# Insights A Hand-Wavy Discussion of the Planck Length - Comments

1. Sep 9, 2015

2. Sep 9, 2015

### Staff: Mentor

This misconception turns up a lot here on PF, too:

I'm glad to have a good article now to point people to, when it comes up again. Thanks!

3. Sep 9, 2015

### Greg Bernhardt

Nice work!

4. Sep 10, 2015

### JDoolin

Have you considered the idea of extremely high blueshift reference frames?

I have a common ordinary lightbulb producing wavelengths of light between 400 to 700 nanometers. However, from the point-of-view of a passing neutrino; with it's velocity negligibly below the speed of light, that same light bulb could be producing light with wavelengths less than the Planck Length.

So, perhaps the light from my lightbulb is producing a black hole in some frames of reference, but producing ordinary visible light in other frames of reference?

I'm highlighting the issue with a rather extreme case--the observer on the neutrino. Some people may argue that neutrino observers are not valid, because they have no ears, no eyes, and no souls, and that their reference frame doesn't exist. But consider if we took a light of wavelength JUST OVER the planck length, and had one observer fly away from it, while another flew toward it. The observer flying toward it would find that the wavelength of the photon was smaller than the Schwarzschild radius of the photon's energy. But the observer flying away would find that the wavelength of the same photon was larger than the Schwarzschild radius of the photon's energy.

Well, I guess my point is that radiant energy-- E = hf = hc/lambda, is simply not the same as mass energy E=mc^2.

The mass has its own reference frame independent of everything else in the universe--mass is an intrinsic property. Also, being a black hole, or NOT being a black hole is an intrinsic feature of matter. The light only has a reference frame in reference to its source and its observer, and frequency and wavelength of light are extrinsic features--observer dependent... Relatively moving observers are going to measure different wavelengths of the same light, so if this idea is accurate, they would also disagree on whether the light spontaneously collapsed into a black hole.

5. Sep 10, 2015

### JDoolin

Ah, upon rereading the article, I see that you really pretty much hit on my issues in my last post.

6. Sep 10, 2015

### BiGyElLoWhAt

I can't remember what it's called, even enough to search it via google, but there is actually a solution to this problem. The example provided on the wiki page that I remember used larger masses, as opposed to photons. Basically it says that as you approach the speed of light and pass a large mass, it can't turn into a black hole due to your reference frame. I really wish I could remember what it was called.

If I remember correctly (I very well could not), it has to do something with the geodesics of spacetime warping under the energy tensor from the relative speed of you and the mass you're observing. Now, this doesn't necessarily apply when we're talking photons. Darn my memory, and I'm only 23! I guess it's all downhill from here =/

Last edited by a moderator: Sep 10, 2015
7. Sep 10, 2015

### JDoolin

I would probably go the other way... Obviously if your theory implies that something is turning into a black hole according to one observer, but is not turning into a black hole according to another observer, then your theory has been essentially discounted by reductio ab adsurdam.

I believe the problem is with the premise than an object's mass increases as it approaches the speed of light. An object's MOMENTUM increases as $$p = \frac{m}{\sqrt{1 - (\frac v c)^2}}v$$; I feel that has been pretty well reasoned out. But the claim that an object's actual mass has increased (and hence it's capacitiy to pull other objects toward it by gravity) is NOT well supported by any reasoning I'm familiar with. I'm pretty sure I've seen this point made explicitly in some texts, but at 43, I'm well into my fifth decade of memory failure.

8. Sep 10, 2015

### Staff: Mentor

The use of relativistic mass is purely historic (and in bad popular science).

General relativity predicts that objects can collapse under certain conditions, usually described as sufficient energy density in their rest-frame. GR does not predict the collapse of something just because it moves at high speed, independent of the reference frame chosen to describe the system.

@JDoolin: That neutrino would need an incredible energy. Neglecting factors of 2, we have $m_\nu m_P = 3 eV \cdot E_\nu$ where the lightest neutrino mass is probably of the order of 1 meV.

9. Sep 10, 2015

### BiGyElLoWhAt

Mass increasing is definitely included in some texts, so you're not losing that memory just yet! My first text that I read on SR had a thought experiment with 2 bouncing balls and 2 observers, and used it to demonstrate relativistic mass.

10. Sep 10, 2015

### Ken G

On the topic of the "Planck pixel," perhaps this overall idea is being rejected too sweepingly. Presumably, the "pixels" would be in 4-D spacetime, not 3-D space, and volumes in 4-D spacetime are invariant, are they not? So I would imagine that if someone wanted to formulate a theory that said spacetime itself was parceled into "Planck pixels", they would play the usual game that in different reference frames, meaning along different world lines, the "pixels" would distort, but they'd still tile the spacetime in the same way. Yes that means objects don't "move one Planck length every Planck time", but that's obvious-- any such object would be perceived as moving at the speed of light. Instead, a "Planck pixel" idea could say that spacetime is discretely tiled, in the sense that world lines cannot be defined with finer precision than that-- similar to the way quantum mechanics "tiles" phase space in statistical mechanics.

Also, if we think of the "Planck pixels" as being in spacetime, their 1-D version also takes on some kind of meaning. If we choose c=1, it is often said that all objects seem to "move through" spacetime at a rate of 1 unit of spacetime displacement per unit of coordinate time. In that sense, an object could appear to move one Planck length each Planck time, and not seem to move at the speed of light, if the "Planck length" was interpreted broadly as also existing in the time dimension. It seems to me that could all be formulated in an invariant way, though its usefulness and/or ramifications I could not say. Most likely it would be some kind of "ultraviolet cutoff" to doing path integrals in spacetime, or some such thing.

11. Sep 10, 2015

### Staff: Mentor

Try to find any publication of the last 30 years using that concept.

You would still get different pixels in each frame. To make it worse, if you transform pixels, the relation between (dilated) Planck time and (contracted in one dimension) distance does not hold any more.

12. Sep 10, 2015

### BiGyElLoWhAt

I'm not going to argue within the last 30 years. I thinknthe book was '56 or there abouts. Fundamentals of modern physics, and it was by a german author, I'll try to dig it up here sometime soon.

13. Sep 10, 2015

### BiGyElLoWhAt

Eisberg?

14. Sep 10, 2015

### JDoolin

I'm not sure if I'm doing this right, but I just googled "energy of a neutrino collision" and found mention of an apparent 5000-10,000 TeV neutrino.

at http://www.pbs.org/wgbh/nova/next/p...ver-detected-has-1000x-the-energy-of-the-lhc/

So with a bit of estimation, assuming (1) the rest mass energy of a neutrino is about equal to 1 meV, (2) oncoming blueshift is approximately equal to the lorentz contraction factor here. (3) $\gamma \approx \frac{10 \times 10^{12} }{1\times 10^{-3}}=10^{16}$

Yes, if we started with visible light, at around $10^{-7}$ meters, it would be blueshifted to a wavelength around $10^{-23}$ meters; a trillion times longer than the Planck Length.

To do what I imagined and have a neutrino observer see my ordinary light-bulb-photon have a wavelength at the Planck Length, it would have to be a Yotta-eV neutrino. So yes, as you say, "an incredible energy"

Last edited: Sep 10, 2015
15. Sep 12, 2015

### BiGyElLoWhAt

Indeed it is.

16. Sep 14, 2015

### john baez

Nice post! Another way to think about the Planck length is that if you try to measure the position of an object to within in accuracy of the Planck length, it takes approximately enough energy to create a black hole whose Schwarzschild radius is... the Planck length! So, one can argue that it's impossible to measure distances shorter than this - though the argument is a bit hand-wavy.

To see how the calculation works, go here:

http://math.ucr.edu/home/baez/lengths.html#planck_length

Last edited by a moderator: Sep 15, 2015
17. Sep 14, 2015

### OCR

18. Sep 14, 2015

### klotza

Hand-wavy is the name of the game here! Thanks for the link, and for the advice.

19. Sep 15, 2015

### BiGyElLoWhAt

That's not how I interpreted that link. It seems to me what the author is saying is that if you try to measure a black hole of the plank scale within the accuracy of a radius, then there is enough uncertainty in the momentum that there could exist another black hole due to the corresponding energy uncertainty of the system (differing by a factor of v/2, classically)

20. Sep 15, 2015

### Staff: Mentor

Hint: compare the user name with the url.
Sorry, could not resist.