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Special Relativity (AQA A Level Physics): Flashcards

Exam code: 7408

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  • Define luminiferous aether.

    The luminiferous aether was the proposed medium through which light waves were thought to travel, since all other known waves (such as sound and water waves) require a medium.

  • Define aether wind.

    The aether wind is the apparent motion of the aether relative to a body (such as the Earth) moving through it.

  • What did Fizeau's experiment with light in moving water demonstrate?

    Light travelling with the current of the water travelled faster than light travelling against it, showing that the motion of a medium affects the speed of light passing through it.

  • What is the role of the beam splitter in the Michelson-Morley interferometer?

    A semi-silvered mirror that reflects some of the incoming light and transmits the rest, splitting a single beam into two coherent beams that travel along the two arms of the interferometer.

  • Why was the Michelson-Morley interferometer floated on a bath of mercury?

    So that it could be rotated with minimal friction, allowing measurements to be taken at different orientations relative to the predicted aether wind.

  • A plane of glass was placed in the path of the reflected beam to ensure both beams travelled through the same distances of glass and ...........

    A plane of glass was placed in the path of the reflected beam to ensure both beams travelled through the same distances of glass and air.

  • True or False?

    The Michelson-Morley experiment detected a significant phase shift, confirming the existence of the aether.

    False.

    The experiment produced a null result — displacements of only around 0.02 fringe widths were observed, far too small to be significant, compared with the predicted 0.4 fringe widths.

  • What three conclusions were drawn from the null result of the Michelson-Morley experiment?

    • The aether does not exist, so light can travel without a medium

    • The speed of light is invariant — unchanged by the Earth's motion

    • There is no absolute motion — everything moves relative to everything else

  • Define the invariance of the speed of light.

    The invariance of the speed of light is the principle that in a vacuum, the speed of light is always 3.0 \times 10^{8} m s-1 for every observer, regardless of the motion of the source or the observer.

  • What is the speed of light in a vacuum, and what symbol is it given?

    3.0 \times 10^{8} m s-1, given the symbol c.

  • Can the speed of light exceed c when travelling through a material medium?

    No. The speed of light may reduce when travelling through a material, but it can never exceed c.

  • Light emitted from a .......... object still travels at speed c for every observer.

    Light emitted from a moving object still travels at speed c for every observer.

  • True or False?

    If a runner holding a torch moves at high speed, a stationary observer measures the light from the torch as travelling faster than c.

    False.

    The stationary observer still measures the speed of light as exactly c, not c plus the velocity of the runner, because the speed of light is invariant.

  • Does the invariance of the speed of light apply to objects other than light?

    No. This concept only applies to light, since light is the only thing capable of travelling at the speed of light.

  • Define reference frame.

    A reference frame is a set of coordinates used to record the position and time of events.

  • Define inertial reference frame.

    An inertial reference frame is a reference frame that is non-accelerating, meaning it moves at constant velocity with respect to other inertial frames.

  • Person A is on a station platform and Person B is on a train pulling away. According to Person A's reference frame, who is moving?

    According to Person A, they themselves are stationary and Person B is moving.

  • Why is there no absolute reference frame in the Universe?

    Because there is no place in the Universe that is completely stationary — everything is always moving relative to everything else.

  • All inertial reference frames are moving at .......... velocity with respect to each other.

    All inertial reference frames are moving at constant velocity with respect to each other.

  • True or False?

    Two people standing on opposite sides of a road will describe the direction of a passing car in the same way.

    False.

    Each person views the car's motion from a different reference frame — one may describe it as moving right, the other as moving left, and both are correct relative to themselves.

  • Define Galilean relativity.

    Galilean relativity is the principle that an object's velocity may differ between reference frames, found using simple addition or subtraction of velocities. It works at everyday speeds but breaks down close to the speed of light.

  • State Einstein's first postulate of special relativity.

    The laws of physics are the same in all inertial frames of reference.

  • State Einstein's second postulate of special relativity.

    The speed of light in a vacuum is the same in all inertial frames of reference.

  • A rocket travelling at 0.7c releases a probe at 0.5c relative to the rocket. Why can a stationary observer not measure the probe's speed as 1.2c?

    Galilean velocity addition does not apply at speeds close to c. Nothing can travel faster than the speed of light, so the observer must measure a speed less than c.

  • Person D is on a skateboard travelling at 4 m s-1 and throws a ball at 2 m s-1 relative to themselves. A stationary observer, Person C, measures the ball's speed as .......... m s-1.

    Person D is on a skateboard travelling at 4 m s-1 and throws a ball at 2 m s-1 relative to themselves. A stationary observer, Person C, measures the ball's speed as 6 m s-1.

  • True or False?

    Einstein's two postulates of special relativity are independent of each other.

    False.

    They are linked: if the speed of light depended on an observer's own motion, that observer could use it to work out they were moving, which would violate the first postulate.

  • Define time dilation.

    Time dilation is the effect where a clock moving relative to an observer is measured to run slower than a clock at rest in its own reference frame.

  • Define proper time, Δt0.

    Proper time is the time interval between two events measured by an observer at rest relative to those events, i.e. in the same reference frame as the clock.

  • State the equation linking the time interval Δt measured by a moving observer to the proper time interval Δt0.

    \Delta t = \gamma \Delta t_{0}

  • Give the equation for the gamma factor, γ.

    \gamma = \frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}

  • What happens to the value of the gamma factor, γ, as v increases towards c?

    γ increases, becoming ever greater than 1, since v is always less than c.

  • An observer on a train platform will view a clock on a moving train as ticking .......... than their own.

    An observer on a train platform will view a clock on a moving train as ticking slower than their own.

  • True or False?

    Only the observer on the moving object experiences their own clock as running slow.

    False.

    Each observer sees their own clock ticking normally. The effect is symmetric — the platform observer sees the train clock as slower, and the train observer sees the platform clock as slower.

  • Define proper time.

    Proper time is the time measured in the reference frame that is stationary relative to the event being timed.

  • Define proper length.

    Proper length is the length measured in the reference frame that is stationary relative to the distance being measured.

  • In the muon lifetime experiment, from which reference frame does an observer measure the muon's half-life as longer than 1.6 μs?

    The observer on Earth, since the muon is travelling close to the speed of light relative to Earth, so its half-life is time dilated.

  • In the muon lifetime experiment, from which reference frame is the 10 km distance to the Earth's surface measured as shorter?

    The muon's own reference frame, due to length contraction of the distance travelled.

  • Muons travel at a speed of .......... relative to Earth and have a half-life of .......... measured in their own rest frame.

    Muons travel at a speed of 0.98*c relative to Earth and have a half-life of 1.6 μs* measured in their own rest frame.

  • True or False?

    Proper length for the muon's journey to Earth's surface is measured in the muon's own reference frame.

    False.

    The observer on Earth is stationary relative to the distance being measured (the path from creation to the surface), so proper length is measured in the Earth's reference frame.

  • What produces muons in the upper atmosphere?

    Muons are produced by pion decays, which result from cosmic rays entering the atmosphere.

  • According to Newtonian mechanics, roughly how many muon half-lives pass during the journey from 10 km up to the Earth's surface, compared to the relativistic prediction?

    Newtonian mechanics predicts around 21 half-lives, but the relativistic prediction (accounting for time dilation) is only around 4.3 half-lives, which explains why far more muons are detected than expected.

  • Define length contraction.

    Length contraction is the apparent shortening of an object's length, as measured by an observer moving relative to that object, compared to its length measured at rest.

  • Define proper length, L0.

    Proper length is the length of an object measured by an observer at rest relative to it (i.e. the object is not moving relative to that observer).

  • The length contraction equation is L = \frac{L_0}{\gamma} Since γ > 1, the observed length, L, measured by a moving observer is always .......... than the proper length, L0.

    The length contraction equation is L = \frac{L_0}{\gamma} Since γ > 1, the observed length, L, measured by a moving observer is always shorter than the proper length, L0.

  • Length contraction is a direct consequence of which of Einstein's postulates?

    Einstein's second postulate (the invariance of the speed of light for all inertial observers).

  • Why must length contraction and time dilation occur together, by the same factor γ?

    Both observers must agree on the relative speed v between their frames. If a clock in the moving frame runs slow by a factor of γ, lengths along the direction of motion must contract by the same factor, otherwise v (and c) would not be invariant between the two observers.

  • True or False?

    Only one of two observers in relative motion measures the other's lengths as contracted.

    False.

    Length contraction is symmetric — each observer measures lengths in the other's reference frame as contracted, since motion is relative.

  • What condition must be true of the object being measured for length contraction to be observed?

    The object (e.g. a ruler) must be stationary in its own reference frame. If it were also moving in the frame doing the measuring, that observer would see it contracting too and would not measure any difference in length.

  • Define rest mass.

    Rest mass (or proper mass), m0, is the mass of an object measured by an observer at rest relative to it.

  • Define mass-energy equivalence.

    Mass-energy equivalence is Einstein's proposal that mass can be converted into energy and energy can be converted into mass, summarised by E = mc^2

  • Mass-energy equivalence is demonstrated in the .......... of hydrogen into helium in the Sun and the .......... of uranium in nuclear power plants.

    Mass-energy equivalence is demonstrated in the fusion of hydrogen into helium in the Sun and the fission of uranium in nuclear power plants.

  • What happens to an object's relativistic mass as its speed approaches the speed of light?

    Its mass increases rapidly and tends towards an infinite mass, which is why the speed of light acts as a speed limit for objects with mass.

  • Give the equation for relativistic mass, m, in terms of rest mass, m0, and the gamma factor.

    m = \gamma m_{0}

  • True or False?

    An observer moving relative to an object measures its mass as smaller than its rest mass.

    False.

    Since γ > 1, an observer moving relative to an object measures its mass as larger than its rest mass.

  • Define rest energy.

    Rest energy, E0, is the energy of an object at rest relative to the observer, given by E_{0} = m_{0} c^{2}

  • Define relativistic kinetic energy.

    Relativistic kinetic energy, Ek, is the difference between an object's total energy and its rest energy: E_{k} = mc^{2} - m_{0} c^{2}

  • The total energy of a moving object is given by E = m_{0} c^{2} + E_{k} where m0 is the object's .......... mass.

    The total energy of a moving object is given by E = m_{0} c^{2} + E_{k} where m0 is the object's rest mass.

  • What happens to an object's total energy as its speed approaches the speed of light?

    It increases at a rapidly increasing rate, tending towards infinity as speed approaches c.

  • Why can an object with mass never reach the speed of light, in terms of energy?

    Reaching the speed of light would require an infinite amount of energy.

  • True or False?

    At high speeds, an object's relativistic kinetic energy is smaller than its Newtonian kinetic energy.

    False.

    At high speeds, relativistic kinetic energy is greater than the Newtonian prediction — for example, at 0.7c the relativistic kinetic energy is almost twice as large as the Newtonian value.

  • Write the equation for an object's total energy, E, in terms of its relativistic mass, m.

    E = mc^{2}

  • Define rest energy.

    Rest energy, E0, is the energy an object has when at rest relative to the observer, given by E_{0} = m_{0} c^{2}

  • What was the aim of Bertozzi's experiment?

    To accelerate electrons to speeds close to the speed of light, measure their kinetic energies, and compare the plot of speed-squared against kinetic energy to Newtonian and relativistic predictions.

  • The work done by an electric field of potential difference V on a charge q equals the energy gained by its kinetic store: qV = E_{k} This gives a way of .......... the kinetic energy of a particle of known charge.

    The work done by an electric field of potential difference V on a charge q equals the energy gained by its kinetic store: qV = E_{k} This gives a way of measuring the kinetic energy of a particle of known charge.

  • How was the speed of the electrons calculated in Bertozzi's experiment?

    As distance divided by time: the distance between two oscilloscope signals (one after the electric field, one at the aluminium target) was divided by the time interval between them.

  • What did Bertozzi's plot of speed-squared against kinetic energy show?

    The results agreed closely with the relativistic predictions rather than the Newtonian ones, showing that electrons cannot exceed the speed of light.

  • How did Bertozzi verify the kinetic energy of the electrons independently of qV?

    By measuring the temperature rise of the aluminium target using \Delta E = mc\Delta \theta and using the total charge collected on the target to find the number of electrons, allowing the kinetic energy per electron to be calculated directly.

  • True or False?

    Bertozzi's two independent methods for finding the electrons' kinetic energy gave conflicting results.

    False.

    The kinetic energy found from qV and from the target's temperature rise agreed, confirming the electrons behaved relativistically at speeds close to c.

  • What equation gives the number of electrons, n, incident on the aluminium target from the total charge transferred, Q?

    n = \frac{Q}{e} where e is the charge of an electron.

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