Minkowski space-time diagrams Watch

langlitz
Badges: 17
Rep:
?
#1
Report Thread starter 4 years ago
#1
Struggling to understand what the hell is going on with these diagrams and how to draw them. Would anyone be able to work through this problem to show me what it's all about?

Cheers

Attached files
0
reply
WishingChaff
Badges: 2
Rep:
?
#2
Report 4 years ago
#2
So, a Minkowski diagram is similar to a cartesian diagram for space. However, in the cartesian diagram we represent points as positions in space, whilst in the Minkowski diagram points represent events in spacetime. i.e. A point in Minkowski space is something like my alarm clock setting off in my bedroom.

In this case we usually represent the y-axis as the time axis and the x-axis as the space axis (to make dimensions agree we usually plot the points ct on the time axis, where c is the speed of light. However, this convention is usually dropped and c is set equal to 1)

Given this, the point (-4,3) on the Minkowski diagram is going to be simply the event at 4 below the origin and 3 along the positive space axis.

To deduce whether to events are causally connected on a Minkowski diagram you must deduce if the two points are time-like/light-like separated. Geometrically this corresponds to the following. Draw a line between your two events on the Minkowski diagram. If the angle between this line and the space axis(horizontal axis) is greater than or equal to 45 degrees then the two events are casually connected.

Hopefully this helps.

(Original post by langlitz)
Struggling to understand what the hell is going on with these diagrams and how to draw them. Would anyone be able to work through this problem to show me what it's all about?

Cheers

0
reply
langlitz
Badges: 17
Rep:
?
#3
Report Thread starter 4 years ago
#3
(Original post by WishingChaff)
So, a Minkowski diagram is similar to a cartesian diagram for space. However, in the cartesian diagram we represent points as positions in space, whilst in the Minkowski diagram points represent events in spacetime. i.e. A point in Minkowski space is something like my alarm clock setting off in my bedroom.

In this case we usually represent the y-axis as the time axis and the x-axis as the space axis (to make dimensions agree we usually plot the points ct on the time axis, where c is the speed of light. However, this convention is usually dropped and c is set equal to 1)

Given this, the point (-4,3) on the Minkowski diagram is going to be simply the event at 4 below the origin and 3 along the positive space axis.

To deduce whether to events are causally connected on a Minkowski diagram you must deduce if the two points are time-like/light-like separated. Geometrically this corresponds to the following. Draw a line between your two events on the Minkowski diagram. If the angle between this line and the space axis(horizontal axis) is greater than or equal to 45 degrees then the two events are casually connected.

Hopefully this helps.
Ok thanks so does the fact that the particle is moving at v=c/2 affect anything? And when you say the angle does that mean the angle between it and the x-axis? Like this..
Attached files
0
reply
WishingChaff
Badges: 2
Rep:
?
#4
Report 4 years ago
#4
That looks pretty good to me. I forgot about the v=c/2. So you appear to have drawn that correctly on the diagram and that has no bearing on the casually connected part.

The point about casually connected/disconnected is to say that can the two events influence each other. You can derive the result about the angle being at 45 degrees using the space-time interval formula. We normally say the following:

If  ds^2 < 0 : The events are time-like separated.
 ds^2 = 0 : The events are light-like separated.
 ds^2 > 0 : The events are space-like separated.

(As an aside, this is the convention using the (-,+,+,+) Minkowski metric)

(Also, looking at your diagram you may want to explicitly calculate the angle)

Hope this helps.

(Original post by langlitz)
Ok thanks so does the fact that the particle is moving at v=c/2 affect anything? And when you say the angle does that mean the angle between it and the x-axis? Like this..
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • Cranfield University
    Cranfield Forensic MSc Programme Open Day Postgraduate
    Thu, 25 Apr '19
  • University of the Arts London
    Open day: MA Footwear and MA Fashion Artefact Postgraduate
    Thu, 25 Apr '19
  • Cardiff Metropolitan University
    Undergraduate Open Day - Llandaff Campus Undergraduate
    Sat, 27 Apr '19

Have you registered to vote?

Yes! (368)
37.28%
No - but I will (74)
7.5%
No - I don't want to (69)
6.99%
No - I can't vote (<18, not in UK, etc) (476)
48.23%

Watched Threads

View All