4 ms·

Can you provide an example of a Lorentz boost that changes the number of particles?

eigenspace 3y ago
It's pretty general. Just draw the worldlines for some particles bouncing off eachother, and then perform a Lorentz boost, which means choosing a new tilted spatial surface to intersect the worldlines. If you perform a boost, then the spatial surface intersect fewer or more worldlines, and worldlines which were for particles in one frame can become antiparticles in another. Consider an electron absorbing a photon at spacetime point x, and then emitting a photon at spacetime point y, where (y0 - x0) > 0. An observer in another lorenzt boosted frame would then say that they see in their boosted coordinated system (x' and y' with rapidity v), that (y'0 - x'0) = cosh(v)(y0 - x0) - sinh(v) (y1 - x1) For large enough v, then you can have y'0 < x'0, so the observer in the boosted frame would see the events in a different order. One observer sees a negatively charged electron moving from x to y, and the other observer sees a positively charged positron moving from y to x.
- AnimalMuppet 3y ago
  If the events in frame 1 are causally connected, then to see the events in frame 2 in reverse order takes a boost of velocity greater than c, which is not a valid boost. Sure, you can do all kinds of things with a boost like that. It's not physically realizable, though. Can you show me an actual experiment to the contrary?
  - eigenspace 3y ago
    Compton scattering with a space-like separation for the absorption and emission points are a well known phenomenon in quantum field theory. Classically these events would be causally disconnected, but in a QFT the propagator is non-zero and instead has an exponential suppression in the space-like interval. This is a phenomenon with experimental consequences and uses:https://arxiv.org/abs/1301.3819 https://arxiv.org/abs/1301.3819 https://www.nature.com/articles/s41567-019-0774-3 https://www.nature.com/articles/s41567-019-0774-3
    - AnimalMuppet 3y ago
      Interesting. I did not know that. Still, we were originally talking about gravitons. "Exponential suppression in the space-like interval" means that it cannot apply to gravitons (or at least, it cannot apply to gravitons on astronomical scales). So, backtracking the argument a ways: Do you have any examples of the numbers of particles being different in different frames or coordinate systems that works at all distance scales?
      - eigenspace 3y ago
        What makes you think this cant apply to gravitons, or more generally, what makes you think that gravitons are relevant over large distance scales? > Do you have any examples of the numbers of particles being different in different frames or coordinate systems that works at all distance scales? Sure, it’s called the Unruh effect. Any accelerated frame (or observer in a gravitational field) will see a different particle vacuum than observers in a inertial frame. This means that if you start in empty space and then accelerate, the space will suddenly not look so empty and will be at a higher temperature with more fluctuating particles.
- scrubs 3y ago
  That example I think is tangential. The better example is free fall in a gravity well v. being accelerated up like in an elevator in space far, far away from gravitational sources
  - eigenspace 3y ago
    They asked for an example with Lorentz boosts, so only inertial frames.

It's pretty general. Just draw the worldlines for some particles bouncing off eachother, and then perform a Lorentz boost, which means choosing a new tilted spatial surface to intersect the worldlines. If you perform a boost, then the spatial surface intersect fewer or more worldlines, and worldlines which were for particles in one frame can become antiparticles in another. Consider an electron absorbing a photon at spacetime point x, and then emitting a photon at spacetime point y, where (y0 - x0) > 0. An observer in another lorenzt boosted frame would then say that they see in their boosted coordinated system (x' and y' with rapidity v), that (y'0 - x'0) = cosh(v)(y0 - x0) - sinh(v) (y1 - x1) For large enough v, then you can have y'0 < x'0, so the observer in the boosted frame would see the events in a different order. One observer sees a negatively charged electron moving from x to y, and the other observer sees a positively charged positron moving from y to x.

AnimalMuppet 3y ago
If the events in frame 1 are causally connected, then to see the events in frame 2 in reverse order takes a boost of velocity greater than c, which is not a valid boost. Sure, you can do all kinds of things with a boost like that. It's not physically realizable, though. Can you show me an actual experiment to the contrary?
- eigenspace 3y ago
  Compton scattering with a space-like separation for the absorption and emission points are a well known phenomenon in quantum field theory. Classically these events would be causally disconnected, but in a QFT the propagator is non-zero and instead has an exponential suppression in the space-like interval. This is a phenomenon with experimental consequences and uses:https://arxiv.org/abs/1301.3819 https://arxiv.org/abs/1301.3819 https://www.nature.com/articles/s41567-019-0774-3 https://www.nature.com/articles/s41567-019-0774-3
  - AnimalMuppet 3y ago
    Interesting. I did not know that. Still, we were originally talking about gravitons. "Exponential suppression in the space-like interval" means that it cannot apply to gravitons (or at least, it cannot apply to gravitons on astronomical scales). So, backtracking the argument a ways: Do you have any examples of the numbers of particles being different in different frames or coordinate systems that works at all distance scales?
    - eigenspace 3y ago
      What makes you think this cant apply to gravitons, or more generally, what makes you think that gravitons are relevant over large distance scales? > Do you have any examples of the numbers of particles being different in different frames or coordinate systems that works at all distance scales? Sure, it’s called the Unruh effect. Any accelerated frame (or observer in a gravitational field) will see a different particle vacuum than observers in a inertial frame. This means that if you start in empty space and then accelerate, the space will suddenly not look so empty and will be at a higher temperature with more fluctuating particles.
scrubs 3y ago
That example I think is tangential. The better example is free fall in a gravity well v. being accelerated up like in an elevator in space far, far away from gravitational sources
- eigenspace 3y ago
  They asked for an example with Lorentz boosts, so only inertial frames.