Exploring 4D Space: Physics & Reality

In summary, 4D space refers to the addition of a fourth dimension, typically identified as time, to the traditional three dimensions of space. This concept has implications for physics and our understanding of reality, as it allows for transformations between spatial and temporal dimensions. The addition of higher dimensions also introduces new conserved quantities and the possibility of symmetries, such as the Kaluza-Klein tower and entanglement, respectively. However, the concept of entanglement is not directly related to 4D space.
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What is the definition and implications of 4D space?

By implications I mean if it existed how will it redefine what we know about physics and reality up to now. (Applications, possibilities, etc)
 
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There are some current, active theories (such as string theory) that require as many as ten spatial dimensions.
 
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Special relativity is a theory in 4D space.

What does it change? There is a difference to the classical Newton mechanics which postulates only 3 dimensions. In Newtonian mechanics we can rotate the coordination system to transform spatial axes one into another.

Adding the fourth dimension (identified with time) allows us to "rotate" over new axes, that means to transform time dimension into spatial ones and vice versa. That means, one observer's time may be mixed with another observer's length. This "rotation" in the fourth dimension is exactly the Lorenz transformation. Lorentz length contraction and time dilation are the effects of looking at an object from different "angles" in the fourth dimension.

Postulating more dimensions gives us just that: the ability to transform some physical quantity into another, specifically length and time. Suppose we postulate the fifth dimension and we identify the electric charge with the momentum in that dimension. So, there must exist a transformation ("rotation") transforming charge into length and time the Lagrangian is invariant under.

These "rotation" transformations in higher dimensions usually have conserved quantities associated with them. Just as the angular momentum is associated with rotation transformation. Postulating the fourth dimension (time) gives us another conserved quantity associated with the resulting rotation group - the spin. That's why many authors write that the existence of spin is relativistic effect. If we postulate the fifth dimension identified with the electric charge, we also get a new spin-like quantity - the isospin. That's why I believe the Kaluza-Klein theories, but that's my personal preference.

Postulating more dimensions implicitly assumes that translations in these dimensions are symmetries. This is not a problem with the time dimension, since it has been translation-symmetrical since the Newtonian dynamics, but with fifth (electrical) dimension this means that there have to exist elementary particles with arbitrary high electric charge. This is called the Kaluza-Klein tower. The hypothetical elementary particle with 2e electric charge is called dilepton and it has been looked for.
 
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So does "entanglement" have anything to do with 4d space?
 
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So does "entanglement" have anything to do with 4d space?
No, this is completely unrelated concept.
 

1. What is 4D space?

4D space refers to a theoretical concept in physics that adds a fourth dimension, in addition to the three dimensions of length, width, and height, to our understanding of space. This fourth dimension is often referred to as time, and together they form the four dimensions of spacetime.

2. How is 4D space different from 3D space?

The main difference between 4D space and 3D space is the addition of the fourth dimension of time. This means that in 4D space, objects not only have length, width, and height, but also a duration or movement in time. This allows for a more comprehensive understanding of the physical world and the interactions between objects.

3. What are the implications of 4D space on our understanding of reality?

The concept of 4D space has significant implications on our understanding of reality. It challenges traditional notions of space and time, and allows for a deeper understanding of the universe and the laws of physics. It also has implications for fields such as cosmology and quantum mechanics, and may provide insights into the nature of time and the possibility of multiple universes.

4. How is 4D space explored and studied?

Exploring 4D space is primarily done through theoretical and mathematical models, as it is not possible to physically observe or experience 4D space. Scientists use concepts such as spacetime diagrams, multidimensional geometry, and mathematical equations to understand the properties and behavior of 4D space.

5. What are the practical applications of understanding 4D space?

While 4D space may seem like a purely theoretical concept, it has practical applications in fields such as physics, engineering, and computer science. Understanding 4D space can help us develop more accurate models and predictions of the physical world, design advanced technologies, and improve our understanding of the universe and our place in it.

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