String theory / Plank length question

[Chas3down]

From whst I have read, anything smaller than Plancks length, you need to account for quantum gravity.. also, it is assumed strings in string theory are Plancks length.. so how could anything be smaller than Plancks length if strings are Plancks length(or greater than)? I thought strings made up everything?

Sorry if my question is stupid or doesn't make sense, I am just a HS student who likes to look up and attempt to understand some ineteresting physics.

 

[mfb]

- String theory is just a hypothesis, it can be wrong.
- String theory does not have particles which are smaller than (the order of the) Planck length, but the strings itself can need descriptions on scales smaller than their own size.

 

[Chas3down]

Okay, that was what I assumed...
anything smaller then Planck length is under the laws of quantum mechanics, correct? and anything larger is not..

 

[mfb]

Anything follows the laws of quantum mechanics*. But for anything smaller than the Planck scale you need an extension of the (current) quantum mechanics, which takes gravity into account.

*well, depends a bit on your favorite interpretation of QM, but at least there is no fundamental size limit

 

[Chas3down]

sorry, QG is what I meant. But if Planck length = length of a string, and nothing can be smaller than that, nothing would be affected by QG. I know this isn't true, I am missing a concept somewhere, but not sure where...

QG is needed when less than Lp(planck length)
Strings of string theory are assumed to be Planck length or higher...
Thus. nothing can be smaller than Planck length and QG wouldn't affect anything.

 

[mfb]

and nothing can be smaller than that

That is not true.

Take apples as an example: An apple has a size of some centimeters. But there are apples with different diameter, and different geometry, and you can compare apples on a scale of millimeters or even micrometers.

In addition, we are talking about a specific theory here.

 

[fzero]

sorry, QG is what I meant. But if Planck length = length of a string, and nothing can be smaller than that, nothing would be affected by QG. I know this isn't true, I am missing a concept somewhere, but not sure where...

QG is needed when less than Lp(planck length)
Strings of string theory are assumed to be Planck length or higher...
Thus. nothing can be smaller than Planck length and QG wouldn't affect anything.

It seems important to explain something about how approximations work in physics. It is not the case that quantum mechanics does not affect anything on long scales. It is the case that quantum effects are very small compared to classical ones when we probe a system on length scales which are long compared to the characteristic size of the object. Quantum effects do not suddenly turn on as we probe to shorter and shorter scales. They are always there, but at long scales they are small enough that we may ignore them for most purposes.

Similarly, QG effects are not zero at 1000 Planck lengths, but they are around 0.1% smaller than the classical description. Depending on the precision of a hypothetical experiment, they might be completely negligible. However, a sufficiently precise measurement could not neglect QG effects.

The Planck length is the length scale at which the quantum effect is as large as the classical prediction, so there is no confusion at all about whether or not quantum gravity effects can be neglected. It is not some magic scale where QG effects get turned on.

 

[suprised]

That is not true.

Take apples as an example: An apple has a size of some centimeters. But there are apples with different diameter, and different geometry, and you can compare apples on a scale of millimeters or even micrometers.

In addition, we are talking about a specific theory here.

This is really a serious misunderstanding, on two related counts. First, in string theory as a complete theory, there are no objects smaller than strings to probe a sub-stringy geometry. Thus "smaller" distances (roughly speaking, see below) are unobservable. If one tried to pump in more and more energy in a scattering process in an attempt to resolve smaller distances, what one actually would find is that the effective size of the string grows again and becomes classical at some point (there is circumstantial evidence for the latter claim, which has not been proven AFAIK). So in a sense the string scale is the smallest scale that can be accessed, and if the latter point turns out as expected, then quantum effects are maximal there.

Which brings me to the second point, which fzero has already touched upon. At the Planck scale, quantum fluctuations of the space-time geometry become of order one, so there is no good notion any more of what a metric is, and thus distance, etc. Thus it does not make sense to use the word "smaller". In the picture alluded to above, Apples can_not_ be compared with each other at a millimeter scale, because there is no way the specify what a millimeter is. This applies more or less to all theories of quantum gravity besides strings.

 

[mfb]

Unobservable to direct measurements is not the same as "not there". As long as you don't consider a discrete spacetime, smaller distances are there - even if there is no direct (!) way to probe them, similar to the problem of measuring millimeters if "hit it with an apple" is your only option.

 

[suprised]

Unobservable to direct measurements is not the same as "not there". As long as you don't consider a discrete spacetime, smaller distances are there - even if there is no direct (!) way to probe them, similar to the problem of measuring millimeters if "hit it with an apple" is your only option.

What is a "smaller distance" if there is no metric, no classical geometry left? How would you compare two "distances" ?

 

[mfb]

If I would know that, I would publish that theory of everything and wait for the Nobel Prize .