# Why are Planck quantities so extreme?

• verdigris

#### verdigris

Why are Planck quantities considered to be maximum and minimum quantities -
Planck distance etc ? If they are,then,since in calculus a maximim/minimum is given by,for example,dy/dx = 0,then,for example,y = Planck quantity when
x = some other quantity.But what is x?

Can you pose the question in another way? For instance, why are the Planck time and the Planck length so tiny while the Planck mass is horrendously large? Is there a problem inherent in these definitions?

Can you pose the question in another way?

well, one thing i think he's asking is why is the Planck Velocity the limiting velocity yet the Planck Mass is not. there are lotsa things bigger and smaller than the Planck Mass.

For instance, why are the Planck time and the Planck length so tiny while the Planck mass is horrendously large? Is there a problem inherent in these definitions?

one other way of saying that the Planck mass is large is to, instead say that the Planck mass defines the norm and ask why the masses of subatomic particles are so small. i think it becomes equivalent to asking why gravity is so weak. there's an interesting quote from Frank Wilczek at the wikipedia article on Planck units about that.

the Planck Mass, Planck Momentum, even Planck Charge are reasonable quantities. i s'pose that since c=1 in Planck units, then the Planck Energy is also a reasonable quantity of energy (but it's released suddenly like a bomb, i would want to be on the other side of the hill). notice that the Planck energy is about as many orders of magnitude bigger than a joule as is the Planck mass smaller than a kg.

Why are Planck quantities considered to be maximum and minimum quantities -

I don't think that is true in general. Nobody I know considers all the Planck quantities extreme.

Some are extreme, like the Planck unit of speed is the speed of light which acts as a top speed of relative motion.

Some are not extreme----for example Planck momentum.

the Planck momentum is roughly speaking the amount of momentum that you give a child on a playground swing if you give them a very gentle push.

If you give them a good firm push, then you impart maybe 3 or 4 Planck units of momentum.
====================

To answer your question about why----I think the Planck quantities which are considered extreme, are considered to be extreme for a very simple reason: they ARE extreme.

And the Planck quantities which are not considered extreme are considered to be so for an equally simple reason: they are not extreme.

Last edited:
Why shouldn't the Planck quantities be the order of magnitude they are? What order of magnitude would you have in preference?

Physicists such as Lee Smolin say that the Planck distance is the smallest length of space.A minimum is given in calculus by an equation such as dy/dx = 0. If y = Planck distance and y is some function of x then x could be something like a mass or a height in a gravitational field, because measured distances vary at different heights in a gravitational field.
So if Smolin is right about the Planck distance being the smallest unit of space
then perhaps the Planck distance can be derived from a relationship in Einstein's General Theory of Relativity - a relationship that relates the length of one mass to its distance from another (height in gravitational field).

well, one thing i think he's asking is why is the Planck Velocity the limiting velocity yet the Planck Mass is not. there are lotsa things bigger and smaller than the Planck Mass.

I would disagree. The Planck mass is meant to be a limit to the mass of an elementary particle. And we don't know of any particle that has this mass (or anything even close to it). The Planck mass really represents a limit to what we can describe with the known laws of physics. At that mass, the event horizon of a particle is comparable to its Compton radius. What this tells us is that we would need a full theory of quantum gravity to describe such a particle. So a Planckian particle cannot be described with the present laws of physics.

Patrick

Physicists such as Lee Smolin say that the Planck distance is the smallest length of space.A minimum is given in calculus by an equation such as dy/dx = 0. If y = Planck distance and y is some function of x then x could be something like a mass or a height in a gravitational field, because measured distances vary at different heights in a gravitational field.
So if Smolin is right about the Planck distance being the smallest unit of space
then perhaps the Planck distance can be derived from a relationship in Einstein's General Theory of Relativity - a relationship that relates the length of one mass to its distance from another (height in gravitational field).

I don't claim any expertise but I think that the Planck length is defined at the length where the compton wavelength is equal to the schwarzchild radius. This essentially makes it the smallest measurable distance. (I haven't done any physics in a couple of decades so please correct me if I am wrong.)

If you try to measure the location of a particle which is smaller than this, then (from what I understand) the outcome is likely to be one of the following:

1. The wavelength used is too long to give any meaningful measurement.

2. A short enough wavelength would have enough energy to theoretically create another particle of equal or greater mass, or alter the location of the original particle to such a degree that the measurement is meaningless.

3. If a particle this small has enough mass to prevent condition #2 from happening, then it would be a small black hole in which case all of the light would be absorbed and no measurement would be possible.

I am not certain but I believe that a Planck mass is a black hole with a schwarzchild radius equal to the Planck length. I also think that the Planck time is the time that it takes light to traverse the Planck length.

I would disagree. The Planck mass is meant to be a limit to the mass of an elementary particle.

what you say is true. I'm just saying that not everything in the universe is an elementary particle (but i suppose everything is made up of them). there are objects, collections of elementary particles if you wish, that are both larger and smaller than a Planck mass which is about a speck of dust. there is no object or particle or collection of particles that has speed, relative to any observer, that exceeds the Planck unit of speed. only less (or equal if it's a photon). that's all i meant.

It is unclear to me whether the original poster is asking how we know that the Planck length is so small, or is asking the much harder question of why is it so small.

As to the 'how we know', it is simply a reflection of the observable fact that gravity is an extremely weak force compared to the other three forces. It is this weakness, which causes the Planck length to be so small (and the Planck energy to be so large).

The reason why gravity is so weak in comparison to the other forces (and consequently why the Planck length is so small) is not understood. Answer that in a convincing way (and test it with experiment) and you will win the Nobel Prize.

It is unclear to me whether the original poster is asking how we know that the Planck length is so small, or is asking the much harder question of why is it so small.

As to the 'how we know', it is simply a reflection of the observable fact that gravity is an extremely weak force compared to the other three forces. It is this weakness, which causes the Planck length to be so small (and the Planck energy to be so large).

The reason why gravity is so weak in comparison to the other forces (and consequently why the Planck length is so small) is not understood. Answer that in a convincing way (and test it with experiment) and you will win the Nobel Prize.

well, maybe that's the ticket. Nobel laureate Frank Wilczek had this to say about the topic:

...We see that the question [posed] is not, "Why is gravity so feeble?" but rather, "Why is the proton's mass so small?" For in Natural (Planck) Units, the strength of gravity simply is what it is, a primary quantity, while the proton's mass is the tiny number [1/(13 quintillion)]...
http://www.physicstoday.org/pt/vol-54/iss-6/p12.html [Broken]

asking why the masses of the fundamental particles are so small (compared to this natural unit of mass) is essentially the same as asking why the Bohr radius is so large (compared to the natural unit of length). don't know the answer, but answering one of these 3 questions will, in effect, answer all.

Last edited by a moderator:
The observed fundamental particles all have masses so small compared to the Planck mass that if one were to write their masses in an expansion in powers of the Planck mass, one would put their masses as zero to first order. The observed masses would be a second order effect, a splitting.

One would then wish to find a way of describing the observed particles as composites of some more fundamental particles whose charges all cancel. For example, see:
http://arxiv.org/abs/hep-th/0507032
and
http://ccdb4fs.kek.jp/cgi-bin/img_index?8103218 [Broken]

Carl

Last edited by a moderator: