Minkowski metric question
The Minkowski metric is a tensor defined as which arises in the definition of the Lorentz transformation.
I've not covered this yet but if we flip the overall sign of the metric, can you still apply the Lorentz transformation? Or does it no longer work?
I'm probably jumping ahead but does this coordinate system work in curved space as well?
Thanks.
I've not covered this yet but if we flip the overall sign of the metric, can you still apply the Lorentz transformation? Or does it no longer work?
I'm probably jumping ahead but does this coordinate system work in curved space as well?
Thanks.
(edited 7 years ago)
Also looking at this spacetime diagram,
why does light always travel at a 45 degree angle? An objects worldline with velocity 0 would be vertical and as an objects speed increases, it's angle on the diagram should get closer to 90 degrees, so why is light 45 degrees instead of 90?
why does light always travel at a 45 degree angle? An objects worldline with velocity 0 would be vertical and as an objects speed increases, it's angle on the diagram should get closer to 90 degrees, so why is light 45 degrees instead of 90?
Were you not asking for stuff to be explained in Layman's terms before? This is very advanced stuff.
As an object's speed increases, it's space-time co-ordinate axes are essentially transformed. You see those blue lines on the image? As velocity increases, the black co-ordinate axes move together, towards the central point, in the same way that those blue lines are, and if the speed hits the speed of light the axes meet at the 45 degree line (hence all the quirky things happening at light speed - space and time essentially unite).
That's why light speed is at that angle. The space and time axes are transformed as a natural result of time dilation and length contraction.
It's hard to explain this stuff in layman's terms. As with most of physics, it's basically a mathematical way of describing the way the world is. Using co-ordinate transforms is a necessary and obvious tool when trying to describe something like this.
This image may help - as speed increases, the red axes become more and more squished. It's not that light is 'at 45 degrees', it's that light is the point where the two axes are unified.
Original post by AishaGirl
Also looking at this spacetime diagram,
why does light always travel at a 45 degree angle? An objects worldline with velocity 0 would be vertical and as an objects speed increases, it's angle on the diagram should get closer to 90 degrees, so why is light 45 degrees instead of 90?
why does light always travel at a 45 degree angle? An objects worldline with velocity 0 would be vertical and as an objects speed increases, it's angle on the diagram should get closer to 90 degrees, so why is light 45 degrees instead of 90?
As an object's speed increases, it's space-time co-ordinate axes are essentially transformed. You see those blue lines on the image? As velocity increases, the black co-ordinate axes move together, towards the central point, in the same way that those blue lines are, and if the speed hits the speed of light the axes meet at the 45 degree line (hence all the quirky things happening at light speed - space and time essentially unite).
That's why light speed is at that angle. The space and time axes are transformed as a natural result of time dilation and length contraction.
It's hard to explain this stuff in layman's terms. As with most of physics, it's basically a mathematical way of describing the way the world is. Using co-ordinate transforms is a necessary and obvious tool when trying to describe something like this.
This image may help - as speed increases, the red axes become more and more squished. It's not that light is 'at 45 degrees', it's that light is the point where the two axes are unified.
(edited 7 years ago)
@Pessimisterious ah ok thank you.
Would you mind explaining the Minkowski metric question I had? If it's too advanced then I'll just leave it for now.
Would you mind explaining the Minkowski metric question I had? If it's too advanced then I'll just leave it for now.
Original post by AishaGirl
@Pessimisterious ah ok thank you.
Would you mind explaining the Minkowski metric question I had? If it's too advanced then I'll just leave it for now.
Would you mind explaining the Minkowski metric question I had? If it's too advanced then I'll just leave it for now.
Yes it can be negative.
The main point of the metric is that it's invariant in all reference frames. This is one of the most important things in relativity - any complete equations need to work no matter who the observer is.
This is directly from my lecture notes:
Original post by Pessimisterious
Yes it can be negative.
The main point of the metric is that it's invariant in all reference frames. This is one of the most important things in relativity - any complete equations need to work no matter who the observer is.
This is directly from my lecture notes:
The main point of the metric is that it's invariant in all reference frames. This is one of the most important things in relativity - any complete equations need to work no matter who the observer is.
This is directly from my lecture notes:
Exactly the sort of answer I was looking for. Thanks.
Quick Reply
Related discussions
- very hard chemistry gcse question
- MSc real estate offers from Henley, Cass(Bayes) and Manchester
- University rankings don’t apply to undergraduate so how to decide
- assessment centre test
- Economics with Econometrics
- science major creative job
- Winchester or Aberystwyth
- Durham university went downhill
- is UCAS website down for maintenance this weekend ?
- Uni of Loughboroug
- Resitting GCSE maths
- St Andrews or LSE??
- Application
- WARWICK
- How many lines of code is your A2 Computing project?
- Sheffield University for History
- I got an A* in maths AMA
- Selection of university for msc marketing
- Do I need a MAT/PAT/STEP score to apply for EEE?
- Cambridge with no scholarship Vs University of St Andrews with full scholarship
