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Special Relativity - Explained Fast

Special Relativity - Explained Fast

Albert and myself are standing by the railway tracks. He just came over to show me his new high power engine.

It looks impressive.

But then Albert pulls out a ruler. He asks me to measure it.

I have a device that can accurately measure the length of any object, even if the object is moving.

I measure the length of Albert's ruler. It's exactly 1 meter.

Then Albert bolts the ruler to the side of his train. He backs up a few miles and accelerates like crazy so he passes me at high velocity.

My device measures the length of the ruler as it passes.

Albert stops his train, walks over to me and asks for the result.

To my surprise I have to report the length was a bit less than 1 meter. Has the ruler shrunk? I measure it again while it's stationary and it's exactly 1 meter. So the ruler has not shrunk.

We both look at each other and ask if the length I measure could be dependent on the velocity of the train.

That's easy to test. Albert backs up his train a greater distance, accelerates more and passes me at a higher velocity.

Sure enough, the length I measure is even shorter.

We do the experiment for higher and higher velocities and I get shorter and shorter lengths for the ruler. But I notice something else strange. The higher the velocity gets the harder it becomes to increase. Meaning, Albert has to accelerate harder and harder just to get a marginal increase in velocity. It's like the velocity has some kind of maximum. I call this maximum vmax.

I then analyze the data and find a formula that fits all the experimental results. Here it is..


x=rv/r0 and y=v/vmax
rv is the length of the ruler when the train has velocity v, r0 is the length of the ruler when the train has velocity 0 i.e. it's stationary, and vmax is the maximum velocity.

It's a neat formula because when I plot the data in terms of x and y I get a circle of radius 1.

Albert then asks the obvious question - what would the length of the ruler be if he measured it on the train?

That's also easy to test. We load my measuring device on the train. Albert accelerates to a high velocity, then zips past me as he measures the length of the ruler.

He stops the train and gives me the result. The length he measured was exactly 1 meter.

At first we think this is crazy, but then we realize it makes sense. When Albert did his measurement the ruler was not moving for him. It was totally stationary, so it should be exactly 1 meter. And it was.

What about the number vmax? When I plot all the train velocities I see them approaching a maximum. They never reach the maximum but they get closer and closer. So from my data I can see what the maximum must be. It turns out to be a very famous number, vmax=c the velocity of light!

Content written and posted by Ken Abbott