S: Understanding Space-Time Confusion

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Understanding space-time involves recognizing that all objects have a fixed total space-time velocity, which combines their movement through space and time. When an object moves in space, its time component decreases to maintain a constant total velocity, meaning that time appears to pass more slowly for that object relative to a stationary observer. The discussion highlights the difference between personal time (t) and the time observed by someone stationary (T), emphasizing that as speed increases, the observed time dilation becomes significant, particularly near the speed of light. The analogy of changing direction while maintaining a constant speed illustrates how velocity components interact in both space and time. This foundational understanding is crucial for grasping the complexities of space-time and its implications in physics.
TwistedmAGPIe
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Hi.

I don't mean to sound stupid but I'm quite new to learning about space but I'm real hooked on understanding how it all works. One thing that I come across a lot is Space-Time...I'm really not sure that I understand how it in itself works...How something can move in a different time if it moves faster etc...I've tried to find documentaries that would help but am finding it difficult to find something specific to space-time itself. Can anyone suggest anything I can watch online or download that would clear this cloud in my mind?!?

mAGPIe
 
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How is this for a simple analogy;

You have to accept first that everything has a fixed total space-time velocity. Let's apply this to regular 3 dimensional space. Say you are traveling and 100 Km/h due east. Your total velocity is 100 km/h. Now let's say you turn a bit so that you are going north-east. Your easterly velocity has become smaller, and your northerly velocity had increased from zero to some value. If you work out the total velocity, you still get 100 km/h.

Now, the trick with space-time is that in addition to the components of velocity in space (i.e. dx/dt, dy/dt, dz/dt) you also have a component in time (dT/dt). If you're not moving with respect to space, then you are just moving in time. Once you start to move in space, say you pick up a component dx/dt, then your component dT/dt becomes smaller to compensate, such that your total '4-velocity' stays constant.

For my two time co-ordinates, t is your time, the time on your watch, and T is the time that someone who is stationary with respect to the x,y,z co-ordinates observers you to have. So if you move with respect to someone, they see your time go slower than theirs.
 
Wallace said:
How is this for a simple analogy;

You have to accept first that everything has a fixed total space-time velocity. Let's apply this to regular 3 dimensional space. Say you are traveling and 100 Km/h due east. Your total velocity is 100 km/h. Now let's say you turn a bit so that you are going north-east. Your easterly velocity has become smaller, and your northerly velocity had increased from zero to some value. If you work out the total velocity, you still get 100 km/h.

Now, the trick with space-time is that in addition to the components of velocity in space (i.e. dx/dt, dy/dt, dz/dt) you also have a component in time (dT/dt). If you're not moving with respect to space, then you are just moving in time. Once you start to move in space, say you pick up a component dx/dt, then your component dT/dt becomes smaller to compensate, such that your total '4-velocity' stays constant.

For my two time co-ordinates, t is your time, the time on your watch, and T is the time that someone who is stationary with respect to the x,y,z co-ordinates observers you to have. So if you move with respect to someone, they see your time go slower than theirs.

Would this not result in a linear decrease of dT/dt instead of what is experimentally observed? A chart of of speed vs time will show small decreases in dT/dt until very close to the speed of light at which time dT/dt decreases rapidly.
 
https://en.wikipedia.org/wiki/Recombination_(cosmology) Was a matter density right after the decoupling low enough to consider the vacuum as the actual vacuum, and not the medium through which the light propagates with the speed lower than ##({\epsilon_0\mu_0})^{-1/2}##? I'm asking this in context of the calculation of the observable universe radius, where the time integral of the inverse of the scale factor is multiplied by the constant speed of light ##c##.
Why was the Hubble constant assumed to be decreasing and slowing down (decelerating) the expansion rate of the Universe, while at the same time Dark Energy is presumably accelerating the expansion? And to thicken the plot. recent news from NASA indicates that the Hubble constant is now increasing. Can you clarify this enigma? Also., if the Hubble constant eventually decreases, why is there a lower limit to its value?

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