For fun: How big of a Microscope is needed to see a Planck Length?

[DynV]

If you had--infinite--resources, material, manpower, energy, but only with current technology, or something that could be learned in a short time, how big of a microscope would it take to see a Planck Length? If there's a current limit, still with infinite resources, how small could you see and how big would the microscope be?

Optionally: If you were Jeff Bezos and decided you were going to burn through your cash down to "only" 10M$ (poor him), how big of a microscope for how small could you get? You can "switch" to Jenn Bezos if you want.

 

[Baluncore]

... how big of a microscope would it take to see a Planck Length?

What do you mean by "see" ?
The wavelength of the "light" will have something to do with it.

 

[DynV]

This is just for fun, I don't know all the details. The "purpose" is for seeing small and estimating the size of the apparatus to see that small.

 

[phinds]

A Plank length is many orders of magnitude smaller than is measurable with any modern technology and is likely to remain that way.

 

[DynV]

If there's a current limit, still with infinite resources, how small could you see and how big would the microscope be?

 

[Baluncore]

Lp = 1.616×10⁻³⁵ m
My eyes can see about 10 um.
Magnification required = 61.88×10²⁸

 

[tech99]

You would need to use radiation with a wavelength comparable to the Planck Length. Light will not be reflected from such a small object. If you use such a wavelength, then a very small microscope would suffice. If you want to see objects using a light microscope you are limited by the finite wavelength of the light rather than the optics.

 

[OmCheeto]

Interesting question.

This site in New Zealand lists the size limits of what things can see:

lower size limit in meters	things
10^-4	eyeball
10^-7	light microscope
10^-10	electron microscope

Contrasting that list with a wiki list of sizes of things:

size in meters	item to be looked at
10^-35	Planck length
10^-24	neutrino
10^-18	electron
10^-15	proton
10^-10	H2O
10^-6	needle tip
10^-3	stonelouse
10^0	human
10^7	Earth
10^21	Milky Way
10^27	Observable Universe

It appears that the smallest thing we can currently see is a water molecule.
Though the New Zealand site said this:

Below the microscopic scale​

Currently, the smallest thing that can be seen using a microscope is about the size of an atom. Anything smaller is below the current limit of resolution of the electron microscope, although the microscopic scale is likely to encompass even smaller objects as the technology of electron microscopes becomes more advanced. We know there are objects smaller than atoms, but they cannot be seen by microscopes. Scientists must turn to other tools to study these objects, including particle accelerators such as the Large Hadron Collider.​

bolding mine

I infer from the bolded statement that we are kind of visualizing smaller scale items with the LHC.

And what a bargain! The price tag of the LHC was only $5 billion? Didn't we just plop down $75 billion for a current war?

Anyways, from the wiki list, the Planck length is 11 orders of magnitude smaller than a neutrino and I can't imagine what things would look like at the neutrino scale. Old fashioned TV static would be my uneducated guess.

Another thing to look into might be X-ray crystallography. Maybe they could extend that into gamma ray crystallography. hmmm... google google google

never mind

wiki on xray crystallography;

At the other extreme, shorter-wavelength photons such as gamma rays are difficult to produce in large numbers, difficult to focus, and interact too strongly with matter, producing particle-antiparticle pairs. Therefore, X-rays are the "sweetspot" for wavelength when determining atomic-resolution structures from the scattering of electromagnetic radiation.​

I forgot about pair production.

 

[tech99]

To produce one photon of the require wavelength would require 10^9 Joules of energy as far as I can calculate.

 

[Baluncore]

To produce one photon of the require wavelength would require 10^9 Joules of energy as far as I can calculate.

10^9 J = 239 kg of TNT equivalent.
You would not want to get that in your eye.
That would not be fun.

 

[tech99]

10^9 J would also seem to require approximately 1000 chocolate bars, a surprisingly low
figure. TNT appears to have lower energy per kg.

 

[DynV]

Microscope using the Hershey technique?

 

[Baluncore]

10^9 J would also seem to require approximately 1000 chocolate bars, a surprisingly low figure. TNT appears to have lower energy per kg.

The impulse is less, because it takes quite some time to get the energy out of the chocolate.

 

[DaveC426913]

How about tweaking the OP to be 'have a field of view of one Planck length'

That sidesteps the 'how can you see it' problem.

 

[phinds]

How about tweaking the OP to be 'have a field of view of one Planck length'

That sidesteps the 'how can you see it' problem.

And it really doesn't matter anyway, considering how VERY far below our abilities it is and will remain, possibly forever, considering the quantum weirdness at that level (HUP, gravity, wavelength required, energy needed, etc)

 

[f95toli]

You would need to use radiation with a wavelength comparable to the Planck Length. Light will not be reflected from such a small object. If you use such a wavelength, then a very small microscope would suffice. If you want to see objects using a light microscope you are limited by the finite wavelength of the light rather than the optics.

While I obviously agree that being able to "see" at the Planck length is impossible, I would nevertheless like to point out that the statement in bold is only true for far field radiation; there is a whole class of instruments that use for exampl "tip enhanced" near field radiation to image objects far smaller than the wavelength of the light used.
The obvious example would be scattering near-field microscopes (SNOMs) which can go down to ~ 10s of nm or so for an off-the-shelf commercial instrument; but SNOM imaging below 10nm has been demonstrated.
There are also related techniques; but they all have in common that it is in possible get spatial resolutions of 1/10 to 1/100 or so of the wavelength used.

 

[phinds]

The obvious example would be scattering near-field microscopes (SNOMs) which can go down to ~ 10s of nm or so for an off-the-shelf commercial instrument; but SNOM imaging below 10nm has been demonstrated.

Yes, but does the OP no good, since you are still talking about MANY orders of magnitude larger than the Plank Length.

 

[f95toli]

Yes, but does the OP no good, since you are still talking about MANY orders of magnitude larger than the Plank Length.

Of course. As I stated above, "imaging" at the Planck length doesn't even make sense conceptually. I was merely pointing out that the idea that the spatial resolution is necessity limited by the wavelength of light isn't always true.
We can use STM to image individual atoms and even the electron distributions around; but at scales smaller than that ( below about 0.1nm or so) the whole idea of what an image "is" becomes quite problematic.

 

[DynV]

If there's a current limit, still with infinite resources, how small could you see and how big would the microscope be?

^ from the OP and post #5.