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Joey Peluka
Joey Peluka
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In space, a photon with momentum $P$ is reflected off a previously at rest mirror, imparting momentum to the mirror. Even if the wavelength of the reflected photon is much smallerlonger than the that of the incident, the reflected photon still has some momentum vector pointing the opposite direction, meaning that the momentum of the mirror must be greater than $P$ in order to follow the conservation of momentum of the entire system. But this would all mean that the sum of the magnitudes of the momentum vectors has increased, so somehow the energy of the system has increased? Where did I go wrong?

In space, a photon with momentum $P$ is reflected off a previously at rest mirror, imparting momentum to the mirror. Even if the wavelength of the reflected photon is much smaller than the that of the incident, the reflected photon still has some momentum vector pointing the opposite direction, meaning that the momentum of the mirror must be greater than $P$ in order to follow the conservation of momentum of the entire system. But this would all mean that the sum of the magnitudes of the momentum vectors has increased, so somehow the energy of the system has increased? Where did I go wrong?

In space, a photon with momentum $P$ is reflected off a previously at rest mirror, imparting momentum to the mirror. Even if the wavelength of the reflected photon is much longer than the that of the incident, the reflected photon still has some momentum vector pointing the opposite direction, meaning that the momentum of the mirror must be greater than $P$ in order to follow the conservation of momentum of the entire system. But this would all mean that the sum of the magnitudes of the momentum vectors has increased, so somehow the energy of the system has increased? Where did I go wrong?

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Joey Peluka
Joey Peluka
  • 107
  • 4

AIn space, a photon with momentum $P$ is reflected off a previously at rest mirror, imparting momentum to the mirror. Even if the wavelength of the reflected photon is much smaller than the that of the incident, the reflected photon still has some momentum vector pointing the opposite direction, meaning that the momentum of the mirror must be greater than $P$ in order to follow the conservation of momentum of the entire system. But this would all mean that the sum of the magnitudes of the momentum vectors has increased, so somehow the energy of the system has increased? Where did I go wrong?

A photon with momentum $P$ is reflected off a previously at rest mirror, imparting momentum to the mirror. Even if the wavelength of the reflected photon is much smaller than the that of the incident, the reflected photon still has some momentum vector pointing the opposite direction, meaning that the momentum of the mirror must be greater than $P$ in order to follow the conservation of momentum of the entire system. But this would all mean that the sum of the magnitudes of the momentum vectors has increased, so somehow the energy of the system has increased? Where did I go wrong?

In space, a photon with momentum $P$ is reflected off a previously at rest mirror, imparting momentum to the mirror. Even if the wavelength of the reflected photon is much smaller than the that of the incident, the reflected photon still has some momentum vector pointing the opposite direction, meaning that the momentum of the mirror must be greater than $P$ in order to follow the conservation of momentum of the entire system. But this would all mean that the sum of the magnitudes of the momentum vectors has increased, so somehow the energy of the system has increased? Where did I go wrong?

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Joey Peluka
Joey Peluka
  • 107
  • 4

How are energy conserved and momentum both conserved in this system?

A photon with momentum $P$ is reflected off a previously at rest mirror, imparting momentum to the mirror. Even if the wavelength of the reflected photon is much smaller than the that of the incident, the reflected photon still has some momentum vector pointing the opposite direction, meaning that the momentum of the mirror must be greater than $P$ in order to follow the conservation of momentum of the entire system. But this would all mean that the sum of the magnitudes of the momentum vectors has increased, so somehow the energy of the system has increased? Where did I go wrong?