def test_lorentz_transform(self):
v = 3 / 5
group_transformed = geom.lorentz_transformed(
geom.PointGroup([(0, 1), (2, 3)]), v)
line_transformed = geom.lorentz_transformed(geom.Line((0, 1), (2, 3)),
v)
ribbon_transformed = geom.lorentz_transformed(
geom.Ribbon(geom.Line((0, 1), (2, 3)), geom.Line((0, 1), (0, 0))),
v)
self.collection.lorentz_transform(v)
self.assertAlmostEqual(self.collection[0][0], group_transformed[0])
self.assertAlmostEqual(self.collection[0][1], group_transformed[1])
self.assertAlmostEqual(self.collection[1].direction(),
line_transformed.direction())
self.assertAlmostEqual(self.collection[1].point(),
line_transformed.point())
self.assertAlmostEqual(self.collection[2][0].direction(),
ribbon_transformed[0].direction())
self.assertAlmostEqual(self.collection[2][0].point(),
ribbon_transformed[0].point())
self.assertAlmostEqual(self.collection[2][1].direction(),
ribbon_transformed[1].direction())
self.assertAlmostEqual(self.collection[2][1].point(),
ribbon_transformed[1].point())
def _get_transformable_and_vrel_in_all_frames(lorentz_transformable, vrels,
origin):
"""Return lists of a LorentzTransformable and vrels in different frames,
where the input vrels can be a scalar or a list of values."""
transformables = [lorentz_transformable]
try:
transformables += [
geom.lorentz_transformed(lorentz_transformable, vrel, origin)
for vrel in vrels
]
return transformables, vrels
except TypeError:
# Single vrel
transformables += [
geom.lorentz_transformed(lorentz_transformable, vrels, origin)
]
return transformables, [vrels]
def setUp(self):
super().setUp()
# Over 3 frames of transformation
self.transition_duration = 2
mid_meterstick = geom.lorentz_transformed(self.meterstick, 2/5)
mid_vel = mid_meterstick.velocity()
mid_length = mid_meterstick.length()
# Round
self.vertices_mid = _arrays_to_lists([
[0, 0],
[mid_length, 0],
[mid_vel*self.tlim[1] + mid_length, self.tlim[1]],
[mid_vel*self.tlim[1], self.tlim[1]],
[0, 0]
])
# Round
self.xdata_mid = [0, round(mid_length, 7)]
'markersize': 10,
'label': 'Arrive home',
}
)
# Collect scene
scene = geom.Collection([
earth, planet,
rocket_forward, rocket_backward,
turnaround_event, return_event,
])
# Plot the scene
tlim = (0, geom.STVector.gamma_factor(v)*t_return)
pad = planetdist/5
xlim = (geom.lorentz_transformed(return_event, v).x - pad,
geom.lorentz_transformed(return_event, -v).x + pad)
# From Earth's point of view
current_time_color = 'limegreen'
instant_pause_time = 0.5
fps = 100
legend = True
earth_fname = '9-twinparadox_earth.mp4'
anim_earth = vis.stanimate_with_worldline(scene,
tlim_anim=(0, return_event.t), tlim_worldline=tlim, xlim=xlim,
legend=legend, legend_loc='upper left', fps=fps,
title="Twin paradox (Earth's POV)",
current_time_color=current_time_color,
instant_pause_time=instant_pause_time)
anim_earth.save(earth_fname)
title='The ladder paradox')
p[0].save('8-ladderparadox.png')
p[0].show()
# Animate the lab frame
fps = 50
current_time_color = 'cyan'
lab_fname = '8-ladderparadox_stationary.mp4'
anim_lab = vis.stanimate_with_worldline(scene, tlim=tlim, xlim=xlim,
fps=fps, legend=True, legend_loc='upper left',
title='The ladder paradox (stationary POV)',
current_time_color=current_time_color)
anim_lab.save(lab_fname)
# Animate the ladder frame
ladder_fname = '8-ladderparadox_ladder.mp4'
anim_ladder = vis.stanimate_with_worldline(geom.lorentz_transformed(scene, v),
tlim=tlim, xlim=xlim, fps=fps, legend=True, legend_loc='upper right',
title='The ladder paradox (ladder POV)',
current_time_color=current_time_color)
anim_ladder.save(ladder_fname)
# Animate the transformation
lt_fname = '8-ladderparadox_transform.mp4'
anim_lt = vis.animate_lt_worldline_and_realspace(scene, v,
tlim=tlim, xlim=xlim, fps=fps, legend=True, title='Transforming frames...',
current_time_color=current_time_color)
anim_lt.save(lt_fname)
# Animate the rewind from the lab frame
rew_fname = '8-ladderparadox_rewind.mp4'
anim_rew = canim.Rewinder(anim_lab, rewind_rate=5)
anim_rew.save(rew_fname)
def setUp(self):
self.original = geom.STVector(2, 3)
self.transformed = geom.lorentz_transformed(self.original, 3 / 5)
grid_with_light.append(origin)
anim = vis.animate_lt(grid_with_light,
v,
origin=origin,
tlim=tlim,
xlim=xlim,
lim_padding=0,
title='The Lorentz transformation (about t = 2, x = 1)')
anim.save('3-lorentztransform_origin.mp4')
anim.show()
# Transform specific object by copying
tlim = (0, 2)
xlim = (-2, 2)
meterstick = phy.MovingObject(-1 / 2, length=1, velocity=1 / 2)
meterstick_copy = geom.lorentz_transformed(meterstick, 1 / 2)
p = vis.stplot(meterstick_copy,
tlim=tlim,
xlim=xlim,
title='Stationary meterstick')
p.save('3-lorentztransform_stationary_meterstick.png')
p.show()
# Transform specific object in place
meterstick.lorentz_transform(4 / 5)
p = vis.stplot(meterstick,
tlim=tlim,
xlim=xlim,
title='Left-moving meterstick')
p.save('3-lorentztransform_reversed_meterstick.png')
p.show()