I came to know about the twin’s paradox with a Italian pocket sold with the Italian version or Scientific American “Le Scienze”
As the book did not explain the math behind it, I went to Youtube to search. I found again DrPhysicsA, who helped me create the page about EFE.
Dr PhysicsA has a BSc (physics) and PhD (nuclear physics) from King’s College, London.
Thanks to “DrPhysicsA” I make good progress in applied and advanced math as well as understanding some of the more advanced Physics.
- The lecture
- Space-time – introduction of rules
- The twin paradox with constant speed
- The twin paradox with speed with accelerations
- Section 5
- Section 6
- Contact me on FB
DrPhysicsA explain the math behind the Twins paradox in this video
When Newton sstudied Cartesius had problems moving forward, it is said that starte to read the book from the beginning. I do the same.
As I need to go back now and then to compare I use the manuscript and add screenshots do do that. See below.
OBS. These are my notations. I recommend you to write your own nottations while listening to the lecture.
A note: Text in Italic is taken from the manuscript
As we understand it is three-dimensional that at least is what we observe. That means to say that in any area of space you can go left and right or up and down or back and forth three dimensions and we usually represent that by three dimensions of space or three coordinates of space
which we often label x y and z and that is space.We now need to add to that time and that’s the fourth dimension but it’s very difficult to draw a picture with four dimensions. In fact it’s not impossible and even three dimensions can be rather confusing so let’s try and keep it simple and we’re just going to think of one dimension of time and one dimension of space so it will look like this time.
change. I do not move along the x-axis or the y axis or the z-axis
I stand still and therefore that point doesn’t change.
If you standstill, time is ticking
change, I stay hereon the x-axis (ed. points to the dot on the chart) of course time is passing by relentlessly.
moving in space I am moving in time if you standstill in the middle of a room, time is nonetheless ticking by.
Now there are some rules about space-time for a start. You can’t go backwards in time. So if we take our space-time chart any movement like that is forbidden because although it implies that you are moving
to the left in space it also suggests you’re going backwards in time and there is no known mechanism for doing that.
suggest you might be able to find some
kind of hole that enables you to go back
to some point in the past there is no
mechanism for doing that and so you
can’t have any mote movement through
space time which involves going
backwards in time.
degrees and the way you do that is you just make sure that the coordinates are appropriate.
So for example time might be
one year and the space might be one Lightyear which is the distance light travels in a year so light travels one light-year in one year and.
That’s how you organize the chart.
So we usually arrange it (ed. the graph) just for presentational purposes so that the speed of light is at 45 degrees.
2. not allowed to exceed C in space-time
Now here’s another rule in about our space time chart here’s the chart time versus space.
going faster than the speed of light.
It suggests it’s getting somewhere faster than light could and you therefore cannot do it so that is not allowed.
backwards in time. You’re not allowed to exceed the speed of light.
What this means
The twin paradox – constant speed
the twin paradox.
So let’s start by drawing a very rough space-time diagram just to show what’s going on and then we’ll do it slightly more accurately so that we can understand.
through time for a period of 10 years.
still on the earth and just travels
through time for ten years.
light up and down between the two
mirrors and every time the light beam
hits a mirror it essentially causes a counter to move on and since the
distance is known and since the speed of light is invariant we know that the time to travel from the bottom mirror to the
top mirror is going to be the distance D
divided by C the speed of light.
and here’s the mirror in the rocket.
(ed. like the image above).
that was the distance we had here. (ed Between the mirrors on the rocket)
The following operations are:
- Adding vt’ on both side and flipping side,
OBS! (ct2) should be (ct)2 in the first line above.
- Dividing both side with c2
- Square root of both side, gives finally this equation with the
- Lorentz transform (sqr root (1-v2/c2)
is defined as a “lineartransformations from a coordinate frame in spacetime to another frame, that moves at a constant velocity relative to the former. (Wiki )
The equation says that the bigger the velocity v, the bigger is the time difference between t and t’.
that clock but from the earth … will be…4/5 of the
time that the person on the earth thinks
it ought to be.
will appear to have gone past in the
the speed of light.
communication. ( ed. from left to right)
The twin paradox – speed with accelerations.
spacecraft to arrive back on earth, the clock will be back on earth 59.000 years into the future.
Twins won’t see each other again.
The two examples are difficult to compare as in the first constant velocity case the twin in the rocket traveled 10 years.
I the second case they talk about 40 years. How many years later would the twin be back on earth with acceleration to v=3/5C and back to v=0?
If calculation 1/4 of 59.000 years is ok, then that would equal to 14700 years on earth. Then the twins won’t met again in both cases
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