Lezione 16 Asimmetria Newton Maxwell e Simultaneità

Scientific Concepts / Discoveries / Phenomena Presented

Einstein relativity motivation from Maxwell’s equations

• Maxwell’s equations (describing electromagnetic waves) do not keep the same form under Galilean transformations, unlike Newtonian mechanics.
• This produces an “asymmetry” between:
  • electrical/magnetic phenomena, and
  • mechanics vs. electromagnetism
• The asymmetry arises when comparing different inertial frames moving relative to each other.

Symmetry (mathematical idea used as a physics tool)

Definition: An object or phenomenon is symmetric under a transformation if applying that transformation leaves its relevant characteristics unchanged.

Types mentioned:

• Discrete symmetries
  • translation
  • rotation by specific angles
  • reflection
• Continuous symmetries
  • invariance under a continuous range of transformations
  • example: a circle looks the same under any rotation

How symmetry is used in physics:

• reduces variables and equations
• helps identify conservation laws
• helps predict system behavior
• enables simplified models (e.g., spherical symmetry in gravity)

Historical path toward special relativity

• 1889 — Oliver H. (Hvide):
  • Using Maxwell’s equations, argued that the electric field around a moving charge distribution would not maintain spherical symmetry when the charge moves relative to the historically framed luminiferous ether.
• 1887 — Michelson–Morley experiment:
  • found no “ether wind” effect
  • light speeds perpendicular to each other showed no expected difference
• George Fitzgerald (conjecture) and Hendrik Lorentz (detailed version):
  • proposed Fitzgerald–Lorentz contraction to explain Michelson–Morley
  • moving matter would contract
  • the course credits Lorentz as giving a more detailed version (often linked to the Fitzgerald contraction hypothesis) that later informed the framework Einstein revised
• Key emphasis:
  • Einstein’s interpretation was not that physical materials contract
  • instead, the structure of space-time changes

Galilean relativity vs invariance of Newtonian dynamics

Galilean principle of relativity (mechanics):

• Newton’s second law (F = ma) keeps the same form in all inertial frames.

Galilean transformations (as stated):

• Spatial:
  • (x’ = x - vt) (and similarly for (y,z))
• Time:
  • (t’ = t) (absolute time)

Consequence shown:

• Newtonian mechanics is invariant under Galilean transformations for uniform relative motion.

Galilean transformations break Maxwellian wave equation form

• Maxwell’s electromagnetic waves lead to a wave equation in which the speed of light depends on constants ( \mu_0 ) and ( \varepsilon_0 ):
  • (c = 1/\sqrt{\mu_0\varepsilon_0})
• When the course applies Galilean transformations to Maxwell’s wave equation:
  • an extra term appears (described as highlighted in red in the video)
• Implication:
  • two observers in relative inertial motion could, in principle, detect their relative motion using electromagnetism
  • this contradicts what Galilean relativity would allow

Einstein thought experiment: invariance of light speed → relativity of simultaneity and time

Setup:

• a train/carriage moves uniformly relative to a station
• two synchronized laser sources on the carriage (or triggered simultaneously from the station, depending on perspective described) send light toward the center point where the other observer stands
• emission events are arranged so they are simultaneous for the station observer

Prior expectation (before Einstein):

• classical velocity addition:
  • light would behave like ordinary projectiles, giving an effective speed (c \pm v) for a moving observer

Einstein’s requirement:

• speed of light is invariant
• light propagates at exactly (c) in all inertial frames, not “added/subtracted” by the motion of the source

Consequences described:

• Relativity of simultaneity
  • the station observer sees the two arrival events as simultaneous
  • the moving observer does not
  • reason: during the finite propagation time, the moving observer changes the required light travel path
• Time dilation (as described)
  • different observers measure different elapsed times between events
  • inertial frames are treated symmetrically (each can regard the other’s clock as running slower/faster)
• Symmetry holds only for inertial motion
  • if one frame accelerates, the symmetry breaks
  • the accelerated observer becomes distinguishable

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Methodology / Logical Sequence Outlined (as presented in the lesson)

Start with symmetry as a conceptual/mathematical lens

• define symmetry under transformations:
  • translation, rotation, reflection
  • discrete vs. continuous symmetry
• argue that symmetry:
  • simplifies physics
  • reveals conservation laws

Historical interlude to motivate changing spacetime notions

• Maxwell results plus ether-era experiments/hypotheses lead to contradictions under Galilean assumptions
• Einstein’s step:
  • reinterpretation based on invariance of the speed of light

Compare invariance under coordinate transformations

• Newton’s laws:
  • invariant under Galilean transformations for inertial frames
  • absolute time: (t’ = t)
• Maxwell’s equations:
  • not invariant under Galilean transformations
  • an extra term appears

Thought experiment to enforce light-speed invariance

• carriage + two light signals
• show:
  • simultaneity depends on observer motion
  • elapsed times between events differ across inertial frames

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Researchers / Sources Featured (Named at End)

• Albert Einstein
• Pablo Picasso (art example used for symmetry; not a physics researcher)
• Oliver Hvide
• George Fitzgerald
• Michelson (from Michelson–Morley; first name not given in subtitles)
• Morley (from Michelson–Morley; first name not given in subtitles)
• Hendrik (Henrik) Lorentz (appears as “Henrik Lawrence/Lawrence” in subtitles)
• Voldemar Vo (appears in subtitles; likely related to Doppler-related work, name shown as “Voldemar Vo”)
• Copernicus
• Galileo
• Isaac Newton
• Ustad Ahmadi Lahori (architect referenced in the Taj Mahal symmetry story)
• Jason Pollock
• Plato
• Nicole Kidman (portrait/art symmetry example; not a scientific researcher)