Is Geometry Simply a Mathematical Model for Physical Bodies?

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In summary, string theory is often compared to a computer program where bodies follow mathematical formulas, but it is unclear how the theory's geometry forces physical bodies to follow a specific path. However, in the General Theory of Relativity, Einstein argues that space is endowed with physical qualities and an Aether, and without it, space would not exist in the physical sense. It is uncertain if this concept has been revisited or discarded in modern physics.
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wolram
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I could understand ST being modeled as some computer program where bodies follow
some imputed mathematical formula, but how does ST as geometry force physical bodies to follow some path?
 
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Well, string theory describes gravity in the IR, so presumably the answer is the same as in GR.
 
  • #3
wolram said:
I could understand ST being modeled as some computer program where bodies follow
some imputed mathematical formula, but how does ST as geometry force physical bodies to follow some path?

At least in this address by Einstein in 1920, he was convinced that geometry existed because of substance:
Recapitulating, we may say that according to the General Theory of Relativity space is endowed with physical qualities; in this sense, therefore, there exists an Aether. According to the General Theory of Relativity space without Aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this Aether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it.

I wonder if this may be revisited or if it has been discarded for good in modern physics.
 
  • #4
wolram---

I was confused... Do you mean ST (string theory?) or SR (special relativity) ?
 
  • #5
dilletante said:
At least in this address by Einstein in 1920, he was convinced that geometry existed because of substance:


I wonder if this may be revisited or if it has been discarded for good in modern physics.


This is what i meant but was unable to verbalise with so much eloquence, Einstein has
once again eclipsed what i imagined was an original thought.
 

FAQ: Is Geometry Simply a Mathematical Model for Physical Bodies?

What does it mean when it's said that "Geometry has no substance"?

When people say that "Geometry has no substance", they are referring to the fact that geometry is a purely theoretical and abstract concept. It does not have a physical form or existence in the real world.

Why is it important to study geometry if it has no substance?

While geometry may not have a physical substance, it is still a fundamental branch of mathematics that helps us understand the relationships and properties of shapes and space. It also has many practical applications in fields such as engineering, architecture, and physics.

Can geometry ever have substance?

No, geometry will always remain an abstract concept. However, it is constantly evolving and being refined through new discoveries and theories.

How did the idea that "geometry has no substance" come about?

The idea that geometry has no substance originated with the ancient Greek philosopher, Plato. He believed that the physical world was an imperfect representation of the perfect and eternal realm of ideas, of which geometry was a part.

What are some common misconceptions about geometry having no substance?

One common misconception is that because geometry is abstract, it is not useful in the real world. However, as mentioned earlier, geometry has numerous practical applications. Another misconception is that geometry is only about shapes and measurements, when in fact it also involves logic, reasoning, and problem-solving skills.

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