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Loren Booda
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What experiment could determine whether our universe is fractal?
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Loren Booda said:What experiment could determine whether our universe is fractal?
DaveC426913 said:From what I understand of fractional dimensions, they are such that there is not complete freedom of movement in them (i.e. their freedom of movement is a fraction of 1). This means there are discrete positions, not a continuum.
There should in principle be a test that could show that an object could not move continuously through that dimension, but would move in quantized jumps.
1] I'm just hypothesizing. None of this comes close to constituting evidence.TalonD said:So since energy is quantized then is that evidence that there are fractional dimensions?
Take a really drunken guy, suppose he can walk in all directions possible, and measure how long it takes for the guy to drift away from a starting point. That is related to the number of dimensions. Some people even call it "spectral dimension".Loren Booda said:What experiment could determine whether our universe is fractal?
A test for fractional dimensions is a mathematical tool used to determine the fractal dimension of an object or system. It involves measuring the scaling behavior of the object or system and using that information to calculate its dimension, which can be a non-integer value.
The test for fractional dimensions is typically performed by plotting the log of the number of smaller copies of an object or system against the log of their size ratio. The slope of this line represents the fractal dimension.
The test for fractional dimensions has been used in various fields, such as physics, biology, and economics, to study and understand complex systems. It has been applied to analyze patterns in natural phenomena, financial market data, and biological structures, among others.
The test for fractional dimensions may not accurately capture the complexity of highly irregular or self-similar objects. It also relies on the assumption that the object or system being studied is self-similar at all scales, which may not always be the case.
Yes, there are other methods for estimating fractional dimensions, such as box counting and correlation dimension. Each method has its own strengths and limitations, and the most appropriate method to use may vary depending on the specific object or system being studied.