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# Relativity/Relativity of length

Question
QUESTION: I've been reading a book of essays on relativity and most of them mension that if something travels half the speed of light it appears half as long to a stationary viewer, but this latest essay says that while say a plane were to travel at the speed of light its length would be undetectable but somehow it would maintain width and height. Why wouldn't all dimensions decrease during the high speed? Have all these things been proven?

ANSWER: James, first I have to explain what relativity means:

Suppose Main Street runs north and south and you are 1 block north of me. Suppose an eagle lands in the road half-way between us. Where is the eagle?  You say south a half-block.  I say north a half-block. Who is right?  You or me?

Obviously both of us are right. The eagle is south with respect to you AND north with respect to me.  Position is "relative" to your "frame of reference".

But how many eagles are there?  We both say one.  Number is not relative; it is "absolute."

Einstein was writing about motion, not position.  Suppose you are riding a bicycle south on Main Street and I am riding south also but slower. The eagle takes off south ahead of us a block away from the point at which you pass me.  The eagle flies at 20 miles per hour with respect to the road;  I am pedaling 5 mph, and you are pedaling 7 mph, both with respect to the road.

How fast is the eagle flying with respect to (w.r.t.) you? 13 mph. How fast w.r.t. me? 15 mph. This is easy stuff known already to Galileo five hundred years ago.

Einstein blew everyone's mind in 1905 when he claimed Galileo was wrong! The eagle is travelling a very, very tiny bit slower than 13 mph w.r.t. you and another different tiny, tiny bit slower than 15 mph w.r.t. than me.  And both numbers are right!!

I would have to write you a book to explain why Einstein is right, according to modern physics, but only kooks and amateur physicists disagree with him today.

Back to your airplane. You, standing on Earth, see it flying overhead at 500 mph w.r.t. the Earth.  The plane has its normal length w.r.t. itself.  We call that its rest length. It is shorter w.r.t. you, standing on Earth. Again the amount is microscopic at 500 mph.  Both statements are true at the same time.  Length is relative to your frame of reference, particularly your velocity.

The amounts are tiny at speeds we can see. Galileo was good enough for any human purpose. But at the speed of light, 186,000 miles per SECOND, the length shrinks to zero.  That cannot happen, however, because only light can travel that fast.

As Arnold Schwarzenegger is supposed to have said, "Hear me now and believe me later."

---------- FOLLOW-UP ----------

QUESTION: Yes I realize that matter can't reach the speed of light, but my concern  is the apparent decrease in length of an object as it gets near the speed of light and why it only affects one of thred dimensions at a time. Why not decrease the entire size? I am somewhat in doubt that the first two dimensions exist so I am interested to know how this phenomena would work.

I am sorry that I did not get any e-mail about your follow-up question and just noticed it now.

Only the length is shorter w.r.t. the earth below, because that length is parallel to the velocity of the plane.  And the length is still the rest length w.r.t. the passengers, since the plane is not moving at all w.r.t. the passengers. Crosswise to the plane's velocity, it is not moving at all.  Hence the width and height of the plane are the same w.r.t. Earth AND the passengers.

It takes a long time to learn the "why" of relativity.  So don't worry if it seems contradictory.

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.