A Minimum Time Interval - Implication From the Universe's Very Existence?

Hi ladies and gents.

Time is generally assumed to be a smooth line which can be divided for infinity. But we have no way to make sure it's not. Thus, the question of, "is there a minimum time interval?" is still an open question, and a most interesting one, too.

Yesterday I realized, though, that an argument could be made in favor of a Minimal Time Interval.

It was brought to my attention that there is an upper limit on the mass of a particle. From Wikipedia:

upper limits on their mass due to the very existence of the universe - which would have collapsed by now if they were too heavy - are about 10^17 GeV/c^2

This article was referring mainly to magnetic monopoles, but I assume the point still stands for normal particles.

Now, an important point: it is theorized (much in accordance with observations) that virtual particles can be created from total vacuum. This feature of the universe is caused by Heisenberg's uncertainty principle, and an equation exists to predict this particle production:



In which "E" is the mass-energy of the particle, "t" is time (invesedly proportional to "E"), and h is roughly equal to 0.00000000000000066 eV*s. The result of E*t must always be equal or below the value of h. Thus it may be more useful to invert the formula so that for a specific amount of energy, we can know how much time it relates to:



Example: if out of total vaccum an electron is to be created, with a mass of 510,998.910 eV, then the formula will be:

0.00000000000000066/510998.910 = 0.000000000000000000001291587882252038463252299305296

Thus the electron may not exist for longer than 0.000000000000000000001291587882252038463252299305296 seconds.


Now let us consider the upper limit, 10^17 GeV/c^2, which a particle may not exceed. This implies that the existence of such particle, by definition, is impossible because of the very existence of the Universe. Yet, applying our formula to such a massive particle states that this particle's duration in time would be h/E = 6.6 x 10^-42 second maximum, or anywhere lower.

My argument follows as such: if such a particle may never exist (otherwise the Universe would have collapsed a long time ago), then it implies it cannot be created out of vacuum's uncertainty principles. Which means, the "t" variable must never be allowed to reach 6.6 x 10^-42 seconds or below, otherwise it would allow for the production of such massive particles. Thus, this finally implies that time does indeed have a minimum duration; effectively preventing such massive particles from exisiting at all.

This concludes the presentation of my argument regarding the minimum time interval.


At Time's End,

Swan

a reply to: swanne

A simpler formulation: any unit of time shorter than the length of time it takes a photon to travel the "Planck length" is meaningless.

Edit to add: Star and flag for your edited version!

Chronon

originally posted by: swanne

I don't know if this is a simple mistake, or a flaw at the heart of your reasoning (or that I'm worse at math than I thought I am), but...

I read this image to read "stuff on the left must be greater-than-or-equal-to stuff on the right":


...but you say:

...The result of E*t must always be equal or below the value of h.

(eta: added underline to be more exact about my question)

everything else is based on that. Did you get the picture wrong? Am I worse at math than I thought I was?

What you are essentially asking is, "What is the frame rate of the universe". How long does it take for the next frame to advance?

I had always considered that it would be related to the time it takes for EM particles to communicate changes of state.

I spent the majority of the night taking calls from a new employee. I am going to have to have a cup of coffee and reread the OP to see if I can understand it.

We've seen on the quantum scale that things can happen literally instantly. Doesn't that demonstrate that 0 is the smallest time interval?

originally posted by: theGleep
I read this image to read "stuff on the left must be greater-than-or-equal-to stuff on the right":

Nice point. But according to wikipedia (en.wikipedia.org...), the sign "≥" means "no more than ħ":

the Heisenberg uncertainty relation, ΔE · Δt ≥ ħ. In effect, the energy needed to create these virtual particles, ΔE, can be "borrowed" from the vacuum for a period of time, Δt, so that their product is no more than the reduced Planck constant

Might be a mistake from Wikipedia.

Am I worse at math than I thought I was?

No, in fact I think you made a very good observation.

But the OP still stands though. We can simply ignore the sign and replace it by the words, "no more than..." ...whatever is on the right. This is what my formula was about, and the symbol which we assign to this operation doesn't change the validity of the said operation. Still, it'd be great to know if Wikipedia made a mistake.

originally posted by: bigfatfurrytexan
What you are essentially asking is, "What is the frame rate of the universe". How long does it take for the next frame to advance?

Exactly.

A minimum time interval has implication in so many deep aspects of the universe.

a reply to: swanne

Is the Wiki quote from the article on electrons? If so then the information is no longer on the page. The symbol is right, but the interpretation is not. It indicates "greater than or equal to," meaning the product of the terms on the left can be no less than the reduced Planck constant. Also, the reduced Planck constant is given the wrong value. The value given is for the standard Planck constant - the reduced Planck constant is that divided by 2*pi. Though the use of the two constants is often interchangeable.

Otherwise, the idea is intriguing. Have you researched the concept of Planck time?

a reply to: swanne

I think you have covered the 'random' creation of particles out of the vacuum. But if im not mistaken, we are able to create fundamental particles on our own out of energy and other materials? For example the family of electron, muon and tao. We have techniques available in which we can form these fundamental particles; I am wondering what about nature disallows more massive fundamental particles to be stable? What causes their decay, and theoretically if we could make them exist in a stable form, lets say a lepton that is twice the mass of a tao, what would it take for the local circumstances and what would need to be different for it to exist as stable? Is this just really expressing the fact that the ultimate building blocks of reality are uber small, and when anything gets bigger as a fundamental building blocks, the protocol is for it to be quickly relinquished of its size, and is this due to thermodynamics of energy taking path of least resistance, it is less efforts or there is not enough force and bondage for a more massive tao to hold itself together?

And something more related to your thread; Is it already figured that with such a question of minimum time interval you would be looking towards the photon as your candidate for achieving that minimality? Are you really asking how fast a quanta of energy can travel? And that is how you would judge the least amount of time that can pass? Or 'how fast energy can decay/transform', which is really another way of saying, how quickly energy can be moved from point A to B?

Could you not maybe solve this problem by thinking of a kind of shutter or frame rate, if you had a camera or video camera, that could capture footage of the smallest areas of the universe, the most micro stuff, and the camera would start with 1 frame per second, then 2 frames per second, then 3 frames per second, and so on until eventually the frame rate would match the fastest frame rate of reality? At which point if you were to hypothetically make the frame rate go faster it would be taking multiple frame shots, say 2 (or more likely 1 and fraction) before reality can respond?

Or are you suggesting there may be a more absolute and ultimate minimum time allotment that is deeper then what is even explorable and testable?

Its interesting to note maybe if you consider the amount of space a photon moves over a Planck length, first of all is a photon not already greater in size then a Planck length? I also might wonder if the theory of expansion of space is true does this mean that planck lengths are being created?

If there was a "minimum interval of Time", which, if I'm understanding the terminology correctly, would mean a minimum length of time which would be identifiable as being discreet from the "next" interval of Time,

What exists between the two discreet intervals?

Would not that "gap" be an area of "no-time", that is to say a period-state in which Time did not exist?
By definition, could not exist.

And if a period were to exist in which Time did not exist, how could Time "span" that gap to advance from one discreet interval of time-existence to the next discreet interval of Time-existence?

originally posted by: Bhadhidar
If there was a "minimum interval of Time", which, if I'm understanding the terminology correctly, would mean a minimum length of time which would be identifiable as being discreet from the "next" interval of Time,

What exists between the two discreet intervals?

Would not that "gap" be an area of "no-time", that is to say a period-state in which Time did not exist?
By definition, could not exist.

And if a period were to exist in which Time did not exist, how could Time "span" that gap to advance from one discreet interval of time-existence to the next discreet interval of Time-existence?

Thats actually a pretty great thought, but almost in the Zeno paradox sense.

Like if people declared, "We know the shortest length of distance, it is the inch!", and then people said, well you have one inch, what about the distance between that, what about half that? And what about half that? and what about half that?

So what you said made me think of that similar thing for time. For spatial that paradox supposedly ends at the Planck length, but if it is a 3d area I dont know how there couldnt theoretically and realistically be a half a planck length.

So for time to be composed of the 'quickest', 'shortest', interval of time (which first one, or many, must do a better and great job at defining what exactly they are referring to when they say the word time, and then ask for the shortest interval of time possible), what is it that stops it from going quicker.

And I think the answer may be that time is continuous. So there is no short interval of time occurring, as it is always occurring at all.

Where one decides to start their stop watch or not, is arbitrary. An arbitrary mode of measurement placed over the universe.

You are measuring how far, or how fast a quanta of energy travels over a certain distance, and saying, from here to here is a time of time.

But in reality, the fact that quanta of energy exists, and is moving at all, means that time is continuous!

So the fact that a wave of energy exists, means it is both the shortest and longest interval of time, it is time, time is energy, and the fact that energy moves and changes.

Now you can compare how differing parts/quanta/conglomerates of this energy, behaves compared to one another. How quanta A vibrates up and down 100 times before you can count to 6. Or how Quanta B can vibrate 100 times before you can count to 4.

But is quanta B, expressing a 'shorter interval of time'?

Is time purely related then, the hierarchy of time related to speed over/in space, that is, the shortest interval of time, the theoretically highest frequency of energy?

Which hypothetically would be I suppose, the entire energy of the universe, besides 1 lowly quanta, and then the entire energy of the universe imploding creating the highest possible force and release of energy, which vibrates the 1 quanta left out, and then that quanta will have created the highest frequency, thus creating 'the thing that utilizes the least amount of time'?

You are right on, when one talks about time in the quantum world, things look quite different. The big problem is we really don't know what creates time.

a reply to: LeviWardrobe

Let us just say, using your logic, that particles are coming into our dimension from some source outside our 3D space on a carrier wave coded in frequencies, i.e. the String Theory implies ' tiny, tiny, tiny strings of energy vibrating at different frequencies give rise to quarks' . The electron is also created with frequencies, a married pair if photons colliding with a virtual particle creates an electron - photons a packets of frequency. So what does this have to do with time?

Time needs an origin, just like everything else, something has to be creating time - it needs an engine. Particles coming into our dimension on a carrier is the engine. Look at the 'Standard Model' beginning, a tiny, tiny, tiny spec of space (Big Bang) energy exists (same thing as a particle); -43 of second later space inflates for another extraordinary -43 of second (Inflation Era) to the size of a proton (basketball or some even say a galaxy to make their universe work). Science proposes everything was there at the beginning, nothing added since, no intelligence (except theirs) at the beginning nor today needed.

Wrong, the engine is still running, still pumping particles into our universe. Time is movement and particles move because the engine is running. The force of transmission of frequencies creating our matter instantaneously right in front of our eyes is what we call gravity - something science discovered but have no idea what its origin is.

This is not my creation, it is thought to been part of Nikola Tesla's papers or notes; upon his dead many experiments were made using his theories. There is no proof it came from Tesla, since all his material was confiscated by unknown entity - there is no proof it did not either, except from the experiments conducted after his death, and his aides.
reply to: swanne

a reply to: bigfatfurrytexan
yes, that is quite correct: however the answer doesn't actually come out as a unit of time but as a unit of space.

time is a physical space. linear time relative to the observer is always the dimension directly above them (4D for us).

what we perceive as time is more of an overlap between two dimensions intersecting at their minimum points. there is no true rate of intersection because speeding a movie up or slowing it down has no effect on the things within the movie.

Time is not a "thing" that "exists." It is a mental construct that enables us to make sense of our experience. As such, it has intuitive aspects that break down upon closer examination. At some point, the phenomena being examined are so far from our realm of comprehension that the answers to our questions become meaningless, ie; what is outside the multiverse? Where was the multiverse before it was created? It is like trying to divide by zero, it falls out of the logical system we have constructed. Gödel proved that no system can be complete and contain no contradictions. When dealing with concepts like time, the best one can do is provide functional definitions, such as time is a dimension at right angles to all the other three, or time is what happens when you spread out entropy. Not very satisfying, but it's a bit like calculating with pi. It's irrational, but it works.

originally posted by: LeviWardrobe
We've seen on the quantum scale that things can happen literally instantly. Doesn't that demonstrate that 0 is the smallest time interval?

Very fair point. But Heisenberg's formula isn't about measuring, say, the elapsed time which a particle takes to move from a point a to point b. It's about the lifetime of the particle itself.

If the value of "t" in Heisenberg's equation was allowed to reach absolute zero, as your point seem to imply, then this would allow for the creation of particles with literally infinite mass or energy (according to the formula: E = h/0 = infinity). Which would have rather severe effect on the state, if not existence, of the Universe which we live in.

a reply to: swanne

I think you need to be very careful when you interpret the time-energy uncertainty relation. It has many subtleties. For example, itonly places a lower bound on the product of the uncertainties. Does this mean it can be arbitrarily large? Not likely, since that would have all kinds of weird implications, like very massive particles existing for very long timespans.

a reply to: CLPrime

Is the Wiki quote from the article on electrons?

Indeed: en.wikipedia.org...

The symbol is right, but the interpretation is not. It indicates "greater than or equal to," meaning the product of the terms on the left can be no less than the reduced Planck constant.

Okay, so the symbol is the right one. Hm, I guess it makes sense - someone should still edit the Wikipedia page regarding the interpretation, though.

But wouldn't the direction of the symbol defeat the purpose behind the computation of a particle's lifetime - that instead of creating particles whose lifetime is inversely proportional to their mass energy, it'd imply that, as long as the product of E and t are "no less" than h-bar, vacuum can create rather exotic particles with infinite energy and which can last for an infinite period of time? In the case of the electron, wouldn't it mean that instead of saying,

Thus, for a virtual electron, t (its lifetime) is at most 1.3×10^?21 s.

the article should say,

Thus, for a virtual electron, t (its lifetime) is at least 1.3×10^?21 s.

?

Also, the reduced Planck constant is given the wrong value. The value given is for the standard Planck constant - the reduced Planck constant is that divided by 2*pi.

Indeed. It's equal to 6.58211899x10^?16 eV*s. Some sources round it off at 6.6x10^-16, which is the value I used in my OP.

Have you researched the concept of Planck time?

I did, but there is not much in Planck's Units which "prevents" time from existing in smaller durations than one Planck Time unit. Classical approaches to the quantization of time are based on "landmarks", such as the speed of light, the value of G, etc. but these landmarks doesn't necessarily mean that the universe stops there; just like the presence of a fence doesn't necessarily mean that the World ends there. I elected on following a different approach. It might just be possible to probe the limit of Time using some equation which relates the Time of a virtual particle to its Mass - since mass must reach a limit so to avoid the collapse of the Universe, then so should (in theory) Time so to avoid the existence of such massive particle. Besides, it is interesting to note that 6.6 x 10^-42 seconds (the limit of time according to the OP) is not that far from 5.39124x10^-44 seconds.

BTW what is your opinion regarding the particle mass limit being set at 10^17 GeV/c^2? Do you reckon it should be higher?

a reply to: ImaFungi

But if im not mistaken, we are able to create fundamental particles on our own out of energy and other materials?

Indeed. But these are created artificially by pumping energy into the particle, and so are their lifetime. As you point out, they are created from energy and other materials, and not from total vacuum. A few of super-massive particles in some particle accelerators on Earth wouldn't destroy the universe. The point is if they can be created out of total vacuum, for if such massive particles could really occur naturally from utter nothingness, then it'd occur almost everywhere in the Universe, and the latter would have collapsed under the combined multitude and magnitude of these particles.

For example the family of electron, muon and tao. (...) Is this just really expressing the fact that the ultimate building blocks of reality are uber small, and when anything gets bigger as a fundamental building blocks, the protocol is for it to be quickly relinquished of its size, and is this due to thermodynamics of energy taking path of least resistance

That is the main explanation indeed. Muons tends to decay into an electron and a neutrino because the latter are less massive than the muon.

or there is not enough force and bondage for a more massive tao to hold itself together?

Tauons (and all fermions and bosons, for that matters) are not known to have any substructure - and a substructure is necessary if one is to theorize that these particles can "hold themselves together". But emerging preonic models might shed some light on this topic. The problem is, models of preons are often considered as fringe science.

Is it already figured that with such a question of minimum time interval you would be looking towards the photon as your candidate for achieving that minimality?

So many people gaze at the photon... Although I admire their perseverance, I nevertheless chose to use my eyes to gaze at another alternative. Instead of focusing on the photon, I focused on the relation between vacuum's maximum mass production and time.

Are you really asking how fast a quanta of energy can travel? And that is how you would judge the least amount of time that can pass? Or 'how fast energy can decay/transform', which is really another way of saying, how quickly energy can be moved from point A to B?

More like the latter. More precisely, there must be a limit where particles, where "dangerous" (universe-threatening) energies cannot be produced in the first place.

Could you not maybe solve this problem by thinking of a kind of shutter or frame rate, if you had a camera or video camera, that could capture footage of the smallest areas of the universe, the most micro stuff, and the camera would start with 1 frame per second, then 2 frames per second, then 3 frames per second, and so on until eventually the frame rate would match the fastest frame rate of reality? At which point if you were to hypothetically make the frame rate go faster it would be taking multiple frame shots, say 2 (or more likely 1 and fraction) before reality can respond?

I've thought about the same thing. But then I realized something important. Let's say, for the sake of the thought experiment, that the Universe's minimum time is 1/1000 a second. What I didn't realized, is that my camera belongs to this universe. Thus its very existence too will be affected by the Universe's frame rate. Let's say I put the camera so that it take one picture each 1/500 seconds. My camera will have time to exist two times for each time it takes a picture. The playback will show no two identical frames. Once I put my camera on 1/1000, my camera's recording rate will match its existence rate. On the playback, I'll see a smooth image with no two identical images. But once I put my camera on 1/2000 a second, the camera still cannot exist for a time shorter than 1/1000 of a second. If it could take a picture each 1/2000 of a second, and my camera phases out of existence each 1/1000 of a second, then my camera doesn't exist for half that time. And thus neither do the pictures which she was set to record. The result is a smooth playback with no two same pictures, since the camera technically never existed between the Universe's frames.

Or are you suggesting there may be a more absolute and ultimate minimum time allotment that is deeper then what is even explorable and testable?

Probably. We can't see past Heisenberg's uncertainty principle anyway...