# Minkowski

In 1895 H.G. Wells published a sci-fi thriller, The Time Machine, about a time traveler who explores the future to discover the fate of mankind.

The story begins with the hero explaining to his friends there are 4 dimensions of space – height, width, length and duration. Time, the scientist claims, is an extra dimension of space. Wells’ character was not quite correct. Space is space and time is time. But he was on to something.

Albert Einstein’s 1905 paper on relativity caught the attention of his old mathematics professor, Herman Minkowski. Minkowski dealt with problems of how moving travelers would experience a pair of events as compared to how a stationary observer would perceive them.

They would disagree on the amount of time between the events. And they would disagree on the amount of distance covered between them. We would call the amount of time difference time separation and the distance difference space separation.

If these observations were assigned distances to the legs of a right triangle, 1 for the traveler and1 for the stationary observer, Minkowski found that if you squared the distances of both legs of a triangle, subtracted them, and took the square root of the difference, you would get the exact same amount if you repeat the process with the other triangle. Minkowski called the value space-time separation- the distance of the hypotenuse.

Sound familiar? In High School Geometry we learn a^2 + b^2 = c^2. Minkowski’s formula is the same formula as the Theorem of Pythagoras – except for 1 distinction. You subtract the squares instead of adding them.

As we have said, time is not the same as space, but the mathematics can be adjusted so that both can be combined to make useful information. Thus Herman Minkowski was able to unify space and time into a 4 dimensional concept – space-time.

But what exactly is “space-time”? In the world of our 5 senses we can not describe space-time as something we experience or the lack of its presence thereof.

In 1915, Albert Einstein introduced to the world his Special Theory of Relativity. He envisioned a universe where the “nothingness” of space was part of a “something” called space-time.

Space-time was like a fabric, that could be warped by mass, like a trampoline being warped by a bowling ball. Anything within the range of this distortion would be pulled toward the large mass. This is the Einsteinian explanation of gravity.

Einstein argued that given enough mass, nearby things in motion will alter their courses –even light.

OK. Isaac Newton said moons go around planets. Planets go around the sun. Small things go around big things. Nothing new there. But light???

In 1919 astronomers observed a solar eclipse in which starlight appeared to move due to the sun’s and moon’s masses. Einstein was confirmed.

Now to recap this is what we have learned so far to help us understand what happens in stars:

1)Matter and energy are interchangeable.

2)Nothing can exceed the speed of light.

3)Electricity and magnetism are intertwined into a force called electromagnetism.

4)Space and time can be unified into a single concept called space-time, which is the true explanation of gravity.

Now is the time to use what we have learned to find out what happens inside of stars and black holes. One of the most important ideas came from a soldier in World War I.