Considerations of Planck length & time

[lifegazer]

Hello.

I want to discuss the meaning of the following statement, which I have pasted from physlink (.com). Because I'm new, I'm not allowed to link you directly to the source.

"The Planck length is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate. This is the ‘quantum of length’, the smallest measurement of length with any meaning.

 

And roughly equal to 1.6 x 10-35 m or about 10-20 times the size of a proton.

 

The Planck time is the time it would take a photon travelling at the speed of light to across a distance equal to the Planck length. This is the ‘quantum of time’, the smallest measurement of time that has any meaning, and is equal to 10-43 seconds. No smaller division of time has any meaning. With in the framework of the laws of physics as we understand them today, we can say only that the universe came into existence when it already had an age of 10-43 seconds."

(I have underlined the points of significance, for me)

 

I would argue that it is completely irrational to posit the meaninglessness of length less than any specific length (planck length, in this instance).

For example, a length of 1mm is meaningless if there is "no meaning to length less than this". If there is no meaning to lengths less than this, then there can be no meaning to that length itself.

In effect, the statement renders the planck length as 'zero'.

So, would you agree that the actual meaningful reality of any length is dependent upon length being an infinitessimally small parameter of universal existence?

 

Of course, a similar argument would apply to planck-time, which would render the last highlighted-sentence of the statement as incorrect.

[Qfwfq]

I quite agree there's a difference between saying that below a given scale the description is very different, and that briefer lengths/times are meaningless. AFAIK the first of these two statements is right and the second is a misconception. It would be better to talk about Planck scale rather than about Planck length/time, not that the second terminology is logically wrong but it tends to be misleading.

 

Here is the source:

 

http://hypography.com/forums/newreply.php?do=newreply&p=191788

[lifegazer]

What can "we can say only that the universe came into existence when it already had an age of 10-43 seconds" mean, if there is no time less than this value?

This question highlights the problem, for if there is no time less than this, then that time (planck time) is effectively rendered as 'zero' from a rational point of view.

[Qfwfq]

Good question! ;)

 

BTW you can write the quantities more clearly by using the math or imath tags:

 

[math]10^{-43}[/math] (with the quote button you can see exactly what I typed in)

[lifegazer]

Good question! ;)

 

BTW you can write the quantities more clearly by using the math or imath tags:

 

[math]10^{-43}[/math] (with the quote button you can see exactly what I typed in)

Thanks for the tip. I'll soon forget though.

 

It seems that you might now agree that the actual meaningful reality of any length is dependent upon length being an infinitessimally small parameter of universal existence.

It appears that space cannot be real unless it is continuous.

[lifegazer]

Nobody is biting. Perhaps I should add more...

 

For any meaningful length 'X', there must be two points separated by a space.

 

If one posits that there is no length less than the planck length, then one is essentially stating that the planck length is a distance which does not exist as a space between two points. In fact, one is stating that the planck length is not a space/distance at all. That is why it is ultimately reducible to a meaningless quantity. The same argument applies to planck-time, of course.

 

I consider this to be quite an important consideration, so I'd like to hear a few more responses.

Thankyou.

[Pyrotex]

I'll bite. :eek:

 

I ran into this same issue in 1973 when I read a then-recent book on particle physics. Rather than strike me as irrational, it struck me as profoundly enlightening.

 

Think of it this way. "Length" can be defined, as you said, by the separation between two objects. The separation itself can be measured, but how? Well, we rely on an intermediate object (yard stick?) that is sub-divided. We place it along side the two objects and count the subdivisions.

 

The question is, how far down the scale toward the infinitessimal can we continue to do this? The "fuzziness" of the quantum world slowly begins to dominate, which means the marks on our ruler become fuzzy, smeared out, wiggly. We cease to have signposts that mark how far we have measured. We can count the atom-widths between two molecules; we can count the proton-widths between two atoms; we can count the electron-widths from one side of a proton to the other side. Then we run out.

 

Even at that point, the "electron-widths" we are using are so blurry, shimmering with what I imagine as "quantum heat waves" (think of the heat waves rising from hot asphalt while driving on a hot summer day in Death Valley). We can hardly distinguish one electron-width from its neighbor. "Length" is no longer a stable commodity, a static property.

 

It's like trying to measure the length of an ocean wave in the midst of a Class-5 hurricane -- with a dress-maker's tape measure -- while floating in an inner tube, and wearing boxing gloves.

 

You've entered the realm of "quantum foam". Where particles appear and disappear continuously, to such an extent that "length" is bubbled, boiled, dissolved, foamed and folded at a furious, frenetic pace. Your measuring stick deforms and melts like a sugar cube held within a cup of boiling water. Length no longer has any "meaning" -- in the sense that we understand it at our macro "peas-to-planets" scale.

 

You're not in Kansas any more :hyper:

[lifegazer]

Think of it this way. "Length" can be defined, as you said, by the separation between two objects. The separation itself can be measured, but how? Well, we rely on an intermediate object (yard stick?) that is sub-divided. We place it along side the two objects and count the subdivisions.

 

The question is, how far down the scale toward the infinitessimal can we continue to do this?

Hello.

You obviously don't think that there is a problem with anything that you've said here, but there is. The problem is that the "intermediate yardstick" placed between two objects, that sub-divides the distance between those objects, can tell us nothing about the distance between those objects if there is no such notion as 'zero' distance. That is the crux of this discussion.

The "fuzziness" of the quantum world slowly begins to dominate, which means the marks on our ruler become fuzzy, smeared out, wiggly. We cease to have signposts that mark how far we have measured. We can count the atom-widths between two molecules; we can count the proton-widths between two atoms; we can count the electron-widths from one side of a proton to the other side. Then we run out.

The issue is that "there is no meaning (a meaninglessness) to distances less than a planck length". (the argument applies to planck-time too.). The issue is not one of whether we lack the technology to measure such minute distances. Indeed, we lack the technology to measure a planck-length itself.

 

Let us not forget the all-important quote under consideration:

"we can say only that the universe came into existence when it already had an age of 10-43 seconds."

 

... It is completely irrational to say that the origin of time started at 10-43 seconds.

You've entered the realm of "quantum foam". Where particles appear and disappear continuously, to such an extent that "length" is bubbled, boiled, dissolved, foamed and folded at a furious, frenetic pace.

At what positions WITHIN a length that has no meaningful extension can foams/particles/bubbles appear? If there is no meaningful length less than the planck-length, then there is no meaningful position for these separate events to occur within that space.

Your measuring stick deforms and melts like a sugar cube held within a cup of boiling water. Length no longer has any "meaning" -- in the sense that we understand it at our macro "peas-to-planets" scale.

If all measuring sticks were to "melt" at a length of 1mm, then kindly inform this forum how any lengths of 1mm were measured in the first place.

 

Since there are a finite number of planck-lengths (which themselves are immeasurable) between all two points, then it should be impossible to measure any length.

[Qfwfq]

The "fuzziness" of the quantum world slowly begins to dominate, which means the marks on our ruler become fuzzy, smeared out, wiggly.

If there is no such thing as a shorter length, what's the meaning of saying that the marks on the ruler are smeared out? The quantum description dominates even at much larger scales than Planck's, only it isn't essential to gravitation which can hence still be regarded as a classical field theory (and troublesome to quantize anyhow).

 

The notion I criticize, and consider a misconception, is that of Planck length/time being a kind of Lego-block. Also, Lifegazer is logically correct in pointing out that, if there is no such thing as a shorter length, it makes no sense to call the block's edge a length. As in the quantum decription of larger stuff, you need to describe a bit more than can actually be measured; the fact that not all of the description is observable simply has some implications, viz symmetry considerations (very tricky, some of them).

 

The only sense which it could strictly make to state there being no meaning of a briefer length would be that length is actually an integer number and not a number times an arbitrary unit... the unit itself not being a length at all. In this manner, Planck's "unit" would only be the inverse of the number which our artificial unit of length actually is. Pythagoras liked this kind of idea so much that he lost his sanity when he realized that the diagonal of a square, also a thing of such elegant simplicity, contradicts the conjecture. Then again space-time isn't strictly flat and pehaps it's just a matter of finding the hidden secrets of [imath]g_{\mu\nu}[/imath]... :shrug:

 

We can count the atom-widths between two molecules; we can count the proton-widths between two atoms; we can count the electron-widths from one side of a proton to the other side.

Which electron widths? While we know hadrons to be composite and have a radial distribution, we know of no such thing for quarks and leptons.

[Pyrotex]

Okay, I surrender!

I am laying my loaded arbalast of physics on the floor, and putting my hands behind my head. Please don't shoot! B):doh::confused:

 

[Damn! When Qfwfq gets on my case, there is NO point in arguing!]

 

I seem to have made at least two mistakes. One is an obvious mistake in scale. You are right, Q, the quantum effects that I so poetically described are many orders of magnitude larger than the Planck scale. Mea culpa. And two, the "width of an electron" currently makes no sense, as Q has indicated. I knew that. That is, I remember knowing that some time ago.

 

Actually, there was a third mistake. And that was reading the first post in this thread perhaps a bit too quickly and responding with undue haste before I fully understood the actual question being posed. Now that I re-read the post, I'm still not sure what the actual question is. I'll get back to you on this.

 

:confused:

[lifegazer]

Now that I re-read the post, I'm still not sure what the actual question is.

Hello again.

At this juncture, it might help if I detail my concerns...

 

Firstly, there cannot be a future for 'planck length/time' if one uses those notions as the smallest possible length/time. It's completely irrational, as discussed.

Secondly, since the 'planck-scale' plays a significant part in other physical theories & mathematics, one also has to question the rationality of those theories.

Thirdly, there is evidence here of physics completely ignoring and/or abusing basic rationale/logic when positing theories about this existence. That is very worrying, imo.

[Qfwfq]

Please don't shoot! :doh::doh::doh:

Bang!!!!!!!!

/forums/images/smilies/devilsign.gif

:hihi:

 

Don't take it badly Pyro, you're post was good enough although not centred on the question posed. As for your "third mistake", it is a conceptually tricky matter. :)

 

Secondly, since the 'planck-scale' plays a significant part in other physical theories & mathematics, one also has to question the rationality of those theories.

Thirdly, there is evidence here of physics completely ignoring and/or abusing basic rationale/logic when positing theories about this existence. That is very worrying, imo.

As long as it is thought of as a scale there is nothing irrational about it. The only thing I find worrisome is the widespread misconception of interpreting it too hastily, as meaning that space and time should be a discrete grid. Many people think this notion is fine, due to erroneous understanding of quantum mechanics or IOW the idea that everything should be discrete.

 

You might get a better, even though vague and qualitative, idea of what I mean by scale (rather than "smallest length") from this quite good page. This guy is good because he says some conceptually fundamental things in a simple and illustrative way; while he deliberately avoids being finicky where it doesn't matter, he makes no real, gross blunders. The only thing he could have better cautioned the reader on is the use of the naïve method of computing the Schwarzschild radius, but never mind that.