Do sound waves in air fall due to gravity, and thus follow a parabolic
trajectory?
Consider a binary star with equal mass components in circular orbits.
The non-zero light-travel time across the orbit causes each component
to feel a force acting toward the position where the companion used to
be, not where it is presently on the diametrically opposite side of
the orbit. Thus, there is a component of force acting in the
direction of motion of the star along the orbit. This force does work
on the star and both stars gain energy continually, violating the law
of conservation of energy.
(Feynman discusses a similar problem between charged particles. In
both cases, each mass (or charge) performs a linear extrapolation of
the companion's apparent position and velocity and determines where
the companion would lie at the moment the signal from it is received.
The force of attraction is found to be directed towards that
extrapolated position. If the actual motion of the companion is not
linear, as in a circular orbit, there will be an observable effect due
to the difference in actual position and the direction of the force of
attraction. In the binary star, the effect is gravitational
radiation.)
By what mechanism is the extrapolation performed?
Why isn't the sky black? The sky should be black when viewed 90 degrees
to the sun because, for every scattering molecule, there is another half a
wavelength more distant from the observer but excited in phase with
the first molecule, and so there should be complete destructive
interference.
A coil around a toroidal solenoid will have an emf induced in it when
the current in the solenoid changes (i.e., a transformer). But, the
magnetic field is zero everywhere outside the toroid, so how can electrons
in the coil know that the current changed?
Consider two black body cavities with different size apertures facing each
other, and a lens in between focusing all the radiation from each aperture
onto the other. Let the two cavities come into thermodynamic equilibrium.
At equilibrium, the two must be at the same temperature. But the apertures
have different areas... if one has twice the area of the other then it
radiates twice the power into the other than the other radiates into it,
and so the system comes to equilibrium with the cavities at different
temperatures, violating the second law of thermodynamics.
Consider a hose carrying water, looped into a ring. Let the water move
through the hose at a speed close to that of light. The Lorentz contraction
will cause the column of water to appear shortened. However the hose
will not have changed length since it remains stationary wrt the observer.
How can the ring of water be shorter than the hose that contains it?
For every wave from a randomly polarized light source, there will be, on
average, another photon with opposite phase that will cancel with it, and
thus the total power will be close to zero.
Feed a dipole antenna from one oscillator, which delivers a current
I.cos(wt) and thus delivers a given power to the antenna. Now connect
in parallel another oscillator, also delivering a current I.cos(wt),
and thus also delivering the same power to the antenna. Now, the
charge separation on the antenna is doubled so the electric field
strength in space is doubled, so the radiated power is increased
four-fold, which violates conservation of energy.
Consider a short pulse of EM radiation (e.g. from an electron-ion
collision). The Fourier transform is broad spectrum, with all
sinusoids adding in phase at the time of the pulse, and destructively
interfering at all other times. One could take a narrow-band radio
receiver to select a small range of components. These components
would be present for all times before as well as after the pulse. The
component seems to anticipate that the pulse will be generated.
If you place a lens between two charged particles, does it focus the virtual
photons that are exchanged between the particles that cause the Coulomb force,
and so change the strength of the electrostatic force?
VLBI can be done between one antenna and itself six months later along
earth's orbit, provided bandwidth is sufficiently small that the
coherence time is longer than six months. (From Wim Brouw.)
While travelling on a bus, if you open a window a breeze comes in.
This is true regardless of which window you open. If all the windows
are open then all have a breeze coming in and none have a breeze
going out. The bus should therefore explode.
I invite discussion.
Back to Alan Roy's home page
Alan Roy
Last modified 3 January 1999.