Mass Increases As Speed Increases? Relativistic Mass?

Saturday, October 06, 2018

Mass Increases As Speed Increases? Relativistic Mass?

Relativistic Mass

Special relativity has had major implications for space and time so far. The main things we have seen is that time can slow, simultaneity is relative and lengths can shrink. Now we will discuss the implications it has for mass and conclude with the famous equation E=mc².

Relativistic Jousting!

Let's imagine a joust.
Person A and Person B are competing in the joust. They are identical in weight, use identical poles and have identical horses.
The competitors ride towards each other on parallel paths 1 meter apart. When they are next to each other, they thrust their poles outwards. The ends of their poles collide and they try to knock the other off their horse. This is depicted in the diagram below.

The competitors ride in the direction of the big arrow. When they are next to each other; they thrust their poles in the direction of
the smaller arrows.

Since the jousters are identical, this will result in a draw clearly. Neither will be able to knock the other off their horse as they are the same mass and thrust their poles at the same speed.

Person A reads this blog and then thinks of a clever way to win. He knows about time dilation so has the following thought process.
"I am moving at a constant velocity and so can consider myself stationary and Person B riding towards me.
Person B is moving and so I see time ticking slowly for him.
This means when he thrusts his pole out towards my pole; he does this very slowly.
If his pole thrusts outward slowly and I thrust mine quickly I can win the joust!"

This seems clever but can't be the case. We can't change the outcome of the joust just by changing frame of reference! So what could have happened?

Who wins the joust depends on the momentum of their poles (mass x velocity). From person A's frame of reference; Person B experiences time dilation and so has a slow moving pole. If the velocity has slowed then the only way to explain why it is still a draw is if the mass of the pole has increased!

We will need to guess what has happened and then verify this in the next post.
The most straight forward guess would be the mass of the slow moving pole increases by a factor of gamma.

m = m₀γ
where m₀is the rest/invariant/intrinsic/proper mass of an object
m is the relativistic/inertial mass of an object

Since gamma is greater than or equal to 1 and increases a velocity increases; this suggests mass is related to speed and increases with speed...

Does Mass ACTUALLY Increase?

Mass doesn't actually increase. The amount of stuff in the material doesn't increase with speed. Extra atoms don't suddenly appear. Atoms don't become bigger or gain extra sub atomic particles.

But...
Mass is a measure of an objects resistance to acceleration. It is true that it becomes harder to accelerate fast moving objects and so it is true that mass increases when referring to inertia (the resistance of any physical object to any change in its position and state of motion). In this respect mass increases and so it makes sense to talk about relativistic mass.

How can you weigh a moving object? To measure mass you need to be in a frame of reference where the object is stationary?
This is why relativistic mass is a touchy subject in physics. There is still debate over what actually happens with relativistic mass however from what I've read, the following is what the majority of scientists believe.

The reason why there is a misconception is that at everyday speeds - inertia = mass. At high speeds however we need relativity to correct this. How hard it is to accelerate an object (inertia) depends on its rest/actual mass and the gamma factor.
It is true that it gets harder to accelerate an object at high speeds but this is because of increases in its inertia, not in its actual mass.

The reason why there is misunderstanding with relativistic mass is because of language. We use mass to describe how much an object resists acceleration and the amount of stuff in an object.
Some equations also looks nicer if you use relativistic mass as one of the terms so a lot of introductory special relativity books use this.

It is better to not use relativistic mass as a concept and say that objects become harder to accelerate as they gain speed because of their increasing momentum, not their mass.

This also explains why objects can't go faster than light. As the velocity of an object approaches the speed of light, gamma goes to infinity. This means it becomes infinitely hard to accelerate an object to the speed of light. In other words you would need infinite force to get an object to the speed of light, which would require infinite energy, which is impossible.

In the next few posts we will continue to look at force and energy in relativity and finally arrive at E=mc².

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