Plot a photon on a space-time diagram

[pepediaz]

Homework Statement

If a spaceship travelling at 0.866c throws a photon towards the Earth, plot the space-time diagram of the photon, in Earth frame and in photon's frame.

Relevant Equations

none

I think that if we plot an inertial frame in the XY axis separated 90º, the photon, which has a velocity of c, should be put on one of the branches of the light cone. The questions are:

Which branch, left or right one?
Which position along the branch, if I don't know the distance it has travelled?
The time in the inertial frame is greater than the time on the photon's reference system? (I suppose so)

Thanks

 

[BvU]

plot an inertial frame in the XY axis

I have difficulty understanding what you say here ? Usually, only one space coordinate is plotted, on the horizontal axis. The vertical axis is for $ct$. Thus you get a space-time diagram - or a Minkowski diagram

on the photon's reference system

Does not exist

 

[pepediaz]

Yes, I meant Minkowski diagram, I have said XY so convinced.

But we should plot the photon on an inertial frame, and also on the reference system on which the photon is at rest, isn't it? Or else, is it possible to plot a photon on Minkowski diagram?

 

[kuruman]

The time in the inertial frame is greater than the time on the photon's reference system? (I suppose so)

The photon's reference frame? Is that the frame in which the photon is, ahem, at rest?

 

[pepediaz]

Yes

 

[kuruman]

I rest my case.

 

[pepediaz]

Okay, there is some mistake there.
But I wanted to differentiate the inertial frame of the Earth (receiving a photon) and the frame which has proper time.

 

[kuruman]

Okay, there is some mistake there.
But I wanted to differentiate the inertial frame of the Earth (receiving a photon) and the frame which has proper time.

If you compare the frequency of the photon received on Earth with the frequency at the source, you will know the relative velocity of source and Earth. The time as measured on the source frame would be the proper time. Does that make sense?

 

[pepediaz]

that's what I don't grasp. Photons travel at constant speed c, and the spaceship travels at 0.866c, so the photon should have its ct and x-axis at a slope of arctg(0.866) each, or it is placed on the light cone in Minkowski diagram?

 

[kuruman]

that's what I don't grasp. Photons travel at constant speed c, and the spaceship travels at 0.866c, so the photon should have its ct and x-axis at a slope of arctg(0.866) each, or it is placed on the light cone in Minkowski diagram?

No. For a photon $ct=x$ and that's a straight line at 45^o on a ct cs. x diagram. The spaceship line would be between the ct axis and the x-axis at whatever angle is appropriate.

 

[BvU]

that's what I don't grasp. Photons travel at constant speed c, and the spaceship travels at 0.866c, so the photon should have its ct and x-axis at a slope of arctg(0.866) each, or it is placed on the light cone in Minkowski diagram?

What spaceship ? Are you feeding us your complete exercise problem statement in small bits ?

Read on in the link I gave, especially this part

 

[pepediaz]

No. For a photon $ct=x$ and that's a straight line at 45^o on a ct cs. x diagram. The spaceship line would be between the ct axis and the x-axis at whatever angle is appropriate.

Nice, so for plotting a photon whose displacement I don't know, it's just a random point on the straight line at 45o on a ct cs. x diagram, isn't it?

 

[pepediaz]

What spaceship ? Are you feeding us your complete exercise problem statement in small bits ?

Read on in the link I gave, especially this part

It wasn't my intention, the full statement is really long, with details which aren't related with this small problem. I haven't included the info about the spaceship, because I thought it is unnecessary for the photon motion, anyway I'll improve the statement, if I don't know how to solve it, I'm the last person to skip details.

 

[kuruman]

Nice, so for plotting a photon whose displacement I don't know, it's just a random point on the straight line at 45o on a ct cs. x diagram, isn't it?

I don't like the use of "random" here. Say you draw a line parallel to the x-axis at some finite time t. This will intersect the spaceship line and the photon line. The x-coordinates of the intersection points denote the position of the spaceship and the position of a photon that was emitted by the blastoff gases (more or less.)

 

[pepediaz]

I get you, so, if we don't know the displacement of the photon (atmosphere thickness + some distance up to the spaceship when it was at the shortest distance to the Earth), we just can obtain a relationship between ct and ct' and another one for x and x', isn't it?