If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Angle of x' axis in Minkowski spacetime

It looks like there might be some relationship between the relative angles of the axes in the two references frames we've considered. Let's take a closer look.

## Want to join the conversation?

• At you show that the for faster speeds the ct' axis converges with the photon. I was wondering, do they actually meet at full light speed? And if so, since the path of the photon would cover the entire axis, does that mean a photon is really everywhere at once?
• the photon is still at a 45 degree angle between ct' and ct". imagine the ct'-x' axis as having been rotated off of the ct-x axis so that the ct' axis is pointing into the screen and the x' axis is pointing up and out of the screen. the ct"-x" is just rotated a little more. the angle between the ct'-x' axis and between the ct"-x" axis is 90 degrees to each other. the 2d drawing makes the 3d situation look like the axes and photons converge, but they don't. the x'/x" axis just swings out in front of the photon path line
• How would this work in circular or spiral frames of reference (since our Earth and solar syst. move in a spiral)?
• A bit late to the party for my response, but...
As I see it (with my limited understanding), the circular movement wouldn't be inertial, as there is some apparent relative acceleration - so it would be a bit more complicated.
• I don't understand what Sal says at - "In one light meter the thing travels a meter" How does this prove that light travels at light speed in Sally's frame of reference?
• From experimental results we have been able to show that regardless the relative velocity of two inertial frames of reference the speed of light is always measured as the same. So since Sally is moving at a constant speed she is in a inertial frame of reference and will measure the speed of light to be the same as Sal does.
• So the spaceship is moving faster than we do, therefore, time and space behaves different for it than our time and space. But aren't we moving with the same speed away from the spaceship? So that we can view the spaceship as the resting point and we are the half-speed-of-light-travelers?
• Why speed of light is absolute ?
• No one can really answer why that's the case, it's just the way it is in our universe.
• I understand from the video that the speed of light is absolute but not relative. Does this mean that the motion of light is absolute? And if it is, then all motion in the universe could also be made absolute by comparing it to frame of reference of a photon! So is motion really relative or can it be viewed as absolute?
• The speed of light being absolute means that all observers will measure the same speed, regardless of what frame of reference they are in. There are an infinite number of photons moving in an infinte number of directions so I don't know what you have in mind to make measurements of the universe absolute by using a reference frame of a photon.
• I understand that if Sally travels at 1.5 * 10^8 m/s in our frame of reference and shoots a beam of light it appears to travel at 3 * 10^8 m/s regardless of the frame of reference, and I understand that this is the case only for light.

But what would happen in our frame of reference if Sally shoots a ball so that in her frame of reference it travels at 2 * 10^8 m/s.

In her frame of reference the ball obeys the laws of physics; nothing travels faster than light. What about our frame of reference? I know that objects' mass increase as they approach the speed of light which should decrease speed to conserve momentum. In Sally's frame of reference it isn't travelling too close to the speed of light so 2 * 10^8 m/s could be achieved, right? But in our frame of reference it should travel beyond the speed of light. How is that possible?
• The addition of velocity does not work the way you are used to, if the speeds are close to the speed of light.

The way that you add the ball's speed to sally's speed with relativity is
(1.5 + 2) / (1 + (1.5*2)/3^2) = 2.62 * 10^8 m/s
• Sal, thanks for the great video. At you remark that the triangle formed by the spacetime path of the photon from the x' axis to the ct' axis is an isosceles triangle because the corresponding lengths of the frame in uniform motion are equal. Why are we allowed to assume that those lengths along the axes of the frame in uniform motion are preserved?
• We are not allowed to assume they are preserved, and in fact they are not preserved. However, they are equal because of the following argument: the angle between the two yellow lines is 90 degrees. By the converse of Thales’ Theorem, you can draw a circle centered at the origin that will pass through both of the pink triangle’s base vertices. This shows that they are equal.
(1 vote)
• At how does the graph show that in one light meter that the thing travels one meter? Also what is the thing? Is it the photon emitted by Sally?