Talk:Planck time

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The following section added no value to the main article so I removed it[edit]

If someone wants to rewrite this so that is has meaning they are welcome to add it back.


Ignoring a factor of , the Planck mass is roughly the mass of a black hole with a Schwarzschild radius equal to its Compton wavelength. The radius of such a black hole would be, roughly, the Planck length.

The following thought experiment illuminates this fact. The task is to measure an object's position by bouncing electromagnetic radiation, namely photons, off it. The shorter the wavelength of the photons, and hence the higher their energy, the more accurate the measurement. If the photons are sufficiently energetic to make possible a measurement more precise than a Planck length, their collision with the object would, in principle, create a minuscule black hole. This black hole would "swallow" the photon and thereby make it impossible to obtain a measurement. A simple calculation using dimensional analysis suggests that this problem arises if we attempt to measure an object's position with a precision greater than one Planck length.

This thought experiment draws on both general relativity and the Heisenberg uncertainty principle of quantum mechanics. Combined, these two theories imply that it is impossible to measure position to a precision greater than the Planck length, or duration to a precision greater than the time a photon moving at c would take to travel a Planck length. Hence in any theory of quantum gravity combining general relativity and quantum mechanics, traditional notions of space and time will break down at distances shorter than the Planck length or times shorter than the Planck time.

I think it was a mistake to remove this section. The articles on planck length and planck time imply that these constants have a special physical significance as being some sort of limits to our theory, and not just unit games - but don't explain why. This text (I have no idea who wrote it, by the way) does, or so it seems.Nyh (talk) 14:01, 14 October 2009 (UTC)

Concerns regarding following statement[edit]

Does anyone else have an issue with the following under 'Simple Definition':

"The speed of any object is limited by Einstein's laws of relativity, which state that nothing can travel faster than the speed of light in a vacuum (denoted c)."

I understand that this is for a simplified explanation, but it's just plain not true. Einstein only stated that an objects mass would become infinite if traveling at the speed of light. Also, faster-than-light observations and thoughts have been carried out and discussed here:

I didn't want to alter the original article since I'm new to the wikipedia, but wanted to leave note of this in case the author would like to respond and possibly reconsider an edit.


Dave Quirus 26 Aug 2005

    Infinite mass is the same thing as impossible, and if an object could actually travel >c in a vacuum (ignoring shenanigans like an alcubierre drive or the casimir effct), it would be capable of carrying information, which IS prohibited in relativity, isn't it?

I could be wrong, but I was pretty sure that's how it worked. The "nothing" could be changed, but other than that... (talk) 03:35, 5 April 2009 (UTC)

14th January 2005 Changes[edit]

Thanks Jim Wae the LaTeX rather mucked up that's not my best attribute, what did you think of the changes the article needed to be merged with Planck's Time so I more-or-less added it as a simple explanation for Planck Time.

I hope I pulled it off, I think that article still could be improved on though. Jordan14 21:09 16th Jan 2005

Merger from Planck's time and beyond[edit]

I've redirected Planck's time to this page. I didn't find any material on that page that adds to any on this one and it's far less (i.e. not) wikified. I've reproduced the text here for anyone who disagrees and wishes to reapply any of it:

Planck's Time
Planck's Time is how long it takes for light to travel Planck's length.
At Planck's length relitivity breaks down and actions across smaller lengths are worthless, as an effect this is the smallest length of significance.
As described by relitivity nothing can travel faster that the speed of light.
So to find Planck's Time/Time Quanta - the smallest amount of time. We have to do the sum:
Planck's constant (The smallest distance) divided by The speed of light (The fastest speed) and this will equal the smallest part of time, which is Planck's Time/Time Quanta.
As and effect we get the following value for Planck's Time:
1 x 10^-34m divided by 3 x 10^8 m/sec
So this means Planck's Time is about 3.3 x 10^-44secs. This is the smallest amount of time.

That done, I think that this article is confusing, for several reasons.

First, there is no mention of the fact that that time is discrete is a very recent finding, it is not universally accepted, and its ramifications are far from fully understood.

Second, the value is derived twice, two (apparently) different ways. The second, the simpler, is just simply the mathematical expression of the definition of of the number. The first is essentially the same thing, but doesn't make clear except to a well informed reader how you get from d = st to tp = (hG/C^5)^1/2 (i.e. that (hG/C^5)^1/2 = ((hG/C^3)^1/2)/c = lp/c.)

Third, the structure seems backward, in that it presents the "simple definition" in the middle of the article, rather than proceeding from simple to complex. Planck length, while not perfect or comprehensive, would seem to provide a good template.

Also, while the fact that things get really wacky before Planck time = 1 is likely notable enough to include in the article, the way its presented now makes it seem like that that is a defining factor for the Planck time.

And, I think the use of the of the word "nonsense" in the second section is problematically vague. I've seen the phrase "does not have meaning" used and think that that (or similar) would be more epistemologically rigorous.

After all that, I'm not going to edit it. I'm not expert enough to do more than reorder the article and apply (what I think should be) a template for the article and leave it only half-filled. Plus, I have no competence with the math markup. But I hope these ideas help someone to edit, improve, expand this article.

VermillionBird 20:04, 2005 Mar 7 (UTC)

A discrete world?[edit]

So there's the Planck length and the Planck time: does this mean the world can be thought of as a 3 dimensional grid, each cell sized to the Planck length, and iterations running in every Planck time (i.e. the Planck time is the "FPS value" of the universe)?

> The Planck time is the time it would take a photon travelling at the speed of light to cross a distance equal to the Planck length. However, this may not be taken as a "quantum of time."

Please elaborate. If it can't be taken as a quantum of time, there must be a reason. 02:41, 19 March 2006 (UTC) Keith

The planck time is the tiny gap,'between the tick and the tock', referred to as the present, that separates the future from the past. Within the Planck time particles such as positrons, electrons, and photons can travel in both directions of time. In the case of the electron it enables the recapture of virtual photons that would otherwise lead to the rapid loss of their charge/magnetic moment over time. Richard Feynman's description of the e->e- + p+>photon + e- pair-producing contribution to the fine structure of atomic spectra was explained by him as a process involving the emission of a photon by the electron accelerating relativistically in the vicinity of the nucleus. The photon is transformed into an electron positron pair. The positron, in the Planck time, travels backwards in time to annhilate with the original electron, resulting in a single electron and photon/s resulting from the annhilation both leaving the Planck time and travelling forwards in time. Planck space and Planck time are intimately associated with the Uncertainty Principle and help to explain the paradoxes raised by quantum mechanics such as non-locality and complementarity. Colin Cumming 23 March 2006.

Referenced from Time under "Time quanta"[edit]

Time references this topic in the "Time quanta section": Time#Time_quanta. I think that is misleading and I opened a discussion at Talk:Time#Time_quanta.3F Your opinion? 18:43, 4 October 2006 (UTC)

person's age in planck units[edit]

I think the current figure is off by two orders of magnitude. From the beginning: 75y/life * 365d/y * 24h/d * 60m/h * 60s/m * 5.3912 * (10^40)tP/s = 1.27512662 × 1050tP/life.

I think the error came as follows: the tP per person was calculated as 77y/13.7By of 8*1060 tP per universe. But 4.3*1017s/universe (which matches my figures) times 5.4*10^44tP/s gives 2*1062, not 8*1060. Anyone concur? Debivort 20:46, 26 March 2007 (UTC)

75 years times about 3.16e+7 seconds/year gives 2.37e+9 seconds per lifetime. Divided by the Planck time, this is about 4.4e+52 Planck times. The lifetime of the universe, at 13.7 GY, is 4.33e+17 seconds, or 8.0e+60 Planck times. The numbers in the article appear to be consistent with each other. Checking your figures, your quotient for division is not quite correct (you're flipping the exponent and multiplying by Planck time, instead of multiplying by (1/tP)). --Christopher Thomas 21:01, 26 March 2007 (UTC)
Yes you are right. I misread the definition as 5.4*10^44tP/s rather than 5.4*10^-44s/tP. Sorry for the confusion. Debivort 22:54, 26 March 2007 (UTC)

Strange value in parenthesis[edit]

How should I understand 1.855*10^43 (600,000,000,000,000,000,000,000,000,000,000,000,000,000,000)? A value of 6... is at least off off 1.855*10^x by a factor of 2. So they can't even be nearly equal. —The preceding unsigned comment was added by (talk) 12:42, August 21, 2007 (UTC)

Gravity is not a force[edit]

In the introduction to this article, it is written that:

"One Planck time after the event is the closest that theoretical physics can get to it, and at that time it appears that gravity separated from the other fundamental forces."

The contemporary view of gravity is based on Einsteins theory of general relativity, which states that the observation of gravity is a consequence of the curvature of space-time. As such, is is completely meaningless to discuss gravity separating from other fundamental forces, since it's not a really a "force" per se. i think what the author was intending to say was that gravity would have been created the moment the universe had size larger than a singularity.

I am refraining from editing this bit until i get some corroboration. any opinions? please CC any replies to my talk page. --Shaggorama 01:29, 13 September 2007 (UTC)

Gravity is a force. It causes acceleration. You can say that in GR gravity is not an interaction from field theory point of view, but gravitational force is still present. Compare with weak interaction: it is an interaction, but is there a force (acceleration, momentum exchange) resulting from it? I do agree that the statement about "gravity separated from the other fundamental forces" sounds highly speculative and I would like to see references. -- (talk) 09:44, 21 January 2008 (UTC)

Planck time challenged?[edit]

The very last paragraph challenges the existence of planck time based on pictures being too crisp from outer space. This sounds bogus to me, because the length and time scales involved are truly miniscule, and you should be able to see crisp images just fine even from the most remote regions of space. We are limited in observation only by the size of the photon, and that size is easily small enough to bring back a high resolution image from space. What do you say to deletion of this paragraph?--MaizeAndBlue86 (talk) 23:49, 3 March 2008 (UTC)

Correct value for planck time?[edit]

I have to question that value for the planck time. Yes, it's true that light can travel the planck length in that amount of time, but no meaningful signal could be interpreted from that short a time (i.e. the wavelength of light is usually so much greater than this length that it would take several, perhaps even billions of planck times to even cover 1 period of oscillation). The shortest wavelength of light possible is 2x planck length because the signal must be able to go from high to low. Shouldn't that be the planck time? - The time it takes light to travel 2 planck lengths? That is the shortest time that one could possibly recover complete information about a signal.--MaizeAndBlue86 (talk) 23:59, 3 March 2008 (UTC)

Hubble telescope challenges planck time[edit]

That is not significant evidence that light is not particulate. My telescope gets bad resolution, does that mean that light is particulate?

It has been proven time and time again that light is a particle, and particles have size, hence the planck length and hence the planck time. You cannot measure something smaller than the measuring particle itself.--MaizeAndBlue86 (talk) 23:40, 6 March 2008 (UTC)

I think you cannot compare the hupple telescope to your telescope. The Deep Field picture is the farest and sharpest ever taken. And it is as simple as that: It shouldn't be that sharp! There has been measured something smaller than the planck time, that is a simple fact in this article. And serious scientists are saying that, publishing their findings in serious journals. So, if we take the "No Original Research" principle serious, we can not depend on your or my opinion as long as you haven't published it (or I haven't published it), lets say in a journal. So let us just stay with the facts, which are: The scientists say something's wrong because the Hupple Deep Field picture is sharper than expected. I assume that is a simple principle we can agree on and will undo the undo. If you're still unhappy with that, please explain me why we shouldn't include it, but not on Original Research by yourself or because of what you think or I think. Bring me an article (placed in time after that one) that says: "Oh my god, we were mistaken" or "Uh, we made a serious error in our measurement", than we will delete it ok? Or if you can bring me an article of another scientists saying "That's nonsense" referring to that publishing in another publishing (journal or so) than we can at least print both opinions (but shouldn't delete one of them). As long as that's not the case, lets stay with the facts, even if they are not how we like them to be... it wouldn't be science if we already know everything and wouldn't have a few problems in our theories right? ;) greetings, ColdCase (talk) 01:52, 7 March 2008 (UTC)
I wanted to add: If you have a good idea for rephrasing the sentences in a way they would satisfy all of us, just say it. A good compromise is still the best way to end a depate ;) ColdCase (talk) 01:58, 7 March 2008 (UTC)

I would like to see a calculation of this. At what distance "should" light appear granular and distort images? The planck length is 10^-35, that's pretty dang small. I can imagine procuring very high resolution photographs for quite a long distance. I just want to know why these "scientists" think their images should be blurry, with numbers to back it up.--MaizeAndBlue86 (talk) 12:57, 28 March 2008 (UTC)

I've been looking all over the internet for recent news and updates for the peculiar findings involving the high-clarity Hubble images. The only site I've found it on(besides the article) was at Can anyone provide any updates or related articles on this topic in a scientific journal or on a renowned science news website? Thanks--Phaethon's Odyssey (talk) 02:31, 2 April 2008 (UTC)

The universe as a discrete-time system[edit]

I don't see how it's original research. I didn't make up the planck time, sampling theorem, or Aliasing. This is what I learn in college as a Digital Signal Processing major. Maybe you haven't heard of it before, but it's just a connection I'm making between things that are known to exist; and I can prove all of it if need-be.

Besides, look at the article without my section. It's small, and it has questionable materials with the "hubble space telescope challenges planck time" section. That's completely erroneous! yes, it is sourced, but completely false, as the planck time is known to exist in quantum physics.--MaizeAndBlue86 (talk) 10:37, 18 March 2008 (UTC)

I am well aware of the sampling theorem and aliasing, thank you, and those are not what is considered original research here (perhaps I should have explained this a bit more in my edit summary). Rather it is the following:
it's just a connection I'm making between things that are known to exist; and I can prove all of it if need-be - That is exactly the problem: This connection is your own private idea. It is not the question if you can prove it, if it is wrong or right and if your hopes that it may have the power to explain several phenomenons in the world of quantum physics are justified: It simply runs against one of Wikipedia's principles to publish new ideas in a Wikipedia article. Read Wikipedia:No original research. It is not the job of Wikipedians to peer-review the proof of a new scientific result.
Instead, you should submit your proof to a peer-reviewed quantum physics journal, and get your new ideas accepted by the scientific community. I promise I will be the first to congratulate you on your scientific breakthrough and to update this article accordingly.
I didn't make a judgement about the rest of the article, but I think it would be independent from the decision about this section.
Regards, High on a tree (talk) 13:14, 18 March 2008 (UTC)
This is my understanding of WP:NOR too. You have to find a "reliable source" (roughly meaning published and reputable) outside Wikipedia that states your idea. If point A and point B are both in the literature, and you believe it is obvious that A and B imply point C, you still have to find an outside published source that explicitly states the implication before you can use it and claim C here. It may pass if it is not challenged, but it will always be threatened with reversion until it is thoroughly sourced. In this particular case, I think it would be challenged. It sometimes seems a bit harsh, but in the context of an encyclopedia and the integrity thereof, it does seem to be necessary and inevitable. It is more important to be reliable and trustworthy here than to be first to report the latest advances. Best, Bill Wwheaton (talk) 19:32, 18 March 2008 (UTC)

You have to admit, though, that it has merit. Maybe I haven't "proved" it to the scientific community, but it makes sense, right? I guess we'll see who laughs last when I've got my nobel prize :) I think you'll be hearing more about this...maybe not today, maybe not tomorrow, but the truth will come out.--MaizeAndBlue86 (talk) 15:46, 18 March 2008 (UTC)

I did not say that it makes sense or that it doesn't make sense, because that is precisely the kind of debate which WP:OR is intended to avoid. I did call the addition "interesting thoughts" in my first edit summary, because I readily admit that it takes some creativity to come up with such an idea, but in science, this is unfortunately only the first step towards valid insights. Regards, High on a tree (talk) 19:56, 18 March 2008 (UTC)

Proposed new section[edit]

This is my proposed contribution to this article, I do not consider it original research, because it doesn't claim any direct conclusions. It merely draws a legitimate connection and leaves open the results, which need to be officially "accepted" by the scientific community to be concluded. I strongly believe it would contribute to the overall quality of the article. Please read:

The Universe as a discrete-time system[edit]

The presence of a ‘smallest time’ in the universe means that time moves in discrete segments, and not continuously. However, since these segments are so small on the scale of human measurability, it is often a good approximation to assume time and space are continuous. The differences become apparent on extremely small length and time scales, and are therefore important for understanding quantum physics.

Discrete-time sampling theorem says that a discrete signal cannot contain higher frequencies than 1 cycle per 2 samples, where a cycle corresponds to a wave going from ‘high’ to ‘low’. In other words:

where fm is the maximum possible frequency, and Ts is the period between each sample. In the case of our universe this sample period is the planck time, and that corresponds to a maximum measurable frequency of

Not to say that higher frequencies can't happen, only that we can't measure them with the limited ‘sampling rate’ of the universe.

So what happens to all of the higher frequencies? In discrete signal processing, if one tries to sample a continuous signal whose frequency content is too high, aliasing occurs. So instead of it being a high frequency, it appears as a low frequency. In effect, going past this frequency limit is the same as starting over at low frequencies again and moving up from there, with most of the original signal content lost in-between samples.

The relevance of this fact for the structure of the universe is not yet known, but it may have the power to explain several phenomenons in the world of quantum physics. For example, why space and time seem to become “fuzzy” around distances near the planck length, and times near the planck time (see quantum foam).

Please post comments, I would like to hear what people think!--MaizeAndBlue86 (talk) 17:18, 18 March 2008 (UTC)


A Planck Unit is the smallest measurable unit. It does not follow that the smallest MEASURABLE unit is a feature of "space-time itself". There has been no determination that either space or time are entities, no less entities with properties. Planck units have definite implications for the limits of measurement, but since it is not clear there IS any underlying "structure of the universe", it is premature (at the very least) to comment in that regard --JimWae (talk) 17:34, 18 March 2008 (UTC)

I'm not sure what an "entity" would be in physics, nor how one would determine what qualifies and what does not. It is not a formal concept I am familiar with, can you clarify or define it? Thanks. Wwheaton (talk) 19:50, 18 March 2008 (UTC)
  • an entity would be a "thing" (technical definition). Not all nouns refer to things. Saying that "time moves in ..." not only speaks of time as a thing, it is speaking of time as if it were an agent that can "do" something. The main topic in ontology is "what nouns are things?"--JimWae (talk) 23:44, 18 March 2008 (UTC)
The vacuum of space and time can, in fact, be modeled statistically as a "sea of photons", or a photon gas. That is consistent with space and time being made up of smallest entities, or "building blocks". If the building block is the photon, then it's hard to measure something that's smaller than that. You definitely can't do it with another photon.--MaizeAndBlue86 (talk) 21:01, 18 March 2008 (UTC)
  • models are certainly useful, but they do not "tell" us anything about the "real" underlying "structure of the universe" - they only help us model the universe. That which we cannot measure, we might be better off not drawing too many conclusions about --JimWae (talk) 23:44, 18 March 2008 (UTC)

I am in doubt also, mostly because it seems to me that any discreteness or granularity in space or time might violate Lorentz invariance. There could be a big hole in my understanding here, and if so I would love to have it filled in, but at the moment I am not convinced. Bill Wwheaton (talk) 19:50, 18 March 2008 (UTC)

Without a quantum theory of gravity any talk about "smallest measurable" stuff, black holes that prevent measurement, "quantization of space" is pure speculation. There are no well established theories that deal with these questions. Recommended reading: , , , -- (talk) 07:27, 28 March 2008 (UTC)

I don't know that the planck scale depends, necessarily, on quantum gravity. For instance, we know that there is a planck scale, even without knowing about quantum gravity. Recommended reading: Tipler and Llewellyn, "Modern Physics" - 5th edition. --MaizeAndBlue86 (talk) 13:05, 28 March 2008 (UTC)

Orders of Magnitude table[edit]

The Orders of Magnitude table indicates that Planck time is the order of 1E-26 sec, but the text shows this should be the order of 1E-44 sec. The text mentions 1E-26 relative to the attosecond. Please resolve. GilesW (talk) 15:06, 24 August 2008 (UTC)

Fine tuning the Plank length?[edit]

I was wondering if the Plank length could be fine tuned, using the neutrino instead of a photon. Brian Pearson (talk) 13:38, 10 September 2008 (UTC)

Shortest measured time[edit]

Both articles talk about "measuring" times on the attosecond scale, but both specify it's around 100 attoseconds as far as I can tell. Here's what the 2006 one said:

"The researchers devised a new technique to 'see' the motion of protons, one of the building blocks of an atom, in molecules of hydrogen and methane. The technique involves firing a very short but intense laser pulse at a molecule, which rips an electron away, leaving the molecule in an excited ionised state. The electron is then drawn back to the molecule, and when it collides a very short burst of x-rays is released. 'That has encoded information within it about the state of the molecule at the point of re-collision, and can give us information about the motion of the protons in this molecule,' Dr Tisch told the BBC News website. The process is ultra-fast, and the team was able to observe the effect the laser had on motion in the molecules with an accuracy of 100 attoseconds - the fastest ever recorded. 'Slicing up a second into intervals as miniscule as 100 attoseconds is extremely hard to conceptualise. It's like chopping up the 630 million kilometres from here to Jupiter into pieces as wide as a human hair,' explained Dr Tisch."

According to the calculation, Planck time is about 5.4E-44 and 100 attoseconds is 1E-16. By my calculations, that's 1.85E26 different although I could have gotten that wrong. Please correct if so. Sln3412 (talk) 19:00, 25 June 2010 (UTC)

Better font / graphic for equations?[edit]

Can't read the equations. They come out as fuzzy gray souble-lines on a black background. Same result in five different browsers. Any chance of using a more legible font, or maybe presenting them as a simple JPG or GIF graphic? —Preceding unsigned comment added by (talk) 23:35, 21 October 2010 (UTC)

Billions of billions of billions??[edit]

The article claims:

All scientific experiments and human experiences happen over billions of billions of billions of Planck times, making any events happening at the Planck scale hard to detect.

Even if that stmt is trying to express "far more", it is an extreme understatement. The human mind is not able to perceive anything shorter than abt 1/24 s, which makes billions³ (= (10⁹)³ = 10²⁷) pretty lame. The number is more like 10⁴² to 10⁴³, which is "one to ten tridecillions" in the short scale of US. Won't an expression like "orders of magnitude more" be more suitable and less malformedly dramatic? Rursus dixit. (mbork3!) 18:38, 28 January 2011 (UTC)

Theoretically, this is the smallest time measurement that will ever be possible[edit]

"Theoretically, this is the smallest time measurement that will ever be possible". This appears in the article, and is cited to a source which doesn't really go into any detail. This needs more of an explanation, as I for one don't see why it is "theoretically" the smallest time measurement that will EVER be possible. --T.M.M. Dowd (talk) 17:25, 24 April 2011 (UTC)

It is fully explained and as well as possibly can be to people who dont study this rather astoundingly complex system, right under "Physical Significance." You would have to try very hard (not reading half the page) to come away with a question about how it funcitons. (talk) 05:02, 2 September 2011 (UTC)

Some sane numbers?[edit]

That all looks really complicated. And Im bad at math. But could someone post what the planck time looks like in standard notation? (as in, 0.0000~1 etc seconds) alternatively if such a page already exists, i'd like to either be pointed to it or have it pointed out on the page here. (talk) 04:56, 2 September 2011 (UTC)

10−43 seconds = 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 1 seconds
5.3910632 x 10−44 seconds = 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 053 910 632 seconds

--JimWae (talk) 19:20, 2 September 2011 (UTC)

"Less than Planck Time"[edit]

The article talks about "processes which happen at less than Planck Time durations" which, please forgive me if I'm a dullard, I had though were not possible. No event takes place at less than a Planck Time, it's granular to the point where it becomes a logical absurdity to speak of "less than Planck" much as it is a logical absurdity to speak of "before the Big Bang." Am I totally wrong? Damotclese (talk) 19:13, 8 December 2011 (UTC)

The smallest time interval that was directly measured was of order of 20 attoseconds.[edit]

The page says that the smallest time interval that was directly measured was of order of 12 attoseconds, but another source says it is 20 attoseconds. Please confirm.

As of May 2010, the smallest time interval uncertainty in direct measurements is on the order of 12 attoseconds (1.2 × 10−17 seconds), about 3.7 × 1026 Planck times.[1]
The one you posted is from June 2010, but writer must not have been aware of May one. Also, 12 attoseconds is the level of accuracy, while 20 attoseconds is the event length.--JimWae (talk) 10:50, 19 April 2012 (UTC)

This article needs to say how long the Planck Time actually is...[edit]

...because not to is just ridiculous. I have reverted an edit from March 2013 which removed it. (It may well have been well-intentioned, but was clumsily done.) Richard75 (talk) 22:02, 16 December 2013 (UTC)


pysics is the biological meaning to quatum asro nominal — Preceding unsigned comment added by (talk) 19:01, 6 October 2014 (UTC)

  1. ^ "12 attoseconds is the world record for shortest controllable time". 2010-05-12. Retrieved 2012-04-19.