Massive episode about relativity

21 Mar

And finally, the conclusion of our four part primer on relativity. Here’s a recap on the topics we’ve covered so far; the laws of physics depend on the frame of reference; the faster an object moves, the slower time moves in that frame; the faster an object moves, the shorter that object appears from a resting frame.  In this episode, we’re look at questions about one more property of an object. Specifically, how does motion affect mass?

Well, if there is one equation that people remember about special relativity, it’s

52c7687643df1c12231b39e324850586

And we’ve established that the speed of light, c, is a constant, so mass just depends on the amount of energy. Shortest fun fact ever…

Unfortunately not. E = mc² is a special solution of the more general equation

f653e9c4c421742eebeca629813279d0

where m should be the mο and p is the object’s momentum (inertial mass [m] x velocity [v]). When the velocity of the object is zero, the momentum expression disappears and we are left with the now famous equation; an equation which describes how the energy stored in an object is related to its resting mass. Hmm. What the heck is inertial mass, and how is it different from rest mass?

Inertia refers to the tendency for an object to continue traveling and resist a force that attempts to change it’s motion.  The rest mass is a measurement of the energy stored in the mass in a resting frame.  The relationship between the rest mass and the inertial mass (sometimes called the effective or relative mass) is

images

where mο is the rest mass and m is the effective mass.  As a result the effective/inertial mass of an object mass increases as the object travels at increasing speed.

Now, let’s put it all together.

  • An object can’t travel fast than the speed of light.
  • As an object’s velocity get’s closer to the speed of light, it’s effective mass increases.
  • In order to conserve resting mass in the Energy-Momentum relation,  energy and momentum vary proportionally.

With these conditions, adding energy to an object and attempting to increase it’s velocity results in an increase in it’s effective mass that grows exponentially as the velocity approaches c.

exponential-growth-graph

This is what exponential growth looks like. Small change initially; infinite change as v approaches c.

One cool implication of this is that if you keep putting energy into an object, it could achieve infinite apparent mass. Before this point it would form a black hole, but it’s still cool to think about.

I think that’s enough mind blowing stuff about relativity. Don’t worry if it seems a little confusing. To adapt a phrase from Niels Bohr, “Anyone who is not shocked by special relativity has not understood it.” If there’s nothing more that you take from these last few episodes, I hope you at least will accept that the most famous equation in physics really ought to be written as Eο = mοc2.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: