Conservation of linear momentum at relativistic speeds

In summary, the conversation discusses the conservation of linear momentum in a scenario where a particle is accelerated in both the x and y directions. It is noted that it takes three times the energy to accelerate the particle in the x direction compared to the y direction. However, the net velocity of the particle will be 86% of c at a 45 degree angle. There is a discussion about the discrepancy in momentum between the x and y axes, but it is determined that there is no discrepancy as the 0.86c is the apparent vectored velocity and not the actual velocity due to the inclusion of time. This is seen in apparent superluminal expansion around supernova remnants.
  • #1
carl fischbach
The question I ask is linear momentum conserved in
in instance cited below?


You place a particle at the origin on a x-y axis
and accelerate it to 61% of c in the y direction.
Then you accelerate it to 61% of c in the x direction.
The net velocity of the particle will be
86% of c at 45 degrees.The key here is that it
takes approximately 3 times the energy to
accelerate the particle in the x direction than
the y direction, due to the fact that the net
velocity change in the y direction is 0%-61% of c
and in x direction the net velocity change is
61%-86% of c.If the rate of acceleration,distance
of acceleration and time of acceleration are the
same on the x and y axis, then force of acceleration on
the x-axis has to be greater than
on the y axis, since the energy of acceleration
on the x-axis is 3 times that of the y axis.
Therefore the momentum on the x-axis is greater
the y axis.

If the particle's final velocity is 86% of c at
45 degrees then the momentum of acceleration
should be equal on both the x and y axis.
Is there a discrepancy in momentum here?
 
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  • #2
Originally posted by carl fischbach
The question I ask is linear momentum conserved in
in instance cited below?


You place a particle at the origin on a x-y axis
and accelerate it to 61% of c in the y direction.
Then you accelerate it to 61% of c in the x direction.
The net velocity of the particle will be
86% of c at 45 degrees.The key here is that it
takes approximately 3 times the energy to
accelerate the particle in the x direction than
the y direction, due to the fact that the net
velocity change in the y direction is 0%-61% of c
and in x direction the net velocity change is
61%-86% of c.If the rate of acceleration,distance
of acceleration and time of acceleration are the
same on the x and y axis, then force of acceleration on
the x-axis has to be greater than
on the y axis, since the energy of acceleration
on the x-axis is 3 times that of the y axis.
Therefore the momentum on the x-axis is greater
the y axis.

If the particle's final velocity is 86% of c at
45 degrees then the momentum of acceleration
should be equal on both the x and y axis.
Is there a discrepancy in momentum here?
I don't think so. No acceleration above 0.61c is used or provides momentum. The 0.86c is the apparent VECTORED V (in your example). But, I don't think that your example is correct since you seem to be using two-dimensional (graph-paper) trig here, while with excluding time. In V calculations, a Y velocity at 0.61c and an X velocity at 0.61c takes time to reach the "end-point" from where you measure the Hypotenuse. The "actual V" of the vectored triangle cannot exceed the V of the greater of the XV or the YV if time is included. The "apparent" V can though, as is seen in apparent superluminal expansion around some supernova remnants.
 
Last edited:
  • #3


Yes, there is a discrepancy in momentum in this scenario. While linear momentum is conserved in all frames of reference, the conservation of momentum at relativistic speeds is not as straightforward as it is in classical mechanics. This is due to the fact that as an object approaches the speed of light, its mass increases and its momentum also increases. In this scenario, the particle's final velocity is 86% of c, which means its mass has increased and therefore its momentum has also increased. However, the discrepancy in momentum arises from the fact that it takes 3 times the energy to accelerate the particle in the x direction compared to the y direction. This means that the force of acceleration on the x-axis is greater, resulting in a greater momentum in that direction. Therefore, while the total momentum of the particle is conserved, the distribution of momentum between the x and y directions is not equal.
 

1. What is the principle of conservation of linear momentum at relativistic speeds?

The principle of conservation of linear momentum at relativistic speeds states that the total momentum of a system remains constant in the absence of external forces. This means that the sum of the momentums of all the objects in the system will remain the same before and after a collision or interaction, even at very high speeds.

2. How does the conservation of linear momentum change at relativistic speeds?

At relativistic speeds, the equations for conservation of linear momentum become more complex due to the effects of time dilation and length contraction. The total momentum of a system is still conserved, but the individual momentums of each object will change due to their changing mass and velocity.

3. Can the conservation of linear momentum be violated at relativistic speeds?

No, the conservation of linear momentum is a fundamental law of physics and cannot be violated even at relativistic speeds. While the equations may become more complex, the principle still applies and is crucial for understanding the behavior of objects at high velocities.

4. How does the conservation of linear momentum at relativistic speeds affect collisions?

At relativistic speeds, the conservation of linear momentum can result in counterintuitive outcomes in collisions. For example, in elastic collisions, the total momentum will still be conserved, but the velocities of the objects after the collision may not be what is expected based on classical physics.

5. How is the conservation of linear momentum at relativistic speeds relevant in real-world scenarios?

The conservation of linear momentum at relativistic speeds is relevant in many real-world scenarios, such as particle accelerators and spacecraft propulsion. Understanding this principle is crucial for accurately predicting the behavior of objects at high speeds, which is important in fields such as astrophysics and engineering.

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