Just a few Relativity Questions

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exfret
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Just a few Relativity Questions

Postby exfret » Sat Jan 04, 2014 1:47 am

My brother said time gets slower when you're in a high gravitational area. Is this right?

Also, how do you tell whether time is slower for one object or another? Isn't it impossible to measure an object's 'true' velocity because no frame of reference is 'the one'? So then, how do you measure kinetic energy and other things that depend on speed/velocity?
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testtubegames
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Re: Just a few Relativity Questions

Postby testtubegames » Sat Jan 04, 2014 2:06 am

exfret wrote:My brother said time gets slower when you're in a high gravitational area. Is this right?

Also, how do you tell whether time is slower for one object or another? Isn't it impossible to measure an object's 'true' velocity because no frame of reference is 'the one'? So then, how do you measure kinetic energy and other things that depend on speed/velocity?


Ah, great questions.

Yes, the passage of time does depend on gravity. So if you're close to a massive object like a black hole, say, your clock will tick at a different rate (slower) compared to someone far away. You wouldn't notice any difference, though. (Just as a running velocity raptor doesn't see herself as length contracted. That's just how another observer sees her.)

For more on that topic, look up 'gravitational time dilation' -- though I did come across a nice (non-mathy) explanation of it here

And back to Special Relativity -- if two people are running past each other, who has the slow clock? Well, that's a pretty central question to understanding relativity, in fact. The answer? Neither. Both. Undefined. Pick your poison. By A's measurements, B has the slow clock. And by B's measurements, A has the slow clock. And neither is more correct than the other. Turns out that in special relativity, there's no right answer to that question. Just as there's no right answer to the question of who is moving. It depends on the observer.

This strange idea led to the Twin Paradox. Because, "hey", our instinct tells us, "it does matter! Either A is right or B is right!" So suppose one twin stays on earth, the other speeds away, then comes back. Who is older? Fascinating subject. Well, I'll let you go down that rabbit hole yourself...

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Re: Just a few Relativity Questions

Postby exfret » Sat Jan 04, 2014 2:51 am

About twin paradox- Ah, but I still don't see how you can tell which one is accelerating...

About gravity- bad explanation- it explained why a falling observer will see a clock moving faster in his reference frame more slowly, but that has nothing to do with gravity. You could be accelerating due to something other than gravity and notice a slower second clock, but how does gravity affect how fast time runs for you besides just accelerating things?
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Re: Just a few Relativity Questions

Postby robly18 » Sat Jan 04, 2014 11:17 am

I'll try to explain the twin paradox based on my own knowledge of the subject.
By which I mean I'll rip off other people's examples.
First, let's come up with a foolproof way to measure time. Let's go with something called the light clock. Thing. I'm not sure if it has a name.
Imagine a sort of tube with two perfect mirrors on either end, a perfect vacuum within, and a single beam of light moving between the mirrors.
So a little bit like this:
Image
Now, for ease of explanation, let's imagine professor Rex decelerated the speed of light, and I just so happened to be holding one of these and moving past you:
Image
Now, if there's something scientists know, and have known for quite a while, it is that light moves at the same speed no matter your point of view
Allow me to exemplify.
Imagine you're on the slowest train in the world, which is going at 2 miles per hour.
Now, imagine that you, on the train, throw a ball in the same direction the train is going at 2 miles per hour.
Now, imagine I'm at the train station. At what speed do I see that ball go? (Ignoring relativistic effects of course)
Yep, I see it going at 4 miles per hour.
However, imagine you're on the same train and you turn on a flashlight. Do I observe the beam of light going at c + 2mph? No. I observe it going at c.
And how does the universe make everything consistent?
Well, from your point of view, c is still the same speed. What happened is, time slowed down for you. You see light going just slightly slower than I do, but since time is slowed down, you perceive it going at exactly c.

There's more to explain, but I'll continue later. But you can already kinda see how movement decelerates you. I'll get more in depth later.
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exfret
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Re: Just a few Relativity Questions

Postby exfret » Sun Jan 05, 2014 12:03 pm

Well, you explained some relativity, but not the answers to my questions. I already knew this, but it's a bit clearer to me now. Also, I don't think your light clock is perfect. I guess it's good for measuring relativistic effects, though.
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testtubegames
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Re: Just a few Relativity Questions

Postby testtubegames » Fri Jan 10, 2014 1:47 am

exfret wrote:About twin paradox- Ah, but I still don't see how you can tell which one is accelerating...

About gravity- bad explanation- it explained why a falling observer will see a clock moving faster in his reference frame more slowly, but that has nothing to do with gravity. You could be accelerating due to something other than gravity and notice a slower second clock, but how does gravity affect how fast time runs for you besides just accelerating things?


Ah, but gravity *is* different than just a spaceship with the rockets blasting. In the second case, the entire ship would be accelerating uniformly. With gravity, though, the force of gravity at your feet is slightly stronger than that at your head. You could figure out (if you were in a ship with precise measurement tools) whether you were sitting on a planet, or accelerating through space.

And that's kinda key to the argument. Since one way to look at it is to think "a person sitting on the ground is like a spaceship accelerating at 9.8m/s2" and a person many earth-radii further away (sitting on an absurdly tall tower, say), feels a much lower force of gravity. So for them sitting still, it feels like they're on a ship accelerating much more slowly.

As you can find out with a bit of experimentation in Velocity Raptor... it's no surprise that the person with the 'higher acceleration' would experience stronger time dilation.

Oh, and as for figuring out which twin is accelerating... close your eyes in the car. You can tell when you're accelerating. You experience different forces, and you can measure acceleration. So in relativity, and with the twins, we may not be able to define who is *moving*, but we can certainly define who is *accelerating*.

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Re: Just a few Relativity Questions

Postby exfret » Fri Jan 10, 2014 11:18 am

testtubegames wrote:
exfret wrote:And that's kinda key to the argument. Since one way to look at it is to think "a person sitting on the ground is like a spaceship accelerating at 9.8m/s2" and a person many earth-radii further away (sitting on an absurdly tall tower, say), feels a much lower force of gravity. So for them sitting still, it feels like they're on a ship accelerating much more slowly.


But, what if you're standing on the surface of the Earth? Gravity isn't just causing time to dilate even though you're remaining still. Also, if what you are saying was the case, then it would be differences in acceleration causing time dilation, not gravity itself, so tell me, how does gravity cause time dilation.
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Re: Just a few Relativity Questions

Postby testtubegames » Fri Jan 10, 2014 12:04 pm

exfret wrote:But, what if you're standing on the surface of the Earth? Gravity isn't just causing time to dilate even though you're remaining still. Also, if what you are saying was the case, then it would be differences in acceleration causing time dilation, not gravity itself, so tell me, how does gravity cause time dilation.


I'm not sure what you mean by your first concern. The reason I needed someone sitting on a really tall tower in my thought experiment is that I needed to compare clocks in two places where the gravity was different. Time dilation still exists if we only talk about people walking around the surface of earth... but doesn't have too much importance until we compare our clocks to clocks that are ticking differently.

And one of Einstein's key realizations when he was creating General Relativity was that acceleration and gravity are intertwined -- as in these rocket ship examples we've been talking about. Since we're not in free-fall (at least I hope you're not in free-fall when you read this), in one way of looking at it, we are treated as if we're accelerating.

For a more hand-wavy (visual and intuitive if not entirely rigorous) reason that gravity causes time dilation -- think of those pictures you've seen where a planet or black hole warps a 2-d sheet that represents spacetime. The nearer you go to the massive body, the more spacetime is curved and stretched. (If it were really just a sheet of fabric, and you tried to flatten the fabric of spactime back out it back out, you'd have way to much stuff in the middle.)

Well, since spacetime is stretched to be a bit bigger, that means that seconds are stretched to be a bit bigger. So the seconds pass by more slowly for you - as compared to someone where space isn't as curved.

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Re: Just a few Relativity Questions

Postby exfret » Fri Jan 10, 2014 6:34 pm

testtubegames wrote:
exfret wrote:But, what if you're standing on the surface of the Earth? Gravity isn't just causing time to dilate even though you're remaining still. Also, if what you are saying was the case, then it would be differences in acceleration causing time dilation, not gravity itself, so tell me, how does gravity cause time dilation.

I'm not sure what you mean by your first concern. The reason I needed someone sitting on a really tall tower in my thought experiment is that I needed to compare clocks in two places where the gravity was different. Time dilation still exists if we only talk about people walking around the surface of earth... but doesn't have too much importance until we compare our clocks to clocks that are ticking differently.


What do you mean by what do you mean by my "First Concern"? I never said that in my reply that you quoted, did I? Now I'm just confused why you included this???


testtubegames wrote:And one of Einstein's key realizations when he was creating General Relativity was that acceleration and gravity are intertwined -- as in these rocket ship examples we've been talking about. Since we're not in free-fall (at least I hope you're not in free-fall when you read this), in one way of looking at it, we are treated as if we're accelerating.


Wait, so if you're accelerating due to free fall, that doesn't count as acceleration in special relativity?


testtubegames wrote:(If it were really just a sheet of fabric, and you tried to flatten the fabric of spactime back out it back out, you'd have way to much stuff in the middle.)


Yeah I know that now, but back when I was younger, I used to wonder why people didn't just make 'perfect maps'. I know that now, of course. Differing geometries always get really fun.


testtubegames wrote:For a more hand-wavy (visual and intuitive if not entirely rigorous) reason that gravity causes time dilation -- think of those pictures you've seen where a planet or black hole warps a 2-d sheet that represents spacetime. The nearer you go to the massive body, the more spacetime is curved and stretched. Well, since spacetime is stretched to be a bit bigger, that means that seconds are stretched to be a bit bigger. So the seconds pass by more slowly for you - as compared to someone where space isn't as curved.


Okay, so the spacetime curve make time travel slower when I'm just sitting here? Also, how does a 'bigger' curve cause 'bigger' seconds?
Last edited by exfret on Sat Jan 18, 2014 5:18 pm, edited 1 time in total.
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Re: Just a few Relativity Questions

Postby testtubegames » Sat Jan 18, 2014 2:40 am

exfret wrote:What do you mean by what do you mean by my "First Concern"?

Just referring to your first question... aka the first point you brought up. "What if you're standing on the surface of the earth?" That is all.

exfret wrote:Wait, so if you're accelerating due to free fall, that doesn't count as acceleration in special relativity?

Exactly! (But, of course, in Special Relativity, there's no gravity, so there's no planet to be in freefall toward, persay. The basic idea is right, though. For GR, when you're in freefall, you are in an inertial frame, and while you're sitting still, you're not.)

exfret wrote:Okay, so the spacetime curve make time travel slower when I'm just sitting here? Also, how does a 'bigger' curve cause 'bigger' seconds?


It's easier to visualize it with space. Think back to the stretched surface. 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)

Again, this is pretty handwavy and non-rigorous. But should be helpful intuitively, I hope.


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