Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: chris on 31/07/2019 18:07:11
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I went to a very good school here in Perth today to entertain the troops; they asked very good questions, including one that I think we have discussed here before but which I wanted to revisit to ensure that the answer I have is right.
We were discussing red-shift; it's the case that a red photon is less energetic than a blue one; so when light is red or blue shifted, what happens to its energy level, and where does the extra energy go / come from?
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The additional (or diminished) energy comes from the different gravitational potentials of the source and receiver (gravitational red/blue shift) and their relative velocities (doppler shift).
Think potential/kinetic energy of a falling body, and the impact energy of a projectile hitting a moving target.
Definitely worth looking at Wikipedia's summary of the Pound-Rebka experiment, which invokes both phenomena.
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We were discussing red-shift; it's the case that a red photon is less energetic than a blue one; so when light is red or blue shifted, what happens to its energy level, and where does the extra energy go / come from?
In the case of relative motion (the Doppler shift Alan mentions), a given photon does not 'shift' somewhere along the way. It was always the same frequency (relative to a given inertial frame) during the entire trip from wherever it came, so no energy is lost.
Alan also describes the gravitational potential case where a blue light shone from the ground appears redder to an observer at high altitude due to being at a less-low (higher) gravitational potential. The inertial frame might be the same here, but the gravitational frame is not, so the photon doesn't actually ever change frequency relative to any particular observer. The same light is being measured, but with clocks running at different rates and thus counting different units of time when measuring the light's waves/time.
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Another way of looking at the gravitational red-shift is to consider it as an effect of time dilation in a gravitational field.
The emitter (on the surface of a planet, deep in its gravitational well, for example) sees the photons emitted at a certain frequency f1.
- The receiver (farther away from the planet, not so deep in its gravitational well) receives the photons with a lower frequency f2.
- The receiver sees the energy of the photon E=hf2 as being lower than the energy seen by the emitter E=hf1
- The photon has not changed along the way - it is the same photon
- But the receiver (outside the gravitational well) measures the the frequency f2 by his local clock, which (according to general relativity) ticks more rapidly than the clock of the emitter. So the receiver measures the photons at f2 to be lower than the emitter who measures them to have frequency f1.
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Okay, so the photon's frequency has never changed, and hence it's energy is the same?
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Okay, so the photon's frequency has never changed, and hence it's energy is the same?
The photon has not changed, but the observer has changed.
Different observers will use a different clock → they will often measure a different frequency ↔ they will measure a different energy.
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Hang on; if I'm looking at a hydrogen absorption spectrum that's red shifted, how will that differ depending upon who and how it's observed?
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If you are at a lower gravitational potential than, or moving towards, the source, it will appear to be blueshifted compared with a hydrogen line (cesium microwave spectrum, or any other frequency standard) generated locally. To an observer at a higher potential or moving away from the source, it would appear redshifted.
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a hydrogen absorption spectrum
A single spectral line in isolation is not very helpful, but hydrogen has a series of lines at specific relative wavelengths, so by looking at a spectrum, you can tell what you are looking at. (Plus, Hydrogen being the most common element in the universe might help you guess that you are looking at a hydrogen spectrum...)
One important absorption line of hydrogen is the hydrogen alpha line.
- Distant quasars produce black-body radiation at every possible wavelength
- But the intergalactic gas clouds in between that qasar and us absorb light at a specific ultraviolet wavelength: 121.6 nm
- After absorbing light of this wavelength, they will re-radiate this energy in a random direction, and perhaps as several photons of lower energy
- Each gas cloud in this path absorbs some energy at 121.6 nm
- But the general expansion of the universe means that when this light reaches the next gas cloud, the absorption line from the previous gas cloud will be red-shifted to a longer wavelength. This new gas cloud absorbs some more energy at 121.6nm
- When it is received by an orbiting ultraviolet satellite, a "forest" of hydrogen absorption lines are visible, superimposed on the quasar's black-body radiation
how will that differ depending upon who and how it's observed?
Every gas cloud (at different distances/red-shifts) "observes" the incoming light from the quasar.
- Every gas cloud absorbs exactly the same wavelength (as seen by that dust cloud)
- When the light arrives at Earth, we see individual absorption lines at different red-shifts, representing individual clouds of hydrogen between us and the quasar, at different distances=different red-shifts.
See: https://en.wikipedia.org/wiki/Lyman-alpha_forest
Another analogy: Doppler Shift
If a fire truck is travelling along a street, different people on the street will hear different things:
- Person "A" who is being passed by the fire truck (for a moment, not moving towards or away from them) will hear the siren at pretty much the original pitch.
- Someone being approached by the fire truck will hear a higher pitch than person "A".
- Someone being who sees the fire truck moving away will hear a lower pitch than person "A".
- The fire truck does not produce a different sound for the benefit of each person; it produces the same sound in every direction, but different observers will hear different things, depending on the radial velocity of the fire truck relative to the speed of sound.
Red-shift of light is slightly different, as each observer sees it traveling at the same speed "c".
- But the frequency measured by each observer will vary, depending on the radial velocity of the source relative to the speed of light.
- If the relative speed gets very high (eg > c/10, such as distant quasars), you also need to take into account time dilation effects due to special relativity.
The big thing about Einstein's Relativity is that everything is Relative - different observers will measure different things, depending on their relative velocity and relative gravitational potential - and that's ok!
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Interesting Evan
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I'm still not clear on this, so apologies for harping on. I understand the logic you have put forward to say that if I observe some light from a differing speed or gravitational potential relative to the origin of the light then I see it as red or blue shifted. But if I measure the actual energy of the photons then I'll record an energy level equivalent to a photon of that wavelength, won't I? But that's not what was issued by the source. So where's the energy gone?
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You can think of energy as relative since it depends on relative velocity. The velocity of an object can be taken as relative to the velocity of light. Which it is in the calculation of time dilation.
It would be better to have a video on this as visualising it may make it clearer. I may try to track a suitable one down.
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Enter stage right, physics girl.
https://youtu.be/GHCc9b2phn0 (https://youtu.be/GHCc9b2phn0)
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The energy difference between source and receiver has "come from" (or "gone to") the gravitational potential difference and/or relative velocity of the source and receiver. The Pound-Rebka experiment demonstrated this brilliantly:
Gamma photon emission from the decay of Fe57 has a very narrow bandwidth. These photons can be absorbed by another Fe57 nucleus if and only if there is no gravitational or velocity difference between emitter and absorber. P and R set up a source at the top of a tower and a detector at the bottom, and the detector did not absorb the photons unless it was moving away from the source at such a speed that the Doppler red shift cancelled the gravitational blue shift. Inverting the experiment, absorption only occurred if the receiver was moving towards the source such that the Doppler blue shift cancelled the gravitational red shift.
In mutual free fall, say in an orbiting spacecraft, there is no impact force between a cricket ball and a hand. But if you drop the ball from any height to a stationary catcher, there will obviously be an impact as the original potential energy of the ball was converted to kinetic energy which is dissipated on impact. The art of catching a hard ball is of course to move your hands to match the ball's speed, so its kinetic energy is dissipated by your entire body (or at least your arm and shoulder muscles) rather than the skin of your hands. Obvious, really , but Pound and Rebka didn't play cricket, so had to find out the hard way.
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Enter stage right, physics girl.
I liked that video, but it really only applies to cosmological redshift.
- But Doppler effect and gravitational redshift are experienced on Earth (eg the Pound-Rebka experiment mentioned by Alan).
PS: I did have one quibble - ripples from a stone dropped in a pond are attenuated with distance because the energy is spread out over a larger circumference of the ripple - this has a bigger impact over a few meters than the viscosity of the water.
I'll record an energy level equivalent to a photon of that wavelength, won't I? But that's not what was issued by the source.
You can treat some of these things in a "classical" (pre-Einstein) manner.
Warning: These are only analogies, so don't take them too literally!
Gravitational Redshift
One mathematician before Einstein successfully predicted black holes by imagining light as little balls, thrown upward against gravity, at a certain speed (c). He imagined the little balls losing energy as they rose against gravity. Once gravity reaches a certain critical value, the speed of light is less than escape velocity, and you have a black hole!
Now he didn't know that light always travels at c (as measured by a local observer), but the principle is correct: light does lose energy as it rises through a gravitational field.
- And he didn't know that the energy of light is proportional to its frequency, so he predicted a change in velocity, rather than a change in frequency (red shift)
Doppler Shift (low speeds)
You can imagine light (or sound) as a wave traveling on a medium as a wave emitted with a certain frequency (eg from a laser beam or a police siren).
If you are moving away from the source (at much less than the velocity of the wave), the waves and crests must travel a little farther every cycle to reach you, so the crests will arrive less frequently than the rate at which they were emitted: you will observe the wave having a lower frequency than the frequency with which it was emitted.
The wave was originally emitted with a certain power.
- For an observer moving away from the source, the received power will decrease over time as the observer moves farther away (due to the inverse-square law).
- In addition to this, the received power is further reduced because the energy of each wave is spread out over a longer period (the time for successive crests to reach the observer).
Translating this to photons (post-Einstein):
- The inverse square law means that as you move farther from the source, the photons are spread out through a greater area of space, so you receive photons less frequently
- The Doppler shift means that the photons are received with a lower frequency = lower individual photon energy.
Doppler Shift (high speeds)
If you are moving away from the source (at close to the velocity of the wave), things get more complex.
For light, Einstein's time dilation starts to have a significant effect when you exceed c/10, so you have to take into account a relativistic correction to the Doppler effect, which you can ignore at low speeds (like police measuring the speed of a car on the highway).
And you don't want to stand too close to a police car travelling at greater than the speed of sound!
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Where does the energy go, (approximately) inertial version. Say you are standing still and a bowler throws a cricket ball at you. It hurts! Now say you are riding a moped past the bowler and he throws the cricket ball at you. Since you are almost matching the speed of the ball it hurts a lot less. So where did the energy go? It was relative to the velocity of the victim and the bowler.
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One experiment where both gravitational red shift and Doppler red/blue shift become important is the NICER experiment on the ISS.
- One of its goals is to measure the physical size and density of neutron stars
- By measuring the red shift of the X-Ray Pulsar beam as it approaches and passes Earth
- The X-Ray photons experience gravitational red-shift as they rise from the surface of the Pulsar
- The X-Ray photons have a Doppler blue-shift as the pulsar rotates towards us, and Doppler red-shift as it rotates away from us
- Because the rotational speed of some neutron stars can approach a significant fraction of the speed of light, the relativistic version of Doppler shift may be needed in certain cases
The goal is to estimate the density of the (presumed) quark-gluon soup in the center of a neutron star. This will have much higher density than can be achieved in the LHC, and may reveal new forms of matter - for example, are the very dense Strange Quarks stable at these pressures?
I haven't seen any specific results, but data collection has been happening for over a year, now.
See: https://www.livescience.com/62436-neutron-star-pulsar-width-quantum.html
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Where does the energy go, (approximately) inertial version. Say you are standing still and a bowler throws a cricket ball at you. It hurts! Now say you are riding a moped past the bowler and he throws the cricket ball at you. Since you are almost matching the speed of the ball it hurts a lot less. So where did the energy go? It was relative to the velocity of the victim and the bowler.
Thanks - that clinched it and made the connection that I was missing in my mind!