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I never said that any Planck Limit was equal to infinity. I am fully aware that Planck Length is 16.163×10 (-36) m and that Planck Time is 5.39121 × 10 (-44) s. These are discrete values.

BTW Redewenur, pleased to finally meet you. If I may resort to an analogy: While Bill S. and I are swashbuckling in the crows nest; you are in the belly of the ship constructing propellers out of rum kegs…most definitely the voice of reason and I welcome it. (You too Bill.)

To me, Planck’s limits serve a greater potential than just being a handy but tiny ruler, stop watch and scale. When Planck said that, nothing meaningful happens at values below these limits; I took this to imply that in many ways the universe has a discrete nature in practice. For right or wrong; I took this concept to the extreme and found that there was no discomfort in viewing the discrete nature as an important functional characteristic.

I think that it’s easiest to present this functionality by first examining the small. There are several possibilities as to how this could work in practice (in reality).

The first is that there are no combinations of force/ matter/ time that will ever challenge length…that no matter what happens all constituents “pigeon hole” neatly into the discrete limits at all times.

Another possibility is that; some combinations of force/ matter/ time will “try” to violate the discrete limits.

There are 2 ways that this can occur; 1 is that the combination (reaction) is so small that it wants to take a partial distance step; the other, is that the object takes a bunch of steps but has a remainder that “tries” to violate PL

At this point, I would like to take a step back. There is no point in continuing with out addressing a more fundamental paradigm.

Of course the universe is analog and continuous in its most basic form. We can’t get from point A to point B if this wasn’t true. I believe that the analog structure immediately conforms to a discrete (dare I say digital) system. If we look closely at any digital system we can see that it is constructed from an analog structure. It takes time to go from one state to another and when we look at the ramp up or down process; it’s usually parabolic. “It’s analog alright”. Once the conversion takes place we are mostly in the digital domain or in this case; Planck’s World.

Now, I feel pretty certain that most people envision Planck’s limits a different way: They “believe” that an operation can originate at any point (analog) but that the result or the change will conform or easily fit within PL They also believe that independent operations can have a result that overlaps or converges.

I come from a different camp: either PL is nonsense and anecdotal or it is functional and important. If it is functional, then IMHO it has rules and rigidity.

Please indulge me for awhile and allow me to “draw up” this analogy:

You are this curious, extremely competent human being who hears music for the first time. Because you have no prior knowledge or preconceptions, you try to understand what you are experiencing. Being both competent and imaginative, you are eventually able to discern individual instruments. You eventually recognize patterns in frequencies and you realize that there are occasional frequencies that fall in between the notes. After much diligence, you are able to reproduce some of what you heard on surrounding objects. Some of the objects have a string-like tension and you able to slide from one note to the next. Now you really go to town and you devise an orderly system that represents all of this. At this point some know-it-all type comes along and tells you that what you listened to came from a digital source…a CD. Do you believe him?

I would love to go through the blow-by-blow detailed ins and outs of how this could work in reality. I think that there’s a lot of insight that can be gained from the exercise but; if Planck’s World is already equal to Bizarro World…I ought to not do that.

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Bill S.
There are many different mathematical infinities. The infinity of integers, the infinity of irrational numbers (.3333... for example), and others. In quantum physics when they start calculating various items they run into infinities, if they don't do renormalization. Since the infinity is applied to different particles/interactions they will be different infinities. Don't get it into your mind that there is only one infinity. Each infinity of a particular calculation is a different infinity. Remember that infinity is not a thing, infinity is more of an adjective. We may say that some thing approaches infinity, but what we are really saying is that the numerical value of the thing approaches infinity. If there were such a thing as an infinite number of oranges that would be one infinity. An infinite number of apples would be another infinity. Remember you can't compare apples and oranges.

Bill Gill


C is not the speed of light in a vacuum.
C is the universal speed limit.
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Originally Posted By: KiryGillis
Of course the universe is analog and continuous in its most basic form. We can’t get from point A to point B if this wasn’t true. I believe that the analog structure immediately conforms to a discrete (dare I say digital) system. If we look closely at any digital system we can see that it is constructed from an analog structure. It takes time to go from one state to another and when we look at the ramp up or down process; it’s usually parabolic. “It’s analog alright”. Once the conversion takes place we are mostly in the digital domain or in this case; Planck’s World.


Kirby, I don't quite get what you are saying here. First you are saying that the universe is analog, then you are saying it is digital. Now you have me confused.

Bill Gill


C is not the speed of light in a vacuum.
C is the universal speed limit.
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"Kirby, I don't quite get what you are saying here. First you are saying that the universe is analog, then you are saying it is digital. Now you have me confused."

Take an oscilloscope. Attach the probe to the output of an AND gate. Reduce the time base so that you can “zoom in”. Observe the transition from a low to a high (0-5V). You will see a slope. This is the analog component that comprises the digital signal. Ideally the signal would be a perfect square wave no matter how short the time base. But it isn’t because all realized digital systems are built from analog. The AND gate itself is a solid-state device with multiple p-n(-p) junctions (transistors, analog devices) that tries to emulate or idealize a digital component. As a retired electronics engineer this has to be something that you knew already.

Is the concept of digital from analog so strange that it can’t be applied to anything else? One time I hit a “home run” when I applied digitization to a chemical polymer application and it had nothing to do with electronics.

The universe is like a logic gate hardware device…an analog/ digital hybrid...(perhaps)

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Kirby
Yes I know all about the rise time of oscilloscopes. When I was an electronic technician I used to calibrate them. And yes any kind of digital signal can be represented as an analog signal. After all, any non-sinusoidal signal can be represented as the sum of a lot of the harmonics of the basic frequency of the signal. But it is a matter of scale. At the nominal scales that we can easily detect things are analog. But if you dig deeper and deeper into things, until you get to the quantum level, you find them more digital, in a way. For example the wave form out of the AND gate consists of the flow of electrons. So at the scale of the electron the digital signal, which can be analyzed as an analog signal, becomes the flow of electrons. And when you look closely you find that the signal rises at a rate of approximately 1 electron at a time. Of course there are so many electrons in a current that you won't be able to detect that. But yes the universe appears to be and can be worked with as analog at large scales, and it is also digital at small scales. When you get to the Planck scale you have a whole different world. At the Planck scale we have no idea what the universe looks like. Well, there are a number of ideas, String Theory, Quantum Loop Gravity, The Holographic Principle, and I'm sure others. But we have no way to be sure which if any of these ideas is the correct one. One thing I think will be true is that at the Planck scale things aren't likely to be analog, and that is the most basic form of the universe.

Bill Gill


C is not the speed of light in a vacuum.
C is the universal speed limit.
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Originally Posted By: Bill
There are many different mathematical infinities.


I have no problem accepting that there is an infinity of mathematical infinities. Cantor, I believe, discovered that a never-ending ascending hierarchy of infinities must exist; that there is no biggest of all that can contain them all.

I think it is unfortunate that the term infinite is used as a mathematical concept and as a description of physical infinity. The examples you give of mathematical infinities might be described as limitless or unbounded, or even endless, but not infinite, and certainly not infinite in the sense of being physically infinite.
A single number is a finite entity, however many other numbers you add to it, that number will always be finite, you can never reach a point where you would be able to say "this is now infinite". Having said that, I acknowledge that "infinite" is an accepted mathematical term, but contend that this should not be confused with physical infinity.


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“But if you dig deeper and deeper into things, until you get to the quantum level, you find them more digital, in a way.”

Couldn’t agree more. Now, I have to go back to using the term discrete (instead of digital) because I’m trying stay off crackpot list. (Probably too late.)

I felt that I couldn’t get into discrete nature without qualifying where contiguous nature sits. I also don’t want to spend time on something that isn’t interesting or palatable. My biggest fear isn't being wrong...it's being boring.

“And when you look closely you find that the signal rises at a rate of approximately 1 electron at a time.”

You don’t know how much I like this. I knew about this but I never looked at it as a digitization “technique” before. The serialization (1 at a time) is a bonus.

“When you get to the Planck scale you have a whole different world.”

Personally, I can’t accept this notion. I believe (reason) that the universe looks the same at all scales. Anything else is the illusion. As a matter of fact, I think that the entire cosmos is consistent and follows the same set of rules. I think that it’s doable. It’s not an impossible task. At the very least, it’s fun to try.

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Kirby
Indeed one of the things about science is the assumption that the universe is consistent and follows the same set of rules. But it is usually a lot easier to work with "effective theories". These are theories that work at a particular scale. For example Newton's laws work extremely well in the areas where they apply. Special and General Relativity work extremely well for higher speeds and larger masses. Quantum Theory works extremely well in the quantum world. These are all examples of effective theories. But there is no well established effective theory at the Planck scale. So we really have no good idea what the universe is like at that scale. As I mentioned above there are several candidates, but nobody has one that is fully realized and can be used to predict both Relativity and Quantum rules. So it is a whole different world. Some day we will have such a theory, but nobody is sure when that will happen.

Bill


C is not the speed of light in a vacuum.
C is the universal speed limit.
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"Some day we will have such a theory, but nobody is sure when that will happen."

If you let me finish; that day will be today.

Naw, I'm just kidding with you.

But seriously; if no one objects I'd like to pick up where I left off pretty soon. It's just that; I know that it's hard to present the idea with being long winded and if nobody cares, I really don't want to waste my time on it.

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For some of us it's not a question of not caring, it's more a matter of taking a while to get the head round some of your ideas.
Patience and simple explanations are the key.


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Originally Posted By: Kirby
Object is traveling at 1.0c, new length is 0.00, time factor is infinity


Still struggling! What do you mean when you say that time factor is infinity?


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Originally Posted By: Bill S.
Originally Posted By: Kirby
Object is traveling at 1.0c, new length is 0.00, time factor is infinity


Still struggling! What do you mean when you say that time factor is infinity?


When the traveler and the observer are both at rest (or share the same IRF); length contraction = 1 (no change) and the time dilation factor = 1 (both clocks run at the same speed).

If the traveler is moving at .866c (as compared to the observer); length contraction = .5 and the time factor is 2. So that means that the traveler’s dimension (in the same direction of travel) is half of what it would be if the traveler was in the same reference frame as the observer. Also, the traveler “sees” the observer’s clock run twice as fast (time dilation factor)…but this also means that the observer sees the traveler’s clock run half as fast as his.

If the traveler is moving at .968c (as compared to the observer); length contraction = .25 and the time factor is 4. So that means that the traveler’s dimension (in the same direction of travel) is a quarter of what it would be if the traveler was in the same reference frame as the observer. Also, the traveler “sees” the observer’s clock run 4 times as fast…but this also means that the observer sees the traveler’s clock run a quarter as fast as his.

So basically, the more that the traveler approaches 1.0c; the higher the time dilation factor. Theoretically, if the traveler could achieve a speed of exactly 1.0c; the observer wouldn’t see the traveler’s clock budge even one millisecond, no matter how long the observer monitored it.

Of course this is theoretical. They say that the traveler can’t actually achieve a perfect 1.0c because she “slams” into bunch of logistical problems. The main obstacle is that the traveler would require an infinite amount of energy to accomplish it. Another is that the observer is probably not “standing still” either.

There is a user friendly calculator on a website that I like:

http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/tdil.html

If you play with it for a little while; I think that it will do a better job of presenting the relationships to you than I can by using just words.

BTW, my new job is cutting into my free time in a big way. Even though, I can keep up with reading the new SAGG posts easily enough; writing and responding is going to be real hit and miss. It’s kind of frustrating because there is a lot of content that I would’ve liked to chime in on.


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Kirby, would I be right in thinking that you are equating the fact that the traveller's clock appears to have stopped with a time factor of infinity?

I can live with that, without being drawn back into infinite discussion. smile

One thing puzzles me, though: "Also, the traveler “sees” the observer’s clock run twice as fast (time dilation factor)…but this also means that the observer sees the traveler’s clock run half as fast as his".

I thought that both traveller and observer saw the other's clock running slow.


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Bill S.
You are right, according to SR both of them see the others clock running at half speed. This has caused some problems in understanding what is going on. I understand that if you include the effects of acceleration using GR that the problem is taken care of. Keep in mind that SR really only applies to reference frames that are moving at constant velocities with respect to each other. GR throws in some other factors. If it didn't then the twin paradox wouldn't work.

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“I thought that both traveller and observer saw the other's clock running slow.”

Right. That’s why I put the word “see” in quotes. This is the “sloshing coffee” scenario.
I just wanted to keep it simple and explain the infinity thing.


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Originally Posted By: Bill 6
Bill S.
You are right, according to SR both of them see the others clock running at half speed. This has caused some problems in understanding what is going on. I understand that if you include the effects of acceleration using GR that the problem is taken care of. Keep in mind that SR really only applies to reference frames that are moving at constant velocities with respect to each other. GR throws in some other factors. If it didn't then the twin paradox wouldn't work.

Bill Gill

Section 4 SR contradicts the twin paradox of sections 1 - 3 showing that it is only clock A (the clock that has changed frames) that ticks over at the slower rate.

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Originally Posted By: Bill6
Section 4 SR contradicts the twin paradox of sections 1 - 3


Enlighten, please. frown


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Bill S., Bill6 is referring to section four of Einstein's 1905 paper on Special Relativity. At the end of section 4 Einstein concludes that a clock traveling on a curved path from point A and back to point A that the traveling clock will lose time with respect to a clock that remained at A. He suggests that a clock sitting on the equator of the Earth would run slower than one at one of the poles. I wasn't aware of that myself, but when I looked up the paper it was right there.

Bill Gill


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Thanks, Bill. If we can manage to cope with 3 Bills on the same thread without becoming confused, what can stand in our way?


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Originally Posted By: Bill
Bill S., Bill6 is referring to section four of Einstein's 1905 paper on Special Relativity. At the end of section 4 Einstein concludes that a clock traveling on a curved path from point A and back to point A that the traveling clock will lose time with respect to a clock that remained at A.
Bill Gill


[Sorry about the delay in responding; I've been having problems logging in.]

Close - my reference was to his section 4 description of clock A (initially synchronous with clock B) moving in a straight path to clock B's location where it is found that A lags behind B. Same thing basically but no need for a curved path.

Originally Posted By: Bill
He suggests that a clock sitting on the equator of the Earth would run slower than one at one of the poles.

Basis of the Hafele-Keating experiment.

Originally Posted By: Bill
I wasn't aware of that myself, but when I looked up the paper it was right there.

Although never having attended one myself I suspect that section 4 may be glossed over - not taught - in physics class perhaps on the basis that it contradicts the reciprocality of sections 1 - 3.

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