A Hand-Wavy Discussion of the Planck Length - Comments

[klotza]

klotza submitted a new PF Insights post

A Hand-Wavy Discussion of the Planck Length

Continue reading the Original PF Insights Post.

 

[jtbell]

There is a misconception that the universe is fundamentally divided into Planck-sized pixels, that nothing can be smaller than the Planck length, that things move through space by progressing one Planck length every Planck time. Judging by the ultimate source, a cursory search of reddit questions, the misconception is fairly common.

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

https://www.google.com/?gws_rd=ssl#q="planck+length"+site:physicsforums.com

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

 

[Greg Bernhardt]

Nice work!

 

[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.

 

[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.

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

 

[BiGyElLoWhAt]

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.

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 =/

 

[JDoolin]

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 =/

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 [tex]p = \frac{m}{\sqrt{1 - (\frac v c)^2}}v[/tex]; 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.

 

[mfb]

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.

 

[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.

 

[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.

 

[mfb]

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.

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

and volumes in 4-D spacetime are invariant, are they not?

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.

 

[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.

 

[BiGyElLoWhAt]

Eisberg?

 

[JDoolin]

@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.

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) [itex]\gamma \approx \frac{10 \times 10^{12} }{1\times 10^{-3}}=10^{16}[/itex]

Yes, if we started with visible light, at around [itex]10^{-7}[/itex] meters, it would be blueshifted to a wavelength around [itex]10^{-23}[/itex] 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"

 

[BiGyElLoWhAt]

Eisberg?

Indeed it is.

 

[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

 

[OCR]

To see how the calculation works, go here:

http://math.ucr.edu/home/baez/lengths.html#planck_lengthFixed that for you.....

BTW, I've been there many, many times.........

 

[klotza]

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

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

 

[BiGyElLoWhAt]

..it takes approximately enough energy to create a black hole whose Schwarzschild radius is... the Planck length!...

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)

 

[mfb]

That's not how I interpreted that link. It seems to me what the author is saying [...]

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

 

[BiGyElLoWhAt]

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

Hahahaha! Observation OP!

 

[OCR]

To see how the calculation works, go here:
http://math.ucr.edu/home/baez/lengths.html#planck_length

Last edited by a moderator: Yesterday at 1:24 PM​

http://math.ucr.edu/home/baez/lengths.html#planck_lengthFixed that for you.....

Aww, gee... thanks for the help......

Last edited by a moderator: Yesterday at 1:24 PM

[/QUOTE]..[/QUOTE]...

 

[haael]

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.

I'm not a fan of this theory, but there is an idea that spacetime is divided into pre-existing irregular grains of 1 Planck volume. This is called spacetime "glass" quantization, as opposed to "crystal" quantization should the grains be regular. The glassy properties of the quantization help it escape the usual problems with Lorentz invariance.

 

[Ken G]

I'm not a fan of this theory, but there is an idea that spacetime is divided into pre-existing irregular grains of 1 Planck volume. This is called spacetime "glass" quantization, as opposed to "crystal" quantization should the grains be regular. The glassy properties of the quantization help it escape the usual problems with Lorentz invariance.

Thank you for that insight. I would indeed think that if one wishes to regard spacetime as in some sense "coarse-grained" at the Planck scale, one must use a version of coarse-graining that is Lorentz invariant, meaning that the grains are defined by their volume but not their shape. This is hardly unprecedented-- the same thing is done to "coarse grain" phase space for statistical mechanical calculations, since there is no need to use a cubic tiling of "equal lengths" of distance and momentum when deciding how to count states. I don't mean to be unresponsive to the comment

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.

I simply didn't understand it. It was my impression that volumes in spacetime would be Lorentz invariant, but perhaps there is something I am missing.

 

[mfb]

A "classical" 4D Planck volume of one Planck length in spatial directions and one Planck time in time direction would be crossed by light diagonally, as light moves by one Planck length per Planck time. A transformed Planck volume with a shorter distance but a longer time loses this property.

 

[Benwade]

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 [tex]p = \frac{m}{\sqrt{1 - (\frac v c)^2}}v[/tex]; 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.

I (a complete physics idiot) actually posted a question that made the assumption that objects gained mass as they approached the speed of light. I was soon set right. Thank you for your explication, hand-wavey or not, of the Planck length, because I was a victim of the (erroneous) Planck-length = pixel size fiction as well.

 

[kalimaa]

I do understand the argument that the Planck length is not fundamental cause there is quite some choice left when it comes to defining such a length. What I don't understand is how you can take arguments from the continuous paradigm (which is theories in terms of differential equations on real numbers) and argue about the invalidity of ideas from the discrete paradigm (universe being pixelated, things moving at the speed of light one unit at a time, ...). From my point of view this chain of argument is invalid, exactly because the continuous paradigm breaks down around the scale when spacetime supposedly becomes discrete.

As for myself I'm taking serious the idea, that all our established physical theories (including GR and QM) are effective theories in the sense, that they don't express anything fundamental about the ultimate nature of reality, but instead are approximations to the inner workings of reality in the discrete paradigm. Any thoughts?

 

[Ken G]

If there is anything that the history of physics has shown us, it is that we don't shoot with high percentage when we try to anticipate the behavior in fundamentally new regimes. So I think what we really need are experiments that are capable of looking for evidence of discreteness. Until we have that, any theory will be pretty much guessing, in my opinion. But I do agree that all theories should be regarded as effective theories until demonstrated otherwise, with attention to the fact that they are impossible to demonstrate otherwise!

 

[Nugatory]

As for myself I'm taking serious the idea, that all our established physical theories (including GR and QM) are effective theories in the sense, that they don't express anything fundamental about the ultimate nature of reality, but instead are approximations to the inner workings of reality in the discrete paradigm. Any thoughts?

Could be... There's no way of disproving the possibility. But absent a candidate theory based on this discrete paradigm, there's also nothing to discuss under the Physics Forums rules.

This thread is closed. As always, PM me or another mentor if you have more to add and want it reopened.