Deriving the Special Relativity Formula: A Scientific Approach

In summary, the conversation discusses the derivation of the formula for relativistic mass, which is often referred to as \gamma m. This definition of mass is not widely used and can lead to confusion. The correct definition of mass is the rest mass, which does not change with velocity. However, some people define \gamma m as the mass, leading to the need for a second concept of mass called the longitudinal mass. The reason for these different definitions is due to the relationship between mass and force in Newton's second law of motion. Ultimately, the conversation concludes with a better understanding of the formula for relativistic mass.
  • #1
dekoi
Deriving SR Formula

edit 3:
How does one go about deriving the formula:[tex]mr =\frac{m0}{\sqrt{1 - \frac{v^2}{c^2}}} [/tex]?
 
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  • #2
Mass in your equation does not change with velocity.

Some people call [itex]\gamma m[/itex] the relatvistic mass and this cleraly does increase with velocity, but this defintion is not widely used and it's not a very good defintion anyway.
 
  • #3
jcsd said:
Mass in your equation does not change with velocity.

Some people call [itex]\gamma m[/itex] the relatvistic mass and this cleraly does increase with velocity, but this defintion is not widely used and it's not a very good defintion anyway.
But [itex]\gamma m[/itex] isn't mass itself; it is the multiple of mass by a factor of [itex]\gamma[/itex]. Or is this the "wrong" way of looking at the situation?
 
  • #4
dekoi said:
[itex][ec^2][\sqrt{1-\frac{v^2}{c^2}}]=m [/itex]

Therefore, as [itex]\sqrt{1-\beta^2[/itex] increases due to the increase in velocity, [tex]m[/tex] increases as well.

I am not sure whether this is right or not.
jcsd said:
Mass in your equation does not change with velocity.
You're right... According to my equation, mass will decrease. If velocity is say, 0.7c, [tex]\sqrt{1-\beta^2[/tex] will equal 0.714 (as compared to the a value of 1 which it would be if velocity was much smaller than c). Therefore, mass would decrease.

I don't understand how this is so.
 
  • #5
Almost universally m is regarded as the mass aka the rest mass, but a few people regard [itex]\gamma m[/itex] as the mass aka the relatvistic or transverse mass.

Defining m as the mass is useful as it doesn't change from frame to frame. Defining [itex]\gamma m[/itex] as the mass means that it does change from frame to frame and you find for conssitency you have to define a second kind of mass [itex]\gamma^3 m[/itex] called the longitudinal of mass.

The reason for the two definitions is due to how the concepts of mass and force are related, if you think that Netwon's second law is [itex]\vec{F} = m\vec{a}[/itex] then you might argue that the concept of relatvistic mass is just sticking with this concpet, but most physicsts like to think of Netwon's second law as [itex] \vec{F} =\frac{d\vec{p}}{dt}[/itex] anyway.
 
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  • #6
Ah. I have confused several concepts in SR. I now understand the fact that:

[tex]mr =\frac{m0}{\sqrt{1 - \frac{v^2}{c^2}}} [/tex]

Thanks.
 
  • #7
edit 3: Topic changed.
 

1. What is special relativity?

Special relativity is a theory developed by Albert Einstein in 1905 that describes how objects in motion appear differently to different observers and how time and space are relative concepts.

2. How does special relativity differ from Newton's laws of motion?

Special relativity differs from Newton's laws in that it takes into account the fact that the speed of light is constant and the laws of physics are the same for all observers in uniform motion.

3. What is the equation for time dilation in special relativity?

The equation for time dilation in special relativity is t' = t / √(1 - v²/c²), where t' is the time in the moving frame of reference, t is the time in the rest frame of reference, v is the velocity of the moving object, and c is the speed of light.

4. How does special relativity explain the twin paradox?

The twin paradox is a thought experiment in which one twin travels at high speeds while the other stays on Earth. Special relativity explains that time will pass slower for the traveling twin, causing them to age less than the twin on Earth.

5. What are some practical applications of special relativity?

Some practical applications of special relativity include GPS systems, particle accelerators, and nuclear power plants. These technologies rely on precise calculations of time and space that are only possible because of special relativity.

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