The Curvature of Space-Time

Contest Context

The 2nd research contest was an internal contest held at the Aerospace Club. This contest consisted of conducting a brief investigation on a topic of interest related to space and performing an experiment to affirm or discard a hypothesis created by the participant or to reaffirm existing knowledge.

The winner of this contest was member Augusto Nóbrega with his research on the curvature of space-time. This was later represented with a video in which he explained this phenomenon with a stretched cloth, placing a heavy mass in the center and releasing smaller ones to accompany his explanation.

Below is his research report:

The Curvature of Space-Time

Introduction

In this report, we will reflect on some of Einstein's discoveries, such as general relativity, why we say that gravity is not a force, among others. We will see what and how he thought about space-time. Each of the discoveries will be explained to understand the final experiment.

Theoretical Framework

To understand the experiment, which is developed in the video, the theory of relativity and its variations will be briefly explained.

Where does this idea come from?

Einstein tried to combine two discoveries that, according to the history of physics, were almost impossible to combine. The two discoveries were: the speed of light and Galileo's relativity.

Galileo's relativity

The name relativity refers to Galileo's statement that all movements are relative. "When we say that the Earth moves, it is relative to the Sun. But we can also say that the Sun moves relative to the center of the galaxy. Therefore, movement is always relative to something. Saying that something moves without referencing anything else makes no sense in physics. This is what we call the principle of relativity. And this is a principle that Galileo first postulated in the 17th century." (Alcubierre, 2024)

The speed of light

In the 19th century, a new theory was being investigated: the theory of electromagnetic waves. At the same time, the speed of light was discovered. At that moment, they realized that this speed is absolute, meaning it cannot be measured and is the same from any point of view. No matter who looks at it, it will always be the same. Being absolute, it was not relative to anything. This seemed to contradict Galileo's principle of relativity.

The unification of discoveries

Einstein said that "if Galileo's principle of relativity is correct but on the other hand the speed of light is a universal constant and is absolute, then our concepts of space-time are wrong. So that is the origin of the theory of general relativity, trying to unify these two things, Galileo's principle of relativity, relative motion, with the fact that there is a speed that is absolute, which is the speed of light. At first, they seem contradictory, and Einstein's genius was realizing that they are not contradictory, that there is a mathematical solution that allows reconciling these two things but the price to pay is that time and space do not behave as we are used to." (Alcubierre, 2024)

What is general relativity?

General Relativity is a theory about space, time, and gravitation formulated by Albert Einstein in 1915. This is a fundamental theory in physics. In simple terms, it states that massive objects like planets and stars deform the fabric of space-time around them.

General relativity also predicts interesting phenomena such as:

• The bending of light when passing near massive objects (gravitational lensing effect)
• Time dilation in strong gravitational fields (such as near black holes)
• Gravitational waves, which are disturbances in space-time that propagate at the speed of light

Einstein proposed that gravity is not a force acting at a distance, as described by Newton's theory, but a curvature of space-time caused by mass and energy.

The curvature of space-time by masses

Albert Einstein said that the happiest thought of his life was imagining a man falling from a roof. What excited Einstein about this was not the suffering of others. It was realizing that this man, when falling, would not feel his own weight.

Demonstrative Experiment

To see the practical demonstration of these concepts, I have conducted an experiment that can be found at the following link:

Hypothesis

My hypothesis is that the experiment will demonstrate and help understand how space-time curves around masses. By adding a mass to the center of the experiment's cloth, the cloth should curve. By throwing smaller masses, they should orbit around the larger mass, forming a kind of orbit.

Conclusion

Although much of the conclusion is in the last part of the video, it is worth noting that Einstein's General Theory of Relativity has been confirmed multiple times through various experimental and observational tests. Although there is always room for new evidence and theories in science that can refine our understanding of the universe, General Relativity is currently one of the best-verified and accepted theories in physics.

Bibliography

• Derek Muller, 2020. Veritasium Channel.
• OMNICIENCIA Channel, Explanation of the origin of relativity by physicist Miguel Alcubierre
• Curvature of space-time

Glossary

• Geodesic: The shortest paths on curved surfaces are called geodesics, and we use the same word for the straight line that inertial observers travel in curved space-time.
• Helical: It is when the path of something through space (an example is the space station around the Earth) is affected by the curvature of space-time produced by a mass.