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# Relativity/Special Relativity

Question
An alien from a distant space but the same time as Earth is approaching Earth at 0.9c (or any other fast speed) with respect to Earth. Earth is the reference frame in this case. Using Special Relativity, the time dilation is about 2.29, and hence the alien experiences time at a slower rate than Earth. When Earth traveled 1 unit time, the alien is not seen because it is at a different time and space. When Earth traveled 2.29 unit time, the alien reached Earth at 1 unit time. Question: How is it possible that the alien reached Earth at 1 unit time, but the Earth did not see it when it was at 1 unit time? (Parallel universes cannot be the answer)

Einstein's first new result in his famous 1905 relativity paper is that the concept of simultaneity is not absolute but is relative. Thus when you say that the alien's time is the same as Earth's time, that is true only in one frame of reference and not in another frame of reference moving with respect to the first.

Suppose that the alien synchronizes his clock with a clock on Earth at the start of his journey.  One hour later (by his time), the Earth clock will read less than 1 hour.  By Earth time, however, one hour later than the start, the alien's clock will read less than one hour.

By Earth time, the alien's clock runs slow. At Earth time 2.29 units, the alien clock reads 1.
By alien time, the Earth's clock runs slow. At alien time 2.29 units, the Earth's clock reads 1.  The same kind of thing is true of distances. By alien meter sticks, the distance to earth is L., while by Earth meter sticks, the distance is 2.29 L.  The same thing is true of speeds. By alien reckoning he is not moving at all; the Earth is moving; by Earth observers, it is the other way around.

The answer to your paradox is in your last sentence: The alien reached Earth in 1 unit of alien time because his journey was for distance L by his meter sticks; but he reached Earth in 2.29 units of Earth time and covered 2.29L units of Earth distance.  When he arrives, their clocks will show very different readings. Not only that, he will be younger than his twin brother who lives on  Earth.

If this seems strange to you, join the crowd! It is strange!  But measurements have proved it correct.  Nature understands it, even if we do not.

The alien's history is not symmetric with his brother's history.  He underwent a great acceleration and then deceleration.  His brother did not.  It makes a difference. Unlike velocity, acceleration is not relative;  it is absolute. The furniture on the space ship may be damaged by the acceleration; no furniture on Earth is damaged.

Relativity

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#### Uncle Ben

##### Expertise

I can answer questions regarding Einstein's Theory of Relativity, particularly in Special Relativity. I will not answer homework questions or mathematical problems that require special symbols.

##### Experience

I have taught physics at the college level, undergraduate and graduate, for many years including Special Relativity. I have taught at Johns Hopkins, Case-Western, and MIT. I have also served as a staff member of the Commission on College Physics, which was supported by the National Science Foundation to recommend improvements in the curriculum of college physics departments in the US. I am also the author of a textbook titled Vector Calculus, which was used at MIT in the teaching of electromagnetic theory and relativity. My research interests were mainly in solid state physics, especially the properties of metals at low temperatures. I am listed in the publication known as American Men of Science.

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I have dozens of papers published in the Physical Review and in the American Journal of Physics.

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I hold a Ph.D. degree in physics from the Johns Hopkins University.

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Johns Hopkins University, Case-Western Reserve University, Massachusetts Institute of Technology, Empire State College, Georgetown University, Commission on College Physics, and UNESCO.