Microscopic World vs. the Macroscopic World

[Jklint]

How bout them knockers.

I studied the subject very deeply and all I can say is according to the Standard Model all good things come in pairs.

[DanLanglois]

I have perhaps lost my interlocutor, which I think is due to my unwelcome extensive digressions into the math subject of dimensional analysis, in response to this assertion:

One way to confirm the identification of the dimensions of permittivity and permeability is to use them in the same expression. One such expression is Maxwell‘s famous result from electromagnetic theory:

c = 1/(oo )½ Sorry about the equation but I could not get the characters to show up right in this editor.

to which I responded:

I think I can pick up the thead here, c^-2 = μ0ϵ0 (permiability times permittivity).

Maybe I can manage a quick summary of what we got bogged down on, here, the notion that one might want to 'confirm the identification of the dimensions of permittivity and permeability', and that one would manage this how? 'use them in the same expression.'

Leaving aside these notions of confirming the identification of the dimensions somehow, and why one would do this, I might back up and explicate the point of introducing this equation, and this undertaking. It was supposed to go to it being the case that the speed of light is able be calculated using just two parameters of the so called ‘vacuum of space’. This supposedly occasions looking more closely at what it is that determines the values of these parameters.

We can speak of the electric permittivity of free space as being the measure of the capacity of space to, well, allow the propagation of, or assist in the transmission of, something or other. And we can also speak of the magnetic permeability as being the measure of the effectiveness of space in propagating, or assisting in the transmission of something or other.

We can talk about the 'capacity of space' to allow the propagation of the force due to an electric charge. And we can talk about 'the effectiveness of space' in propagating magnetic lines of force to a distance from the source. And, we can multiply 'the capacity of space' etc. by 'the effectiveness of space' etc. We do that, we get a number, of which the speed of light is inversely proportional to the square root.

Or, simply stated, the speed of light is inversely proportional to both the electrical permittivity and magnetic permeability of free space. And one might easily suppose, then, that if, by some chance, space was either more permissive, or more permeable, or both, then the speed of light would be less. This seems to make sense.

I'm kind of just restricting myself to playing devil's advocate here, arguing my interlocurtor's case. In that spirit, it may also be significant that the resonant frequency of a capacitive, inductive electrical circuit is *also* inversely proportional to the inductance and capacitance of a circuit--in *exactly the same way* that the speed of light is inversely proportional to, shall we way, the inductance and capacitance of space.

That, may also be significant, why? Because, the inductance of a medium will depend on its ability to convert electric current to a magnetic field, which is another way of saying that it ultimately depends on the types of atoms of which it is comprised and the way they are arranged. And, the capacitance of a medium depends on the dielectric properties of the medium, which is another way of saying that it ultimately depends on the atoms that comprise the material and the way they are arranged.

In other words, neither inductance nor capacitance are, as it were, fundamental properties.

And then we get, based on this reasoning, a notion that the inductance and capacitance of space will ultimately depend on something or other. And then, again based on this reasoning, we get a notion ultimately it is something or other that determines both the speed and frequency of light.

But there is a problem, we are told that the speed of light is a 'constant'--will it, then, vary? How is this 'constant' artificially determined? How can we reconcile this apparent contradiction? And this amounts, I believe, to an assertion that there is some a regularity the 'fluctuations of space'.

I'm feeling generous, I've made an effort to give my interlocutor his argument, as I understand it--I haven't restricted myself to what I believe, this is my best effort to articulate his point. If he wants to add anything. But I do think that this argument can be broken down..

[Wanderer101]

For DanLanglois,

You have not lost me. I am still working on my next reply. I have a lot going on at home right now and I am having a bit of trouble getting back to the PC to add comments to this thread. Hang in there as soon as I take care of my business at home and chores and such I will continue the conversation. Do not worry I am not offended or angry. I just got a lot going on. The math stuff by the way is a real good idea. I am excited about it. I think I now see where you are going with it.

[DanLanglois]

The math stuff by the way is a real good idea. I am excited about it. I think I now see where you are going with it.

Okay, then I'll reiterate something. This is you:

I am going to say this clearly and succinctly. I have never seen a statement more incorrect than this one. “Products, ratios, powers, exponential, other functions, trigonometric functions, logarithms, have no physical correspondence in operations involving actual physical quantities.”

I'll stand by that quote. This is me:

Not defined in terms of physical operations are: product, ratio, power, logarithmic, exponential, trigonometric, other special functions of physical quantities.

I'll add, that this is not government work, here, we're not trying to hit the side of a barn with a basketball, I'm making a fastidious, technical point, I'm not trying to convey, informally, some attitude that I don't like being told that 2+2=4, why can't 2+=5? You're not the boss of me, I do what I want WHATEVER!! Not what i'm trying to say.

For clarity, I'll even rephrase again--how about like this:

Products, ratios, powers, exponential, other functions, trigonometric functions, logarithms, *are defined for numbers*, but have no physical correspondence in operations involving actual physical quantities.

What is the upshot of this? Well, you take c^-2 = μ0ϵ0 (permiability times permittivity), and add that:

So what I am saying is if this equation explains the speed of light in the medium of space and the values of both permeability and permittivity are not zero, space must be a physical object.

Okay, and then to prove it, or illustrate the point, you add this:

Plug in the number zero for both permittivity and permeability. 1 divided by 0 = infinity. The speed of light now becomes infinite. Think about this. This makes sense.

Okay, we have this: c^-2 = μ0ϵ0 (permiability times permittivity)

And we plug in the number zero for both permittivity and permeability:

c^-2 = 0*0

1 divided by 0 = infinity. Supposing that to be the case, sort of, what are you doing here, something like this?:

1c^-2 = 0*0

1/(infinity)^2=0*0

Right? Not right, something's off, here. But, in fact, you started with a slightly different equation:

c = 1/(μ0ϵ0)½

From here, you figure that:

c = (1/0*0)^½

And you get: c = 1/0

And, since 1/0 = infinity, sort of, therefore c = infinity. Which is different than 1/(infinity)^2=0*0 or is it? I guess that would mean the same thing, but what about that square, or square root business in there, are we tripping over that, handling that correctly? Let's start over. Here is your exact formula:

c = 1/(μ0ϵ0)^½

or, c = 1/(permiability times permittivity)^½

Here is what you are doing wrong--this formula should display 'c' on both sides, before you start manipulating it. I mean, something like this:

1c = 1/(permiability/c times permittivity/c)^½

Or, 1=1.

Now, your notion of setting permiability and permittivity to zero, well, we'd get something like this:

c = 1/(0/c times 0/c)^½

Somehow you are convinced that this means c = infinity because 1/0 = infinity. But, plug infinity into that formula for c, and you get this:

infinity = 1/(0/infinity times 0/infinity)^½

And c isn't even in the equation anymore. But the equation is fine, it's better than fine, it works for our own universe, is it were. Look at your inferences from this again: ' If space were equal to nothing there would be no value for distance. Since D=Rate * Time. Then Distance / time =Rate. Since there is no distance it will always take zero amount of time to traverse zero amount of distance. Once again you get infinite light speed. These formulizations clearly prove this is not the case.'

Okay, space is equal to nothing, there is no value for distance, it will always take zero amount of time to traverse zero amount of distance. That is all true of our universe ('space is equal to nothing', that's true of our universe).

What do these formulazations clearly prove, then, what is 'not the case'?

Look at this equation again, which I think I get from you:

infinity = 1/(0/infinity times 0/infinity)^½

Well, okay, while we're at it, it's also true that:

1 = 1/(0*infinity)

or,

0 = 1/(1*infinity)

So, looking at this again: c = 1/(0/c times 0/c)^½

Set c = 1 and you get: 1 = 1/(0/1 times 0/1)^½

Set c= infinity and you get: infinity = 1/(0/infinity times 0/infinity)^½ = 1/0

Set c = 0 and you get: 0 = 1/(0/0 times 0/0)^½ = 1/(infinity*infinity)^½

So, looking at this equation: c = 1/(μ0ϵ0)^½

What is this telling us about the speed of light? That it is 0. That it is 1. That it is infinity. In any case, the formula works. What have I proven? I don't think it's that 'space must be a physical object.'

Probably, it's pretty hard to follow these spitballed formulas, or at least to follow how it could possibly be correct to do any of this, but that's my point. I see you doing this. To you, perhaps, these all looks as proper as the queen of england. It ain't correct. But I'm willing to avoid doing it, if you are. What am I doing wrong, if anything, in your view?

-- Updated August 11th, 2012, 10:37 pm to add the following --

Hi, stop me before I successfully immanentize the eschaton. Or don't, maybe that's a debate that you feel you can afford to lose. But remember I'm trying to relate all this back to my point, that:

Products, ratios, powers, exponential, other functions, trigonometric functions, logarithms, *are defined for numbers*, but have no physical correspondence in operations involving actual physical quantities.

And, more simply, that to do dimensional analysis, you have do handle physical quantities, and equations, properly. And furthermore, not only do you take yourself do be ahead of this game, you are doing what I might dub 'advanced dimensional analysis', which you dub 'realism'. I don't think that it is 'realism', to forget, thatdimensional analysis must be based on a complete set of independent quantities that determine the quantity of interest. Or, all the quantities whose values determine the quantity of interest must be included, regardless of whether some of them happen to be the same values in the problems that are of interest.

Specifically, omitting even one independent variable can fatally damage the analysis, and I don't think that you have seen this. Backing up considerably, I'll hold forth a bit in conclusion, about this term 'dimensional analysis'. Dimensional analysis reduces the number of variables that must be specified to describe an event. This often leads to an enormous simplification. Also, dimensional analysis provides a similarity law for the phenomenon under consideration. What do I mean? Similarity, in this context, implies a certain equivalence between two physical phenomena that are actually different.

Or I might try putting it this way:

Premise: The form of any physically significant equation must be such, that the relationship between the actual physical quantities remains valid, independent the magnitudes of the base units.

Conclusion: Dimensional analysis derives the logical consequences of this premise.


A physical equation must be dimensionally homogeneous. An important consequence of dimensional homogeneity is that the form of a physical equation is independent of the size of the base units.

What I really want to hear from you is a clear position on why you think that physical properties of space do not prove that space is a real independent physical object.

How formally, are you using this term 'physical properties'? The physical properties of an object are traditionally defined by classical mechanics. You leaped to offer permeability and permitivtity as examples. However, the point here, I think, is that often, it is difficult to determine whether a given property is physical or not, and the confusion between perception and physical properties is increased by the existence of numeric scales for many perceived qualities.

Also, an 'intensive' property does not depend on the size or amount of matter in the object, while an 'extensive' property does. And, in addition to extensiveness, properties can also be either isotropic if their values do not depend on the direction of observation or anisotropic otherwise.

Physical properties are referred to as observables.

Here is an Einstein quote, [/quote]
To deny the ether is ultimately to assume that empty space has no physical qualities whatever..Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. [/quote]

Your loving this, but Einstein added that 'The idea of motion may not be applied to it.' Which I take it, is where you think he was wrong. He does say that:

The ether of the general theory of relativity is a medium which is itself devoid of all mechanical and kinematical qualities, but helps to determine mechanical (and electromagnetic) events.

You probably don't like that much better. I'm not sure, you may consider yourself to be in agreement with that. Perhaps you believe this much, that in classical physics, the empty space has no properties or structures. But, space and time change under the effect of the contained mass and energy. I, however, am a little unhappy with, well, putting it that way. There are equations describing the physical properties of moist air, but what Einstein has in mind, when he speaks here, of the ether, as a medium having 'physical qualities', is how tensors characterize the properties of a physical system. This is not like saying that space has a length. That space has a boiling point, a melting point.

In my preferred parlance, perceptions are fundamentally different from physical properties. Am I, then, 'not a realist'? I am at least not a realist about giving you so much homework to do. But, for example, the colour of a solution is not a physical property.And, the confusion between perception and physical properties is increased by the existence of numeric scales for many perceived qualities.

What is a 'physical quantity'? There are physical quantities that can be classified as neither 'extensive' nor 'intensive', for example angular momentum, area, force, length, and time. This is not like physical properties, which can be 'intensive' or 'extensive'. Physical properties are referred to as 'observables'. What about 'physical quantities', that are not 'physical properties', are they, then, 'observables'? Well, physically meaningful 'observables' must also satisfy transformation laws which relate observations performed by different observers in different frames of reference. Let us consider again these physical quantities, angular momentum, area, force, length, time. Are these, physically meaningful 'observables'?

What I really want to hear from you is a clear position on why you think that physical properties of space do not prove that space is a real independent physical object.

I allowed that '(W)hat Einstein has in mind, when he speaks here, of the ether, as a medium having 'physical qualities', is how tensors characterize the properties of a physical system.' The idea, is that, tecause they express a relationship between vectors, tensors themselves must be independent of a particular choice of coordinate system. Vectors and scalars themselves are also tensors. There are several approaches to defining tensors. There are a number of basic operations that may be conducted on tensors that again produce a tensor.

We definitely can't understand Einstein's theory of gravity without using tensors (many of them), but also, you can't align the wheels on your car without using a tensor (the inertia tensor). A tensor is a particular type of function.

What, is the 'physical' significance of tensors? To me, it is this,when the laws of physics are expressed in a manner which makes their invariance under various transformation groups manifest, then they tend to take a particularly simple form. In general, the larger the group of transformations, the simpler the form taken by the laws of physics. Tensors are of primary importance in connection with coordinate transforms. They serve to *isolate* *intrinsic geometric and physical properties* from those that merely depend on *coordinates*. It follows that the laws of physics are expressible as interrelationships between tensors.

Note, in special relativity, you are only allowed to use inertial frames to assign coordinates to events. In general relativity the laws of physics are required to exhibit tensor behaviour under all non-singular coordinate transformations.

There are different ways of viewing a non-singular linear transformation Y = AX.

1. Y = AX can be viewed as a change of basis – a change to a basis whose basis vectors correspond to the columns of matrix A. In two and three dimensional space this corresponds to a change to a different coordinate system, a rotated coordinate system (the transformation Y = AX involves no translation).

2. You input a point and it outputs another point. In this way, matrix A maps the points of some figure in space into some other figure in space.

Now let us consider, as you suggest, the laws of electromagnetism. We wish, shall we say, to demonstrate that these laws are compatible with the relativity principle. In order to achieve this, it is necessary for us to make an assumption about the transformation properties of electric charge. The assumption we shall make, is that charge, is invariant. Unlike, say, mass. In particular, the charge carried by a particle does not vary with the particle's velocity. There are many ways of writing the laws of electromagnetism. This already tells me that there are no net sources or sinks of electric charge in nature. It is obvious from the form of these equations that the laws of electromagnetism are invariant under translations, rotations, special Lorentz transformations, parity inversions, or any combination of these transformations.

Physical phenomena are conventionally described relative to some frame of reference which allows you to *define* fundamental quantities such as position and time. I'll let that sink in, is it possible to disagree, here?

-- Updated August 12th, 2012, 2:52 am to add the following --

Put it this way, it seems obvious to me, that if one theory has a property assigned to space, there is another equally valid parallel theory that assigns that property to something other than space. I believe space is inherently unobservable. Shall we, then, nevertheless, assign any attributes to space? Other than to say, perhaps, 'the universe exists in space'. It must have measurable properties, otherwise, why need it? The key to this theory is understanding time.

[Narnug]

SNIP (and allot of it)

The key to this theory is understanding time.

I agree so much to this last sentence. In my opinion the key to understanding the whole universe lies in understanding time.

Do me a favor and have a look at this: http://onlinephilosophyclub.com/forums/ ... =12&t=6909

This might be a coincidence but I do not think so. This can so easily fit in what you have been discussing here, at least how I see it and understand it. This is all about space and time. The universe is more of a subjective "place/thing" then something solid. We only experience it as a place we could describe as a room with furniture in it. That is just because we experience time. I think that over the next 10 to 20 years we will start looking at time in a completely new way and that will allow us to evolve and maybe even reach the stars. But first thing first, understanding time is the key.

What do you think about the post in the link above? Do you "see" the connection like I do? Or do you think this is just a coincidence?

All my best

narnug

[DanLanglois]

What do you think about the post in the link above? Do you "see" the connection like I do? Or do you think this is just a coincidence?

Something is missing, and what’s missing is the “mechanism of the cause,” the logic that describes how the purported cause causes the observed effect.

"Correlation is not causation" is a statistics mantra. It was drilled, military school-style, into me as a budding statistician. Our preconceptions and suspicions about the way things work tempt us to make the leap from correlation to causation without any hard evidence.

Alternatively, I might put it this way, correlation may not imply causation, but it sure can help you insinuate it. Consider this situation: During the months of March and April, the weekly weight increases of a puppy in New York were collected. For the same time frame, the retail price increases of snowshoes in Alaska were collected. The data was examined and was found to have a very strong linear correlation. So, this must mean that the weight increase of a puppy in New York is causing snowshoe prices in Alaska to increase.

While we're on the subject of time, I'll add that one area in which we humans are particularly tempted to make the leap from correlation to causation is around time.

The universe is more of a subjective "place/thing" then something solid.

Well, I don't rattle on about tensors, because I'm trying to make this point, not exactly. I do not for a moment doubt that we know a great many things about objects external to ourselves. I post about relativity, because I want to accommodate and explain the success of physics--I mainly just am learning about it, it's a great time-killer, the best. This stuff is fascinating to me.

[Narnug]

Yes DanLanglois, this is fascinating.

I do agree that weight of puppies and what boots are worth does not connect.

This is kind of the response I have had so far. And I respect it. I do not agree to it in this case and I have my reason.

I can by no means argue for a connection between the puppies and boots. But I can argue for a connection between time and how we observe/experience our surroundings, in this case the sun. I found this information after I found understanding, correct or not. I did not find the information first and then make a theory around it.

In relativity your time slows down if you travel fast. I want to say that speed has nothing to do with time slowing down. It is using energy that slows time down. Some want to define time as a motion. To "create" a motion you have to use energy. I want to define it as a sequence since I see it as a sequence of motions that can interact.

Using energy=time. Using energy=slowing down according to your surroundings. Slowing down here on Earth=seeing the sun "going faster". This is where my understanding of relativity is. This is just an "introduction" on how I see this. I often end up on a monologue, do not know if it is because my views are "primitive" or if nobody understands me, lol. Well either option I cant care to much about it. Just like to throw in my view now and then if I dont fit into the discussion.

Amb

narnug

[DanLanglois]

I want to say that speed has nothing to do with time slowing down. It is using energy that slows time down. Some want to define time as a motion. To "create" a motion you have to use energy.

Actually, I'm sort of with you so far on this. About, it being 'using energy' that slows time down. The only thing that travels at the speed of light is kinetic energy. I look at e=mc^2, and I look at mass as potential energy, I'm not sure how I'm wrong. You eat every day, the food doesn't all come back out, your body is a machine that consumes mass and transforms it into movement. But in the universe, there is conservation of energy, of course a big principle of physics. If you look at the formula for energy, which is measured in joules, there is time and length in that formula. I see conservation of energy, here. Not speed, you say, but okay, acceleration, it's like giving some 'time' back--there must be conservation of energy--again, can we see the formula for energy in these terms? Also, I puzzle over the assertion that there is no time passage at the speed of light. Suppose, that this is because photons with no 'rest mass', no potential energy, are all kinetic energy, all wave, and in becoming a particle, there's a process of 'storing time up'--energy is 'configured', and we have mass. But that energy can be released again, how? Movement--which slows time down.

Using energy=time. Using energy=slowing down according to your surroundings. Slowing down here on Earth=seeing the sun "going faster". This is where my understanding of relativity is. This is just an "introduction" on how I see this. I often end up on a monologue, do not know if it is because my views are "primitive" or if nobody understands me, lol. Well either option I cant care to much about it. Just like to throw in my view now and then if I dont fit into the discussion. narnug

Well, you're probably pleased w/my comments, we can 'often end up on a monologue', together. I'm not sure about '(S)lowing down here on Earth=see the sun 'going faster.' I mean, I'm not sure how we get into economic recession and solar activity, from this. Sounds rather like 'what's your sign?', to me. But to roll w/this, what about the rest of the sky? If we have an economic boom, are there also a bunch of supernovae? I'm afraid you might like this idea too much. I live in California, I know this kind of patter, it's useful, if you want to get laid.

[Narnug]

I have to read the first part of your post a little better to answer that, allot in there.

Regarding the second part I can say this.

First of all I am married, so getting late is not what drives me regarding this (written with a smile).

I can so understand that this is hard to understand, how our time can be different from our surroundings.

Lets say for a minute that using energy slows time down. Then lets imagine that you are in a gymnastic hall. In the ceiling there is a light shining constantly. You start to run in circles in the gymnastic hall. Your heart uses more energy because of that and beats faster. If using energy slows down time your heart changes its speed of time according to the light in the ceiling. If your heart could "see" then it would see the light in the ceiling "behaving" faster. Your heart and the light in the ceiling are both a part of a larger time "zone" which is defined as the gymnastic hall. Your heart and the light in the ceiling can have their own speed of time within that ruling time. That is what is so hard to "see" (or that I am just making it up).

I am talking about the light/light bulb in the ceiling, not the light coming from it. Light it self does not obey to this. Like relativity explains it always seems to travel at the same speed no matter the speed of the observer. (if the light bulb in the ceiling would "behave" in any way, this is just to explain, a heart can't see either)

Being stuck with this might be a wish of some kind. I have thought about things like these long enough to learn to criticize my self. Till I find a flaw in my thoughts or a proof that this might not be how time works I will look at it as a possibility. This is the best explanation I have "found" till now, the only one which can tie up all ends.

I will "study" the beginning of the reply.

Amb

narnug

[DanLanglois]

Your heart and the light in the ceiling can have their own speed of time within that ruling time. That is what is so hard to "see" (or that I am just making it up).

Or, there is no 'ruling' time, I'm toying with this thought, that there is only a postulate that I am not moving, something outside me is moving, or, alternatively, I am moving, something outside me is not moving. Either way, you are interacting with something external. If you look at something outside you and say, it is not moving, then at that spot, you see time pass. You see a material object at rest, you are seeing time pass, at that spot. And, if you look something outside you and say, it is moving, then for you, time passes--you are not moving, except that you are 'moving in time'. What is really moving is what you see moving. One cannot, however, simply say, here that 'movement is time', or that 'the speed of light is time', rather, there is a difficult concept of a relation between time and distance?

I am talking about the light/light bulb in the ceiling, not the light coming from it. Light it self does not obey to this. Like relativity explains it always seems to travel at the same speed no matter the speed of the observer.

Ah, well, yes, maybe I see where you are going with this, yep..it's a beguiling intellectual exercise.

[Wanderer101]

For Danlanglois,

Well I was going to respond to some of the other things you said before this last comment but you went ahead and did the math and made your points so I’ll skip that one and respond to your latest post.

Products, ratios, powers, exponential, other functions, trigonometric functions, logarithms, *are defined for numbers*, but have no physical correspondence in operations involving actual physical quantities.

I think that is said much clearer. I really get what you are meaning. Unfortunately I still believe it is a very incorrect philosophical and logical idea. Here is why I say this. We do indeed have a basic philosophical difference in what we believe. You think that numbers and math are just an invention from the mind of man. I agree with that. The difference in what you and I believe is fundamental and it occurs in the next statement I make. I believe that even though mathematics is an invention of the mind it is also a language that when properly devised works for explaining physical objects. In other words mathematics has a deeper meaning and connection to nature than you and a lot of other people who are non realists can believe. This idea is most difficult to put to words.

I look at mathematics as more of a discovery of truth than an invention of man. It is the language that explains the physical laws of the Universe and therefore has a direct connection to that which is physical and real. We use math to help us describe and comprehend the observable objective Universe.

Now for the math... c = 1/(μ0ϵ0)½

I substitute the number zero for both permeability and permittivity. Before I proceed I want to point out a difference in thinking between you and I. To you the number zero is just a number and it has no connection to anything physical. On the other hand to me the number zero represents in this case a deeper meaning. Zero means the absence of a value, a physical value for the terms in this case which are permeability and permittivity. You want to think in terms of abstract philosophy of numbers. I on the other hand am connecting the numbers as our representation to real physical objects and properties of space. The equation means more to me than it does to you. You believe the equation in your words to mean this. “ Products, ratios, powers, exponential, other functions, trigonometric functions, logarithms, *are defined for numbers*, but have no physical correspondence in operations involving actual physical quantities.”

What is the point of making equations describing things in nature if in fact the numbers and operations actually have no connection to nature which is the thing we are describing with these equations?

So now back to the equation. We now have c=(1/0)½. Oh, by the way infinity to any power is still infinity. So we still get c = infinity. We should agree on this. For some reason you just end up and replace C with infinity and say we have a great working equation. You miss the entire point of mathematics by drawing this incorrect analysis. The equation is in reality broken now. First of all you just cannot replace a constant in nature with another number. That’s bad form. This is what you should have gotten from the point I was making. You just cannot replace C with a value of infinity. Sorry but mathematics has rules. So you see the equation in truth is not fine, and it's not better than fine. It is broken and that tells us that something is wrong. We get meaning from equations when the math is done right and it’s properly interpreted. The truth is only specific values for permeability and permittivity make this equation match what we experience in reality. That of course is the actual speed of light.

C is not equal to infinity. This is clearly how the interpretation of the equation should be taken. The equation is not okay now since we substituted the value of zero for both permeability and permittivity. You should have been able at this point to make the cosmic connection that these to quantities cannot be zero and have the speed of light remain the speed of light, which is a constant of nature. In physical reality the speed of light is never infinite.

Mathematics has meaning and it talks to us when we clearly understand what it really means. Equations have a direct correspondence to what is real and physical in nature and all of our experience and experiments confirm this point of view.

DanLanglois you are over thinking this problem. Consider this simple question. Why is the speed of light the specific value that it is? That is what this discussion is really all about. This is what I want you to do. In your next post, just try and answer this question first before you take on the rest of my post. You can use any mathematics you want. Oh, by the way don’t bother bringing up that we humans chose the units of measurement and therefore everything is relative to our culture and is meaningless. We have already heard that argument and it is irrelevant. What is important is that the rate at which light moves corresponds to a very specific rate of motion and the number it is not zero nor is it infinity it is a number somewhere in between those two. No matter where you go in the Universe and no matter what mathematical system you choose to use when you transform between the 2 systems the number you get will be the same speed. Stop and think about this. Why is the speed of light it the specific value that it is?

What have I proven? I don't think it's that 'space must be a physical object.

Sorry my good friend but that is definitely not what you have proven. Hey but on the bright side you did help me prove that space does equal something.

What am I doing wrong, if anything, in your view?

Well since I think that your logic and math were not correct according to my reckoning I guess that be my reply. I do appreciate your efforts. This is why I like these discussions so that I can test my ideas. Had your logic been flawless I would have had to rethink my ideas but you have not convinced me to change my mind. I am very open to that happening but it never seems to happen when it comes to this subject.

Yes, You are correct in this quote I am familiar with it. It is from his speech about the Aether given at Leyden in 1920.

Here is an Einstein quote, To deny the ether is ultimately to assume that empty space has no physical qualities whatever..Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether.

Your loving this, but Einstein added that 'The idea of motion may not be applied to it.' Which I take it, is where you think he was wrong. He does say that:

First it is presumptuous to think that you know what I think in this case. Second you take a comment out of context with improper/incomplete interpretation. I don’t think he was wrong here because he was talking about motion of a constant velocity. There is another type of motion that he does speak of in the same speech. It’s funny but you managed to leave this quote out. He is talking about Mach ideas here.

Since he classes his absolute space together with real things, for him rotation relative to an absolute space is also something real. Newton might no less well have called his absolute space "Aether"; what is essential is merely that besides observable objects, another thing, which is not perceptible, must be looked upon as real, to enable acceleration or rotation to be looked upon as something real.

This is so important. Do you know why? He has noticed something that few have noticed and most still do not fully grasp. What do you think that might be? To the very perceptive this is a clue of great importance.

You probably don't like that much better. I'm not sure, you may consider yourself to be in agreement with that.

Hey, you forgot this quote right above the one you just provided.

This Space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that "empty space" in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials), has, I think, finally disposed of the view that space is physically empty.

Space is not empty according to Einstein. I agree with him.

Time for a trivia break. Do you know why the speech was made and for who the speech on the aether was really for?

I don’t expect you to buy what I say next or understand it without a great deal of explanation by me. I’ll give it a try anyway. At this time in his life Einstein was just beginning to know that there was something more to the Universal story than just General Relativity. He did not want to give it away in this speech. Gravity is a condensate of Electromagnetism and that is the Unified Field Theory.

You also forgot to include the entire quote from the same speech which by the way dramatically changes the meaning of what you were trying to convey.

Recapitulating, we may say that according to the General Theory of Relativity space is endowed with physical qualities; in this sense, therefore, there exists an Aether. According to the General Theory of Relativity space without Aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this Aether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it.

The last two lines he plays it safe and this is because of the null result of the Michelson and Morley experiment. In my opinion the jury is still out on the idea that “this Aether may not be thought of as endowed with the quality characteristic of ponderable media.”

I believe that eventually the M&M will be reversed when the experiment is done properly. Even if absolute motion relative to an aether is not detectable it still is not a show stopper. It would just mean that whatever this physical substance is you cannot detect motion relative to it. Okay, so what. That on its own still does not disprove the existence of an aether.

Physical properties are referred to as 'observables'.

Before I comment more on this statement please define what you mean by observables. I believe this definition is somewhat limited and therefore maybe unacceptable. I read through your next several paragraphs with no problem. Then I came upon this statement. You are speaking about charge being Invariant.

This already tells me that there are no net sources or sinks of electric charge in nature. Please explain what you mean by sources or sinks of electric charge.

Moving on further in the discussion. Not clear on what you are saying here as it does not make sense.

I said this: Look at your inferences from this again: ' If space were equal to nothing there would be no value for distance. Since D=Rate * Time. Then Distance / time =Rate. Since there is no distance it will always take zero amount of time to traverse zero amount of distance. Once again you get infinite light speed. These formulizations clearly prove this is not the case.'

You said this: Okay, space is equal to nothing, there is no value for distance, it will always take zero amount of time to traverse zero amount of distance. That is all true of our universe ('space is equal to nothing', that's true of our universe). Huh? What? Are you making a joke here? Please clarify.

And finally you bring up time. That’s a very big topic that can fill up a book not sure if we need to bring it up in this discussion. At some point we could start another topic for the discussion of time as it is fascinating topic.

[DanLanglois]

We do indeed have a basic philosophical difference in what we believe. You think that numbers and math are just an invention from the mind of man. I agree with that. The difference in what you and I believe is fundamental and it occurs in the next statement I make.

Actually, I'm not positive what 'just an invention' means. The 'invention'/'discovery' distinction here, is not simple, for me.

I believe that even though mathematics is an invention of the mind it is also a language that when properly devised works for explaining physical objects.

Very carefully worded, but 'explain' is not careful enough for me, perhaps. 'Describe', has different connotations.

In other words mathematics has a deeper meaning and connection to nature than you and a lot of other people who are non realists can believe.

Who are these other people and what is a non realist?

I look at mathematics as more of a discovery of truth than an invention of man.

>sigh< There is a philosophical perplexity in the matter of 'invention'/'discovery', in my view. I don't think one can take sides in that opposition, one must tread carefully here, in describing mathematics. You don't, I suspect, actually understand my views. I'll probably agree with everything that you say about mathematics is some way cool stuff etc.

It is the language that explains the physical laws of the Universe and therefore has a direct connection to that which is physical and real.

Mathematics is some way cool stuff etc.

We use math to help us describe and comprehend the observable objective Universe.

etc.

Now for the math... c = 1/(μ0ϵ0)½

To you the number zero is just a number and it has no connection to anything physical.

Okay, what is the number zero, to me? This question is a great introduction to mathematical philosophy. If we can make progress here, that is not small, it's, like, well, it's a lot. What is 'just a number'? As opposed to what? No 'connection to anything physical'? Then we agree, that the number itself is not physical, what then, is the nature of this connection? Not 'no connection', not my position. What connection? Tell me please, what is the connection? My own answer would get rather involved, but not 'no connection'.

On the other hand to me the number zero represents in this case a deeper meaning. Zero means the absence of a value, a physical value for the terms in this case which are permeability and permittivity.

Zero is a value, am I quibbling? How much money is in my bank, zero. But also we're bringing up permeability and permittivity. As 'terms'. Okay, well, I'm concentrating on your point..

You want to think in terms of abstract philosophy of numbers.

Do I like the sound of this? Shall we say, that I want to think. Give me something in which to think in terms of.

I on the other hand am connecting the numbers as our representation to real physical objects and properties of space.

I know that it might seem like we're ready to play basketball, and I'm like, wait, how does one tie one's shoes properly? But walking through that sentence, I see 'our representation', kind of a mouthful. I see 'properties of space', of course I don't really know how to accept that, there are some technical issues, what is a 'property'? I asked 'what connection?', and now it's 'I am connecting the numbers'. What are you doing, precisely? But let's get your point out..

The equation means more to me than it does to you. You believe the equation in your words to mean this. “ Products, ratios, powers, exponential, other functions, trigonometric functions, logarithms, *are defined for numbers*, but have no physical correspondence in operations involving actual physical quantities.”

Beautiful, that's exactly what I believe the equation to mean, in my words. I note that there are no actual physical quantities in that equation. c = 1/(μ0ϵ0)½

Let's walk through some terms, consider a feature, a noticeable part of something. What do you notice about the line? Then, consider a characteristic, a typical feature of something. What is characteristic of the vehicle? Consider a property, something that gives an object its characteristics. What do you notice when a piece of rubber band is pulled? What is physical, something that can be seen? Felt? Not imaginary, right? And thus can be described in terms of what you observe. Or, perceive. You can feel the effects of a force as you stand at the edge on a merry-go-round.

What is a physical property, then? Now, we are talking about something composite, we've considered properties, we've considered what is physical, what is a physical property? First, some easy examples. Length, mass, color, temperature, solubility, resistivity. A physical property is measurable. Or, perceived, at least. Is that good enough for now, I'm not sure, on what is a physical property.

There are mechanical properties, electrical properties, thermal properties, optical properties.

What is a quantity? Something that can be quantified. We give a number to it. You 'connect the numbers'.

What is a physical quantity? A physical quantity is a physical property, that can be expressed in numbers.

“ Products, ratios, powers, exponential, other functions, trigonometric functions, logarithms, *are defined for numbers*, but have no physical correspondence in operations involving actual physical quantities.”

c = 1/(μ0ϵ0)½

What is the point of making equations describing things in nature if in fact the numbers and operations actually have no connection to nature which is the thing we are describing with these equations?

Excellent question, you really would like to know?

What is a system of units? What is a meter? A kilogram? A second? A foot? A pound?

Base physical quantities are expressed in base units. I've posted a bit, about base/derived. It's a big deal, you want to slow down here, I'm not being figurative, there are base physical quantities, which are described in base units, and there are derived physical quantities. How are they described? This is something that you need to know, and even, that you needed already to know, before you tried to get a handle on my wacky math philosophy. I keep saying that there is a matter of technique here, of competence, that these are not my ideas, I say a lot about dimensional analysis. You don't, I'm here to inform you, have the luxury of going through life with any opinions about physics, if you're not a bigger expert than me on these very issues. Which, are you? Don't blame the messenger. This is what I have to say. Dimensional Analysis. It's a field of math. Spend a few months on it, and you still won't be any kind of expert. Your days of winging it without knowing any dimensional analysis, are over. Right? Because your interest is authentic. Correct? You're really for real, man, this isn't a game, it's serious business. Fine, I believe you.

Then, what is a base quantity, what is a base unit, what is a derived quantity, and etc., specifically, how are derived quantities expressed? Live it. Know it. Tell me the answer. Get it right. The questions, will get harder. That is the relationship that we have. I, at least, am serious about getting to where we are with this stuff--I, at least, think it's interesting, and I'm willing to learn about it. About what? Dimensional Analysis. Tell me something that I don't know about Dimensional Analysis. It's a real, actual field of math, that you need to be more of an expert than me on. I'm a broken record, get into Dimensional Analysis, that's our song. 'You're some kind of non-realist!' my reply: 'Dimensional analysis'. 'I believe that there is meaning in this equation!' my reply: 'Dimensional analysis'. Doesn't matter if it takes you 5 years, wouldn't kill you to take an hour or 90 minutes, might not help much, but you Will do this, before we move on. Dimensional Analysis. What's the other part? Dimensional analysis. Oh, and btw about infinity, infinity to any power is still infinity. Is that, then, Dimensional Analysis?

So now back to the equation. We now have c=(1/0)½. Oh, by the way infinity to any power is still infinity.

Oh, we've mastered zero, now I'm learning about infinity. Infinity to any power is still infinity. This is an exciting moment, probably for the first time in my life I'll be dealing with infinity. Where did you learn, that infinity to any power is still infinity. Seems logical to you? I insist that you tell me something edifying, about Cantor and cardinality, before we proceed. Who was he? Why is he famous? I don't require a doctoral dissertation about it. You want to tell me something that I don't know, let's start with telling me something that I do know. Who was Cantor, why is he famous?

Sadly, on the infinity discussion, I'm calling the game, we're done. There is only one way that you can get me to read the rest of your post. This is a homework assignment. Read about Cantor, paste something, one sentence, about who he is and why he is famous. And be GRATEFUL, that I asked you to do this.

Cheers, allthebest.

-- Updated August 13th, 2012, 3:39 am to add the following --

I was in a bit of a snit, but have read some more of your post, and I have to admit, you make a simple request here. Especially, why I want to take a whack at this, is your interest in the Einstein quotes, especially where you have Einstein uttering the word 'homogenous'..

Your simple request:

Consider this simple question. Why is the speed of light the specific value that it is? That is what this discussion is really all about. This is what I want you to do. In your next post, just try and answer this question first before you take on the rest of my post..Why is the speed of light the specific value that it is?

In my view, it is clear, that when wave meets another medium which has different strength and pattern of M&E field, wave travels according to the M&E field of the medium. We agree on this. I imagine, then, that everything rides on a notion of what wave requires in space, this 'virtual medium'. What about space? Why, exactly, is it, that the traveling speed of wave is the speed of light, c. My answer, is that I consider that wave possesses the magnetic and electric components.

This Space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that "empty space" in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials), has, I think, finally disposed of the view that space is physically empty.

Space is not empty according to Einstein. I agree with him.

I have extreme patience for going through this Einstein stuff, but I don't really think I would have put it the way that he does here. The 'empty space' that he is talking about, is plain-vanilla, Euclidean, 3-dimensional empty space, like in the room that you are sitting in, height, width, depth, the lines are parallel, the curves are eh, curvy. And then, well, no, it turns out that he's not talking about 'space', when he says space, or even 'empty space', no. By 'space', by 'empty space', he means 'empty space in its physical relation'.

Okay, let us walk through this, I want to sit with this. What is 'empty space in its physical relation'? That is not space. That is some mathematical construct, as is made clear by Einstein's comments that it is neither homogenous nor isotropic. As, what do these terms mean? I maybe am being presumptuous, I think you'll be delighted to learn that I know exactly what 'homogenous' means, as Einstein is using the term here. I'm a little disappointed, that you offered this quote without leaping to define it for me, I do hope that you haven't simply glossed over these math terms, assuming that it's not necessary to THROTTLE the MEANINGS HERE to the GROUND. You assumed that I would know this? But, how many people know something like this?

Einstein is referring to homogeneous coordinates, introduced by Möbius. They make calculations of graphics and geometry possible in projective space. I might add that homogeneous coordinates are a way of representing n-dimensional coordinates with n+1 numbers. In brief, we're familiar with how the cartesian coordinates of a 2d point can be expressed as (x, y). But, what if this point goes far away to infinity? The point at infinity would be (infinity,infinity), and it becomes meaningless in Euclidean space. The parallel lines should meet at infinity in projective space, but cannot manage it, in Euclidean space. What do to about this, what to do. How to solve this issue.

To make 2d homogeneous coordinates, you simply add an additional variable, into existing coordinates. Therefore, a point in cartesian coordinates, (x, y) becomes (x, y, w) in homogeneous coordinates. And x and y in cartesian are re-expressed with x, y and w in homogeneous as: x = x/w y = y/w

For instance, a point in cartesian (1, 2) becomes (1, 2, 1) in homogeneous. And now, if a point, (1, 2), moves toward infinity, it becomes (infinity,infinity) in cartesian coordinates. And it becomes (1, 2, 0) in homogeneous coordinates, because of (1/0, 2/0) = (infinity,infinity).

So, for review, we ran into an issue, something to do with how two parallel lines can intercept, and Euclidean geometry therefore now being approached as a subset of projective geometry.

Are we clear, though, on why is it called "homogeneous"? Homogeneous coordinates are scale invariant. Like, the points (1, 2, 3), (2, 4, 6) and (4, 8, 12) correspond to the same Euclidean point (1/3, 2/3).

I have a handle on this stuff, because homogeneous coordinates are very useful and fundamental concept in computer graphics, such as projecting a 3D scene onto a 2D plane. But back to Einstein, and his ' "empty space" in its physical relation is neither homogeneous nor isotropic.' What does he mean, not homogenous. He is talking about the relation of Euclidean space to projective geometry. I don't think he's got a very perspicuous clear view, of what a mathematician makes of this, as opposed to an admittedly brilliant physicist. He of course had some math skill, and certainly ran in circles with others who did as well. But also, it's a few generations ago. They didn't have computers, some recent progress in math hadn't really settled in people's minds, hey he had lots on his plate. I don't view math the way he did, when he makes these kinds of comments. Not to say that he wasn't a genius. But I'm glad that you posted this quote, for me it is clear that Einstein is confused, here, talking about how space can be attributed many qualities, how space has a specific geometry that will be determined by experiment.

I don't mean to be smug about it, I'm not Einstein, but it's the 21st century, it's so much easier to get a grip on what is going on with projective geometry, if you have some experience with computer graphics. Einstein is, again, talking about the relation of Euclidean space, which he kind of confuses in a Newtonian way, here, with space out there, in the external world. And then, he is saying that it is not homogenous. What is not homogenous? If you treat Euclidean space as being homogenous, then it's homogenous. Call it a subset of projective geometry. Projective geometry has axioms, everybody gets very confused about axioms. Does 'space', look up in the sky at space, does 'space' have 'axioms'? Close your eyes and put some effort into visualizing 'space'. Are you staring at a list of axioms? It's a real intellectual adventure, sorting these issues out, philosophically, but I disagree with Einstein even trying to make a determination as to whether space is or is not homogenous.

Whether it is or it isn't, is a purely methodological distinction. The idea here in Einstein's mind is kind of like one notion is true and the other is false. Is space homogenous or is it not? In my mind, both propositions stand or fall together. They're both good, or neither are good. The question is meaningful, or it isn't, shall we treat space as being homogenous or not. The real issue being, what makes this talk meaningful in the first place? That we're even discussing it meaningfully, that there's something 'objective' to the question, I say space is homogenous, you say it isn't, we go back and forth about it, that means that we're both right. What enables this kind of debate? Space has no specific "geometry."

I'm not optimistic about getting any of this notion across, let's move on to 'isotropic'. "Empty space" in its physical relation is neither homogeneous nor isotropic. I don't know, maybe I'll let you get in on the fun? You can believe that I know what this means, that I have my opinion in which you are hardly interested. Do you know what this means--'isotropic'?

Hit me.

You also forgot to include the entire quote from the same speech which by the way dramatically changes the meaning of what you were trying to convey.

Recapitulating, we may say that according to the General Theory of Relativity space is endowed with physical qualities; in this sense, therefore, there exists an Aether. According to the General Theory of Relativity space without Aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this Aether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it.

No, I've seen this stuff, I have in mind, what Einstein is saying here..

The last two lines he plays it safe and this is because of the null result of the Michelson and Morley experiment. In my opinion the jury is still out on the idea that “this Aether may not be thought of as endowed with the quality characteristic of ponderable media.”

Yes, well. Um. I'm not trying to win a debate. I figured as much, about your views.

I believe that eventually the M&M will be reversed when the experiment is done properly. Even if absolute motion relative to an aether is not detectable it still is not a show stopper. It would just mean that whatever this physical substance is you cannot detect motion relative to it. Okay, so what. That on its own still does not disprove the existence of an aether.

I don't know how to conceive of the M&M being reversed, are you doubting the length contraction equation? I'll suppose that you are doubting the interpretation.

Please explain what you mean by sources or sinks of electric charge.

I'm making out w/the principle of conservation of energy, that's all, pretty much. What is most basic, most fundamental in Physics? What is the program? I take it to be principles, the principle of conservation has a few sub-branches, there is the principle of conservation of energy. Energy has been conserved, since the big bang. I don't take it as being really possible to transcend the way that the subject, the field, of physics, has been conceived, without it not being physics anymore. What defines physics? Where does the rest of it come out of? The equations, all this jazz. A few principles are being researched. The principle of conservation of energy is important. When I look at time, when I look at how energy is measured, when I look at mass, at all these equations, note that an 'equation' has an 'equality' in it. That's about conservation. That's the big epiphany. Why is the speed of light constant? Because everything else is a degeneration, a storing up of potential energy, by configuring kinetic energy. Which, is not really an explanation--I guess I'm saying that I don't look to Physics for explanation, I look to it for description of conservation of energy.

-- Updated August 13th, 2012, 6:17 am to add the following --

We do indeed have a basic philosophical difference in what we believe. You think that numbers and math are just an invention from the mind of man. I agree with that. The difference in what you and I believe is fundamental and it occurs in the next statement I make.

Actually, I'm not positive what 'just an invention' means. The 'invention'/'discovery' distinction here, is not simple, for me.

I believe that even though mathematics is an invention of the mind it is also a language that when properly devised works for explaining physical objects.

Very carefully worded, but 'explain' is not careful enough for me, perhaps. 'Describe', has different connotations.

In other words mathematics has a deeper meaning and connection to nature than you and a lot of other people who are non realists can believe.

Who are these other people and what is a non realist?

I look at mathematics as more of a discovery of truth than an invention of man.

>sigh< There is a philosophical perplexity in the matter of 'invention'/'discovery', in my view. I don't think one can take sides in that opposition, one must tread carefully here, in describing mathematics. You don't, I suspect, actually understand my views. I'll probably agree with everything that you say about mathematics is some way cool stuff etc.

It is the language that explains the physical laws of the Universe and therefore has a direct connection to that which is physical and real.

Mathematics is some way cool stuff etc.

We use math to help us describe and comprehend the observable objective Universe.

etc.

Now for the math... c = 1/(μ0ϵ0)½

To you the number zero is just a number and it has no connection to anything physical.

Okay, what is the number zero, to me? This question is a great introduction to mathematical philosophy. If we can make progress here, that is not small, it's, like, well, it's a lot. What is 'just a number'? As opposed to what? No 'connection to anything physical'? Then we agree, that the number itself is not physical, what then, is the nature of this connection? Not 'no connection', not my position. What connection? Tell me please, what is the connection? My own answer would get rather involved, but not 'no connection'.

On the other hand to me the number zero represents in this case a deeper meaning. Zero means the absence of a value, a physical value for the terms in this case which are permeability and permittivity.

Zero is a value, am I quibbling? How much money is in my bank, zero. But also we're bringing up permeability and permittivity. As 'terms'. Okay, well, I'm concentrating on your point..

You want to think in terms of abstract philosophy of numbers.

Do I like the sound of this? Shall we say, that I want to think. Give me something in which to think in terms of.

I on the other hand am connecting the numbers as our representation to real physical objects and properties of space.

I know that it might seem like we're ready to play basketball, and I'm like, wait, how does one tie one's shoes properly? But walking through that sentence, I see 'our representation', kind of a mouthful. I see 'properties of space', of course I don't really know how to accept that, there are some technical issues, what is a 'property'? I asked 'what connection?', and now it's 'I am connecting the numbers'. What are you doing, precisely? But let's get your point out..

The equation means more to me than it does to you. You believe the equation in your words to mean this. “ Products, ratios, powers, exponential, other functions, trigonometric functions, logarithms, *are defined for numbers*, but have no physical correspondence in operations involving actual physical quantities.”

Beautiful, that's exactly what I believe the equation to mean, in my words. I note that there are no actual physical quantities in that equation. c = 1/(μ0ϵ0)½

Let's walk through some terms, consider a feature, a noticeable part of something. What do you notice about the line? Then, consider a characteristic, a typical feature of something. What is characteristic of the vehicle? Consider a property, something that gives an object its characteristics. What do you notice when a piece of rubber band is pulled? What is physical, something that can be seen? Felt? Not imaginary, right? And thus can be described in terms of what you observe. Or, perceive. You can feel the effects of a force as you stand at the edge on a merry-go-round.

What is a physical property, then? Now, we are talking about something composite, we've considered properties, we've considered what is physical, what is a physical property? First, some easy examples. Length, mass, color, temperature, solubility, resistivity. A physical property is measurable. Or, perceived, at least. Is that good enough for now, I'm not sure, on what is a physical property.

There are mechanical properties, electrical properties, thermal properties, optical properties.

What is a quantity? Something that can be quantified. We give a number to it. You 'connect the numbers'.

What is a physical quantity? A physical quantity is a physical property, that can be expressed in numbers.

“ Products, ratios, powers, exponential, other functions, trigonometric functions, logarithms, *are defined for numbers*, but have no physical correspondence in operations involving actual physical quantities.”

c = 1/(μ0ϵ0)½

What is the point of making equations describing things in nature if in fact the numbers and operations actually have no connection to nature which is the thing we are describing with these equations?

Excellent question, you really would like to know?

What is a system of units? What is a meter? A kilogram? A second? A foot? A pound?

Base physical quantities are expressed in base units. I've posted a bit, about base/derived. It's a big deal, you want to slow down here, I'm not being figurative, there are base physical quantities, which are described in base units, and there are derived physical quantities. How are they described? This is something that you need to know, and even, that you needed already to know, before you tried to get a handle on my wacky math philosophy. I keep saying that there is a matter of technique here, of competence, that these are not my ideas, I say a lot about dimensional analysis. You don't, I'm here to inform you, have the luxury of going through life with any opinions about physics, if you're not a bigger expert than me on these very issues. Which, are you? Don't blame the messenger. This is what I have to say. Dimensional Analysis. It's a field of math. Spend a few months on it, and you still won't be any kind of expert. Your days of winging it without knowing any dimensional analysis, are over. Right? Because your interest is authentic. Correct? You're really for real, man, this isn't a game, it's serious business. Fine, I believe you.

Then, what is a base quantity, what is a base unit, what is a derived quantity, and etc., specifically, how are derived quantities expressed? Live it. Know it. Tell me the answer. Get it right. The questions, will get harder. That is the relationship that we have. I, at least, am serious about getting to where we are with this stuff--I, at least, think it's interesting, and I'm willing to learn about it. About what? Dimensional Analysis. Tell me something that I don't know about Dimensional Analysis. It's a real, actual field of math, that you need to be more of an expert than me on. I'm a broken record, get into Dimensional Analysis, that's our song. 'You're some kind of non-realist!' my reply: 'Dimensional analysis'. 'I believe that there is meaning in this equation!' my reply: 'Dimensional analysis'. Doesn't matter if it takes you 5 years, wouldn't kill you to take an hour or 90 minutes, might not help much, but you Will do this, before we move on. Dimensional Analysis. What's the other part? Dimensional analysis. Oh, and btw about infinity, infinity to any power is still infinity. Is that, then, Dimensional Analysis?

So now back to the equation. We now have c=(1/0)½. Oh, by the way infinity to any power is still infinity.

Oh, we've mastered zero, now I'm learning about infinity. Infinity to any power is still infinity. This is an exciting moment, probably for the first time in my life I'll be dealing with infinity. Where did you learn, that infinity to any power is still infinity. Seems logical to you? I insist that you tell me something edifying, about Cantor and cardinality, before we proceed. Who was he? Why is he famous? I don't require a doctoral dissertation about it. You want to tell me something that I don't know, let's start with telling me something that I do know. Who was Cantor, why is he famous?

Sadly, on the infinity discussion, I'm calling the game, we're done. There is only one way that you can get me to read the rest of your post. This is a homework assignment. Read about Cantor, paste something, one sentence, about who he is and why he is famous. And be GRATEFUL, that I asked you to do this.

Cheers, allthebest.

-- Updated August 13th, 2012, 3:39 am to add the following --

I was in a bit of a snit, but have read some more of your post, and I have to admit, you make a simple request here. Especially, why I want to take a whack at this, is your interest in the Einstein quotes, especially where you have Einstein uttering the word 'homogenous'..

Your simple request:

Consider this simple question. Why is the speed of light the specific value that it is? That is what this discussion is really all about. This is what I want you to do. In your next post, just try and answer this question first before you take on the rest of my post..Why is the speed of light the specific value that it is?

In my view, it is clear, that when wave meets another medium which has different strength and pattern of M&E field, wave travels according to the M&E field of the medium. We agree on this. I imagine, then, that everything rides on a notion of what wave requires in space, this 'virtual medium'. What about space? Why, exactly, is it, that the traveling speed of wave is the speed of light, c. My answer, is that I consider that wave possesses the magnetic and electric components.

This Space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that "empty space" in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials), has, I think, finally disposed of the view that space is physically empty.

Space is not empty according to Einstein. I agree with him.

I have extreme patience for going through this Einstein stuff, but I don't really think I would have put it the way that he does here. The 'empty space' that he is talking about, is plain-vanilla, Euclidean, 3-dimensional empty space, like in the room that you are sitting in, height, width, depth, the lines are parallel, the curves are eh, curvy. And then, well, no, it turns out that he's not talking about 'space', when he says space, or even 'empty space', no. By 'space', by 'empty space', he means 'empty space in its physical relation'.

Okay, let us walk through this, I want to sit with this. What is 'empty space in its physical relation'? That is not space. That is some mathematical construct, as is made clear by Einstein's comments that it is neither homogenous nor isotropic. As, what do these terms mean? I maybe am being presumptuous, I think you'll be delighted to learn that I know exactly what 'homogenous' means, as Einstein is using the term here. I'm a little disappointed, that you offered this quote without leaping to define it for me, I do hope that you haven't simply glossed over these math terms, assuming that it's not necessary to THROTTLE the MEANINGS HERE to the GROUND. You assumed that I would know this? But, how many people know something like this?

Einstein is referring to homogeneous coordinates, introduced by Möbius. They make calculations of graphics and geometry possible in projective space. I might add that homogeneous coordinates are a way of representing n-dimensional coordinates with n+1 numbers. In brief, we're familiar with how the cartesian coordinates of a 2d point can be expressed as (x, y). But, what if this point goes far away to infinity? The point at infinity would be (infinity,infinity), and it becomes meaningless in Euclidean space. The parallel lines should meet at infinity in projective space, but cannot manage it, in Euclidean space. What do to about this, what to do. How to solve this issue.

To make 2d homogeneous coordinates, you simply add an additional variable, into existing coordinates. Therefore, a point in cartesian coordinates, (x, y) becomes (x, y, w) in homogeneous coordinates. And x and y in cartesian are re-expressed with x, y and w in homogeneous as: x = x/w y = y/w

For instance, a point in cartesian (1, 2) becomes (1, 2, 1) in homogeneous. And now, if a point, (1, 2), moves toward infinity, it becomes (infinity,infinity) in cartesian coordinates. And it becomes (1, 2, 0) in homogeneous coordinates, because of (1/0, 2/0) = (infinity,infinity).

So, for review, we ran into an issue, something to do with how two parallel lines can intercept, and Euclidean geometry therefore now being approached as a subset of projective geometry.

Are we clear, though, on why is it called "homogeneous"? Homogeneous coordinates are scale invariant. Like, the points (1, 2, 3), (2, 4, 6) and (4, 8, 12) correspond to the same Euclidean point (1/3, 2/3).

I have a handle on this stuff, because homogeneous coordinates are very useful and fundamental concept in computer graphics, such as projecting a 3D scene onto a 2D plane. But back to Einstein, and his ' "empty space" in its physical relation is neither homogeneous nor isotropic.' What does he mean, not homogenous. He is talking about the relation of Euclidean space to projective geometry. I don't think he's got a very perspicuous clear view, of what a mathematician makes of this, as opposed to an admittedly brilliant physicist. He of course had some math skill, and certainly ran in circles with others who did as well. But also, it's a few generations ago. They didn't have computers, some recent progress in math hadn't really settled in people's minds, hey he had lots on his plate. I don't view math the way he did, when he makes these kinds of comments. Not to say that he wasn't a genius. But I'm glad that you posted this quote, for me it is clear that Einstein is confused, here, talking about how space can be attributed many qualities, how space has a specific geometry that will be determined by experiment.

I don't mean to be smug about it, I'm not Einstein, but it's the 21st century, it's so much easier to get a grip on what is going on with projective geometry, if you have some experience with computer graphics. Einstein is, again, talking about the relation of Euclidean space, which he kind of confuses in a Newtonian way, here, with space out there, in the external world. And then, he is saying that it is not homogenous. What is not homogenous? If you treat Euclidean space as being homogenous, then it's homogenous. Call it a subset of projective geometry. Projective geometry has axioms, everybody gets very confused about axioms. Does 'space', look up in the sky at space, does 'space' have 'axioms'? Close your eyes and put some effort into visualizing 'space'. Are you staring at a list of axioms? It's a real intellectual adventure, sorting these issues out, philosophically, but I disagree with Einstein even trying to make a determination as to whether space is or is not homogenous.

Whether it is or it isn't, is a purely methodological distinction. The idea here in Einstein's mind is kind of like one notion is true and the other is false. Is space homogenous or is it not? In my mind, both propositions stand or fall together. They're both good, or neither are good. The question is meaningful, or it isn't, shall we treat space as being homogenous or not. The real issue being, what makes this talk meaningful in the first place? That we're even discussing it meaningfully, that there's something 'objective' to the question, I say space is homogenous, you say it isn't, we go back and forth about it, that means that we're both right. What enables this kind of debate? Space has no specific "geometry."

I'm not optimistic about getting any of this notion across, let's move on to 'isotropic'. "Empty space" in its physical relation is neither homogeneous nor isotropic. I don't know, maybe I'll let you get in on the fun? You can believe that I know what this means, that I have my opinion in which you are hardly interested. Do you know what this means--'isotropic'?

Hit me.

You also forgot to include the entire quote from the same speech which by the way dramatically changes the meaning of what you were trying to convey.

Recapitulating, we may say that according to the General Theory of Relativity space is endowed with physical qualities; in this sense, therefore, there exists an Aether. According to the General Theory of Relativity space without Aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this Aether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it.

No, I've seen this stuff, I have in mind, what Einstein is saying here..

The last two lines he plays it safe and this is because of the null result of the Michelson and Morley experiment. In my opinion the jury is still out on the idea that “this Aether may not be thought of as endowed with the quality characteristic of ponderable media.”

Yes, well. Um. I'm not trying to win a debate. I figured as much, about your views.

I believe that eventually the M&M will be reversed when the experiment is done properly. Even if absolute motion relative to an aether is not detectable it still is not a show stopper. It would just mean that whatever this physical substance is you cannot detect motion relative to it. Okay, so what. That on its own still does not disprove the existence of an aether.

I don't know how to conceive of the M&M being reversed, are you doubting the length contraction equation? I'll suppose that you are doubting the interpretation.

Please explain what you mean by sources or sinks of electric charge.

I'm making out w/the principle of conservation of energy, that's all, pretty much. What is most basic, most fundamental in Physics? What is the program? I take it to be principles, the principle of conservation has a few sub-branches, there is the principle of conservation of energy. Energy has been conserved, since the big bang. I don't take it as being really possible to transcend the way that the subject, the field, of physics, has been conceived, without it not being physics anymore. What defines physics? Where does the rest of it come out of? The equations, all this jazz. A few principles are being researched. The principle of conservation of energy is important. When I look at time, when I look at how energy is measured, when I look at mass, at all these equations, note that an 'equation' has an 'equality' in it. That's about conservation. That's the big epiphany. Why is the speed of light constant? Because everything else is a degeneration, a storing up of potential energy, by configuring kinetic energy. Which, is not really an explanation--I guess I'm saying that I don't look to Physics for explanation, I look to it for description of conservation of energy.

-- Updated August 13th, 2012, 6:17 am to add the following --

A brief additional comment (brief, right), Mach, you mentioned Mach. He was known to argue that the only way to explain the phenomenon of inertia was to assume that all of the masses in the universe were somehow connected. Albert Einstein later identified this argument as Mach’s Principle.

Mach’s Principle can be viewed as an entire universe being altered by changes in a single particle -- much in the same manner as hurricanes and tornadoes occurring in Florida because of an El Nino weather pattern in the Pacific Ocean, or perhaps more aptly, the flapping of a butterfly’s wings in Peru causing rains in Kansas.

I have a strong suspicion, that you make the world of this kind of thinking, so I thought I'd toss the ball back about it.

Generally, the way the story that you lament is told, Einstein declared Maxwell’s ether unobservable, and thus abolished the ether forever. Nevertheless, inertial frames seem quite real. Ultimately, then, am I left with the idea that Mach’s Principle implies that the whole universe matters locally?

What is most difficult about special relativity, I mean, to understand? It is the elimination of absolute space and absolute velocity, or, in other words, the rejection of Mach's Principle, I suppose.

Some kind of purely mathematical concept of space-time, which discards absolute space and absolute velocity, this is the difficulty. I might try rephrasing Mach's principle again, because I find it very interesting. Say, that it requires that inertia of mass, and, consequently, potential energy of inertial mass, must be generated by the rest of the universe. I suppose that it might be possible to write this in mathematical terms. Some cosmic gravitational tension, or amount of potential energy per mass, generated by the universe, which might, off the cuff, wind up equalling c^2, I mean if we get it extended to the universe as a whole.

I'll rephrase Mach's principle again: The inertia stems from an interaction between a body and the mass of the Universe as a whole. I'm not sure that the origin of inertia isn't still somewhat of a mystery. I mean, I know the basis for Einstein's 'origin of inertia'.

I have a slightly vague understanding, I mean. I think, actually, that Einstein saying that it does have to do with Mach's principle, or with the matter in the Universe at large, but just with what's going on within every object's spatial and temporal relations. I had a phase, where I was examining rather breezily, some of Einstein's papers that concern the special and general theory of relativity together with a small proportion of his correspondence related to relativity. That's not much to go on.

Sub, surfing the net a bit, to confirm this, I find: 'To be sure, for a number of years Einstein expressed the ambition of the general theory of relativity to fully implement Mach's program for the relativization of all inertial effects, even appending the so-called "cosmological constant" to his field equations for this purpose.'

And: 'Einstein's attempt to realize Machian ideas in the construction of general relativity was undoubtedly a very major stimulus to the creation of that theory.' Suppose, that Einstein's theory of gravity represents a major swing back toward the relational view of space and time. Nevertheless, I am given to understand, that the equations of general relativity are perfectly consistent with spacetimes that contain no matter at all. The theory does not make spacetime more relative than it was in special relativity. Even, if Einstein was 'undoubtedly' inspired by Mach's relational views. What can be Machian, here, if matter and spacetime remain logically independent? Wasn't Einstein forced to admit that he had not achieved his aim of showing, that a cosmological model without matter was impossible? Perhaps these comments about the dream, it's not precisely 'your dream'. But, as I understand it, the absolute space and time of Newton are amalgamated and endowed with a more flexible mathematical skeleton, the metric tensor. Which is to say, that space and time do act on matter, by guiding the way it moves, and matter does act back on spacetime, by producing the curvature that we feel as gravity, as they say, and beyond that, what? If there is something beyond that, I would put it like this, currently, matter can act on spacetime.

Do you want me to say that spacetime behaves relationally but exists absolutely? Fine, you win. What difference does it make? I think the notion that we concentrate directly on the universe as a whole, describing it, the global approach, well, I have a doubt. The spirit, as it were, as I understand it, the strategy, what is almost breathtaking, what lends his theory such grandeur, for me, is the way in which he was not afraid to tamper with space and time. This is an almost ruthless willingness to do just whatever he pleased to space and time. And, I see a general cosmological framework here. Relativistic cosmology. All the pieces came together, almost miraculously. In any case, questions of absolute versus relational spacetime are rendered anachronistic by the notion that even "empty space" is populated by matter in the form of virtual particles, zero-point fields and more.

As usual, I am eager to draw attention to the nature of math. To do physics, you have to learn math. To do math, you don't need to learn any physics. What does that tell us? I don't think people meditate on this, and come to the same conclusions that I do, so very much. I don't belong to any existing school of thought that I'm aware of.

But enough about that, I saw and mentioned once, and you repeated it back, that you think Because the traditional strong and weak forces can be derived from the electric, magnetic, and gravitational fields, or some such. The traditional strong and weak forces are not, then, mutually exclusive from the electric, magnetic, gravitational fields, not to be considered as fundametal, as has been the tradition?

What, now?

eh?

[Wanderer101]

For Dan,

I am in the process of checking out your massive post. Whew it's something and its going to take some time to plow through this one. I am enjoying the conversation though. Its very good and thought provoking. Our posts seem to be growing in size exponentially. I think we should throttle back on the volume and try and just work on some of the specifics in detail.

I will attempt a reply later to day.

[DanLanglois]

That post has a structure, 1,2,1,2,3 what I mean is, 2/3 of it is somehow duplicated. It's still too long. As to working on specifics, I'd want to leave you an opening for offering some of what you take to be relevant equations--I kind of end on that note.

[Stormy]

My guess is, we are but a trace of what has already taken place..a residue, a sounding trumpet a crashing cymbal, aloud to make sense within the brakes of infinity...in order to matter. I guess.

-- Updated August 13th, 2012, 9:16 pm to add the following --

Or indeed...to matter to make sense..