Understanding Relativistic Kinetic Energy in Lab Experiments

[Pengwuino]

Ok this'll probably change my perception on what relativistic kinetic energy is so here goes.

Lets say you have a lab experiment ready to fire a particle at .6c into a wall or something (or maybe even another group of particles). Let's say you fire the entire lab experiment off from an observer at .35c. Now, using relativistic kinetic energy, the particle according to people traveling with the lab experiment will hit the other particles with a certain KE right? Now, what would the KE be relative to the observer whos standing still? It seems like it would be a different KE and deliver more energy to the particles according ot the observer.

I think i might have realized why that's not the case (as i was writing the question!), but i just wanted to ask to make sure i know why I am wrong.

 

[HallsofIvy]

Before you go saying it would "deliver more energy to the particles according ot the observer." notice that the observer also sees the target particles as moving with speed 0.35c.

Suppose you are driving down the road at 30 mph and crash into a parked car! Heckuvalot of energy transfer!
Suppose you are driving down the road at 60 mph and crash into a parked car.
Heckuvalot more energy transfer!
Suppose you are driving down the road a 60 mph and hit the back of a car doing 30 mph. Which of the above two cases has the same energy transfer (at the time of the hit- ignore what happens when both cars start skidding across the road!)?

 

[R0man]

First of all, it's great that you are thinking critically about this concept and trying to understand it better. Relativistic kinetic energy can definitely be a tricky concept to wrap your head around, but with some explanation and examples, it can become clearer.

In your example, the particle is traveling at .6c and the observer is at .35c. The KE of the particle as observed by someone traveling with the lab experiment would be calculated using the relativistic formula KE = (γ - 1)mc², where γ is the Lorentz factor and m is the mass of the particle. This formula takes into account the effects of relativity, such as time dilation and length contraction, and gives a more accurate measure of the particle's energy.

Now, let's consider what the KE would be for the observer standing still. The key thing to remember is that everything is relative in relativity. So, if the observer is standing still, they are the reference point for measuring the KE. In this case, the KE of the particle would be calculated using the classical formula KE = 1/2mv², where v is the velocity of the particle relative to the observer. This is because from the observer's perspective, there is no time dilation or length contraction affecting the measurement of the particle's energy.

So, to answer your question, yes, the KE would be different for the observer standing still compared to someone traveling with the lab experiment. This is because they are measuring the energy from different reference points. However, both measurements are correct and valid for their respective frames of reference.

I hope this helps clarify the concept of relativistic kinetic energy for you. Keep asking questions and exploring this fascinating topic!