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Author Topic:   Purple dosn't beleve in relativity
Raymon
Inactive Member


Message 61 of 114 (166355)
12-08-2004 7:57 PM
Reply to: Message 19 by PurpleYouko
12-07-2004 1:29 PM


explaining the paradox
Sorry I didn't reply to this comment sooner, but I haven't been keeping a very close eye on EvC lately.

You got a lot of replies to this statment that basically said that the math works out, as well as posts that pointed out that your picture implies a 3rd observer. But there is an interesting paradox going on here that is taught to students learning relativity. Of course, it's not a real paradox. Just as the Twins paradox can be resolved, so can this notion of A's time is shorter then B's time while the converse is also true. As long as you know that length contracts at relatavistic speeds just like time slows down it's pretty straighforward. The way it is usually presented is like this-

Suppose the Flash, a man who can run at relatavistic speeds, wants to test relativity. He reasons thus: "If I have a barn that's 10m long and has doors on both ends that can be closed very quickly and a 15m long pole I can show relativity doesn't work. If I run fast enough that length contraction is 50% then I can hold the pole horizontally, run through the barn, and have the farmer try to close both doors on while I'm inside the barn. From the farmers perspective it should work because my pole is length conracted to 7.5 m. So he should be able to close both doors while I'm inside. Of course he'll have to open then again to let me out so I don't undergo acceleration and go into General Relativity's realm.

But for me, the barn is only 5m long, so there is no way I'm going to get my entire pole in there. So when the doors close at the same time they are going to hit my pole. So if the doors are able to close then the farmer's reference frame is the correct one and if they hit my pole on the way down then mine is."

This is basically the same scenario as you proposed, except instead of two times, you are comparing two lengths. So what happens?

From the farmer's reference frame, he closes the doors at the same time and Flash's pole fits inside. From Flash's reference frame, as he is running into the barn the far end closes before he gets there and then opens again to let him pass though. Then, after the entire length of the pole has passed through the near end of the barn, the near end door closes and opens. Thus we have another lesson to learn from relativity.

Simultanius events in one reference frame aren't simultanius in another.

Suppose a farmer is sitting on his porch, over-looking a long stretch of road with syncronized clocks placed every mile. Say the clocks are just striking noon as the Flash wizzes by him. To the Flash, the clocks far in front of him read to be 1pm while the ones far behind him read to be 11 am.

Personally, I think it's one of the wierdest aspects of relativity.

I hope this cleared up the "paradox".

This message has been edited by Raymon, 12-08-2004 07:59 PM


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Hangdawg13
Member (Idle past 3071 days)
Posts: 1161
From: Texas
Joined: 05-30-2004


Message 62 of 114 (166669)
12-09-2004 7:18 PM
Reply to: Message 53 by The Dread Dormammu
12-08-2004 4:54 AM


Question
Okay, let's say that there is nothing else in this universe and we know Zorg's ship is the one that is fine and Viola is the one racing away at .5c. Viola travels a full year (her time) before she fixes her ship. Then she returns directly to Zorg at .5c. Will Zorg have aged twice as much as Viola or vice versa? and why?

Put another way,
Let's say we launched a space shuttle from earth and it traveled away from earth at .5c and there was an atomic clock on board originally synchronized with an atomic clock on earth. Let's say the shuttle returns a year later (earth time), the atomic clock on the shuttle would only have half a year elapsed time, right? But who's to say that the shuttle's clock should not be the standard? If a year had passed on the shuttle's clock, would half a year have passed on the earth clock?

If both observers do believe that time is moving slower for the other one, why do atomic clocks tell us which one is moving and which one is stationary? This question is really confusing to me.

Many times I've heard people explain how a space ship traveling at close to the speed of light for many years (ship time) and returning to the earth would find that many many more years had passed on earth. I had no problem with this, but how can this happen if both observers believe time is moving slower for the other one????


This message is a reply to:
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NosyNed
Member
Posts: 8842
From: Canada
Joined: 04-04-2003


Message 63 of 114 (166698)
12-09-2004 8:06 PM
Reply to: Message 62 by Hangdawg13
12-09-2004 7:18 PM


Which ends up older?
Okay, let's say that there is nothing else in this universe and we know Zorg's ship is the one that is fine and Viola is the one racing away at .5c. Viola travels a full year (her time) before she fixes her ship. Then she returns directly to Zorg at .5c. Will Zorg have aged twice as much as Viola or vice versa? and why?

Two points:

One minor; you'd have to travel at near .99c to have time slow down by half. It is not linear and it is not time moving at half speed if you do half light speed. Doesn't really matter to the overall question it is just a nit.

There is a difference between Zorg and Viola or the shuttle and the earth.

Once the trip out and back is complete you can distinguish between the two. One of them has undergone accelerations and decelerations. That is the one whose clock will show up as slow.

That is when the shuttle returns (at some speed so that it's clock runs at half the rate when observed from earth) then it will show less time passing.

I don't actually know if this is a purely special relativisitc effect (which I think is the case) or if general relativity is involved.

The reason I wonder about that is because time is dilated in a gravitational field as well as by speed. And GR says that acceleration is exactly equivalent to a gravitational field. For this reason the clocks on the shuttle will be slowed by the accelerations. What I don't know is whether the numbers work out.

Remember that the shuttle would have to undergo very large accelerations or very long times accelerating to get to .5 (or more correctly .99c). That would definitely have a general relatavistic effect. Does anyone know if the numbers work out?


This message is a reply to:
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Replies to this message:
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jar
Member
Posts: 30984
From: Texas!!
Joined: 04-20-2004
Member Rating: 4.6


Message 64 of 114 (166700)
12-09-2004 8:17 PM
Reply to: Message 62 by Hangdawg13
12-09-2004 7:18 PM


Re: Question
Remember that the whole thing depends on your point of view. It is equally reasonable for the travelers to say that everyone on earth aged twice as fast as the travelers or for the people on earth to say that those on the spaceship aged only half as fast as those who stayed.

The standard is totally arbitrary and exists only withing a single POV.


Aslan is not a Tame Lion
This message is a reply to:
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The Dread Dormammu
Inactive Member


Message 65 of 114 (166715)
12-09-2004 8:51 PM
Reply to: Message 62 by Hangdawg13
12-09-2004 7:18 PM


It is confusing
Many times I've heard people explain how a space ship traveling at close to the speed of light for many years (ship time) and returning to the earth would find that many many more years had passed on earth. I had no problem with this, but how can this happen if both observers believe time is moving slower for the other one????

I've gone through a few drafts of this post and I think the best way to explain it is to use yet another story.

Ok so Zorg and Viola are drifting away from eachother and both of them see the other as moving slower through time. When Zorg says he has "had enough" and accelarates towards Violas ship.

When Zorg turns his ship around and acccelerates back TOWARDS Viola what does he see? Does he see time dialation? Yes he does but she seems to be moving through time FASTER than him.

As he approaches her ship on his return trip he sees her undergo BLUEshift, Her voice sounds HIGHpitched and squeaky on the radio (due to the same doppler effect etc. When he finaly pulls up to a stop next to her ship she is OLDER than him (slightly more rusted etc.).

The exact same thing happens in the classical twin paradox. The only difference is that instead of two ships, witch we tend to view as symetrical, they use something we tend to think of as relatively stationary (the earth) and something we think of as non-Stationary (the accelarating ship).


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Lammy
Member (Idle past 20 days)
Posts: 3607
From: Chicago
Joined: 03-29-2004


Message 66 of 114 (166718)
12-09-2004 8:56 PM
Reply to: Message 62 by Hangdawg13
12-09-2004 7:18 PM


Re: Question
I was writing out a lengthy explanation when I remembered reading a very good webpage on this a while back. I think this does a better job at explaining it than me.

http://www.phys.unsw.edu.au/~jw/twin.html


Hate world.

Revenge soon!


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Lammy
Member (Idle past 20 days)
Posts: 3607
From: Chicago
Joined: 03-29-2004


Message 67 of 114 (166719)
12-09-2004 8:57 PM
Reply to: Message 62 by Hangdawg13
12-09-2004 7:18 PM


Re: Question
I was writing out a lengthy explanation when I remembered reading a very good webpage on this a while back. I think this does a better job at explaining it than me.

http://www.phys.unsw.edu.au/~jw/twin.html


Hate world.

Revenge soon!


This message is a reply to:
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Replies to this message:
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The Dread Dormammu
Inactive Member


Message 68 of 114 (166749)
12-09-2004 9:48 PM
Reply to: Message 67 by Lammy
12-09-2004 8:57 PM


The animation realy explains it very well!
Yeah The animation shows very well how it works.

Added by edit: in praticular look at the seeming flurry of responces from Joe, in Janes perspective after she turns around.

This message has been edited by The Dread Dormammu, 12-09-2004 09:50 PM

This message has been edited by The Dread Dormammu, 12-09-2004 09:51 PM


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The Dread Dormammu
Inactive Member


Message 69 of 114 (166756)
12-09-2004 10:12 PM
Reply to: Message 61 by Raymon
12-08-2004 7:57 PM


Check this one out for length contraction
Here is the soulution to the "pole in the barn problem" from the site that Lam found.

http://www.phys.unsw.edu.au/~jw/pole.html


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Sylas
Member (Idle past 3425 days)
Posts: 766
From: Newcastle, Australia
Joined: 11-17-2002


Message 70 of 114 (166825)
12-10-2004 12:59 AM
Reply to: Message 63 by NosyNed
12-09-2004 8:06 PM


Re: Which ends up older?
NosyNed writes:

One minor; you'd have to travel at near .99c to have time slow down by half. It is not linear and it is not time moving at half speed if you do half light speed. Doesn't really matter to the overall question it is just a nit.

Strictly speaking, the factor for time dilation is sqrt(1-v2/c2). This means you can travel at about 0.87c, and time slows down by half.

That is when the shuttle returns (at some speed so that it's clock runs at half the rate when observed from earth) then it will show less time passing.

I don't actually know if this is a purely special relativisitc effect (which I think is the case) or if general relativity is involved.

You want numbers... we got numbers!

Both velocity and gravity effects contribute to time dilation of an astronaut, but by comparison with ground control the velocity effects dominate, because a shuttle orbit is not that much higher than the surface, by comparison with Earth's radius. Hence the shuttle astronauts age fractionally less than ground controllers, simply because they move faster.

But astronauts in a very high orbit will age fractionally more, since the relative velocity has little effect, and ground controllers are deep inside a gravitational well, so their clocks run more slowly.

The effect of gravity is sqrt(1-2GM/Rc2). M is mass of the Earth, and R is distance from the center. For a circular orbit, velocity is sqrt(GM/R). When you put it all together, the time dilation for a body in circular orbit is sqrt(1 - 3GM/Rc2).

For the ground controller, the effect of velocity can be ignored, and they experience only sqrt(1 - 2GM/Rc2). This means that the orbit clock matches the ground clock at an orbit with a radius of 3/2 times earth's radius; an altitude of 3200 km. Astronauts at that orbit experience no time dilation with respect to ground control; those above age more.

We can try some numbers here. G is 6.7e-11, M is 2e30, c is 3e8 and R is 6.4e6. (R being radius of the earth.)

We can approximate sqrt(1-x) by (1-x/2) for small x. Hence the factor sqrt(1-2GM/Rc2) is close enough to running slower by GM/Rc2 seconds every second. This is about 7e-10

Put another way, time dilation for a ground controller with respect to an observer way out in space is a bit more than two hundredths of a second every year. A shuttle astronaut, at an orbit of 200 km, is a bit more than three hundredths of a second per year younger with respect to the distant observer. Hence the shuttle astronauts age about one hundredth of a second less than the ground controller over a year, or about 200 micro seconds in a one week mission. This effect is measurable, and confirms the relativistic calculations.

Hi gang. I'm back... for a bit anyway.

Cheers -- Sylas


This message is a reply to:
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Replies to this message:
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NosyNed
Member
Posts: 8842
From: Canada
Joined: 04-04-2003


Message 71 of 114 (166830)
12-10-2004 1:09 AM
Reply to: Message 70 by Sylas
12-10-2004 12:59 AM


Re: Which ends up older?
Thank you.

sure beats remembering off the top of my head (and wrong).


This message is a reply to:
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Sylas
Member (Idle past 3425 days)
Posts: 766
From: Newcastle, Australia
Joined: 11-17-2002


Message 72 of 114 (166843)
12-10-2004 1:31 AM
Reply to: Message 71 by NosyNed
12-10-2004 1:09 AM


Re: Which ends up older?
Here are four individuals, given in order of age, from oldest to youngest. The first person on the list experiences the greatest elapsed time, and has the largest readings on her watch at the reunion party when they all get together again.


  • Oldest is the one riding on a geosychronous orbit, at about 36,000 km altitude.
  • Next oldest is the ground controller who is not in orbit at all; and also the astronaut orbtting at an altitude of 3,200 km. These two are the same age.
  • Youngest is the shuttle pilot, orbiting at 200 km altitude.

You age more slowly by moving faster, and also by being deeper down in a gravitational well. Both effects contribute to making your watch and also your body clock run more slowly, and as a result you end up being younger than those who moved more slowly or lived at higher altitudes.

Cheers -- Sylas (who always wanted to live in the mountains anyway)

PS. I had a special hello for you in my original post Ned! But it somehow got lost before I posted it. Nice to see you again!

This message has been edited by Sylas, 12-10-2004 01:35 AM


This message is a reply to:
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The Dread Dormammu
Inactive Member


Message 73 of 114 (166893)
12-10-2004 6:04 AM
Reply to: Message 72 by Sylas
12-10-2004 1:31 AM


What about 0 gravity at the bottom of the well?
What about someone in the center of a massive object (like the earth)? It's 0g so there should be no dialation right?

What about someone in the center of mass between two nutron stars orbiting eachother? (I think frame dragging might influence this one) the net is still 0g's or am I making a mistake somewhere?

This message has been edited by The Dread Dormammu, 12-10-2004 06:05 AM


This message is a reply to:
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Replies to this message:
 Message 74 by Sylas, posted 12-10-2004 7:09 AM The Dread Dormammu has responded
 Message 75 by RAZD, posted 12-10-2004 7:56 AM The Dread Dormammu has responded

  
Sylas
Member (Idle past 3425 days)
Posts: 766
From: Newcastle, Australia
Joined: 11-17-2002


Message 74 of 114 (166897)
12-10-2004 7:09 AM
Reply to: Message 73 by The Dread Dormammu
12-10-2004 6:04 AM


Re: What about 0 gravity at the bottom of the well?
The Dread Dormammu writes:

What about someone in the center of a massive object (like the earth)? It's 0g so there should be no dialation right?

What about someone in the center of mass between two nutron stars orbiting eachother? (I think frame dragging might influence this one) the net is still 0g's or am I making a mistake somewhere?

This is out of my league; I'm reduced to guessing.

Time dilation should always be measured as a difference between two observers; not as a comparison against an absolute. I am pretty sure that the center of the earth would have time synchronous with an observer at infinite distance from the earth. I have no idea about frame dragging, however.

Cheers -- Sylas


This message is a reply to:
 Message 73 by The Dread Dormammu, posted 12-10-2004 6:04 AM The Dread Dormammu has responded

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RAZD
Member
Posts: 19871
From: the other end of the sidewalk
Joined: 03-14-2004
Member Rating: 5.3


Message 75 of 114 (166904)
12-10-2004 7:56 AM
Reply to: Message 73 by The Dread Dormammu
12-10-2004 6:04 AM


Re: What about 0 gravity at the bottom of the well?
false.

there is zero net gravitational attraction in any one direction, but there is still massive gravity affecting the universe fabric.


we are limited in our ability to understand
by our ability to understand

RebelAAmerican.Zen[Deist
{{{Buddha walks off laughing with joy}}}


This message is a reply to:
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