Can we quantize Aristotelian Physics?

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In summary, Aristotelian physics, when stripped of its historical context, is similar to Newtonian physics. The main difference is that rather than "an object in motion stays in motion unless acted on by an unbalanced force," we have "an object at rest stays at rest unless acted on by an unbalanced momentum." This also leads to a change in the equations, with Newton's F=ma becoming p=mv. The question is then posed if this theory can be quantized, using a simplified version of the Galilei group. It is speculated that this may result in fewer conserved quantities. Any assistance in exploring this idea would be appreciated.
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lugita15
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Aristotelian physics, shorn of whatever the historical Aristotle actually believed, is pretty similar to Newtonian physics. Instead of "An object in motion stays in motion unless acted on by an unbalanced force", we have "An object at rest stays at rest unless acted on by an unbalanced momentum." Newton's F=ma, which is a second order differential equation, becomes p=mv, which is a first order differential equation. Otherwise, we have business as usual.

My question is, can we quantize this theory? Instead of constructing Hilbert space operators using the representation theory of the full Galilei group, we just use the representation theory of the Galilei group excluding Galilean transformations, i.e. just consisting of spatial translations, spatial rotations, and time translations. What would such a quantum theory look like? I can tell right off the bat there will probably be fewer conserved quantities, but not much more.

Any help would be greatly appreciated.

Thank You in Advance.
 
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Aum, any thoughts on this?
 

1. Can we accurately quantize Aristotelian Physics?

Quantization is the process of representing continuous physical quantities in discrete units. While Aristotelian Physics is based on continuous motion and change, it is possible to quantize it by breaking it down into smaller, discrete components. However, this may not accurately represent the complexity and nuances of Aristotelian Physics.

2. What are the challenges in quantizing Aristotelian Physics?

One of the main challenges in quantizing Aristotelian Physics is the fact that it is based on continuous motion and change, rather than discrete units or particles. This makes it difficult to apply traditional quantization methods used in modern physics. Additionally, there may be conflicting interpretations and debates about how to quantize certain aspects of Aristotelian Physics.

3. How does quantizing Aristotelian Physics impact our understanding of the universe?

The quantization of Aristotelian Physics can provide new insights and perspectives on the workings of the universe. It may also help bridge the gap between classical and modern physics, allowing for a more integrated understanding of the laws of nature. However, it is important to note that quantization is just one approach and may not fully capture the complexity of Aristotelian Physics.

4. Are there any practical applications of quantizing Aristotelian Physics?

Quantizing Aristotelian Physics can have practical applications in fields such as philosophy, history, and education. It can help us better understand the development of scientific thought and the evolution of our understanding of the universe. It may also have implications for how we approach and teach physics in the future.

5. What are the potential criticisms of quantizing Aristotelian Physics?

Some may argue that quantizing Aristotelian Physics goes against the fundamental principles and concepts of the original theory, and therefore may not accurately represent it. Others may argue that it is unnecessary to quantize a theory that has been widely accepted and studied for centuries. There may also be concerns about the validity and accuracy of the quantization methods used.

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