=========================== ASTRO 130 - NIEL BRANDT QUESTIONS FROM THE STUDENTS =========================== If you find errors in the questions or answers below, please let me know. I'll work to improve them. ------------------------------------------------------------------------------ What is an inertial frame? What is an inertial force? Inertial frames are the "arena" in which special relativity can correctly describe Nature. In special relativity (where there is no spacetime curvature), an inertial frame is one where * A free particle released from rest stays at rest. * A particle launched with a given velocity maintains the magnitude and direction of that velocity. Thus, in special relativity, a frame where there is gravity would _not_ be an inertial frame. However, a frame moving with constant velocity out in isolated space would be an inertial frame. You can think of the word "inertial" as meaning "freely floating." An inertial force is a force arising from the acceleration of an observer's frame of reference. ------------------------------------------------------------------------------ Given that light is the fastest thing to exist in the Universe, how fast do other wavelengths of light move in proportion to it? In a vacuum will gamma-rays travel faster or slower than visible light? All types of light travel at the same speed, c, in a vacuum. This includes Radio waves Microwaves Infrared radiation Visible light Ultraviolet light X-rays Gamma-rays ------------------------------------------------------------------------------ According to special relativity, is the speed of light the only thing that is not relative? No, there are other things that are not relative too. Some examples include... The Minkowski absolute interval (see Chapter 2 of the Thorne book) The underlying mathematical form of the laws of physics (for example, Maxwell's laws of electromagnetism) Some physical constants, such as Planck's constant For another interesting possible example, see the short article by Giovanni Amelino-Camelia in Nature 418, 34 (4 July 2002). This should be available from the library on the second floor of Davey Lab. ------------------------------------------------------------------------------ What special and general relativity effects need to be taken into account for Global Positioning System (GPS) satellites? Some examples include... The satellites are moving relative to a person on the Earth. This has a "slowing" effect on their atomic clocks. The satellites are high up above the surface of the Earth. The gravitational potential there is less. This has a "speeding up" effect on the satellites' atomic clocks. The satellites move through Earth's gravitational field, and this changes the rate at which the atomic clocks on them run. The Earth is not a perfect sphere, and its gravitational field is actually complex. In total, relativistic effects are about 10,000 times too large to ignore. When you fly in an airplane during bad weather, the GPS is one of the key things that lets the pilots fly safely. So thank Einstein the next time you make a safe landing. Thank the pilots too, of course! For a detailed discussion of this topic, see the article by Neil Ashby on page 41 of the May 2002 issue of Physics Today. This should be available from the library on the second floor of Davey Lab. Also see Project A in the book _Exploring Black Holes_ by E.F. Taylor and J.A. Wheeler. ------------------------------------------------------------------------------ In the book by Begelman & Rees, they say that "Nowhere is gravity stronger than near the objects we call black holes." Is this statement absolutely conclusive? How do they know that even when we haven't explored all of space? We have not been able to prove this strictly in an observational sense, since as commented above we have not explored all of space. However, we have good evidence that general relativity applies throughout the entire Universe. Since we think it is universal, we theoretically expect that the statement by Begelman & Rees is correct. ------------------------------------------------------------------------------ Do photons of light have mass? If not, what implications does this have? Photons of light have no rest mass. One implication from special relativity is that any particle without rest mass _must_ move at the speed of light. ------------------------------------------------------------------------------ Why is the speed of light 300,000 km/s? Why does the speed of light not have some other numerical value? Nobody knows the full answer to this deep question. Someday, when we know all the laws of physics, we hope to be able to calculate the speed of light from first principles. For some further discussion on this see the book _The Life of the Cosmos_ by Lee Smolin (chapter 7 is the most relevant one to my knowledge). One could imagine a universe where the speed of light has a different numerical value, say 200 miles per hour. Einstein's laws of relativity could still hold in such a universe, although the mathematical equations would contain a different numerical value for the speed of light (all velocities in Einstein's relativity enter the equations only relative to the speed of light). If we could exist in such a universe, we would see relativistic effects when we drive our cars! Also see http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/fast_light.html ------------------------------------------------------------------------------ You mentioned that we've known about the aberration of light for quite some time now. How and when did the first signs of this come to light? Was this pre-relativity? Aberration of light was discovered in 1725 by James Bradley. He found that all distant stars displayed an apparent systematic movement related to the direction of the motion of the Earth in its orbit. This stellar aberration is analogous to the well-known falling-raindrop situation. A raindrop, although falling vertically with respect to an observer at rest on the Earth, will appear to change its incident angle when the observer is in motion. Special relativity effects make the real situation more complex than the falling-raindrop analogy. For further discussion see http://www.fourmilab.ch/cship/aberration.html. Aberration of light was known well before Einstein's relativity. ------------------------------------------------------------------------------ If I travel at 87% the speed of light and I see everyone on Earth's clock slowed, why when I return to Earth from my journey is everyone so much older than me? In your journey away from Earth and back to Earth, this is not actually what you will "see." You need to take into account the "standard" Doppler shift effect as well as relativistic time dilation. This issue is often discussed as part of the "twin paradox." For full discussion see http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_doppler.html and the associated World Wide Web pages. Take the twins in the twin paradox to be named Stella = Flying in the spaceship Terrence = At home on Earth The situations of Stella and Terrence are not "symmetric." Stella felt the acceleration on her trip outward as well as when she fired her thrusters to turn around and return to Earth. Terrence did not feel this acceleration. More technically, special relativity does not declare that all frames of reference are equivalent, only so-called "inertial frames." Stella's frame is not inertial while she is accelerating. ------------------------------------------------------------------------------