Uncertainty principle and limit of momentum.

In summary, the conversation discusses the uncertainty principle in the relativistic case and the assumption that p must be less than the limit E=m\gamma. However, there is a question about whether this assumption is always valid and if there are cases where the momentum can exceed the limit. It is also mentioned that in quantum field theory and relativistic wave equations, there are instances where particles can travel faster than the speed of light, but these are usually small contributions. Finally, it is noted that in relativity, classical postulates may not always hold and there are exceptions to energy conservation, number of particles in a volume, and the concept of a single path.
  • #1
kof9595995
679
2
To solve one of my textbook problems about uncertainty principle in relativistic case, I found that for every individual measured momentum p, I needed to assume [tex]p < \gamma mc[/tex] to get the correct answer, where [tex]\gamma = \frac{1}{{\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} }}[/tex].
But I keep suspecting whether the assumption is valid,because I have a vague memory that I heard that a particle can exceed the speed limit c when considering uncertainty principle. Then why can't the momentum exceed this limit?
Are these information enough for you guys? Or do I need to stick my textbook problem in this post?

Actually I was originally going to title this post as Uncertainty principle and FTL, but what I am going to ask is not that fancy so I change the title. :)
 
Physics news on Phys.org
  • #2
In SR, [tex]p^2=E^2-m^2[/tex] (with c=1), so p must be less than
[tex]E=m\gamma[/tex].
 
  • #3
Meir Achuz said:
In SR, [tex]p^2=E^2-m^2[/tex] (with c=1), so p must be less than
[tex]E=m\gamma[/tex].
But if there's always a uncertainty associated, can some measured momentum exceed the classical limit?It makes sense to me <p> should not exceed the limit, but is it true for all sample points of p?
 
  • #4
It depends whether you are doing quantum field theory or relativistic wave equations. In quantum field theory, you can have virtual particle "traveling faster than c" but all virtual contributions must be added together to produce a physical answer, and eventually they conspire to have real particles inside the light-cone. If you are doing relativistic wace equations, Meir Achuz's answer applies. The full understanding of the approximations behind would have to wait a little bit.
 
  • #5
Thanks for all the clarifications. I think I get it now.
 
  • #6
In relativity is a classical theory in the sense that all the classical postulate hold once that you assume space-time dimension and Lorentz transforms. In quantum mechanics many of the classical postulate are relaxed. So you find
- that particle can travel faster that c (with "small" contribution to the final probability)
- that the variational principle is not exactly satisfied
- the energy conservation is not exactly satisfied
- that the number of particle in an isolated volume is not constant
- there is not a single path linking two points
- that this message to arrive to you after few seconds can passes from alpha centauri (violating c).
and so on.
 

FAQ: Uncertainty principle and limit of momentum.

1. What is the uncertainty principle?

The uncertainty principle is a fundamental concept in quantum mechanics that states that it is impossible to simultaneously know the exact position and momentum of a subatomic particle. This means that the more precisely we know the position of a particle, the less we know about its momentum, and vice versa.

2. Why is there a limit to the precision of momentum measurements?

The limit to the precision of momentum measurements is a consequence of the uncertainty principle. According to the principle, the more precisely we try to measure the momentum of a particle, the less we know about its position. This is because the act of measuring the momentum of a particle causes a disturbance in its position, making it impossible to have perfect knowledge of both at the same time.

3. How does the uncertainty principle impact our understanding of the physical world?

The uncertainty principle has significant implications for our understanding of the physical world, as it challenges our classical, deterministic view of the universe. It suggests that at the subatomic level, the behavior of particles is inherently unpredictable and that our ability to measure and observe these particles is limited by the uncertainty principle.

4. Can the uncertainty principle be violated?

No, the uncertainty principle is a fundamental principle in quantum mechanics and has been extensively tested and confirmed through various experiments. It is a fundamental aspect of the behavior of particles at the subatomic level and cannot be violated.

5. How does the uncertainty principle relate to Heisenberg's uncertainty principle?

Heisenberg's uncertainty principle is a specific form of the uncertainty principle that applies to the position and momentum of a particle. It is named after Werner Heisenberg, who first proposed the concept in 1927. The uncertainty principle is a more general principle that applies to other pairs of complementary variables, such as energy and time or angular momentum and spin.

Similar threads

I Possible paradox in the uncertainty principle?
Replies
16
Views
1K
I Understanding the meaning of "uncertainty" in Heisenberg's UP
Replies
10
Views
2K
I Momentum-Position vs. Energy-Time Uncertainty Relations
Replies
10
Views
2K
I Momentum of a stationary particle/wave?
2
Replies
36
Views
4K
A Angular momentum uncertainty principle and the particle on a ring
Replies
3
Views
876
A The uncertainty principle in quantum gravity
Replies
1
Views
1K
I Measurement problem - will this work?
Replies
3
Views
856
I Is the uncertainty principle an ontological statement?
Replies
10
Views
2K
I Making sure about the spreads in the Uncertainty Principle
Replies
6
Views
1K
I Uncertainty between position and angular frequency - is this correct?
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top