# Different frames of reference and particle production? a contradiction maybe?

• jeebs
In summary, the dilemma is that if one observer is moving such that he sees a collision with just barely enough energy to produce this new particle, and it is produced, but another observer is moving such that the collision does not have enough energy to produce this new particle, what happens then?If two observers are in different reference frames, then the new particle is only produced in the frame of the observer that has more kinetic energy.
jeebs
Hi,
Second time I'm writing this question, the first one seems to have been lost in cyberspace but sorry if it somehow comes back and appears twice.

Anyway, you know how kinetic energy depends on velocity, so that the energy of a particle collision will be different for two frames of reference moving relative to one another?
And also, how when particles collide with sufficient energy, a new particle can be created if the rest mass can be reached?

Well, what if one observer is moving such that he sees a collision with just barely enough energy to produce this new particle, and it is produced, but another observer is moving such that the collision does not have enough energy to produce this new particle, what happens then?
Surely if a particle exists in the universe, either everyone can see it or no one can?
What's the deal here?

thanks.

jeebs said:
Well, what if one observer is moving such that he sees a collision with just barely enough energy to produce this new particle, and it is produced, but another observer is moving such that the collision does not have enough energy to produce this new particle, what happens then?

Can you set up a specific numeric example to illustrate this?

If I understand jeebs correctly, his concern is about heavy particles productions. But to answer, I think it is helpful to begin with the decay of a single heavy particle into two (or more) lighter ones. The decay is best thought of in the rest frame of the heavy particle where the decay products have the minimal kinetic energy. Going to another reference frame will just give them more kinetic energy. The same thing happen when you collide two light particles to create heavier ones. You can always think of them being produced from an initial state which looks like the decay of a system from far away enough. The final decay products have minimal energy in the center-of-mass frame of the initial incoming particles. Transforming to another referential just gives them more kinetic energy.

The problem is with :
another observer is moving such that the collision does not have enough energy
This is an impossibility. There is no such observer or referential. In particular
if one observer is moving such that he sees a collision with just barely enough energy to produce this new particle
in this frame, the new particle is produced at rest.

Now that I think of it, for a particular collision, the energy available for production of new particles is independent of reference frame (i.e. it's a Lorentz invariant), isn't it?

In the reference frame in which the total momentum of the incoming particles is zero, all this "available energy" can be used to produce new particles, in which case the new particles are at rest.

If we now switch to a reference frame in which the total momentum is not zero, the incoming particles have more kinetic energy than in the zero-momentum frame; but this "extra" KE is not available for producing new particles. The outgoing particles must now also have KE, which comes from the "extra" KE of the incoming particles.

jtbell said:
Now that I think of it, for a particular collision, the energy available for production of new particles is independent of reference frame (i.e. it's a Lorentz invariant), isn't it?
Yes, it is usually written s

I think jtbell explained it better than I did

## 1. What is a frame of reference?

A frame of reference is a coordinate system that is used to describe the position and motion of an object. It is an essential tool in understanding the physical world and is based on the observer's perspective.

## 2. How do different frames of reference affect our perception of particle production?

Different frames of reference can greatly affect our perception of particle production because the laws of physics, such as conservation of energy and momentum, can appear different in different frames. This can lead to discrepancies in the observed number and type of particles produced.

## 3. Can there be a contradiction in different frames of reference?

Yes, it is possible for there to be a contradiction in different frames of reference. This is because each frame has its own set of laws and rules that may not always align with each other. This can lead to conflicting observations and interpretations of events.

## 4. How do scientists deal with contradictions between different frames of reference in particle production?

Scientists use the principle of relativity, which states that the laws of physics should be the same in all inertial frames of reference, to reconcile contradictions between different frames. They also use mathematical equations, such as the Lorentz transformation, to translate between different frames.

## 5. Can understanding different frames of reference improve our understanding of particle production?

Yes, understanding different frames of reference is crucial in fully comprehending the complex processes involved in particle production. It allows us to see the same event from different perspectives and helps us make sense of conflicting data. By studying different frames, we can gain a more comprehensive understanding of the fundamental laws of physics.

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