Unit 4 and 4 Detailed Study Options

[Kiro Kompiro]

I looked at the twin paradox video. Conceptually i get stuck on this point:  If the rocket moves at a velocity of say 0.8c as seen from the twin on earth, then the twin on Earth sees the time on the rocket go slower.  BUT from the frame of reference of the rocket,  the earth is moving away at 0.8c.  Why doesn't the twin in the rocket see the time on earth run slower?

[Lasercookie]

I looked at the twin paradox video. Conceptually i get stuck on this point:  If the rocket moves at a velocity of say 0.8c as seen from the twin on earth, then the twin on Earth sees the time on the rocket go slower.  BUT from the frame of reference of the rocket,  the earth is moving away at 0.8c.  Why doesn't the twin in the rocket see the time on earth run slower?

That's time dilation.
If I remember correctly, the twin on the rocket does see time on the Earth run slower.

I just watched through the video then and I don't believe it suggested anything of the kind? 
It did mention that you could say that the Earth is moving away as seen by the twin in the rocket and then went on to say that only the rocket physically experienced acceleration. It would just appear to the twin on the rocket that Earth is moving at 0.8c (and therefore sees time running slower). So if you calculated this, the paradox is that who would actually end up being the older twin.

The paradox is resolved because the twin in the rocket would have to decelerate/accelerate non-uniformly to turn around (therefore no longer being an inertial reference frame) and not adhering to special relatvity. Non-inertial frames are covered by general relativity I believe.

This is a good resource for SR that I used extensively.
http://www.phys.unsw.edu.au/einsteinlight/
Specifically about time dilation (and the twin paradox) there is:
http://www.phys.unsw.edu.au/einsteinlight/jw/module4_twin_paradox.htm

[Kiro Kompiro]

OK having read your post and the link to unsw, the twin on the rocket is younger when he comes back to earth because of the change in direction that occurs to begin the return trip(=change in velocity=acceleration=non-inertial frame).  Thats the way I read it anyway.

So what if the rocket goes on a one-way trip at 0.8c to a base located 4 light years away. He flies past the base without slowing. 

As measured on earth, can we simply use velocity=distance/time to calculate at the instant the rocket flies past the base? ie On Earth do 4c/0.8c=5 years elapse until the rocket ship gets to the base?.

How many years will a clock on the rocket read at as the rocket flies past the base? Is it =5*sqr(1-0.8c^2/c^2)=5*0.67=3 years?

[pi]

Don't drop relativity, its the closest thing to physics in the VCE course

[Lasercookie]

Before I start, I have to say good work - it looks like you've been able to get your head around relativity pretty well.

you can use v=x/t, x=vt, t=x/v for when you're trying to solve for proper velocity, time, displacement etc.

This is where it gets a bit confusing, trying to figure out which frames are proper or not.
So if you're taking Earth to be the proper reference frame, then yes 4c/0.8c = 5 years.

What happens next depends on who is observing.
A clock on the rocket - observed by the person inside the rocket - will not observe the effects of relativity. To him/her, time will flow as normal. This is stated in one of the postulates (first one I think) - "The laws of physics are the same in any inertial frame, regardless of position or velocity".

However, if the person on the Earth (outside the reference frame) was to look at the clock on the rocket - they will observe the effects of relativity.
(I just like to write everything out to get my head around the problem)
So

(can't be bothered typing up the calculations - but you ended up getting 0.67?) - Also have to point you shouldn't ever use rounded off answers mid-answer. Only round off/apply sig figs for the final answer.
So

I haven't done any relativity problems since the exam and I've already started to get a bit rusty on my SR knowledge . I may have made some errors somewhere, but I'm pretty sure what I've said is correct.

[Kiro Kompiro]

Before I start, I have to say good work - it looks like you've been able to get your head around relativity pretty well.

you can use v=x/t, x=vt, t=x/v for when you're trying to solve for proper velocity, time, displacement etc.

This is where it gets a bit confusing, trying to figure out which frames are proper or not.

Yes this where I think I lose my train of thought.  Is there a simplified definition (or method to follow to work out ) of proper time and proper length

So if you're taking Earth to be the proper reference frame, then yes 4c/0.8c = 5 years.

What happens next depends on who is observing.
A clock on the rocket - observed by the person inside the rocket - will not observe the effects of relativity. To him/her, time will flow as normal. This is stated in one of the postulates (first one I think) - "The laws of physics are the same in any inertial frame, regardless of position or velocity".

So- according to the person in the rocket- looking at the clock in the rocket,  the trip takes 5 years as well?

However, if the person on the Earth (outside the reference frame) was to look at the clock on the rocket - they will observe the effects of relativity.
(I just like to write everything out to get my head around the problem)
So

(can't be bothered typing up the calculations - but you ended up getting 0.67?) -

sorry my bad gamma should have been 1.67 instead of 0.67

 Also have to point you shouldn't ever use rounded off answers mid-answer. Only round off/apply sig figs for the final answer.

So

So this is the time that elapses on clock on the rocket as seen by someone on earth looking into the rocket?

[Lasercookie]

Yes this where I think I lose my train of thought.  Is there a simplified definition (or method to follow to work out ) of proper time and proper length

This is really a skill you'll pick up by practicing questions. Sometimes questions will explicitly state the proper reference frame, sometimes it'll be implied. It's really tricky at first - as it depends on the wording of the question.
"So what if the rocket goes on a one-way trip at 0.8c to a base located 4 light years away. He flies past the base without slowing."
I took 4 light years to be the proper length. It would have said something about the length being contracted or something if they meant relativistic length.

If you then derived the proper time using the point of view of Earth (using t=x/v), that means that 5 years is the proper time.

You could have taken it from the point of view of the rocket though. So he's travelling a distance of 4 ly at 0.8c



To find out the dilated time that

blah blah blah and you get the same answer.

If you knew the dilated time, you could figure out t_0 that way etc.

Have a go at the relativity section of VCAA 2009.
http://www.vcaa.vic.edu.au/vcaa/vce/studies/physics/pastexams/2009/2009physics1-w.pdf
You can definitely do Q1-Q6. Skip Q7 and Q8 (they are about energy-mass equivalence, you might know Q8 though),
Q9 and Q10 are about time dilation/length contraction again, Q11 - maybe (it's about work/masses again) and then Q12 and 13 definitely.

So basically every question except for Q7, Q8, Q11 I reckon you would be able to do. Most of them involve differentiating between proper and relativistic values as well. Hopefully that will give you a better idea. There's no tricky questions there though.

http://www.tsfx.com.au/vic/vcedgeonline/trialexampapers/index.htm
If you want another simple relativity section (slightly trickier worded questions from memory), I'm pretty sure you should be pretty good with TSFX 2010.  Again skip the simultaneity, mass-equivalence, kinetic energy questions (unless you've learnt about them already). TSFX exams are available freely on their website, you have to register for free though (bugmenot.com should have some working usernames/passwords if you can't be bothered registering).

http://engageeducation.org.au/practice-exams/physics/74-unit-3-physics-practice-exam
The engage education one also had some pretty easy questions (the last couple were about masses/kinetic energy though). That one is also free off their site - don't need to register.

I had these simple rules on my cheatsheet:
- Relativistic time is slower than proper time. (time slows down)
- Relativistic length is shorter than proper length (lengths contract)
- Relativistic mass is heavier than proper mass (masses get heavier)

So- according to the person in the rocket- looking at the clock in the rocket,  the trip takes 5 years as well?

Yep, people travelling at relativistic speeds will observe everything in their reference frame to be behaving normally.

So this is the time that elapses on clock on the rocket as seen by someone on earth looking into the rocket?

Yes, they see the rocket moving slower.

[Kiro Kompiro]

You are a legend laser!  Many thanks!

[Lasercookie]

You are a legend laser!  Many thanks!

Thanks

So I hope you've decided to stick with relativity and synchrotron. If you can learn all that by yourself, you should be perfectly fine understanding relativity when the teacher explains it.

[Shark 774]

... I would only recommend relativity if you are a keen physics student ...

I disagree, most of my class are not what you would call 'keen' physics students yet they grasped relativity quite well.

It might have been more difficult for you, since you did it by yourself, but doing it with the rest of the class and the teacher
explaining makes relativity a breeze. Self-studying any physics (or any science or maths for that matter) would require a keen
student.

Ah ok fair point. I just got the impression, from some kids I spoke to who had to do it, that they found it very strange and weren't keen physics students, hence couldn't be bothered to put in the extra effort required to fully understand it and just learned how to apply the formulas, thus making it very dull and easy to get tricked on.