Moving Center of Mass Collisions

[metastable]

If I fire an electron and positron bunch both in the same direction away from my experimental accelerator rest frame such that the electron bunch is fired with higher energy towards a "read end" collision with an already fired positron bunch and they collide a short distance away from the accelerator inside a chamber of full of detectors completely surrounding the collision. Before the collision both bunches have substantially similar momentum vector away from the accelerator. After the collision I expect the energies of the detected photons to add up to the rest energies of the annihilated particles plus the additional kinetic energy of the electron and positron bunches moving relative to the detector. But when I look at the momentum vectors of the some of the photons, they appear to have changed up to 180 degrees from the original momentum vectors of the electron-positron bunches (ie I expect some of the detected radiation to be heading in the momentum vector back towards the accelerator). The part I don't understand is where did the energy come from to change the momentum vectors of the radiation back towards the accelerator? Why does it consume no energy to change these vectors, such that the photons add up to the rest mass + kinetic energy (ie is there no energy allotment for changing the vector of the radiation detected heading back towards the accelerator)?

 

[mathman]

https://en.wikipedia.org/wiki/Electron–positron_annihilation

Above is a description of what the possibilities are. Since the collision results in many particles as output (such as gamma ray pairs), it is not surprising that some are in the direction you observed.

 

[mfb]

Did you write down the momenta and energies? The sum is the same before and after the process. Your massive particles have quite a lot of momentum.

 

[metastable]

The collisions appear to be neither elastic nor inelastic, as in either case the mass/energy would continue its path away from the accelerator.

 

[mfb]

You can't expect descriptions of collisions of macroscopic objects to work for annihilation processes.

 

[Vanadium 50]

. But when I look at the momentum vectors of the some of the photons,

How exactly did you do this? Do you have your own collider and detector?

 

[metastable]

I had asked mfb privately what mechanism would prevent radiation from proceeding back towards the accelerator in such a collision and his reply indicated there would be no such mechanism.

 

[mfb]

... and?
If you throw a hand grenade away you can still get hit by its fragments. Same concept.

You didn't answer my question from post 3.

 

[metastable]

You didn't answer my question from post 3.

Ok suppose a 1 coulomb bunch of positrons acquires 100kev per particle relative to the rest frame of the accelerator, then a 1 coulomb bunch of electrons acquires 200kev per particle energy along the same vector and collides with the positron bunch, so I have 2 coulombs of electron-positron rest mass + 1 coulomb @ 200kev per particle kinetic + 1 coulomb @ 100kev per particle kinetic energy entering the detector chamber, how do I assess the photon energies I could expect to see heading back towards the accelerator as well as towards other areas of the detection chamber?

 

[Vanadium 50]

You didn't answer my question from post 6.

 

[mfb]

how do I assess the photon energies I could expect to see heading back towards the accelerator as well as towards other areas of the detection chamber?

Use conservation of energy and momentum.

 

[metastable]

Use conservation of energy and momentum.

If the electron-positron pairs are traveling in opposite directions with combined 300kev kinetic:

200kev kinetic electron --> * <-- 100kev kinetic positron

I count 300kev kinetic + rest mass in the collision's center of mass frame (& also 300kev kinetic + rest mass in the detector/accelerator rest frame)

But if the particle bunches are both initially heading the same direction with different energies relative to the accelerator/detector:

200kev kinetic electron --> 100kev kinetic positron --> *

As the electrons move in the direction of the positrons, the positrons are still moving in the direction away from the electrons from the detector's rest frame, so I've probably made a mistake but now I only count 100kev kinetic (between the particles) + rest mass in the collision's center of mass rest frame (but still 300kev in the detector rest frame)

So in a collision between the 200kev electron bunch -> 100kev positron bunch initially traveling along the same vector do I expect to detect photons totaling (rest mass + 300kev) or photons totaling (rest mass + 100kev) in the rest frame of the detector?

--------------------------

I attempt the analogy of a car collision (head on vs rear end):

Car "A" 100 mph --> * <-- Car "B" 50mph = 150mph relative velocity collision
200kev kinetic electron --> * <-- 100kev kinetic positron = rest mass + 300kev kinetic

Car "A" 100 mph --> Car "B" 50mph --> * = 50mph relative velocity collision
200kev kinetic electron --> 100kev kinetic positron --> * = rest mass + 100kev kinetic

 

[mfb]

I count 300kev kinetic + rest mass in the collision's center of mass frame (& also 300kev kinetic + rest mass in the detector/accelerator rest frame)

No, the sum of kinetic energies will be lower in the center of mass frame.
Do the calculations. Don't just assume something and then be surprised that it leads to strange results.

so I've probably made a mistake but now I only count 100kev kinetic (between the particles) + rest mass in the collision's center of mass rest frame

Again: Do the calculations, don't just assume something. In the center of mass frame the total kinetic energy is lower than 100 keV.

So in a collision between the 200kev electron bunch -> 100kev positron bunch initially traveling along the same vector do I expect to detect photons totaling (rest mass + 300kev) or photons totaling (rest mass + 100kev) in the rest frame of the detector?

Energy is conserved in every frame. Different frames will get different values for the total energy, that is no problem.

 

[metastable]

Energy is conserved in every frame. Different frames will get different values for the total energy, that is no problem.

So with many repetitions of this experiment with 2 accelerators:

Lab Frame Detector/Accelerator --> 10gev kinetic electron --> <--*Collision*--> <-- 10gev kinetic positron <-- Lab Frame Detector/Accelerator

^I expect to detect some radiation other than gamma photons at the detectors because the 10gev + 10gev combined kinetic energy + rest mass is sufficient energy to produce other particles

If I modify experiment such that both particles are fired sequentially in the same vector from the same accelerator:

Lab Frame Detector/Accelerator --> 10gev + 1ev kinetic electron --> 10gev kinetic positron --> <--*Collision*--> Lab Frame Detector

Initially from the rest frame of the positron, the electron only has 1ev kinetic energy in the vector towards it available for the collision, because both particles move away from the accelerator with 10gev each plus the electron's 1 extra ev of kinetic energy. Is it sufficient to produce any other particles besides gamma? Or will I only detect gamma rays at the detectors? Will the 20gev + 1 ev + 0.510mev + 0.510mev mass/energy seen entering the chamber be observed by the lab frame detectors as gamma photons with total energy equivalent to 0.510mev + 0.510mev + 20gev + 1ev?

 

[Vanadium 50]

Enough already!

You are wasting everybody's time. Mfb was 100% right when he said Do the calculations. Don't just assume something and then be surprised that it leads to strange results. As far as I can tell, you are making up situations and guessing at the answer without doing the calculations and then being surprised at the "answer". That's not going to work very well. Neither is adding complication on top of complication before you have the basics down.

 

[metastable]

I'm not making things up, I'm trying to solve the following problem, but instead of assuming opposite directions and low energy I want to solve for when the particles have higher energy and that the particles are initially on the same vector with different energies:

 

[Vanadium 50]

Then you should start by a) understanding that calculation and b) understand the conceptual differences between this problem and your variations on it.

 

[mfb]

Initially from the rest frame of the positron, the electron only has 1ev kinetic energy in the vector towards it available for the collision

No, the energy will be different.

This thread is going nowhere, I closed it. If you stop making assumptions and actually calculate what happens feel free to send me a message, then I will open the thread again.