CAN WE TRAVEL TO THE STARS?

 

   

 

Yes....... but there are a few little things that may be worth noting before you pack your suitcase.

 

Before we can even think about going to the stars, we need to consider the above questions.  In particular the first question is obviously important.  How far do we have to travel in order to get there?  Well the nearest star (out of 200 billion others) is Proxima Centauri.  This star is a reasonable 4.23 light years away.  But just how far is this I here you ask? Let me explain...  very simply, a hell of a long way !!!!

1 light year = 5.8 trillion miles, so 4.23 light years = 24.8 trillion miles or 99 million times further than the moon

To get to the nearest star we need to travel 24,877,381,030,000 miles.

If you think that Pluto is an average 3.6 billion miles from the sun, then we need to travel 7,000 times further away than Pluto.  If you then think that even at 40,000 mph it would take over 10 years to get to Pluto, we can work out that it will take 71,400 years to get to  Proxima Centauri....I hope they have in-flight entertainment.

Obviously this is not acceptable, even if you travelled for 80 years (average human lifetime) you would only have gone 28 billion miles (0.11% of the total distance).......  What you need to do is increase your speed.  But by how much?

Although impossible, lets imagine we could somehow travel at light speed.  How would we propel ourselves to 670 million mph.  We would need some sort of fuel, but which type?  Unleaded, Diesel.....not quite!

Could we use liquid chemicals like on the Space shuttle?  Put it this way, the space shuttle burns around 211,500 gallons of fuel per minute.  It burns a total of 528,616 gallons of fuel in under three minutes just to get to 3,500 mph.  To accelerate the Space shuttle to the speed of light you would need a fuel tank as big as the Sun.  If you were to use rockets that used fission (splitting the atom) you would need to carry behind you 1 billion super-tankers of radioactive fuel.  Even if we resorted to fusion (fusing two particles) which is more efficient, we would need 1 thousand super-tankers of hydrogen isotopes.

If we look a little bit further toward the star-trek side of things, there is always the ion drive or antimatter drive.  We would still need to take with us enough fuel to fill 10 coal trains, which would still require tens of thousands of tons of fuel. 

If we were to go ahead with the fusion idea, we would require 1 thousand super-tankers worth of fuel just to get there.  We would need ANOTHER 1 thousand super-tankers just to stop!  We would need a little bit of fuel to turn us around, yet ANOTHER 1 thousand super-tankers to get us home, and yet ANOTHER 1 thousand super-tankers to stop us.  

In all, 4 and a bit thousand super-tankers (1,025,000,000 tons) of fuel...  not so efficient after all.

So we have discussed that anything below light speed is really not acceptable, and getting to the speed of light is not possible...why?

 

Why can't we travel at the speed of light?

The speed of sound is around 741 mph at sea level.  The speed of light is around 670 million mph in a vacuum.  Apart from the obvious fact that you need to go a lot faster (to say the least) to get to the speed of light, why can you not cross the magic barrier of C, after all it's only a certain velocity, right?  Not quite!  The actual speed of light is nothing special, the problem lies in the way that matter behaves when accelerated to high speeds.  

Special relativity

Special relativity is the English term for the most famous equation ever written, E=MC2.  But what does this equation mean?

Put simply is means 'Energy = Mass x (light speed)2'.  The mass is measured in kg, and light speed is based on light speed in a vacuum (300 million metres per sec).  As this value for 'C' is squared, we effectively are multiplying the mass by 90,000 trillion.  This means that the final value for E becomes very very large.  The bombs that almost completely destroyed Hiroshima and Nagasaki contained just 64kg and 6kg of fissionable material respectively.  Although the bomb dropped on Nagasaki (fat man) was 10 times smaller than that dropped on Hiroshima (little boy), it was in-fact 10 times more efficient and was equivalent to 21,000 tons of TNT, compared to just 15,000 tons for little boy.  Even considering that the efficiency of both bombs were very low, each bomb was able to kill almost 100,000 people in seconds and level a large city.  This is surprising given that the efficiency of little boy detonated over Hiroshima was less than 1.4%, and just 14% for fat man.

For much more efficient weapons, a bigger and better bomb was required.  In 1952, 7 years after the 1st A-bomb was tested, the US army tested the 1st of a series of fusion devices.  Nuclear fusion works on the combining of particles to form a new heaver atomic nuclei and is around 3 times more efficient than nuclear fission.  The first fusion device called Ivy Mike produced a yield of just over 10 Megatons, around 660 times more powerful than little boy.  9 years later in 1961 the USSR carried out the largest nuclear test ever detonated measuring over 50 Megatons.  It was called Tsar Bomba....the king of bombs.

Originally designed as a 100 Megaton bomb, worries about potentially causing a global radioactive fallout plus the fact that the aircraft which dropped the device would have been blown out the sky, the USSR limited it to just under 60 megatons.  The fireball produced measured almost 130 miles in diameter, 43 times larger than the first fission weapon, and the shockwave was still being measured on its third time around the planet.  The mushroom cloud produced was over 40 miles high and windows were reported to have been broken over 600 miles way  ....quite impressive for an object just 24 ft long 

       

As well as being immensely powerful for developing weapons, special relativity has a few side effects which almost defy belief.  Although Einstein had accurately understood what these effects were, he found them so strange that he thought he had made a mistake in his equations.

These effects were... 

These are all completely bizarre, so what's happening?  The reason that time dilation and length contraction occur is because light speed is constant.  This means that no matter what speed you travel at, you will always measure a constant speed of light regardless of your relative motion or velocity.  i.e. If you were to travel at 100,000 miles per second, and you were to measure a beam of light heading your way, you would presume its velocity would measure 286,291 miles per sec (Galilean velocity addition...V = V1 + V2).  Wrong, you would in-fact measure 186,291 miles per sec.  Einstein realised that regardless of your velocity, when measuring light you can no longer use standard Galilean velocity addition, you now require relativistic velocity addition.  The difference being another term added to the standard Galilean velocity addition formulae.

Galilean velocity addition → Vtot = V1 + V2

Relativistic velocity addition → Vtot = V1 + V2 / 1 + V2 C / C2       →           If V1 = C....

                                                Vtot = C + V2 / 1 + V2 C / C2                       & C = 1....

                                                Vtot =  1 + V2 / 1 + V2 1 / 1           →   1 + V2 / 1 + V2 / 1

                                                Vtot = 1/1 = 1 = C

                                                Vtot = C......so regardless of V2        V always = C ..amazing

The shocking thing about this prediction is, that if C is constant, and you are moving very fast, as speed = distance/time...then if your speed does not change, then your time and/or distance must decrease to keep C constant!  What Einstein had discovered was that in simple terms...........if you travel very fast your time actually slows down and your length contracts relative to a stationary observer.  Worryingly this was not just a mathematical error or strange theory, and was scientifically proven in 1971.

The Lorentz gamma factor

The Lorentz gamma factor is a number by which time dilation, length contraction, and relativistic mass for a moving object can be calculated.  It is a simple equation showing that the faster an object moves, the slower its time runs, the shorter lengths become and the heavier things get.

                                                                                                                                                                       

                                                                                                                                          γ = 1/(1 - V2/C2)1/2              

 

In plain English this equation means:  Gamma = 1 divided by the square root of 1 - V2 divided by C2.

 

Where V is the velocity of the moving object, and C is the speed of light.

 

The units for V are given as a decimal relative to the speed of light C.  So if V = 10% of C, then V = 0.1...etc.  Because of this, C is given in the same units, and obviously has the value of 1.  As C2 = 12 = 1, and V2 divided by 1 = V2, the C2 component can be removed from the equation.  An example is shown below:

 

A spacecraft travelling toward a star 5 light years away at 90% light speed (v = 0.9) would be expected to take 5.5yrs to get there.  Classically it would be expected to take 5yrs at light speed, so at 90% light speed it would indeed take 5.5yrs.  Hence a round trip to the star and back to Earth would be expected to take 11yrs.  Lets see what happens when we use the Lorentz gamma factor.

 

  γ = 1/(1 - 0.92)1/2    <------ Substituting V for 0.9

 

  γ = 1/(1 - 0.81)1/2    <------ 0.92 = 0.81

 

  γ = 1/(0.19)1/2        <------ (1 - 0.81) = 0.19

 

  γ = 1/0.43               <------ Sqrt of 0.19 = 0.43

 

  γ = 2.29                  Final value

 

So our gamma factor = 2.29.  What does this mean?

 

It means that relative to a stationary observer on Earth, the clocks onboard the spacecraft (both mechanical and biological) appear to slow down by 2.29 times that on earth i.e. 1hr on Earth is only 26min on the spacecraft.  So although according to observers on the ground the spacecraft will take 11 years to get back to Earth, the lucky Astronauts onboard will only experience a period of 4.3 years.  This means that only 4.3 years will pass on the spacecraft, and so the astronauts will actually travel 6.7 years into the future.  Strangely from the perspective of the astronauts, they actually measure their time as running normally, and to them it appears that the time on Earth is running slowly.  So how can both be running slowly?  They don't.  Although they both appear to run slowly it is actually the astronauts who's time is running slowly as they are the ones moving at near light speed.  To make up for lost time, the astronauts actually experience length contraction, so the star now becomes just 2.18 light years away and so takes just 2.4 yrs to reach.  This means that although they see time on Earth as running slowly (which it isn't) their trip now takes just 4.8yrs while 11 yrs has past on Earth.....they are in for a shock when they get home.

They also observe the mass of the spacecraft as being 2.29 times heavier than it was at rest, so a 5 ton spacecraft on Earth will weight 11.45 tons when at 90 % C.

 

However.....special relativity allows for even stranger things to be possible.

 

The pole-barn paradox (advanced)

important information is highlighted in red

 

The problem with relativity is that everything is.....well...relative.  This means that although somebody on Earth may measure one thing, people aboard a space ship will measure something else.  Neither are wrong, but both answers do not make sense.  So who is right?  They both are.  Still confused?  Let me explain with a famous problem...the pole-barn paradox.

                                      

According to Wikipedia, a Paradox is "an apparently true statement or group of statements that leads to a contradiction or a situation which defies intuition".  That's a good way to describe this problem.  So what is the problem?

 

Imagine you have a barn in a field which is 10m in length.  On either end of the barn are doors which can open and close very fast.  Your task is to fly through the barn on a pole.  The first door (front) is designed to close as soon as the back of the pole has entered the barn, and the second door (back) will open as soon as the front of the pole almost touches it.  The idea is to get the pole inside the barn and let the back door close before the front door is opened, momentarily trapping you inside.  The only problem is that the pole is 20m in length.  Surely this is impossible, how do you get a 20m pole into a 10m barn?

 

 

Easy....accelerate the pole to near light speed.  As we said earlier, an object in motion will undergo length contraction.  So how fast do we need to accelerate the pole in order for it to measure less than 10m?  We need a gamma factor of more than 2 in order for the pole to be more than half its initial length (10m in its rest frame).  From the example given above, we know that a gamma factor of 2.29 is possible if a velocity is 0.9 C is achieved.  So if we accelerate the pole to 0.9 C the pole will measure 20/2.29 = 8.73m....perfect.

 

 

So is that it?  No.  So far we have only viewed the pole from the perspective of the person inside of the barn.  This is where the word relative becomes very important.  It is important to note a number of things:

 

1:  According to the person in the barn, the barn is 10m in length, and the pole is 8.73m in length (because the pole is moving relative to the observer).  In this frame there is no problem.

2:  According to the person on the pole, the pole is 20m in length, while the barn is only 4.37m in length (because according to him, he and the pole are stationary and the barn is moving toward him at 0.9 C...so 10m/2.29 = 4.37m).  Big trouble.

 

 

From the perspective of the barn observer, the pole and its rather insane rider successfully make it through the barn, allowing the back door to momentarily close completely enclosing the rider in the barn with over 60cm to spare on each side.  However, according to the pole rider, the barn is now more than half the size is was originally, over 4 times shorter than the pole he is riding, strangely he does make it through, so how can he fit inside the barn?

 

We must now replay the events from each perspective in detail, and in chronological order.

 

Barn observer

 

The front of the pole enters the barn at t = 0

The back of the pole enters the barn and the front door closes at t = 8.73m/2.7 x 108ms-1 = 32.33ns.... (note: 2.7 x 108ms-1 = 0.9 C)

The back door opens and the front of the pole leaves the barn at t = 10m/2.7 x 108ms-1 = 37.03ns

The back of the pole leaves the barn at t = 32.33ns + 37.03 = 69.36ns

 

As we can see there is a difference of 4.7ns between the back of the pole entering the barn and the front of the pole leaving the barn.  Hence, as long as the doors can close and then open in less than 4.7ns, there is no problem.

 

Pole observer

 

 

The front of the pole enters the barn at t' = 0.......(we use t' instead of t so as to not confuse the two reference frames)

The front of the pole leaves the barn at t' = 4.37m/2.7 x 108ms-1 = 16.18ns (time required for front of pole to pass through the barn)

The back of the pole enters the barn and the front door closes at t' = 20m/2.7 x 108ms-1 = 74.07ns

The back of the pole leaves the barn at t' = 16.18ns + 74.07ns = 90.25ns

 

Now, if we include the information from the barn observer into that of the pole observer we view the following:

The front door of the barn closes at 32.33ns (which according to the barn observer is when the back of the pole entered the barn).  However according to the pole rider, the front door closed at 16.18ns due to the shortened length of the barn.

The back door opens at 37.03ns according to the barn observer, which appears to happen in 16.17ns for the pole rider due to time dilation, opening 20.86ns before the pole reaches it from the pole riders perspective.

 

So....although the pole rider observes the font doors closing earlier, he also observes the back doors opening earlier.  And, as physics would have it, the back door opens before the front door closes....so the pole is never trapped.  The difference being just 4.71ns, almost exactly what was calculated for the barn observer.......easy (honest)

 

To illustrate this in another slightly easier (but graphically more complicated) way, we can use a space-time diagram. 

 

 

If your head is hurting as much as mine, you will not want me to go through this.  But the important thing to note, is that a line joining events E1 and E2 will never touch the dark black line (the doors as observed by the barn observer).  This shows graphically...I hope...that in the pole riders perspective (the diagonal stripe) that the doors are never both closed....allowing safe passage through.