Instances of the 4th dimension include:
Time in Minkowski’s space-time (Raum und Zeit).
As flow or motion in various 4/3 laws.
But:
In a space-time distance, time squared is preceded by a sign opposite to that of the other lengths squared. Time is different.
Flow, motion and time trace a moving point along a line. The 3 spatial dimensions are static.
In the 4/3 law pertaining to energy the same energy in 4 dimensions has 4/3 as much energy in the corresponding 3 dimensional space. How can energy occupy a 4th dimension that models a moving point? Perhaps the model in the 4/3 law is wrong or incomplete? If it is incomplete, how is it incomplete? Is some aspect of time missing? In this portion of the comment on the question, accounting for the 4th dimensional status of motion affects understanding of the 4/3 laws.
Or is the 4th dimension nothing more than a mathematical construct?
The three dimensions that we are familiar with are a human Cartesian geometric construct. Dimensions are a human perspective of reality, not something in nature themselves. From the human perspective of change and motion one can understand the necessity of including time as a dimension.
Take the universe as a whole, for instance. Stop time. That would mean nothing would ever change in it. It would always look exactly the same with no change or motion within it. The forth dimension of time would be missing. Start time up again and one would see our changing universe and then realize time as being the forth conceptually and mathematically necessary dimension to describe reality.
Dear Sydney Ernest Grimm
I agree with most of your points, except where you said:
The forth dimension is not a dimension, it represents a path inside 3 dimensional space.
My viewpoint: a path in 3 dimensional space doesn't need any fourth dimension to be quantized. We live in a three dimensional space, and our motion trajectory is determined through the Euclidean space, without any fourth dimension.
However, to characterize variation, we need a fourth dimension named time or explicitly t. For example, if we want to find the vibrational modes of a solid cube, as a deflection function of time; w=w(x,y,z,t).
When we want to plot a function u=f(x,y), we have enough dimensions for 3d visualization. However, if there is another dimension, for example u=u(x,y,z), or, u=u(x,y,t), then we lack one additional dimension. Lack of this fourth dimension has been the cause for too many baseless sophistries about the so called fourth dimension. We can imagine a function of million of dimensions as u=u(x1,x2,x3,x4...), but this is not related to objective reality which as you mentioned:
The universe is just a box without walls: 3 dimensional Euclidean space.
Moreover, I think the string-theory is a sophistry by freemason scientists, and the number 33 implies some connections in this regard. Freemasons only want to disinform and divert the reality as they are enemies of God and the genuine truth.
And the question:
Or is the 4th dimension nothing more than a mathematical construct?
I think of a straight Yes.
All dimensions are mathematical constructs and singling out some particular result like the 4/3 law doesn’t make sense.
One reason is that it doesn’t matter, whether someone decides to give some particular name to some quantity. The only thing that matters is to clearly formulate a question and show what’s the answer, in an impersonal way.
I've recently published a series of papers on relativity that may answer your question.
Guoxu Feng
Thank you, can you provide links to the papers you wrote that most closely connected to this question?
Regards.
The three dimensions that we are familiar with are a human Cartesian geometric construct. Dimensions are a human perspective of reality, not something in nature themselves. From the human perspective of change and motion one can understand the necessity of including time as a dimension.
Take the universe as a whole, for instance. Stop time. That would mean nothing would ever change in it. It would always look exactly the same with no change or motion within it. The forth dimension of time would be missing. Start time up again and one would see our changing universe and then realize time as being the forth conceptually and mathematically necessary dimension to describe reality.
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