What is the significance of a massive relativistic particle?

[hasan_researc]

Homework Statement

My teacher has written in his lecture notes that
For massive relativistic particles, E = 0.5mv² = p²/2m.

Homework Equations

The Attempt at a Solution

I don't understand why the particle has to be massive for the equation to work.

Please help!

 

[kuruman]

Usually, by "relativistic particles" one means particles with speeds close to the speed of light. If that's the case, then the equations that you have are not appropriate. They are appropriate when the speed is much less than the speed of light. Assuming that to be the case, what do the equations predict that the momentum and energy of the particles would be if you set m = 0?

 

[hasan_researc]

m = 0 is for a photon. In that case, E = pc is the energy-momentum relation.

But if we set m = 0 for particles and use the Newtonian relations, then E = 0. But how does that help??

 

[graphene]

Newtonian mechanics do not work on photons.
At high speeds, you will have to resort to Special Relativity.

 

[kuruman]

m = 0 is for a photon. In that case, E = pc is the energy-momentum relation.

But if we set m = 0 for particles and use the Newtonian relations, then E = 0. But how does that help??

Your original question was "I don't understand why the particle has to be massive for the equation to work." You have just deduced that if the particle is not massive (m=0) and you use that equation, you get E=0. There can be two cases

1. The use of the equation is correct for a massless particle and a massless particle has no energy, ever.
2. The use of the equation is incorrect for a massless particle and you need a different equation to express its energy.

You have already stated that for a massless particle E = pc, therefore you believe that case 2 is what's happening and I agree. It follows then that these equations do not work for massless particles which means that they work only for ___________ particles.

 

[hasan_researc]

for massive particles, then??

But why use the word "massive"? I thought a massive body is a body with a very large mass.

 

[kuruman]

for massive particles, then??

But why use the word "massive"? I thought a massive body is a body with a very large mass.

In ordinary language yes. In physics "massive" is normally used as opposed to "massless".

 

[hikaru1221]

But why use the word "massive"? I thought a massive body is a body with a very large mass.

Then what is "very large mass"? 1 tons? 1000 tons? 1 million tons? The terms large and small are relative.