Can an Alternating Metric Define a New Spacetime Topology?

  • Thread starter Phrak
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In summary: I was thinking of the metric tensor. But now that you've brought it up, and I've had a chance to look at the Wiki page on the metric, I think the latter is what I want to know about. Thanks!In summary, an alternate topology of spacetime can be defined upon an alternating form/structure. This new metric must be a function of the metric because the metric define the topology of spacetime completely. The metric tensor is not a metric -not non-neg and no triangle inequality.
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Phrak
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Can an alternative topology of spacetime be defined upon a "mertic" of alternating forms?

A less stringent question: Can a topology be defined, without first premising a metric, but premising an alternating structure instead?
 
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What do you mean by "alternating forms/structure"?
 
  • #3
Phrak said:
Can an alternative topology of spacetime be defined upon a "mertic" of alternating forms?

A less stringent question: Can a topology be defined, without first premising a metric, but premising an alternating structure instead?

Yes ... but this new metric must be a function of the metric because the metric define the topology of spacetime completely.
 
  • #4
Mueiz said:
Yes ... but this new metric must be a function of the metric because the metric define the topology of spacetime completely.

What is the metric?

And, yes a metric will define a topology via it's open balls, the metric topology. But can we define another topology perhaps for other purposes? Can't the space be given another topology other than the metric topology?
 
  • #5
Phrak said:
Can an alternative topology of spacetime be defined upon a "mertic" of alternating forms?

A less stringent question: Can a topology be defined, without first premising a metric, but premising an alternating structure instead?
When you use the word "metric" do you mean in the topological-space sense or the metric tensor, which are two different concepts?
 
  • #6
That is a key point, Dr. Greg.
Where does that other metric come from, the one that defines the topology? The metric tenser is not a metric -not non-neg and no triangle inequality.
Also see my 'Flat spatime topology-metric?' thread in math -> topology and geometry sections
 
  • #7
DrGreg said:
When you use the word "metric" do you mean in the topological-space sense or the metric tensor, which are two different concepts?

I was thinking of the metric tensor. But now that you've brought it up, and I've had a chance to look at the Wiki page on the metric, I think the latter is what I want to know about. Thanks!
 

1. Can an alternating metric define a new spacetime topology?

Yes, an alternating metric can define a new spacetime topology. In fact, some theories in physics, such as string theory, propose the existence of multiple dimensions and alternate spacetime topologies.

2. What is an alternating metric?

An alternating metric is a mathematical tool used to define distances and angles in non-Euclidean spaces. It is also known as a pseudo-Riemannian metric and is often used in general relativity to describe spacetime.

3. How is a new spacetime topology defined?

A new spacetime topology can be defined by altering the structure of the underlying metric. This can involve changing the number of dimensions, the curvature of spacetime, or the way in which distances and angles are measured.

4. What implications could a new spacetime topology have?

A new spacetime topology could have significant implications for our understanding of the universe. It could potentially provide explanations for phenomena that cannot be explained by our current understanding of spacetime, such as dark matter and dark energy.

5. Are there any experiments or observations that could support the existence of a new spacetime topology?

There are ongoing experiments and observations that could potentially support the existence of a new spacetime topology. For example, studies of the cosmic microwave background radiation and gravitational lensing could provide evidence for alternate dimensions and spacetime topologies.

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