# Introduce Newtonian Metric for SR & Lorentz

• kent davidge
In summary, the conversation is about the use of a Newtonian metric in analogy with special relativity and the Lorentz metric. The metric for Euclidean three-dimensional space is considered meaningful, and while tensor methods may be seen as overkill for this simple manifold, it can be educational to rewrite the metric in a more complex coordinate system. However, this does not make it a "Newtonian metric" and it is not directly related to Newtonian physics, as tensor methods are necessary for expressing the fundamental laws of physics even in classical mechanics.
kent davidge
Is it meaningful to introduce a Newtonian metric ##ds^2 = dx^2 + dy^2 + dz^2## in analogy with special relavity and the Lorentz metric?

That's the metric for Euclidean three-dimensional space, and as such it's meaningful. Tensor methods are generally a bit of overkill for this trivial manifold, but it's educational to rewrite the metric in some truly bizarre coordinate system with off-diagonal elements as a demonstration of how the formalism works before taking on the non-trivial manifolds of GR.

However, it's not a "Newtonian metric" and it doesn't have much to do with Newtonian physics.

kent davidge
Tensor methods are no overkill but the only way to express the fundamental laws of physics already in Newtonian mechanics ;-)).

weirdoguy and kent davidge

## 1. What is the Newtonian Metric for Special Relativity (SR) and Lorentz?

The Newtonian Metric is a mathematical framework used to describe the effects of gravity on space and time. It is based on Isaac Newton's laws of motion and describes how objects interact with each other in a three-dimensional space.

## 2. How is the Newtonian Metric different from the Einsteinian Metric?

The Newtonian Metric is a simplified version of the Einsteinian Metric, which is used in Einstein's theory of General Relativity. The Newtonian Metric assumes that space and time are absolute and do not change, while the Einsteinian Metric takes into account the effects of gravity on the curvature of space and time.

## 3. What is the significance of the Newtonian Metric in SR and Lorentz?

The Newtonian Metric is significant in SR and Lorentz because it provides a framework for understanding how gravity affects the motion of objects in space. It also allows for the prediction and calculation of various phenomena, such as gravitational time dilation and gravitational lensing.

## 4. How does the Newtonian Metric relate to the Lorentz transformation?

The Lorentz transformation is a mathematical equation used to describe the relationship between two reference frames in SR. The Newtonian Metric is used in this transformation to account for the effects of gravity on space and time, allowing for accurate predictions of how objects will behave in different reference frames.

## 5. Can the Newtonian Metric be applied to all situations involving gravity?

No, the Newtonian Metric is only applicable in situations where the effects of gravity are relatively weak and the speeds of objects are much slower than the speed of light. In extreme cases, such as near black holes or at very high speeds, the Einsteinian Metric must be used instead.

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