How is the -(ct)^2 term in Minkowski metric conceived?

In summary, the article has some questionable explanations of the Minkowski formulation, and the speed of light is not necessarily constant for all observers.
  • #1
jakesee
17
0
Hi,

I am just trying to understand Special Relativity by reading http://en.wikipedia.org/wiki/Introduction_to_special_relativity

All is ok except where in "The Minkowski formulation: introduction of spacetime",
the introduction of -(ct)^2 term is not clearly justified (or so it seems to me) in the article.

Will someone explain to me, or guide me to some reference where I can find answers to:
1. Why is it negative instead of positive?
2. Why is speed of light chosen?

On another related note, I have read about the claim/observation/proposition that speed of light is constant for all observers in their own reference frames. But it is not clear whether this is the consequence of experimental result or the inherent characteristic of modelling the space-time coordinate using speed of light as one of the parameters. If it is an experimental observation, what is the experimental set up like? i.e. How is the measurement taken? Any help is appreciated. thanks!
 
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  • #2
jakesee said:
Will someone explain to me, or guide me to some reference where I can find answers to:
1. Why is it negative instead of positive?
2. Why is speed of light chosen?
1) Because that is how the dimensions of Minkowski space time are defined. See this thread:
https://www.physicsforums.com/showthread.php?t=333705

2) Convenience. It makes nice graphs if you scale the axes like this.
jakesee said:
If it is an experimental observation, what is the experimental set up like?
Did you see the sticky thread on top the forum?
https://www.physicsforums.com/showthread.php?t=229034
Look for "Michelson and Morley"
 
  • #3
A.T. said:
Did you see the sticky thread on top the forum?
https://www.physicsforums.com/showthread.php?t=229034
Look for "Michelson and Morley"

Opps, my bad. I read the "READ ME FIRST" but totally missed the first sticky. Sorry.
 

1. What is the Minkowski metric?

The Minkowski metric is a mathematical tool used in the theory of special relativity to describe the geometry of spacetime. It is a four-dimensional metric that combines space and time into a single entity, allowing for the calculation of distances and intervals between events.

2. How is the Minkowski metric derived?

The Minkowski metric is derived from the fundamental postulates of special relativity, which state that the laws of physics are the same for all observers in uniform motion. By applying Lorentz transformations to these postulates, the Minkowski metric is obtained as a way to measure spacetime intervals.

3. What is the significance of the -(ct)^2 term in the Minkowski metric?

The -(ct)^2 term in the Minkowski metric represents the time component of the metric. It is squared and has a negative sign to account for the fact that time behaves differently from space in special relativity. This term allows for the inclusion of time in the metric and enables the calculation of spacetime intervals.

4. How does the Minkowski metric differ from the Euclidean metric?

The Minkowski metric differs from the Euclidean metric in that it includes a time component and has a signature of (-1,1,1,1) compared to the Euclidean metric's signature of (1,1,1,1). This difference is necessary for the description of spacetime in special relativity, where time is treated as a fourth dimension.

5. Can the Minkowski metric be extended to higher dimensions?

Yes, the Minkowski metric can be extended to higher dimensions. In fact, it is often used in theories such as general relativity and string theory, which involve more than four dimensions. In these cases, the metric takes on a more complex form, but still retains the same fundamental principles of measuring spacetime intervals.

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