Why is there a Minus in Spacetime Interval Formula?

In summary, relativity relies on a minus sign in the spacetime interval formula to make sure that the time dimension is different to the spatial dimensions. This is because the fundamental geometry of 4D spacetime is non-Euclidean, and the Minkowski metric (featuring the negative sign) applies.
  • #36
nitsuj said:
That's well into the realm of "physically possible according to theory", or leaning heavily on the theory. In what sense could I meet up with an earlier version of myself? Everything I know about SR tells me that isn't even remotely possible. Are there "real world" examples of this, or is it strictly hypothetical?

EDIT: Reading about the Gödel metric the wiki seems to say it is possible to "See" an earlier version of yourself. I see that as a world of difference...womp womp womp...I can "see" old light that I shouldn't be able to "see". That said I still don't know about CTCs or what they are.

Einstein said this in retort to the metric "It will be interesting to weigh whether these are not to be excluded on physical grounds."

A CTC is a physically accessible path (for massive particles) that forms a complete loop. So essentially you end up at the same point of time and space, after some finite proper time. I don't really want to get into the details of causal structure, it's a huge topic and my ability to replicate it from memory is not exceptional. However, CTC's are typically considered unphysical, and there are some reasons to believe there are no CTC's outside of just "they are confusing" (in order for there to be an initial value formulation, space-time has to be globally hyperbolic, which has no CTC's).

My point with CTC's was just to note that the relative minus sign in the minkowski metric is not by itself enough to ensure causality. That said, there aren't any CTC's in minkowski space, but it's just one of many examples of a metric without CTC's. So while the minkowski metric ensures causality, causality does not ensure the minkowski metric.
 
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  • #37
DimReg said:
My point with CTC's was just to note that the relative minus sign in the minkowski metric is not by itself enough to ensure causality. That said, there aren't any CTC's in minkowski space, but it's just one of many examples of a metric without CTC's. So while the minkowski metric ensures causality, causality does not ensure the minkowski metric.

Ah, thank you, your point went over my head. It'll take some time to "see" why that is; it doesn't "jump out at me".

Perhaps I feel too strongly that the simple logic of causality has a physical significance & that properly defined measurements do too.
 
<h2>1. Why is there a minus in the spacetime interval formula?</h2><p>The minus sign in the spacetime interval formula represents the concept of relativity and the difference between space and time. It is used to account for the fact that time and space are not independent, but rather are interconnected in the fabric of spacetime.</p><h2>2. How does the minus sign affect the calculation of the spacetime interval?</h2><p>The minus sign affects the calculation of the spacetime interval by accounting for the fact that time and space are not independent, but are connected in a four-dimensional spacetime. This means that the spacetime interval must take into account both the spatial and temporal components of an event.</p><h2>3. Can the minus sign be removed from the spacetime interval formula?</h2><p>No, the minus sign is a crucial part of the spacetime interval formula and cannot be removed. Without the minus sign, the formula would not accurately represent the relationship between space and time in the fabric of spacetime.</p><h2>4. How does the minus sign relate to the concept of time dilation?</h2><p>The minus sign in the spacetime interval formula is related to the concept of time dilation by accounting for the fact that time can appear to pass at different rates for different observers depending on their relative motion. This is a key aspect of the theory of relativity.</p><h2>5. Is the minus sign in the spacetime interval formula always negative?</h2><p>No, the minus sign in the spacetime interval formula is not always negative. It depends on the frame of reference of the observer. In some cases, the minus sign may result in a positive value, indicating that the event occurred in a different frame of reference than the observer.</p>

1. Why is there a minus in the spacetime interval formula?

The minus sign in the spacetime interval formula represents the concept of relativity and the difference between space and time. It is used to account for the fact that time and space are not independent, but rather are interconnected in the fabric of spacetime.

2. How does the minus sign affect the calculation of the spacetime interval?

The minus sign affects the calculation of the spacetime interval by accounting for the fact that time and space are not independent, but are connected in a four-dimensional spacetime. This means that the spacetime interval must take into account both the spatial and temporal components of an event.

3. Can the minus sign be removed from the spacetime interval formula?

No, the minus sign is a crucial part of the spacetime interval formula and cannot be removed. Without the minus sign, the formula would not accurately represent the relationship between space and time in the fabric of spacetime.

4. How does the minus sign relate to the concept of time dilation?

The minus sign in the spacetime interval formula is related to the concept of time dilation by accounting for the fact that time can appear to pass at different rates for different observers depending on their relative motion. This is a key aspect of the theory of relativity.

5. Is the minus sign in the spacetime interval formula always negative?

No, the minus sign in the spacetime interval formula is not always negative. It depends on the frame of reference of the observer. In some cases, the minus sign may result in a positive value, indicating that the event occurred in a different frame of reference than the observer.

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