How Einstein proved equation about speed

In summary, Einstein's famous equation, E=mc², was first proven in his theory of special relativity by combining the principles of mass-energy equivalence and the constant speed of light in a vacuum. This equation revolutionized our understanding of the relationship between energy and mass and introduced the concept of spacetime. It has been supported by various experiments and has had a profound impact on modern science and technology, influencing fields such as nuclear physics, astronomy, and space exploration.
  • #1
Hepic
118
0
How einstein proved that equation: U=(V1+V2)/(1+(V1*V2)/c^2) ?
Thanks !
 
Physics news on Phys.org
  • #3
As I see Lorentz helped a lot to this equations.
How lorenz proved them?
 
  • #4
What did you not understand about the answer you got?
 
  • #5


Einstein's theory of special relativity revolutionized our understanding of space and time, and his famous equation, E=mc^2, is a cornerstone of modern physics. However, Einstein also developed another important equation that relates the velocities of two objects in motion. This equation, U=(V1+V2)/(1+(V1*V2)/c^2), is known as the velocity addition formula.

Einstein's proof of this equation is based on the principles of special relativity, which state that the laws of physics are the same for all observers in uniform motion. This means that the way we measure velocities should be the same for all observers, regardless of their relative motion.

To prove the velocity addition formula, Einstein started with two objects, A and B, moving at different velocities, V1 and V2, respectively. He then considered a third object, C, that is stationary in relation to B. According to the principles of special relativity, the velocity of C as observed by A should be the sum of the velocities of C as observed by B and B as observed by A.

Using this principle, Einstein derived the following equation:

U = (V1 + V2)/(1+(V1*V2)/c^2)

This equation shows that the velocity of C as observed by A is the sum of the velocities of A and B, divided by a correction factor that takes into account the relative motion between A and B.

Einstein's proof of this equation is complex and involves mathematical manipulations, but it ultimately shows that the velocity addition formula is consistent with the principles of special relativity. This equation has been confirmed through numerous experiments and is an essential part of our understanding of motion and relativity.

In conclusion, Einstein's proof of the velocity addition formula is a testament to his brilliance as a scientist and his groundbreaking contributions to the field of physics. This equation has stood the test of time and continues to play a crucial role in our understanding of the universe.
 

1. How did Einstein prove the equation for speed?

Einstein's famous equation, E=mc², was first proven in his theory of special relativity. He derived this equation by combining the principles of mass-energy equivalence and the constant speed of light in a vacuum. He also used thought experiments and mathematical equations to demonstrate the relationship between energy, mass, and the speed of light.

2. What is the significance of Einstein's equation for speed?

Einstein's equation for speed, E=mc², revolutionized our understanding of the relationship between energy and mass. It showed that matter and energy are interchangeable and that even a small amount of mass can contain a large amount of energy. This equation also laid the foundation for the development of nuclear energy and the atomic bomb.

3. How did Einstein's equation for speed change our understanding of the universe?

Einstein's equation for speed, E=mc², introduced the concept of spacetime and showed that the laws of physics are the same for all observers moving at a constant speed. It also challenged the traditional notions of absolute space and time and paved the way for further scientific breakthroughs, such as the theory of general relativity.

4. What experimental evidence supports Einstein's equation for speed?

There have been many experiments conducted that support Einstein's equation for speed, including the famous Michelson-Morley experiment that showed the constant speed of light in a vacuum. Other experiments, such as nuclear reactions and particle accelerators, have also provided evidence for the relationship between energy, mass, and the speed of light.

5. How has Einstein's equation for speed impacted modern science?

Einstein's equation for speed, E=mc², has had a profound impact on modern science and technology. It has been used in various fields, including nuclear physics, astronomy, and space exploration. It also serves as the basis for many scientific theories and has greatly influenced our understanding of the universe and the laws of physics.

Similar threads

B Time Dilation in Non-Stationary Reference Frame: A, B, C
    • Special and General Relativity
Replies
10
Views
1K
A Electrodynamics of moving bodies - §2: On the relativity of... (again)
    • Special and General Relativity
2
Replies
35
Views
2K
B Speed of Light Reflection: Einstein's Train & Mirrors
    • Special and General Relativity
2
Replies
38
Views
2K
B Speed of Light in Free Space - Einstein's Second Principle
    • Special and General Relativity
Replies
8
Views
1K
I Gravity Wave Speed: Deriving Constancy from Maxwell Eqs.
    • Special and General Relativity
Replies
34
Views
2K
I A Hidden Zero in Einstein's Simple Derivation
    • Special and General Relativity
Replies
22
Views
1K
I Is the sign of the Einstein equation right in Chandrasekhar's Black holes?
    • Special and General Relativity
Replies
13
Views
1K
I Understanding Einstein's second postulate of special relativity
    • Special and General Relativity
2
Replies
57
Views
4K
B Define a vector that transfers the reference systems to the future
    • Special and General Relativity
Replies
8
Views
817
Comparing Newton and Einstein - Who is Correct?
    • Special and General Relativity
Replies
22
Views
3K

Hot Threads

Recent Insights

Back
Top