Mathematical Proof for Hubble Constant

In this episode, we aim to provide mathematical proof for the Hubble Constant, shedding light on the correct structure of space. In 1929, astronomer Edwin Hubble observed that distant galaxies appeared to be moving away from Earth, a discovery he made by analyzing their light through telescopes. This observation led to the formulation of what is now known as the Hubble Constant.

The Hubble Constant quantifies the rate at which the universe is expanding. For every 3.3 million light-years from Earth, the fabric of space itself is expanding at a rate of 72 kilometers per second.

This value is derived from observations, not from direct mathematical proof. Currently, there is no mathematical proof for these observations. However, by understanding correct fundamentals of the framework of space, it is possible to calculate and validate the Hubble Constant mathematically. In this episode, we will walk through the process of calculating the Hubble Constant, demonstrating that the observational data collected by telescopes is indeed supported by mathematical reasoning.

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Transcript

In this episode, we aim to provide mathematical proof for the Hubble Constant, shedding light on the correct structure of space. In 1929, astronomer Edwin Hubble observed that distant galaxies appeared to be moving away from Earth, a discovery he made by analyzing their light through telescopes. This observation led to the formulation of what is now known as the Hubble Constant.

The Hubble Constant quantifies the rate at which the universe is expanding. It is currently measured at approximately 72 kilometers per second per megaparsec. To clarify, a megaparsec is a unit of astronomical distance equal to one million parsecs, or about 3.3 million light-years. In essence, this means that for every 3.3 million light-years from Earth, the fabric of space itself is expanding at a rate of 72 kilometers per second.

This value is derived from observations, not from direct mathematical proof. Currently, there is no mathematical proof for these observations. However, by understanding correct fundamentals of the framework of space, it is possible to calculate and validate the Hubble Constant mathematically. In this article, we will walk through the process of calculating the Hubble Constant, demonstrating that the observational data collected by telescopes is indeed supported by mathematical reasoning.

Expansion of the Universe

Is the universe expanding? According to scientific observations, the answer is yes, the universe is indeed expanding. But this raises further questions: Why is the universe expanding, and how quickly is this happening? Science continues to search for definitive answers to these questions.

Astronomers use advanced telescopes to observe the motions of planets and galaxies. What they have discovered is that the expansion of the universe is not uniform everywhere. In some regions, the universe appears to be expanding more rapidly, while in others, the expansion is slower. So far, there is no clear explanation for this irregularity in expansion rates.

To answer these challenging questions, it is important to have a clear understanding of the fundamental nature of space. By deepening our knowledge of the spacetime framework, we may be able to explain why the universe expands the way it does and uncover the mysteries behind its uneven growth.

Fundamentals of the Spacetime Framework  

Grasping the nature of the spacetime framework is essential to comprehending the universe’s expansion. But what exactly is the structure of spacetime? Here is where confusion often arises. According to scientific understanding, the spacetime framework began with the Big Bang, which occurred about 13.7 billion years ago. This marks the origin point of spacetime. However, is this really the correct way to think about it? While it’s true that the Big Bang represents the beginning of spacetime, that event took place 13.7 billion years in the past. So, where is the “beginning” of spacetime right now? It isn't located at the Big Bang anymore; in fact, the Big Bang can be thought of as the farthest edge of the universe, not its current starting point. Since no one has ever observed the edge of the universe, it’s misleading to call the Big Bang the present beginning of spacetime. Please note in this episode we are using the terms space and spacetime interchangeable. They are synonymous for usage in this episode. 

This misunderstanding about where spacetime starts is at the root of much of the confusion surrounding the nature of space itself. Such misconceptions make it difficult to accurately understand how space is constructed, the rate at which it is expanding, and why this expansion is uneven throughout the universe

The Observer as the Start of Space

What serves as the true starting point for space? Surprisingly, it is you—the observer. Space begins with the observer inside each of us: within you, within me, and within every living being. This personal perspective is what I refer to as t = 0, the starting point of space. 

Admittedly, viewing the observer as the foundation of spacetime is a radical shift from conventional thinking—it's fundamentally different from prevailing scientific views. But is there any way to support this idea with established scientific theories or sound reasoning? Fortunately, there are methods to examine and justify this perspective.

1.      Through Einstein’s Theory of Special Relativity

2.      By applying logical reasoning

In the following sections, we will explore these approaches to demonstrate why this hypothesis holds merit.

1. By using Einstein Theory of Special Relativity

Einstein’s special theory of relativity marked a groundbreaking moment in scientific history by revealing a deep connection between motion, time, and space. If you’re interested in delving deeper, we offer a complete episode dedicated to the Einstein Theory of Relativity. Please consider listening when you have the opportunity.

At its core, this theory shows that whenever something is moving, both time and space are affected. Specifically, as an object moves faster, time slows down for it and space contracts in the direction of motion. This means time and space are not rigid, unchanging entities; instead, they depend on the speed at which something is moving. These conclusions have been repeatedly confirmed by scientific experiments.

The faster something moves, the greater the effects: time passes more slowly, and space becomes more compressed. If, hypothetically, you could reach the speed of light, time would stop altogether, and space would shrink to nothing. In this extreme scenario, the usual concepts of time and space no longer apply.

Everyday Implications of The Theory of Relativity

While these ideas might seem abstract, the relationship between motion and time actually has significant meaning in our daily lives. Motion is all around us—from an ant crawling to someone walking, cycling, or driving a car. Each of these motions occurs at different speeds.

According to Einstein’s principles, this means that the “clock” for every moving object or person tick at a slightly different rate. Our everyday clocks are not sensitive enough to measure these tiny differences, but the theory tells us they are real. If two people are standing still, their clocks move in sync. As soon as one person starts to walk, their clock slows ever so slightly compared to the stationary person.

Since time passes differently for each moving person, the way space compresses also vary. This implies that everyone is essentially creating their own unique spacetime framework. In other words, the starting point for time and space for each living being is the observer within themselves. This starting point is t = 0 for space. This shows that Einstein’s theory of relativity firmly supports this remarkable idea.

2. By using Logical Reasoning

Let’s explore how we perceive objects in the universe by considering the time it takes for their light to reach us. When we observe a distant star located 5 million light years away, the light we see today actually left the star 5 million years ago. Similarly, sunlight takes about 8 minutes to reach Earth, while light from the moon arrives in just 3 seconds. If we notice an airplane flying overhead at an altitude of 30,000 feet, the light from it reaches us in approximately 300 milliseconds.

As the distance between us and the object decreases, the time required for light to travel from the object to our eyes gets shorter. Moving closer, light from a tree just outside your window reaches you in about 10 microseconds. When you look at your computer screen only a foot away, the light takes roughly 1 nanosecond to reach you.

The closer the object, the less time light takes to arrive. If we continue to reduce the distance, the only logical point where light will take zero seconds to reach us is the observer within you. This suggests that observer within is the start of the spacetime framework. So logically the t = 0 for the spacetime framework is the observer within us. 

No matter who observes the universe, this reasoning leads to the same conclusion: every individual has their own unique t=0 for the spacetime framework. This applies to every living being. In essence, each observer creates a personal spacetime framework beginning with t=0. Thus, this line of reasoning supports the idea that the space of the universe, for each person, begins with the observer themselves.

From these discussions, it is correct to conclude that the individual person or the observer’s location is the starting point for the spacetime framework. It does not matter if the observer moves from Delhi to New York. Space always starts with the observer, which is t = 0 for space. 

Let us now try and estimate the size and the expansion rate of the universe. 

Size and Expansion of the Universe

Scientific research estimates that our universe is about 13.7 billion years old. Imagine light traveling from the farthest edge of the universe toward us; it would take 13.7 billion years to reach us. The distance light travels in a single year is known as a light-year. If you do the calculations, you will find that one light year is equal to 9.46 trillion kilometers. So, light from the universe’s edge travels 13.7 billion light-years to get here. This enormous distance essentially defines the size of our universe.

The Expansion of Space Driven by Time

Let’s experiment with how the universe’s age relates to its size. Suppose the universe is exactly 13.7 billion years old right now. This means its size is 13.7 billion light-years. One second later, the universe’s age becomes 13.7 billion years plus one second. In that second, light needs to travel an additional 300,000 kilometers. Therefore, the universe’s size increases by 300,000 kilometers, making it 13.7 billion light-years plus 300,000 kilometers.

After 10 seconds, the age of the universe is 13.7 billion years and 10 seconds, and the universe grows by 3,000,000 kilometers in size. If a whole year passes, the universe is now 13.7 billion years plus one year, and the size of the universe has increased by exactly one more light-year. 

These observations make it clear: as the universe grows older, its size increases. Every second that passes, space becomes larger by 300,000 kilometers. It means the outer edge of the universe is expanding by 300,000 kilometers per second. This is an important conclusion to keep in mind. 

Calculation of the Hubble Constant

From the above discussions we can summarize the spacetime framework as follows:

1. The point of origin, or time zero (t = 0), for space is defined by the observer—essentially, each of us serves as the starting point for our own spacetime framework.
2. The universe's outer boundary is expanding outward at the speed of light, which is 300,000 kilometers per second.

Visualizing Spacetime Expansion

Imagine spacetime as an elastic rubber sheet. One end of the sheet—your end—is held fixed at t = 0. The other end, representing the universe's outermost edge, is being stretched outward at the speed of light. This means that every second, the edge moves 300,000 kilometers farther away. As time passes, the universe continues to expand at this rate.

However, this expansion is not uniform throughout the entire sheet. Only the very edge moves at the full speed of light. The regions in between, closer to the observer, expand more slowly; the rate of expansion for any point on the sheet depends on its distance from the observer. In the rubber sheet analogy, the stretching is greatest at the edge and decreases as you move closer to the fixed point.

This concept helps us understand that objects farther from the observer move away faster than those nearby. The rate at which space stretches between us and distant galaxies is proportional to their distance from us. Nearby stars move away more slowly because the fabric of space is not stretched as much in that region compared to regions farther out.

Calculating the Hubble Constant

With this understanding, let’s calculate the Hubble Constant for an object 3.3 million light years from us. An object 3.3 million light years is used because that the distance Edwin Hubble used to come up with Hubble Constant.  

The universe is 13.7 billion light years in size.

Its outer edge expands to 300,000 kilometers per second.

Based on these parameters, let us do a simple proportional analysis to calculate the Hubble Constant:

Divide the distance of the object which is 3.3 million light years by the size of the universe which is 13.7 billion light years to get a ratio:

3,300,000 / 13,700,000,000 = 0.000240

Now, multiply this ratio by the speed of light, which is the expansion rate of the outer edge:

0.000240 × 300,000 kilometers per second = 72 kilometers per second

This means that a galaxy 3.3 million light years away is receding from us at 72 kilometers per second, which matches the observed value for the Hubble Constant.

The mathematical results presented here are consistent with the established value of the Hubble Constant, offering compelling support for the reliability and precision of the proposed spatial framework. A central finding of this work is the recognition that every observer occupies the origin of their own spacetime continuum, thereby creating a distinct spatial reality for each individual. This perspective not only corroborates well-known scientific observations related to the Hubble Constant but also introduces an innovative way of conceptualizing our universe.

By positioning each observer as the central point of their personal spacetime, this approach provides a fresh alternative to conventional cosmological models, many of which face significant uncertainties and unresolved challenges. The proposed framework holds promise for addressing persistent questions about the cosmos and could open up new pathways for research in astrophysics and cosmology.

We hope this discussion has offered a fresh viewpoint on the structure of space. By demonstrating the precision of the Hubble Constant, it suggests that our current approach to understanding space may require revision. Viewing each observer as the origin of space is a bold idea, yet it may be essential for a more accurate understanding of the universe.

If you’re interested in delving deeper into topics like this, we invite you to explore our blog at Vedanta. and Science dot com or discover more in my book, Science Meets Vedanta., available on Amazon. Additionally, we offer a growing library of episodes covering many different topics —feel free to browse through them at your convenience.

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