Energy-Momentum Relation: Am I the only one whose noticed?

[TheLivingMartyr]

this whole thread assumes that momentum is the same as movement through space-time, please tell me if i am wrong.

 

I was browsing around some articles on particle physics and relativity and the like, and I stumbled across a short article on Energy-Momentum Relation. It stated that mass and energy are proportional (which I already knew), but then that Energy, Mass and Momentum are also proportional. i found this intruiging, but didn't expect to discover anything exceptional. the equations stated that: (i can't use superscript characters in this, so ^ indicates superscript)

 

E^2=m^2c^4+p^2c^2

where E is the total energy, m is the mass, p is the momentum and c is the speed of light

 

then we have the good old Mass-Energy Relation equation that is used in nuclear physics

 

E=mc^2

 

and then there was the E-p relation for massless particles (eg. photons)

 

E=pc

 

i looked at this and thought, "hang on a minute, this means that if you give a massive body momentum, then the energy produced from it will be greater than the energy produced from a still body"

so i did some quick calculations with this and here is an example

 

we'll say that:

m=10

p=5

c=300000000

 

for a body with no mass, but with momentum:

E=1.5x10^9

 

for a body with mass, but no momentum:

E=9x10^17

 

and for a body with both mass and momentum:

E=8.1x10^35

 

what i am thinking from this is, "why don't they just move nuclear fuel around in generators?" because this obviously shows that a body with momentum produces more energy than a body without momentum.

 

could anyone who is knowledgable on this subject please reply to this and tell me whether or not i am right or have made a "discovery"

[swansont]

i looked at this and thought, "hang on a minute, this means that if you give a massive body momentum, then the energy produced from it will be greater than the energy produced from a still body"

 

Energy due to motion is kinetic energy. While it's nice that you had this insight, it is nothing new or revolutionary. The amount of energy you give the body will be equal to the extra energy you could get out of it. There's no way to leverage this — total energy is conserved.

[ajb]

You have discovered for yourself that energy is not a Lorentz invariant, but [math]m^{2}c^{4} = E^{2}-p^{2}c^{2}[/math] is.

 

All physical particles obey the above law known as the mass shell condition.

[TheLivingMartyr]

Energy due to motion is kinetic energy. While it's nice that you had this insight, it is nothing new or revolutionary. The amount of energy you give the body will be equal to the extra energy you could get out of it. There's no way to leverage this — total energy is conserved.

oh dear, i have made a fool of myself. *slaps face*

so the actual momentum of the object cannot be converted into pure energy (by this i mean photons)?

[michel123456]

oh dear, i have made a fool of myself.

 

No.

 

I liked your first sentence:

this whole thread assumes that momentum is the same as movement through space-time, please tell me if i am wrong.

 

Tell him if he is wrong.

[ajb]

Energy-momentum is to space-time what momentum is to space and energy is to time.

 

See Noether's theorem.

[swansont]

oh dear, i have made a fool of myself. *slaps face*

so the actual momentum of the object cannot be converted into pure energy (by this i mean photons)?

 

I would urge you not to think of being curious, even when it turns out you're incorrect, as making a fool or yourself. You're a huge leg up on people who don't even think about such things and as a result never ask the question.

 

If the object has kinetic energy, you can convert that into another form in a collision. However, it cannot do this spontaneously, because there will always be a frame (for massive particles) where the object is at rest. If an interaction is forbidden in one frame, it can't happen in another.

[michel123456]

You're a huge leg up on people who don't even think about such things and as a result never ask the question.

 

"when you don't know, and ask the question, you are stupid once. If you don't ask the question, you will remain stupid for your entire life." Chinese proverb

[TheLivingMartyr]

I would urge you not to think of being curious, even when it turns out you're incorrect, as making a fool or yourself. You're a huge leg up on people who don't even think about such things and as a result never ask the question.

 

If the object has kinetic energy, you can convert that into another form in a collision. However, it cannot do this spontaneously, because there will always be a frame (for massive particles) where the object is at rest. If an interaction is forbidden in one frame, it can't happen in another.

well, thanks for explaining it to me

and the reason I often say things like "I'm such an idiot" is because i'm quite a self-concious/anxious person, but i learnt something, so i'm not complaining!

[Mr Skeptic]

so the actual momentum of the object cannot be converted into pure energy (by this i mean photons)?

 

Anything with momentum is going to have kinetic energy. However, the amount of kinetic energy does not relate directly to momentum -- for the same momentum, a lighter object will have more kinetic energy.

 

Energy is conserved but can change forms. For kinetic energy, we use a device called a generator to convert it into electricity, which can be converted to light via one of the many varieties of light bulbs. However, some of the energy will be lost along the way, not lost as in "disappeared" but lost as in "dissipated as waste heat". So, at least some of the kinetic energy can't be converted to photons.