# Wavelength or amplitude < a Planick length?

• labrat3004
In summary: You're asking about something that has nothing to do with the size of the particle. If you want to know the size of the particle, you need to know its velocity. This question is not relevant to the discussion.
labrat3004
Is it possible for an object's size to be great enough to make it's wavelength or amplitude < a Planick length? If so, does it's position become certain, and, applying the uncertainty principle, can you not know the velocity?

The position and velocity of any object is uncertain to a small degree

No can know position AND velocity at SAME time.

labrat3004 said:
Is it possible for an object's size to be great enough to make it's wavelength or amplitude < a Planick length? If so, does it's position become certain, and, applying the uncertainty principle, can you not know the velocity?

Can you indicate where you got the idea that the "wavelength or amplitude" is related to an object's size?

Zz.

To help clearify:

Firstly the Planck length comes from both quantum mechanics and classical GR so let's forget it for a moment.

Purely within quantum mechanics you can localize a particle (and hence its wave-function) to an arbitrarily small uncertainty but this would be at a given instant.
Given the uncertainty principle the particle's momentum becomes highly uncertain and you won't have any idea where it is at a later time since momentum = mass x velocity.

Part of this is that to measure so localized a position for the particle you must hit it with other particles (say a photons) with momentum sufficiently high that you can distinguish small variations of the original particle's position based on how these others bounce off.

This is a crude way of saying it. Viewed purely in QM terms a localized particle is in a superposition of many widely spread momentum modes and so defining a particle as having a specific momentum = mass x velocity, automatically means you are talking about a different particle.

Anyway invoking GR you also have that given you are trying to localize a particle (at an instant) near the Planck scale you must concentrate so much energy in that region that gravitational effects will mess up your measurement process. At the Planck scale you have a substantial probability of creating a gravitational singularity (black hole) and this in essence destroys your particle entirely.

Note there are other larger scales at which localization breaks down. At the Compton wavelength were the same thing happens, not due to gravitation but rather because in trying to make the position measurement you create electron-positron pairs in a random way, again upsetting the measurement process.

A final note. My thesis advisor David Finkelstein generalized the Planck scale argument to resolving field measurements (such as the value of the E field) within a certain region. You get two parameters representing how big the region and how small the sub-division. It shows that Field theory itself is not meaningful over a large enough scale and/or small enough resolution. What was interesting was how, if you let the large scale parameter approach the size of the observable universe, you get a minimum subdivision roughly on the scale of the Compton wavelength. Maybe a coincidence maybe significant. ?

ZapperZ said:
Can you indicate where you got the idea that the "wavelength or amplitude" is related to an object's size?

Zz.

In Chemistry classes they commonly describe a baseball by it's De Broglie wavelength. It's put forward mostly as a joke though it always causes people to take it seriously.

DeepThought42 said:
In Chemistry classes they commonly describe a baseball by it's De Broglie wavelength. It's put forward mostly as a joke though it always causes people to take it seriously.

I know about de Broglie wavelength. What does that have anything to do with size?

Zz.

ZapperZ said:
I know about de Broglie wavelength. What does that have anything to do with size?

Zz.

The length is inversely proportional to the mass.

DeepThought42 said:
The length is inversely proportional to the mass.

I hate to sound like a broken record, but what does this have anything to do with "size"? And what "length"? The de Broglie wavelength has nothing to do with the size of the particle. If it does, then you're saying that the size depends on the velocity of the particle, which in the non-relativistic scenario makes no sense.

Zz.

ZapperZ said:
I hate to sound like a broken record, but what does this have anything to do with "size"? And what "length"? The de Broglie wavelength has nothing to do with the size of the particle. If it does, then you're saying that the size depends on the velocity of the particle, which in the non-relativistic scenario makes no sense.

Zz.

Wavelength = h/p ~ h/mv in non relativistic terms. The question is not about a particle, but the theoretical wavelength of a macroscopic object. If the mass were so large the wavelength could become infinitely small.

DeepThought42 said:
Wavelength = h/p ~ h/mv in non relativistic terms. The question is not about a particle, but the theoretical wavelength of a macroscopic object. If the mass were so large the wavelength could become infinitely small.

This is what the OP wrote:

labrat3004 said:
Is it possible for an object's size to be great enough to make it's wavelength or amplitude < a Planick length? If so, does it's position become certain, and, applying the uncertainty principle, can you not know the velocity?

Aren't you re-interpreting what was being asked? Why don't we wait until the OP comes back and provides further explanation?

Zz.

I am assuming that when he says "object" he is talking about a cow, or a planet and the theoretical wavelength that this object has as a whole. Labrat, please clarify :)

DeepThought42 said:
I am assuming that when he says "object" he is talking about a cow, or a planet and the theoretical wavelength that this object has as a whole. Labrat, please clarify :)

You need to read a bit more... the OP is talking about an object's SIZE. A "size" is not a well-defined operator in QM. While you have a position operator, a "size operator" is unknown. That is why I am asking all this first rather than drawing my own conclusion.

Zz.

I'm sorry I did not expect so much activity so quickly.

I'm sorry, by size I meant to imply high mass, because, obviously, if the object were small with high mass, you would encounter errors as you approach the schwardzchild radius...

In any case, yes, I was talking about the De Broglie wavelength and the uncertainty principle, and I'm sorry my original question was so confusing and inaccurate.

An "object" with any fixed deBroglie wave-length is not localized (it's momentum has been exactly specified). The Planck scale argument has to do with localizing an object within a certain scale and this requires the object be in a superposition of many wave-lengths.

So to the OP yes it is possible within QM (in principle) for an object's deBroglie wavelength to be smaller than the Planck scale. It doesn't imply anything odd will happen as you are not talking about localizing the object to that scale.

ah, thank you, that's very helpful.

jambaugh said:
So to the OP yes it is possible within QM (in principle) for an object's deBroglie wavelength to be smaller than the Planck scale.
Well, in conventional QM there is really nothing special about the Planck scale, it would only take on a special role in theory of quantum gravity, which we don't have yet. And it might not be possible for an object's wavelength to be smaller than the Planck scale in a theory of quantum gravity (at least in the case of a photon this would imply its energy was greater than the Planck energy).

## 1. What is a Planck length?

The Planck length is the smallest unit of length that has physical significance in the universe. It is approximately 1.6 x 10^-35 meters, which is incredibly tiny and difficult to conceptualize.

## 2. How does wavelength relate to a Planck length?

Wavelength is a measure of the distance between two consecutive peaks or troughs in a wave, while a Planck length is a fixed distance. The two are not directly related, but the Planck length is often used as a reference point for extremely small wavelengths in quantum mechanics.

## 3. What is the difference between wavelength and amplitude?

Wavelength and amplitude are both characteristics of a wave. Wavelength is the distance between two consecutive peaks or troughs, while amplitude is the maximum displacement of a wave from its resting position. In other words, amplitude measures the strength or intensity of a wave, while wavelength measures its size.

## 4. Can a wavelength or amplitude be smaller than a Planck length?

According to the laws of quantum mechanics, it is not possible for a wavelength or amplitude to be smaller than a Planck length. This is because the Planck length is believed to be the smallest possible unit of length that has physical significance in the universe.

## 5. How does the Planck length relate to other units of measurement?

The Planck length is an extremely small unit of measurement and is not commonly used in everyday applications. It is often used in theoretical physics and quantum mechanics to describe the behavior of particles at the smallest scales. It is related to other units of measurement, such as the meter, through physical constants like the speed of light and Planck's constant.

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