The Barn Paradox and Climbing in Wales

Hi everyone sorry for the delay, I’ve been taking a tiny break. This month has been pretty hectic both in and outside of university.

The Mountaineering Society has been holding events and generally getting the ball rolling as far as training sessions are concerned. We have hosted 3 weekends away at the Peaks, Pembroke and Bowderstone (Lake District). So far I have only been to the Peaks! It was a pretty fun day, I was allocated a group of first years to teach and together we managed to accomplish 5 out of 6 routes! Pretty impressive since most were complete novices. The views were breath-taking and it was sunny all day. In the evening the society took over a local pub and we were each given huge portions of carvery, digesting the food with lots of party games. My particular favourite was a race to see who could build a 13-strong human pyramid. Since I am the smallest I got to go on top – being a hobbit has its advantages! Our bi-weekly training sessions have been fun so far and we are currently organising both internal and external bouldering competitions which are always a good laugh. I’m off to Snowdonia this weekend to do some sport climbing (which will probably be gibberish to those of you who haven’t climbed before). Hopefully it won’t be too rainy in Wales – I’m cheekily bringing some work just in case!

A picture I took on the Fresher’s Meet as I headed to the carvery

My course has stepped up in difficulty but it’s definitely getting more and more fascinating. As a masters student you are required to take 4 fourth year options in advance and these are proving conceptually harder than anything I have studied before. However the hardest course, and my favourite this term, has to be Further Relativity. The course acts as an introduction to general relativity and studies special relativity in greater depth than we did previously in our second year  ‘Relativity’ course.  I’ve decided to post a few of the common paradoxes covered by special relativity in my blogs since these are fun and highlight the strangeness of the universe. I would recommend the course to anyone who studies physics at the university since through its strange maths Further Relativity is proving to be challenging and mind-blowing in scale. It is courses like this that drove me to study Physics.

The Barn Paradox

Consider a 20m pole carried horizontally by a runner travelling at 0.866 times c (the speed of light). Those of you with knowledge of special relativity will know when an object travels at relativistic speed it’s length contracts. You may also know this contraction is by a factor 1/gamma, where gamma is related to the ratio between the velocity of the object and the speed of light. In this instance the gamma factor is 2 resulting in the pole contracting to a length of 10m.

The pole enters a 10m long barn with a concrete back wall. Due to this length contraction it can fit, however as it rapidly decelerates to a standing point it resumes it’s normal length, bursting the barn door open or breaking the pole.

This all seems fine, however some of you may have spotted a flaw in the logic. Not only is the pole travelling relative to the barn with a velocity of 0.866c, but from the pole’s point of view the barn is travelling towards it with a velocity of 0.866c. So surely the barn would also experience length contraction and ‘shrink’ to 5m?

It does. However if we consider things from  the view point of the pole we can explain why the pole cannot just fit in the barn but can do so with room to spare. As the pole enters the barn it hits the concrete wall 5m in. Since the concrete block cannot be broken, the barn keeps hurtling towards the back end of the pole even after the front end has hit it. Since the signal that the front end of the pole has been struck can only ever propagate at a maximum speed of c down the 20m of the pole, the front of the barn will reach the back of the pole before the signal does since it only has 15m to travel. This means the pole fits in with room to spare!

A beautiful diagram created by me on Paint to illustrate the situation

For those of you mathematically minded you may notice at a specific barn length the race between signal propagation and the front of the barn would be tied then below this length the signal would reach there first.

Relativity is filled with these paradoxes which make it bizarre but very interesting if you’re up for the challenge!

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Lilian

About Lilian

Lilian has now graduated from the University of Leicester and is no longer blogging for this site. Lilian was blogging as a fourth year MPhys student, explaining how Physics can be rocket science – but then it can be chemistry, nanotechnology, biology and astronomy too.

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