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The energy of a photon depends on its wavelength, so theoretically when it is blueshifted it should have more energy right?

Then what if a spaceship with a solar panel on the front is traveling towards the sun at relativistic speeds. An incoming photon undergoes a blueshift from the observer on the spacecraft. So does the solar panel read the same energy as if the light wasn't blueshifted? I see two options here: 1. Either the solar panel reads two different numbers depending on the observer. (almost like 2 realities exist) 2. Or it reads the same because the energy of the photon is not actually based on wavelength

To keep it simple let's imagine we're only talking about one photon, because time dilation might affect the power level the solar panel was reading.

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    $\begingroup$ I just want to point out that the relativity of energy is not limited to special (or general) relativity. The kinetic energy of a moving object depends on the reference frame even in Newtonian mechanics. It shouldn't be surprising that such a thing occurs for light in relativistic mechanics. In fact, conservation of energy in matter/light interactions dictates that a photons energy must depend on reference frame since the matter's kinetic energy does. $\endgroup$
    – josh314
    May 14, 2018 at 16:10
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    $\begingroup$ @josh314 The question here is not why the energy is different in different frames. This is obvious. The question is why the energy measured by the panel is the same in both frames. (1) In the ship frame the panel is stationary, the photons are blueshifted. (2) In the Earth frame the panel is moving (it is in the ship), the photons are not blueshifted. In the Earth frame, why does a moving panel register a blueshifted energy of the non-blueshifted photons? The speed of light is the same in all frames. Neither of the 3 answers so far actually answer the question. $\endgroup$
    – safesphere
    May 14, 2018 at 16:32
  • $\begingroup$ "the solar panel reads two different numbers depending on the observer" There's only one "observer" of the photon. Observers of the solar panel aren't measuring the photon themselves. $\endgroup$
    – Beanluc
    May 14, 2018 at 18:39
  • $\begingroup$ @safesphere If you work in the panel's rest frame, the photons are blueshifted. If you work in some other observer's frame, the panel is moving, which shifts its absorption frequencies. Either way the actual numbers come out the same in the end. It might help to read up on how Doppler cooling works, as this is an effect which directly depends on atoms "observing" shifted wavelengths of light depending on their own motion. $\endgroup$
    – zwol
    May 14, 2018 at 23:22
  • $\begingroup$ upload.wikimedia.org/wikipedia/commons/thumb/d/d4/… $\endgroup$ Jul 30, 2020 at 5:41

4 Answers 4

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The energy of a photon is related to its frequency or wavelength. However the energy is a conserved quantity in a specific reference frame, but it is not an invariant. Another reference frame in relative motion vs. the former measures a different energy.

In the example the observer on the spaceship approaching the sun experiences the blueshift of the solar photons. The solar panel on the spaceship reads a higher energy of the solar radiation.

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    $\begingroup$ While energy is not invariant, the device reading is invariant and does not depend on the observer. $\endgroup$
    – safesphere
    May 14, 2018 at 8:01
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    $\begingroup$ @safesphere. The 4-momentum is a conserved quantity, while the norm or the square of the 4-momentum is an invariant. As energy is a component of the 4-momentum, it is conserved, but not an invariant. Same consideration as for the 3-momentum. $\endgroup$ May 14, 2018 at 9:10
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    $\begingroup$ Sorry if my comment was not clear. If a device is used that measures energy and this device shows a particular value measured, this value would be invariant and the same in any reference frame despite the fact that the energy is different in different frames. Your answer seems to contradict this. (May be it doesn't, but it seems to.) I believe the OP question is to explain the spaceship device reading high energy in the frame of the observer on the Earth where the photons are not blueshifted. Your answer does not explain it. $\endgroup$
    – safesphere
    May 14, 2018 at 14:43
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    $\begingroup$ Ah. My interpretation of the OP's question is that they are considering two frames, one "stationary" on earth, and the other flying towards the sun with some speed. Then they are asking if an identical solar panel in each frame measures the same or different results. $\endgroup$
    – Chris
    May 14, 2018 at 15:30
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    $\begingroup$ @safesphere. The number on the display of the solar panel shows what is measured in that specific reference frame. It is like a ruler on the spaceship which is a unit length, but in another frame that length is measured contracted. $\endgroup$ May 14, 2018 at 16:35
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Yes, blueshift increases the energy the observer receives from the photon. An analogue would be a ball thrown at a moving car - the hit will be much harder when the car is moving towards the ball than when the car is moving away from the ball.

The second part of your question can be read in two ways:

I see two options here: 1. Either the solar panel reads two different numbers depending on the observer. (almost like 2 realities exist) 2. Or it reads the same because the energy of the photon is not actually based on wavelength.

Interpretations:

  1. "Do different human observers get different readings from the same solar panel?" No. There are no quantum effects here. Only thing that matters is the velocity of the solar panel relative to the photon.
  2. "Does moving solar panel get a different reading than a stationary solar panel?" Yes. The photon will give more energy to the solar panel that is moving towards it, because of blueshift.
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    $\begingroup$ Your interpretation 2 is not justified (not incorrect, but unsupported), because there is no blueshift in the frame of the Earth. Your analogy of a massless photon with a massive ball also does not hold. The energy of the ball is defined by the relative speed. The energy of the photon is defined by its frequency and again, the photon is not blueshifted in the frame of the Earth. Your answer does not explain the higher energy registered by a moving panel in the frame of the Earth. $\endgroup$
    – safesphere
    May 14, 2018 at 16:13
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    $\begingroup$ The extra energy should be accounted for by the loss of kinetic energy. $\endgroup$ May 14, 2018 at 22:49
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    $\begingroup$ @safesphere I don't quite follow you. By "frame of earth", do you mean the frame of the source emitting the photon? Also you can interpret "moving panel" as moving relative to the source of the photon (though situation gets more complex if the source is accelerating) - and in that case, I can't see how there could be a "moving panel in the frame of the Earth". A moving panel is by definition not in the same frame as the source of the photon. $\endgroup$
    – jpa
    May 15, 2018 at 6:05
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Yes.

Energy depends on frequency. An observer on earth and an observer on a relativistic spaceship moving towards the sun will see different frequencies due to the Doppler shift. This means the different observers will record different energies for the photons coming from the sun.

While it is a bit surprising that the relative velocity between the source of light and an observer of that light changes the observed frequency, this does not lead to the conclusion that there are "two realities".

Incidentally this doppler change in energy is leveraged in Doppler Cooling to laser cool atoms to $\mu K$ temperatures. The idea is that a laser is shot at atoms which is red detuned from the atomic transition wavelength (not resonant). If an atom is moving towards the source of the laser beam it will see that laser as being in resonance and thus will absorb the photon. This absorption will cause the atom to slow down a little bit. In contrast, if the atom is travelling the opposite direction it will see that beam red shifted even further so it is even less likely to absorb the photon. By pointing laser beams in towards the atom at all directions the atom can be slowed down because no matter which way it moves it is moving towards a beam so it always slows down.

Of course you can't use this to cool an atom indefinitely because eventually other heating effects take over and a final temperature is achieved as a balance of laser cooling and these heating effects.

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What the previous answer didn't state (at least not obviously):

Yes.

$E = h \nu$ remains true whatever happens.

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