Just a few Relativity Questions

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testtubegames
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Re: Just a few Relativity Questions

Postby testtubegames » Sun Mar 23, 2014 3:33 pm

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

Yup, that's the idea.

Not too much unlike the fact we sometimes discuss distance in 'light-years'.

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Re: Just a few Relativity Questions

Postby exfret » Sun Mar 23, 2014 9:03 pm

Except I'm asking the distance of time, while 'light-years' are no where near a measure of time. When we measure with 'light-years', they're purely distances, because we're measuring speed (of light) * time (in years), which cancels it out to give us distance. I don't see why this is such a big deal just because it has a word measuring time in it. It's like saying we measure energy in distance, because a common name for the unit of energy is the Newton-Meter.
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Re: Just a few Relativity Questions

Postby testtubegames » Mon Mar 24, 2014 11:15 am

Sure. "Light-years" are a measure of distance. The unit is based on time (years) and the speed of light is used as the conversion factor to get you to distance (light-years).

So back to your original question, one could say that the distance of the time unit "year" was a light-year. And the distance of a "second" was a light-second.

So when I said:
testtubegames wrote:So 1 second would be 3x10^8m... or more generally, distance=time*c.

That distance is a light-second.

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Re: Just a few Relativity Questions

Postby exfret » Mon Mar 24, 2014 6:29 pm

Oh. So is it just a shorthand, or is a second of time really a light-second of meters, or is there no way to know, or does it not really work that way?
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Re: Just a few Relativity Questions

Postby testtubegames » Mon Mar 24, 2014 8:22 pm

exfret wrote:Oh. So is it just a shorthand, or is a second of time really a light-second of meters, or is there no way to know, or does it not really work that way?

Good question. Yes and no.

A second does not equal a light-second. One is time, the other is distance. *But* if you want to convert between time and distance in relativity, you generally do use distance = speed-of-light * time to figure it out.

Now, if instead of talking about relativity, we were talking about something else, like driving, maybe we'd use another conversion factor (like 55mph... so two towns can be two hours apart, or 110 miles apart, interchangeably). And maybe that's a good analogy for thinking about this. It doesn't mean that the distance '110 miles' is literally the same thing as the time '2 hours', but in the context of the car going 55 mph, you can equate the two. (And the answer to "How much longer do we have to drive" can be answered equally well with either)

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Re: Just a few Relativity Questions

Postby exfret » Mon Mar 24, 2014 8:28 pm

Oh. That's a little disappointing. I'm kind of confused about relativity now. I wish it wasn't one of those wait-a-few-years-until-you've-learned-college-mathematics topics. ):
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Re: Just a few Relativity Questions

Postby testtubegames » Mon Mar 24, 2014 8:38 pm

I know, right? Nothing beats learning the math of physics...

My big recommendation would be to grab an awesome book if you're yearning to learn a bit more. One I absolutely love that I first read during high school was Black Holes and Time Warps by Kip Thorne. That was a formative read for me, and used copies are pretty cheap/easy to come by.

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Re: Just a few Relativity Questions

Postby 19683 » Tue Mar 15, 2016 12:45 pm

So is the center of the Earth an inertial frame since it is in 'free-fall' around the sun?
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Re: Just a few Relativity Questions

Postby testtubegames » Thu Mar 17, 2016 1:34 pm

Yeah, I suppose so. Anything that's allowed to free-fall is in an inertial frame (as far as General Relativity is concerned). If you jump off a chair, for instance, you'll spend a few moments in an inertial frame before landing.

I'll note, while in Special Relativity, an inertial reference frame can be a global thing ("everybody sitting still with respect to me"), in General Relativity that's not the case. In GR, inertial frames are constructs that are infinitesimally small. Basically, my left arm isn't free-falling the exact same direction that my right arm is (the vector towards the center of the earth points at sliiiightly different angles for each of them).


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