## How Einstein reinvented Reality in Scientific American of September 2015 - page 28

This document contains comments about the article How Einstein reinvented Reality by Walter Issacson In Scientific American of September 2015.

### "Introduction"

The general theory of relativity began with a sudden thought. "If a person falls freely he will not feel his own weight"
The personnal experiences of humans (his feelings) should not be considered as good practice in physical science.
Einstein soon refined his thought experiment so that the falling man was in an enclosed chamber, such as an elevator, in free fall. In the chamber he would feel weightless.
This is the same as before.
Next he write:
Any objects he dropped would float alongside him.
Falling objects only fall at the same rate in vacuum.
Next:
There would be no way for him to tell - no experiment he could do to determine - if the falling at an accelerated rate or was floating in a gravity-free region of outer space.
gravity-free regions in outer space do not exist. Our Sun moves through the Milky Way galaxy under influence of gravity.
Then Einstein imagined that the man was in the same chamber way out in space, where there was no perceptible gravity and a constant force was pulling the chamber up at an accelerated rate. He would feel his feet pressed to the floor.
Of course. However there is a certain issue.
On earth, In order to take care that chamber does not fall you need a constant force. When you "free" the ball, the ball will fall.
In outer space you need a constant force to mimic a similar effect. Starting point is a reference object and a chamber. Both will float identical. With a constant force the distance between the chamber and the reference point will change at an accelerated rate. When you free the ball the distance between the ball and the chamber will also change at an accelerated rate. The distance between the reference object and the ball changes at a constant rate.
Einstein dubbed this the "the equivalence principle". The local effects of gravity and of acceleration are equivalent. Therefore, they must be manifestations of the same phenomenon, some cosmic field that accounts for both acceleration and gravity.
You have to be very carefull what is equivalent.
• On earth it is the falling man which speed increases at an accelerated rate.
• In outer space it is the constant force which causes an accelerated rate
Those two "behaviours" are equivalent.
You only need a physical explanation for gravity i.e for the gravitational field.

### Bending Light

As Einstein developed his equivalence principle, he realized that it had some surprising ramifications. For example his chamber thought experiment indicated that gravity would bend light.
Imagine that the chamber is being accelerated upward.
By the time it reaches the opposite wall, the light is a little closer to the floor because the chamber has shot upward.
See picture 2 in Reflection 2 - Two thought experiments? part 2
And if you plot the beam's trajectory across the chamber, it would be curved because of the upward acceleration.
What you are observing here is a relatif effect. Light through outer space in this case follows an almost straight line. Ofcourse if the chamber/man is moving under an extra constant force the light ray is observed bended.
The equivalence principle says that this effect should be the same whether the chamber is accelerating upward or is resting still in a gravitational field.
This situation is depicted in picture 1A in "Reflection 1"
For more about the equivalence principle related to thought experiments, read this in the same issue of Scientific American: How Einstein reinvented Reality
In other words, light should bend when passing through a gravitational field.
IMO it is tricky to draw this conclusion using this principle.
IMO it is "impossible" by means of a thought experiment to demonstrate that light rays in early morning at sun rise or at sun set, ie. close to the surface of the earth, are bended.
In reality there could be also other physical processes involved which cause a similar behavior.
But now Einstein realized that math could be a tool for discovering - and not merely describing - nature's laws.
Nature's law are descriptions of almost identical physical processes. Math is a part of these descriptions. IMO you can only unravel the laws of nature by performing measurements and experiments.
Einstein's goal as he persued his general theory of relativity was to find the mathematical equations describing two interwoven processes: how a gravitational field acts on matter, telling it how to move and how matter generates gravitational fields in spacetime telling spacetime how to curve.
This requires much more text.

### A rivalry

He tested a set of revised equations to see if they would yield the correct results for the anomalous shift in Mercury's orbit.
This ofcourse should be the final Einstein field equation discussed below.
The answer came out right: his equations predicted the perihelion should drift by about 43 arc seconds per century.
That ofcourse is a tremendous achievement.
"Today I am presenting to the Academy a paper inwhich I derive quantitatively out of GR without any guiding hypothesis, the perihelion motion of Mercury, No gravitational theory has achieved this until now"
The problem is what exactly does he mean with "guiding hypothesis". GR is some kind of (mathematical) model based on certain assumptions. So what does he mean?
IMO, using Newton and taking care that gravity does not act instantaneous you can do the same.
Regardless, he produced in time for his final lecture on November 25 - entitled "The Field Equations of Gravitation" - a set of covariant equations that described a general theory of relativity. etc
In one of its many variants, it can be written as:
Ruv - 0.5guv*R = -8pi*G*Tuv
The indices uv stand for a four by four matrix.

## Reflection 1 - Two thought experiments?

The purpose of this paragraph is not so much to explain a thought experiment, but the difference between two experiments.
 ``` ^ y A || y S --> E |V x x Picture 1A ```
 ``` ^ | S --> B | x x Picture 1B ```
• In the experiment depicted by picture 1A S is the Sun, E is the Earth and A is an observer at the "North Pole". The large arrow shows the direction of movement of the Earth (and observer A combination)
• In the experiment depicted by picture 1B S is the Sun and B is an observer. The large arrow shows the direction of movement of observer B. There is no Earth. That is the only difference between both experiments.
• What is also depicted in both pictures what happens when a test particle (or light ray) is emitted from the Sun.
• In picture 1A the horizontal arrow shows the "original path" and the letter X the final position. What the picture 1A shows that the path is bended for a "light ray" passing close to the surface of the earth.
The cause is gravity. It is important to understand that this is the only situation where a "light ray" is physical bended and does not follow a straight line i.e. close to the surface, near the "North Pole"of the earth.
A "light ray" passing close to the "South Pole" will travel towards point y.
• In picture 1B the horizontal arrow and the letter X are on the same line implying that the test particle or "light ray" follows a straight line (through outer space).
• In the next part it is assumed that each observer is in a chamber with a hole in the middle of the left wall.
• In picture 1B the chamber has a constant vertical upward speed. The particle or lightray will enter the chamber in the middle at the left side. The particle will leave at a lower position at the right side. This comes because during the travel time inside in the chamber the chamber has moved upwards. Observer B will interpret this as a bended trajectory, but in reality the path of the test particle or lightray is in a straight line.
1. In picture 1A when the observer is at rest the test particle also enters the chamber at the left side in the middle and leaves at the right side at a lower position. The cause is the gravitational force of the earth which physical bends the path of the test particle or lightray.
2. The purpose of Picture 1A also to discuss what happens when the chamber is dropped. This is the downward vertical error.
When you assume that the light ray follows a straight line than lightray enters the chamber at the middle and leaves the chamber more towards the top at the right side. The cause is the difference in height above the earth during the time that the lightray is inside the chamber. This bending increases during the time that the chamber drops.
3. In reality both effects can be observed
When the chamber is at rest the lightray touches the right wall below the middle.
When the chamber is dropped this point moves upwards towards the ceiling.
If this whole description is correct the question remains to what extend you can invent these experiments purely by using your mind?
A different issue is that earth athmosphere can also influence the behaviour of light rays or a test particles, which is not assumed.

## Reflection 2 - Two thought experiments? - part 2

The following 4 pictures demonstrate a chamber in out space undergoing a constant force. As a result of this constant force the speed of the chamber is increasing.
In picture 1B the speed of the chamber is "Constant"
 ``` ********* * * * * * * ccc * * ccc * ********* * * ********* ********* * * * * * * bbb * * bbb * bbb aaa * ^ * aaa * * aaa aaa * * | * * * * * * | * * ********* * * | * * * * * * * * ********* ********* 2A 2B 2C 2D ```
• The first part of the lightray is drawn as aaa in 2A. The light ray aaa moves towards the right in a straight line in 2B, 2C and 2D
• The second part of the lightray is drawn as bbb.
• The third part of the lightray is drawn as ccc.
The trajectory is observed curved downwards.

The following 4 pictures demonstrate the falling chamber situation of picture 1A.
That means a chamber which falls on earth, under the influence of gravity.

 ```********* * * ********* * * | * * * * | * * * * | * * ********* * * | * * * * aaa V * aaa * * aaa aaa * * bbb * * bbb * bbb ********* * * * * ********* * * ********* ccc * * ccc * * * * * ********* * * 3A 3B 3C 3D ```
The above picture shows the falling chamber at equally spaced moments.
• In picture 3A the lightray comes in true a hole at the left and is represented by the line aaa
• In picture 3B the lightray aaa moves a lttle upwards because the chamber drops.
Also the next part bbb enters. But now the hole is lower.
• In picture 3C the lightray aaa moves upwards towards the right and reaches the right wall.
What is important is that the lightray in this case moves in a straight line (towards the right) but is observed (by an observer at rest in the chamber) to be bended.

When you compare the sequence 2A,2B,2C and 2D with the sequence 3A,3B,3C and 3D they are identical.
 ``` m1 ^ ****************** | * * | * aaaaaa * -> a a -> a ****************** a | eeee | | e e | V e e V m2 g Picture 4 ``` In the above pictures (3A, 3B etc) the bending of light around the earth is not taken into account. For the above sketch this should mean that the highest point is in the middle of the chamber. This is the closest point between the light ray and earth . Only for a very long chamber this becomes visible. That is what picture 4 demonstrates. The light ray (a) enters at the left. The earth is the letter e. This consideration makes this whole experiment very tricky because on Earth both effects (ie Picture 3 and Picture 4) have to be taken into account on earth.
 ``` a cccccccccccccccc a cccccccccccccc b dddddddddddd b dddddddddd b dddddddd V > Picture 5 ``` Picture 5 shows two falling objects: At the left we have a falling object (identified with the letters a and b) which falls straight towards the earth. The duration of the letters aa and bbb is identical.That means the object is accelerating. The letters c and d define a second object. The object has a constant horizontal speed v. The total number of letters c and d is 30. The question is if this picture also can be used in case a lightray is demonstrated.

## Reflection 3 - Comparision between thought experiment and "reality"

Einstein's reasoning follows 4 steps:
• We start with the "equivalence principle" which claims that gravitational force and a constant force are identical.
• Next we claim that the law of physics are identical.
• The next step is that in outer space when you give an object (observer) a constant force the observer observes the light ray as bended.
• The "logical conclusion" is that light rays are also bended when undergoing a gravitational force.
The question is are these four steps correct.
The tricky part is when you observe that lightrays are actual bended it does not mean that the 4 steps are correct.

In picture 1B (no earth) we have three issues.

1. We have a chamber which moves around the Sun at a constant velocity. Light from the Sun moves in a straight line.
2. Light through a hole in the chamber also follows a straight line. From the reference point of chamber, with a very small angle because the chamber moves at a constant speed.
3. When the chamber undergoes a constant force the speed of the chamber increases which results that, from reference point of chamber, the light after the hole also follows a bended path.
In picture 1A (with earth) there are also three issues.
1. We have the earth and chamber which both move around the Sun at a constant velocity. Light from the Sun is bended around the earth. The result is that the light in the chamber is also bended. See also picture 4. The star is at the left.
2. Light through a hole in the chamber also follows this bended path but with a very small angle because the chamber moves in a constant speed.
This is a very complex process because it depends in which direction the movement of the earth is. This are the arrows m1 and m2 in picture 4.
3. When the chamber is dropped (undergoes a constant force) the speed of the chamber increases which results that, from the view point of the chamber, the light after the hole follows (an even more) bended path. In picture 4 this is the arrow g (gravity)

The specific purpose of this refelection is, how detailed you can have thoughts and perform experiments in your mind which are in accordance with the reality and real experiments.
In this particular case the issue is to what extend, just by reasoning, you can come to the conclusion that light rays around matter do not follow straight lines but are bended and "attract" each other?
A much simpler explanation is if matter and lightrays have something in common than this behavior is not that strange
Gravity is explained interaction between gravitons. If lightrays can also interact with gravitons than you have some type of explanation. This raises the issues that photons and gravitons should be considered as two "totally" different physical entities.

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Created: 5 September 2015
Modified: 14 December 2015 - Reflection 1, 2 and 3.