BurtJordaan
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December 2014
Cosmic Engineering (Quasi-Newtonian Gravity)
December 28th, 2014, 2:35 am
Cosmic Engineering (Einstein's "Bridge")
December 22nd, 2014, 4:25 pm

April 2014
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In the last installment I attempted to cross the bridge from Special relativity to General relativity by means of things that are accelerated. We will now let gravity do the acceleration and see what it implies in simple situations.

Relativistic gravity is mostly about spacetime geodesics - the shortest path (or rather path of least action) that particles, objects or whatever, take through spacetime. When gravity is present, those paths are curved in most coordinate systems. Pictured below is a two-dimensional cut of a spacetime geodesic ($c\Delta t'$) in quasi-Newtonian spacetime.[1]

At the origin sits a large mass M and a small object is released from rest at position $r = r_0$. The object is moving upward at a "speed $c$",...

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Last edited by BurtJordaan on December 28th, 2014, 6:30 am, edited 3 times in total.
1 Comment Viewed 1198 times

After wrapping my head around the biggest issues of special relativity theory, I obviously had to move on to general relativity, where gravity takes the center stage. Einstein used uniformly accelerated frames to 'build a bridge' between special relativity and gravity. He established that a uniformly accelerated frame is precisely equivalent to a hypothetical 'uniform gravitational field' - a thing that does not really exist. However, reasonably small stretches of space and time (in a 'real gravitational field') will very, very closely resemble a uniformly accelerated frame.

Engineers normally understand gravity pretty well in terms of how to calculate it and use it in their designs, be it a tall building or the trajectory of a missile or a rocket. They understand that gravity is 'stronger' at ground level than at altitude, and they understand the equivalence between acceleration and gravity in broad terms. But, tell them that the tail end of a uniformly accelerated frame in free space...

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I'm trying to understand Lincoln's values for frame C. So I added some values from GrayGhost's Minkowski diagram for essentially the same (ABC) scenario:

With $\large v= 0.866c$, $\large L/v =4$ and $\large \gamma = 2$:

Lincoln's transformations with Gray's values calculated:
$\large (x,t)_{1A} = (0, 0)$
$\large (x,t)_{2A} = (L, \frac{L}{v})=(3.464,4)$
$\large (x,t)_{3A} = (0, \frac{2L}{v})=(0,8)$

$\large...$

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Last edited by BurtJordaan on December 23rd, 2014, 12:45 am, edited 4 times in total.

In my prior Post, I have discussed the present scientific view on the relativity of simultaneity and more specifically the misstatement: “the actual one-way speed of light (in vacuum) equals the constant ‘c’ in every inertial frame of reference”. I have shown that Einstein chose it as a very convenient convention and that it is in fact the best convention to choose – it makes the physics “as simple as possible, but not simpler”. In this delivery of Cosmic Engineering, I want to discuss an equally common misstatement about the actual tick rates of clocks in relative inertial motion.

Relativity 'controversy' 2The actual tick rates of clocks in relative inertial motion in free space are necessarily different”. The correct interpretation of the facts is that for clocks moving inertially in free space, it is impossible to determine any tick rate difference, because they can only meet once. In order to compare tick rates, one of the two cl...

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Last edited by BurtJordaan on April 10th, 2013, 1:01 pm, edited 4 times in total.
Reason: Fixed typo

I promised to help readers to walk the relativity and cosmology landscape, telling them where I discovered dead-ends. I will start with perhaps the biggest "controversies", those that kept me out of sleep for many nights. But, be warned, battle-hardened relativists will probably raise an eyebrow at what I have to say. To them, do not worry, I will not deviate from the mainstream, just from some dogmatic statements that have been proven untenable by reputable theorists in the field.

Relativity 'controversy' 1. “The actual one-way speed of light (in vacuum) equals the constant ‘c’ in every inertial frame of reference”. The correct interpretation of the facts is that although the two-way speed of light is an absolute constant of nature, the one-way speed of light is a convenient convention. Why? Because one has to define 'simultaneity' before you can measure speed as time over a distance.

In his 1905 paper on Special Relativity, Einstein wrote in his ...

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Last edited by BurtJordaan on December 21st, 2012, 4:19 am, edited 4 times in total.
Reason: Changed "misconception" to "controversy"