Why does light have invarient speed?

[Xeinstein]

i think that the fact that we don't measure anything except against like-dimensioned quantities means that whether the dimensionful parameter is c or G or \hbar or \epsilon_0, any variation of any of these dimensionful parameters is "operationally meaningless" (those are Michael Duff's words) or "observationally indistinguishable" (those are John Barrow's words). and that does have something to do with Planck Units.

if we measure everything in Planck Units, we'll have dimensionless numbers, which are meaningful. but a consequence of that is the speed of light (which is more generally the speed of all fundamental interactions, not just E&M), the gravitational constant, the Coulomb electric constant, and Planck's constant all just go away. they turn into the number 1.

so God decides to turn the knob marked "c" on his control panel from 299792458 m/s (or whatever units he likes) to, say, half that value, and guess what? c still equals 1 (in Planck Units, that is c = 1 Planck Length per Planck Time, no matter what the knob is set to) and if all of the dimensionless parameters remain the same as before (those are the salient parameters), then the number of Planck Lengths per meter remain the same, the number of Planck Times per second remain the same, and then when we get our meter sticks and clocks out to measure c again (after God has twisted the knob marked "c") we still find out that light still travels 299792458 of our new meters in the time elapsed by one of our new seconds. so how are we going to know the difference?

If that's the case, how come Einstein never used Planck's constant in relativity?

 

[W.RonG]

... how come Einstein never used Planck's constant in relativity?

Just off the top of my head, I would say it isn't necessary to concern oneself with the granularity/resolution of space and time to develop concepts of relative measurement methodology. Nor would the specific units of measure cause the Theory to change. If I understand correctly, Einstein concerned himself with the overarching concepts and left much of the hard-core mathematics to others (if this really is not true then I apologize in advance).
Quantized space and time answers the ancient conundrum of the arrow shot at a target. In half of the travel time it goes halfway to the target. Half again it is closer and if this is repeated ad infinitum the arrow will never reach the target. But we know it does so there must be a minimum distance unit and a minimum time unit and all speeds are integer ratios thereof.
The inclusion of quantization was meant to describe the speed of light based on the nature of space-time and local interaction which propagates energy. It can only be 1/1=1. Everything else is that or a lower ratio; the only way to propagate faster would be 1/0=?
rg

 

[rbj]

Here's where I'm going - the nature of space is to propagate energy (rbj's interactions) at a fixed rate.

and even if it wasn't a fixed rate from the POV of some god-like observer, if it were to change from this observer's POV (the observer isn't governed by the laws of physics that we are, which is only reason this observer could sense a change in that rate of propagation), we would not sense a difference unless some dimensionless parameter changed. but as far as we're concerned, since we only measure of perceive physical quantities in relationship to other like-dimensioned quantities - we count tick marks on rulers or ticks of a clock. we perceive how long a distance is relative to how big we are, we perceive how long in time some event is in proportion to about how long a fleeting thought is, inverse proportion to how fast our brains can think. so if somehow we think we measured c to be a different number of meters (the pre-1960 definition of the meter) per second, the salient parameter(s) that changed were the number of Planck Lengths per meter (and if the platinum-iridium meter stick is a "good" meter stick, then it doesn't lose or gain any atoms so this would be reflected in the number of Planck Lengths per Bohr radius) and/or the number of Planck Times per second. those are the important numbers.

The nature of our measurements of space and energy propagation causes them to always get the same result. But we realize that we may be moving relative to another system that got the same answer that we did, and we are puzzled. The answer lies in understanding the nature of our physical existence in natural space-time. That includes our measuring rods and our ticking clocks with which we describe our motions.
I have to get going so if I can put more thoughts into words I'll try to expand on this later. I hope others see the connections between the material in post #15 (too much to quote) and the ultimate answer to the initial question, and can help this process along.

Ron, this was pretty close to how i have trying to express this. thanks.

If that's the case, how come Einstein never used Planck's constant in relativity?

it's because, measured with our meters and seconds and kilograms, Planck's constant doesn't affect any of the physical consequences that are addressed in either SR or GR. now, if memory serves, i thought Einstein also wrote a sort of seminal paper about the photoelectric effect, and perhaps he made a reference to the constant of proportionality between the energy of emitted electrons and the frequency of the light onsetting the emittor surface. whether he called it "Planck's constant" or not, that's what it would have been.

 

[JesseM]

Quantized space and time answers the ancient conundrum of the arrow shot at a target. In half of the travel time it goes halfway to the target. Half again it is closer and if this is repeated ad infinitum the arrow will never reach the target. But we know it does so there must be a minimum distance unit and a minimum time unit and all speeds are integer ratios thereof.

But this problem is also simple to resolve in the case of continuous space and time, using calculus. Yes, you can divide the trip into an infinite series of smaller and smaller increments, but the time for the arrow to cross each successive increment will be also be getting smaller and smaller, and in calculus it is quite possible to have an infinite decreasing series which sums to a finite number, like 1/2 + 1/4 + 1/8 + 1/16 + ... = 1

The inclusion of quantization was meant to describe the speed of light based on the nature of space-time and local interaction which propagates energy. It can only be 1/1=1. Everything else is that or a lower ratio; the only way to propagate faster would be 1/0=?
rg

Why couldn't an object move more than one units of space in a single unit of time? After all, for slower-than-light objects, they'd have to move more than one unit of time for each unit of space along their path. In any case, if you think the notion of quantized space and time is established physics you're wrong; it's a speculation that emerges out of some approaches to quantum gravity, and I'm not even sure if it's true if it's technically true in string theory, although something weird does happen when you try to talk about distances smaller than the Planck length in string theory...as http://library.thinkquest.org/27930/stringtheory5.htm says,

A major detail of winding modes involves size. According to string theory, physical processes that take place while the radius of the encircled dimension is below the Planck length and decreasing are exactly identical to those that take place when the radius is longer than the Planck length and increasing. This means that, as the encircled dimension collapses, its radius will hit the Planck length and bounce back again, reexpanding with the radius grater than the Planck length again. In other words, attempts by the encircled dimension to shrink smaller than the Planck length will actually cause expansion.

The Logic Behind Contraction/Expansion Relationships

Wound strings' energy come from two different sources: the familiar vibrational motion and the new winding energy. Vibrational motion can be separated into two categories: ordinary and uniform vibrations. Ordinary vibrations are the usual oscillations discussed in preceding pages; for simplicity, they will temporarily be ignored. Uniform vibrations are the simple motion of a string's sliding from one place to another. There are two important observations related to uniform motion that will lead to the essence of the contraction/expansion relationship.

First, uniform vibrational energies are inversely proportional to the encircled dimension's radius. By the uncertainty principle, a smaller radius confines a string to a smaller area and thus increases the energy of its motion. Second, winding energies are directly proportional to the radius because the radius causes a string to have a minimum mass, which can be translated into energy. These two conclusions show that large radii imply large winding energies and small vibrational energies, and small radii imply small winding energies and large vibrational energies.

This conclusion yields the essential realization: for any large radius there is a corresponding small radius in which the winding energies of the former are the vibrational energies in that latter and vice versa. Since physical properties depend on the total energy of a string, not its individual winding or vibrational energy, there is no observable physical difference between the corresponding radii.

Now consider an example of the preceding principle. Imagine that the radius of the encircled dimension is 5 times the Planck length (R=5). A string can encircle this dimension any number of times; this number is called the winding number. The energy from winding is determined by the product of the radius and the winding number. The uniform vibrational patterns, which are inversely proportional to the radius, are in this case proportional to whole-number multiples (due to the fact that energy comes in discrete packets, or quanta) of the reciprocal of the radius (1/R). This calculation yields the vibration number. If the radius is decreased in size to R=1/10, the winding and vibration numbers simply switch, yielding the same total energy (see table below).

 

[mdeng]

Here's where I'm going - the nature of space is to propagate energy (rbj's interactions) at a fixed rate. The nature of our measurements of space and energy propagation causes them to always get the same result. But we realize that we may be moving relative to another system that got the same answer that we did, and we are puzzled. The answer lies in understanding the nature of our physical existence in natural space-time. That includes our measuring rods and our ticking clocks with which we describe our motions.

I like this view from another angle, though I have yet to see what I may reap from it. How would you think about the relation between this view of nature and the locality principle? Some claims that from that principle, it entails that the propagation speed must be finite, have an upper bound, and must be constant to all observers. If this claim is true, then the locality principle would be a more fundamental feature of the nature.

I think all the answers I have got so far have partially answered my original question. I now see SR as not dependent on some "ad-hoc" feature of light as it might appear, but rather as being built upon a more fundamental assumption of the energy/effect/force propagation speed of the nature. I am not sure whether Einstein thought that way when he presented his SR initially.

My other question, arising from the course of the discussion, was whether the 2nd postulate of SR is necessary (vs. whether it can be derived from Maxwell's equation). At this stage of my understanding, it seems that Maxwell's equation did not prove it was true for all reference frames (stationary, moving, or non-inertial) and its underlying assumption was there was aether in the vacuum. I think Einstein's 2nd postulation effectively says that the equation is assumed to be true for all moving inertial reference frames, regardless whether aether exists or not.

 

[W.RonG]

But this problem is also simple to resolve in the case of continuous space and time, using calculus. Yes, you can divide the trip into an infinite series of smaller and smaller increments, but the time for the arrow to cross each successive increment will be also be getting smaller and smaller, and in calculus it is quite possible to have an infinite decreasing series which sums to a finite number, like 1/2 + 1/4 + 1/8 + 1/16 + ... = 1

If I recall, calculus is based on the assumption that the summation of a very large number of very small increments is for our purposes the equivalent of a continuous function. I'll wait while someone adds up all the above fractions. Oops, there's an infinite number of them so it would take (literally) forever and I don't have that long. In this case we can only have faith that the asymptote actually reaches the final value.

Why couldn't an object move more than one units of space in a single unit of time? After all, for slower-than-light objects, they'd have to move more than one unit of time for each unit of space along their path. ...

I see it as being very difficult to travel two Planck distances in space without first having moved one Planck distance. The only way to achieve more than one Planck distance of movement in one time increment is to traverse all Planck distances simultaneously. Not happening. So I see it as all movement is 1Lp/1Tp, 1Lp/2Tp, 1Lp/3Tp, etc. This implies (since we can't occupy space in an interval smaller or between Lp), that all movement is described by spending a number of Tp's at each location of Lp. Then on to the next Lp location, wait another number of Tp's. etc.
rg
(does this forum have a sig. function? mine is "I thought I was wrong once, but I was mistaken". Oh and smileys.)

 

[JesseM]

If I recall, calculus is based on the assumption that the summation of a very large number of very small increments is for our purposes the equivalent of a continuous function.

No it isn't. It's based on limits, and in the case of a continuous function, you're talking about the limit as the size of the increments goes to zero (and the number of increments in the sum goes to infinity).

I'll wait while someone adds up all the above fractions. Oops, there's an infinite number of them so it would take (literally) forever and I don't have that long. In this case we can only have faith that the asymptote actually reaches the final value.

Again, you seem not to understand the idea of limits which is the foundation of calculus. To say the sum of the infinite series is 1 means the limit as you increase the number of terms in the sum is 1, so that for any tiny number "delta" (say, delta = 0.0000000000000000000000000000000001), there's some rule that gives you a finite number N such that, if you add together the first N terms of the series, the sum will be larger than 1 - delta, but it's also possible to prove that no finite number of terms will ever give a sum larger than 1. This can all be proved in a rigorous way, you don't have to wait around to test every possible delta to make sure there are no exceptions to the rule.

I see it as being very difficult to travel two Planck distances in space without first having moved one Planck distance.

Why? If space is quantized, then things are always "jumping" discontinuously through space anyway. We could certainly program a computer so that simulated objects could hope more than one pixel in single unit of time, and I see no reason that the universe can't be following any conceivable algorithm that could be programmed into a computer.

 

[W.RonG]

Are the wheels spinning out there or did everyone else bail?
Hi JesseM. Since these posts are contiguous I won't re-quote; I believe we've said essentially the same thing regarding calculus, just that I've used more colloquial terms. Since we don't want to wait around to add an infinite number of infinitesimally small items, we just say "close enough" (within your delta) and project the result as if we had added everything up (invoking the limit). Kind of a to-may-to to-mah-to scenario. You can add 0.9 + 0.09 + 0.009 ... til you're exhausted and you won't (and never will) reach "1". When the result gets within "delta" of "1" we say "done" but you have to admit it's still not "1".
I'll stop retorting about calc - if you look at my bio you'll see that I'm more in line with the practical side of things and less of the theoretical (my 3-decade-old degrees are in applied science and engineering technology), plus the fact that I've spent your lifetime not using calculus since I last had it in class.
rg

 

[matheinste]

W.RonG.

I think the sum of the infinite series 0.9+0.09 and so on is 1. If it is not so can you give me a number which is between this sum and 1.

Matheinste.

 

[JesseM]

Since we don't want to wait around to add an infinite number of infinitesimally small items, we just say "close enough" (within your delta) and project the result as if we had added everything up (invoking the limit).

A limit is not just "close enough", it is the number that we can rigorously prove the sum would get arbitrarily close to if we kept adding terms forever.

Kind of a to-may-to to-mah-to scenario. You can add 0.9 + 0.09 + 0.009 ... til you're exhausted and you won't (and never will) reach "1". When the result gets within "delta" of "1" we say "done" but you have to admit it's still not "1".

But what if the terms themselves represent actual physical times? In other words, you know the arrow takes 0.9 seconds to traverse the first interval, 0.09 to traverse the second, and so forth. Then how long it would take you to add them in your head is irrelevant, unless you can add each new term in the exact amount of time it is supposed to represent (and if you could, then you'd add an infinite number of terms in 1 second total).

 

[W.RonG]

W.RonG.

I think the sum of the infinite series 0.9+0.09 and so on is 1. If it is not so can you give me a number which is between this sum and 1.

Matheinste.

My point is in the real world there is not an infinite number of infinitesimally small items to add together, and if one really attempted to do so the effort would (a) never achieve an end and (2) never reach the ultimate result. Mathematics allows for a conceptual model of a real thing, it is not the real thing itself. Delta is an arbitrary number that is by definition not zero. Oops I retorted. no more. I promise.
rg

 

[matheinste]

In the real world the arrow reaches the target.

Matheinste.

 

[W.RonG]

...what if the terms themselves represent actual physical times? In other words, you know the arrow takes 0.9 seconds to traverse the first interval, 0.09 to traverse the second, and so forth. Then how long it would take you to add them in your head is irrelevant, unless you can add each new term in the exact amount of time it is supposed to represent (and if you could, then you'd add an infinite number of terms in 1 second total).

Maybe this is what got Max Planck started on his way to figuring out what the limits are for time and distance in the real world.
rg

 

[W.RonG]

Mdeng, I hope you don't feel left out. There were some good questions in #95 and some very insightful statements in #105. I think we should get back to the main question and continue the progress made up to that point. I'm going to brave the blizzard and head home now so I'll be checking in later.
rg

 

[rbj]

The inclusion of quantization was meant to describe the speed of light based on the nature of space-time and local interaction which propagates energy. It can only be 1/1=1. Everything else is that or a lower ratio; the only way to propagate faster would be 1/0=?

Why couldn't an object move more than one units of space in a single unit of time? After all, for slower-than-light objects, they'd have to move more than one unit of time for each unit of space along their path. In any case, if you think the notion of quantized space and time is established physics you're wrong; it's a speculation that emerges out of some approaches to quantum gravity,

i thought that it was a speculation that reality might be quantized in time and space, similar to cellular automa, where something around the Planck Time and Planck Length are the units of quantization which, since they're so damn small, all of these differential equations for EM, QM, and GR get turned into difference equations via Euler's method and these difference equations have no constants of proportionality (except maybe an occasional 2 or 1/2) in them since the quantities are in Planck Units. as cellar automa, some "action" can only propagate to adjacent discrete spatial cells in one discrete time unit, thus imposing a speed limit of 1 Planck Length per Planck Time.

but, of course it's not anywhere near established physics. just speculation and probably full of holes. but as a practitioner of Discrete-Time Signal Processing (sometimes called "DSP"), it's sort of gratifying to think about reality possibly as a sampled data system also (with a sampling frequency of about 10⁴⁴ Hz, the reciprocal of the Planck Time).

 

[JesseM]

Maybe this is what got Max Planck started on his way to figuring out what the limits are for time and distance in the real world.
rg

Someone correct me if I'm wrong, but I don't think Planck himself made any claims about "limits for time and distance", he just came up with "Planck units" as a convenient system of units for physicists to use, ideas about the physical significance of the Planck length and Planck time are modern speculations which emerge out of quantum gravity, which suggests that quantum gravitational effects should become significant at this scale.

 

[mdeng]

Quantized space and time answers the ancient conundrum of the arrow shot at a target. In half of the travel time it goes halfway to the target. Half again it is closer and if this is repeated ad infinitum the arrow will never reach the target. But we know it does so there must be a minimum distance unit and a minimum time unit and all speeds are integer ratios thereof.

TBH, I never understood why this is a conundrum. If time/distance are not infinitely divisible, the answer is obvious, no conundrum. Assume that time is infinitely divisible. Now, if we keep looking at only half of the remaining distance as the puzzle requires, we are just fooling ourselves by not looking beyond (and including) the target where the arrow is. The truth is, the arrow does not stop just because we willingly chose not to look beyond the time it takes the arrow to fly over the distance, or beyond the distance that the arrow will need to cover to reach the target.

If the conundrum is about "if we can move with an arbitrarily small step that can take infinitely small amount of time, can we ever cover a given finite distance?" Then the answer will depend on whether distance and time can be infinitely divided.

Thus I fail to see why the arrow's reaching of the target proves anything about whether time and distance must have a smallest unit or not (or whether they must be discrete).

 

[pervect]

This thread has nothing to do anymore with relativity,and has other severe problems as well. I'm locking it.