does EM energy decrease with red-shifting?

[gib65]

The minimum energy carried by a wave of electromagnetic radiation is given by E=fh, right? When an object emitting radiation moves away from us, the radiation emitted in our direction is red-shifted, right? But doesn't that imply that frequency (f) should decrease? Therefore, does the minimum energy of the radiation decrease when it red-shifts?

 

(If the answer is yes, I'm assuming energy is one of those dilating variables that relativity predicts - like time, length, mass, etc. - of course, "dilating" would be the wrong word in this case).

[swansont]

Energy is a frame-dependent quantity. Within a frame, energy is conserved, but the value of a given energy depends on the frame.

[gib65]

Energy is a frame-dependent quantity. Within a frame, energy is conserved, but the value of a given energy depends on the frame.

 

So "frame-dependent" is the word I'm looking for (as opposed to the "dilation" of energy), correct?

[Severian]

In fact, energy is the 'time'-component of a 4-vector, so its transformation properties are just like those of time.

[Meir Achuz]

"Therefore, does the minimum energy of the radiation decrease when it red-shifts?"

Yes.

[gib65]

Thanks for the answers.

 

Now a follow up question:

 

How does this fit into energy "quanta"? What I mean is, according to quantum mechanics, energy only comes in multiples of E=fh, but if f can vary continuously (because the objects emitting it can be moving away at any arbitrary speed), then does this conflict with the central idea behind quantum mechanics?

 

My understanding of energy quanta is simply that it comes in discrete indivisible packets (called photons), but the amount of energy carried by these photons isn't necessarily limited to specific amounts themselves. So if f can vary in a smooth continuous way, the photons making up the radiation whose frequency is f should also be allowed to vary in a smooth continuous way (in the context of a frame of reference, of course). Is this sound reasoning?

[Fred56]

gib65:

You might be having a problem with the way you're looking at frequency (of light). This is usually represented by a Greek v (nu), and is a quantised, not analogue or continuously variable, quantity. Any shift in frequency (into the red "end" of the spectrum) is due to the source receding, and blue shift is due to the opposite effect. Any photon otherwise stays the same frequency (energy), amplitude is meaningless to a photon's "wave".

[swansont]

gib65:

You might be having a problem with the way you're looking at frequency (of light). This is usually represented by a Greek v (nu), and is a quantised, not analogue or continuously variable, quantity. Any shift in frequency (into the red "end" of the spectrum) is due to the source receding, and blue shift is due to the opposite effect. Any photon otherwise stays the same frequency (energy), amplitude is meaningless to a photon's "wave".

 

The shift is due to any relative motion, but if there is motion, then different frames exist. Also, the quantized energies occur in bound systems; unbound systems can have a continuum. There's nothing about Doppler shifts that conflict with QM.

[Fred56]

Also, the quantized energies occur in bound systems; unbound systems can have a continuum.

I know about bound systems, are you talking about electrons...? Does a "free" electron emit a continuum of EMR? I know about Bremsstralung (really fast electrons).

(Perhaps, for the eluctation of some, one would expand somewhat...?)

[timo]

How does this fit into energy "quanta"? What I mean is, according to quantum mechanics, energy only comes in multiples of E=fh, but if f can vary continuously (because the objects emitting it can be moving away at any arbitrary speed), then does this conflict with the central idea behind quantum mechanics?

As you are about to find out, energy coming in discrete quanta is not a central idea in (modern) QM - it is a result that is true for some (important) scenarios.

 

My understanding of energy quanta is simply that it comes in discrete indivisible packets (called photons), but the amount of energy carried by these photons isn't necessarily limited to specific amounts themselves. So if f can vary in a smooth continuous way, the photons making up the radiation whose frequency is f should also be allowed to vary in a smooth continuous way (in the context of a frame of reference, of course). Is this sound reasoning?

As I told you in the discussion about your QM intro, you need to have some reasons why the frequency would be restricted. For the redshift caused by relative movement and the spectral lines in your text, this is pretty simple: If you burn something that stands on your table, neither the system as a whole nor a significant amount of the individual atoms/molecules is moving with a significant fraction of c relative to you => assuming there is a reason why some burning substance could only emit certain frequencies (and that is the point your text lacks, not that you didn't consider relativistic effects), you get your spectral lines. If now the whole system was moving away with a significant fraction of c (say, in a distant star), then the whole system of spectral lines is shifted to the red (but still is discrete spectral lines), because all emitted frequencies got red-shifted equivalently. You could even use that to determine the speed that the source moves away from you.

 

Reading tip for you (assuming you have access to some library - if you are just interested in QM, then the book is not worth buying): Atkins, "Physical Chemistry", chapters 11 (Quantum theory: Introduction and principles), 12 (QT: Techniques and application) and 13 (Atomic structure and atomic spectra). It's written for laymen (undergrad chemicists ) but probably contains a lot of valuable information for you. And don't be disappointed if you're not reading through the three chapters in a day or two - a few weeks and half a block of paper for personal notes and checking calculations is a much more realistic scale.

[swansont]

I know about bound systems, are you talking about electrons...? Does a "free" electron emit a continuum of EMR? I know about Bremsstralung (really fast electrons).

(Perhaps, for the eluctation of some, one would expand somewhat...?)

 

Yes. The blackbody spectrum is a continuum.

[Fred56]

Does "equipartition law" have anything to do with a blackbody spectrum? viz:

 

"The law of equipartition breaks down when the thermal energy kBT is significantly smaller than the spacing between energy levels. Equipartition no longer holds because it is a poor approximation to assume that the energy levels form a smooth continuum, which is required in the derivations of the equipartition theorem" --Wikipedia

 

Which obviously all means that our THERMODYNAMIC view of heat isn't quite on target...

 

P.S. This chart, which has at least 2 other links in this forum, might help anyone understand our "picture" of EMR and so on. It's got descriptions of all the kinds of radiation "excitation": (luminescence, flourescence, ...). Covers absorption, nice pretty pictures... take a look (go on). I wonder how many reading this realise that HEAT is the result of, and itself causes infrared EMR to be absorbed, or emitted....?

http://www.lot-oriel.com/site/site_down/cc_light_deen01.pdf