# Energy wavelengths

I just read “A Brief History of Time,” so now I know quantum physics.

1. Is there any relationship between wavelength and speed? They say nothing is faster than light. I’m assuming when scientists talk about “light,” they are thinking of the visible spectrum, like I am.

2. And there are a couple energy types that have shorter wavelengths than visible light…ultraviolet and gamma, I believe. Are there any others?

3. Finally, what would happen if you had a source of the highest form of energy, you were traveling towards it, and it was travelling towards you? It should be “blue-shifted” (if that’s the correct term), up to what? Do we have any guesses or experimental evidence?

Hiebram

Not for light travelling in a vacuum. Light is Light, regardless of the wavelength. But, as it passes thru matter, the speed does depend on the wavelength (hence the prsim effect).

X-rays, as well. Plenty more. Visible Light is just part of the electromagnetic spectrum– a very small part.

I don’t understand the question.

Here’s a link to my website, This calculator converts wavelength to frequency (and vice versa) and calculates energy per photon.
http://www.1728.com/freqwave.htm

Actually, in this context “light” refers to electromagnetic wave of any energy. In vacuum, speed is constnant (c) regardless of wavelength. In other materials, speed can be different depending on wavelength.

Ultraviolet -> X-ray -> Gamma ray.

or near-UV -> far UV -> soft X-ray -> hard X-ray -> gamma ray.

But these are just names with arbitrary (and not very consistent) thresholds. The wavelength can vary continuously.

If you had a high-energy gamma ray and move towards it, the gamma ray would be blueshifted into an even higher energy gamma ray. I don’t think there’s a limit.

As a side note, what would be the theoretically minimum wavelength?

Not in a vacuum where the speed of light is specified but speed in mediums like glass, air and water where the refractive index and thus the velocity of light is dependant on frequency. This is why a prism splits “white” light into it’s component wavelengths to form a rainbow and is consequently a problem with lenses which do the same thing. With a plain lens different colors focus at slightly different distance causing a defect called chromatic aberration. This can be corrected by making complex lenses out of multiple elements, often of different types of glass, and is why simple lenses such as in cheap binoculars and magnifying glasses often show color fringing at the edges of objects and light sources.

X-rays are between gamma and UV.

You’d need Ray-Bans? Hell if I know. :rolleyes:

The light from objects traveling toward is is blue shifted. There are blue shifted objects nearby. It just so happens that all far objects are red shifted because of the expansion.

Are you asking if we have an emittler of the highest possible energy traveling toward us how can it be blue shifted?

If that’s the question I really don’t know. First we have to find out if there is a highest possible energy. I haven’t really thought about that but I’m inclined to doubt that there is. For example temperature is a measure of average kinetic energy of particles making up whatever it is we are taking the temperature of. Kinetic energy is m*v[sup]2[/sup]/2. As v increases so does m (mass) and when we approach the highest possible speed, that of light, the mass approaches infinity. There doesn’t seem to be any upper limit.

I’m not sure about this, but it doesn’t seem like any wavelength shorter than a Planck length would have any physical validity. If that is the case, then with flambda = c (for light) and E = hf, you have

E=hc/lambda = 6.6310[sup]-34[/sup]Js * 3.0010[sup]8[/sup]m/s / 1.62*10[sup]-35[/sup] m

which gives 1.2310[sup]10[/sup]J as the upper end for energy of a single photon. This corresponds to a frequency of lambda=1.8510[sup]43[/sup] 1/s.

Above this frequency light would appear to blueshift into virtual invisibility, insofar as it would be smaller than the smallest possible increment of measurement. I’m not at all clear on what the QED implications of that would be, or if indeed there is some other mechanism to take into account that might limit this.

Stranger

I don’t think there is intrinsically an upper limit to photon energy possible, but there is an upper limit to temperature, the Planck temerature (around 10^32 IIRC).

There is a constant c in nature that has dimensions distance per time, and it is the limit at which causality spreads, and also the proportionality constant between the mass and enery manefestations of information (turns out that mass and energy are actually constructed out of information, and a bit weighs about 10^-65 kg). That is, c is the limiting speed at which distant things can interact. In special relativity you can construct graphs relating time and distance, and do coordinate transforms to represent the view of observers moving at different relative speeds. An event at a time and place radiates “world lines” at the velocity (slope) c, and other events at other times and places can possibly be caused by the first event if they are between its world lines, but not if they aren’t. This is powerful because causality works the same way regardless of the observer. There is no way you can move that will have you see effects preceeding causes.

Now, then - light, and X-rays and gamma rays and radio and all the other forms of electromagnetic radiation travel at the speed c. In lay speech it is common to refer to c as “the speed of light”, but this might create the mistaken impression that light itself is somehow fundamentally important in c. They aren’t. It’s simply that nothing slows EMR below this fundamentally limiting speed. Similarly, the USA is the country of Cecil Adams, but having everybody call it that would imply something more than it should.

correct me if I am wrong but I think its nothing that starts out slower than light can accelerate to a speed faster than light…arent there theorectical particals that move faster than c?

yeah its a nitpick but its another interesting side of physics

The Planck length is not a minimum length. It’s the length scale of gravitational interactions, and gravity has a shorter length scale of any known force, but there’s nothing that makes it a fundamental lower bound on wavelength. I emailed Tom Banks about this issue, and he said that there are string theories that allow for “arbitrarily small” wavelengths and there is no theoretical reason not to allow them. (He’s a string theorist, so he should know.)

I also asked him about the Planck temperature. He said that the existence of a maximum temperature depends on the properties of space; generally, for infinite spaces, there is no maximum. He added that there could be localized systems for which, “there is a physical bound on the relevant definition of temperature, but it is certainly not the Planck scale.”

caveat: string theorists actually tend to get around this by positing a duality which says that geometry below a certain length behaves (in some “flipped” sense) like geometry above it. Of course, they leave it to the mathematicians to justify their flights of fancy, but…

My goodness, the simplest question, “Can the ‘light’ from an object with the highest possible energy be blue shifted?” results in esoteric analyses and emails to string theorists.

Planck length is the maximum displacement you could measure between any point and a particle moving at c; below that, the Indeterminacy Principle makes it impossibly to measure more accurately . So it is, in a certain sense, a minimum length at which the granularity of space appears. One can conceive of shorter distances, but there is no way to measure in between them. You are correct (if I understand what you are saying) that it is the scale at which gravity becomes quantized, but given our current understanding of QM, the same is true for all interactions; everything acts in a stepwise manner at that level, and I’m not clear that a wavelength shorter than the Planck scale would have any meaning, in terms of being able to interact with quantized particles.

You’ll have to pardon me if I take any claims based upon string theory with a grain of salt; it’s a nice model, but until it makes some falsifiable predictions (or at least comes to some kind of general consensus among proponents) it should be considered speculative at best. String theories offer the hope of bridging between the continuous world of general relativity and the granular world of QM, but only in the sense that a blind man in a vast warehouse might find the door by searching for the light sneaking in around the door jamb. He can imagine what it might look like but can’t actually see it, so he has to feel around until he finds a spot that is slightly warmed from the outside light and extrapolate the location of the door.

Stranger

Accurate, more or less. I believe it was Feynman that posited the existence of tachyons, which are confined to speeds higher than c. According to the answers to questions which I raised five years ago, there are theoretical reasons involving Cherenkov radiation which is in fact not observed but would be induced by tachyonic reactions to think that they do not in fact exist.

However, they would be exceptionally useful in explaining some of the “non-causal” supposed phenomena such as precognitive events, induced action at a distance, etc.

What I’m wondering is, is there a fundamental minimum size to wavelengths? In other words, what happens as wavelength approaches 0?

Tangentially, as I’m hearing Planck’s name, I’m thinking that he was the one who first suggested that energy has to come in “packets,” which was important because otherwise we would be getting infinite amounts of energy from all of the stars. Just a quick yes/no, am I right on that?

Thanks all.

Hiebram

Umm, Cerenkov radiation is observed all the time. It’s connected with particles travelling faster than the speed of light in a given medium.

Actually, they wouldn’t. See, when you actually set up the relevant differential equations for a tachyon and solve them, there are two classes of solutions. One has packet velocities (the speed at which disturbances propagate) greater than c, but cannot be localized in space. The other is localizable, but has packet velocity less than c. That is, if you can send a signal from “here” to “there” on a tachyon field, the tachyons themselves may travel faster than c, but the signal will travel slower than c.

Thiss would appear to be analagous the the phase and group velocities in a wave guide. The phase velocity is that velocity at which you would have to travel to stay even with the crest of a steady-state sinusoid in the guide and it is always greater than c. The group velocity is the velocity at which energy, or information, is transmitted and it is always less than c.

Indeed, what’s happening when a wavelength of one Planck length or a frequency of one cycle per Planck interval is encountered?

In what theory? In most theories that care about such things, we’re not even sure your question makes sense on the Planck scale.