For
six years ago we did an episode about the speed of light and why we can't travel that fast.
Now it's still high time.
att göra en fortsättning på det avsnittet och prata om hur vi ska göra då om vi vill ta oss ljusår bort utan att behöva frysa ner oss och spendera tiotusentals år på ett generationsskett.
Mm,
och det visade sig att det räckte inte riktigt med ett avsnitt för att förklara det här.
Nej,
vi fick det lite i två delar.
Först lite tid och rum och sånt.
Och så fortsätter vi i nästa avsnitt med självaste resan i...
Ja,
och tiden går,
så det är bara att dra igång här.
Jag heter Susanna Levenhaupt.
Jag heter Marcus Pettersson.
Och du lyssnar på
Har vi åkt till Mars än?
Okej,
så nästa avsnitt kommer att handla om maskhål och tipsresor.
And to make it easier to understand,
we have some other things to keep an eye on.
Yes,
the speed of light,
for example.
It's 299,792,458 meters per second.
That's about 300 million meters per second.
That's
300,000 kilometers per second in vacuum.
Do you want to put it in perspective?
And like four and a half laps around the Earth in one second?
That fast?
And time?
What is that?
Well,
you could think it's a simple thing,
but not.
So before we start talking about time travel and travel through mass holes that can move us light years in just seconds,
let's start from the beginning.
Sören Holst,
university lecturer in theoretical music at Stockholm University.
What is time?
You can answer that question in different ways,
but the easiest answer is to say that time is what you measure with a clock.
And that might sound a little trivial,
but it's actually more deep-seated than you might think.
But the other answer that you can also give,
and that is also deeper than it sounds,
is that time is one of the dimensions in space-time.
And space-time is...
both space and time as one unit.
And one can say that the basic insight in
Einstein's special relativity theory is that one cannot see space and time as separate,
but that one must see them as one unit,
which we call space-time.
And time is one of those dimensions.
Yes,
and it was also Einstein who said that the easiest way to explain time is to measure it with a clock.
Yes,
exactly.
But you also told me when we talked earlier that my clock doesn't have to go in the same tempo as your clock.
No,
so that's also one of the core insights here in the special relativity theory.
And it sounds very strange if you have,
so to speak,
a Newtonian picture of space and time,
that is,
the picture that also rotted in physics before relativity theory,
before Einstein came up with his relativity theory.
Then you thought,
even in physics...
That time is something universal,
it's the same for everyone,
it's ticking on no matter what we do,
what we are somewhere in the universe.
It's what drives the scenes forward,
and it's universal and absolute.
And I think it's just in contrast to what Einstein says,
that time is what we measure with a clock,
to get away from this idea of the absolute universal time that Newton thinks of.
Einstein says,
well...
We shouldn't think of a universal time,
but think that time is what you measure on your clock.
And that insight in combination with the fundamental thing here is space-time as a whole.
That makes it a little less strange that time can go differently fast depending on how you move.
And actually also a bit dependent on where you are in the universe.
But let's keep in mind that time may depend on its movement.
There are several ways to understand why it is so.
And one way is to connect it with the speed of light,
which I know you've talked about earlier.
And...
Then you might feel that the speed of light is universal.
It's the same speed for everyone.
So no matter who measures the speed of light,
you get the same value.
It's also the case that the speed of light is a max speed,
so nothing can move faster than the speed of light.
But if we focus on this strange condition that whoever measures the speed of light in a vacuum gets the same value.
By the way,
what is that value?
Do you remember that?
299
000.
Something.
Yes,
exactly.
Good.
Kilometers per second.
Exactly.
Okay,
but the point now is that the speed is the same for everyone who measures it.
And that actually has a lot to do with the fact that time goes differently quickly depending on how we move.
Because you can express it in different ways.
The reason that the speed of light can be the same for all observers is simply that our clocks go differently depending on...
So if a light pulse passes us here in the studio,
and you Marcus decide to try to go past this light pulse,
so you set off in the same direction as the light pulse in your super fast spaceship,
then the claim is that you will still think that the light pulse is decreasing with the speed of light.
How fast you even move,
even if you move at 99%
of the speed of light,
you will think that the light is decreasing from you.
So if you move at 99%
of the speed of light,
you will think that the light is decreasing
with the speed of light.
The reason is that it can be that your clocks go slower than mine and Susannas studio clock here,
when you move.
Exactly.
So if we say that I can go 99.9%
of the speed of light,
and then
I look at the light and it moves away from me...
In the speed of light.
The difference is 0.1%.
And then my clock goes 0.1%
of the speed that yours does.
Yes,
almost.
Say yes.
There is a complication.
It's not just the time that goes differently when you move.
The lines you measure up also become different in a corresponding way.
If you want to express it completely correctly,
you should take into account that as well.
But if we move away from that complication,
it's about as you say.
I thought it felt nice.
Do you know what a reasonable explanation is?
Yes.
So then we can,
we take that,
we say that it's true.
Yes,
so let me try to make an analogy.
So,
so let's skip time first.
Just think of the room.
Think,
think,
think of the studio table in here.
Consider two points on the studio table.
You can draw a lot of different curves between those two points on the studio table.
and those curves are different lengths,
of course.
And it's clear that the straightest path between two different points on the table is the shortest path,
right?
Yes.
So if you first draw a straight line and measure how long it is,
then it has a certain length.
If you then make a crooked line,
then it will be longer.
Okay.
Now,
Marcus,
we can imagine that you would ask me now,
why is it that the crooked line becomes longer?
But I understand that.
Yes,
but the question is if you do that.
The question is if you don't just feel that you understand it,
because you're so used to it being like that.
The reason it's like that is that this study table has a certain geometry.
It's about some geometric laws here that say it's like that.
And the answer when it comes to space-time,
and that time can go differently depending on how you move,
is actually completely analogous.
Space-time has a geometry.
that light has these characteristics and time has these characteristics.
And there are a lot of other characteristics too.
But if we do it more concretely,
then we say that we look at a space journey.
Okay,
so Susanna,
we say that you take off in a super fast spaceship.
And me and Marcus,
we sit and wait for you here in the studio.
And our studio clocks are ticking here somehow.
So you leave,
on a long journey,
and then you come back.
It may have been a few days here,
we have been sitting and waiting for you for a few days in the studio when you came back.
Then we can say that the event when you left us,
it's one point in the room time.
The event when you came back to us,
it's another point in the room time.
You're back to the same point in the room,
namely the studio,
but it's a different time,
so it's a different point in the room time.
Yes,
and Marcus,
we've been sitting here and waiting for you all the time,
so we can say that we've moved on a straight line in the room time.
But you've moved on a crooked line in the room time,
because you've moved away from us first and then back.
So if we were to draw this in the room time,
in some way,
it would be...
A curvy line that you've moved around in the time.
And the time along your line is different than the time along our line.
Very analogous in fact,
that the distance in the room is different depending on which curve you take between two points.
So there is one important difference here,
and that is that when you come back,
say that it has been,
what did I say,
a couple of days for us.
We've been sitting here waiting for two days.
When you come back,
say that it might have only been a few hours for you.
That's what it could be if you moved at a speed close to the speed of light.
The closer to the speed of light you moved,
the greater the effect would be,
that is,
the shorter the time would have been for you.
So you've moved on a crooked line in the room time,
and it's shorter than the straight line that Marcus and I have moved on.
So the difference is that the space-time has a different kind of geometry than the space.
And the fact is that one can express the core in the special relativity theory in this way,
by saying that in the space-time it is the case that the straight line between two points is the longest.
So it's the opposite of the room,
but it's still like that,
it goes back to geometry,
geometric properties.
And now Marcus thinks,
why does the room-time have that geometry?
And the answer will be that we don't know.
What Einstein discovered is that if you assume that the room-time has that geometry,
then you can explain extremely many things in physics,
which makes all modern physics today based on relativity theory and his insights on this.
But we have no fundamental answer to why space-time has this strange geometry.
Can you explain this with the distance?
It also changed when I moved fast.
Yes.
If I go at 99.99999%
of the light speed,
the distance becomes shorter.
Yes.
Why?
Then we have to ask ourselves what do you mean by the distance here?
Because in space time,
if you want to mark a distance between two points in space time,
you have to talk about at what time both points meet.
9.47 I go on a straight line at 99.999 the speed of light to
Mars. And I know,
a really stupid place for both points to move,
but we assume that they stand still.
Yes,
we do.
Exactly.
But the question is,
on your clock you can absolutely say,
now the clock is this much.
But if you're talking about the distance to Mars,
then you want to ask yourself what time zone you're considering to compare with.
Let's make an analogy.
Say you're driving on the motorway.
Okay,
you have a car in front of you.
You wonder how far the distance to the car in front of you is.
I wonder.
Yes,
and you might think it's 10 meters.
It's too short a pause.
I was going to say that.
The road is completely...
Let me try it this way.
Say that there's an explosion in the sun.
Do you see it now?
I say it in eight minutes.
Exactly!
That's right.
So if you see it now,
then you say,
it happened eight minutes ago.
And then you say,
it happened at the same time as I drank a cup of coffee eight minutes ago.
That's a concept of simultaneity.
You have connected different times on the sun with different times on the earth and said that the explosion happened at the same time I drank a cup of coffee eight minutes ago.
But I see it now.
You see it now,
exactly.
Someone who passes you and the sun in a super fast space-travel won't think that those two points are simultaneous.
And therefore,
that person will also measure another distance between...
Jorden och solen än vad du gör.
Kommer den personen att uppfatta att det sker samtidigt som Marcus ser?
Alla kommer vi överens om att det finns en händelse när Marcus ser explosionen och det finns en annan händelse när explosionen äger rum.
Och det finns en tredje händelse när Marcus dricker kaffe.
Men man kommer vara lite oeniga om vilka tids- och rumskoordinater man ska fästa på de där händelserna.
Och det är det som gör att...
The distance is different depending on who measures them.
You use different conventions for your coordinates.
How to divide the room time into room and time,
you could say.
Right.
And since the solar radiation goes in the speed of light,
it's everywhere at the same time.
But it only goes in 99.999%
of the speed of light.
then it's not really everywhere at the same time.
Yes,
that's right.
But the time before it is very short.
Exactly.
Which means that as it is connected,
the distance is also short.
Yes,
that's right.
Why didn't you say that?
Yeah,
so it's for an extra complication layer to measure distance.
It's easier to keep it to...
It's easier to keep it to just measure the time that flows on one's own clock.
Can I just ask,
because we're talking about room time,
we're talking about room and we're talking about time.
I understand how to measure time and I understand how to measure room.
But what do you measure room time in for unity?
I would say that you measure distance in room time on your clock.
As time?
Yes.
The fact is that even spatial distances can be measured as time.
And we do that when we talk about how many light years it is somewhere.
If I say that it is four light years to
Alpha Centauri,
then it means that it takes the light four years to travel to Alpha Centauri.
So I express a distance with a time.
Given the fact that the speed of light is what it is,
so to speak,
we can actually express all distances as times.
Distance between two spatial points,
like distance from the Earth to a star somewhere,
then we measure it in light years,
that is,
the time that the light takes to go there.
If it is the time that flows between two time-like separated events,
as they say,
for example
For example,
when you left the studio and came back to your studio on your journey,
we measure it with a clock,
but in both cases we can express it as a time.
Right,
and that's when my time is different.
Yes,
it's shorter.
You age less during your journey than when Marcus and I age here in the studio.
In the beginning you were a bit concerned that time is also affected by time.
of where we are.
Yes,
so what we have talked about so far is actually the special relativity theory.
But Einstein has also come up with another relativity theory,
namely the general relativity theory,
which is Einstein's theory for gravitation,
how gravitation works.
And he explains gravitation by saying that space-time not only has this geometry we have talked about now,
but also it is curved.
It has an even more strange geometry.
The extra component of the geometry of space-time explains the phenomenon of gravity.
And that means,
in turn,
that in areas with very strong gravity,
like at very heavy stars,
or neutron stars,
or even black holes,
in the vicinity of them,
space-time will be curved in such a way that
That time goes very slowly for someone who is close to the neutron star or the black hole.
So in that sense,
time also goes differently quickly depending on where you are,
how strong the gravitation is where you are,
you can say.
And it is so clear that it even gives effect if you are close to the surface of the earth or higher up from the earth.
In principle,
yes.
In practice,
no.
Yes,
you can measure the effect.
It is extremely small.
It actually has one practical allocation area,
and that is this position determination system.
You know that you determine your position via satellites.
And the satellites are on a different height than what we do.
And they also move in relation to us.
And in order to be able to...
Yes.
The whole technique is based on the fact that you can compare time here on Earth with the time on board the satellites.
And that makes both of these effects that we have talked about actually important for this system to work properly.
So you have to take into account both that the clocks go too slowly in the satellites because the satellites move,
and you have to take into account that the clocks in the satellites move faster.
than on Earth because they are further away from Earth.
Those two effects are in the same order of magnitude,
but they are not really the same,
they don't take each other out,
so you have to take care of both for this GPS system,
the position determination system,
to work.
Okay,
we have a little bit of a hunch on what time it is.
Yes,
like half an hour into the conversation and we start to land on what time and room time it is.
But that's good,
that's really the basis.
Then you walk away and understand the rest.
Yes,
this thing about traveling in time.
That's right.
Is it possible?
Yes,
if it is possible,
you will find out in the next episode,
which will be released in just a few days.
Men spännande det där sista,
om att hastighet och avstånd till jorden ger effekt på tiden i satelliter,
som ju ligger ganska nära jorden och rör sig relativt sakta.
Så då kan ni ju tänka er hur det är på längre avstånd,
som miljontals ljusår,
i höga hastigheter,
som ljusets hastighet.
Ja,
alltså jag har jättesvårt att tänka mig det.
Också lite svårt att tänka på det här som Sören nämnde,
att avstånd krymper.
when we move fast.
It's like a perfect way to make this subject even more confusing.
But now we have at least a little tip on what time is.
And we're ready for the next episode,
where we're going to talk about traveling in time.
Absolutely,
but before we learn to travel through time and space via mass holes,
we have to stick to the usual way.
Spacecrafts and rocket engines.
And then we can use gravity.
When we're going far out in the solar system,
or like with Voyager 1 and 2,
out of the solar system,
it takes a very long time if you just accelerate with the engines.
And the fuel easily runs out.
But then you can use something called a gravitational slung,
or gravity assist.
You simply take the help of one of the planets on the way out to give the rocket a little extra push.
René Laufer is...
professor in space technology at
Space Campus at Luleå Techniska Universitet.
And we asked him to explain more about Gravity Assist and what we can do with it.
Gravity Assist helps us save fuel.
And that's great,
because when we launch rockets and spacecraft into space,
the majority of what we launch into space is fuel,
basically.
Rockets are 90%
fuel.
So if we can save fuel by going somewhere,
that's great.
One great way to do this is so-called gravity assist.
So we use kind of a slingshot maneuver and we fly very close to a planetary body,
the bigger the better,
so Jupiter is wonderful actually,
and then we get basically caught by the gravitational pull from this large body and this tiny spacecraft basically is thrown like a slingshot around the planetary body and thrown with...
even higher velocity than before,
further away from that planetary body.
So that's the simple explanation.
In reality,
it's of course a little bit more complex.
It's not so simple to fly precisely and so close to a body without crashing into something or having the wrong trajectory.
But we have demonstrated this many times.
The Pioneer 10 and 11 probes showed it already.
Then the famous Voyager 1 and 2 probes.
enabled with gravity assist to do this grand tour through the gas giants of the outer solar system.
What we actually do is actually a little bit of energy transfer.
So a little bit of the energy of this gigantic planetary body while it orbits the sun is basically transferred to this tiny spacecraft.
And it has this tremendous effect because of this huge difference of mass.
Jupiter,
huge mass.
You know,
more than 100 times the mass of Earth,
something like that,
and this tiny little spacecraft that is maybe the mass of a little van or something like this.
And when you fly close by,
you transfer a little bit of energy,
of the momentum,
the energy of the planetary body moving in the solar system to this tiny little spacecraft,
and that turns into additional velocity.
So with the Voyager spacecrafts,
we have seen that this was enough to increase every time.
It flew by another planetary body,
Jupiter,
then Saturn,
then Uranus,
then Neptune,
was enough to always increase the velocity and at the end of the day get enough velocity to even leave the solar system.
And because you go so close to something that is like Jupiter,
it's so big,
it's lots and lots of gravity,
how do you leave the planet?
Well,
actually,
you are already on a trajectory that doesn't bring you into the situation that you become an orbiter of that planet.
So to get really from one planetary body to another in spaceflight,
you know,
we launch from Earth.
We accelerate enough to leave the Earth gravitational sphere of influence.
Then we fly to another planet.
And then,
again,
we do a maneuver that we basically transfer energy to...
fly from a trajectory that would basically pass by another planetary body like Mars to enter an orbit around Mars.
So there's always dedicated maneuvers that we do.
It's a decision that we do and we fire an engine and things like this.
So when we come to Jupiter and we do this the right way,
Precise navigation is the key here.
Then we don't end up in the orbit around Jupiter.
We basically come to Jupiter,
fly very fast,
and then we are thrown like a slingshot further out,
and we leave Jupiter faster than we came in.
And then we are never entering an orbit around Jupiter.
Could you do this around...
I mean,
Jupiter is big,
but the Sun is bigger.
Can we do it around the Sun?
We can,
and many people already thought about that and said,
you know,
one day when we want to have other probes,
not human spaceflight,
probes,
robotic probes,
that we want to get to the outer edges of our solar system even faster,
we should not do it the way as it was done with the Voyager probes or with flying
New Horizons to Pluto and further outwards.
We should just first fly inwards and do this gravity assist.
at the Sun and get such a huge slingshot trajectory that we are much faster at the edges of the solar system and shorten flight times.
So,
an example,
if we want to explore,
you know,
the outer areas of our solar system or even have faster interstellar probes,
then doing a slingshot at the Sun,
a gravity assist in the Sun would be the way to do.
And could we send something in,
do a slingshot with the Sun and then also Jupiter on the way out?
And
Absolutely,
absolutely.
But,
you know,
it becomes more and more complex.
So you have to plan very carefully.
Maybe these opportunities are not available every month or every year.
So with the Grand Tour,
NASA really calculated very carefully and that is a once in a career type of chance.
So the next generation can try this again,
maybe something like this.
But with the sun,
of course,
and then if Jupiter is at the right position.
So the direction where you want to go anyway,
then this is an opportunity to even gain more velocity.
There's always a body that is bigger than you or your spacecraft.
And how fast can you go?
Which speeds can you gain?
So,
you know,
in the spaceflight field,
we often like to calculate in kilometers per second.
And when we go into Earth orbit,
we need to have the minimum velocity for an orbit around Earth.
A little bit over 7 km per second,
but when we launch with rockets,
we often provide enough energy for more than 9 km per second because there are losses and stuff like this.
When we want to fly away from Earth and it's more than 11,
realistically more than 12 km per second and further down the road,
we have reached velocities that exceeded...
30,
around 40 kilometers per second,
if I remember correctly.
But at the end of the day,
it's just a matter of how close you want to get to that body that throws you outwards.
And velocities more than that are certainly a possibility.
So maybe somebody comes up with a very,
very good trajectory,
but gets very close to the sun and says,
hey,
we can do 80 kilometers per second,
100 kilometers per second.
And then...
Getting to the outer edges of the solar system gets us much faster there.
You don't have to wait your whole career to get there.
When you do this,
how do you aim?
Interplanetary navigation is hard.
There's no GPS out there,
right?
Once we leave Earth orbit,
it's a bit more difficult.
No precise navigation possible.
But we learned a lot over the last 50,
60 years.
And we are able to do this.
We use...
Like back in the days with ships,
we use optical navigation.
We look at the stars,
we triangulate.
We use help from Earth,
you know,
with ground stations that send signals that help us with navigation,
like we do this with planes.
And there are many different ways.
We even use catalogs of smaller objects like known asteroids because we know their trajectory,
their orbits very precisely.
They can help us to improve.
and make our navigation better and our accuracy higher.
So it's possible.
We have done that.
We have done that many times.
We have very precisely flew by at even very small objects,
like comets and asteroids,
at very close distances of just a few dozens of kilometers,
for example.
So
I think this is not so much of an issue.
We can do that and we have the technical means for that.
Spännande!
Jag ser fram emot kommande avsnitt,
då vi kommer fortsätta att prata helt andra rymdiga saker med René Laufer.
Jag ser också fram emot nästa avsnitt,
där vårt samtal med Sören Holst fortsätter,
och vi gräver ner oss i maskhålen.
Och i väntan på det kan ni göra en egen tidsresa,
och gå tillbaka och lyssna på avsnitt fyra,
där vi pratar mer om ljusets hastighet.
And then in episode 32,
where we talk about gravitation and black holes.
A lot of good extra repetition to listen to before the trip.
Another good thing to listen to is our music.
It's written by Armin Pendek and is also available in the background on our website,
havioaktimarsen.se My name is Marcus Pettersson.
My name is Susanna Levenhaupt.
Havioaktimarsen is made on Beppo by Rundfunk Media in collaboration with Saab.
Hello,
the program is made by Rundfunk Media.