Redshifting/Blueshifting Radiation beyond limits

[Kerbin Dallas Multipass]

What happens if radiation is dopplershifted so much that it falls out of the physical spectrum?

Let's say an object approaching me at relativistic speeds is emitting gamma rays which get blueshifted so much that their wavelength is below a planck length

Is the energy, photon, information "gone"? Or just undetectable?

[SargeRho]

You can't shift light that far into the blue, I think.

[Temstar]

Need a theory of quantum gravity to explain that.

[GreatWyrmGold]

Well, to answer your question, we need to understand what, exactly, a wavelength is for light in the physical sense.

...

Sadly, I've got no clue what that would be. Does anyone else know?

[Ralathon]

Correct me if I'm wrong, but isn't the planck length(and mass, time etc) just a convenient unit of measurement for quantum mechanics because all physical constants equal 1 when working in it?

As far as I know there isn't anything that prevents objects from being smaller. In fact, the de Broglie wavelength of most macro scale objects is many times smaller.

[Kerbin Dallas Multipass]

@Ralathon

I read this on Wikipedia, thats basically why I came up with the question:

The limit for long wavelengths is the size of the universe itself, while it is thought that the short wavelength limit is in the vicinity of the Planck length,[5] although in principle the spectrum is infinite and continuous.

[Sillychris]

The quickest an object can approach you is just shy of c, which places a limit on blueshift that could actually occur.

Assume c for your emitter's velocity and throw that into the relativistic doppler shift formula. I don't think it will be less than the planck length.

[Winter Man]

The quickest an object can approach you is just shy of c, which places a limit on blueshift that could actually occur.

Assume c for your emitter's velocity and throw that into the relativistic doppler shift formula. I don't think it will be less than the planck length.

Depends how many 9's you put after the decimal point.

[Skyler4856]

Any reason why all f's have been replaced with *'s?

NOW *'s?!?!

[Skyler4856]

On contrary the energy has risen to unimaginable heights!

The physical spectrum is theoretically infinite, but energy requirements place a practical limit.

[SuperFastJellyfish]

Any reason why all f's have been replaced with *'s?

NOW *'s?!?!

I'm assuming April Fools'.

[Skyler4856]

I'm assuming April Fools'.

So am I...

[Sillychris]

Depends how many 9's you put after the decimal point.

Place all the 9's after the decimal point you like, you still can't exceed c.

0.999999...999c is still strictly less than c.

[Ralathon]

Place all the 9's after the decimal point you like, you still can't exceed c.

0.999999...999c is still strictly less than c.

Look at the formula for redshift:

z = sqrt( (1+(v/c)) / (1-(v/c))) -1

If you get arbitrarily close to c the lower term in the sqrt approaches zero. Thus your formula tends to infinity, meaning that there is no upper cap to your blueshift/redshift.

[Sillychris]

Oops... I take it back

[Idobox]

The Planck length does not have any magic properties.

The main problem with this length is that particles with enough energy to make measurements of this precision are so energetic (ie heavy), they would collapse into a black hole when colliding with anything. In practice, it means it is impossible to measure anything at tht scale.

For your thought experiment, on the high end of the spectrum,you would be limited by your photons being so energetic they bend space time and create black holes every time they hit something, but they could totally have wavelengths shorter than the Planck length. Another way to look at it: if the light source is static and you move very fast towards it, there is nothing special about the photons, and by the equivalence principle, it's the same if you are static and the sources moves very quickly towards you.

[K^2]

Need a theory of quantum gravity to explain that.

Actually, this is one of the cases where you don't.

Regardless of how short the wavelength is, if it's just a matter of coordinate system change to red shift it back to "reasonable" range, we can describe it. Global coordinate transformations work without limits. It's only when you have to make different coordinate adjustments at different points on a very short length scale when you can't correct for these problems and you need Quantum Gravity. But that will never be the case for a single particle propagating through vacuum.

The Planck length does not have any magic properties.

The main problem with this length is that particles with enough energy to make measurements of this precision are so energetic (ie heavy), they would collapse into a black hole when colliding with anything. In practice, it means it is impossible to measure anything at tht scale.

Nope. We can do computations with black holes without any problems. Plank scale is a much more serious issue, and it has to do with the fact that quantizing gravity results in a non-renormalizable theory. This can be addressed with an effective field theory, but only down to Plank scales. I don't know all of the details of algebra involved, but that's the general idea behind it. And it's a very serious theoretical limit.

But yeah, it's not that world breaks down at Plank scale. It's our theory that breaks down.

Edited April 2, 2014 by K^2

[Idobox]

Nope. We can do computations with black holes without any problems. Plank scale is a much more serious issue, and it has to do with the fact that quantizing gravity results in a non-renormalizable theory. This can be addressed with an effective field theory, but only down to Plank scales. I don't know all of the details of algebra involved, but that's the general idea behind it. And it's a very serious theoretical limit.

But yeah, it's not that world breaks down at Plank scale. It's our theory that breaks down.

I've heard that many times, without justification.

But the measurement problem is real. It doesn't just mean we can never built a microscope that powerful, but that the idea of shorter lengths doesn't really mean anything, because measures and observation don't just mean human ones, but also interactions between particles.

We can do math with black holes, as long as we don't try to describe the singularity, where everything breaks down. If any gauge boson turns into a black hole, you're going to have singularities and infinities popping out everywhere, and the theory that can describe singularities will likely be able to describe what happens at the Planck scale, because the issue is very similar.

[K^2]

Gauge bosons already are point particles, and contain a number of singularities. The important bit is that these are integrable.

[Idobox]

Gauge bosons already are point particles, and contain a number of singularities. The important bit is that these are integrable.

Photons are gauge bosons, and they collapse into black holes at the Planck scale, meaning there shouldn't be any electromagnetism at this scale, or at least a very different form. And I assume it's the same for other bosons.

[K^2]

I don't know where you get this from, because there are coordinate systems from which an ordinary photon has a sub-Plank scale wavelength. And like I said earlier, unlike local coordinate transformations, global transformations don't have limits. And if the photon collapses to a black hole in one coordinate system, it should do so in all of them*. Normal photons don't collapse, so the ones past Plank limits aren't going to either.

* General Covariance. AKA, Diffeomorphism Invariance. Very important consequence of space-time topology.

[Idobox]

I don't know where you get this from, because there are coordinate systems from which an ordinary photon has a sub-Plank scale wavelength. And like I said earlier, unlike local coordinate transformations, global transformations don't have limits. And if the photon collapses to a black hole in one coordinate system, it should do so in all of them*. Normal photons don't collapse, so the ones past Plank limits aren't going to either.

* General Covariance. AKA, Diffeomorphism Invariance. Very important consequence of space-time topology.

They won't spontaneously collapse, but they will as soon as they interact with anything. Which means they can't work as gauge bosons.

A photon with the Plank's length wavelength carries 12GJ, the Schwarzschild radius for that energy is about 12 times the Plank length. And you can't have EM if your virtual photons turn charge carriers in ultra short lived black holes.

And the same thing happens with other bosons: they are so energetic, they can't interact with stuff in the normal way.

As a result, you can't probe this kind of distances, which is often poorly explained as "distance looses its meaning". It doesn't, but you can't have meaningful objects of that scale.

[K^2]

They won't spontaneously collapse, but they will as soon as they interact with anything. Which means they can't work as gauge bosons.

[...]

As a result, you can't probe this kind of distances, which is often poorly explained as "distance looses its meaning". It doesn't, but you can't have meaningful objects of that scale.

Ah, that's where you were going with that. Yeah, that's completely fair.

But I would still call it more of a symptom than the underlying cause of such limit existing. It's like observations altering the observed being frequently used as a hand-waving explanation for Heisenberg Uncertainty. It's not wrong, but Heisenberg Uncertainty works regardless of whether someone is trying to make measurements or not, and that's far more interesting.

Similarly, field theory as we know it breaks down at Plank Scale regardless of whether anyone is trying to measure anything. The theory itself just doesn't work anymore.