Last week, we did an example involving cause and effect.
And what we showed is that if you can have a situation where something is traveling
faster than the speed of light.
A material object like a spaceship or it actually generalizes to any message,
any information type message, where you can get from one point to another point.
Then you run into problems with cause and effect.
There are contradictions with all.
So let's just review what that situation was, and
then we're also going to apply our space time diagram to the situation and
visualize it in another way to get a better idea, perhaps of what was going on.
So remember that the situation we set up was that we had the bad guys and
the good guys.
And they signed a treaty at the bad guy's planet and you're zero, at which point
the good guys took off in their ship at 0.6 times the speed of light.
And remember of course, they're traveling along the X axis, this is their
world line on the space-time diagram of the bad guy's frame of reference.
Frame of reference of the bad guy's planet, so it's XBG here, and
TBG for the bad guys.
In the intervening years, the four years between when the treaty was signed,
and the good guys took off.
The bad guys invented a faster than light spaceship.
And so, in year four, by which time they perfected it, they set off in their faster
than light spaceship, which would go a speed three times the speed of light and
caught up to the good guys at time equals five years.
At which time the good guys have traveled three light years away.
Remember, they were traveling at 0.6C.
So what that enables them to do within five years,
five times 0.6C gives you that the three light years.
Bad guys could travel three times the speed of light and therefore,
it only took them one year between four and five to get to that point.
So, they met actually, remember if you're visualizing this along the X axis,
this is not the actual intersection point on the X axis where it actually occur.
That would be right here.
In other words, the good guys are traveling along the X axis.
This is a space-time diagram, showing you their progress through time as well,
and the bad guys catch up to them and pull off their sneak attack at that point.
And we analyze it from the bad guy frame.
The launch occurred at four years and the attack was at five years.
And then we analyzed it from the good guys frame of reference
using Lorentz transformation, and discovered that the attack occurred
at four years in their frame of reference but the launch occurred at five years.
In other words, the attack occurred even before the super spaceship had
been launched and therefore, clearly a violation of cause and effect.
You can't have an attack if the spaceship hasn't maybe even been invented yet and
certainly hasn't been launched at that point.
And therefore,
the conclusion is that faster than light travel is impossible because
we've never seen in all our observations a violation of cause and effect.
Now, that doesn't mean perhaps in some case in the future,
we may discover something like this, there's a violation.
But everything we know,
all the experiments we do, says there's no violation like this of cause and effect.
Again, some of you may be thinking of things like in quantum physics
which get a little strange.
But even in quantum physics, the special theory of relativity has been shown
to hold in situations like this where you can't travel faster than light.
So here's a redrawn diagram, same diagram except what we've done here is drawn
our combined diagram so again, we have the axis for the bad guys frame of reference.
And then we put in the good guy axis.
The X axis and the time axis for the good guys.
And we've also drawn in the lines of simultaneity, and I've tried as much as
possible to make this to scale, didn't quite get it all right there.
But the key thing here is that, of course,
you've got your two axis as we've shown here.
The speed of light in these units, with again, it's light years and years.
Speed of light would be a 45 degree line there.
And so what do we see from this?
Well, remember the lines of simultaneity in any frame of reference
are going to be parallel to the X axis.
The X axis defines everything that occurs at a certain time, or
any given horizontal line in the bad guy diagram.
And you're given a horizontal line to find the line of simultaneity,
everything that's going on say, T equals four, is on this line.