- Slower and shorter -
Time dilation (f.ex. time of a moving train ticks slower) and length contraction (f.ex. moving trains are shorter than if not moving) follow from the Relativity of Simultaneity. Explaining in detail how it works would take too much space and time here, but by means of a little video that I found on the internet I will show you what role time dilation and length contaction play for the constancy of the speed of light. And in one go I will also show you how critical you should be reading about Special Relativity. I can not resist the temptation to give you an example of the kind of nonsense you can find on the internet. The following video has the intention teaching you how the speed of light is constant for different space travelers. But the explanation is wrong. Dead wrong. The problem is that many viewers will swallow it because it is so nicely presented.
Please have a look at this video clip. You can skip the first part and go directly to 6:30 minutes (slide the horizontal scrollbar).
Fantastic, isn't it?
Let's scrutinize what's been showing:
Time in stationary frame = 12 sec
Time in moving spaceship = 9 seconds.
(This means the slowing factor Gamma equals 1.333).
Length contraction of 12 ls (lightseconds) ruler makes it 9 ls long (12/1.333).
Then at about 7:15 min the video guy says: "The rulers aboard are contracted just enough to make the measurement work.... 9 ls in 9 seconds ... correct speed of 1 ls per second ..."
Not at all!
They made two big mistakes to make it work.
I photoshopped a few screen shots to illustrate this:
The time of the moving spaceship slows down from 12 to 9 seconds. Let's stick to this as a given.
This 'slowing factor' of 1.333 corresponds with a traveling speed of 0.6614 c.
This means that when the light has traveled
12 ls, the 'moving' spaceship has traveled 7.937 (=0.6614 x 12). Hence the start of the moving measuring stick should be at 7.937 ls on the stationary stick. Not at 6 ls as shown in the video!
If his moving measuring stick 'shrinks' gamma factor 1.333, (making it 9 ls long in the stationary frame) the moving spaceship will measure -with his contracted 12 ls ruler- the remaining 6 ls of stationary length as 8 ls, not 9 ls as shown in the video!
I'm not sure whether the author of the video did it on purpose, probably he did, or whether he simply does not know how to make ends meet with the correct data.
This should be shown:
If we keep the times correct (the video started with time adjustments), hence gamma = 1,333.
This is what the top spaceship astronaut says:
The moving rod starts to measure at 7,937 ls of the stationary rod. The light beam is at 5,4173 ls on the contracted rod.
The authors do not show this correct scenario because at first sight the correct numbers do not give constant speed: at 9 seconds the lightbeam should be at 9 ls, not at 5,4173 ls!
But this is because the video does not show Special Relativity, but some ether world scenario where everyting happens in one 3D world of events only. Special Relativity is about different 3D worlds cutting through 4D Spacetime, not about contracting rods in one ether 3D world.
You will hardly believe it, but for the 'moving' astronaut (bottom spaceship) this is what happens:
He says his own measuring stick does NOT contract. For him, the other spaceship (top spaceship) and measuring rod contract! (And the time of the top spaceship slows down: 4,06 relative to 5,4 ...).
When the light beam is at 5.4 ls, his clock time is at 5.4 seconds. At 5,4 seconds on the traveler's clock (bottom spaceship) the lightbeam is at 5,4 ls on his -not contracted- measuring stick. Speed of light is correct: 5,4 ls in 5,4 seconds!
(Event light beam at 5.4 ls and event traveller clock at 5.4 are two simultaneous events for the for bottom spacehip, but not for the top spaceship! Realtivity of Simultaneity...)
I bet this is too crazy to be true, but that's what really happens.
To really grasp what's going on you need a 4D spacetime diagram. Without a 4D spacetime diagram you will never understand Special Relativity, because it is the only way to see how 4D Spacetime (Block Universe) works.
Special Relativity is about different 3D worlds cutting through 4D Spacetime, not about contracting rods in one ether 3D world. Spacetime diagrams are the best tool to illustrate this.
I made a Minkowski diagram and Loedel diagram. In the Loedel diagram the time and space units are equal on all axes. Not in a Minkowski diagram. A Minkowski diagram suffices for illustrating relativity of simultaneity, but is rather clumsy to grasp what's really going on with time and space.)
In the Loedel diagram (bottom) I show the 3D worlds of both spaceships. I reckon that without a Loedel diagram you are unable to grasp the full extent of Special Relativity.
At first sight such a diagram looks very frightening, but once you know how to read (and draw!) them, they are very addictive. Great fun! (In the 'Further reading' section on this site you will find a link for more information on spacetime diagrams.)
The guys who made the video probably know nothing about Special Relativity and have never heard of 4D Spacetime (Block Universe). They are stuck in a 3D ether concept and then do everything to make the numbers work out properly. But it's all wrong. A real catastrophy!
It's a nice illustration of how much time and money is wasted on wrong Special Relativity tutorials. And for the layman there are a lot of Special Relativity tutorials available with plenty of these "The rulers are contracted just enough to make the measurement work ..." without understanding what it is all about: different physically real 3D space world cuts through 4D Spacetime (BLock Universe).
Let me end with a positive note.
What follows in the video at 7:45 min is interesting. The lady wonders whether all that time dilation and length contraction 'really' happens. The guy answers: "It sure does."
Indeed, it's no illusion. At least they got that fully correct!