Part 2

~2:30 : Since all observers will see the same laws of physics hold, and since the speed of light (c) is a part of the laws of physics, all observers will see c the same, regardless of their state of motion. c is constant. In order to agree on the speed of light, observers may need to disagree about distance and time.

As I was trying to explain to my wife (my weakness, not hers), the reason classic relativity (CR) says object move with different speeds in different reference frames, is actual because the equations work only by keeping c constant. (That this was not known, but that the equations still worked, raises an interesting point about counterfactuals and scientific theory.) A pitcher P on a moving truck will see his pitched ball B move at 100mph, whereas an observer O of the truck-ball system TB would see the ball B moving at 150mph (cf. part 1 of video series). Since the time of measurement is the same for both P and O, and since c must remain constant, the speeds must rise as the relative distances increase. O is removed from TB to an extent that speed will rise in order to keep the ratio between distance and speed constant relative to c. P is closer to TB, so the speed decreases to preserve the c-ratio. In fact, P is "inside" TB so that he will detect no motion (unless he pitches B), which just means that as distance (between P and TB) shrinks to 0, the speed of B in TB shrinks to zero--all the while c is constant.

~7:00 : Reflected-photon clocks C1 and C2 would be precisely synchronized for an outside observer O. If C1 is stationary while C2 is in motion, O will see the time of C2 pass more slowly. why? Since both reflected-photon beams move at the same speed, and the moving clock C2 covers a farther distance than C1, the time of C2 must increase in order to keep c constant (despite other changes like increased distance).

Part 3

~1:30 : All the rulers aboard the moving ship S2 shrink just enough to keep c constant invariantly with respect to increased speed. Time dilation and length contraction.

I was trying to get length contraction clearer in my mind tonight, and here is what I thought of:

The faster object moves towards me, the faster its "trailing photons" will reach me relative to its "leading photons". In other words, when I observe a normal stationary ruler, with one end pointed at me, light from its front end reaches me at no discernibly different time than light from its rear end. But if it is moving at an appreciable fraction of the speed of light, photons from its front end will reach me at about the same time as photons from its back end, and thus it will appear that both ends are closer together (i.e. that the ruler is shrunken). I "understand" that this compression is not merely a result of my neural-observational limitations, but actually holds in a Lorentzian way (cf. Wiki). But what of non-Lorentzian relativity?

~3:30 : The faster you go through space, the slower you go through time. If you could travel at the speed of light in space, you would make no progress in time. If you could surpass c through space, you could travel back in time. If different observers must always agree on c, they must disagree on time and distance.

~5:15 : There is no single time or space on which everyone can agree. [Thus, unless the universe transcends space and time, there is no universe. There is a universe, however, in which c is constant. Therefore the universe as known by humans transcends space and time.] Velocity depends on distance (viz. from which frame of reference it is observed, i.e. how far from its center it is clocked), and time depends on velocity (viz., as velocity increases, time decreases, and distance increases). What is observed far apart in space, appears near in time. What is observed near in space, appears far apart in time (relative to something farther away).

~6:30 : The faster a particle goes, the heavier it goes. In order to maintain acceleration, as mass increases, energy must increase. E = mc^2. Once again, c must remain constant. In a given time, an object's velocity depends on the energy given to its mass.

Part 4

~0:20 : Einstein's STR says that an observer at a constant velocity Ov will observe the same laws of physics as an observer at rest Or. [I think "at rest" here could only mean "an observer moving at the speed of light (Ol). Cf. Einstein's scenario of sitting on a photon.]

~1:55 : Einstein argued that there's no way to tell a difference between being stationary under the influence of gravity versus being accelerated through space. Hence, given the universality of the laws of physics, the laws of gravity must be equivalent to (i.e. transformable into) the laws of acceleration through space.

======

Basic maths for time dilation

γ = 1/√(1 - (v

^{2}/c

^{2}))

This helps me make sense of the "substantial fraction of the speed of light" condition (i.e. the focus on "motion at relativistic speeds"). As v increases, the ratio of v

^{2}/c

^{2}nears 0, and the divisor under 1 therefore nears 0, which would make

*γ*into an increasingly large (and potentially infinite) amount. In turn, as

*γ*increases,

*Δt'*decreases. As observed time (

*t'*) decreases, time "flows more slowly". Time dilation at relativistic.

======

Time dilation with Dr Wittman

~0:00 : "Moving clocks run slowly and moving things contract in the direction of their motion. Those are two of the amazing conclusions of special relativity."

~ 2:30 : "We have to measure the same speed of light, even if the clock is moving. ... Let's see if it can get to the top of that clock." The faster the photon clock moves, the less distance it travels inside the apparatus, and therefore the less time it traverses. "Moving clocks go slower."

~ 4:05 : γ = c(1/√(1 - (v

^{2}/c

^{2}))

So as speed increases, time increases and length decreases. Anything beyond the speed of light would be eternal and sub-spatial (i.e. immaterial). And you're telling me natural theology is dead??

~6:30 : In order for the truck driver to maintain c, he must measure "our" v as vγ.

## No comments:

Post a Comment