I would like to expand on what I mean by the title of this question to focus the answers.

Normally whenever a theory (e.g. General Relativity) replaces another (e.g. Newtonian Gravity) there is a correspondence requirement in some limit. However there is also normally some experimental area where the new larger theory makes predictions which are different from the older theory which made predictions of the same phenomena. This is ultimately because the newer theory has a deeper view of physics with its own structures which come into play in certain situations that the old theory didn't cover well. Additionally the newer theory will make predictions based on its novel aspects which the older theory did not consider. I know that String Theory is quite rich in this regard, but am not interested in that here. Nor am I concerned as to whether experiment has caught up, as I know that ST (and Quantum Gravity in general) is not easy to test.

So for the GR to Newtonian example an answer to this question would be: bending of light rays; Mercury perihelion movement - GR had a different results to Newton. What would not count as an answer would be new structures which GR introduces like Black Holes or even gravitational curvature per se.

So does ST have anything like Mercury perihelion movement waiting to be experimentally verified, and thus "improving" on GR within GR's own back yard?

a ball is thrown up onto a roof, landing 3.60 s later at height h = 25.0 m above the release level. The ball's path just before landing is angled at ? = 64.0?with the roof. (a) Find the horizontal distance d it travels. (Hint: One way is to reverse the motion, as if it is on a video.) What are the (b) magnitude and (c) angle (relative to the horizontal) of the ball's initial velocity?

A light modifier that is commonly used in studio photography is a honeycomb grid.

It narrows the beam of light to a circle with soft edges, as it can be seen here:

My question is: how is this happening?

A small reporter flash has a rectangular shape, if you place a rectangular shaped grid on it, it produces a "soft" circle of light. How is the light travel modified by the structure of the grid?

A uniform electric field exists in the region between two oppositely charged parallel plates 1.70cmapart. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate in a time interval 1.45

Consider the well known demonstration of diffraction by a narrowing slit. (See for example the demonstration at the 30 minute mark of this lecture at MIT by Walter Lewin)

It is my (possibly mistaken) understanding that the light emerging after the slit becomes substantially slimmer than one wavelength is polarized.
This would seem to imply that light of perpendicular polarization would not be transmitted, thus implying a fairly substantial and dramatic difference in the results of the experiment with parallel and perpendicularly polarized light. That is, instead of spreading out, the light polarized in the wrong direction would essentially just shut down as the slit narrows below one wavelength. Is this true?

According to the first law of thermodynamics, sourced from wikipedia "In any process in an isolated system, the total energy remains the same."

So when lasers are used for cooling in traps, similar to the description here: http://optics.colorado.edu/~kelvin/classes/opticslab/LaserCooling3.doc.pdf where is the heat transferred?

From what I gather of a cursory reading on traps, whether laser, magnetic, etc the general idea is to isolate the target, then transfer heat from it, thereby cooling it.

I don't understand how sending photons at a(n) atom(s) can cause that structure to shed energy, and this mechanism seems to be the key to these systems.

What are three possible locations at which the electrostatic potential of a point can be defined as having a value of zero?

Two 53.0 x 10^-9 C point charges are located on the x axis. One is at x = 0.35 m, and the other at x = - 0.35 m.

a) A third identical charge is placed on the y axis at y = 0.35 m. Find the magnitude of the force acting on this third charge? Answer in Newtons.

b) Now the third identical charge is placed on the y axis at y = 2 x 0.35 m. Find the magnitude of the force acting on this third charge? Answer in Newtons.

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Four charges are placed at the corners of a square. The side of the square is a = 0.30 m.

a) If the charge are identical and positive q = 21.0 x 10^-9 C what would be the magnitude of the force acting on each of the charges? Answer in Newtons.

b) We change the charges by q₁ = 21.0 x 10^-9 C, q₂ = 11.0 x 10^-9 C, q₃ = -12.0 x 10^-9 C, q₄ = -31.0 x 10^-9 C. What would be the magnitude of the force acting on charge q₃? Answer in Newtons.

c) We place the same charges at the corners of a rectangle of sides a and b (instead of a square). If b=2a/3 what would be the magnitude of the force acting on charge q₃? Answer in units of Newtons.

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Two 2.20-?C point charges are located on the x axis. One is at x = 1.57 m, and the other at x = -1.57 m. Determine the magnitude of the electric field on the y axis at y = 0.530 m. Answer in units of N/C.

During the Apollo XI Moon landing, a retroreflecting panel was erected on the Moon's surface. The speed of light can be found by measuring the time it takes a laser beam to travel from Earth, reflect from the panel, and return to Earth. If this interval is found to be 2.51 s, what is the measured speed of light? Take the center-to-center distance from Earth to Moon to be 3.84 X 10⁸ m. Assume that the Moon is directly overhead and do not neglect the sizes of the Earth and Moon. (Assume the radius of the Earth and the Moon are 6380 km and 1740 km respectively.)

Two identical objects each hold a net charge of q = 2e. If the gravitational force between the two objects exactly cancels the electrostatic force between the objects, what is the mass of each object?

According to Hubble's law, light and other kinds of electromagnetic radiation emitted from distant objects are redshifted. The more distant the source, the more intense is the redshift. Now, the expansion of the universe is expected to explain the redshift and its nearly linear dependence on distance between source and observer. But isn't there an other source influencing the redshift? We know that a light beam passing the Sun is deflected by the Sun's gravity in accordance with predictions made by Einstein's general theory of relativity. This deflection is dependant on a gravitational interaction between the Sun and the light beam. Thus, the position of the Sun is affected by the light beam, though by such a tiny amount that it is impossible to detect the disturbance of the Sun's position. Now, during its journey to the Earth a light beam, originating from a distant source in the Universe, is passing a certain amount of elementary particles and atoms. If the light beam interacts gravitationally with those elementary particles and atoms, affecting the microscopic mechanical properties of the individual elementary particles and atoms at issue, can this interaction be detected as a redshift of the light beam? If so, could we use this gravity redshift to measure the mean density of matter and energy in space? The beginning of the sentence "If the light beam interacts gravitationally with those elementary particles and atoms..." should be interpreted to say "If the light beam interacts gravitationally with those elementary particles and atoms by way of leaving them in a state of acceleration different from their initial state of acceleration...." This clarification seems to necessitate the additional question: "why would a gravitationally interacting object (a cluster of photons) passing another gravitationally interacting object (a mass) leave that mass in the same state as before the passage?"

Atomic and molecular spectra are discrete. What does discrete mean, and how are discrete spectra related to the quantization of energy and electron orbits in atoms and molecules?

I read this artice: Physicists Prove Einstein Wrong with Observation of Instantaneous Velocity in Brownian Particles

There is a common analogy about the structure of an atom, such as the nucleus is a fly in the centre of a sports stadium and the electrons are tiny tiny gnats circling the stadium (tip of the hat to 'The Greatest Show on Earth') but what is in the space between the 'fly' and circling 'gnats'?

Differences? They are both an electron and a proton, since the neutron decays to a proton and an electron, what's the difference between a neutron and proton + electron? so is it just a higher binding energy between the two?