Relativistic Momentum: Is It a Vector in Relativistic Energy?

In summary, relativistic momentum is a vector quantity that takes into account the effects of special relativity on an object's motion. It is dependent on an object's mass, velocity, and the speed of light, and follows the principles of relativity, such as the addition of velocities and the conservation of momentum. However, unlike classical momentum, relativistic momentum is not always conserved and can vary depending on the observer's frame of reference. This makes it a crucial concept in understanding the behavior of objects at high speeds and in the study of relativistic energy.
  • #1
jaketodd
Gold Member
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Relativistic momentum is a vector, just as non-relativistic momentum is a vector, right? Part of the relativistic energy equation includes relativistic momentum. See here please: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/releng.html"

Could the relativistic momentum energy part of the relativistic energy equation be considered as a vector when the equation is computed for total relativistic energy? That is, does relativistic momentum, when taken in the context of relativistic energy as a whole, still have a vector? The answer to this question must be yes, because otherwise, without a vector for some of the relativistic energy, then the object would remain stationary. Another question please: I suppose the relativistic momentum could do without a vector in the context of relativistic energy, but then what would keep the object going...Is the relativistic kinetic energy portion of total relativistic energy a vector? Or, are both relativistic kinetic energy, and relativistic momentum, vectors in the context of computed relativistic energy? Or, I suppose you could simply say: Does relativistic energy, as a whole, have a vector component or components, and if so, what part of the relativistic energy has this/these vectors? Maybe this could sum it up: Relativistic energy must have some vector component because otherwise the object would be stationary, right?

Many Thanks,

Jake :zzz:
 
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  • #3


bcrowell said:
It sounds like you're asking about the energy-momentum four-vector: http://en.wikipedia.org/wiki/Four-momentum The hyperphysics link you gave doesn't seem to discuss it.

Very good; thank you! Another question please: Is there such a thing as four-kinetic energy?
 
  • #4


jaketodd said:
Very good; thank you! Another question please: Is there such a thing as four-kinetic energy?

The fact that you're asking that question makes me think that you haven't read the WP article yet...?
 
  • #5


bcrowell said:
The fact that you're asking that question makes me think that you haven't read the WP article yet...?

So you're talking about four-velocity? I'm not sure if that creates four-kinetic energy or just goes into four-momentum.

Your wisdom please?

Thanks!

Jake
 
  • #6


Anyone please?
 
  • #7


Did you read the wiki yet? If so, what's your current understanding of the energy-momentum 4 vector?

If not - do you have some reason why not?
 
  • #8


pervect said:
Did you read the wiki yet? If so, what's your current understanding of the energy-momentum 4 vector?

If not - do you have some reason why not?

I think I understand it now. I think I just needed to read the article a couple more times for it to set.

Thanks,

Jake
 

1. What is relativistic momentum?

Relativistic momentum is the measure of an object's motion in terms of its energy and mass, taking into account the effects of special relativity.

2. Is relativistic momentum a vector or a scalar?

Relativistic momentum is a vector quantity, meaning it has both magnitude and direction. This is in contrast to scalar quantities, which only have magnitude.

3. How is relativistic momentum different from classical momentum?

Relativistic momentum takes into account the effects of special relativity, such as time dilation and length contraction, while classical momentum does not. This means that relativistic momentum will be different from classical momentum at high speeds, approaching the speed of light.

4. Can relativistic momentum be negative?

Yes, relativistic momentum can be negative if the direction of motion is opposite to the direction of the momentum vector. This is similar to classical momentum, where negative momentum indicates motion in the opposite direction of the positive momentum vector.

5. How does relativistic momentum relate to relativistic energy?

Relativistic momentum and relativistic energy are closely related, as they are both measures of an object's motion in terms of mass and energy. In fact, the formula for relativistic momentum, p = γmv, is derived from the formula for relativistic energy, E = γmc², where γ is the Lorentz factor, m is the mass, v is the velocity, and c is the speed of light.

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