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Posted By: KirbyGillis Relativity, Time Dilation and Space/Time - 01/21/11 08:50 PM
For the sake of thoroughness, I would like to preface the “meat and potatoes” of this concept with other concepts.

The first is reduction or consolidation:

There is a nightmare of a formula called the Quadratic Equation. Basically this formula sets up the inter-relationship between the 3 sides and 3 angles of any triangle. When one of the angles is “known” to be 90 degrees or there is a side length that will result in a 90 degree angle, the Quadratic Equation can be reduced (or consolidated) to the Pythagorean Theorem. It’s amazing that one filled-in variable can reduce that monstrosity to a one-liner and it sure is convenient.

It behooves math, science and man to consolidate whenever possible. We reduce things down to their basic elements, rules and equations. Of course there is nothing that prohibits anyone from using the quadratic equation to solve right triangles either but it seems insane to do so.

The next concept is over-reduction:

Let’s run a quick mind experiment.

You and I just returned from a heist and being mindful of reduction I declare that my take was 1/2 of the total loot. You say; to hell with that, I got 2 out of 4 dollars!

Your (non-reduced) definition contains more information regarding the actual nature of the heist which was a complete and utter failure. My definition is justified but highly misleading. This time, consolidation of the math has gone too far and good information has been lost. Such are the dangers of over-reduction…over-simplification. Just because something is reducible doesn’t mean that it will remain intact.

Space/ Time and Relativity:

If we look at all of the Lorentz Transformation formulas for length contraction, time factor (dilation) and mass increase it is readily apparent that all of these formulas inter-relate. Specifically, at any given speed, length contraction and time factor are reciprocal values. Lets me throw out some examples:

Object is traveling at 0.0c, new length is 1.00, time factor is 1.000
Object is traveling at .25c, new length is .968, time factor is 1.032
Object is traveling at .50c, new length is .866, time factor is 1.154
Object is traveling at .75c, new length is .661, time factor is 1.512
Object is traveling at 1.0c, new length is 0.00, time factor is infinity

Another way of looking at this is that; new length and new time is exactly equal. For instance; if you are traveling at .5c, your length is 86% of what it was at rest, and time is passing 86% slower for you then when you were at rest.

If we take the dimensional (space) contraction and lump it together with time dilation; rather than do the calculation twice we can simply do it once. Likewise, we can treat space and time as the same thing…hence space/time…an underlying fabric. This is the very essence of the immutable connection between space and time…this is the justification…same formula – same thing.

I am proposing that the connection between space and time does not occur at this point in reality. There is the possibility that an over-reduction has occurred. Just because they both “enjoy” the same formula does not make them the same thing.

Ok. If the fabric of space/time is not how they are connected then where is the connection? How can we possibly retain the obvious immutable (fixed) relationship between the two of them without space/time?

Here goes:

Hollywood movies love to manipulate and exercise time dilation. There aren’t any movies set against a background of length contraction. Time dilation gets all the glory. Time travel…grandfather paradoxes are cool and interesting….flat as a pancake, well that just doesn’t make it into the script.

Time dilation gets all of the glory while length contraction does all of the work.

I propose that the characteristic of length contraction results in time dilation and that this is where the connection between time and space should be made. Why would it be surprising that they share a common formula?

Perhaps there is something about the dynamics of length contraction that brings about a corresponding “proportion” of time dynamics.

BTW, the reciprocating relationship between length contraction and time factor isn’t the only interesting aspect of LT:

Object is traveling at .500c, new length is .866
Object is traveling at .866c, new length is .500
Object is traveling at .707c, new length is .707

In the future, I would like to discuss this tidbit also.
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 01/21/11 10:12 PM
Quote:
if you are traveling at .5c, your length is 86% of what it was at rest, and time is passing 86% slower for you then when you were at rest.


Would it not be that if this relationship didn't work the Time/distance calculations would not add up for someone travelling at (for example) 0.5c; so she would know she was in motion.
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 01/21/11 10:16 PM
I should have started by complimenting you on starting a thought provoking thread. It requires some pondering, but should spark some fascinating discussion.
Originally Posted By: Bill S.
Quote:
if you are traveling at .5c, your length is 86% of what it was at rest, and time is passing 86% slower for you then when you were at rest.


Would it not be that if this relationship didn't work the Time/distance calculations would not add up for someone travelling at (for example) 0.5c; so she would know she was in motion.


I’m not sure that I follow. They say that from her (the traveler’s) viewpoint, that her boobies are just fine (not flatter) and that she is unaware that time is passing slower. Even at .5c, without additional acceleration she is unaware that she is in motion…she feels like she’s floating in space. However, just like us; if she conducts some external measurements she’ll be able to verify her current speed.
Posted By: Bill Re: Relativity, Time Dilation and Space/Time - 01/22/11 03:55 PM
That's odd. I posted a reply last night, but it doesn't show up here now. I will try again

Originally Posted By: KirbyGillis
There is a nightmare of a formula called the Quadratic Equation. Basically this formula sets up the inter-relationship between the 3 sides and 3 angles of any triangle. When one of the angles is “known” to be 90 degrees or there is a side length that will result in a 90 degree angle, the Quadratic Equation can be reduced (or consolidated) to the Pythagorean Theorem. It’s amazing that one filled-in variable can reduce that monstrosity to a one-liner and it sure is convenient.


That isn't quite right. A Quadratic Equation is any equation of the form aX^2 + bX + c = 0. This can be solved algebraically to give the Quadratic Formula. Using the Quadratic Formula you can determine the roots of the equation, that is the values of X for which the equation is true. It may be possible that it simplifies to the Pythagorean Theorem for a right triangle, I don't know.

As far as the relativity formulas being similar, that is perfectly natural. They are derived from the observation that C is that fastest that anything can travel in the universe. They match because they are different solutions to the same formula.

For your last point:

Originally Posted By: KirbyGillis
BTW, the reciprocating relationship between length contraction and time factor isn’t the only interesting aspect of LT:

Object is traveling at .500c, new length is .866
Object is traveling at .866c, new length is .500
Object is traveling at .707c, new length is .707

Did you happen to notice that those values match a sine (or cosine, which ever way you start) function?

Create a spacetime graph with space on the X axis and time on the Y axis. Now in your frame of reference an object on the graph will be spacelike, that is it will have a projection on the space axis that is the same length as the object. On the time axis it will have a zero projection. Assume somebody in another frame of reference moving with respect to yours. In effect their frame of reference will be rotated from yours. If you place the graph of their reference frame on yours with the origins coinciding their graph space and time axes will be rotated from yours. In their view your object will project a smaller distance on their space axis and a larger distance on their time axis. Therefore you will appear to be partly spacelike and partly timelike. And this change will be related to the tilt of their graph from yours, and this tilt of course is related to the speed at which they are traveling.

I hope that is clear, but I can fully expect it to look like a lot of gobbledegook when you read it.


Bill Gill
“That isn't quite right. A Quadratic Equation is any equation of the form aX^2 + bX + c = 0. This can be solved algebraically to give the Quadratic Formula. Using the Quadratic Formula you can determine the roots of the equation, that is the values of X for which the equation is true. It may be possible that it simplifies to the Pythagorean Theorem for a right triangle, I don't know.”

I agree. The quadratic is a subset of the polynomial. The Pythagorean Theorem is a subset of the quadratic. However, in practice, the quadratic is a rearrangement of the terms of the polynomial that places the x variable on the left-side while the Pythagorean is a reduction of the formula when one of the terms are given. My goal was to demonstrate simplification not rearrangement.

“Did you happen to notice that those values match a sine (or cosine, which ever way you start) function?”

Why yes, I did. As a matter of fact, I found the last set to be most interesting and that’s the one that I honed in on. Right away I recognized this value as the sine/cosine of 45 degrees. The sine of 45 degrees is equal the square root of 2 divided by 2. As a retired electronics guy, I knew that you would probably be the first to latch onto this. At first it’s helpful in understanding AC power…, then RMS, then integration, then sampling. It runs the full gamut from analog to digital.

In a linear universe, .5 is halfway between 0 and 1. In an exponential universe the mid-point between 0 and 1 is .7071 (BTW, this isn’t for your benefit…this is for the benefit of anyone who may be reading that isn’t quite clear on the concept.)

So, what am I really getting at?

Let’s pretend that speed is money. (Actually this isn’t too far from the truth.) Next, let’s pretend that there is a benefit derived from saving time…time is money.

So we’re going to arbitrate speed vs. time in the relativistic universe or speed in c vs. time dilation/ length contraction.

Not surprisingly, the biggest bang for the buck is the mid-way point - .7071c. (I wish that all cost/ benefit analysis were this simple.)

Man may dream of traveling near the speed of light (aka the Concord) but people will be traveling at .707c (aka the 747).

“As far as the relativity formulas being similar, that is perfectly natural. They are derived from the observation that C is that fastest that anything can travel in the universe. They match because they are different solutions to the same formula.”

Agreed. As a matter of fact, there’s nothing magical about the math and there’s nothing magical about relativity (although that could be a hard sell to some). In my OP my goal is to leave relativity alone and intact, as-is. It is space/time that I want to alter. This is a blasphemous thing to try to do and to me, relativity is the litmus test for any alternate ideas.

My goal isn’t to actually replace space/time as an idea…but rather to add alternative ideas to the viability mix. To me, the space/time fabric is a theory that’s being treated like a fact. I would like to loosen that up a bit.
Posted By: Bill Re: Relativity, Time Dilation and Space/Time - 01/22/11 09:15 PM
Originally Posted By: KirbyGillis
My goal isn’t to actually replace space/time as an idea…but rather to add alternative ideas to the viability mix. To me, the space/time fabric is a theory that’s being treated like a fact. I would like to loosen that up a bit.


The problem with trying to get loose from the spacetime business is that it works. Einstein incorporated it into his General Theory of Relativity, because with it he could make GR work. Since GR has been extensively tested without finding any problems with it, at least at the scale at which it doesn't conflict with Quantum Theory, any changes are unlikely. If you can come up with an alternate theory that works as good maybe you can sell somebody on your idea. If that it is also simpler, or fixes the conflict with Quantum Theory.

Bill Gill
"The problem with trying to get loose from the spacetime business is that it works. Einstein incorporated it into his General Theory of Relativity, because with it he could make GR work. Since GR has been extensively tested without finding any problems with it, at least at the scale at which it doesn't conflict with Quantum Theory, any changes are unlikely. If you can come up with an alternate theory that works as good maybe you can sell somebody on your idea. If that it is also simpler, or fixes the conflict with Quantum Theory."

Bullseye. I whole-heartedly agree. Any alternate ideas should be more compatible with Quantum Mechanics and must be compatible with Relativity.
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 01/23/11 08:37 PM
Quote:
Any alternate ideas should be more compatible with Quantum Mechanics and must be compatible with Relativity.


Such a theory would have to be compatible with QM and relativity in that it would have to produce the same results to a certain degree; but it could reach these results by a completely different route, so the world is your oyster, as far as imaginative thought is concerned.
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 01/26/11 05:33 PM
Originally Posted By: Kirby
They say that from her (the traveler’s) viewpoint, that her boobies are just fine (not flatter) and that she is unaware that time is passing slower.


Notwithstanding any lack of deleterious effects on the traveller's figure; the fact that she does not measure and slowing of time would cause her calculations to disagree with those of "mission control" if it were not for the fact that, in her F of R, the distance to destination would be appropriately contracted.
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 01/26/11 05:45 PM
Originally Posted By: Kirby
Object is traveling at 1.0c, new length is 0.00, time factor is infinity


Does this run into the perennial problem that goes something like this:

SR says that nothing with mass can travel at "c".
The only thing that can travel at "c" is a photon.
Because a photon has no rest mass, it is not possible to define a F of R for a photon.
In view of these considerations, the infinite time factor that would be relevant to the F of R of a photon has no meaning?

To some extent I am playing devil's advocate here, because if this line of reasoning is right I have a lot of re-thinking to do.
Quote:
Notwithstanding any lack of deleterious effects on the traveller's figure; the fact that she does not measure and slowing of time would cause her calculations to disagree with those of "mission control" if it were not for the fact that, in her F of R, the distance to destination would be appropriately contracted.


I offer up the following mind experiment:

Let’s say that our traveler is departing Earth and the destination is Alpha Centauri (4.3 LY distant). Through the marvels of modern science she somehow conducts the entire trip at a speed of .75c. Her length contraction will be .66 and her time dilation factor is 1.5 (her clock will run .66 as fast as ours). We have 2 omnipotent telescopes. One is located on Earth and is exactly lined up with the traveler and Alpha Centauri (viewing her from behind). The other telescope is at a stationary midpoint and lined up 90 degrees from the other one (viewing her from the side). Of course, she will only be lined up for a brief instant from the side view. When I take my snapshot (brief video) from the side view; it verifies that she is .66 as thick but more importantly, all of her motions look slower. You can tell that she seems to be slothy and purposeful.

Now the telescope back on Earth sees something different. From their perspective, she is dimensionally just as wide as when she was on Earth but more importantly, all of her lateral motions are quite normal…there’s nothing slow about her.

Now, from the viewpoint of the Earth, traveling at .75c it takes her 5.73 years to transverse the 4.3 LY to the destination. From her viewpoint it took 3.78 years. (5.73 x .66). All of this was done without distance contraction.

Now, let’s do this with distance contraction. She departs from Earth at .75c and her new length as viewed from the side is .66 of what it was on Earth. She measures the distance that she has to travel as 2.83 LY (4.3 x .66). At .75c it takes 3.78 years to do the trip.

Either method works out to be exactly the same. In the first scenario she measures her speed to be faster than she “knows” it ought to be. In the second scenario, she measures the distance to be shorter than she “knows” it ought to be.

“Pick your poison.”

Without a doubt, a flat person would see distances in the direction of travel differently.
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 01/30/11 11:26 PM
Quote:
From her viewpoint it took 3.78 years.


That is 4.3 LY in 3.78 years. Without length contraction that would be about 1.14c, wouldn't it?
Quote:
That is 4.3 LY in 3.78 years. Without length contraction that would be about 1.14c, wouldn't it?


Right. Without distance contraction that is the equivalent of 1.14c. But, this is unavoidable. Regardless of her observation that the distance was 2.8 LY; “people” on Alpha Centauri could verify that her clock says 3.78 years and that the true distance was 4.3 LY. It’s also true that she never exceeded .75c.

BTW, I don’t know if you noticed but the mind experiment was an unconventional treatment of inertial reference frames. Reference frames are considered 3 dimensional. By viewing reference frames as 2 dimensional we are able to view the same event (3D reference frame) simultaneously and remain “compatible” with relativity. Well, not quite. The difference is the rear view. The 2D reference frame allowed her lateral movements to be normal while a 3D reference frame forces her movements to be slow even though there is no visible length contraction in that direction. It does seem to work well though…that is until you replace the traveler with a pendulum swinging at a 45 degree angle. Still, I think that it’s a good mind experiment. (It’s interesting to see how time “works” in this scenario).
"SR says that nothing with mass can travel at "c".
The only thing that can travel at "c" is a photon.
Because a photon has no rest mass, it is not possible to define a F of R for a photon.
In view of these considerations, the infinite time factor that would be relevant to the F of R of a photon has no meaning?"


There are some who say that; at rest the photon has a duration that is infinitely small (1 Planck time limit?). At c its duration is infinitely long (1 universe time limit?)

I don't know. I haven't spent much time on EMW. I sure hope that I can get around to it (1 life time limit?)



Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 02/02/11 08:26 PM
Quote:
There are some who say that; at rest the photon has a duration that is infinitely small (1 Planck time limit?). At c its duration is infinitely long (1 universe time limit?)


Am I reading this incorrectly, or does it equate infinitely small with Planck time, and infinitely long with the life span of a universe?

That would have to be a new take on infinity.
"Am I reading this incorrectly, or does it equate infinitely small with Planck time, and infinitely long with the life span of a universe?"

In a way...except instead of equate it would be more like qualify/quantify.

I'll have to return to this because duty calls but I do want to give this a thorough treatment because I think that it relates to the incompatibility between mathematical and physical infinities that you've mentioned quite a bit.
Originally Posted By: KirbyGillis
[i]There are some who say that; at rest the photon has a duration that is infinitely small (1 Planck time limit?).

Correct me if I'm wrong, but the planck time is the time taken for a photon to travel the planck length*. So planck units are excedingly small, but not infinitely small - merely the smallest units that could (theoretically) ever be measured. Moreover, am I not right in thinking that a theory of quantum gravity would require that certain processes occur in intervals less than the Planck time? This just springs to mind, and I haven't done my homework, so forgive if I'm off track.

*1.616252(81)×10−35 meters.
Posted By: Bill Re: Relativity, Time Dilation and Space/Time - 02/03/11 03:47 PM
Rede,
You have a good point. The Planck units are indeed very small, but confusing them with being infinitely small can lead to some significant confusion. They are not infinitely small because they do have numeric values. I am afraid that this discussion may be based on a poor understanding of what infinity means. I'm not going to try to define infinity. It requires a much deeper study, and discussion with other people who have also made a deep study, than I have ever made or intend to make. Just letting ones mind run loose without investigating the literature on the subject doesn't help anybody to understand it very well. And of course understanding the literature probably means going back to the beginning math of infinity. Physical infinities may be different from mathematical infinities, but an understanding of physical infinities will require and understanding of mathematical infinities.

Bill Gill
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 02/03/11 08:29 PM
Bill,
I think I agree completely with your last post. However, I have to question your plurality of physical infinities. I think there can only be one.
Nit-pickers of the world, unite! smile
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.
Posted By: Bill Re: Relativity, Time Dilation and Space/Time - 02/03/11 11:47 PM
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
Posted By: Bill Re: Relativity, Time Dilation and Space/Time - 02/03/11 11:50 PM
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
"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)
Posted By: Bill Re: Relativity, Time Dilation and Space/Time - 02/04/11 03:07 AM
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
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 02/04/11 03:26 AM
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.
“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.
Posted By: Bill Re: Relativity, Time Dilation and Space/Time - 02/04/11 03:11 PM
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
"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.
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 02/07/11 05:25 PM
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.
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 02/11/11 08:04 PM
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?
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.
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 02/13/11 08:42 PM
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.
Posted By: Bill Re: Relativity, Time Dilation and Space/Time - 02/13/11 11:30 PM
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
“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.
Posted By: Anonymous Re: Relativity, Time Dilation and Space/Time - 02/14/11 01:25 AM
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.
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 02/21/11 08:22 PM
Originally Posted By: Bill6
Section 4 SR contradicts the twin paradox of sections 1 - 3


Enlighten, please. frown
Posted By: Bill Re: Relativity, Time Dilation and Space/Time - 02/21/11 09:02 PM
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
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 02/21/11 11:41 PM
Thanks, Bill. If we can manage to cope with 3 Bills on the same thread without becoming confused, what can stand in our way?
Posted By: Bill 6 Re: Relativity, Time Dilation and Space/Time - 03/01/11 12:16 AM
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.
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 03/02/11 09:17 PM
I would like to return to the earlier consideration of Planck's time, about which I have a thought.


Peter Lynds, “Time and Classical and Quantum Mechanics: Indeterminacy vs. Discontinuity” (Obtainable from the CERN document server). Makes the point that there can be no static instant of time, during which change could be considered as having paused. He reasons that if there were such an instant, then all change, all motion, would come to a permanent standstill at that point. Presumably, if we consider time as being static, in its entirety, then we have to regard any motion through time as being a smooth, continuous motion that cannot be frozen at any particular instant.

If Planck’s time is defined as the smallest interval of time that has any meaning, beyond which it is not possible to further sub-divide time, then, surely, we must regard this as the quantum of time.

Planck’s time has a duration, albeit unthinkably small. That being the case, it must be possible to attribute a degree of change, during that period, to any object in relative motion; otherwise, as Lynds points out, that object would be stationary.

There is something more than a little familiar about this line of reasoning. In the same way that light has to be regarded as a wave for some purposes, and as a particle in other situations, could something similar be true of time?

The discussion about whether time is continuous or quantised is ongoing, but it may be no more meaningful than trying to resurrect the argument about whether light is a wave or a particle. Time could be particulate or continuous depending on what question you are asking about it.
Posted By: Bill Re: Relativity, Time Dilation and Space/Time - 03/02/11 11:41 PM
Bill S.
Can you provide a link to the CERN document server? I found the server, but couldn't find the document you referenced. I searched under both the title and the author, and couldn't find it.

Bill Gill
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 03/03/11 02:46 AM
Bill.
You should find it at http://arxiv.org/pdf/physics/0310055 or you could Google "Time and Classical and Quantum Mechanics: Indeterminacy vs. Discontinuity". Its about 3 yrs since I originally found it and the link seems to have changed, but this one should get you there.
Posted By: Bill Re: Relativity, Time Dilation and Space/Time - 03/03/11 03:03 AM
Thanks I found it. I don't have any more comments right now. I am currently printing it out. That way I can sit down and try to read it and make out what he is saying. I sat here and read about half of it and didn't make much sense of it. On paper it will be better. Maybe tomorrow I will be ready to comment.

And I thought I had spoken to you about making me think. I told you I don't like to think, you are going to have to do better in the future.

Bill Gill
Posted By: Bill Re: Relativity, Time Dilation and Space/Time - 03/03/11 03:56 PM
Well, I'm not sure that I am any more informed than I was before I read it. However, I will try a few comments. Just remember that my comments are strictly my thoughts, and may not have any relevance to the subject.

I can kind of see that if you look at any changing quantity at a single instant in time there will be no change in the quantity, since there is no time for the change to occur. I can see this, it is like looking at one frame of a motion picture. His idea seems to be that since there is no change in that instant there is no way for the quantity to change so that it can move to another instant, so if there is a quantum of time, as there is of energy, then there can be no change and the universe would be static and unchanging. I hope I have that right. Frankly the concepts he is talking about are not really easy to understand, which he admits in the last paragraph of Section 1.

Now to my thoughts on this, keeping in mind that I am not really qualified to do a deep analysis of the paper. An undergraduate degree in physics doesn't get you far enough to really qualify a person to get this deep.

Having made my disclaimer:

It seems to me that one of the problems with his idea is that he speaks of a single instant of time. I'm not sure that any of the hypotheses of quantum time really talk about an instant of time. They mostly assume that the quantum of time is closely related to the Plank Time, which has a definite "duration" if you can call it that. Basically this is just as short an interval as can be determined within the bounds of Quantum Theory (QT).

Another possible problem is that he isn't taking into consideration is the way QT handles state transitions. For example; take a hydrogen atom and consider the electron in the ground state. If a photon having sufficient energy strikes the atom the electron will immediately transition to the first (or higher) excited state. As far as I know there is no mention of time in this transition. If I am correct about this then there is a quantity that changes within an instant of time. So now the universe isn't static, it can move from one instant of time to another.

Of course there is always the view that there is no such thing as time. Scientific American had an article on it last year. I can't tell you what issue, I have already passed it on to my daughter. But here is a link Forget time to an essay about that.

Bill Gill
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 03/03/11 06:46 PM
Bill.
Thanks for the comments and the link, I know it's going to make me struggle, but I shall try to get something out of it.

Any thoughts about the possibility that time could be particulate or continuous depending on what question you are asking about it.
Posted By: Bill Re: Relativity, Time Dilation and Space/Time - 03/03/11 08:14 PM
Originally Posted By: Bill S.
Any thoughts about the possibility that time could be particulate or continuous depending on what question you are asking about it.


I don't have any real thoughts about it, but my thinking about a granular structure to both time and space is that I am willing to accept the idea. This is based on the fact that QT has pretty convincingly shown that energy, in its many manifestations, is granular. Since 1 of the 3 major constituents of the universe works that way I am quite ready to accept it for the other 2. QT has also convincingly show the particle/wave duality exists. Based on that I would certainly not want to throw out the idea of a "particle/wave" duality for time and space, at least not without some pretty convincing evidence. I am not sure just what such a duality would look like, I will have to wait for some theorist to come up with that. I will bet that it wouldn't look anything like what I might expect.

Bill Gill
“If Planck’s time is defined as the smallest interval of time that has any meaning, beyond which it is not possible to further sub-divide time, then, surely, we must regard this as the quantum of time.

Planck’s time has a duration, albeit unthinkably small. That being the case, it must be possible to attribute a degree of change, during that period, to any object in relative motion; otherwise, as Lynds points out, that object would be stationary.”


I’m glad that everyone is considering the possible equivalence (function) of Planck limits and quanta.

I would like to introduce a concept:

We are aware of time solely due to change. Since the change of particle positions occur in discrete quantities (herky-jerky motions), it is easy to believe that time is moving the same way. There may be a difference between observed time change and the actual nature of time. Once again, let me resort to an analogy:

You are in a supermarket and you notice a large “cube” of perfectly stacked boxes. You single out one box located at the bottom corner. With a quick horizontal motion, you snatch away the corner stone. What happens next is that you observe the change of box positions. a single stacked column drops by one box height. The amount of time that it takes to complete the transition is how we mark time.

Now think about this: Does it really matter if the corner box is snatched away at 48 kpm (like you did) or at a million kph? All we observe is the motion of the stack which seems to take the same amount of time to change its position.

Time does not have to be quantized for the universe to behave the way that it does. Don’t get me wrong…a quanta of time is perfectly compatible with the scheme and it very well may be true. I wanted to point out that it is not a requirement. With 2 out of 3 constituents quantized; the third does not need to be.

I need to clarify something here. There is a bit of a semantics problem and I’ve been changing some terminology to suit the relationships that you setup: I think that time is only the change marker…a phenomenon of sorts…not a real stand-alone physical entity. The agent of change is kinetic energy…he’s the “guy” that doesn’t have to be quantized.

There seems to be another conceptual problem that arises from the compatibility of static positions and being “stuck”. There are two important aspects to this. The first is potential energy (tensor fields).

Let’s revisit the stacked boxes. This time, while you are snatching away the corner box; someone snaps a picture of it with a decent camera set to a high shutter speed at just the “right” time. When you both look at the photo you see a perfectly stacked cube of boxes with the bottom corner missing. The picture taker offers this as proof that the boxes are in a static position and doomed to remain that way. You of course know differently. Potential energy guarantees that the change will take place.

The second aspect is simultaneity. If we observe the cantilever of a mechanical clock… (That’s the part that falls in between the teeth of a gear, braking it), we see that it spends most of it’s time in a static position but it is not stuck. The main reason is that motion is occurring elsewhere inside this closed system. Likewise, I propose that the universe is never motionless or static everywhere at the same time.
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 03/07/11 05:15 PM
Originally Posted By: Bill
If a photon having sufficient energy strikes the atom the electron will immediately transition to the first (or higher) excited state. As far as I know there is no mention of time in this transition.


My understanding is that you are absolutely right.

This is probably a red herring, but it is prompted by the mention of individual frames of a film. We are all familiar with the situation in which a wheel on film appears to be rotating backwards. Has anyone else wondered why we see the same effect in real life? Watching an accelerating wheel, we see it pass through a particular speed where it "goes backwards". Does this mean that our vision is "quantised"?
Posted By: Bill Re: Relativity, Time Dilation and Space/Time - 03/07/11 08:01 PM
Bill S.

I'm not sure that I have ever seen that effect that isn't in a moving picture of some sort, or created by a stroboscopic light source. However, I think that under certain conditions you might see something like that if you were looking at something with the light coming from something like a flourescent lamp, which can have a sort of a 60 Hz (50 Hz many places) blink to it. I do seem to recall that you used to be able to buy a gadget to check the speed of the turntable on your record player. It came with a little disk that you slipped over the spindle of the turntable. The disk had radial lines engraved on it. You also got a special little lamp that used something like neon. The gas would be energized at a 120 Hz (or a 100 Hz rate in may countries) rate (once for each half of the power line frequency). If your turntable was turning at the correct speed the lines on the disk stood still, otherwise they rotated one way or the other. You may have been seeing something like that.

Bill Gill
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 03/08/11 12:38 AM
Bill.

I first noticed the odd effect with an accelerating wheel over 60 years ago when watching the flywheel on a then quite elderly tractor that was starting up. In spite of having known about it for so long, it is only recently that I started wondering why it happened. The only explanation I can think of is that although our vision seems smoothly continuous, it is in fact like a series of snapshots. From there I got to wondering if our perception of time could be the same. If you get the speed right you can see the effect at any time, especially if the wheel has spokes.
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 03/08/11 12:46 AM
Originally Posted By: Kirby
I think that time is only the change marker…a phenomenon of sorts…not a real stand-alone physical entity.


Does this place you in the ranks of those who believe that time does not exist?
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 03/08/11 03:54 PM
Originally Posted By: Kirby
Time does not have to be quantized for the universe to behave the way that it does.


In fact time does not have to exist for the universe to behave the way that it does.

The fact that relativity involves time dilation, and makes a strong link between time and space, certainly suggests that time is a real entity, but if we substituted "change" for "time" I suspect the equations would work out just as well.
Quote:
Does this place you in the ranks of those who believe that time does not exist?


Unfortunately time is such a handy word. Time is a characteristic of realism so it’s hard to say that it doesn’t exist. I think that it’s all in the definition or description. Time is more of a characteristic of change like distance. To me, it’s not a fundamental constituent of the universe i.e. matter/ space/ energy. When energy acts; matter changes its position in space. It moves a certain distance and takes a certain amount of time. I can’t discard the reality of time any more than the reality of distance… nor their cousins rate and speed.

I just have my doubts about time as a stand-alone physical entity…a fabric. In this manner, it doesn’t exist. There’s really no problem with this notion. As I have said before, the attachment is based upon the theory of space/time.

Quote:
In fact time does not have to exist for the universe to behave the way that it does.

The fact that relativity involves time dilation, and makes a strong link between time and space, certainly suggests that time is a real entity, but if we substituted "change" for "time" I suspect the equations would work out just as well.


I think that this statement hits its mark like a Zen arrow. I can’t add or subtract anything.

Time is difficult to talk about because of semantics. It’s real… it exists… it’s how it exists. Kind of like differentiating between the distance of dimension and the distance of travel. Time only exists in dynamics not statics.

Just my humble opinion.
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 03/09/11 02:27 PM
Kirby, it seems as though we may both be with St. Augustine on this one: "What then is time? If no one asks me, I know; if I wish to explain it to someone who asks, I know not".
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 03/09/11 03:19 PM
Originally Posted By: Kirby
I’m glad that everyone is considering the possible equivalence (function) of Planck limits and quanta.


On the subject of quanta; does anyone consider the chronon as a possible quantum of time these days, or has it been relegated to the "recycle bin"?
Originally Posted By: Bill S.
Kirby, it seems as though we may both be with St. Augustine on this one: "What then is time? If no one asks me, I know; if I wish to explain it to someone who asks, I know not".


I’m not really with St. Augustine. To me, that’s the old philosophical issue of non-perceived existence: (If a tree falls in the forest and no one is around to hear; does it make a sound?). I think that it does. Those trees in Russia were knocked down by sound as far as I’m concerned. The scientific definition of sound is just a technicality. Deep down inside everyone knows that it made a sound…we can even hear it. smile
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 03/13/11 01:25 AM
Surely, sound waves are just vibrations, until an auditory organ converts them into sound. No ears, no sound.
Sounds like it depends on your definition of "sound". If you define it as vibrations in the air made by a moving object, then yes, there is sound. If you define sound in terms of a receptor/interpreter of those airwaves, then no, no sound is made. I happen to prefer the first definition myself, but that is just my opinion, fwiw.
Originally Posted By: Bill S.
Surely, sound waves are just vibrations, until an auditory organ converts them into sound. No ears, no sound.


At either rate, I think that all change (and time along with it), adheres to a discrete registration scheme. It is these functional limits that should be the Planck Limits. If there is some form of change that turns out to be smaller or shorter than the existing values then; it’s these values that need to be adjusted to reflect reality. Of course, all of this would have to be corroborated by quantum mechanics. And it would have to be both the discrete nature as well as the final values. Besides, what good is a grid of quantum foam with out a functional purpose?

BTW, what is a chronon? I must have missed that one.
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 03/13/11 11:52 PM
Quote:
what is a chronon?


It was proposed as a quantum of time some years ago. If I remember rightly it has a value of about 6.9x10^-24s
Posted By: Bill S. Re: Relativity, Time Dilation and Space/Time - 03/18/11 02:42 PM
Originally Posted By: Kirby
The scientific definition of sound is just a technicality. Deep down inside everyone knows that it made a sound…we can even hear it.


Originally Posted By: Amaranth Rose II
Sounds like it depends on your definition of "sound".


A tsunami is just a wave until it hits something; then it's a disaster. No "something", no disaster - no ears, no sound.

One trouble with philosophical stuff is that it can go round in circles for ever. (Oh, no, we are back to infinity). smile
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