The Biggest Ideas in the Universe Quotes

“There's nothing wrong with defining "the total energy contained in a region of space" as "the sum of the energies of all the things within that region", and admiting that this number changes over time.”
― Sean Carroll, The Biggest Ideas in the Universe: Space, Time, and Motion

“Now comes the real magic. In pre-relativistic Newtonian mechanics, momentum is represented by a three-vector given by mass times velocity, . In the world of relativity, we define the four-momentum in an analogous way, as mass times four-velocity:”
― Sean Carroll, The Biggest Ideas in the Universe: Space, Time, and Motion

“The main trick is to define the four-velocity as a derivative with respect to the proper time τ along the trajectory, rather than with respect to the coordinate time t. We write the”
― Sean Carroll, The Biggest Ideas in the Universe: Space, Time, and Motion

“The minus sign in the proper-time formula (6.2) opens up an interesting possibility. If we consider a straight path that traverses equal amounts of space and time, (Δx)2 = (Δt)2, we will have τ = 0. So the object moves, but no proper time elapses along its journey.”
― Sean Carroll, The Biggest Ideas in the Universe: Space, Time, and Motion

“not a conclusion we derive from deeper principles. Straight lines in space are the shortest possible distance; straight paths in spacetime are the longest possible time.”
― Sean Carroll, The Biggest Ideas in the Universe: Space, Time, and Motion

“argued for new ways of thinking about length and duration.”
― Sean Carroll, The Biggest Ideas in the Universe: Space, Time, and Motion

“Rocky Kolb has put it, “To compare the accomplishment of Newton to that of the first manned flight, one would have to imagine Orville and Wilbur Wright pulling up on the sands of Kitty Hawk on December 17, 1903, behind the controls of a modern jetliner and flying off to New York.”[*]”
― Sean Carroll, The Biggest Ideas in the Universe: Space, Time, and Motion