Furthest redshift possible?

[Baby Astronaut]

Is there a limit to the amount of redshift that light can experience before it stops redshifting any further?

 

I'm asking separately for redshift caused by space expansion, and redshift caused by normal star movement.

[Gilded]

I don't think so. AFAIK current theories predict that a photon's wavelength will asymptotically approach zero or infinity as the energy increases or decreases.

[insane_alien]

well, the wavelength can't get any bigger than the universe so i guess that imposes a physical limit on it.

[npts2020]

well, the wavelength can't get any bigger than the universe so i guess that imposes a physical limit on it.

 

Nor can the wavelength get any smaller than the total energy in the universe?

[insane_alien]

yes but there are other limits to it as well that will keep the photons at a much lower energy.

 

a photon of high enough energy can turn into an electron-positron pair which will promptly annihilate and result in two photons of lesser energy.

[npts2020]

yes but there are other limits to it as well that will keep the photons at a much lower energy.

 

Just wondering what that upper limit is and any idea why at that point?

Edited September 15, 2008 by swansont
fix quote tag

[insane_alien]

well, i don't know the exact number but i would imagine it would be impossible to have a wavelength smaller than the plank length but before that it is a practical limit as the photon will split up via electron-positron annihilation.

[Mr Skeptic]

well, the wavelength can't get any bigger than the universe so i guess that imposes a physical limit on it.

 

Now there is an interesting thought, possibly worthy of its own thread. What happens when your photon is large enough that the expansion of the universe would "split" it in pieces? Or would it be impossible to get a photon with less than the Plank energy? But then what happens when you red-shift that photon?

[Martin]

Is there a limit to the amount of redshift that light can experience before it stops redshifting any further?

 

I'm asking separately for redshift caused by space expansion, and redshift caused by normal star movement.

 

a lot of good responses.

 

in the standard cosmology model, the universe keeps on expanding indefinitely, so according to that model wavelengths of the CMB light (which dates from around 380k and has already been stretched by a factor of some 1090 so far) will keep on getting stretched indefinitely.

 

I don't know of any physical limit to how much wavelengths can be stretched, if you wait long enough for the universe to expand enough, the light just becomes less and less detectable.

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you say you are asking separately about cosmological redshift (i.e. caused by space expansion) and about Doppler shift, caused by proper motion of the source. I only responded to the part about cosmological redshift.

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About Doppler shift, other people obviously have ideas about this, but I will quote the Doppler formula and try to say something anyway.

 

sqrt((1+beta)/(1-beta))

 

beta is v/c and this formula gives the ratio the wavelength increases by.

If you make beta good and close to one then the fraction approaches 2/0 which is infinite, so you can make the number be as big as you like. Meaning you can increase the wavelength by as large a ratio as you like.

 

the only thing is, you again might have to wait. And practically the light becomes undetectable.

If the departing rockship is going very fast, so the signal sent back to you has a wavelength that is very very long, then you have to wait a very very long time before even one cycle of the wave comes in.

 

The current size of the universe wouldn't be much of a limit because you are going to have to wait a long time and the universe will expand while you wait. It will expand enough to accomodate whatever.

 

If you think of it in quantum terms, and imagine a detector sensitive enough, then waiting comes down to waiting for the detector to click. You might have to wait a billion years, if the light is Dopplershifted a way lot.

 

OK, I will hazard a guess that there is probably no theoretical limit to either kind of redshift, if you have a sensitive enough detector and can wait long enough.

[Baby Astronaut]

And here I'd have thought the photon would snap in half. They're so tiny, it's incredible to imagine a photon stretched as long as the universe.

 

So when a photon is stretched very long, in order to see it directly with a powerful enough scope, will you be unable to see it when the photon's beginning length enters your eye, instead having to wait for its end length to catch up in order to see it?

 

In other words, can our vision process the as of yet incomplete, first section of an overstretched photon, before the rest of it catches up?

 

 

In regards to my original question, I didn't ask how long a photon can be stretched, but what's the reddest it can become. Is there a limit, for example, will the photon keep stretching but stop becoming more red after a certain point?

[swansont]

well, i don't know the exact number but i would imagine it would be impossible to have a wavelength smaller than the plank length but before that it is a practical limit as the photon will split up via electron-positron annihilation.

 

The planck length is the scale at which you need a theory of quantum gravity. I don't see a reason (though I'm not looking very hard) why a limit on a photon's wavelength would necessarily be tied to that.

[Baby Astronaut]

And here I'd have thought the photon would snap in half. They're so tiny, it's incredible to imagine a photon stretched as long as the universe.

 

So when a photon is stretched very long, in order to see it directly with a powerful enough scope, will you be unable to see it when the photon's beginning length enters your eye, instead having to wait for its end length to catch up in order to see it?

 

In other words, can our vision process the as of yet incomplete, first section of an overstretched photon, before the rest of it catches up?

 

 

In regards to my original question, I didn't ask how long a photon can be stretched, but what's the reddest it can become. Is there a limit, for example, will the photon keep stretching but stop becoming more red after a certain point?

I would like to revisit the first statement in this quote and the unanswered questions. If no one minds

 

Also, I just found out about gravitational redshift. So now there exists Doppler, Cosmological, and gravitational redshifts. How can anyone tell the difference? Are there various shades of redshift corresponding to each particular source?

[Martin]

And here I'd have thought the photon would snap in half. They're so tiny, ...

 

Baby, where did you get the idea that photons are tiny? The only size scale a photon has is its wavelength.

 

For radio waves that could be 10 meters

 

I didn't ask how long a photon can be stretched, but what's the reddest it can become.

 

What's the difference? Stretching is just another way of talking about expanding the wavelength. Making red is just technical jargon for the same thing---redder means longer wavelength.

 

Is there a limit, for example, will the photon keep stretching but stop becoming more red after a certain point?

 

How could there be? It is the same thing. Redness is tech slang (in certain limited contexts) for "long wavelength". Most light has no actual color----infrared, microwaves, radio waves etc obviously have no color.

 

Yet if you redshift infrared 1000-fold it becomes microwave, and if you redshift microwave another 1000-fold it becomes radio wave.

 

We are using imprecise words to talk about an underlying mathematical reality. Focus on the math. Using the words without having the math clearly in mind will just confuse you.

 

You seem to be drawing an exaggerated distinction between Doppler and cosmological redshift. The distinction is one of convenience, one has to learn which formula to use. There are two formulas, Doppler and cosmo-redshift.

At a deep fundamental level it's all the same thing---fields and observers---but you have to learn to use the right formula in the right situation. Taking the wrong approach makes calculation disappointingly messy.

 

Photon is a human concept useful in some contexts. Quantum field theory is still being worked out in the case where there is no fixed prearranged background spacetime---it's not clear in what form the concept of particle will survive. Photon is probably not a reliable mental token to use in all situations. Lighten up>. Think about fields some.

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[Baby Astronaut]

Thanks for clarifying.

 

I may have pinpointed my confusion. I had been imagining a photon occupied the distance between each light wave. But judging from more recent definitions of light, it seems people are tending away from the idea of a photon anyway.

 

Still, I have a few questions about light wavelength that may help me understand it better.

 

1. Is light detectable if the first wave in its wavelength has reached the light detector, but the second wave hasn't yet (due to its tremendous length)? In other words, do you have to wait until the entire wavelength from end to end has passed completely through the detector before you can detect the light?

 

2. a) Waves in the ocean do not exist in isolation. They are connected to waves in front and waves behind. I imagine the same holds true for light. A wavelength being the distance between two waves, is it possible for the two light waves that form one wavelength of light to exist as a pair in isolation?

 

b) Even though a liquid wave is normally followed by other waves, it seems possible to cut the second wave off and isolate the first wave, allowing it to continue alone. Is it possible for a single light wave to exist in isolation if one tried a similar approach? The result might be no detectable wavelength, since there'd be no second wave ever coming.

 

3. If redshifting can transform light from one state to another, for example a microwave to a radio wave, then how does the observer know that a distant light was redshifted and that it's not just in its original state?

[Martin]

3. If redshifting can transform light from one state to another, for example a microwave to a radio wave, then how does the observer know that a distant light was redshifted and that it's not just in its original state?

 

Visible light, microwave, radiowave are not different states. They are all just vibrations in the EM field. with different frequency is all.

 

Focus on the field. We are just gradually getting to understand fields.

They are well-understood in the idealized case of FLAT space. The theory is called QFT (quantum field theory). So far physicists have only managed to construct QFT on some fixed setup space usually flat.

 

Photons and waves are human concepts taken over from everyday experience of throwing pebbles (particles) and watching ripples (waves).

They don't exactly fit QFT.

 

You can picture a photon as a wave-packet----more or less bunched waves more or less all the same frequency. But when you picture it this way you aren't sure when it will register in the detector box!

It might detected at the peak of the packet (if there is one) or half way, or before halfway, or after halfway. Perhaps you could say the overall envelope or shape of the packet tells you the probability of when you might detect it. But only a probability, and what does that mean? More complication, having to repeat something over and over.

 

So everyone agrees that QFT underlies what we see, and we don't know exactly what QFT is except in flat-and-suchlike case, and our analogies of pebbles and ripples are wrong. And if you think wavepackets you aren't supposed to expect it will always be detected at the same place in the packet. There's uncertainty..

 

Now you ask. How does an astronomer know the light from a star has been stretched? Because he takes the light from the star and makes a rainbow of it---a kind of bar-code band called a spectrum. And there are recognizable patterns of lines in the spectrum which are the work of particular atoms----hydrogen, sodium, iron. If you see the hydrogen PATTERN of bright and dark lines in the barcode, and you see that the whole pattern has been shifted towards longer wavelengths than you get by heating hydrogen in the lab then it is a NO-BRAINER that the light has been uniformly stretched out to longer wavelengths.

[Mr Skeptic]

Now you ask. How does an astronomer know the light from a star has been stretched? Because he takes the light from the star and makes a rainbow of it---a kind of bar-code band called a spectrum. And there are recognizable patterns of lines in the spectrum which are the work of particular atoms----hydrogen, sodium, iron. If you see the hydrogen PATTERN of bright and dark lines in the barcode, and you see that the whole pattern has been shifted towards longer wavelengths than you get by heating hydrogen in the lab then it is a NO-BRAINER that the light has been uniformly stretched out to longer wavelengths.

 

But there are more than one type of redshift. Is it possible to tell from the light which type of redshift to do, or do they need to do additional calculations an apply them separately (eg, the star is so far so it has so much Hubble redshift, differs from nearby stars so it has velocity redshift, ...)?

[Klaynos]

IIRC relativistic redshift reduces to Doppler shift for non-relativistic speeds...

[Martin]

IIRC relativistic redshift reduces to Doppler shift for non-relativistic speeds...

 

As usual it depends on what one means by non-relativistic and how accurate one wants to be. I think for speeds like 1/10 of c it might work OK. We can check it out using

http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html

Have to prime it by putting 0.27, and 0.73, and 71 into the boxes then it says that if the speed was 0.66c when it emitted light then redshift z = 1.

 

But the relativistic Doppler formula says z = sqrt(1.66/.34)- 1 = 1.2

So the error is not too terrible. One formula, the actual cosmological redshift, says z = 1 and the relativistic Doppler formula says 1.2.

 

Again, for a much smaller speed, the actual cosmological redshift formula says if the speed was 0.1c when it emitted the light then the redshift z = 0.11.

 

This is much better! The relativistic Doppler formula says

z = sqrt(1.1/0.9)- 1 = 0.106, which rounds up to 0.11.

 

So the Doppler formula is definitely safe for recession speeds around 0.1c and less.

 

(That could be what you mean by "non-relativistic". So you are right)

 

On the other had it doesn't work so well for recession speeds like 0.66c.

 

And it doesn't work at all for recession speeds of c and greater than c.

 

Unfortunately for the Doppler formula, most of the objects in the observable universe had recession speeds which are greater than c, the speed of light, when they emitted the light we are now receiving from them*. So for the majority of observable objects in our universe, the Doppler formula is useless!

 

It's important to make that point clearly, I think. Otherwise people get confused and think that the Doppler formula is generally useful as an approximation!

 

*To see this, try any z = 1.7 or greater in the calculator. One sees that the recession speed was greater than c when the light was emitted and started on its way to us. But our observable volume goes out to z = 1090, the redshift of the Cosmic Microwave Background. Therefore the portion of observable space which only goes out to z = 1.7 is a small fraction of the total.

The portion that goes out only to z = 0.1 is of course an even more tiny fraction. This is one reason students are not encouraged to use the Doppler formula as an approximation for cosmo redshift except in narrowly restricted applications.

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... do they need to do additional calculations an apply them separately (eg, the star is so far so it has so much Hubble redshift, differs from nearby stars so it has velocity redshift, ...)?

 

You have the right idea! You take an average (of a cluster of stars, or a galaxy, or a cluster of galaxies). You see what the average light's redshift is. Then you take the center of that cluster as your reference and measure individual objects' redshifts.

 

Since all the stars in the cluster, or the galaxy, are at about the same distance, it must be true that the cosmological stretching effect is the same for all (all their light took about the same time to reach us during which the universe expanded so and so much). Therefore any individual differences must be due to individual motion (conceivably a gravitational redshift effect in some special circumstance, but almost always individual motion.)

 

Beyond that, deducing how larger assemblies move involves clever detective work, inference. It isn't always possible. Fortunately individual motions are usually small like a few hundred km/s. While recession speeds are typically on the order of c or greater, c is 300 thousand km/s. So even if objects are moving around individually their private motion is dwarfed by their recession speed and for many purposes can simply be neglected.

 

Good question!

Edited January 11, 2009 by Martin
Consecutive post/s merged.