We can’t physically see or understand how complex numbers exist or work in our world in a nice way, but we know they do exist. Because we’ve made massive advancements in science and technology off the assumption that they exist and work, and our understanding of many things in the world including stuff as basic as the solutions to quadratic equations would fall apart. By the same token, there are many problems for which vectors and problem spaces of nth degree are used, where n>3, and there’s that whole adage where time is considered a 4th dimension. In that way, we often solve many problems, even rudimentary linear algebra ones, using sets in R⁴, R⁵, etc, and there are many, many invisible forces at work in our world such as gravity. We know how easily our brain can trick us, we still are easily fooled by optical illusions even when we know they’re there and what they are/how they work, despite our visual cortex being the one of the most powerful and most used part of our brain. So the idea of forces and things which we don’t have the capacity to perceive existing in the world is not anything new or foreign. There are frequencies we can’t hear, colors we can’t see, etc which other animals can and do. So why is the concept of n dimensions in the world so widely rejected? There must be a simple reason, I have heard that it has to do with the volume of a gas in a container being proportionate to its dimensionality or something
In: 2497
Let’s break this down:
**1. Do we really live in just 3 dimensions?**
While our daily experience is primarily rooted in three spatial dimensions (length, width, height), theoretical physics suggests more dimensions, especially when exploring concepts like string theory.
**2. Time as the Fourth Dimension:**
Yes, time is often referred to as the fourth dimension. In relativity theory, time and space are intertwined into a 4-dimensional spacetime continuum. So, when we talk about events in our universe, we reference them in four dimensions (3 space + 1 time).
**3. Higher Dimensions in Theoretical Physics:**
Some theories in physics, especially string theory, postulate the existence of more than four dimensions. One common version of string theory proposes 10 dimensions. Here’s a simple breakdown of these dimensions:
– **0th Dimension:** A point in space.
2. **1st Dimension:** A line connecting two points.
3. **2nd Dimension:** A plane, having length and width.
4. **3rd Dimension:** Depth is added to the plane, forming a volume.
5. **4th Dimension:** Time, forming the spacetime continuum.
6. **5th Dimension:** This is where the idea of a multiverse comes in. At this level, we can imagine another world slightly different from ours.
7. **6th Dimension:** A plane where all possible worlds with the same start conditions exist. If you imagine a world where, say, you turned left this morning instead of right, it would be in this dimension.
8. **7th Dimension:** A plane containing all possible universes with different start conditions.
9. **8th Dimension:** All possible worlds, starting with all possible start conditions and laws of physics.
10. **9th and 10th Dimensions:** The specifics get even more theoretical here, but in essence, these dimensions encompass all possible universes, histories, and laws of physics. Every possible universe exists in these dimensions.
**4. Why don’t we see/experience these higher dimensions?**
Just because certain dimensions might exist doesn’t mean we can perceive or interact with them. Much like a 2D being on a flat plane wouldn’t be able to perceive or understand the third dimension, we, as 3D beings, might be limited in our perception of higher dimensions.
**5. Gases and Higher Dimensions:**
The argument you referenced about gas volume comes from a physics thought experiment. If our universe had more than three easily perceivable spatial dimensions, the behavior of gas molecules would be different than what we observe. The inverse square law governing forces like gravity and electromagnetism would be different in a universe with more than three spatial dimensions. Our observations match a universe with three spatial dimensions and one of time.
In conclusion, while our immediate experiences are grounded in a 4D spacetime, theoretical physics delves deep into the possibility of higher dimensions. The exploration of these ideas is ongoing, and it’s one of the many intriguing aspects of modern science!
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