Einstein's theory of relativity is not easy to understand because it defies common-sense, and does not apply in obvious ways to our daily life and experiences. For this reason I have decided to use the common "twin goes on a fast space voyage" scenario without the scientific jargon. This is not a proof of the theory, just a description of how it works.

I have an animated sequence of all the images below to give an idea of what happens over the journey.

Relativity will become part of our daily life eventually. For example, NASA is designing now (1998) a craft to travel to Mars, launched from a planned space station, Alpha. This craft is intended to travel at an average speed of 1/100 the speed of light with a maximum speed of around 1/80 the speed of light. Even at 1.25% the speed of light, the effect of relativity needs to be taken into account in communicating with the craft.

Firstly I must credit Paul Davies, whose example I have expanded upon. Paul is a talented Professor of Natural Philosophy at the University of Adelaide, Australia. He has written an excellent series of books published by Penguin on the topics of time, space, the cosmos, the start and end of the universe, and so on. The 'thought experiment' here is from his book 'About Time'. I heartily recommend these books to you if you're interested in a far more authoritative account of the universe than you will find here.

I would also like to thank Paul Alan Cardinale for his help and patience in correcting a serious error with my initial time calculations, his tables to clarify what each twin sees and can calculate, and for adding some valuable "Relitavistic Tidbits".

The Scenario

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Ann and Bob are twins on Earth, and Bob visits a star 8 light-years away, stops for an instant, then returns home to Earth. All the time, he travels in a super-rocketship at a constant 240,000 kilometres per second (80% of the speed of light).

For the sake of the example, we assume that the acceleration is instantaneous, although of course these g-forces would crush any mortal. We also ignore any movement of the Earth (which is truly trivial compared to a star 8 light years away).

The twins are each equipped with a clock and powerful telescopes so they can view each other's time. For the sake of interest, an obliging alien has placed a clock on the star synchronised to Earth time, which can be viewed both by Ann from Earth, and Bob during his space flight.

Please read this important concept!

It is actually completely irrelevant to compare Ann's and Bob's times over this journey, as if we could be everywhere in the universe at all times to be able to observe. What Ann and Bob each see at these times are different, and even what they calculate about each other's times (knowing Einstein's formulas, the speed of light, etc) will be different!

To put it another way, observers separated by large distances, and moving relative to each other, will calculate different actual times and rates of time for each other. "rate of time" is how fast they see and calculate each other's clock changes compared to their own.

Also, they can only guess when calculating what each other's "now" might be like. They will not be able to confirm that their calculations were correct until much later when light has had time to travel from each person's location to the other.

The pictures below show how meaningless it is to compare these events when they are far apart and moving. Nevertheless, I have chosen to present it this way, because I think that most readers will want to understand things like: "Where is Bob when Ann sees him arrive at the star?" and "What does Ann see when Bob stops at the star?"

Before Bob Leaves

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Here is what the twins see just before Bob departs on the 1st of January in the year 2000. The clocks are "year clocks", showing 2000 for January 1, 2000 (so 2000.5 would be July 1 2000, etc). I have shown pictures below at various times through Bob's journey.

click here for an animated sequence

Both Ann and Bob are stationary on Earth, and read the clock on the star as 1992. Remember, this clock is showing Earth time, and it takes light 8 years to travel from this star because it is 8 light years away. They both see the star as it was in the earth year 1992. The distance of this star in kilometres is:

At each stage of the journey, I have shown a picture of what each person sees, with some text to describe some of the interesting points. Each section also has an more details link so you can see a table to compare the difference between what each person sees and calculates about the other.

As Bob Leaves

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Here is what the twins see at the instant Bob departs on the first of January in the year 2000.

click here for an animated sequence

Notice that Bob is now travelling at 240,000 kilometres per second. This is 80% of the speed of light (which is nearly 300,000 kilometres per second). 80% of the speed of light corresponds to a time-space dilation factor of 60%. That means that they each calculate the other's time to be passing at 60% of the rate of their own time.

To both Ann and Bob, their own time will pass normally. Bob in this case will not see his watch moving faster or slower than he thinks it should. He is in his "own time" and it will pass normally; it is only his view of Ann's Earth time that will be different.

The other difference is that the space between Earth and the star is reduced to 60%. Note that this distance does not just appear to be less, it really is less. Of course, the star does not physically move, space is warped just like time. Bob's perception of the size of the rocket ship is also normal, because he is travelling with it; it is only the space through which he travels that is contracted.

Remember, that Bob perceives his own time passing at a normal rate. At 240,000 km/sec he will expect to arrive at the star in 6 years. Just as this speed reduces the time Ann sees pass on Bob's rocket ship over the entire journey, it also reduces the distance to travel for Bob.

More details here

Bob Halfway to the Star

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Here is what the twins see in Ann's Earth year 2005, and Bob's rocket year of 2003.

click here for an animated sequence

There are 3 things that affect how you see time on distant objects:

• It takes time for light to travel from the object to you. In this example, Bob and Ann synchronised their times when he left, so Bob knows what the Earth time was in his past, and can use this to calculate what he thinks it ought to be during his journey.
  
  
• If you're moving, the rate that time advances on a distant object changes, due to the Doppler effect. It appears to run faster when you approach the object, and slower when you travel away.
  
  
• Also if you are moving, relativity reduces how fast you see time pass on other objects.

The combination of these three effects determines how we calculate the actual time and aging rate of other objects.

Notice that they see each other having "time rates" slowed to 33%, and each person's view of the other is delayed by the time it takes light to travel between them. This delay means that at Ann's 2005, she will see the rocket in the position it was when light left it. Ann sees Bob's rocket 2.2 light years away, showing the time as 2001.7.

At Bob's 2003, he sees his position halfway between the Earth and star. He can now see that the clock on the star actually is synchronised with Earth time, because they both show the same time: 2001. At the halfway point, it takes light the same time to reach his rocket from both Earth and the star (regardless of whether he is moving or not). During his 3 years travel so far, he has seen the Earth clock running at 33% of his own rate, and the Star clock racing ahead at 3 times his own rate, from 1992 to 2001.

More details here

Bob Arrives at the Star

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Now Bob has actually reached the Star, and is still travelling at 80% of the speed of light towards the it. It took Bob only 6 of his years to get to the there. In Ann's time 2010 she sees Bob 4.4 light years away from Earth, with the rocket time showing 2003.3.

click here for an animated sequence

More details here

Bob Stops at the Star

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For the sake of this example, Bob only stops for an instant to check all the times and distances before he returns home again.

click here for an animated sequence

Now that he has stopped, Bob sees both the Earth clock and the Star clock advancing at the same rate as his own. He sees the Star time as 2010, and the Earth (being 8 light years away when he is stopped) showing 2002.

Even though the diagram shows that Bob now sees the Earth 8 light years away, the Earth or Star have not moved, it is the space between them that has increased (that is, it is not contracted).

Ann still sees Bob on his way to the Star, 4.4 light years away with the rocket clock showing 2003.3.

More details here

Bob leaves the Star

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Bob is still at the star, but travelling back towards Earth at 240,000 km/second.

click here for an animated sequence

Now that Bob is travelling away from the Star, and towards the Earth, he sees the Star clock advancing at 33% of his own rate, and the Earth clock advancing at 3 times his own rate. Also, because he is moving at 80% of the speed of light, the Earth is now 4.8 light years away instead of 8.

More details here

Bob Halfway Back from the Star

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Now Bob is actually half way back, but at Ann's time of 2015, she still sees Bob on his journey to the star, 6.7 light years away. She will not see Bob at the half way point on the return journey until Earth year 2019.

On the journey to the star, Bob has seen the Earth clock running at a third of his own time rate (due to the time it takes light to travel this distance, and the Doppler effect of him moving away from the Earth). On the way back, he sees Earth time running 3 times faster than his own. He knows from the relativity formula that Earth time is running at 60% of his own rate during the entire trip (ignoring his brief stop at the Star).

click here for an animated sequence

Bob is now halfway between the Earth and Star, and can again confirm that the Earth and Star clocks show the same time at the same time: 2011.

More details here

Ann Sees Bob Arrive at the Star

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After 18 of Ann's years, she finally sees Bob arrive at the star. Ann sees both the rocket and the Star 8 light years away, with the rocket clock showing 2006, and the Star time showing 2010. Remember this is exactly how Bob saw the rocket and Star times when he arrived. Ann is correctly seeing this as is was, and it has taken 8 of Ann's years for this image to reach Earth.

click here for an animated sequence

This is not a special time for Bob, who is by now well on his way home.

More details here

Ann Sees Bob Stopped at the Star

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Ann also sees Bob stop at the Star for an instant. The only thing Ann sees change is the rocket's time rate is now the same as her own, and no longer advancing at 33% of her own rate, because the rocket is now stopped and not moving away from her.

click here for an animated sequence

More details here

Ann Sees Bob Leave the Star

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This time, the only change Ann sees is the rocket is now heading towards her at 80% of the speed of light, and its time is racing forward at 3 times her own rate.

click here for an animated sequence

More details here

Ann Sees Bob Halfway Home

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After 19 of Ann's years, she sees Bob halfway home. Of course, Bob will actually arrive home in 1 more of Ann's years. Ann sees the rocket time showing 2009, and still advancing 3 times faster than her own.

click here for an animated sequence

More details here

Bob Arrives Home

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And finally, Bob arrives back home! In the picture, Bob is still moving at 240,000 km/sec towards Earth, so they still see each other's time rates running 3 times their own.

click here for an animated sequence

More details here

Bob Stops at Home

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When Bob stops moving, and the twins are together again in the same time and place, they will see that on average Bob's rocket clock has been running 60% slower than Ann's Earth clock, and that Bob has actually only aged 12 years compared to Ann's 20. Bob or Ann have not been "short-changed" in their life; Ann has lived 20 years while Bob was living just 12.

Notice that they both measure the same average speed of Bob's journey. Ann on Earth sees that Bob has taken 20 years to travel 16 light years, while Bob sees himself taking 12 years to travel 9.6 light years. Both give the same answer of 240,000 km/sec, because Ann sees Bob's time run slower by the same factor that Bob sees distances reduced.

click here for an animated sequence

Now that they are finally in the same place at the same time (and not moving in relation to each other), they can agree again on what each other sees and calculates.

More details here

Summary

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Bob and the rocket have aged only 12 years while Ann and the Earth have aged 20 years.

Just after he left, he saw Ann's clock was advancing at ¹/₃ normal. Six years later he saw Ann's clock at 2002. When he turned around he saw Ann's clock advancing at 3× normal. Six years later, he saw Ann's clock at 2020. Half the time, he saw Ann's clock running at ¹/₃ speed, and the other half he saw it running at 3× speed; that averages out to ⁵/₃ normal.

(⁵/₃) × (12 years on Bob's clock) = (20 years on Ann's clock).

Just after he left, Bob knows his speed relative to the Earth, and calculates that Ann's clock advances at 60% of his own rate. Six years later he calculates that Ann's clock shows 2003.6. When he turns around, he calculates that Ann's clock jumps ahead by 12.8 years to 2016.4, and as he returns, he knows it is again advancing at 60% of his own rate. Another six years later, he calculates Ann's clock shows 2020. So ...

(60% of 12 years on Bob's clock) + (12.8 year jump at turnaround) = (20 years on Ann's clock).

Ann sees Bob's clock running at ¹/₃ speed for 18 years, then running at 3× speed for 2 years. This gives an average of (¹/₃ × 18+3 × 2) / 20 = 0.6 (i.e. 60%).

(60% of 20 years on Ann's clock) = (12 years on Bob's clock).

Ann calculates Bob's clock running at 60% of her time rate for 20 years.

(60% of 20 years on Ann's clock) = (12 years on Bob's clock).

"How can people age different amounts of time, then meet together later in the same place and time?"

Even if you've understood none of the above, the simplest answer I can give is that travelling at high speed changes how fast you see time pass on distant objects.

For this example, Ann who stays on Earth sees Bob's rocket time progress at ¹/₃ of her own rate for 18 years while she sees it flying away from Earth. She then sees the rocket's time run 3 times faster for 2 years while watching it return to Earth.

In the rocket, Bob sees Earth time progress at ¹/₃ of his own rate for 6 years while flying away. He then sees Earth time progress 3 times faster than his own for another 6 years while returning to Earth. The twins' times are different when Bob returns because Ann has seen Bob's time running slower than her own on average, while Bob in the rocket has seen Earth time running faster than his own on average.

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