Can anyone help to explain the top of page 54 to me? It says the circumference of the ring could be reduced from the point of view of the muon to explain why the muon can make 400 laps in 2.5us. It says space is Malleable. It says real objects do shrink when they move. I can just about accept that the muon shrinks but why does the ring shrink and hence reduce its circumference? The ring is not moving. Ok, it is moving relative to the muon but the ring is not moving at 0.9994 x the speed of light so why does its circumference decrease? Any help appreciated!
If relative to the ring the muon is travelling at 0.9994c then if we look at the point of view from the muon the ring is travelling at 0.9994c. Hence, relative to the muon the ring is length contracted. Imagine a person standing still on the side of a road and a car driving past at 30 mph. Relative to the car the person on the road is travelling at 30 mph. I apologise if any of this sounds patronising. If this was of no help let me know, ill try to eloborate further.
That was helpful for me! Now, why should a box of hot gas/ flask of hot coffee be more massive than the cold version? The additonal energy to heat up the fluid is reflected in the the greater kinetic energy of the molecules, not additional mass? And how much does a box with a flying pigeon inside weigh (in Newtonian physics)? Thanks!
I had the exact same problem in reading this. I couldn't undersatand how the circumference of the ring could possibly be reduced. Obviously I don't doubt the physics of Prof Cox, I'm a big fan, but the explanation left me standing.
I also had difficulty with the second equation at the top of p77, where he introduces a minus sign. He had been very careful up to that point to explain every step to the non-mathematician, but he seemed to pluck this totally out of the air. It's not implied (at least not in any way I understand) by the diagram on p74 from which it is apparently derived. Wouldn't matter, except the whole of the explanation of why E=mc^2 then rests on that equation.
Energy and mass are aspects of the same thing. Kinetic energy implies, means, equals, IS a small increase in mass of the moving (from your point of view!) particle. That's what e=mc2 means; it explains what is meant by energy AS SEEN BY THE PARTICULAR OBSERVER only from a particle's momentum. Birds flying about (in a box or not) have extra kinetic energy compared with sitting on their perches. That has no consequence in Newtonian physics, what do you think it implies in relativistic terms?