# Dynamical Spacetime: Time or Space Dependent?

• kau
In summary, the conversation discusses the relationship between spacetime and dynamical systems, specifically in the context of AdS/CFT theory. It is mentioned that time is necessary for observing and differentiating length, and traditionally time is associated with dynamical systems while space is not. However, the speaker also brings up the possibility that this may not hold true in the context of AdS/CFT theory.
kau
when do you call a spacetime dynamical...when metric is time dependent or it depends on space ??...

Time.

bapowell said:
Time.
Ok...then AdS geometry has spatial dependence then why it is written that fixed boundary theory has a correspondence to bulk gravity theory which is dynamical..(in the context of AdS/CFT)...

One of the reasons the concept of spacetime eventually became a natural concept to me is due to some conclusions one can make regarding any direct observation of length and time.

Length only exists (observationally) in conjunction with time, that may not be intuitive but what differentiates lengths like a meter from a kilometer is time. We tend to think of those lengths as static but if time is 0 both lengths are infinite. Time > 0 is required to observe and differentiate length; however the same holds true for direct observations of time, such observations include a length > 0 too. Please remember I am referring to direct observations above.

Traditionally time is associated with dynamical systems whereas space is not. I’d only be guessing if that holds true in the context of AdS/CTF theory. Perhaps what I brought up above might give you a little better insight into it.

A spacetime is considered dynamical when its metric, which describes the curvature of spacetime, is either time-dependent or space-dependent. This means that the geometry of the spacetime is changing over time or varies in different regions of space. This concept is an essential aspect of Einstein's theory of general relativity, which states that the curvature of spacetime is influenced by the distribution of matter and energy.

In other words, when there are changes in the distribution of matter and energy in a particular region of spacetime, the metric will also change accordingly. This can result in changes in the passage of time or the shape of space in that region. Therefore, a dynamical spacetime is one that is constantly evolving and changing due to the presence of matter and energy.

To identify a spacetime as dynamical, we need to observe the effects of its changing metric. This can be done through measurements of the curvature of spacetime, such as gravitational lensing or the bending of light around massive objects. Additionally, the study of the evolution of the universe, including the expansion of space, also provides evidence for a dynamical spacetime.

In summary, a spacetime is considered dynamical when its metric is time-dependent or space-dependent, reflecting the ever-changing nature of our universe. This concept is crucial in understanding the fundamental workings of the universe and is a key aspect of modern physics and cosmology.

## 1. What is dynamical spacetime?

Dynamical spacetime is a concept in physics that describes the relationship between space and time. It suggests that space and time are not fixed entities, but rather are influenced by matter and energy, and can change depending on their interactions.

## 2. How is dynamical spacetime different from classical notions of space and time?

In classical physics, space and time are considered absolute and separate entities. Dynamical spacetime, on the other hand, takes into account the effects of gravity and other forces on the fabric of space and time, and how they can be influenced by matter and energy.

## 3. Is dynamical spacetime a proven concept?

Yes, dynamical spacetime is a well-supported concept in modern physics, particularly in the field of general relativity. Many experiments and observations have confirmed its predictions, such as the bending of light around massive objects and the gravitational time dilation effect.

## 4. Can dynamical spacetime exist without matter and energy?

No, according to current scientific understanding, matter and energy are necessary for the existence of dynamical spacetime. Without these entities, there would be no gravitational forces to cause the curvature of spacetime.

## 5. How is dynamical spacetime relevant in our daily lives?

Dynamical spacetime may seem like a complex and abstract concept, but it has many practical applications in our daily lives. For example, it helps us understand the behavior of celestial objects, such as planets and stars, and allows us to make accurate predictions about their movements. It also plays a crucial role in technologies such as GPS, which relies on precise measurements of spacetime to function.

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