# The Naked Scientists Forum

### Author Topic: Special relativity question  (Read 4172 times)

#### Dick1038

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##### Special relativity question
« on: 02/11/2007 00:59:58 »
Special relativity states that the mass of a moving object increases with increasing speed.  However, speed is a relative quantity and mass is an absolute quantity. Please explain how a relative quantity can affect an absolute quantity.  An observer on a speeding spaceship sees the Earth receding at high speed.  Has the Earth's mass increased?

#### ukmicky

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##### Special relativity question
« Reply #1 on: 02/11/2007 01:24:20 »
No because Relativistic mass the type of mass which they are talking about is not real mass and shouldnt really be called mass

#### lightarrow

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##### Special relativity question
« Reply #2 on: 02/11/2007 15:54:48 »
No because Relativistic mass the type of mass which they are talking about is not real mass and shouldnt really be called mass
Exactly. More precisly "relative" and "absolute" in this case are referred to inertial ref. frames: "relative" means that depends on the ref. frame, "absolute" means that it doesn't depend on it.

In this last case we say it's "Lorentz invariant" because it doesn't vary under a Lorentz transform (which is the transformation of coordinates from 2 different inertial rif. frames).

Mass is invariant, that is remains the same in every (inertial) ref. frame. Relativistic mass (but this concept is almost never used in physics) is not invariant (it's not used just for this reason!)

#### lyner

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##### Special relativity question
« Reply #3 on: 04/11/2007 18:26:05 »
The idea of increasing mass as you get faster relates to kinetic energy that you gain.
Who gains the mass when there are two observers involved in an experiment?
The one who had his engine running.
Physicists are made very aware of relativistic mass increase when they try to accelerate electrons to moderately high velocities. If you use a simple cyclotron, then they just reach a limit to their top speed. You need to modify the magnetic field or driving frequency to get higher speeds to make the increased masses go in a circle of appropriate diameter. It's called a betatron.
I'm not sure how that relates to your foregoing statements, lightarrow. Of course, the electrons aren't in an inertial frame when they're in the betatron.

#### Dick1038

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##### Special relativity question
« Reply #4 on: 05/11/2007 17:01:51 »
Well, kinetic energy depends upon the "relative" quantity velocity. So a moving object has different kinetic energy for different observers?

The Earth is speeding around the sun, the sun is speeding around the galaxy, the galaxy is speeding through the universe.  So, the Earth's kinetic energy depends on where the observer is located.

I know that I solved physics problems involving kinetic energy by using the velocity stated in the text book or on the exam and I got the right answer if I didn't make any algebra or computational errors.

#### lightarrow

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##### Special relativity question
« Reply #5 on: 05/11/2007 20:30:10 »
The idea of increasing mass as you get faster relates to kinetic energy that you gain.
Who gains the mass when there are two observers involved in an experiment?
The one who had his engine running.
Physicists are made very aware of relativistic mass increase when they try to accelerate electrons to moderately high velocities. If you use a simple cyclotron, then they just reach a limit to their top speed. You need to modify the magnetic field or driving frequency to get higher speeds to make the increased masses go in a circle of appropriate diameter. It's called a betatron.
I'm not sure how that relates to your foregoing statements, lightarrow. Of course, the electrons aren't in an inertial frame when they're in the betatron.

And I'm not sure if you want to say that relativistic mass is a useful concept or not or whatever.
Anyway, considering a fast moving charged particle's trajectory, it's true that  you can ascribe the effect to a greater mass, but the problem is that this would be a "transverse mass" which dependence on the particle's velocity v is different from that of the "longitudinal mass" and this makes the concept of relativistic mass too complicated.

If you call F the force on the particle, m, v and a its (rest) mass, velocity and acceleration (in bold to mean they are vectors), you have:

F =  ma/Sqrt[1 - (v/c)2] + m(va)v/c2[Sqrt[1 - (v/c)2]]3

where "•" means scalar product.

So, when the particle's speed v is transverse to its acceleration a, F =  ma/Sqrt[1 - (v/c)2] and you can say that F/a, that is, the "mass", is m/Sqrt[1 - (v/c)2] = relativistic mass.

But when the acceleration is not transverse to the velocity, you see well that the result is different.
« Last Edit: 05/11/2007 20:33:56 by lightarrow »

#### lyner

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##### Special relativity question
« Reply #6 on: 05/11/2007 23:08:38 »
Even in linear motion,  the energy for incremental speed change gets disproportionately high as  you approach c. The simple   m v squared /2 no longer applies.  Why does this not imply an increase in mass?

#### lightarrow

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##### Special relativity question
« Reply #7 on: 06/11/2007 17:13:43 »
Even in linear motion,  the energy for incremental speed change gets disproportionately high as  you approach c. The simple   m v squared /2 no longer applies.  Why does this not imply an increase in mass?

Please, give me your preferred definition of mass and then I can answer you. In the case you have written it would seem that your definition of mass should be (1/v)dE/dv; is it the case?

#### The Naked Scientists Forum

##### Special relativity question
« Reply #7 on: 06/11/2007 17:13:43 »