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Postmaster

Reged: 04/28/03

Loc: Atlanta, GA
Re: Is science dead? [Re: Qwickdraw]
#5325357 - 07/19/12 04:13 PM

When the ancient Greeks were trying to figure out the ratio between the circumference and diameter of a circle, their measurement accuracy was important. Until someone worked out the math. Now you can calculate pi to as many decimals as you care to with a computer, based on a formula without measuring anything.

Before relativity, we assumed that a meter was a fixed distance, and a second was a fixed period of time. Therefore C could be defined in terms of meters and seconds.

What relativity changed is that C is not defined in terms of meters and seconds, the relationship between meters and seconds is defined by C.

So we know C exactly. What we measure with limited precision is distance and time. And if our velocity changes, our measurement of distance and time will change as well. But our measurement of C will not.

To go back to the water example, we know the density of water is 1 g/mL. We can measure a volume of water imprecisely, and its mass imprecisely, but the two have a fixed relationship to each other.

To make a simpler example, how many milliliters in a liter? Exactly 1000. Not 1000.01, exactly 1000. Now, if I take a 1L bottle fill it up, them use a 1mL pipette to measure it out, I probably won't measure exactly 1000mLs. But that's due to errors in my measurement. In other words, if I come up with a number other than exactly 1000, it's either because I mis-measured the original 1L, or the individual milliliters, not because there are more or less than 1000mLs in a liter.

There are lots of things that do depend on measurement accuracy. But there are some things that don't - they are part of the mathematics of the system. The density of water is an artificial constant because it is an artifact of the units of measurement we have chosen (i.e. we could have defined the gram based on the density of oil instead of water). Same for the number of mLs in a liter - there are 1000 because we defined a liter that way.

C, pi, e, etc. are all called natural constants because they are not artifacts of our measurement system.

Edited by Jarad (07/19/12 10:43 PM)

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deSitter
Still in Old School

Reged: 12/09/04

Re: Is science dead? [Re: barasits]
#5325736 - 07/19/12 08:10 PM

Quote:

Quibbling about the speed of light is a distraction from the gist of Quickdraw's point, which is, to use Korzybski's words, "the map is not the territory." Maps and models, mathematical or otherwise, are transforms of reality.

Geoff

Well it's a very important point - it's not quibbling. There is an analogy in Euclidean geometry, which believe it or not, has a speed of light - but it's imaginary! It's "i" where i^2 = -1. This is a really amazing connection that shows how similar relativistic geometry is to the one we know in everyday life. From the point of view of projective geometry, which comes before metric geometry and involves fewer assumptions, Minkowski and Euclid are just different cases of the same underlying thing. So the speed of light is really, really, 1.

-drl

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Qwickdraw
sage

Reged: 03/03/12

Loc: Ann Arbor, Mi
Re: Is science dead? [Re: deSitter]
#5326389 - 07/20/12 06:40 AM

Well, it’s all fascinating from the notion of has science been relegated the original idea of this post which I believe is that mathematical models can now take the place of hard physical science. I still contend that due to measurement accuracies and the fact that some things cannot be measured without affecting their values puts us in the position that we will always be dealing with some proximity of real world values that are not ideal. Yes, math is true and repeatable but still it is a constraint of the mind which is and always will be unsuitable to perfectly describe the universe. I believe this may be a correct statement... The physical constants that are measurable are all analog or maybe more accurately have an infinite precision while the math used to describe them is bound by the mechanism of math itself.

I refer once again to Heisenburg when he said
"It is not surprising that our language should be incapable of describing the processes occurring within the atoms, for, as has been remarked, it was invented to describe the experiences of daily life, and these consists only of processes involving exceedingly large numbers of atoms. Furthermore, it is very difficult to modify our language so that it will be able to describe these atomic processes, for words can only describe things of which we can form mental pictures, and this ability, too, is a result of daily experience. Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme—the quantum theory—which seems entirely adequate for the treatment of atomic processes; for visualization, however, we must content ourselves with two incomplete analogies—the wave picture and the corpuscular picture."

— Werner Heisenberg

I believe when he used the word "language" he was refering to both spoken and mathmatical examples.

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Postmaster

Reged: 04/28/03

Loc: Atlanta, GA
Re: Is science dead? [Re: Qwickdraw]
#5326446 - 07/20/12 08:01 AM

Quote:

Well, it’s all fascinating from the notion of has science been relegated the original idea of this post which I believe is that mathematical models can now take the place of hard physical science.

That's not my point at all. Mathematical models do not replace hard science. The relationships are first determined by hard measurements, then followed by theory to explain those measurements. But once the theory is set up, the mathematical models have some factors that must be determined by measuring (for example, the gravitational constant G, or the Hubble constant), and other factors that do not depend on measurements (for example, pi, e, and C).

Some things are just built into the math. Here is a different example - we don't have to measure the radius of a circle in every direction to prove they are all the same - the definition of a circle is that it is the set of points where the radius is the same. When applying that model to orbits, we have to measure to answer the question "is the orbit a circle?" Of course, the answer turned out to be no, orbits are ellipses. But we don't conclude from that that a circle has different radii, just that orbits are not circular.

To follow on with that, when we observe the motion of a planet to calculate it's orbit, we have error in our measurement of its position, error in our measurement of its velocity, error in our measurement of its mass, the mass of the sun, the mass and positions of the other planets, and the gravitational constant G. The limit of precision of all those factors limits how well we can predict its future orbit. One thing that does NOT limit our prediction of its orbit is the error in the value of pi - we can calculate that out to whatever precision we want so that it is insignificant compared to the others.

Quote:

I still contend that due to measurement accuracies and the fact that some things cannot be measured without affecting their values puts us in the position that we will always be dealing with some proximity of real world values that are not ideal.

Yes, we have uncertainty in every measurement. That is true of all the constants that require measurement. It's not true of the ones that don't require measurement, of which I have already given many examples. My point is that there are 2 different cases here - measureable values, and mathematical constants or relationships. One type has error, the other does not. I think the part that is confusing is that in relativity, C falls into the mathematical constant category, while distance and time fall into the measureable category. Before relativity, we thought it was the other way around.

One last example:

1 + 1 = 2. Exactly 2, not 2 +/- some error.

But if I use a pipette to measure out 1 mL of water, and it has a precision of +/- 0.005 mL, then I add a second mL measured the same way, that would be expressed either as:
1.00 + 1.00 = 2.00
or
1.000 +/- 0.005 + 1.000 +/- 0.005 = 1.000 +/- 0.01

The first is a calculation, and contains no error. The second is a measurement, and contains error.

Edited by Jarad (07/20/12 09:30 AM)

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deSitter
Still in Old School

Reged: 12/09/04

#5326510 - 07/20/12 08:58 AM

Here's another example from relativity of something that is "intrinsic" to the theory. It was naturally assumed that a wave phenomenon - propagation in the abstract sense - required a medium of propagation. The constancy of C rendered this idea untenable, because properties would have to be imputed to the medium that are, if not impossible, then so complex and contradictory as to ruin the simple idea of a wave in a medium.

In relativity the situation is fundamentally changed. Because of the new geometry, the "wave operator", the object that appears in equations of wave propagation, is now simply an aspect of 4-d geometry, and no medium of propagation is needed. The idea of propagation has been built into geometry itself.

The equations are exactly the same as before, but their meaning is completely changed. This is the real interface between math and physics. The physics is in the equations - the math represents the sensible, logical structure that supports them.

Once there is a mathematical structure in place, it can be used to suggest new ideas that lead to progress. If light propagation is now just an aspect of geometry, then why not all propagation, that is, can all motion be regarded as an aspect of geometry? That was Einstein's real goal. (It is partially realized in quantum field theory, where all particles are represented by "propagators".)

-drl

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star drop
Snowed In

Reged: 02/02/08

Loc: Snow Plop, WNY
Re: Is science dead? [Re: scopethis]
#5326617 - 07/20/12 10:23 AM

Quote:

hey...if one puts something in a vacuum then it's no longer a vacuum...

True. Then your wife will nag you until you empty the vacuum.

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Wordsmith

Reged: 03/22/05

Re: Is science dead? [Re: deSitter]
#5326797 - 07/20/12 12:06 PM

Quote:

Here's another example from relativity of something that is "intrinsic" to the theory. It was naturally assumed that a wave phenomenon - propagation in the abstract sense - required a medium of propagation. The constancy of C rendered this idea untenable, because properties would have to be imputed to the medium that are, if not impossible, then so complex and contradictory as to ruin the simple idea of a wave in a medium.

In relativity the situation is fundamentally changed. Because of the new geometry, the "wave operator", the object that appears in equations of wave propagation, is now simply an aspect of 4-d geometry, and no medium of propagation is needed. The idea of propagation has been built into geometry itself.

The equations are exactly the same as before, but their meaning is completely changed. This is the real interface between math and physics. The physics is in the equations - the math represents the sensible, logical structure that supports them.

Once there is a mathematical structure in place, it can be used to suggest new ideas that lead to progress. If light propagation is now just an aspect of geometry, then why not all propagation, that is, can all motion be regarded as an aspect of geometry? That was Einstein's real goal. (It is partially realized in quantum field theory, where all particles are represented by "propagators".)

-drl

I'm learning a lot here, and please don't take any of my questions as challenges in any way. I'm just trying to learn more.

So I have another question.

I already knew that one of the effects of relativity was to obviate the need for a medium (sometimes called the "aether") to propagate "light" (I'm putting that word into scare quotes because I am learning that nothing in physics is what I once thought it was). But here's my question: if propagation is an aspect of 4D geometry (which is fine by me), why aren't sound waves propagated in a vacuum? Or are they?

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barasits
sage

Reged: 06/12/11

Loc: Chicago
Re: Is science dead? [Re: deSitter]
#5326869 - 07/20/12 12:54 PM

Quote:

Quote:

Quibbling about the speed of light is a distraction from the gist of Quickdraw's point, which is, to use Korzybski's words, "the map is not the territory." Maps and models, mathematical or otherwise, are transforms of reality.

Geoff

Well it's a very important point - it's not quibbling. There is an analogy in Euclidean geometry, which believe it or not, has a speed of light - but it's imaginary! It's "i" where i^2 = -1. This is a really amazing connection that shows how similar relativistic geometry is to the one we know in everyday life. From the point of view of projective geometry, which comes before metric geometry and involves fewer assumptions, Minkowski and Euclid are just different cases of the same underlying thing. So the speed of light is really, really, 1.

-drl

As I see it, the quibble in question is whether to privilege reality in which case the speed of light can't be perfectly known or to privilege a mathematical model in which case the speed of light can be perfectly known by definition. Meanwhile, the more fundamental philosophical issue arising from your rejection of Quickdraw's Heisenberg quote goes unaddressed. Having pooh-poohed Heisenberg, you haven't yet explained the nature of your objection.

Geoff

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Postmaster

Reged: 04/28/03

Loc: Atlanta, GA
Re: Is science dead? [Re: barasits]
#5326907 - 07/20/12 01:25 PM

Quote:

As I see it, the quibble in question is whether to privilege reality in which case the speed of light can't be perfectly known or to privilege a mathematical model in which case the speed of light can be perfectly known by definition.

The issue is the definition. We are used to thinking of speed as a measurement of something that can change, while length and time are constant and unchangeable. That holds reasonably well at low speeds with physical objects. But one of the central points of relativity is that it does NOT hold at higher speeds.

As you approach C relative to some other object, your measurement of distance becomes different from theirs. Your measurement of time becomes different from theirs. But you both see C as the same, and the changes in time and distance measurements have a specific relationship which is based on C.

Because of this, the definitions of our units of time and distance have been intentionally changed to be based on C. It is like the density of water - it is exactly 1 g/mL by definition. The gram is defined based on the density of water. Our units of meters and seconds are based on C, not the other way around. We know C goes at 299,792,458 meters per second, because a meter is defined as the distance that light travels in a vaccuum in 1/299,792,458 of a second.

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scopethis
Postmaster

Reged: 05/30/08

Loc: Kingman, Ks
#5326971 - 07/20/12 02:03 PM

is "time" moving faster than light?

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Postmaster

Reged: 04/28/03

Loc: Atlanta, GA
Re: Is science dead? [Re: scopethis]
#5327015 - 07/20/12 02:40 PM

In a sense, we are all always moving at C. If we are standing still in space, we are moving at C in the time dimension. If we move in space, then we tilt our vector slightly out of line with the time dimension, towards the space dimensions, but the length of the vector is still C. Therefore we slow down a bit in time. It doesn't beocme very noticeable until the speeds become a significant fraction of C.

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deSitter
Still in Old School

Reged: 12/09/04

#5327362 - 07/20/12 07:13 PM

Quote:

if propagation is an aspect of 4D geometry (which is fine by me), why aren't sound waves propagated in a vacuum? Or are they?

Because the equation for light propagation is (Dx = derivative with respect to x)

(Dx^2 + Dy^2 + Dz^2 - Dt^2) Am = 0

where Am is the electromagnetic potential, while that for sound is

(Dx^2 + Dy^2 + Dz^2 - K Dt^2 + M Dt) S = 0

where S is the density of air, and K and M are phenomenological parameters that characterize the medium, with K < 1 in natural units in which C = 1. K and M may in fact depend on position and time. So the equations are not even really the same, they just appear similar when the sound propagation medium is tenuous so the linear approximation works and the first order time derivative drops out.

Feynman was fond of saying "The same equations have the same solutions." But this is sort of a trap, because the same equations do not necessarily have the same meaning.

-drl

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llanitedave
Humble Megalomaniac

Reged: 09/26/05

Loc: Amargosa Valley, NV, USA
#5329071 - 07/21/12 11:22 PM

Quote:

Quote:

As I see it, the quibble in question is whether to privilege reality in which case the speed of light can't be perfectly known or to privilege a mathematical model in which case the speed of light can be perfectly known by definition.

The issue is the definition. We are used to thinking of speed as a measurement of something that can change, while length and time are constant and unchangeable. That holds reasonably well at low speeds with physical objects. But one of the central points of relativity is that it does NOT hold at higher speeds.

As you approach C relative to some other object, your measurement of distance becomes different from theirs. Your measurement of time becomes different from theirs. But you both see C as the same, and the changes in time and distance measurements have a specific relationship which is based on C.

Because of this, the definitions of our units of time and distance have been intentionally changed to be based on C. It is like the density of water - it is exactly 1 g/mL by definition. The gram is defined based on the density of water. Our units of meters and seconds are based on C, not the other way around. We know C goes at 299,792,458 meters per second, because a meter is defined as the distance that light travels in a vaccuum in 1/299,792,458 of a second.

Well, the "speed of light" as a universal constant is not necessarily the same as the "speed of light" in some particular physical situation. It also kind of gets into Joad's question above. Space doesn't need a medium in order to transmit packets of electromagnetic radiation -- in the absence of a medium that transfer velocity will be c. However, there often is a medium to consider, such as the glass of a lens, a body of water, the air, a hydrogen cloud, etc. In those circumstances the speed of light will be some value less than c.

"Privileging reality" means nothing more than applying fundamental and universal laws to local circumstances (and vice versa), which add complicating influences and may skew the measurement results.

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Postmaster

Reged: 04/28/03

Loc: Atlanta, GA
Re: Is science dead? [Re: llanitedave]
#5329501 - 07/22/12 09:43 AM

Quote:

Well, the "speed of light" as a universal constant is not necessarily the same as the "speed of light" in some particular physical situation.

Well, I did specify the speed of light in a vacuum in a couple of posts. By C, I mean speed of light in a vacuum. When light goes through some medium like air or glass, it slows down some. This slow down also determines the index of refraction, and is wavelength dependent. So that speed would need to be measured, and would have some amount of error (although you could call that the error in the index of refraction for that medium, which better captures the nature of what you are measuring).

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llanitedave
Humble Megalomaniac

Reged: 09/26/05

Loc: Amargosa Valley, NV, USA
#5329600 - 07/22/12 10:58 AM

I'm not disagreeing, Jarad -- I was hoping just to extend the scope of the discussion. It's C that is established by definition and is a mathematical constant. But the speed of light is not necessarily always c -- and when you're conducting a measurement, you have to look at these other variables before you can interpret your results. Neither of you is wrong, actually, you are just looking at different sides of the coin.

Which brings us back to the OP question: Is science dead? The discussion I'm reading above is proof that it's not.

In practice, science is an ugly thing, full of argument, variations of perspective, messy details, and an unknown but vicious monster called "reality" just outside the walls, trying to rip to shreds any beautiful and elegant idea you may come up with.

It's a pretty wonderful thing, actually. Science is not dead. Disagreement and disputation is its lifeblood. Testing and experimentation is its nourishment. And that's what's happening in physics, cosmology, and as far as I know, geology.

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Wordsmith

Reged: 03/22/05

Re: Is science dead? [Re: llanitedave]
#5329609 - 07/22/12 11:07 AM

I agree. Not only is science not dead, it is probably the last area of thinking wherein reality is still respected.

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ColoHank
Carpal Tunnel

Reged: 06/07/07

Re: Is science dead? [Re: deSitter]
#5329623 - 07/22/12 11:18 AM

Quote:

Something like this makes you think it is at least on its death bed:

http://arxiv.org/abs/1206.1616

Here is an extraordinary claim, concocted from who knows how many layers of computer code, to see, not just dark matter, but its annihilation into gamma rays. Not a trace of this stuff has ever been seen, the entire idea is almost certainly just a mistake in applying GR to large scale systems, yet here is a paper that claims to see dark matter annihilation. In fact, nothing at all is really visible, just the plots from some mysterious code to which is applied a very fluid and artistic interpretation.

The computer has become the universe. Whatever comes out is taken as real. Thought is optional. Understanding and experience are of no value at all.

Anyone whose data and conclusions differ from those of others are free (dare I say obligated?) to publish and defend their own findings and interpretations, though such counter arguments probably won't gain much traction if aired only in a popular forum like this. Further observation, testing, and rigorous peer review and informed debate will continue to refine our understanding of the universe. That process of mulling things over in the collective mind and separating the wheat from the chaff is called science, and it's very much alive.

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