# Why does the Electro Magnetic Spectrum have limits?

1. Jul 30, 2012

### questionalot

we set limits by what we can measure; therefore, it is what we have. This is my general understanding. I think it extends at both ends and we haven't found the means to measure it as of current. what are we doing to expand the spectrum? my simple question.

2. Jul 30, 2012

### vanhees71

There is no known principle limit on the range of possible frequencies of electromagnetic waves in free space. Of course, to practically produce very rapidly changing fields is not so simple.

3. Jul 30, 2012

### CWatters

4. Jul 30, 2012

### Vantenkeist

One obvious lower limit would be when the frequency approaches zero. Or perhaps as the wavelength approaches the length of the universe.

5. Jul 30, 2012

### Darwin123

I don't think that is true. General relativity sets approximate limits on the wavelength which are fairly simple to understand.
1) The wavelength of an electromagnetic wave can't be shorter than the Planck length.
-Otherwise, the photon would be trapped in its own black hole.
-Therefore, the wavelength of an electromagnetic wave can't be shorter than 1.6x10^-35 meters.
2) The wavelength of an electromagnetic wave of an electromagnetic wave can't be longer than the diameter of the universe as determined by the Hubble constant.
-The oscillation of any electric charge can't have begun before the Big Bang.
-Therefore, the period of an electromagnetic wave can't be longer than the age of the universe.
-The wavelength of an electromagnetic wave that exists today can't be longer than the speed of light times the age of the universe, 13.5 BLY.

So to satisfy general relativity, the wavelength of an electromagnetic wave has to be between 1.6x10^-35 meters and 13.5 billion light years.

Last edited: Jul 30, 2012
6. Jul 30, 2012

### mikeph

I don't follow this- you're asserting that a photon must have completed one cycle by now. What is so important about "now"? Surely we live in an arbitrary time. Can't a photon exist with a period of 500 bn years, and we just haven't been around long enough to observe it?

7. Jul 30, 2012

### Darwin123

If we can't measure it even in principle, then it doesn't exist.
In terms of electronics, the bandwidth of a measurement is inversely proportional to the time it takes to do the measurement. I am hypothesizing an observer patiently doing an experiment in measuring the frequency of the wave from the beginning of the universe until today. No human observer can live this long, but I hypothesize this observer for this problem. This observer can't determine a frequency less than the uncertainty of the frequency, which is inversely proportional to the age of the universe.
Look at it in terms of the uncertainty principle. Suppose one measures a very slow change in the electric field strength in a region far from any electric charge. The uncertainty relationship that I am talking about is:
ΔωΔt≥1
where Δω is the uncertainty in angular frequency of the electromagnetic wave, and Δt is the uncertainty in time. I will assume that this is a classical system in the sense that we know the phase of the electromagnetic wave precisely. One can thus let Δt be the uncertainty in the starting time of the oscillating charge that generates that electric field.
A free electromagnetic wave (i.e., real photons) can have existed in the time just after the big bang. The electric charges of the plasma are too close together. Therefore, we know that:
Δt≤13.5×10^9 years.
Therefore,
Δω≥7.4×10^-11 /years.
The uncertainty in time has to be set by the age of the universe. Of course, this uncertainty increases with age of the universe. Therefore, the uncertainty in frequency decreases with the age of the universe.

Note that I used a "classical" uncertainty principle that exists independent of quantum mechanics. Radio engineers regularly use this uncertainty principle to determine the cut on frequency of their receivers.
I am taking electronic engineering to an extreme that some may say is ridiculous. However, I think that I answered the OP. General relativity does establish bounds on the measurable frequency of an electromagnetic wave.
The range of frequency is so broad that one may call it "unlimited for all practical purposes". However, the range is finite in a mathematical sense.
One can consider also consider the ratio between the two limits as the maximum dynamic range of any physical experiment. I seriously doubt there is any instrument or technique that will require the precision indicated by this dynamic range.

8. Jul 30, 2012

### DennisN

Hmm, neither I am sure why this would be the case. I can imagine that there might be possible limits on the wavelength, like e.g. ~Planck length < wavelength < size of the entire Universe. But I do not see how the age of the Universe would have anything to do with this. Why would the age have any influence at all on the energy of a photon? That sounds like spooky action to me . This would set temporal limits on the energy of photons during the entire development of the Universe, and this is something I've never heard of (any astrophysicist reading this, please help us out here ).
I believe that is taking the Uncertainty Principle quite too far. AFAIK the principle does not say anything about what can exist or not. It's about precision of observables.

Btw, I found two articles while searching for info on this;

I'm not saying I'm right here, I'm just saying I'm doubtful.

Last edited: Jul 30, 2012
9. Jul 31, 2012

### AlephZero

I think you are getting confused over the issuses of aliasing in signal processing here.

Think of the extreme example: suppose you take a finite number of measuremends of the amplitude of the signal, at equally spaced times, and they are all the same value.

Are you claiming that it is impossible the signal is actually a constant (i.e. the frequency is zero?)

Certainly there are other possible values for the frequency which would give the same result (though they depend on the sample rate, not on the total sampling time) but IMO it makes no sense to deny that the frequency could be zero, or that the "simplest" interpretation is that the frequency is zero.

The same logic applies to a low but non-zero frequency. Finding the Fourier transform (which of course does limit the frequency resolution you can achieve, based on the total length of the sampled data) is not the only way to estimate the frequency content of a finite length sample from a signal, and it is often not the best way.

10. Aug 2, 2012

### Darwin123

The size of the universe is changing. The universe is getting larger at a rate determined by the Hubble constant. There is nothing special about the size of the universe at this moment that makes you think that it limits wavelength. If you want to replace the upper limit of wavelength by a bigger limit of wavelength, just wait a while.
So I think that we are talking about essentially the same thing. Limiting the lower frequency by the inverse of the age of the universe is homologous to limiting the upper limit on wavelength by the size of the universe.
I am not going to champion either idea. The OP was very general. I presented one conjecture as a potential answer to his question.
Ultimately, it is up to the OP to decide whether this conjecture is even relevant to his question. Apparently it isn't, since he has has not responded to my post. Well, I tried!

11. Aug 3, 2012

### mikeph

There is no evidence that I know of to convince us that the universe is not infinite, so I would say there can be no known reason why the longest possible wavelength of light must be bounded above.

The way I understand it, the Hubble constant doesn't necessarily tell us anything about the rate of increase of the size of the universe, it tells us, more specifically, of the rate of expansion of space within the universe. Infinite space can still expand, and the Hubble constant measures this.

12. Aug 6, 2012

### DennisN

The reason I expressed doubts was because the expansion of space has (probably) not been and is not linear with respect to time (depending on Hubble parameter and different expansion models). Also, a "photon period/Universe age hypothesis" won't cover all possible scenarios like e.g. Big Crunch (not that I think a Big Crunch is likely ).
I agree. There are many unknown parameters regarding this issue, so it's very difficult to to even try to draw any conclusions.

Last edited: Aug 6, 2012
13. Oct 11, 2012

### temporalshift

To have an electro-magnetic field you have to have a flow of electrons. Electrons repell each other and can't occupy the same place. Eventually the space for the electrons will run out.

∞ x electron's diameter > area

14. Oct 11, 2012

### Darwin123

The Big Crunch fits the Photon Period picture even better.

The Big Crunch refers to the conjecture that visible universe that eventually will collapse into a singularity the way it began. The ultimated compression of the visible universe is called the Big Crunch. Or as Scott Adams referred to it in "Restaurant at the End of the Universe", the Gnab Gib. So the universe is bounded on one side of time by a Big Bang and on the other by the Big Crunch.

The evidence so far seems to contradict the Big Crunch hypothesis. However, lets consider it briefly (very, hopefully). First, let me say something about what I mean by "visible universe".

When I say "visible universe", I am talking about the region defined by an event horizon at the edge of our region of the universe. The event horizon is the boundary where the galaxies are receding from us at the speed of light in a vacuum. Thus, I am not talking about a universe defined by the strength of our telescopes. For purposes of this discussion, it doesn't matter if there is anything beyond this event horizon.

If the "universe" is infinite, but we live inside an event horizon, then the limits that we talk about only have to be relevant within this event horizon. Semantically, we can redefine the "universe" as every object bounded by this event horizon. Everything outside the universe can be considered part of "other universes". We can talk about everything as belonging in a multiverse. Since scientists can't know what goes on outside the event horizon, the photons that scientists know and love have to be inside the visible universe.

The issue of whether the expansion of the universe is a real expansion or an expansion of space is irrelevant. I think what the OP was really asking for a a heuristic model that can give him a feel for what a limit is.

If the Big Crunch hypothesis is correct, then the visible universe will reach its maximum size midway between the Big Bang and the Big Crunch. One can define the upper bound to the wavelength of an electromagnetic wave as the diameter of the universe at this midway point. This places a lower bound on the energy of the photon. The minimum energy of a photon is hc divided by this maximum wavelength (h=Placks constant, c=speed of light). According to this definition, the minimum possible energy of a photon has a value that does not change with time.

One can even make the heuristic statement that this minimum possible energy of the photon is the rest mass of the photon. The photon has over the length scale of galaxies a zero rest mass. Therefore, the photon presumably has no minimum energy. Particles with mass supposedly are different from a photon in having a minimum of energy defined by their rest mass. However, if the photon has a minimum possible energy than it is like any other particle. The minimum possible energy of a photon is the rest mass.

Please note that the forum rules are not being intentionally broken. I am not presenting this either as a challenge to main stream science or even as a description of ultimate reality. I think the OP was merely asking for a heuristic picture of what cosmologists were saying about the electromagnetic field. I suggest that discussions on the size of the visible universe may be equivalent to asking about the rest mass of a photon. If the rest mass of a photon is zero, then the universe is infinite in size.

Experimental indications so far indicate that the rest mass of a photon could be zero and that the visible universe could be infinite in size. Until either is proved false, this should be considered merely a mathematical exercise in dimensional analysis.

15. Oct 11, 2012

### Staff: Mentor

EM fields exist with or without moving electrons. Remember that the EM field includes the electric portion as well, not just the magnetic. Not to mention that all charged particles have an internal magnetic moment, and thus a magnetic field. Plus I don't see how this argument applies to EM waves. What does the spacing of electrons have to do with EM radiation?

16. Oct 12, 2012

### mrspeedybob

Please elaborate on this. Any photon will have a wavelength shorter then this if I am moving toward it fast enough, but the existence of an event horizon should be frame invariant. So how can a photon be, and not be a black hole depending of F.O.R.?

17. Oct 12, 2012

### Q-reeus

A good point, but if we restrict to a frame in which an EM wave is generated, the lower wavelength limit should be governed by something much more restrictive than Planck scale imo. Namely, roughly at onset of vacuum breakdown which theorists put at when Ec ~ 1.3*1016V/cm - see eq'n (3) at http://www4.rcf.bnl.gov/~swhite/erice_proc/adrian2.ps
That limit does not apply for a traveling wave but will apply for a source outputting oppositely traveling waves and that's what should be generally expected for high energy events capable of generating such intense radiation. Just what frequency limit Ec implies I'm not sure and will depend on geometry of source, duration etc., but surely many orders of magnitude less than Planck scale would imply.