Key Concepts from Relativity to Quantum Mechanics.

Exam Overview

• Format and Timing

  • Online test on Canvas (available for one week).

  • Expected to go live on Thursday morning or Wednesday afternoon.

• Content

  • Three questions covering:

  1. Hume

  2. Einstein

  3. Instrumentalism

• Grading Criteria

  • 95: Specific answers indicating attendance and understanding.

  • 85: Good effort with evidence of research but without classroom engagement.

  • 70: Minimal effort, heavily reliant on external sources.

Special Relativity

• Definition: A framework for understanding the relationship between space, time, and velocity.

• Key Concepts:

  • Spacetime: Space and time are intertwined and relative.

  • Velocity's Role: Relativity depends on how fast an object is moving.

• Critical Insight: Time and space are dynamic; they change with velocity, contrary to Newton's view of fixed measurements.

• Implication: A faster velocity can alterTime is perceived in different frames of reference.

General Relativity

• Definition: Expansion of special relativity, incorporating mass into spacetime dynamics.

• Mass-Energy Equivalence: E=mc^2 (Energy equals mass times the speed of light squared, showing mass is interchangeable with energy).

• Historical Context: The Washington muon experiment in 1962 validated Einstein's predictions over Newton's.

The Washington Muon Experiment

• Concept: Muons are produced by cosmic rays from the sun, traveling near the speed of light.

• Setup:

  • Detectors at the summit and base of a mountain.

  • Prediction vs Actual outcomes:

  • Newton’s Prediction: 27 muons detected due to their decay during travel.

  • Einstein’s Prediction: 400 muons detected due to relativistic effects lengthening their lifespan.

• Results: Actual measurement confirmed Einstein's prediction, establishing the validity of relativity.

Philosophy and Physics

• Incommensurability Problem: The discrepancy between deterministic classical physics (general relativity) and probabilistic quantum mechanics.

  • Quantum mechanics as variable since each subatomic particle behaves probabilistically rather than deterministically.

• Determinism vs. Probabilism:

  • Determinism (General Relativity): Same cause leads to the same effect consistently.

  • Probabilism (Quantum Mechanics): Same cause can lead to different outcomes with specific probabilities.

Quantum Mechanics and Entanglement

• Principles:

  • Quantum mechanics involves probabilistic outcomes, defying deterministic expectations.

• Quantum Entanglement:

  • Implies particles can instantaneously affect each other's states over distance ("spooky action at a distance").

• Experimental Evidence: Two-slit experiment highlights entangled behavior and the unpredictable nature of particles.

Proposed Solutions in Physics

• Multiverse Theory: Suggests the reality of multiple universes, each deterministic but emerging from probabilistic choices.

  • Critique: While logically coherent, it lacks predictive power, hence its rejection by the scientific community.

Instrumentalism in Philosophy

• Definition: A philosophical approach that views theories as instruments for predicting observable phenomena rather than as literal truths.

• Relevance: Offers a potential resolution to the incommensurability problem, bridging the gap between general relativity and quantum mechanics.

• Conclusion: Philosophical advancements can provide frameworks that physicists can build upon.

Exam Overview

Format and Timing

• Online test on Canvas, ensuring ease of access for students.

• The test will be available for one week, allowing flexibility for students to choose their optimum time for taking the exam.

• The expected launch period is Thursday morning or Wednesday afternoon, making it strategic for students preparing.

Content

• The exam will consist of three questions, specifically covering the following key areas of study:

  1. Hume:

  • Focus on Hume's empiricism, skepticism, and philosophy of human understanding.

  • Consideration of Hume's impact on modern philosophy and science.

  1. Einstein:

  • Essential concepts of both special and general relativity, including the implications of mass-energy equivalence.

  • Examination of Einstein’s revolutionary contributions to physics, transforming our understanding of space and time.

  1. Instrumentalism:

  • Exploration of the instrumentalist perspective in philosophy of science, particularly in relation to the theories of quantum mechanics and relativity.

Grading Criteria

• Grading will be as follows:

  • 95-100: Specific and thorough answers indicating not only attendance but a strong understanding of the concepts discussed in class and readings.

  • 85-94: Good effort demonstrated with evidence of external research; while not fully engaged in classroom discussions, some understanding is shown.

  • 70-84: Minimal effort with answers heavily reliant on external sources, demonstrating a lack of comprehension and engagement with course material.

Incommensurability Problem: The discrepancy between deterministic classical physics (general relativity) and probabilistic quantum mechanics. Quantum mechanics is seen as variable since each subatomic particle behaves probabilistically rather than deterministically. Additionally, the incommensurability problem highlights the challenges in comparing theories that operate under fundamentally different principles and frameworks, creating gaps in understanding. Select examples of these differing paradigms include the operations of classical mechanics and the unpredictability present in quantum theory. This disconnection impedes the formation of a unified theory that can adequately encompass both realms.