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Author Topic: How much can a lightwave be stretched?  (Read 12385 times)

Offline DoctorBeaver

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How much can a lightwave be stretched?
« on: 23/05/2008 20:53:49 »
I was thinking about blue-shifted light at an event horizon when BING! - my mind did a flip & I thought of this litle poser.

Can a lightwave be so red-shifted that it becomes a flat line? If so, what would be the effect?

Would the lightsource have to be moving away at c? Or at infinite velocity? Would a photon have to have zero energy for its wave to be flat? Can a photon with zero energy exist?

« Last Edit: 23/05/2008 20:56:55 by DoctorBeaver »


 

Offline Soul Surfer

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How much can a lightwave be stretched?
« Reply #1 on: 23/05/2008 23:06:10 »
A photon with zero energy cannot exist for several reasons. 

Firstly if it has zero energy it cannot have any effect on anything and cannot be detected.

Secondly it cannot fit into our universe which has a finite size because it has an infinite wavelength.  like the casimir effect where photons longer than a particular wavelength canot exist in a cavity causig a negative pressure in that cavity against the vacuum energy.

This leads on to an interesting thought that I have had for some time on the assumption that  gravitons or gavitomagnetic waves (which are in some ways similar to photons are mostly very low frequency compared with photons  ie frequuiencies are measured in cycles per year(earth's orbit down to a few cycles per second for a binary neutron star  assuming that the quantum enegy is plancks constant times the frequency the quanta are very low energy and there are lots of them.

The motions of galaxies in clusters represent cycles per billion years or more and there may be a lower limit to the frequency of gravitions in the universe because they just cant fit in.  Can this be the source of some form of modified dynamics for very low frequency gravitiational effects like MOND?
 

Offline DoctorBeaver

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How much can a lightwave be stretched?
« Reply #2 on: 23/05/2008 23:18:09 »
A photon with zero energy cannot exist for several reasons. 

Firstly if it has zero energy it cannot have any effect on anything and cannot be detected.

Secondly it cannot fit into our universe which has a finite size because it has an infinite wavelength.  like the casimir effect where photons longer than a particular wavelength canot exist in a cavity causig a negative pressure in that cavity against the vacuum energy.

I had a feeling the answer was something like that. But I hadn't considered the finite size of the universe as being a reason zero energy photons cannot exist.

Quote
This leads on to an interesting thought that I have had for some time on the assumption that  gravitons or gavitomagnetic waves (which are in some ways similar to photons are mostly very low frequency compared with photons  ie frequuiencies are measured in cycles per year(earth's orbit down to a few cycles per second for a binary neutron star  assuming that the quantum enegy is plancks constant times the frequency the quanta are very low energy and there are lots of them.

The motions of galaxies in clusters represent cycles per billion years or more and there may be a lower limit to the frequency of gravitions in the universe because they just cant fit in.  Can this be the source of some form of modified dynamics for very low frequency gravitiational effects like MOND?

I'm not sure how you arrive at this. Are you suggesting that the frequency of the graviton/gravitomagnetic wave determines orbital velocity, or vice versa?
 

Offline LeeE

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How much can a lightwave be stretched?
« Reply #3 on: 24/05/2008 19:27:45 »
I was thinking about blue-shifted light at an event horizon when BING! - my mind did a flip & I thought of this litle poser.

Can a lightwave be so red-shifted that it becomes a flat line? If so, what would be the effect?

Would the lightsource have to be moving away at c? Or at infinite velocity? Would a photon have to have zero energy for its wave to be flat? Can a photon with zero energy exist?


This is what happens to light emitted by galaxies that are presumed to exist beyond the limits of the observable universe.  Because they are receeding at >= c the frequency of the light drops to zero, equivilent to infinite wavelength, and zero energy.  The receeding object needs to be travelling at c or greater but it doesn't have to be receeding at infinite velocity.

It's interesting to note that although we can't see anything beyond the observable universe, as centered upon us, we can see regions within the observable universe where energy originating from beyond the observable universe must be present, so although this energy will be present and interacting within those regions, we shouldn't be able to detect it's presence or it's interactions.  Hmm...  might just be a timing issue...
« Last Edit: 24/05/2008 19:49:37 by LeeE »
 

Offline DoctorBeaver

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How much can a lightwave be stretched?
« Reply #4 on: 24/05/2008 20:04:39 »

It's interesting to note that although we can't see anything beyond the observable universe, as centered upon us, we can see regions within the observable universe where energy originating from beyond the observable universe must be present, so although this energy will be present and interacting within those regions, we shouldn't be able to detect it's presence or it's interactions.  Hmm...  might just be a timing issue...


Definitely timing. The information from those interactions hasn't had time to reach us yet.

I find it "interesting" to think that although nothing can travel faster than c, there are probably parts of the universe that, due to expansion, are receding from us >c. And how fast does the recession get, from our frame of reference, when you reach the outer limits of the universe?
 

Offline lightarrow

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How much can a lightwave be stretched?
« Reply #5 on: 24/05/2008 20:51:03 »

Can a lightwave be so red-shifted that it becomes a flat line?
More precisely, it would become a constant electric and magnetic field.
 

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How much can a lightwave be stretched?
« Reply #6 on: 24/05/2008 21:35:01 »

Can a lightwave be so red-shifted that it becomes a flat line?
More precisely, it would become a constant electric and magnetic field.

Alberto - can you explain that, please?
 

Offline LeeE

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How much can a lightwave be stretched?
« Reply #7 on: 24/05/2008 22:47:46 »
Hmm... I'm not sure if it is just a timing issue.  Let's say it's sometime in the future where sub-lightspeed interstellar travel is possible and you've hiked off to another system a few lightyears away.  Now, because the center of the observable universe is located at the observer, you can see light from a source located a few lightyears outside the boundary of the observable universe when seen from Earth.

Once you've got there and unpacked, you radio a message back to us about a supernova that has just been observed, just within the limit of your observable universe, but just outside ours - "nice bang fellas - pity you'll never see it.  I'll send you a picture".  Your radio message gets to us but the light from the supernova doesn't because it's too red-shifted for us to see?

In this case, we're seeing at least one result of the interaction between the supernova, which should be unknown to us, and the remote region of space - you sending us the message.

If you want to do away with the human element, we could just substitute a remote probe to relay the information.  The radiation from the supernova interacts with a sensor on the probe and is detected, triggering the appropriate reponse routines in the probe's C&C subsytems, resulting in the data being sent to us.

Either way though, we've ended up knowing about something outside our observable universe.  Time doesn't seem to be a factor.
 

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How much can a lightwave be stretched?
« Reply #8 on: 25/05/2008 00:46:02 »
Lee E
Your scenario is interesting but I think the apparent paradox can be resolved in terms of Energy.
One effect of the Universe's expansion is to reduce the energy of the photons as they are traveling through the expanding space.
The photons from the distant event have, effectively, lost nearly all of their energy (the frequency has got to near DC) by the time they reach the  remote observation post. Once the frequency has reached zero, no information about the original event can be carried because there is zero bandwidth in which to transmit it. The remote observer gets photons with enough energy to detect the event and then produces some new photons for communicating with 'base' by introducing more energy and regenerating the information.
The expression 'observable universe' should really only be used for 'direct' observation. There isn't a fundamental reason why information shouldn't get to us from beyond this limit as long as some energy can be supplied on the way.
btw, I think the apparent duration of the supernova would be stretched as well as the wavelength of the em waves received at the remote observer. It would take longer for the observer to actually register the  occurrence than if it took place nearby.
 

Offline DoctorBeaver

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How much can a lightwave be stretched?
« Reply #9 on: 25/05/2008 10:10:19 »
LeeE - let me make sure I've got this right. The light from the supernova has enough energy to reach the observer, but not enough to reach Earth. Correct?
 

lyner

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How much can a lightwave be stretched?
« Reply #10 on: 25/05/2008 10:52:58 »
That's 'one way of looking at it'. The fact that the wavelength has been stretched can be interpreted as if the photons have less energy - this tends to zero as you get far enough away and the frequency approaches zero.
The mechanism of Relativistic Doppler effect means that the effect is asymptotic so there is no actual distance which corresponds to a 'limit'; it just gets harder and harder to detect the energy / information.
 

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How much can a lightwave be stretched?
« Reply #11 on: 25/05/2008 11:02:28 »
Like an inverse square law where the value can approach, but never reach, zero?

So with a mega-powerful telescope we would still be able to detect the supernova?
 

lyner

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How much can a lightwave be stretched?
« Reply #12 on: 25/05/2008 11:47:05 »
It depends on what you mean by 'mega-powerful'. A better word would be 'sensitive' and, possibly, 'directive' too.
As the wavelength stretches you need a receiver tuned to a lower and lower frequency (it's not light anymore!) and, for the same resolving power / gain you need a bigger and bigger aperture. With a reflector the size of the solar system, presumably, you could 'look' a bit further and then, with one the size of a galaxy, presumably, with one the size of a Galaxy, you could look further still. There is also the problem that, as well as the photon energy getting less and less, the original signal will spread out and the inverse square law would also apply (or, at least, some equivalent version of it which would be affected by the actual geometry of Space on that sort of scale).
 

Offline LeeE

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How much can a lightwave be stretched?
« Reply #13 on: 25/05/2008 17:24:42 »
Sophie - that's an interesting comment re adding energy along the way, at the remote observer's location.

As I understand it, the light isn't red-shifted by the expansion of the universe, which increases the distance the light has to travel, but by the speed of recession from us of the emitting body at the time of emission.  If the light was red-shifted due to the wavelength being streched by expansion during it's journey it would mean that everything else in the universe would also be stretched - everything would be getting bigger and the universe would not appear to be expanding at all.

Everything beyond the observable universe is receeding from us at >= c, so any light emitted from anything beyond that limit starts with zero frequency at the time of emission and has zero energy, from our point of view.  It can't ever reach us directly because, from our point of view, it never existed.

Even with the most sensitive instruments, we'd still just see zero frequency.

The result seems to be that we should be able to see things in remote regions of space that appear to have no directly observable cause.

But then thinking about it again, if we imagine that this supernova was taking place now, it would take nearly 13 billion years for the light to get to the remote location, and by the end of that time we could be receeding from the remote probe at >= c, so perhaps we wouldn't be aware of it and perhaps it _is_ a timing issue after all:)
 

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How much can a lightwave be stretched?
« Reply #14 on: 26/05/2008 01:06:50 »
If everything expanded by 0.001%, the space between two very separated objects would expand by a huge distance but the objects would not expand significantly. So that particular objection doesn't apply to the expanding Universe idea. Remember, it's the speed of recession which increases with distance - not the distance increasing with distance.
The concept of a distance increasing at >c is not meaningful. 
It would be regarded as nonsense to talk of two objects moving apart at 1.1c in the Lab so how can it make sense for two well separated objects?
Just because we are discussing something going on at a great distance we should still be talking in terms of the limits imposed by Relativity. The 'limit of visibility' doesn't have to be a 'hard edge' it just needs to be where the recession speed is near enough to c for the effects of relativity to become significant.
The idea of the Hubble recession applying at all distances, without Relativity coming into it, can't be really sensible.
As far as receiving photons from great distances goes, my point is that you would never be presented with a signal with 'zero frequency'. You would see a signal with a frequency approaching zero frequency from a very distant object. As with all ideas involving 'infinity', it is much more fruitful to discuss the limits as distance (or whatever other variable you are discussing approaches infinity. Anything else can lead you into serious problems and non existent solutions.
I know there is a sort of comfort in the idea of limits but there don't in fact, have to be limits of the kind we associate with familiar objects when we are dealing with the Universe.
 

Offline lightarrow

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How much can a lightwave be stretched?
« Reply #15 on: 26/05/2008 13:10:49 »

More precisely, it would become a constant electric and magnetic field.

Alberto - can you explain that, please?
Let's consider electric field only, for simplicity, and in a specific instant of time.
If the wavelenght is, let's say, one metre, it means that in one metre the electric field varies from zero at the initial point, to its maximum positive, e.g., 1 (25 cm away the initial point) to zero again (50 cm away) then to -1 (75 cm away) then to zero again at the final point 1 metre away.

If however we limit our analysis to what happens between two points separated by 1 mm only, you understand that the electric field doesn't vary much between them: if they are near E = 0, then the field will vary let's say from 0 to 0.01, if they are near 0.8 the will vary, e.g., from 0.8 to 0.78 ecc. The same if you take a wavelenght of 1 km and you consider two points 1 metre apart, or a wavelenght of 1000 km and two points 1 km apart ecc. If you imagine an almost infinite wavelenght, you understand that you will need billions of light years of distance to find a slight variation in E field.

If we instead stay in the same point and we want to analyse variations in time, we can have that previous variation letting light arrive: it travels at c so you have to wait billions of years to have that slight variation; in other terms, we can compute the variation in time, fixed the point in space, simply by dividing that space separation by light's speed c.
In formulas:

ν = c/λ

ν = frequency; λ = wavelenght.

If λ goes to infinite, frequency goes to zero; but frequency is the number of cycles per second in a specific point. If this number is almost zero, it means the field is almost non varying; when ν = 0 the field is constant.
 

Offline DoctorBeaver

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How much can a lightwave be stretched?
« Reply #16 on: 26/05/2008 13:51:11 »
Thank you, Alberto. Nicely explained.
 

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How much can a lightwave be stretched?
« Reply #17 on: 26/05/2008 13:55:50 »
Quote
You would see a signal with a frequency approaching zero frequency from a very distant object.

Sophie - taking into account what Alberto has just explained, wouldn't it take an inordinate length of time to measure a frequency that is approaching zero?
 

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How much can a lightwave be stretched?
« Reply #18 on: 26/05/2008 16:38:23 »
Absolutely. Measuring a change in level of a signal of frequency f would involve observing a fair number of cycles. A cycle takes i/f seconds so, if 0.01Hz is 'slow enough for you' and you needed to look at10 cycles, to decide if it was there or not, you'd need 1000 seconds. To avoid the effects of interference, you'd actually be looking at thousands of cycles, probably.
 

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How much can a lightwave be stretched?
« Reply #19 on: 26/05/2008 18:15:55 »
There is another point involving red shift observations.
The amount of red shift which has been measured actually only represents recession velocities which are far from c. I am not aware that anyone has identified optical spectral ines being shifted down into the microwave region. This implies that we are looking far from the limit, at the moment.
 

Offline Soul Surfer

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How much can a lightwave be stretched?
« Reply #20 on: 26/05/2008 23:33:54 »
The cosmic microwave background radiation is the result of a great flash of light as the universe became transparent and a lot of the atoms deionised being stretched into the microwave recion of the spectrum.
 

Offline LeeE

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How much can a lightwave be stretched?
« Reply #21 on: 26/05/2008 23:53:40 »
Oops! - got myself confused there.  I was thinking that a red-shift of 1 equalled recession at c, for some reason.
 

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How much can a lightwave be stretched?
« Reply #22 on: 27/05/2008 00:18:56 »
I've seen something similar explained by measuring drips from a tap (faucet). If you measure for 10 seconds and count 10 drips, you can have an error of 10%. If you measure for 100 seconds & count 100 drips, you can have an error of 1% etc. (I think that's how it works)

So, if the tap drips only once every billion years, you'd be hard pressed to get any kind of accuracy. The same must apply to measuring wavelengths.
 

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How much can a lightwave be stretched?
« Reply #23 on: 27/05/2008 00:27:00 »
Yes; the noise in the system is the main problem. For a tiny signal such as you'd get from even a massive event, the noise can only be eliminated by observing for an inordinately long time; millions of your water drops! That is effectively using a vanishingly narrow bandwidth for your measurement.
 

Offline DoctorBeaver

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How much can a lightwave be stretched?
« Reply #24 on: 27/05/2008 19:09:41 »
So what we're saying is that any photon-emitting event that occurs anywhere in the universe will, theoretically, eventually be detectable anywhere that falls within its lightcone given enough time and sensitive enough equipment.
 

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How much can a lightwave be stretched?
« Reply #24 on: 27/05/2008 19:09:41 »

 

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