General Relativity on a School Exam?!

ZPhysics
6 Mar 202403:59
EducationalLearning
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TLDRThis script explores the impact of gravity on photons through a British physics Olympiad challenge, using general relativity and energy conservation concepts. It illustrates how a falling mass gains kinetic energy, which could theoretically be converted back into photons. The script challenges the notion that if photons were unaffected by gravity, it would violate energy conservation, leading to an impossible increase in mass. It then mathematically calculates the change in photon frequency due to gravity, using classical approximations and the concept of a fictitious mass, concluding with a small but significant frequency shift.

Takeaways
  • 🔍 Photons are affected by gravity, as explained through the conservation of energy.
  • ⚖️ Dropping a small mass causes it to gain kinetic energy, which can be converted into photons.
  • 🌍 If photons were not affected by gravity, it could result in an apparent increase in mass, violating energy conservation.
  • 📚 The problem is explored using general relativity and energy conservation principles.
  • 💡 The energy of a photon near the ground is the sum of its initial energy plus the gravitational potential energy.
  • 🔬 Quantum physics shows that the energy of a photon is proportional to its frequency, expressed as E = hf.
  • 📐 A fictitious mass (M_gamma) is introduced to calculate the change in photon frequency due to gravity.
  • 🧮 The frequency change (Delta f) is derived using the fictitious mass, gravitational constant (G), height (H), and speed of light (c).
  • 📉 The calculated change in frequency due to gravity is 2,601 Hz, which is small compared to the original photon frequency.
  • 🎓 This type of problem is typical for students preparing for the British Physics Olympiad Senior Challenge.
Q & A

  • Why must photons be affected by gravity according to the concept of energy conservation?

    -If photons were not affected by gravity, a system where a mass falls and is converted to photons could lead to an increase in energy after reflection, violating the principle of energy conservation. Gravity must affect photons to prevent this energy discrepancy.

  • How is the kinetic energy of a mass related to the energy of photons when it reaches the ground?

    -The kinetic energy gained by the mass as it falls can be converted into photons when it reaches the ground. These photons will carry the energy equivalent to the kinetic energy the mass gained during its fall.

  • What is the significance of the fictitious mass M gamma in the context of the problem?

    -The fictitious mass M gamma is introduced to calculate the effect of gravity on the photon. It allows us to treat the photon as if it had mass, thereby applying classical gravitational potential energy concepts to find the change in the photon's frequency.

  • How is the energy of a photon related to its frequency according to quantum physics?

    -In quantum physics, the energy of a photon is directly proportional to its frequency, given by the equation E = h * f, where E is the energy, h is Planck's constant, and f is the frequency.

  • How do we derive the fictitious mass of a photon using the equation E = mc²?

    -The fictitious mass M gamma of a photon can be derived by rearranging the equation E = mc² to m = E/c². Since the energy of a photon is E = h * f, the fictitious mass becomes M gamma = h * f / c².

  • What is the equation for the change in frequency of a photon as it falls in a gravitational field?

    -The change in frequency (Δf) of a photon as it falls is given by the equation Δf = (M gamma * g * h) / h, where M gamma is the fictitious mass, g is the acceleration due to gravity, and h is the height from which the photon falls.

  • Why is the change in frequency of the photon considered to be small?

    -The change in frequency is considered small because the gravitational potential energy (M gamma * g * h) is typically very small compared to the original energy of the photon (h * f), leading to a minor shift in frequency.

  • What role does Planck's constant play in the equation for the change in photon frequency?

    -Planck's constant (h) appears in both the energy equation (E = h * f) and the fictitious mass equation (M gamma = h * f / c²). However, it cancels out during the calculation of the change in frequency, simplifying the final expression.

  • How can the change in photon frequency be practically calculated using given values?

    -To calculate the change in frequency, you would use the known values for the original photon frequency, gravitational acceleration (g), height (h), and the speed of light (c). Substituting these into the derived equation gives the change in frequency.

  • Why is understanding this problem important for students preparing for the British Physics Olympiad Senior Challenge?

    -This problem introduces concepts from general relativity and quantum physics, testing students' understanding of energy conservation, gravitational effects on light, and the mathematical skills needed to derive and manipulate complex equations, all of which are critical for the Olympiad.

Outlines
00:00
🌌 Photons and Gravity in the British Physics Olympiad

This paragraph introduces a physics challenge from the British Physics Olympiad Senior competition, focusing on the effects of gravity on photons through the lens of general relativity. It presents a hypothetical scenario where a small mass is dropped, gaining kinetic energy, which could theoretically be converted into photons upon impact. The reflection of these photons back upwards implies that they must be affected by gravity, as energy conservation dictates that the energy gained during the fall must be accounted for. The paragraph also introduces the concept of fictitious mass for photons and sets the stage for a mathematical exploration of this phenomenon.

Mindmap
Keywords
💡Photons
Photons are elementary particles that are the basic units of light and other forms of electromagnetic radiation. In the video, photons are discussed in the context of how they are affected by gravity, which is a key concept in exploring the interaction between light and gravitational fields. The script mentions that if photons were not affected by gravity, it would violate the principle of energy conservation, as more energy could be gained than initially put into the system.
💡Gravity
Gravity is a natural force that attracts two objects with mass towards each other. In the video, it is discussed in relation to its effect on photons, which is a fundamental aspect of general relativity. The script uses the example of a mass falling and gaining kinetic energy to illustrate how gravity influences the energy states of objects and photons, leading to a change in their frequency when they are near a massive body like Earth.
💡General Relativity
General relativity is a theory of gravitation developed by Albert Einstein, which describes gravity not as a force but as a curvature of spacetime caused by the uneven distribution of mass. The video touches upon this concept by exploring how photons, which are traditionally thought to be unaffected by gravity, actually are influenced by it according to general relativity.
💡Kinetic Energy
Kinetic energy is the energy that a moving object possesses due to its motion. In the script, it is mentioned that as a mass falls, it gains kinetic energy, which is then theoretically convertible back into photons. This concept is central to the discussion of energy conservation and the effect of gravity on different forms of energy.
💡Energy Conservation
Energy conservation is a principle stating that the total energy of an isolated system remains constant over time. The video uses this principle to argue that photons must be affected by gravity, as the energy gained by a falling mass must be accounted for when it is converted back into photons, ensuring no energy is created or destroyed in the process.
💡Fictitious Mass
In the context of the video, fictitious mass is a hypothetical attribute assigned to photons to simplify the mathematical treatment of their behavior under gravity. The script uses this concept to calculate the change in a photon's frequency as it moves in a gravitational field, which is a classical approximation to address a quantum phenomenon.
💡Frequency
Frequency refers to the number of occurrences of a repeating event per unit of time, and in physics, it is often used to describe the number of wave cycles of a wave per second. The video discusses how the frequency of a photon changes as it moves in a gravitational field, which is a direct consequence of the energy changes the photon undergoes.
💡Potential Energy
Potential energy is the stored energy of an object due to its position in a force field, such as a gravitational field. In the script, potential energy is discussed in the context of the energy a photon gains as it moves closer to a massive body, which contributes to the change in its frequency.
💡Quantum Physics
Quantum physics is a branch of physics that deals with the behavior of matter and energy at the atomic and subatomic level. The video mentions quantum physics when discussing the energy of an individual photon, given by the equation E = hf, where h is Planck's constant and f is the frequency of the photon.
💡Einstein's E=mc²
Einstein's mass-energy equivalence formula, E=mc², states that energy (E) is equal to mass (m) times the speed of light (c) squared. The video uses this equation to relate the energy of a photon to its frequency and to explain how the fictitious mass of a photon can be calculated in the context of its gravitational interaction.
💡British Physics Olympiad
The British Physics Olympiad is a competition for high school students that tests their understanding of physics. The video script is related to a problem from this competition, which explores advanced concepts such as the effect of gravity on photons, and is aimed at preparing students for the challenge of the Olympiad.
Highlights

Exploring the effect of gravity on photons through the lens of general relativity.

Theoretical conversion of a small mass's kinetic energy into photons upon reaching the ground.

The possibility of converting reflected photons back into mass, indicating the effect of gravity on light.

The paradox of energy conservation if photons were unaffected by gravity, leading to potential energy surplus.

Introduction of a physics problem involving a light object falling and gaining kinetic energy.

The mathematical approach to understanding the change in photon frequency due to gravity.

Assumption of a constant acceleration due to gravity for classical approximations.

The concept of a photon's fictitious mass, denoted as M gamma, in the context of this problem.

Energy of a photon on the ground being the sum of its original energy and potential energy.

Quantum physics connection through the equation E=hf, where E is energy and f is frequency.

Derivation of the fictitious mass of a photon as E/(c^2), linking energy and frequency.

The necessity of a change in photon frequency as it approaches the ground due to energy change.

Simplification of the equation to isolate the change in frequency (Δf) due to gravity.

Calculation of the change in photon frequency using known constants and variables.

Result of the calculation showing a tiny change in frequency compared to the original.

Recommendation for British physics Olympia senior challenge participants to watch a helpful tips video.

Transcripts

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Related Tags
General RelativityPhoton GravityEnergy ConservationPhysics ChallengeBritish OlympiaKinetic EnergyFictitious MassQuantum PhysicsFrequency ChangeLight ReflectionEducational Content