Do we also travel at a fixed velocity?

In summary, since light is always traveling at a constant velocity with respect to everything else, it means that everything else is also traveling at a constant velocity with light. However, this statement is only true if you adopt a weird mathematical definition of "speed through spacetime".
  • #1
The_Thinker
146
2
Since, light is always traveling at a constant velocity with respect to everything else, does it also mean that everything else is also traveling at a constant velocity with light?

As in, since light is always traveling at C irrespective of our velocity, then does it not also mean that we are also traveling at a constant fixed velocity with respect to light? Is our velocity then taken as 0? If that is the case what does velocity actually mean?

With respect to one photon, what would be the velocity of another photon that is traveling towards it?

Sorry about these basic questions, I am just a fan pf physics and don't really know anything much about it in detail.. :biggrin:
 
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  • #2
The_Thinker said:
Since, light is always traveling at a constant velocity with respect to everything else, does it also mean that everything else is also traveling at a constant velocity with light?
When physicists talk about the speed of one object "with respect to" another, they usually mean the speed of the first object in the inertial rest frame of the second ('rest frame' is a coordinate system where the object is at rest, and 'inertial' means the coordinate system is moving at constant velocity, not accelerating), but light doesn't have its own inertial rest frame in relativity--see this post for a little more info.
 
  • #3
JesseM said:
... light doesn't have its own inertial rest frame in relativity...
Yes, and in this is the answer to your question. You cannot pretend to "stand next to a photon" and measure the speeds of other objects. It is meaningless.
 
  • #4
Actually, I think the main question was asking it from the other direction. That makes this the answer:
the speed of the first object in the inertial rest frame of the second
In other words, the OP asked the speed of "everything else" -- but since the speed of light is measured from our rest frame (and not the other way around), the answer [to a slightly different question maybe] is zero.
 
  • #5
The_Thinker said:
Since, light is always traveling at a constant velocity with respect to everything else, does it also mean that everything else is also traveling at a constant velocity with light?
If you consider traveling trough spacetime, instead of space only, then everything is traveling at a constant velocity c, just in different directions:
http://www.adamtoons.de/physics/relativity.swf
 
  • #6
A.T. said:
If you consider traveling trough spacetime, instead of space only, then everything is traveling at a constant velocity c, just in different directions:
http://www.adamtoons.de/physics/relativity.swf
The statement that everything moves at c spacetime is only true if you adopt a weird mathematical definition of "speed through spacetime" (which isn't a term used by most physicists), see my post #3 on this thread.
 
  • #7
JesseM said:
The statement that everything moves at c spacetime is only true if you adopt a weird mathematical definition of "speed through spacetime" (which isn't a term used by most physicists), see my post #3 on this thread.
I don't find it that weird. It a consequent extension of the classical "speed through space" by the adding the time dimension.
 
  • #8
A.T. said:
I don't find it that weird. It a consequent extension of the classical "speed through space" by the adding the time dimension.
But nothing actually "moves" in a spacetime diagram, spacetime is just a fixed 4-dimensional structure with worldlines embedded in it, so this terminology tends to be confusing to people who haven't learned to take this geometric perspective on spacetime. What you're really doing when you talk about "speed through spacetime" is taking the spacetime interval between two events on the object's worldline and dividing by the proper time experienced by the object between those events, so it's really quite trivial that this will equal c since the spacetime interval is essentially defined as c * proper time (with the c there just to ensure that the spacetime interval has units of distance rather than time).
 
  • #9
JesseM said:
But nothing actually "moves" in a spacetime diagram,
Yes it does! Just press "play" http://www.adamtoons.de/physics/relativity.swf" [Broken] and see it move. ;-)
JesseM said:
spacetime is just a fixed 4-dimensional structure with worldlines embedded in it, so this terminology tends to be confusing to people who haven't learned to take this geometric perspective on spacetime.
The picture of objects moving along their worldline doesn't seem confusing to me. It is a way to visualize the meaning of spacetime diagrams.
JesseM said:
so it's really quite trivial that this will equal c since the spacetime interval is essentially defined as c * proper time.
The nice thing about these space-propertime diagrams is that you directly see all the quantities (space, coordinate time. proper time) as geometrical lengths. And the fact that everything "moves" with c trough this diagram is a nice simple rule.
 
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  • #10
A.T. said:
The picture of objects moving along their worldline doesn't seem confusing to me.

But they don't move. In these diagrams time is fixed and unmoving.

To set anything moving is to introduce an additional component that doesn't exist.
 
  • #11
A.T. said:
The picture of objects moving along their worldline doesn't seem confusing to me. It is a way to visualize the meaning of spacetime diagrams.
But what "meaning" is that? If you adjusted the animation so that objects traveled twice as fast along their worldline, or twice as slow, these types of "changes" would not seem to have any physical meaning, since the worldline itself would be unchanged. And to make sense of anything moving through spacetime, it seems you must implicitly be imagining a second time dimension, no?
 
  • #12
The_Thinker said:
Since, light is always traveling at a constant velocity with respect to everything else, does it also mean that everything else is also traveling at a constant velocity with light?

As in, since light is always traveling at C irrespective of our velocity, then does it not also mean that we are also traveling at a constant fixed velocity with respect to light? Is our velocity then taken as 0? If that is the case what does velocity actually mean?

With respect to one photon, what would be the velocity of another photon that is traveling towards it?

Sorry about these basic questions, I am just a fan pf physics and don't really know anything much about it in detail.. :biggrin:

Either these guys are answering the wrong question, or I am.
Velocities don't add like you would expect in relativity.
30000 km/s combined with 30000 km/s does not equal 60000 km/s.
 
  • #13
Thank you for your replies,

So, the way I understand what you people have said so far is this:

1) All velocity is judged from an initial rest frame.

2) Light has no initial rest frame, so judging velocity from its perspective is meaningless.

Okay... this is just like another one of those, rules apply to everything, except electromagnetic ray things.

Only EMRs can travel at c. Only EMRs can have no mass yet they can have energy and be affected by gravity. Only EMR's can have no initial rest frame.

Is there any explanation of mass given by SR or GR that explains that light does not possesses it yet it can affect things that do possesses mass?
 
  • #14
Virtually none of what you have just posted is correct. You might want to reread the rest of the thread.
 
  • #15
The_Thinker said:
Thank you for your replies,

So, the way I understand what you people have said so far is this:

1) All velocity is judged from an initial rest frame.

2) Light has no initial rest frame, so judging velocity from its perspective is meaningless.

Okay... this is just like another one of those, rules apply to everything, except electromagnetic ray things.

Only EMRs can travel at c. Only EMRs can have no mass yet they can have energy and be affected by gravity. Only EMR's can have no initial rest frame.

Is there any explanation of mass given by SR or GR that explains that light does not possesses it yet it can affect things that do possesses mass?

No no; not "initial," "inertial"! Meaning "not accelerating," from the root word "inertia."
 
  • #16
DaveC426913 said:
But they don't move. In these diagrams time is fixed and unmoving.
JesseM said:
If you adjusted the animation so that objects traveled twice as fast along their worldline, or twice as slow, these types of "changes" would not seem to have any physical meaning, since the worldline itself would be unchanged.
Yes of course. The whole point of a time axis is to visualize movement in a static diagram. The animation is just meant to help to understand the relationship between the diagram and real world observation. Therefore the animated parameter is the coordinate time expierenced by the observer.
DaveC426913 said:
To set anything moving is to introduce an additional component that doesn't exist.
JesseM said:
And to make sense of anything moving through spacetime, it seems you must implicitly be imagining a second time dimension, no?
In the case of a space-propertime diagram this "additional component" or "second time dimension" is the coordinate time measured by the observer. It determines how far the objects "move" along their worldlines. And since they all "move" the same "distance" in a given period of coordinate time, you could say: Everything moves at c trough space-propertime in regards to coordinate time.
 
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  • #17
If you consider traveling trough spacetime, instead of space only, then everything is traveling at a constant velocity c, just in different directions:

Technically precise or not I have found Brian Greene's explanation a very simple geometric way to think about relativity. It's real easy to visualize how motion in space "diverts" motion in time and linear acceleration becomes curved and rotational acceleration spiral (corkscrew) shaped.
 
  • #18
Naty1 said:
Technically precise or not I have found Brian Greene's explanation a very simple geometric way to think about relativity. It's real easy to visualize how motion in space "diverts" motion in time and linear acceleration becomes curved and rotational acceleration spiral (corkscrew) shaped.
But the fact that linear acceleration gives a curved worldline and rotational acceleration gives a corkscrew is just a fact about the shape of the worldlines, it has nothing to do with any notion of "moving" along the worldlines at speed c.
 
  • #19
JesseM said:
But the fact that linear acceleration gives a curved worldline and rotational acceleration gives a corkscrew is just a fact about the shape of the worldlines, it has nothing to do with any notion of "moving" along the worldlines at speed c.

The notion of "moving" trough spacetime is only a visualization, just like the idea of spacetime itself. It is accessible to beginners, because it naturally extends the idea of spatial motion:

space displacement during a period of observers time

by adding a temporal component (proper time period) to the displacement vector, making it:

spacetime displacement during a period of observers time
 
  • #20
A.T. said:
The notion of "moving" trough spacetime is only a visualization, just like the idea of spacetime itself. It is accessible to beginners, because it naturally extends the idea of spatial motion:

space displacement during a period of observers time

by adding a temporal component (proper time period) to the displacement vector, making it:

spacetime displacement during a period of observers time
Mere spatial displacement doesn't specify whose time-coordinate you're using (whether the observer's or someone else's), it just involves the spatial distance between two different events on the object's worldline. Spatial velocity depends on a choice of time-coordinate, but it's not defined as space displacement divided by a period of observers time, it's defined as space displacement divided by a period of coordinate time in the same coordinate system you're using to measure space displacement. There isn't any obvious intuitive reason why it is more "natural" to define an object's "speed through spacetime" in terms of the object's own time rather than in terms of the time-coordinate of some outside observer's rest frame. And if you do choose to define "speed through spacetime" in terms of spacetime displacement divided by the object's own proper time, then as I said, my biggest problem with this is that the statement "everything moves at c through spacetime" is often presented as a significant physical insight when in fact it's basically a tautology given that the spacetime interval which measures "distance" in spacetime can be defined as proper time * c (with the only purpose of the c being to give the spacetime interval units of distance rather than time, c being the only physical constant that has units of distance/time). There's no reason we couldn't define the metric in terms of proper time itself rather than proper time * c, it's just a convention which I suppose owes to the fact that people find it more natural to think of the metric in terms of spatial distances than temporal distances.
 
  • #21
A.T. said:
I don't find it that weird. It a consequent extension of the classical "speed through space" by the adding the time dimension.
I don't find it weird either. You are just talking about the proper-time derivative of the spacetime coordinate (ct,x,y,z) which, IMO, is a reasonable definition of velocity regardless of the fact that worldlines don't move.
 
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  • #22
JesseM said:
And if you do choose to define "speed through spacetime" in terms of spacetime displacement divided by the object's own proper time,
DaleSpam said:
You are just talking about the proper-time derivative of the spacetime coordinate (ct,x,y,z)
You both got me wrong, so it must be my fault. With "speed through spacetime" I mean space-propertime displacement divided by coordinate time (the coordinate time derivate of the space-propertime coordinate (ctau,x,y,z)). So it could be called the speed through space-propertime (which is c for all objects).
JesseM said:
my biggest problem with this is that the statement "everything moves at c through spacetime" is often presented as a significant physical insight
It's a nice simple rule that helps in geometrical visualizations, of SR & GR.
JesseM said:
given that the spacetime interval which measures "distance" in spacetime can be defined as proper time * c
You are thinking about the Minkowski spacetime. In space-propertime the distance is sqrt((delta proper time * c)^2 + (delta space)^2)
 
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  • #23
My mistake. I do find it weird after all.
 
  • #24
A.T. said:
It's a nice simple rule that helps in geometrical visualizations, of SR & GR.
How does it "help"? You can't even use the rule until you've already come up with the visualization of the worldlines, and then the only additional thing it does is make you imagine something moving along those worldlines (as in the animation you posted). If you think it actually helps draw the worldlines in the first place, could you give a simple example?
A.T. said:
You are thinking about the Minkowski spacetime. In space-propertime the distance is sqrt((delta proper time * c)^2 + (delta space)^2)
OK, I was going by Brian Greene's definition of speed through spacetime which I quoted in post #3 here, but if you divide your space-propertime displacement by the coordinate time rather than the proper time, your definition works too. The basic point remains the same--the fact that you get a speed of c for everything is not an interesting physical insight, but just a trivial consequence of the way you are defining space-propertime displacement. After all, we know proper time is related to coordinate space and time measurements like so:

delta proper time = sqrt((delta coordinate time)^2 - (delta space / c)^2)
So, naturally (delta proper time * c)^2 = (delta coordinate time * c)^2 - (delta space)^2

Now you plug this into your definition of space-propertime displacement:
space-propertime displacement defined as sqrt((delta proper time * c)^2 + (delta space)^2)
= sqrt((delta coordinate time * c)^2 - (delta space)^2 + (delta space)^2)
=sqrt((delta coordinate time * c)^2)
= delta coordinate time * c.

So, with space-propertime displacement essentially defined as delta coordinate time * c, it's not a great surprise that if you divide by delta coordinate time and call this "speed through space-propertime", you'll find that everything has a "speed through space-propertime" of exactly c!
 
  • #25
It's sort of OK to visualise a red dot moving along a worldline in spacetime when there is just a single point-particle being considered. It's problematic if you want to consider two or more particles. If you think of two red dots each moving along their own worldlines there is a problem of how to synchronise the dots. There is no unique solution to that problem, and the danger is you might be misled into thinking in terms of one specific choice of synchronisation to the exclusion of all others. It's better to think in terms of the geometry of the curves themselves and forget the dots.

It's even more of a problem if you want to consider a large object (i.e. with non-zero volume).
DaleSpam said:
You are just talking about the proper-time derivative of the spacetime coordinate (ct,x,y,z) which, IMO, is a reasonable definition of velocity regardless of the fact that worldlines don't move.
I'm sure you know, DaleSpam, but others might not, that the entity you refer to is called "4-velocity". The technical differential-geometrical interpretation is that the 4-velocity is the tangent vector to the worldline, in other words it's the direction in spacetime that the worldline points. As we are only interested in direction, its magnitude is constant.


A.T. said:
You both got me wrong, so it must be my fault. With "speed through spacetime" I mean space-propertime displacement divided by coordinate time (the coordinate time derivate of the space-propertime coordinate (ctau,x,y,z)). So it could be called the speed through space-propertime (which is c for all objects)
I've never understood how Euclidean "space-propertime" could make sense. The problem is that each object has its own proper time. Consider, for example, the standard twins paradox. At the end, both twins are at the same event in spacetime, but in a "space-propertime" diagram they would be at two different points (because they have each elapsed a different proper time). This shows there is no one-to-one mapping between points (events) in spacetime and points in space-propertime. Being "at the same place at the same time" is a physical reality independent of any choice of spacetime coordinates, but "space-propertime" seems not to recognise the concept.
 
  • #26
JesseM said:
How does it "help"? You can't even use the rule until you've already come up with the visualization of the worldlines, and then the only additional thing it does is make you imagine something moving along those worldlines
DrGreg said:
If you think of two red dots each moving along their own worldlines there is a problem of how to synchronise the dots.
This is how the rule of constant velocity trough space-propertime helps: to synchronize the "dots". In space-propertime which allows you to determine when they meet: Your dots move at the same speed trough space-propertime so they leave equal distance behind them(coordinate time * c). And when they have the same space coordinate, they meet (same position at the same coordinate time). See twins example below.

DrGreg said:
Consider, for example, the standard twins paradox. At the end, both twins are at the same event in spacetime, but in a "space-propertime" diagram they would be at two different points (because they have each elapsed a different proper time).
Which is great because it allows to visualize the age difference geometrically. In a Minkowski diagram you don't see the age difference. In this visualization you see the standard twins paradox in both types of diagrams (space-propertime diagram is called Epstein diagram):
http://www.adamtoons.de/physics/twins.swf

DrGreg said:
Being "at the same place at the same time" is a physical reality independent of any choice of spacetime coordinates, but "space-propertime" seems not to recognise the concept.
Is does! But the coordinate time in space-propertime-diagrams is the length of every worldline (due to the constant speed rule above). You can see in the space-propertime-diagram of the "[PLAIN]http://www.adamtoons.de/physics/twins.swf" [Broken], that both travel the same distance(= coordinate time) to end up at the same place in space. So the are "at the same place after the same period of coordinate time" -> they meet.

The advantage of the space-propertime-diagrams is that they show both: coordinate time and proper time. This allows them to visualize effects like time dilation. Even in GR they come handy to visualize gravitational time dilatation:
http://www.adamtoons.de/physics/gravitation.swf (Help -> Examples)
 
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  • #27
A.T. said:
This is how the rule of constant velocity trough space-propertime helps: to synchronize the "dots". In space-propertime which allows you to determine when they meet: Your dots move at the same speed trough space-propertime so they leave equal distance behind them(coordinate time * c). And when they have the same space coordinate, they meet (same position at the same coordinate time). See twins example below.
But this is obvious, since space-propertime distance is just coordinate time * c. You'd lose absolutely nothing by dispensing with the confusing term "space-propertime distance" and just talking about coordinate time. Of course if you advance the dots forward according to their respective positions at the same coordinate time, their positions will be "synchronized" according to that coordinate system's definition of simultaneity, and there is a single coordinate time when they meet. I don't see how anything is gained by adopting confusing talk about "space-propertime distance" and "speed through spacetime".
A.T. said:
Which is great because it allows to visualize the age difference geometrically. In a Minkowski diagram you don't see the age difference. In this visualization you see the standard twins paradox in both types of diagrams (space-propertime diagram is called Epstein diagram):
http://www.adamtoons.de/physics/twins.swf
I'm confused, in the second animation on this page it looks like you aren't moving the dots forward at the same rate of coordinate time (i.e. you aren't moving each dot at a rate of c in 'space-propertime'), since the two dots don't meet at the point in spacetime where the twins meet, even though the two worldlines naturally meet at the same coordinate time. When I mouseover the second animation it says something about an "Epstein spacetime diagram"--are you saying that in such a diagram, two paths which meet at the same point in spacetime in the physical sense may end at different positions in the diagram? And you say that the time dimension is the moving object's proper time while the length of each path is the coordinate time, but how do you determine the angle that the green path is drawn at, or equivalently, how do you determine the vertical height of the bend in the green path if the vertical dimension represents the other observer's proper time (which doesn't tell you anything about simultaneity).
 
  • #28
JesseM said:
I'm confused, in the second animation on http://www.adamtoons.de/physics/twins.swf" [Broken] it looks like you aren't moving the dots forward at the same rate of coordinate time (i.e. you aren't moving each dot at a rate of c in 'space-propertime'),
In the space-propertime-diagram(Epstein) the dots move at the same speed, so both world lines have the same length, at every coordinate time (which is animated).
JesseM said:
are you saying that in such a diagram, two paths which meet at the same point in spacetime in the physical sense may end at different positions in the diagram?.
Yes of course. They aged differently so their proper times differ. And in the diagram you actually see "why": Twin A takes the direct way and gets ahead of twin B in proper time.
JesseM said:
And you say that the time dimension is the moving object's proper time while the length of each path is the coordinate time, but how do you determine the angle that the green path is drawn at,
I twin B travels with v_B(relative to the observer), the angle(to the proper time axis) would be asin(v_B / c). Light travels horizontally in space-propertime-diagrams (you can switch on light signal worldlines on the right).
JesseM said:
or equivalently, how do you determine the vertical height of the bend in the green path if the vertical dimension represents the other observer's proper time (which doesn't tell you anything about simultaneity).
The vertical dimension represents the moving object's proper time, as you correctly stated above. The proper time of twin B at the turn point is a frame invariant quantity. And that's the vertical coordinate of the turn in this diagram.
 
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  • #29
A.T. said:
The vertical dimension represents the moving object's proper time, as you correctly stated above. The proper time of twin B at the turn point is a frame invariant quantity. And that's the vertical coordinate of the turn in this diagram.
Ah, so the vertical axis doesn't represent just the yellow twin's proper time, it represents both their proper times? For a pair of points on each twin's worldline that are at the same vertical height, the clock reading of each twin at those points would be the same? If so, I think that clears up my confusion. One remaining problem I have with this is that it doesn't really generalize to arbitrary sets of worldlines that may not have set their proper times to zero at a common origin point. So you can't really create an "Epstein spacetime diagram" corresponding to just any Minkowski diagram, it only works for specific situations like the twin paradox.
 
  • #30
JesseM said:
Ah, so the vertical axis doesn't represent just the yellow twin's proper time, it represents both their proper times?
Yes, it is just as the space coordinate. Every object has its own.
JesseM said:
One remaining problem I have with this is that it doesn't really generalize to arbitrary sets of worldlines that may not have set their proper times to zero at a common origin point.
I see no problem there. They don't have to start at zero proper time, but it is convenient to use the starting proper times as zero. What you want to visualize, are different rates of proper time. An initial proper time offset is not really relevant.
JesseM said:
So you can't really create an "Epstein spacetime diagram" corresponding to just any Minkowski diagram
That's true in the sense that Epstein diagram doesn't contain the space like part of the Minkowski diagram. So you can "only" visualize world lines of massive objects and light.
 
  • #31
A.T. said:
Which is great because it allows to visualize the age difference geometrically. In a Minkowski diagram you don't see the age difference. In this visualization you see the standard twins paradox in both types of diagrams (space-propertime diagram is called Epstein diagram):
http://www.adamtoons.de/physics/twins.swf
Oh, I don't like that diagram at all! The end of the green line corresponds not to the point where it touches the yellow line but to the end of the yellow line. That is very confusing to me.
 
  • #32
A.T. said:
That's true in the sense that Epstein diagram doesn't contain the space like part of the Minkowski diagram. So you can "only" visualize world lines of massive objects and light.

A.T.,
How would one draw an Epstein diagram for a radar experiment with light rays?

More specifically, consider two inertial observers with different velocities that met at event O. One observer, after a short [proper-]time interval T1, sends a light-signal to the other. (The ratio of the time-intervals from O is the Doppler Factor.) After a [proper-]time interval T2, the first observer receives the radar echo.
How are these features shown on an Epstein diagram?
 
  • #33
A.T. said:
Which is great because it allows to visualize the age difference geometrically. In a Minkowski diagram you don't see the age difference.

You can count off the age difference in a Minkowski Diagram:
http://physics.syr.edu/courses/modules/LIGHTCONE/LightClock/#twins [Broken]
and you can relate it to the geometry of Minkowski spacetime.
 
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  • #34
A.T. said:
JesseM said:
One remaining problem I have with this is that it doesn't really generalize to arbitrary sets of worldlines that may not have set their proper times to zero at a common origin point.
I see no problem there. They don't have to start at zero proper time, but it is convenient to use the starting proper times as zero. What you want to visualize, are different rates of proper time. An initial proper time offset is not really relevant.
I think you misunderstand--I'm not talking about the fact that two observers in a twin paradox situation might not set their proper times to zero at the moment they depart from one another, since as you say we can always imagine resetting their clocks to zero at that moment for convenience. I'm talking about a situation involving multiple worldlines that don't depart from a common point (in Minkowski spacetime) at all, like objects that have been drifting towards each other from infinity until they finally meet, or multiple worldlines that never cross at all, or three worldlines that each cross the others but all three never cross at a single point.
 
  • #35
robphy said:
A.T.,
How would one draw an Epstein diagram for a radar experiment with light rays?

More specifically, consider two inertial observers with different velocities that met at event O. One observer, after a short [proper-]time interval T1, sends a light-signal to the other. (The ratio of the time-intervals from O is the Doppler Factor.) After a [proper-]time interval T2, the first observer receives the radar echo.
Lets call the guys A and B. Which scenario do you mean:
1) T1 after O, B sends signal to A, which A receives T2 after O
2) T1 after O, B sends signal to A, which A mirrors, so it returns to B T2 after O

robphy said:
You can count off the age difference in a Minkowski Diagram:
http://physics.syr.edu/courses/modules/LIGHTCONE/LightClock/#twins [Broken]
and you can relate it to the geometry of Minkowski spacetime.
I like this too. It's a bit more complicated tough, and involves an understanding of pseudo Euclidean geometry.
 
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