resides and remains a prolific critic of Islam. She regularly speaks out against the treatment of women in Islamic doctrine and society and is a proponent of free speech and the freedom to offend.

Writing in a column in November 2023, Ali announced her conversion to the Christian faith, saying the Judeo-Christian tradition is the only answer to the problems of the modern world.

Others

Others have either self-identified as or been classified by some commentators as new atheists:

• Dan Barker (b. 1949), author of Godless: How an Evangelical Preacher Became One of America's Leading Atheists
• Peter Boghossian (b. 1966), philosopher and author of A Manual for Creating Atheists
• Greta Christina (b. 1961), author of Why Are You Atheists So Angry?: 99 Things that Piss Off the Godless
• Jerry Coyne (b. 1949), author of Faith Versus Fact: Why Science and Religion Are Incompatible
• Rebecca Goldstein (b. 1950), philosopher and author of 36 Arguments for the Existence of God
• Michel Onfray (b. 1959), author of Atheist Manifesto: The Case Against Christianity, Judaism, and Islam
• Michael Schmidt-Salomon (b. 1967) author of Manifesto of Evolutionary Humanism and identified as Germany's "Chief Atheist"
• TJ Kirk (b. 1985), YouTube personality and podcast host known for his YouTube Channel Amazing Atheist
• Victor J. Stenger (1935–2014), author of God: The Failed Hypothesis
• Rebecca Watson, author of the blog Skepchick

Some writers sometimes classified as new atheists by others have explicitly distanced themselves from the label:

• A. C. Grayling (b. 1949), philosopher and author of The God Argument
• John W. Loftus (b. 1954), author of The Outsider Test For Faith
• P. Z. Myers (b. 1957), critic of intelligent design, the creationist movement, and other pseudoscientific concepts

Perspective

The scarlet A, symbol of Out Campaign

Many contemporary atheists write from a scientific perspective. Unlike previous writers, many of whom thought that science was indifferent or even incapable of dealing with the "God" concept, Dawkins argues to the contrary, claiming the "God Hypothesis" is a valid scientific hypothesis, having effects in the physical universe, and like any other hypothesis can be tested and falsified. Victor Stenger proposed that the personal Abrahamic God is a scientific hypothesis that can be tested by standard methods of science. Both Dawkins and Stenger conclude that the hypothesis fails any such tests, and argue that naturalism is sufficient to explain everything we observe. They argue that nowhere is it necessary to introduce God or the supernatural to understand reality.

Scientific testing of religion

Non-believers (in religion and the supernatural) assert that many religious or supernatural claims (such as the virgin birth of Jesus and the afterlife) are scientific claims in nature. For instance, they argue, as do deists and Progressive Christians, that the issue of Jesus' supposed parentage is a question of scientific inquiry, rather than "values" or "morals". Rational thinkers believe science is capable of investigating at least some, if not all, supernatural claims. Institutions such as the Mayo Clinic and Duke University have conducted empirical studies to try to identify whether there is evidence for the healing power of intercessory prayer. According to Stenger, the experiments found no evidence that intercessory prayer worked.

Logical arguments

In his book God: The Failed Hypothesis, Victor Stenger argues that a God having omniscient, omnibenevolent, and omnipotent attributes, which he termed a 3O God, cannot logically exist. A similar series of alleged logical disproofs of the existence of a God with various attributes can be found in Michael Martin and Ricki Monnier's The Impossibility of God, or Theodore Drange's article, "Incompatible-Properties Arguments: A Survey".

Views on non-overlapping magisteria

Richard Dawkins has been particularly critical of the conciliatory view that science and religion are not in conflict, noting, for example, that the Abrahamic religions constantly dabble in scientific matters. In a 1998 article published in Free Inquiry magazine, and later in his 2006 book The God Delusion, Dawkins expresses disagreement with the view advocated by Stephen Jay Gould that science and religion are two non-overlapping magisteria (NOMA), each existing in a "domain where one form of teaching holds the appropriate tools for meaningful discourse and resolution".

In Gould's proposal, science and religion should be confined to distinct non-overlapping domains: science would be limited to the empirical realm, including theories developed to describe observations, while religion would deal with questions of ultimate meaning and moral value. Dawkins contends that NOMA does not describe empirical facts about the intersection of science and religion. He argued: "It is completely unrealistic to claim, as Gould and many others do, that religion keeps itself away from science's turf, restricting itself to morals and values. A universe with a supernatural presence would be a fundamentally and qualitatively different kind of universe from one without. The difference is, inescapably, a scientific difference. Religions make existence claims, and this means scientific claims."

Science and morality

Main article: Science of morality

Harris considers that the well-being of conscious creatures forms the basis of morality. In The Moral Landscape, he argues that science can in principle answer moral questions and help maximize well-being. Harris also criticizes cultural and moral relativism, arguing that it prevents people from making objective moral judgments about practices that clearly harm human well-being, such as female genital mutilation. Harris contends that we can make scientifically-based claims about the negative impacts of such practices on human welfare, and that withholding judgment in these cases is tantamount to claiming complete ignorance about what contributes to human well-being.

Politics

In the context of international politics, the principles of New Atheism establish no particular stance in and of themselves. P. Z. Myers stated that New Atheism's key proponents are "a madly disorganized mob, united only by [their] dislike of the god-thing". That said, the demographic that supports New Atheism is a markedly homogeneous one; in America and the Anglo-sphere more generally, this cohort is "more likely to be younger, male and single, to have higher than average levels of income and education, to be less authoritarian, less dogmatic, less prejudiced, less conformist and more tolerant and open-minded on religious issues." Because of this homogeneity among the group, there exists not a formal dynamic but a loose consensus on broad political "efforts, objectives, and strategies".

For example, one of the primary aims is to further reduce the entanglement of church and state, which derives from the "belief that religion is antithetical to liberal values, such as freedom of expression and the separation of public from private life". Additionally, new atheists have engaged in the campaign "to ensure legal and civic equality for atheists", in a world considerably unwelcoming to and distrustful of non-religious believers. Hitchens may be the atheist concerned most with religion's incompatibility with contemporary liberal principles, and particularly its imposed limitation on both freedom of speech and freedom of expression. Because New Atheism's proliferation is accredited partly to the 11 September attacks and the ubiquitous, visceral response, Richard Dawkins, among many in his cohort, believes that theism (in this case, Islam) jeopardizes political institutions and national security, and he warns of religion's potency in motivating "people to do terrible things" against international polities.

Criticisms

See also: Criticism of atheism § New Atheism

According to Nature, "Critics of new atheism, as well as many new atheists themselves, contend that in philosophical terms it differs little from earlier historical forms of atheist thought."

Scientism, accusations of evangelicalism and fundamentalism

Critics of the movement described it as militant atheism and fundamentalist atheism. Theologians Jeffrey Robbins and Christopher Rodkey take issue with what they regard as "the evangelical nature of the New Atheism, which assumes that it has a Good News to share, at all cost, for the ultimate future of humanity by the conversion of as many people as possible", and believe they have found similarities between New Atheism and evangelical Christianity and conclude that the all-consuming nature of both "encourages endless conflict without progress" between both extremities. Political philosopher John Gray asserts that New Atheism, humanism, and scientism are extensions of religion, particularly Christianity. Sociologist William Stahl said, "What is striking about the current debate is the frequency with which the New Atheists are portrayed as mirror images of religious fundamentalists."

The atheist philosopher of science Michael Ruse states that Richard Dawkins would fail "introductory" courses on the study of "philosophy or religion" (such as courses on the philosophy of religion), courses which are offered, for example, at many educational institutions such as colleges and universities around the world. Ruse also says that the movement of New Atheism—which is perceived by him to be "a bloody disaster"—makes him ashamed, as a professional philosopher of science, to be among those holding to an atheist position, particularly as New Atheism, as he sees it, does science a "grave disservice" and does a "disservice to scholarship" at a more general level. Paul Kurtz, editor in chief of Free Inquiry, founder of Prometheus Books, was critical of many of the new atheists. He said, "I consider them atheist fundamentalists... They're anti-religious, and they're mean-spirited, unfortunately. Now, there are very good atheists and very dedicated people who do not believe in God. But you have this aggressive and militant phase of atheism, and that does more damage than good." Jonathan Sacks, author of The Great Partnership: Science, Religion, and the Search for Meaning, feels the new atheists miss the target by believing the "cure for bad religion is no religion, as opposed to good religion". He wrote:

Atheism deserves better than the new atheists whose methodology consists of criticizing religion without understanding it, quoting texts without contexts, taking exceptions as the rule, confusing folk belief with reflective theology, abusing, mocking, ridiculing, caricaturing, and demonizing religious faith and holding it responsible for the great crimes against humanity. Religion has done harm; I acknowledge that. But the cure for bad religion is good religion, not no religion, just as the cure for bad science is good science, not the abandonment of science.

The philosopher Massimo Pigliucci contends that the new atheist movement overlaps with scientism, which he finds to be philosophically unsound. He writes: "What I do object to is the tendency, found among many New Atheists, to expand the definition of science to pretty much encompassing anything that deals with 'facts', loosely conceived ... it seems clear to me that most of the New Atheists (except for the professional philosophers among them) pontificate about philosophy very likely without having read a single professional paper in that field ... I would actually go so far as to charge many of the leaders of the New Atheism movement (and, by implication, a good number of their followers) with anti-intellectualism, one mark of which is a lack of respect for the proper significance, value, and methods of another field of intellectual endeavor."^[109]

In The Evolution of Atheism, Stephen LeDrew wrote that New Atheism is fundamentalist and scientist; in contrast to atheism's tradition of social justice, it is right-wing and serves to defend "the position of the white middle-class western male". Atheist professor Jacques Berlinerblau has criticised the new atheists' mocking of religion as being inimical to their goals and claims that they have not achieved anything politically. Roger Scruton has extensively criticized New Atheism on various occasions, generally on the grounds that they do not consider the social effects and impacts of religion in enough detail. He has said, "Look at the facts in the round and it seems likely that humans without a sense of the sacred would have died out long ago. For that same reason, the hope of the new atheists for a world without religion is probably as vain as the hope for a society without aggression or a world without death." He has also complained of the new atheists' idea that they must "set people free from religion", calling it "naive" because they "never consider that they might be taking something away from people".

Criticisms of responses to theistic arguments

Edward Feser has critiqued the new atheists' responses to arguments for the existence of God:

It can safely be said that if you haven't both understood Aquinas and answered him – not to mention Anselm, Duns Scotus, Leibniz, Samuel Clarke, and so on, but let that pass – then you have hardly "made your case" against religion. Yet Dawkins is the only "New Atheist" to offer anything even remotely like an attempt to answer him, feeble as it is.

— Edward Feser, The Last Superstition (2008)

Criticism from David Bentley Hart

Atheist Delusions: The Christian Revolution and Its Fashionable Enemies by David Bentley Hart was published by Yale in 2009. Philosopher Anthony Kenny called Hart's book "the most able counsel for the defence in recent years". Writing for Commonweal, poet Michael Robbins described the book as "an unanswerable and frequently hilarious demolition of the shoddy thinking and historical illiteracy of the so-called New Atheists." On 27 May 2011, Hart's book was awarded the Michael Ramsey Prize in Theology by the Archbishop of Canterbury, Rowan Williams. Hart argues positively that Christianity was a progressive factor in human history and the only factor that "can be called in the fullest sense" a revolution. In his negative case against New Atheism, Hart argues that the Enlightenment was actually "a reactionary flight back toward a comfortable, but dehumanizing, mental and moral servitude to elemental nature."

Accusations of bigotry

See also: Elevatorgate

The New Atheist movement has been accused of sexism, especially prominent figures such as Richard Dawkins. In 2014, Sam Harris said that New Atheism was "to some degree intrinsically male". Sebastian Milbank of The Critic stated that anti-Catholic rhetoric by the New Atheist movement reached its pinnacle in 2010, during the state visit by Pope Benedict XVI to the United Kingdom, where "many mainstream newspapers (especially The Guardian) engaged in more or less naked anti-Catholic rhetoric of a sort that seemed more suited to the eighteenth century than the twenty-first".

Some commentators have accused the New Atheist movement of Islamophobia. Wade Jacoby and Hakan Yavuz assert that "a group of 'new atheists' such as Richard Dawkins, Sam Harris, and Christopher Hitchens" have "invoked Samuel Huntington's 'clash of civilizations' theory to explain the current political contestation" and that this forms part of a trend toward "Islamophobia ... in the study of Muslim societies". William W. Emilson argues that "the 'new' in the new atheists' writings is not their aggressiveness, nor their extraordinary popularity, nor even their scientific approach to religion, rather it is their attack not only on militant Islamism but also on Islam itself under the cloak of its general critique of religion."

Antitheism

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

Antitheism, also spelled anti-theism, is the philosophical position that theism should be opposed. The term has had a range of applications. In secular contexts, it typically refers to direct opposition to the belief in any deity.

Etymology

The word antitheism (or hyphenated anti-theism) has been recorded in English since 1788. The etymological roots of the word are the Greek anti and theos.

The Oxford English Dictionary defines antitheist as "One opposed to belief in the existence of a god". The earliest citation given for this meaning dates from 1833. The term was likely coined by Pierre-Joseph Proudhon.

Opposition to theism

Antitheism has been adopted as a label by those who regard theism as dangerous, destructive, or encouraging of harmful behavior. Christopher Hitchens (2001) wrote:

I'm not even an atheist so much as I am an antitheist; I not only maintain that all religions are versions of the same untruth, but I hold that the influence of churches, and the effect of religious belief, is positively harmful."

Opposition to the idea of God

Other definitions of antitheism include that of the French Catholic philosopher Jacques Maritain (1953), for whom it is "an active struggle against everything that reminds us of God".

The definition of Robert Flint (1877), Professor of Divinity at the University of Edinburgh was similar. Flint's 1877 Baird Lecture was titled Anti-Theistic Theories. He used "antitheism" as a very general umbrella term for all opposition to his own form of theism, which he defined as

the "belief that the heavens and the earth and all that they contain owe their existence and continuance to the wisdom and will of a supreme, self-existent, omnipotent, omniscient, righteous, and benevolent Being, who is distinct from, and independent of, what He has created."

Flint wrote

"In dealing with theories which have nothing in common except that they are antagonistic to theism, it is necessary to have a general term to designate them. Anti-theism appears to be the appropriate word. It is, of course, much more comprehensive in meaning than the term atheism. It applies to all systems which are opposed to theism. It includes, therefore, atheism, but short of atheism, there are anti-theistic theories."

"Polytheism is not atheism, for it does not deny that there is a deity; but it is anti-theistic since it denies that there is only one. Pantheism is not atheism, for it asserts that there is a god; but it is anti-theism, for it denies that God is a being distinct from creation and possessed of such attributes as wisdom, and holiness, and love. Every theory which refuses to ascribe to a god an attribute which is essential to a worthy conception of its character is anti-theistic. Only those theories which refuse to acknowledge that there is evidence even for the existence of a god are atheistic."

However, Flint also acknowledged that antitheism is typically understood differently from how he defines it. In particular, he notes that it has been used as a subdivision of atheism, descriptive of the view that theism has been disproven, rather than as the more general term that Flint preferred. He rejected the alternative non-theistic

"not merely because of its hybrid origin and character, but also because it is far too comprehensive. The theories of physical and mental science are non-theistic, even when in no degree, directly or indirectly, antagonistic to theism."

Other, similar terms

Opposition to the existence of a god or gods is frequently referred to as nontheism, or dystheism, or misotheism.

• Dystheism would actually mean "belief in a deity that is not benevolent".
• Misotheism, strictly speaking, means "hatred of God".

Examples of belief systems founded on the principle of opposition to the existence of a god or gods include some forms of Atheistic Satanism and maltheism.

Different definitions of "antitheism"

See also: Misotheism § Terminology

Christopher New (1993) proposed an altered definition of the word antitheism as part of a thought experiment. He imagines what arguments for the existence of an evil god would look like, and writes

"Antitheists, like theists, would have believed in an omnipotent, omniscient, eternal creator; but whereas theists in fact believe that the supreme being is also perfectly good, antitheists would have believed that he was perfectly evil."

New's changed definition has reappeared in the work of W.A. Murphree.

Action at a distance

From Wikipedia, the free encyclopedia

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

Action at a distance is the concept in physics that an object's motion can be affected by another object without the two being in physical contact; that is, it is the concept of the non-local interaction of objects that are separated in space. Coulomb's law and Newton's law of universal gravitation are based on action at a distance.

Historically, action at a distance was the earliest scientific model for gravity and electricity and it continues to be useful in many practical cases. In the 19th and 20th centuries, field models arose to explain these phenomena with more precision. The discovery of electrons and of special relativity led to new action at a distance models providing alternative to field theories. Under our modern understanding, the four fundamental interactions (gravity, electromagnetism, the strong interaction and the weak interaction) in all of physics are not described by action at a distance.

Categories of action

In the study of mechanics, action at a distance is one of three fundamental actions on matter that cause motion. The other two are direct impact (elastic or inelastic collisions) and actions in a continuous medium as in fluid mechanics or solid mechanics. Historically, physical explanations for particular phenomena have moved between these three categories over time as new models were developed.

Action-at-a-distance and actions in a continuous medium may be easily distinguished when the medium dynamics are visible, like waves in water or in an elastic solid. In the case of electricity or gravity, no medium is required. In the nineteenth century, criteria like the effect of actions on intervening matter, the observation of a time delay, the apparent storage of energy, or even the possibility of a plausible mechanical model for action transmission were all accepted as evidence against action at a distance. Aether theories were alternative proposals to replace apparent action-at-a-distance in gravity and electromagnetism, in terms of continuous action inside an (invisible) medium called "aether".

Direct impact of macroscopic objects seems visually distinguishable from action at a distance. If however the objects are constructed of atoms, and the volume of those atoms is not defined and atoms interact by electric and magnetic forces, the distinction is less clear.

Roles

The concept of action at a distance acts in multiple roles in physics and it can co-exist with other models according to the needs of each physical problem.

One role is as a summary of physical phenomena, independent of any understanding of the cause of such an action. For example, astronomical tables of planetary positions can be compactly summarized using Newton's law of universal gravitation, which assumes the planets interact without contact or an intervening medium. As a summary of data, the concept does not need to be evaluated as a plausible physical model.

Action at a distance also acts as a model explaining physical phenomena even in the presence of other models. Again in the case of gravity, hypothesizing an instantaneous force between masses allows the return time of comets to be predicted as well as predicting the existence of previously unknown planets, like Neptune. These triumphs of physics predated the alternative more accurate model for gravity based on general relativity by many decades.

Introductory physics textbooks discuss central forces, like gravity, by models based on action-at-distance without discussing the cause of such forces or issues with it until the topics of relativity and fields are discussed. For example, see The Feynman Lectures on Physics on gravity.

History

Early inquiries into motion

Main articles: Scientific Revolution and History of gravitational theory

Action-at-a-distance as a physical concept requires identifying objects, distances, and their motion. In antiquity, ideas about the natural world were not organized in these terms. Objects in motion were modeled as living beings. Around 1600, the scientific method began to take root. René Descartes held a more fundamental view, developing ideas of matter and action independent of theology. Galileo Galilei wrote about experimental measurements of falling and rolling objects. Johannes Kepler's laws of planetary motion summarized Tycho Brahe's astronomical observations. Many experiments with electrical and magnetic materials led to new ideas about forces. These efforts set the stage for Newton's work on forces and gravity.

Newtonian gravity

Main article: History of gravitational theory

In 1687 Isaac Newton published his Principia which combined his laws of motion with a new mathematical analysis able to reproduce Kepler's empirical results. His explanation was in the form of a law of universal gravitation: any two bodies are attracted by a force proportional to their mass and inversely proportional to the square of the distance between them. Thus the motions of planets were predicted by assuming forces working over great distances.

This mathematical expression of the force did not imply a cause. Newton considered action-at-a-distance to be an inadequate model for gravity. Newton, in his words, considered action at a distance to be:

so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it.

— Isaac Newton, Letters to Bentley, 1692/3

Metaphysical scientists of the early 1700s strongly objected to the unexplained action-at-a-distance in Newton's theory. Gottfried Wilhelm Leibniz complained that the mechanism of gravity was "invisible, intangible, and not mechanical". Moreover, initial comparisons with astronomical data were not favorable. As mathematical techniques improved throughout the 1700s, the theory showed increasing success, predicting the date of the return of Halley's comet and aiding the discovery of planet Neptune in 1846. These successes and the increasingly empirical focus of science towards the 19th century led to acceptance of Newton's theory of gravity despite distaste for action-at-a-distance.

Electrical action at a distance

Main article: History of electromagnetic theory

Jean-Antoine Nollet reproducing Stephan Gray's “electric boy” experiment, in which a boy hanging from insulating silk ropes is given an electric charge. A group are gathered around. A woman is encouraged to bend forward and poke the boy's nose, to get an electric shock.

Electrical and magnetic phenomena also began to be explored systematically in the early 1600s. In William Gilbert's early theory of "electric effluvia," a kind of electric atmosphere, he rules out action-at-a-distance on the grounds that "no action can be performed by matter save by contact". However subsequent experiments, especially those by Stephen Gray showed electrical effects over distance. Gray developed an experiment call the "electric boy" demonstrating electric transfer without direct contact. Franz Aepinus was the first to show, in 1759, that a theory of action at a distance for electricity provides a simpler replacement for the electric effluvia theory. Despite this success, Aepinus himself considered the nature of the forces to be unexplained: he did "not approve of the doctrine which assumes the possibility of action at a distance", setting the stage for a shift to theories based on aether.

By 1785 Charles-Augustin de Coulomb showed that two electric charges at rest experience a force inversely proportional to the square of the distance between them, a result now called Coulomb's law. The striking similarity to gravity strengthened the case for action at a distance, at least as a mathematical model.

As mathematical methods improved, especially through the work of Pierre-Simon Laplace, Joseph-Louis Lagrange, and Siméon Denis Poisson, more sophisticated mathematical methods began to influence the thinking of scientists. The concept of potential energy applied to small test particles led to the concept of a scalar field, a mathematical model representing the forces throughout space. While this mathematical model is not a mechanical medium, the mental picture of such a field resembles a medium.

Fields as an alternative

Main article: History of field theory

Glazed frame, containing "Delineation of Lines of Magnetic Force by Iron filings" prepared by Michael Faraday

Michael Faraday was the first who suggested that action at a distance was inadequate as an account of electric and magnetic forces, even in the form of a (mathematical) potential field. Faraday, an empirical experimentalist, cited three reasons in support of some medium transmitting electrical force: 1) electrostatic induction across an insulator depends on the nature of the insulator, 2) cutting a charged insulator causes opposite charges to appear on each half, and 3) electric discharge sparks are curved at an insulator. From these reasons he concluded that the particles of an insulator must be polarized, with each particle contributing to continuous action. He also experimented with magnets, demonstrating lines of force made visible by iron filings. However, in both cases his field-like model depends on particles that interact through an action-at-a-distance: his mechanical field-like model has no more fundamental physical cause than the long-range central field model.

Faraday's observations, as well as others, led James Clerk Maxwell to a breakthrough formulation in 1865, a set of equations that combined electricity and magnetism, both static and dynamic, and which included electromagnetic radiation – light. Maxwell started with elaborate mechanical models but ultimately produced a purely mathematical treatment using dynamical vector fields. The sense that these fields must be set to vibrate to propagate light set off a search of a medium of propagation; the medium was called the luminiferous aether or the aether.

In 1873 Maxwell addressed action at a distance explicitly. He reviews Faraday's lines of force, carefully pointing out that Faraday himself did not provide a mechanical model of these lines in terms of a medium. Nevertheless the many properties of these lines of force imply these "lines must not be regarded as mere mathematical abstractions". Faraday himself viewed these lines of force as a model, a "valuable aid" to the experimentalist, a means to suggest further experiments.

In distinguishing between different kinds of action Faraday suggested three criteria: 1) do additional material objects alter the action?, 2) does the action take time, and 3) does it depend upon the receiving end? For electricity, Faraday knew that all three criteria were met for electric action, but gravity was thought to only meet the third one. After Maxwell's time a fourth criteria, the transmission of energy, was added, thought to also apply to electricity but not gravity. With the advent of new theories of gravity, the modern account would give gravity all of the criteria except dependence on additional objects.

Fields fade into spacetime

Main article: Luminiferous ether

The success of Maxwell's field equations led to numerous efforts in the later decades of the 19th century to represent electrical, magnetic, and gravitational fields, primarily with mechanical models. No model emerged that explained the existing phenomena. In particular no good model for stellar aberration, the shift in the position of stars with the Earth's relative velocity. The best models required the ether to be stationary while the Earth moved, but experimental efforts to measure the effect of Earth's motion through the aether found no effect.

In 1892 Hendrik Lorentz proposed a modified aether based on the emerging microscopic molecular model rather than the strictly macroscopic continuous theory of Maxwell. Lorentz investigated the mutual interaction of a moving solitary electrons within a stationary aether. He rederived Maxwell's equations in this way but, critically, in the process he changed them to represent the wave in the coordinates moving electrons. He showed that the wave equations had the same form if they were transformed using a particular scaling factor, $${\displaystyle \gamma =\frac{1}{\sqrt{1-(u^2/c^2)}}.}$$ where ${\displaystyle u}$ is the velocity of the moving electrons and ${\displaystyle c}$ is the speed of light. Lorentz noted that if this factor were applied as a length contraction to moving matter in a stationary ether, it would eliminate any effect of motion through the ether, in agreement with experiment.

In 1899, Henri Poincaré questioned the existence of an aether, showing that the principle of relativity prohibits the absolute motion assumed by proponents of the aether model. He named the transformation used by Lorentz the Lorentz transformation but interpreted it as a transformation between two inertial frames with relative velocity ${\displaystyle u}$. This transformation makes the electromagnetic equations look the same in every uniformly moving inertial frame. Then, in 1905, Albert Einstein demonstrated that the principle of relativity, applied to the simultaneity of time and the constant speed of light, precisely predicts the Lorentz transformation. This theory of special relativity quickly became the modern concept of spacetime.

Thus the aether model, initially so very different from action at a distance, slowly changed to resemble simple empty space.

In 1905, Poincaré proposed gravitational waves, emanating from a body and propagating at the speed of light, as being required by the Lorentz transformations and suggested that, in analogy to an accelerating electrical charge producing electromagnetic waves, accelerated masses in a relativistic field theory of gravity should produce gravitational waves. However, until 1915 gravity stood apart as a force still described by action-at-a-distance. In that year, Einstein showed that a field theory of spacetime, general relativity, consistent with relativity can explain gravity. New effects resulting from this theory were dramatic for cosmology but minor for planetary motion and physics on Earth. Einstein himself noted Newton's "enormous practical success".

Modern action at a distance

Main article: Wheeler–Feynman absorber theory

In the early decades of the 20th century, Karl Schwarzschild, Hugo Tetrode, and Adriaan Fokker independently developed non-instantaneous models for action at a distance consistent with special relativity. In 1949 John Archibald Wheeler and Richard Feynman built on these models to develop a new field-free theory of electromagnetism. While Maxwell's field equations are generally successful, the Lorentz model of a moving electron interacting with the field encounters mathematical difficulties: the self-energy of the moving point charge within the field is infinite. The Wheeler–Feynman absorber theory of electromagnetism avoids the self-energy issue. They interpret Abraham–Lorentz force, the apparent force resisting electron acceleration, as a real force returning from all the other existing charges in the universe.

The Wheeler–Feynman theory has inspired new thinking about the arrow of time and about the nature of quantum non-locality. The theory has implications for cosmology; it has been extended to quantum mechanics. A similar approach has been applied to develop an alternative theory of gravity consistent with general relativity. John G. Cramer has extended the Wheeler–Feynman ideas to create the transactional interpretation of quantum mechanics.

"Spooky action at a distance"

Albert Einstein wrote to Max Born about issues in quantum mechanics in 1947 and used a phrase translated as "spooky action at a distance", and in 1964, John Stewart Bell proved that quantum mechanics predicted stronger statistical correlations in the outcomes of certain far-apart measurements than any local theory possibly could. The phrase has been picked up and used as a description for the cause of small non-classical correlations between physically separated measurement of entangled quantum states. The correlations are predicted by quantum mechanics (the Bell theorem) and verified by experiments (the Bell test). Rather than a postulate like Newton's gravitational force, this use of "action-at-a-distance" concerns observed correlations which cannot be explained with localized particle-based models. Describing these correlations as "action-at-a-distance" requires assuming that particles became entangled and then traveled to distant locations, an assumption that is not required by quantum mechanics.

Force in quantum field theory

Main article: Force carriers

 

Quantum field theory does not need action at a distance. At the most fundamental level, only four forces are needed. Each force is described as resulting from the exchange of specific bosons. Two are short range: the strong interaction mediated by mesons and the weak interaction mediated by the weak boson; two are long range: electromagnetism mediated by the photon and gravity hypothesized to be mediated by the graviton. However, the entire concept of force is of secondary concern in advanced modern particle physics. Energy forms the basis of physical models and the word action has shifted away from implying a force to a specific technical meaning, an integral over the difference between potential energy and kinetic energy.