# Neutrino vs. Photon Momentum at Fixed Energy

#### bob012345

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I'm interested in knowing the ratio of momentum for a neutrino vs. a photon when both have the same energy. Alternatively, my spaceship engine can release 1GW of either a photon beam or a neutrino beam. How much relative thrust will the neutrino beam give me for the same energy (and power) as compared to the photon beam. Thanks.

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#### bob012345

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This is a serious question. The second part was just put there for fun to illustrate the nature of the issue. I wish it hadn't been moved to here from particle physics. Makes me feel like I asked a stupid question.

#### Orodruin

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This depends on the energy. Photons are massless so their momentum is equal to their energy. Neutrinos are massive so their momentum is anywhere between zero and their energy - depending on the energy.

#### bob012345

Gold Member
This depends on the energy. Photons are massless so their momentum is equal to their energy. Neutrinos are massive so their momentum is anywhere between zero and their energy - depending on the energy.
Makes it sound like photons have more momentum than neutrinos for the same energy. Seems backwards. I also have an issue with the statement that the photon momentum equals it's energy. Only in the units where c=1. Please use MKS.

#### Orodruin

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Makes it sound like photons have more momentum than neutrinos for the same energy. Seems backwards.
If you are not going to accept the correct answer and calling it backwards without saying why then why do you bother to ask?

#### bob012345

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If you are not going to accept the correct answer and calling it backwards without saying why then why do you bother to ask?
I didn't say it WAS backwards, I said it SEEMS backwards. If I was clear I wouldn't have asked the question. Anyway, I see the answer now. When you create the neutrinos, a lot of the energy gets locked up in the mass and the momentum of that moving mass probably doesn't match the momentum of the photon if we are talking about the total relativistic energy of both entities being the same. So the photon always has the highest ratio of momentum to total relativistic energy of anything. Thanks.

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#### Orodruin

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When you create the neutrinos, a lot of the energy gets locked up in the mass and the momentum of that moving mass probably doesn't match the momentum of the photon if we are talking about the total relativistic energy of both entities being the same.
Well, ”a lot” is overstating it a bit, neutrinos are very light - so light that in all cases where we have studied them, their momenum has been so close to their energy that they have been experimentallt indistinguishable (only through a quantum interference phenomenon do we have knowledge of the neutrino mass being non-zero).

The appropriate equation relating energy, momentum, and mass is $E^2 = m^2 + p^2$.

I didn't say it WAS backwards, I said it SEEMS backwards.
If you reread your post and think about how it comes across after someone spent time to give you an answer, try to reconstruct how it will be perceived. You gave no indication of a further question or about what you thought was strange. This reads very dismissive and not at all as if you are ready to accept the answer if convinced on the issues you find weird. Essentially everything that was missing from the cookiecutter post of such a person was the ”LOL” in the end.

#### bob012345

Gold Member
Well, ”a lot” is overstating it a bit, neutrinos are very light - so light that in all cases where we have studied them, their momenum has been so close to their energy that they have been experimentallt indistinguishable (only through a quantum interference phenomenon do we have knowledge of the neutrino mass being non-zero).

The appropriate equation relating energy, momentum, and mass is $E^2 = m^2 + p^2$.

If you reread your post and think about how it comes across after someone spent time to give you an answer, try to reconstruct how it will be perceived. You gave no indication of a further question or about what you thought was strange. This reads very dismissive and not at all as if you are ready to accept the answer if convinced on the issues you find weird. Essentially everything that was missing from the cookiecutter post of such a person was the ”LOL” in the end.
I apologize for my tone. I didn't intend it to come across so strong. I thank you for your answers.

#### Orodruin

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I apologize for my tone.
Don’t worry, we all write things that come across the wrong way from time to time. Myself included. What sets people apart is if they can realise and accept when it has happened and learn from it or not. (I myself still have to work very hard not to start many posts ”This is wrong.” when correcting posts I disagree with. I typically do not mean it as something personal, just factual, but it can really come across awkwardly if the recipient takes it the wrong way. Tone is not conveyed well in writing.)

"Neutrino vs. Photon Momentum at Fixed Energy"

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