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### Course: Physics library>Unit 16

Lesson 2: Minkowski spacetime

# Introduction to special relativity and Minkowski spacetime diagrams

Including multiple observers in the "most obvious" way led to some problems. Let's see how we can start to solve those problems by introducing (what we'll later call) Minkowski spacetime diagrams.

## Want to join the conversation?

• how do we know that the speed of light is absolute?? how did we conclude that?? Sal has been saying that, observations proved that?? what kind of observations?
• Its a mathematical consequence of Maxwell's equations, which were deduced from experimental equations.
Yes, there are proofs. Pictures from stars during an eclipse show that a light ray does, indeed, bend near gravitational fields (a consequence of the general relativity theory). Nowadays, we also have pictures of gravitational lenses created by clusters of galaxies took by Hubble Telescope.
As for the special relativity theory, GPS systems and jets moving around the Earth with superclocks inside were used to show that it also holds.
Also, the Michelson-Morley experiment was repeated countless times, it intended to show how light speed wasn't absolute. The experiment never succeeds in doing so.
PS: The special relativity theory was built by 2 postulates, and one states that the speed of light is absolute. By proving this theorem's predictions (like what happened to the superclocks inside jets), we were able to make sure its a solid theory.
• At 10;10 ,how to we exactly know the point of reflection?
• Sal drawn the line from -1s prime at a positive 45 degree angle in relation to our point of view to stay consistent that light speed is absolute. Again he drawn a line at negative 45 degree angle from the +1s prime to meet with his previous line for the same reason that light speed is absolute.
• at about the tenth minute of the video, when we are drawing the photons movement in the graph with a forty five degree angle.. Angle from t' axis i guess. (Enlighten me if I am wrong on this!). And then he says we won't know where the photons get reflected, the point where the photon changes its direction! Why can't we have that point (point of change of direction of the photon) on the X axis of "our" reference?
• In a spacetime diagram like is being used the observers frame of reference O has the non-prime axes t and x and light will always move moving at a 45 degree angle and the observer will always be on their t axis.

When we look at the spaceship that is moving at 0.5c they are in O' and we are in O.
From the perspective of O the spaceship is moving in a line that is 30° from the t axis and since from the perspective of O' the position of the space ship traces out t' this is also t'. A photon of light emitted from the spaceship travels at a 45° angle with respect to t by definition. Since we know that we know that the photon was emitted at 0 seconds on t' and received at 2 seconds on t' we can find the bounce point by drawing the 45° up to the right from t' = 0 and an 45° down to the right from t' = 2. We know that the reflection point is on x' at 3*10^8 meters so if we draw a line through the reflection point and t' = 0 you get the x' axis which ends up being 30° from the x axis.

In general the angle that t' is from t will be the same angle in the opposite direction that x' is from x.

I am not sure if I made this more or less clear.
• OK.. I accept that time has to get dilated. But how do we see that practically?
Does a watch slow down? Should not be because the internal mechanisms with which the clock works are not dependent on speed. I mean the battery still provides the current and the clock rotates at the same speed.
Or,does our ageing process slow down. Well our biological clock should also not feel the time to slow down. Why will the pineal gland stop the circardian rhythm if we are travelling at half the speed of light?
In practice how can we feel the time to slow down??
• From your frame of reference of being inside the spaceship, you experience time going at a normal rate (you always experience time going at the same rate for yourself). However you also experience space in the direction of your motion being contracted.

From the frame of reference of an outside observer watching you in the spaceship, they view your time as being slowed down, but they do not experience any spatial contraction.

In the end when the spaceship returns to the observer, you in the spaceship say you traveled for less time because the distance you travelled was reduced from the spatial contraction; and the observer also agrees with you that you travelled for less time because they saw your time slow down even though they also saw you travel a longer distance. So in the end, both people agree on the amount of time that has passed, but for entirely different reasons (spatial contraction vs time dilation).
• In the SpaceTime Graph for Sally at Sal says that light will take 1 second to go from Sally to the space ship and another second for its reflection, so it means that Sally is also travelling at the speed of light which contradicts his previous saying and in the SpaceTme Graph in his frame of reference that Sally is travelling at half the speed of light, so I`m a bit confused as to what to take in to consideration.
• Sally is not travelling at the speed of light. The distance to the space ship with the mirror is exactly 1 light second, meaning it takes two seconds for the light to reach back to Sally. Sally and the spaceship with the mirror are both travelling at the same speed of `c/2` from Sal's point of view.
(1 vote)
• During the video, Sal mentions 'spacetime' several times, to emphasize that they become a single entity. How does the 'relative time and space' coordinate system have space and time as a single entity, as opposed to the Newtonian system? I mean where do we derive that 'spacetime' part from?
• but clocks are made out of gears and stuff like that but these stuff don't have any sense of what Time dilation is and they should operate the same way in every situation.i really need help.pls som1 help me understand this
• What do you think makes gears and stuff operate in a way that things like bouncing photons or vibrating atoms don't? Gears are made of these simpler things.

Nothing has a sense of what time dilation is that "makes" it follow what special relativity says it should, special relativity is a theory that describes what we have observed.

The effects of time dilation and length contraction in special relativity have been observed and measures to extreme accuracy.
• Why is Non Eucidean Geometry not famous and is not known to many?
• It is much newer and many of its derivations ( AAA congruence ) seems very unorthodox. However, it is not inferior to Euclidean geometry.