Question for the maths able..

[dellzeqq]

if a bicycle and a car were to travel toward each other, each moving at over half the speed of light, what would be the point of the cyclist wearing hi-viz?

Or a helmet.

(Sounds of mods approaching stage left)

OK. Skip the helmet thing.

 

[compo]

Thank you for the explanations.........!
I am not much wiser. So is there just one answer or does it depend on many variables. I like answers that depend on many factors. It makes it harder for the questioner to tie one down to an answer or to say "wrong".

 

[thom]

if 2 cars travel in opposite directions at .6 the speed of light, are thay traveling at 1.2 the speed of light from each other?

No, speed is not additive, noticably so at relativistic velocities.
I do not understand enough of the detail but time is a bit like being in a queue: when you're in a hurry, it slows down.
Once you start to grapple with that notion, I think you have the idea that the relative speed of 2 bodies depends on your own motion relative to them.
Special Relativity should provide enough theory to sustain you over the Christmas period.

 

[Wobblers]

It depends on your frame of reference (hence the name "Relativity"). It is a fundamental postulate of Special Relativity that nothing can move faster than the speed of light. An observer who is stationary relative to both cars will see both as moving at 0.6c in opposite directions. If you're in one of the cars you'll find that the other car is moving away from you at a speed of less than 1.2c - it will be about 0.9c (I can't be bothered to work it out exactly - you can use the Lorentz Transformation to do so if you want!). So, yes, what you see depends just where you are in relation to what you are observing.

 

[thom]

If they were on opposite facing treadmills, and had wings...

Then it depends on the speed of the mirror on the wall.

 

[Wobblers]

if a bicycle and a car were to travel toward each other, each moving at over half the speed of light, what would be the point of the cyclist wearing hi-viz?

Or a helmet.

(Sounds of mods approaching stage left)

OK. Skip the helmet thing.

Then it's probably not worthwhile pointing out that the kinetic energy of the helmet alone exceeds that of a large strategic nuclear weapon....

 

[marinyork]

Thank you for the explanations.........!
So is there just one answer or does it depend on many variables. I like answers that depend on many factors. It makes it harder for the questioner to tie one down to an answer or to say "wrong".

It does get more complicated actually. When discussing these types of questions we are are just talking about a 'boost' in one direction and assume this is the x direction. There are other boosts and rotations. These form a group called the Lorentz Group which is a sub group of the Poincaré group (a Lie Group infact) which physicists talk about a lot. So you have all kinds of symmetries - the rotations and boosts in the Lorentz Group and a whole load of other stuff. But most of this stuff is extended reading or higher modules on a undergraduate course in Physics or Maths or a refresher or beefed out on a postgrad course or just for yourself to read. Not that there is anything particularly exclusive about it it is in any half decent textbook on relativity and these days as someone else said a fair bit of it is on wikipedia (certainly the main ideas - history, lorentz transformations, rapidity, symmetry, minkowski space and so on).

The basic idea though, the x boost is fairly elementary and can be understood by anyone.

 

[Archie_tect]

In more technical language than you may care for in 'Newtonian Mechanics' the frames of references have Galilean Transformations. This means you can add up the 'relative motions' to be whatever you want.

Special Relativity uses something called Lorentz transformations (which was actually around before SR as we know it today, it's just that it was a slight puzzle) where the speed of light cannot be exceeded. Consequences are that a reference frame for different observers may be completely different.

The confusion really arises because the Newtonian is an approximation to SR for low speeds.

The term that mucks it up is called the Lorentz factor. The terms for the two do look not totally dissimilar for the two types of transformations (there are many variants). Instead of x' = x -vt you end up with a γ term in front x' = γ(x-vt) and for time things are a bit more complicated, but not much. The idea being that between the two objects under Galilean transformations the distance/displacement will be different by vt i.e. speed x time = a distance if you're wondering where it comes from. In other words what you'd 'expect'.

And the reasoning for mentioning the names is that you may find it instructive to look them up and find out more.

He means he dosen't know Compo...

 

[marinyork]

He means he dosen't know Compo...

I have several semi-serious textbooks on relativity on my bookshelf. Still doesn't mean I know what the smeg I'm talking about and it has been about 3-4 years since I seriously studied the stuff. Just utterly hopeless at explaining a load of stuff. It wasn't a first interest either, a sharp mind would be able to guess what was.

 

[marinyork]

But I would say that if people wanted to that I would recommend Penrose, Greene and Feynman (e.g. Six-not-so-easy-pieces) in general for popular science books in this area and related ones - available at all good libraries (if we have any left). I suppose people say to that well I wouldn't enjoy it, but I would say that they probably would even if they find it hard going and it might go in a bit more than reading a few bits on the internet. Just might take you a while that's all.

 

[Archie_tect]

I'd give it a go Marin, but the conceptual theoretical stuff hurts my brain... that people can discuss and develop these ideas, and understand them, melts my synapses.

 

[biggs682]

if 2 cars travel in opposite directions at .6 the speed of light, are thay traveling at 1.2 the speed of light from each other?

no still going at same speed

 

[marinyork]

I'd give it a go Marin, but the conceptual theoretical stuff hurts my brain... that people can discuss and develop these ideas, and understand them, melts my synapses.

Try Feynman Six-Easy-Pieces and Six-not-so-easy-pieces. They even used to be available in libraries . You're an architect and an intelligent bloke. Feynman was one of the best widely known communicators in science in the 20th century. They aren't even long popular science books.

 

[slowmotion]

Dunno....but both drivers should get 16 points on their licenses. Can you get 16 points on your licence? Over to you marinyork.

 

[srw]

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I usually take "I was just drinking coffee - you owe me a new computer screen" as a bit of flimflam. Perhaps I should revise my estimation.

Feynmann is a good recommendation. I think it was James Gleick's book on the man - Genius - which draws heavily on Feynmann's own work - that convinced me that I could understand theoretical physics. I can't remember much of it, and unlike MY have never studied it.

I wouldn't be so sanguine as MY that anyone could understand it. Like a lot of maths, it's easy, or at least comprehensible, if you've got the sort of brain that does abstraction, pattern recognition and logical reasoning as a matter of routine. But there are plenty of people who don't. Compo's OP suggests that he does - to recognise the question as one that's worth asking is a sign of being able to recognise when well-known patterns fail, and to recognise that that gives rise to interesting questions.