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## Physics library

### Course: Physics library>Unit 16

Lesson 2: Minkowski spacetime

# Visualizing multiple Newtonian path–time diagrams

Now that we know what path–time diagrams are, let's see what happens when we bring along a friend!

## Want to join the conversation?

• I don't understand why Sal labeled the line t', the friends frame of reference, at ? If this is the friend's time axis, it would mean t' is longer (it's the hypotenuse of the triangle) than Sal's time t but later in the video says both people think "1 second" has gone by.
• Hey jp11235,

Okay, I'll try my best explaining. Yes, you are correct by saying that the t' looks longer than the t axis. However, look back at the t' against x' axis. Do you notice t' is slanted to a 45º angle, while the t and x axis are perpendicular? Well, that means that for the same position of time, you will get a smaller value of x' than x. The way I think about it is that if you kind of 'push' the slanted axis, it would make all the rhombi turn into squares (if you know what I mean)... I find it quite challenging to explain this. Hopefully this helped a little bit, even though you asked this such a long time ago...

All the best!

swishswish123
• I m not getting the idea the speed of photon with respect to stationary observer and moving observer is same or not?
• Hi Sid,

In the future videos you will learn how that the speed of light (3 x 10^8 m/s) is absolute - it is always constant no matter from what frame of reference we look at it (even if we are moving).

The Newtonium way of looking at things thought of space and time like this;
1) The passage of time is the same for all frame of references, meaning time is absolute.
2) Measured space is the same for all frames of references.

But as you will learn, this can't be.

Instead, Einstein's Theory of Special Relativity talks about how light is absolute, but space and time are not.

Now we know space and time are not absolute, they are really just different directions in this continuum spacetime. That is why people say space/the universe has 4 dimensions, the last one being time. Space = 3D and time = 1D, when you put these together you get Spacetime which is is representing that time isn't a separate absolute, and space a separate absolute, they are just different directions of spacetime.

This switch from Newtonian/Galilean thinking may take a while to sink in - just keep learning!

Hope this helps,
- Convenient Colleague
• Why do we use the tilted blue line(the world line of Sally) to define the system of spacetime relative to Sally, Why should we think that the coordinates along this "static path"(worldline) would be the time coordinates of Sallys spacetime system? Relative to my orange worlline photon "static path" based system of mine.
• Keep in mind that there is no preferred inertial frame of reference and that every inertial observer's view of the events has that observer as stationary with a world line that is vertical. Things moving relative to the observer have tilted/non-vertical world lines. Photons (or anything that moves at the speed of light) will always have a world line at a 45 degree angle.
• How would it look like with t' drawn as the y axis instead of t?
• Yeah, like Ashikur Rahman said, it make things a bit simpler because if you did put t' on the y-axis, you are considering the spaceship as being the stationary object, and so all the dark blue lines representing spaceships would be parallel to the y-axis at their different distances. As for the light photon that is moving away from Sal, it would still seem to be travelling away from the spaceship. Therefore, you can now picture the new shape of the graph, which would be like considering this same graph that was shown, but kind of pushing it until the t' axis is completely vertical.

Now, that is what it would be like if it were any other thing travelling faster than Sally, BUT... it is in fact light we're talking about, so since we know that light has the same velocity, even if you're already moving relative to it, (assuming the light is travelling in a vacuum throughout), this graph will not apply. If you haven't already, I would recommend you watch the next few videos to learn how to go about this problem!

I hope that was at least a little bit clear!

Swishswish123
(1 vote)
• Why is that Sally's t' axis is on her movement line (the light blue), but your t axis is on the y axis (not on your orange movement line)?
• It looks like just a notation thing with the graph. The t values aren't different. And the orange line is not Sal's movement, but the movement of a photon emitted by Sal at time zero. So the orange line is the movement of light, not Sal. Hope this clarifies it a bit!
(1 vote)
• t' axis is slanting compared to the t axis. does this mean that every second is going to be slightly longer for the moving observer as compared to the stationary observer? Can we consider this a proof of time dilation?
• Hi Pranav,

The reason for the axis being tilted/slanted is because the time and space happening to Sal's friend, will look different with respect to his point of view.

Basically, space and time are not absolute - they can be different depending on what frame of reference we look at them.

This is a switch from the Newtonian way of thinking (that space and time are absolute), and may take a while to sink in.

Hope this helps,
- Convenient Colleague
(1 vote)
• In your videos on Sp relativity you used a system(train) of spaceships all travelling at the same speed .5c relative to Sals S system to set up the coordinate grid lines of Sally S’ system. These lines are all parallel to the tilted t’axis of Sally herself(her spaceship) at the origin of her system because they are the lines along which the time, of that particular spaceship that is at rest relative to Sally but moving at .5c relative to Sal ,evolves along. All these lines of coincidence define the time axis for all these positions that are at rest relative to each other namely all the positions of the ships and the positions in Sallys system which system moves at .5c relative to Sals system. Since the motion causes Sallys time axis to tilt relative to Sals all the time axies of all the positions in Sallys system are tilted at the same angle and are all parallel to the t’axis. They are the direction that time evolves at(in spacetime) in Sallys system.
Is there a way analogous to this system of ships that we can use to set up line of simultaneity for all time in Sallys system that is can we find a line along which all positions on it have the same time. That is can we find directions in spacetime so that all positions on the line(this axis) occurs at the same time and are simultaneous?
IN the first case the set of Sallys spaceships define all the times at each point of the Sally system along the lines of coincidence. Now I am wondering if we can find some other system of Sallys that will define at each time in Sallys system all positions which will occur at this same time (be simultaneous) and the lines a will be called simultaneity lines of Sallys system and all be parallel to the tilted x’axis of Sally who moves at .5 c relative to Sals system.
Whereas the line of coincidence are all parallel to the t’axis of Sally and each line gives all the times at that one position that the line intersects the x’ axis at; the lines of simultaneity, on the other hand, are all parallel to the x’axis of Sally and each of these line gives all the positions which are simultaneous to that one time where it intersects the t’axis at.
The fact that these lines form Sallys system which moves relative to Sals at .5c means that since the t’ and x’ axis of Sally are tilted due to the motion by Q=tan^-1( v/c) results in the coordinates in Sallys system being transformed from Sals by this tilt reflected into the transformations since Y=[1/sqrt(1-v/c)^2] and x’=Y(x-Bct) and t’=Y(ct-Bx) which shows the symmetry of the concept of spacetime . B=v/c
• These lectures are extraordinarily good, and very helpful. I would add only 2 small caveats. Sal says he's both "stationary" and "drifting". This is confusing. He should also reiterate that he is STATIONARY, at the beginning of each one of these lessons. Thanks!
• Drifting and stationary are relative states of motion.

As long as you are not accelerating you are always stationary with respect to yourself.

So if you are drifting through deep space far away any source of gravity you are stationary in relation to yourself.
• At wouldn't Sal see the spaceship train at 1/4 the speed of light every second? I say this because the light would have to reflect off of the hulls that are going at 1/2 the speed of light, so wouldn't it be seen as going 1/4 the speed of light because the actual light in reference to Sal is traveling twice the distance, and so 1/2 the time the light travels is back toward Sal, doubling the denominator in reference? (I know he's doing this to represent his friend's point of view, but he intoned that he saw his friend 1/2 the speed of light away after 1 second, yet didn't mention how it would look different in his view)
• what will be the distance traveled by a person in a train of 100m when he moves from ?end to the front of the train if the train travels at the speed of light?