Imagine how time flies……
On the 20th of August, 1977, NASA launched the first and only spacecraft to have visited the two “ice giants” planets Uranus and Neptune. The spacecraft was named “The Voyager 2” and it was set into motion 16 days before “The Voyager 1”. Its expedition was to explore each of the outer planets and take real life photograph and other calculations. It took the spacecraft 12 years to get to Neptune which was its final destination in the Solar System. It has now been voyaging in the direction of a star called Sirius, leaving the Solar System at a speed of 10km/s. Sirius is a relatively near star, about 8.6 light years away. It is estimated that Voyager 2 should be near the star on a journey lasting 300 000 years.
The laws of relativity restrain anybody or object that has mass from traveling faster than the speed of light, a constant approximately about 3×108 metres per second. But the same laws also say that a starship could get to Sirius in a shorter time than you would calculate in the usual way. But, If we could succeed in defying the laws of physics and travel at the speed of light, we could journey to and fro Sirius in 17.2 years. And if that should happen, then, relativity theory will reveal that our starship clock would record a time interval of zero!
But how quickly could we do it, traveling at a speed close to the speed of light? The answer is a factor of not only on how fast the starship goes but also on the exact location of the clock that measures the time. The maths is very simple albeit the ideas are very unusual. Assume NASA wants a starship to land in Sirius 8.6 light years away in just 9 years. To achieve this, the ship would have to travel at a speed of 0.96c, that is, 8.6c/9.0. Relativity treats distance and time as almost identical, and a version of Pythagoras’ theorem can be used to calculate the time i.e
Putting in the values, we get:
This gives the ship’s time interval of 2.7 years.
The Mission Control Center back at Houston would have aged 9 years. For a round trip, the astronauts would be 5.3 years older, the NASA ground team 18 years older. This is the simple explanation of the famous ‘twin paradox’: a twin in the spacecraft would come back younger than her brother back at NASA. It is a paradox because it is hard to explain why the effect is not symmetrical, which is, why each twin is younger than the other!
Source: Wikimedia, Minkowski; CC BY-SA 3.0
My idea of writing this post
This post is meant to serve three purposes. The first of which is to make it a sequel to my last post on moving through space and time and the second is to try as much as possible to answer
’s question on the ambiguity of time travel as best as I can, although some discussions would come before then. The third purpose is to explain the early 20th-century revolution in our understanding of space, time and movement caused by that famous “Old man” Albert Einstein. Using just two uncomplicated ideas, Einstein was able to prove that time and distance are somehow connected to one another. This led to simple deductions that seemed to be inconceivable paradoxes. No massive object can move faster than light. Time for a moving body passes more slowly than for one that’s not or at rest. And it is practically unattainable to say which one is at rest. Moving objects appear smaller. Energy and mass are comparable using the relation E = mc2. Light rays are distorted by gravity. Time elapses more slowly near a gravitational mass than in emptier space. Etc.
We will have to cogitate hard to effectively deal with all this. Certainly, we will encounter the concept of a “thought experiment” and also learn about the basic experiments that strengthen this still bizarre view of the Universe. Those experiments are none other than the Michelson-Morley experiment, and the extra Life of muons. But, in the meantime, let’s try to understand what space and time entail before we go deeper into the discussion.
SO, WHAT IS SPACE AND TIME ALL ABOUT?
My previous post explains the tight relationship that occurs in modern physics between distance and time, and we could observe that the most important connection is the speed of light, c. We measure distance in the unit of the metre. And, even the metre itself is established on the distance light travels in a unit of time. I’ll like to write more on this fundamental relationship.
The two principal ideas
Einstein’s special theory of relativity was built using two basic ideas otherwise known as “Postulates”. They are:
• The speed of light is constant
• The laws of physics are similar for any two different systems (e.g aeroplane, laboratories) that move or change their position relative to each other at a constant speed.
Although, the first postulate is difficult to stomach it’s still relatively easy to comprehend and work with, while the second is more delicate and difficult to analyze or even describe. But, don’t be fazed, more “light” is coming on it later.
What is the idea behind the Speed of Light?
The common idea that the speed of light (in a vacuum) is a constant for all observers seems unreasonable. It says that no matter how fast you travel, light still blazes away from you or maybe towards you and it’s at the same speed of 2.997 924 58 x 108 m/s. If you are a fast rider, you can drive faster and catch up with the driver at your front. But notwithstanding how fast you race your spacecraft, you can never even reach the light wave in front. Light defies the normal laws of relative Motion. So, this was what led Einstein to name his theory a “principle of relativity”.
Source: Wikimedia, public domain
The effect of the principle is that distances, time intervals and the time at which an event happens will be contrasting for observers who travel at a constant velocity with respect to one another. This post will talk more on such similar occurrences where objects are traveling at constant velocities.
In time dilation it is observed that actions take longer to take place in objects that are moving relative to us. The effect is most obvious at relative speed very close to the speed of light. Time dilation opens on to some other effects such as objects shrinking in the direction of travel while the mass increases. An effect which explains “the Lorentz contraction”. Let’s start by studying the idea of time.
A QUICK HISTORY OF TIME
The concept of time appears to be very elemental to Einstein’s relativity. So, I will start by reminding us of some characteristics of time and its measurement that we probably fail to appreciate.
Time and Clocks
Clocks perform basically two functions. They are useful in telling us the time of the day and also for describing a time interval. In the early 17th century, an idea surfaced, shortly after the automatic clocks were made better and widely accessible. The idea was that the clocks should be used to measured things that flowed steadily, as described by Isaac Newton thus and I quote:
>Absolute, true and mathematical time, of itself, and from its own nature, flows equably without relation to anything external.
Newton had defined a kind of clockless time. But it doesn’t work. Then whose time is it?
A muon is a very small particle of matter created in a place that witnessed an energetic collision, for example, a collision in a particle accelerator. A muon can also be caused by cosmic rays. It is a very fast but highly unstable particle, having a half-life of about a millionth of a second. But when particle physicists study muons, they found out that their lifetime is longer. So, the external observer and the high-speed muon seem to encounter time at a different pace.
Setting a Clock
A Clock is anything that can be used to determine time. Traditional clocks are usually made of a pendulum or a vibrating quartz crystal. But, when we are considering the measurement of very long times like the Earth, then the half-lives of radioactive substances can be used. The half-life of a beam of muons can also report the time. The radioactive material and the beam of muons are sorts of clocks. But how can we actually compare clocks?
Source: Pixabay, darksouls; CC0
Let’s assume that watches and clocks could easily be fixed to microsecond accuracy. Assume you check your watch by looking across the town square at the mall clock. If it says ten o’clock exactly and your watch agrees exactly, you will be happy. But do you take into consideration that the mall clock is at a distance of100 metres from you? Do you know that when you see the town clock at ten o’clock it is already ten o’clock + (100/c) seconds, where c is the Speed of light? So, that means you don’t know your wristwatch will be slow by 0.3 microseconds. If you set your watch by the radio time signal beeps, it might be slower by far more.
Taking, for instance, The National Master Clock in England which is at Rugby, Warwickshire. Its signal for ten o’clock would have to travel to the radio station, then to you let’s say 500 km altogether. Measured precisely according to this signal, your watch would be slow by 1.7 milliseconds. This is quite a whole lot of time by the standard, for example, of the clock in a computer running at 100 MHz which simply measures time to an accuracy of 10-8s.
But it’s no problem to a person looking for utmost accuracy. If you know how far you are from the master clock, you can smartly calculate the correction to ensure that your watch tells the same time of day. Besides, no matter how fast or slow the signal or process that ‘carries’ the time, your watch could still be an accurate determiner of time intervals. But, problems would start to occur when clocks begin to move, relative to one other. Now, let’s briefly ponder about moving clocks with respect to the law of physics.
MOVING CLOCKS AND MOVING FRAMES OF REFERENCE
Before I proceed, have a quick reminder of relativity and frame of reference from my previous post. In a nutshell, a reference frame can be as simple as just you, your room and your measuring instruments. About four hundred years ago, Galileo realized that he could not show beyond doubt whether the Earth was moving or standing still by merely making measurements of objects traveling about on Earth. The example he used was that of a goldfish bowl in a ship’s cabin. The fish moved about the container in exactly the same way whether the ship is sailing or not (so far the ship is sailing at a constant speed on still water). The movement or direction of the goldfish or water in the bowl can’t give you a clue about the movement of the ship. To know the direction of the ship, you would be compelled to look out through the porthole at the shore and then have to imagine that it is the ship and not the shore that is really moving.
Imagine you are lying on a bed and drop your book on to it at a distance of a few centimetres. It should fall directly on where you let it go. Exactly the same would happen if you were sitting or reclining in an aircraft moving at a steady speed where you and the cabin are the reference frame. But from a reference frame outside yours, dropping the book would be seen as moving sideways as well as falling down. The movement of the aircraft is attaching a sideways motion to the book. This is simply in accordance with the laws of mechanics which implies that “speeds do add up”.
Why does light not behave like pens or any other form of matter?
The unusual fact that sprang up towards the end of the 19th century was that light does not behave like falling pens, with a distinguished movement that’s different in a manner corresponding to the frame of reference. Neither does it behaves as bullets shot from a moving gun. For instance, if a gun is shot while coming in the direction of a stationary target. The bullets travel faster to the target than if both the gun and target are stationary. This conforms to the ideas of Galileo and Newton, that any object in a moving reference frame has the speed of the reference frame of the gun’s bullets in addition to any extra speed of its own.
Some researchers thought that light would act like objects and gain extra speed when the light source and the observer were moving towards one another kind of. But in spite of very meticulous and painstaking measurements, the experiments all showed otherwise.
Albert Michelson and Edward Morley actually conducted an experiment on the behavior of light but they both arrived at a null result; a type of result that refutes the starting assumption. The consequence of that null result is as follows: If you are traveling in a spacecraft at half the speed of light and projects a light beam ahead of you, you would quantify the speed of the light as c, as you would expect. But c would also be the speed calculated by any other observer traveling at any other constant speed relative to your rocket. Compare this with tossing a pen towards the front in a train.
For the pens: pen speed, vp plus train speed, vt , equals (vp + vt)
And for the light: light speed, c, plus spacecraft speed, 0.5c, equals c
This is illustrated in the figure below.
The interpretation of this null result was overwhelming and life-changing. Even its explanation was one of the greatest landmarks in physics.
In my next post, I shall be discussing more on The Michelson-Morley's experiment on light behavior and some other interesting parts of Einstein’s theories. Till next time, I remain my humble self,
Thanks for reading.
REFERENCES
1. What is the difference between moving through space and moving?
2. What Does Moving Through Space-time Mean?
3. Relativity abyss.uoregon.edu › lectures › lec06
4. Einstein's Theory of General Relativity
5. Theoretical physics: The origins of space and time
6. Time in physics
7. Spacetime
8. Space-Time - Special and General Relativity
9. Space-time physics
10. The Voyager 2
11. Newton's Principia (1846).djvu/83 - Wikisource
12. Michelson–Morley experiment - Wikipedia
13. Twin paradox - Wikipedia
14. Collins Advanced Physics by Ken Dobson, David Grace and David Lovett pg 459
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