How Does Time Dilation Explain the Twin Paradox?

[aglo6509]

Hello,

I was talking with my Physics professor the other day about something I could do in Special Relativity, since I'm only in Physics III and haven't experienced much of it, yet find it very interesting. He mentioned that I could do stuff with the Twin Paradox. Now I know the basic idea of the paradox, but he mentioned showing the mathematics of it because I generally won't see that in an introductory physics course, and I could handle it given I haven't been exposed to higher level mathematics yet. I was thinking however instead of just looking up how its done to take some time and figure it out myself.

So if someone could please explain the question surrounding the paradox so I have some sort of a starting point. I'm asking here because I can't seem to find a good form on the question when I searched the internet and I hope to find some form of clarity asking here directly. I would only like to have the question posted so I can start there and work my way to the end.

And of course if I solve (or think I do) the paradox I'll post my writing here for you all to see

Thanks for reading my post and hope you can help me in anyway

Adam.

 

[raymo39]

Im guessing that Physics III is a pre undergraduate course?
i guess the most important part of the twin paradox in its elementary form, is that it is used to describe the effects of time dilation. which pretty much just means that different reference frames have different times elapsed when one is traveling at a speed, and one is not, and then you compare events according to each clock.
this might sound a bit weird, but ideally, nearly every problem (as in homework problems) or paradox can be cleared up by understanding how to transfer an event (which basically means something that happens at a point in space time with co-ordinates [x,y,z,t]) into a different reference frame (which generally uses the co-ordinates [x',y',z',t']) to describe the same event.
An interesting thing to do at your level (because the maths isn't too difficult, and the thinking is slightly more intuitive) would be to either show length contraction or time dilation occurring by transferring one or two events into a different reference frame, and seeing how that changes things.
if you wanted to take this further, once you have that level of understanding, you might be able to say why the article http://www.nature.com/nature/journal/v195/n4845/abs/195985a0.html
which is titled "the case against special relativity" by Dingle, is incorrect?
this would be more of a challenge question...

let me know what you think, because i can happily give you some guidance in where to look/ help you understand changes of frame

 

[aglo6509]

Hey thanks for responding.

I don't know if its a pre undergraduate course, in my school it's just a course in introducing ideas like SMH, waves (mechanical and EM), little Special Relativity and old quantum theory.

When talking with my professor I remember him saying that both twins sees the other aging at a different time, but only one can be right in their thinking. Does this have to do with time dilation in different frames because one is traveling near the speed of light and the other is stationary?

 

[raymo39]

basically what i meant with being pre undergraduate was that you arent out of high school yet?
and yes both the twins see each other as aging at different rates, but how can you define which one is correct?

 

[aglo6509]

Oh no, I'm a sophomore in college.

and my attempt would be something like making t=0 right when the one twin leaves plant x in a spaceship traveling near c.

then compare times somehow between them?

 

[raymo39]

yeah, the comparison between them is using what's called lorentz transformations. You would take the time elapsed since leaving, and then transform it from the "co-moving frame" to the stationary frame. the twin on the Earth can be thought of as being in the stationary frame, and the co-moving frame is a frame that travels along with the spaceship at some velocity V (which should be comparable to the speed of light, but you won't need to substitute a value for the velocity, because at your level you should be able to do this all algebraically)

 

[Dale]

You will definitely want to check out the FAQ on the Twin Paradox. It gives something like a half-dozen different ways to solve it:
http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

 

[HallsofIvy]

When talking with my professor I remember him saying that both twins sees the other aging at a different time, but only one can be right in their thinking. Does this have to do with time dilation in different frames because one is traveling near the speed of light and the other is stationary?

The first part of that is incorrect. While one twin is moving away from the other at constant velocity[/itex] each sees the othe ranging more slowly and both are "right in their thinking". It is what happens when one twin changes speed in order to turn around an come back to the other that "breaks the symmetry". You are correct in saying that it is due to time dilation.

 

[Mordred]

Perhaps a full write up on twin paradox will help excluding the solution.

" Suppose one of a pair of 20 year old twins tkaes off in a spaceshp traveling at very high speed to a distant star and back again, while the other twin remains on Earth. According to the Earth Twin the traveling twin will age less. Whereas 20 years may pass for the Earth twin, perhaps only one year (dependng on the crafts speed) would pass for the traveling twin. Thus when the traveler returns, the Earthbound twin could expect to be 40 years old whereas his twin would be only 21.

This is the essentail part of the paradox.

This is the viewpoint of the twin on the Earth. But what about the traveling twin? If all inertial reference frames equally valid, won't the traveling twin make all the claims the Earth twin makes? only in reverse? Can't the traveling twin claim that since the Earth is moving away at high speed, time passes more slowly on Earth and the twin on the Earth will age less? This is opposite of that the other twin predicts. They cannot both be right, for after all the spacecraft returns to Earth and a direct comparision of ages and clocks can be made. "

What your professor is asking you to do is mathematicaly decide which twin is correct.
a key to this lies within how the spaceship reaches its traveling speed. To say more would give away the answer spoiling the question so I will stop there.

 

[jtbell]

I can't seem to find a good form on the question when I searched the internet and I hope to find some form of clarity asking here directly.

Tip: you can make Google restrict its search to a particular site, e.g. physicsforums.com:

http://www.google.com/#sclient=psy&hl=en&source=hp&q="twin paradox" site:physicsforums.com

(look at the search box at the top of this search results page to see how to do it)

People have discussed the twin paradox many times here on PF. If you hunt through these threads, you'll find some nice worked-out examples and diagrams.

 

[aglo6509]

Perhaps a full write up on twin paradox will help excluding the solution.

" Suppose one of a pair of 20 year old twins tkaes off in a spaceshp traveling at very high speed to a distant star and back again, while the other twin remains on Earth. According to the Earth Twin the traveling twin will age less. Whereas 20 years may pass for the Earth twin, perhaps only one year (dependng on the crafts speed) would pass for the traveling twin. Thus when the traveler returns, the Earthbound twin could expect to be 40 years old whereas his twin would be only 21.

This is the essentail part of the paradox.

This is the viewpoint of the twin on the Earth. But what about the traveling twin? If all inertial reference frames equally valid, won't the traveling twin make all the claims the Earth twin makes? only in reverse? Can't the traveling twin claim that since the Earth is moving away at high speed, time passes more slowly on Earth and the twin on the Earth will age less? This is opposite of that the other twin predicts. They cannot both be right, for after all the spacecraft returns to Earth and a direct comparision of ages and clocks can be made. "

What your professor is asking you to do is mathematicaly decide which twin is correct.
a key to this lies within how the spaceship reaches its traveling speed. To say more would give away the answer spoiling the question so I will stop there.

Thank you for the question. Would I need time dilation formulas or can I work it out with geometry or something along those lines?

 

[Mordred]

Time dilation formulas would show the problem a hint is deciding who's viewpoint is more consistent during the entirety of the trip.