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# Relativity/Relativity, defining the constant on something which is not

Question
Hi there!

Some time ago while sitting in class at the University I had a random thought which has truly boggled my mind. The speed of light is constant, according to relativity, and time is on the other hand not constant.
Speed is defined as distance per time.

My question is therefor: How can we define something constant on something which is not?   Can the speed of light (given our definition) be altered? or does distance (space) also distort in the same manner as time?

Yours truly

Lars, I must clarify what it means for time to be "relative".

Time intervals are measurable quantities that characterize the interval between two events, along with the three spatial variables. Given two events and a frame of reference, the time coordinate of each is a certain number, just as the space coordinates are.  For the two events and the frame of reference, the coordinates are fixed constants.

But one can change the frame of reference. Given a second frame of reference, the four coordinates of the two events are again constants, but different constants. One can calculate their values in the second frame from the values in the first frame by use of the Lorentz Transformation Equations. It is not a problem that the coordinates are not the same in the two frames.  You would not expect the space coordinates to be the same.  You might expect the time coordinates to be the same if you were Isaac Newton, but today we know that they are not.

When you measure the speed of light, you get the same result no matter what inertial frame of reference you use. That was a surprise in 1905. That is not true of the difference in the coordinates of events compared between the two frames of reference. In the case of a measurement of the light speed, it happens that the change in the difference of space coordinates matches the change in time coordinate so that the calculated speed comes out the same. That is a mystery to us humans, but we physicists have to get used to it.

Our intuition is based on our experience, and none of us has experience in daily life about the speed of light. Nature does not have to obey our intuitions! What we measure is our only way to the truth.

Ben
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Very good answer. Thank you!

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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