By Brian Cox and Jeff Forshaw

pub. 2009

This book was a real gem. It surprisingly provided a deep and partially mathematical background on space-time and relativity. Authors Brian Cox and Jeff Forshaw clearly know how to explain complex ideas lucidly. I thoroughly enjoyed the read, and was able to pull a lot of material out. Ironically however, the actual mathematical derivation of E = mc^{2} was quite meager, and didn’t quite fundamentally explain the equation; instead, an approximate mathematical approach was used that relied heavily on drawings and though-experiments. Nevertheless, there’s a lot of fun facts and deep insight to be gained.

# Relativity

There are many things about the world that appear at first sight to be self-evidently true, and one of them is that we are standing still

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As a bizarre example, imagine a 4.0 meter long car trying to fit into a 3.9 meter long garage. Einstein predicts that if the car is traveling faster than 22% of the speed of light, then it will just about squeeze into the garage, at least for a split second before it crashes through the back wall.

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Distances in space-time are invariant.

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Distances between points and space time can be calculated using: s

^{2}= (ct)^{2}– x^{2}

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Everything moves at the same speed through space-time

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Why does everything move at the same speed through space time? Consider that for all observers, they are not moving relative to themselves. Thus the space-time distance equation: s

^{2}= (ct)^{2}– x^{2}, had x=0, which leads to s=c. In other words everything is moving through space-time at the same speed and that speed is the speed of light!^{6}Rishi, 94

Fundamental equations should be built out of objects that live in space time, not objects that live in space or in time separately because those types of objects are subjective.

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The part of the momentum space-time vector the points in the space direction has a length equal to ymv; The part of the new momentum that through the points off in the time direction has a length equal to ymc. y is 1/sqrt(1-v

^{2}/c^{2}) and is the quantity by which time slows down from the point of view of someone observing a clock fly past at speed.^{8}127, 128, 129

ymc [is] conserved… which is tantamount to saying that mass is conserved… if ymc is conserved than so too is ymc

^{2}. Thus, if we take the kinetic momentum in space (ymv) out of objects, we are left with only ymc- which is the energy contained in the mass. (130-132, Rishi)

The speed of massless particles is the universal constant.

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Einstein’s journey to special relativity was triggered by a simple question – what would it mean if the speed of light were the same for all observers? The rather more torturous journey to general relativity began with an equally simple observation that impressed him so much that he could not rest until he had recognized it’s true significance. The fact is this: all things fall to the ground with the same acceleration.

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The force of gravity is actually nothing more than a signal to us that space-time itself is curved.… since gravity is found in the vicinity of matter, we might conclude that space-time is warped in the vicinity of matter and, since E = mc

^{2}, energy.^{11}226

The GPS system is ubiquitous throughout the world, and it’s successful functioning depends upon the accuracy of Einstein’s theory’s… apart from the gravitational effects, the satellites are also whizzing around at around 14,000 km/h and the time dilation predicted by Einstein special theory amounts to a slowing down at the clocks by 7 µs each day. Taken together, the two affects amount to a net speeding up of 38 µs per day… equivalent to over 10 km in position per day.

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Robert pound and Glenn Rebka of Harvard University performed an experiment to “drop” light from the top of the laboratory to the basement 22 m below… they discovered that even light accelerates, not in the form of speed but in the form of modified frequency and shorter wavelengths.

^{13}236, Rishi

# On Science

Devising a theory that cannot be proved by observation is pointless in the sense that it teaches you nothing, irrespective of how passionately you may believe in it

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If a way of thinking about the world confers a survival advantage, then that way of thinking will become ubiquitous. The scientific correctness is irrelevant.

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Einstein was not a freak of nature and his intellect was not supernatural. He was simply a great scientist who did what scientists do: he took simple things seriously and followed through the consequences logically. His genius laid in taking seriously the constancy of the speed of light, as implied by Maxwell’s equations, and the equivalence principal, first appreciated by Galileo

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Science at its best is driven by inquiring minds afforded the freedom to dream, coupled with the technical ability and discipline to think.

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# On Deep Mysteries

In the early history of the universe… matter and antimatter almost completely canceled themselves out… initial mass… was utterly destroyed and converted 100% into energy… today we see the remnant of that cancellation. Astronomers have observed that for every matter particle in the universe there are around hundred billion photons. In other words, for every hundred billion matter particles made just after the big bang, only one survived. The rest took the opportunity available to them, to divest themselves of their mass and become photons.

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Neutrinos interact with the other particles in the universe only very weekly. The master equation tells us that is the case, for the neutrinos are the only particles that interact solely through the weak force.

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References

1. | ↑ | 10 |

2. | ↑ | 54 |

3. | ↑ | 64 |

4. | ↑ | 82 |

5. | ↑ | 93 |

6. | ↑ | Rishi, 94 |

7. | ↑ | 121 |

8. | ↑ | 127, 128, 129 |

9. | ↑ | 138 |

10. | ↑ | 221 |

11. | ↑ | 226 |

12. | ↑ | 235 |

13. | ↑ | 236, Rishi |

14. | ↑ | 12 |

15. | ↑ | 57 |

16. | ↑ | 240 |

17. | ↑ | 241 |

18. | ↑ | 200 |

19. | ↑ | 204 |