### The books GRAVITATION and Spacetime physics

 1 Nicolaas Vroom The books GRAVITATION and Spacetime physics Friday 22 September 2017 2 Nicolaas Vroom Re :The books GRAVITATION and Spacetime physics Friday 13 October 2017 3 Nicolaas Vroom Re :The books GRAVITATION and Spacetime physics Wednesday 25 October 2017

The books GRAVITATION and Spacetime physics.
3 posts by 1 author

### 1 The books GRAVITATION and Spacetime physics

From: Nicolaas Vroom
Datum: Friday 22 September 2017
On Wednesday, 6 September 2017 17:32:34 UTC+2, Tom Roberts wrote:
 > On 9/6/17 12:55 AM, Nicolaas Vroom wrote: Get a GOOD book on Special Relativity: Taylor and Wheeler, _Spacetime_Physics_. When you understand that, get a GOOD book on General Relativity: Misner, Thorne, and Wheeler, _Gravitation_.

For a review of the book GRAVITATION see: https://www.nicvroom.be/Book_Review_GRAVITATION_by_MTW.htm For a review of the book Spacetime Physics (chapter 1) see: https://www.nicvroom.be/Book_Review_Spacetime_Physics.htm See also: http://www.eftaylor.com/download.html The main reason of these comments is that I like to write my thoughts on paper for further reference.

One very important page of GRAVITATION is box 16.2 page 394: "Proof that a pendulum clock at rest on the earths surface is ideal." IMO all clocks at rest are ideal (one more than an other) compared with moving clocks.

A very important concept of Spacetime is a lattice at page 18 A grid with at equally spaced points a clock. The problem is how do these clocks function and how are they synchronised. Synchronization is discussed at page 18.

In Spacetime at page 20 two types of lattices are discussed: laboratory frames (or rest frames) and rocket frame or moving frame. That means the lattice is at rest or moving.

Synchronisation uses a reference flash. A clock uses two mirrors and a flash (see page 4,5). That means the clock at the origin uses both.

This raises no problems when the clock is at rest, because the reference flash goes to the clocks x1, x2, x3 etc in the x direction. But also in the y direction to the clocks y1,y2 etc. For the z direction this is the same. All directions are treated equally. From a physical point for a clock this means that the light flash is both reflected by the mirror (in order for the clock to tick) but also should go through the mirror (to be synchronised) in all three directions. See 'reflections' in book review.

When you move the lattice in the x direction, including all the clocks then it takes longer for the clock to tick, because the mirror moves away. The distance to the clock at x1 also increases.

For the clocks in the y and z direction these clocks also tick slower but Less. The reason is because the path of the lightpath is tilted. The mathematics is the same as used in the Michelson and Morley's experiment. The lightbeam in the horizontal direction is used to sync to clocks in the direction of motion and the vertical direction in the y and z direction. However all these 3 beams should reach the origin simultaneous in order for the clock to tick. If that is true than the only solution is physical length contraction in the x direction.

When you start with synchronised clocks at rest in x direction it is possible to demonstrate if there is length contraction involved? To do that you need a rod at rest with markings at the same distance as the clocks. You also need a second rod with the same length and markings. When you move the second rod and compare them with the synchronised clocks you can test: length contraction. When one clock (tick) coincides with a mark of the moving rod all clocks should coincide with a mark of the moving rod. IMO that will be the case.

Nicolaas Vroom

### 2 The books GRAVITATION and Spacetime physics

From: Nicolaas Vroom
Datum: Friday 13 October 2017
In the book Spacetime physics 2nd edition at page 12 a clock is defined as a flash of light that bounces back and forward between two parallel mirrors. I prefer a slightly different clock. The light source is in the center of the two mirrors. To make the clock slightly more complex: the clock has 6 mirros; two in each direction. IMO this clock (when at rest, with the light source at the center and which sends out a flash of light in all 3 directions to each of the six mirrors) behaves in the way, that all the reflections will return simultaneous at the origin (the light source) in the center.

To make a grid we start with a cube in the shape of one cube and place one clock at each grid corner. That means 8 clocks in total. To make things easy the size of each clock (the distance between two mirrors is 1 meter) and the distance between the center of two clocks is also 1 meter. That means the clocks touch each other.

To synchronize, the clock at position O=(0,0,0) sends out a synchronisation signal. This signal is special, besides that it is used for the clock to tick, it will also go in the 6 directions (through the mirrors) towards the 3 adjacent clocks (1,0,0) (0,1,0) and (0,0,1) and start these clocks at time t1. Because the distances are identical at moment t1 the clock at position O also ticks 1, which mean that the initial start value of each of these three clocks should be tick 1. Starting from these clocks the next nearest rings of cloclk will be synchronised. This are the clocks at the positions (1,0,1) (1,1,0) and (0,1,1). The initial start value of these 3 clocks will be a 2 the same value as the number of ticks of 4 already ticking clocks. The final clock at position (1,1,1) will be initialized with the value 3. At that moment all the 8 clocks are synchronised.

What this means is that a clock at position x,y,z will be synchronized after x+y+z ticks of clock O at position (0,0,0).

What happens if the frame is not at rest but moves with a speed vx in the x direction. The strange thing is that this will influence all the clocks in the frame, inclusif the synchronisation process. The synchronisation process in a frame at rest is symmetric in all directions In a moving frame this is not the case. The synchronisation signal of the clock at O in the x direction is used to synchronize all the clocks (x,0,0). In a moving frame all these clocks will run slower. The synchronisation signal of the clock at O in the y direction is used to synchronize all the clocks (0,y,0). In a moving frame all these clocks will run slower, but at a different rate as in the x direction. The z direction follows the same logic as in the y direction for all the clocks (0,0,z).

What this means that IMO in order to study the laws of nature only a reference frame at rest can be used.

For more details see: Reflection 5 - Worldline Parallel Mirrors - Synchronisation See: https://www.nicvroom.be/Book_Review_Spacetime_Physics.htm#ref5 The same idea is also expressed in the book Gravitation at page 393. See: https://www.nicvroom.be/Book_Review_GRAVITATION_by_MTW.htm#ref3

Nicolaas Vroom

[[Mod. note -- Analysing the "Vroom synchronization" process in a moving reference frame isn't as simple as "In a moving frame all these clocks will run slower":
* You need to look at how both space *and* time coordinates transform as measured by moving observers.
* You defined Vroom synchronization to use (only) light signals moving in the three orthogonal coordinate directions. But a light signal which the stationary observers measure to be moving in (say) the +y direction (i.e., to have time-independent x and z coordinates), will be measured by the moving observers to NOT be moving in the in the +y direction -- its x coordinate will clearly be time-dependent.

Assuming that we're in flat (Minkowski) spacetime, if you use Einstein's special relativity then you can study the laws of nature in any reference frame you want

[though things are usually a lot simpler if you choose an inertial reference frame]
and you'll still get consistent results.

If you use some other (non-Einstein) relativity theory, well, your results will depend on what theory you use. -- jt]]

### 3 The books GRAVITATION and Spacetime physics

From: Nicolaas Vroom
Datum: Wednesday 25 October 2017
On Friday, 13 October 2017 01:24:07 UTC+2, Nicolaas Vroom wrote:
 > [[Mod. note -- Analysing the "Vroom synchronization" process in a moving reference frame isn't as simple as "In a moving frame all these clocks will run slower": * You need to look at how both space *and* time coordinates transform as measured by moving observers.

Why do we need moving observers.
The first step is to define a clock at rest which consists of 6 mirrors (light can also go through these mirrors. The characteristic of this clock is when a light signal is send towards each mirror the reflection will real the origin simultaneous meaning that the clock ticks simultaneous in all three directions.
The second step is to use this clock to synchronize all clocks in a latticework.
There is a problem if even these clocks at rest are influenced by gravity. Using this latticework you can study the behaviour of one moving clock which is identical as each of the clocks in the latticework. What tests will reveal that such a moving clock will run slower compared with the clocks in the latticework.
However it is even slightly more complicated. If you study a moving clock in the x direction its ticking in the x direction will run slower, but also its ticking in the y direction will be affected (differently). The same for the z direction.

 > * You defined Vroom synchronization to use (only) light signals moving in the three orthogonal coordinate directions. But a light signal which the stationary observers measure to be moving in (say) the +y direction (i.e., to have time-independent x and z coordinates), will be measured by the moving observers to NOT be moving in the in the +y direction -- its x coordinate will clearly be time-dependent.
See above.

 > Assuming that we're in flat (Minkowski) spacetime, if you use Einstein's special relativity then you can study the laws of nature in any reference frame you want [though things are usually a lot simpler if you choose an inertial reference frame] and you'll still get consistent results.

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