What is the Relationship Between Energy and Time in Different Frames?

In summary, energy and time both transform like zeroth components of four-vectors, with energy being the zeroth component of the momentum four-vector and time being the zeroth component of the position four-vector. This is why E' = gamma * (E - p.v) and t' = gamma * (t - x.v).
  • #1
chewwy
6
0
something which seems so fundamental that i can't find anywhere that derives it is the following:

E' = gamma * (E - p.v)

where E is the energy in one frame, p the momentum, v the relative velocity of the other frame, and E' the energy in the other frame.

i.e. energy transforms like time. i can't quite see where this comes from though.. help?
 
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  • #2
It comes from the fact that energy is the "zeroth" component of the momentum four-vector [itex](p_0, p_1, p_2, p_3) = (E/c, p_x, p_y, p_z)[/itex], just like time is the "zeroth" component of the position four-vector [itex](x_0, x_1, x_2, x_3) = (ct, x, y, z)[/itex].
 
  • #3
Welcome to PF!

Hi chewwy! Welcome to PF! :smile:

(have a gamma: γ :wink:)
chewwy said:
energy transforms like time. i can't quite see where this comes from though.. help?

Yes, it's because (E,p) is defined as the derivative of (t,x),

so E' = γE - γ(p.v),

just as t' = γt - γ(x.v)
 
  • #4
jtbell said:
It comes from the fact that energy is the "zeroth" component of the momentum four-vector [itex](p_0, p_1, p_2, p_3) = (E/c, p_x, p_y, p_z)[/itex], just like time is the "zeroth" component of the position four-vector [itex](x_0, x_1, x_2, x_3) = (ct, x, y, z)[/itex].

okie doke. thanks everyone!
 

1. What is the concept of energy in different frames?

The concept of energy in different frames refers to the idea that energy can be measured and observed from different perspectives or reference frames. This means that the amount of energy in a system may appear different depending on the observer's point of view.

2. How does energy behave in different frames of reference?

Energy behaves differently in different frames of reference due to the principle of relativity. This means that the laws of physics, including those governing energy, are the same for all observers, regardless of their relative motion. However, the measurements and observations of energy may vary between different frames.

3. Why is it important to consider energy in different frames?

It is important to consider energy in different frames because it allows for a more complete understanding of physical systems. By observing energy from different perspectives, we can gain a better understanding of how energy is conserved and transformed in different situations.

4. How does the concept of energy in different frames relate to the theory of relativity?

The concept of energy in different frames is a fundamental aspect of the theory of relativity. The theory states that the laws of physics, including those governing energy, are the same for all observers regardless of their relative motion. This means that the measurements and observations of energy may vary between different frames, but the underlying principles remain consistent.

5. Can energy be created or destroyed in different frames?

No, energy cannot be created or destroyed in different frames. This is a fundamental principle of physics known as the law of conservation of energy. While the measurements and observations of energy may differ between frames, the total amount of energy in a closed system remains constant.

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