Answers to Idea 4 Study Questions -- 7 Ideas Sec. 005

(1) Because a basic idea in it is that there is no "special" inertial reference frame - all motion is relative (If I say that Bob is going at half the speed of light, I am referring to his motion *relative* to me, i.e., viewed from

my inertial reference frame).

(2) Light is made of periodically varying electric and magnetic fields, that is, an electromagnetic wave (another view of light is that of quantum mechanics - light as "photon" energy bundles. This is a more useful view when we talk about tiny amounts of light, e.g., single photons).

(3) A reference frame is a particular view of the universe that depends on the motion and position of the observer (for example, the cars on a road move differently for someone in a car driving on the road versus someone standing by the side of the road). "Inertial" means not accelerating - an inertial frame of reference is one of an observer who is not accelerating.

(4) This idea, which is part of both Galileo's and Einstein's theories of relativity, simply says that if you do any experiment (anything at all) within one inertial reference frame you will get the same answer as in another. (The experiment has to be done within the frame itself, not "looking out the window" at another frame). For example, let's say you try to test conservation of momentum standing by the side of a road and then inside a bus travelling at constant velocity - you will get the same answer both times! Another way of saying this is that there is no way to tell which inertial frame you are in without looking at another frame (looking out the window of a moving bus, say).

(5) A car changing speed or going around a corner is a good example. In non-inertial frames you feel forces due to the accelerations.

(6) Galilean relativity is based on simple additive velocities - two drivers heading at each other, each going 60 mph relative to someone on the side of the road, thinks that the other driver is going 120 mph.

(7) Something that is the same in all inertial frames - length, mass, time, and son on.

(8) See above.

(9) Maxwell created a really neat, very successful theory of light, electricity, and magnetism.

(10) People believed in

(a) equivalence of inertial frames (4 above) and

(b) Galilean relativity (6 and 7 above).

Now Maxwell's theory (9 above) conflicted with these beliefs - see for example our discussion of the person in a car with a lightbulb behind them (slide on the net). Thus either

(1) All inertial frames are not equivalent or

(2) Galilean relativity is wrong

(11) Michelson did a nice experiment to try to measure the motion of the Earth relative to that very special hypothetical inertial frame, the frame of the "Ether". If he had found this motion then all frames would not be equivalent - there would have been a special frame across the Universe to which all motion could be compared. However, the experiment (using the Michelson Interferometer discussed in class) found nothing. Oddly, Michelson still believed in the Ether to the end of his days.

(12) Interference is the name for the ways two waves can add up. Here is *constructive* interference: the two waves on top are "in-phase" - their peaks and troughs line up and the waves add up to a wave twice as big.

Here is *destructive* interference: the two waves on top are "out of phase" with peaks lining up with troughs and cancel out when you add them.

We met interference in the context of the Michelson interferometer, and

will see it again in quantum mechanics.

(13) (1) All inertial frames are equivalent.

(2) The speed of light is the same in all inertial frames (no matter how fast the source of observer is moving).

(14) Number 1 was also known to Newton.

(15) Galilean relativity adds velocities - 2*3/4 = 1 1/2 times the speed of light.

(16) This one is more complicated than I had intended. The important thing is that the answer is greater than the speed of light - Galileo adds the velocity of the light to that of the on-coming car.

(17) They would say that the light is going at the speed of light minus their velocity (minus since the car and light are going the same direction: 1-3/4 = 1/4 the speed of light.

(18) The answer to 15 is that nothing ever goes faster than the speed of light in Einstein's theory - there is an "ultimate speedlimit". Thus each driver sees the other as going faster than 3/4 the speed of light but less than the speed of light (the actual formula is a bit complicated and is in your book if you want it).

For 16 and 17, light always goes the same speed for any (inertial) observer.

(19) Suppose that, relative to my frame, some object is traveling by me. Then I will measure a shorter length in the direction of motion for that object the faster it goes. Similarly, an observer in the frame of reference of the object will see me get shorter and shorter since, to that observer, *I* am the one moving.

(20) Again, if I look at a clock in a frame moving with respect to mine, that clock will be running more slowly.

(21) The faster Aggie goes, the larger the mass Klytemestra will measure. Similarly, Aggie will see K's mass go up.

(22) The rest mass of an object is simply the mass measured by an observer in the reference frame of the object itself. In other words, it is the mass measured by someone not moving relative to the object.

(23) We have seen (# 21) that, the faster something goes, the more mass it has. (Nothing can go the speed of light - it would have infinite mass.) Thus somehow the energy added to an object to give it a velocity near the speed of light does not go into increasing the speed so much as the mass - energy gets converted to mass! Einstein had the idea that even the rest mass had an equivalent energy: E=mc^{2}, the energy of the rest mass is equal to the mass multiplied by the speed of light twice (c is the speed of light, c^{2}=c*c).

(24) Well, let's see (I will do the math - you will not need to know how). m=1 kg (which weighs about 2 pounds on Earth). Putting in the speed of light in metric units (3 x 10^{8} m/s) I get E = 9 x 10^{18} Joules. This is a HUGE energy - Kent and much more will simply go bye bye! (This is about the energy used as electricity by the entire United States over an entire year, all released in one burst!)

(25) The twin paradox is not simple but the following is correct (I am avoiding the "paradox part of the answer - if you are interested see the book). The twin on the Earth would age much faster than the twin moving on the rocket ship - when that twin returned he would find the twin left on Earth probably dead while the moving twin might only have aged a couple of days!

(26) The speed of a car, an airplane, or even one of our spaceships is so slow compared to light that all of these cool effects are only observable using very sensitive instruments - not just our senses. There is no fundamental reason we cannot go faster, near the speed of light - it is just not practical given our technology.

(27) About 186,000 miles per second. This works out to about 700 million miles per hour!

(28) It is a wonderful theory and agrees very well with experiments (including those done on tiny particles moving very very near the speed of light). Of course, it only works in *Inertial* reference frames (Einstein's General theory of relativity tells us what happens in accelerated frames…)

(29) Gamma (written g ) is a mathematical quantity that tells us how much, e.g., length contracts, time slows, and mass increases as we approach the speed of light Gamma becomes infinite just at the speed of light. (For you info (not the test), where v is the velocity of the moving frame and c is the speed of light.)

(30) See #23.

(31) See #18.