1.
Velocities don't add normally in relativity.  As shown on p. 152, the correct expression for velocity addition doesn't give us 1.7 c -- since nothing (except perhaps tachyons) can travel faster than light, and only massless things like light can travel at the speed of light -- but instead gives [0.9 c + 0.8 c] / [1 + (0.9)(0.8)], which is a bit less than 0.99 c.





































2.
No, it's not possible, or else you'd get into impossible paradoxes in which you convince your mother not to have any children (which sounds far more polite than "in which you kill your mother before she gives birth to you").

It's certainly true that the time between your mother's birth and your birth will be different in different reference frames, but the order can't change: Your birth is in the absolute future of the "your mother's birth" event, and your mother's birth is in the absolute past of the "your birth" event.  The only way that the order of two events can depend on the observer is if those two events are in each other's elsewhere, so that there's no causal relationship between them (i.e., neither one can physically influence the other).  So, for example, if I observe that I was born in Brooklyn in 1961 and that your mother was born on Alpha Centauri (over four light-years from Brooklyn) in 1960, some other observer might instead perceive that I was born before your mother.





































3.
All of the choices are correct: This famous equation applies to the conversion of rest energy to (or from) any other form of energy.  This is simply more noticeable in nuclear reactions than in other kinds of energy conversions -- the fractional change in rest energy is large enough to be measured -- but it doesn't follow that it only applies to nuclear energy.  So the equation does apply to an atomic bomb exploding, but no more so than it applies to a hot cup of coffee cooling off.





































4.
Only the second choice is correct.  Time intervals are frame-dependent, which is what "time dilation" is all about; length intervals (distances in 3-D space) are also frame-dependent, which is what "length contraction" is all about.  But the spacetime interval between two events is the same for every uniformly moving observer.





































5.
Let's use the book's definition of spacetime interval, which is the negative of the one I gave in lecture (one can find both versions in different books):

I  =  t² - x² - y² - z²

I  =  t² - x²  =  13² - 12²  =  25

This means that according to Harry -- who thinks that he hasn't moved at all -- the trip covered 5 years and 0 light-years, since 5² - 0² also equals 25.

According to Dick, the distance covered was 6 light-years, so we have

25  =  t² - 6²

Note that tachyons could never slow down to the speed of light or slower: They would be condemned to travel faster than light at all times.





































7.
Neither choice is correct.  An event can only influence other events located within its future, that is, within the forward-in-time light cone.  An event can be influenced by other events within its past, but can't influence those events.  It can't influence or be influenced by other events in its elsewhere.  So (Farmington, 2008) can influence (Portland, 2009) but can't be influenced by it; it can be influenced by (Alpha Centauri, 1996) but can't influence it; and it can't influence or be influenced by (Alpha Centauri, 2005).





































8.
We can take the equation E = mc² and rearrange it to read m = E/c². Since the square of the speed of light is a huge number, it follows that adding even a large amount of energy to something results in only a tiny amount of extra mass.  So we don't notice the change, even though chemists 200 years ago (who thought that heat might be some kind of material substance with mass) carefully checked for such changes.





































9.
The full set of events that cover your life -- from (birthplace, date of birth) to (place of death, date of death) -- is your worldline.

There's some very interesting philosophy that results from this.  Imagine walking northward along a fence that's 100 m long.  You would never claim that the north end of the fence hadn't existed until you reached it; no, every slat in the fence was there the whole time, even before you got as far as that slat.  So if relativity implies that time is merely a dimension, past-future like south-north, why treat it any differently than south-north?  Why claim that the year 2016 doesn't exist until you reach it?  No, your entire worldline is just there, your entire 4-D life, just like the fence.  On this view -- the "block universe" -- our psychological impression that time is "flowing," that the future doesn't yet exist but comes into being at the moment when it's the present, is a mere illusion.





































10.
The amount of energy an object possesses is γmc², where γ (gamma) is the same relativistic factor we've seen in the context of time dilation and length contraction.  If an object isn't moving (v = 0), we have γ = 1 and hence rest energy equal to mc².  If, on the other hand, the speed approaches c, γ gets larger and larger.  In order to move at exactly c we would have γ blow up to infinity: infinite energy required.  Since the universe has only a finite amount of energy, it follows that no object with any mass, be it a car or a planet or an electron, can move at the speed of light -- although it can get very close if we have a lot of energy to give it.

The energy required to create a particle-antiparticle pair is just 2mc², where m is the mass of the particle.  That might be large or it might be small, but it's certainly finite.  If we go in the other direction -- pair annihilation -- we destroy a particle-antiparticle pair and get 2mc² worth of some other form of energy, such as a pair of photons; this is conversion of matter to light.