Just a few Relativity Questions

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exfret
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Re: Just a few Relativity Questions

Postby exfret » Sat Jan 18, 2014 5:38 pm

testtubegames wrote:If there were rulers in that world we stretched, they'd actually be a bit longer in the stretched part. So the bigger curve causes bigger rulers. And since it works for space, it works for time, too. (Yay for spacetime)


I just don't understand how just being in a more elongated geometry in the spatial directions causes the time direction to elongate as well... or, does gravity elongate the time direction just like it elongates the spatial directions??? Oh, if you ever make hyperbola land...

http://testtubegames.com/forums/download/file.php?mode=view&id=40

You could add in this dilation, or make it so you can add masses and what not that change the curvature of space!!!
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testtubegames
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Re: Just a few Relativity Questions

Postby testtubegames » Mon Jan 20, 2014 12:40 am

exfret wrote:... or, does gravity elongate the time direction just like it elongates the spatial directions???


Bingo! Space and time are connected. So even though the example was about a 2D spatial surface being stretched... it really represents 3 spatial dimensions and 1 time dimension.

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Re: Just a few Relativity Questions

Postby exfret » Mon Jan 20, 2014 2:10 pm

testtubegames wrote:
exfret wrote:... or, does gravity elongate the time direction just like it elongates the spatial directions???


Bingo! Space and time are connected. So even though the example was about a 2D spatial surface being stretched... it really represents 3 spatial dimensions and 1 time dimension.


So maybe you could include the ability to stretch time as a dimension in hyperbolawesome hyperboland hyperboplease hyperbowhen hyperbyou hypgetrbola hyperbto hyperbolafinishing hypershocktolapus and hyperbogravity hyperbosimulatorla?
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exfret
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Re: Just a few Relativity Questions

Postby exfret » Sat Mar 22, 2014 11:35 am

Wait, so time is a dimension, right? Then how many meters are in a second of time dimension?
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robly18
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Re: Just a few Relativity Questions

Postby robly18 » Sat Mar 22, 2014 1:21 pm

It's hard to explain, but this should clear things up for ye:

https://www.youtube.com/watch?v=M9sbdrPVfOQ
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exfret
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Re: Just a few Relativity Questions

Postby exfret » Sat Mar 22, 2014 3:04 pm

That video is in complete agreement with what I said. There is a time dimension, and we measure its length in seconds. My question was what the conversion factor of seconds to meters was. Basically, we measure 'oil' in seconds and 'water' in meters, so how many seconds of 'oil' will give you the same 'volume' as a meter of 'water'?
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robly18
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Re: Just a few Relativity Questions

Postby robly18 » Sat Mar 22, 2014 6:23 pm

exfret wrote:That video is in complete agreement with what I said. There is a time dimension, and we measure its length in seconds. My question was what the conversion factor of seconds to meters was. Basically, we measure 'oil' in seconds and 'water' in meters, so how many seconds of 'oil' will give you the same 'volume' as a meter of 'water'?

Well, that was an example.
See, the thing is, there really isn't a scale. Time isn't a spatial dimension. There isn't a concept of length as we know it.

Remember, time is relative. Time is different based on where you are. There's no such scale, because time is dynamic. If there was, there would be no way to find out "how many meters are in a second" because meters are a way to measure space, not time.
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exfret
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Re: Just a few Relativity Questions

Postby exfret » Sun Mar 23, 2014 11:47 am

I always thought that time's differentness place-to-place was because sometimes, the time dimension was 'longer' (ie. like in places where it was affected by gravity). It would be like how hyperbolic geometry has different curving than Euclidean geometry. Also, I thought time was just space dragged through another dimension, thus 'space-time'. I mean, I can kind of see there not being a relative length, but then, how come we can measure in three spatial dimensions without having to have a special measurement for each? How come the 'time' dimension has to have its own special measurement?
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Re: Just a few Relativity Questions

Postby testtubegames » Sun Mar 23, 2014 2:59 pm

exfret wrote:Wait, so time is a dimension, right? Then how many meters are in a second of time dimension?

In physics, we do sometimes use the same units for time and distance. In which case, the speed of light is the conversion factor.

So 1 second would be 3x10^8m... or more generally, distance=time*c.

This is sometimes called 'letting c=1'. A common way to choose your units in advanced physics such that there are a)no c's in your equations, and b)there's a lot more symmetry and elegance in the equations.

So instead of E=mc^2, you get E=m. (Which also means that energy and mass have the same units in this system! If you go down the rabbit hole it gets really mind boggling.) You never do this in high school, or standard physics classes. But if you're dealing with a lot of relativistic stuff, it's a helpful shorthand.

As a further note, even when we *aren't* going out of our way to change units like this (and letting c=1) -- the same idea holds true. There are equations where you have to add space and time units. For example, finding the distance between two events. In normal 3D Newtonian space, spatial distance is just d^2 = x^2+y^2+z^2 (assuming one of the things is at the origin, of course). But in relativity, you want the distance to include the *time* dimension, too. In which case, the equation becomes d^2 = x^2+y^2+z^2-(c*t)^2

So to get the units to be the same, here, too, 'c' gets multiplied onto the time variable. (The negative sign is a whole 'nother can of worms)

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Re: Just a few Relativity Questions

Postby exfret » Sun Mar 23, 2014 3:12 pm

So, then, the average person's supervolume is average_volume_in_m^3*average_lifespan_in_seconds*c m^4 ?
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