Minkowski diagram, where to put an event

In summary, the conversation discusses the correct way to draw a Minkowski diagram and determine if an event is inside the cone of light. It also mentions a problem involving two cars, A and B, where B sends a light signal to A but it is unclear if the signal will reach A. The conversation concludes that the event is not inside the cone of light and therefore the signal will not reach A. No information is given about the speed of car A.
  • #1
Redwaves
134
7
Homework Statement
At t=0 A is moving
At t = -1/3 ms B is at 300km north and send a light beam
Draw the Minkowski diagram then tell if the light beam will reach A
Relevant Equations
##-\frac{1}{3} ms = -\frac{10^{-3}}{3}s##
##300km = 3\cdot10^5 m##
##ct = -\frac{10^{-3}}{3}s \cdot c##
I drew the Minkowski diagram, but I'm not sure if this is correct.
From what I drew the angle between x and ct ##\approx 0##
then the event is "inside" the light ray and will eventually reach A.
AvEzfoO.png
 
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  • #2
Is there any relative velocity between A and B, and if so, how much?
 
  • #3
Chestermiller said:
Is there any relative velocity between A and B, and if so, how much?
No, that's all I have
 
  • #4
Redwaves said:
No, that's all I have
Well, it seems like there is something missing from the problem statement. What is the exact wording?
 
  • #5
Chestermiller said:
Well, it seems like there is something missing from the problem statement. What is the exact wording?
The statement is in french, here is the google translate.

A and B are two cars At t = 0, car A starts to move forward. B sent a light signal to try
to warn him: B is 300 km to the North and sends his signal at t = - (1/3) ms;

I have to draw the world line of that light signal
I'm wondering if I should have draw the cone of light instead of the diagram above?

Thus, since opposite/adjacent < 1, the event in inside the cone of light and if the event in inside the cone of light, the light signal will eventually reach A. Is it correct?

Edit: Since ##ct = 300000000 \cdot -\frac{10^{-3}}{3} = 100000m##
And ##100000/300000 < 1## this is not inside the cone of light, so it will not reach A.
 
Last edited:
  • #6
Redwaves said:
The statement is in french, here is the google translate.

A and B are two cars At t = 0, car A starts to move forward. B sent a light signal to try
to warn him: B is 300 km to the North and sends his signal at t = - (1/3) ms;

I have to draw the world line of that light signal
I'm wondering if I should have draw the cone of light instead of the diagram above?

Thus, since opposite/adjacent < 1, the event in inside the cone of light and if the event in inside the cone of light, the light signal will eventually reach A. Is it correct?

Edit: Since ##ct = 300000000 \cdot -\frac{10^{-3}}{3} = 100000m##
And ##100000/300000 < 1## this is not inside the cone of light, so it will not reach A.
Any information on the speed with which car A starts to move forward?
 
  • #7
Chestermiller said:
Any information on the speed with which car A starts to move forward?
That's all I have.
 

FAQ: Minkowski diagram, where to put an event

What is a Minkowski diagram?

A Minkowski diagram is a graphical representation of the relationship between space and time in special relativity. It was developed by the mathematician Hermann Minkowski in 1908.

How do you read a Minkowski diagram?

In a Minkowski diagram, the horizontal axis represents space and the vertical axis represents time. The diagonal line at a 45-degree angle is the "light cone," which represents the maximum speed at which information can travel. Points on the diagram represent events in space and time.

Where do you place an event on a Minkowski diagram?

An event can be placed anywhere on a Minkowski diagram, as long as it falls within the boundaries of the light cone. The location of the event on the diagram will determine its coordinates in space and time.

What is the significance of the light cone on a Minkowski diagram?

The light cone represents the maximum speed at which information can travel, which is the speed of light. Events that fall within the light cone can be causally connected, meaning that one event can influence the other. Events outside of the light cone cannot be causally connected.

Can a Minkowski diagram be used to represent events in both space and time?

Yes, a Minkowski diagram can be used to represent events in both space and time. It is a useful tool for understanding the relationship between space and time in special relativity, and for visualizing how events can be affected by the speed of light.

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