The Theory of Relativity

[Tensorman]

Namely?

The principle of relativity - that is, the physical laws should be the same in all intertial reference frames - combined with the constancy of the speed of light. From that the Lorentz equations follow automatically.

[Capitalism Forever]

The principle of relativity - that is, the physical laws should be the same in all intertial reference frames

That is not an explanation, but much rather another fact of reality calling for an explanation. The kind of explanation I am looking for would explain what it is about the nature of entities that makes them contract (or appear contracted) and their internal processes slow down (or appear slow) when they move relative to me. Physical laws are man's conceptual identification of certain facts of reality, and as such they are an epistemological tool; they have no power to change the lengths of entities or slow down their internal processes, but rather it is the contraction and slowing that actually happens to concrete entities that should affect our formulation of physical laws.

There is nothing about this that necessarily makes all physical laws the same in all inertial frames; the fact that they are the same is a consequence of something about the nature of entities. It is that something that a philosophically sound interpretation of the Lorentz equations would seek to find--but modern physicists do not even seem to be aware that there is something of this sort to look for. If I told them I wanted to know this, they would literally have no idea what I am talking about, or (the more philosophically interested ones) would think I was some kind of quaint throwback to the eighteenth century who still thought knowledge about "things in themselves" was possible.

[y_feldblum]

The principle of relativity (going back to Galileo) states that the motions of and interactions among bodies remain independent of the bodies' locations and velocities with respect to yet other bodies, because there is no causal connection between these other bodies and the moving and interacting bodies in question.

It is a very good natural explanation.

[poignant1]

...The kind of explanation I am looking for would explain what it is about the nature of entities that makes them contract (or appear contracted) and their internal processes slow down (or appear slow) when they move relative to me.

I'll try.

Man, in his infinite vanity, feels that there should be an absolute reality that he can correctly plumb, and that way he can enjoy a God's-Eye view of the Creation. But the fact is that there is no such static entity as the Universe-as-it-is-right-now. The unfolding of circumstances relies on causation and causation, like everything else, can travel from place to place at no more than the speed of light (it has been found). The sum total of causations converging on a particular time and place dictate what occurs there and then. Each time-place combo is therefore a unique station (or platform), and cannot be a peer or slave to any other/greater realm. Anyway, we are forced to concede that every conceivable such platform also rightly claims its own proprietary linear (regular) time flow and regular 3D rectilinear space. There are myriad individual platforms but no one God's-Eye view, so there can be no universal clock. It is sort of a function of perspective that vantages alien to one's own come across slightly askew as regards their dynamic. But all the formulations bear out and light illuminates everyone's little world just as magnificently as it illuminates our own. And the variances are just plain infinitesimal in all but the most absurdly bizarre circumstances, such as at relative speeds in excess of 500 million miles per hour. It's some teensy little trick that the Creator plays in order for all venues to be blessed with normalcy. The skew is hardly noticeable at all, and ignorance of it leads to no particular harm.

[Capitalism Forever]

The principle of relativity (going back to Galileo) states that the motions of and interactions among bodies remain independent of the bodies' locations and velocities with respect to yet other bodies, because there is no causal connection between these other bodies and the moving and interacting bodies in question.

It is a very good natural explanation.

You realize that it does not imply the Lorentz equations, though?

[y_feldblum]

The Lorentz equations are known to hold experimentally, independently of the principle of relativity (Galileo's, Newton's, or Einstein's).

[Capitalism Forever]

The Lorentz equations are known to hold experimentally

So where's the explanation for them?

[y_feldblum]

A previous post explains that the Lorentz equations are very analogous to the equations modeling rotation about an angle. In fact, that is not exactly true: the Lorentz equations can be immediately derived from the much simpler equations which are the equations of rotation about a hyperbolic angle (which are very similar to the equations of rotation about an angle).

That is not to say that rotation is a good physical explanation of the Lorentz transformation. Contrary to certain popularizations, it does not assert that entities actually change length, duration, or mass simply by changing velocity with respect to another entity - it asserts that partial observations of interrelated aspects of an entity depend on the relationship between entity and observer, but full observations of the actual properties of an entity do not so depend, as philosophically expected. Moreover, it is a very simple theory and does not assume into existence any new entities, thus abiding by Occam's Razor. By contrast, any and every aether theory proposed sports a distinct lack of physical evidence - while assuming into existence new entities, namely, the aether.

[Capitalism Forever]

it asserts that partial observations of interrelated aspects of an entity depend on the relationship between entity and observer, but full observations of the actual properties of an entity do not so depend, as philosophically expected.

Could you elaborate? (On things like "full" vs. "partial" observations and "actual properties" ?)

[agrippa1]

So where's the explanation for them?

I believe the Lorentz equations were used by Lorentz to explain the reciprocal interaction between magnetic and electric fields, which interaction mathematically explains the propagation of EM through space. They were adjustments to Maxwell's equations and were not an attempt to address the apparent lack of motion of Earth wrt light. (on edit: that's from a Feynmann lecture - after further reading, I may be wrong on that point)

Einstein, using simple geometry and algebra independently derived the same equations when exploring the explanation for Michelson-Morley:

Based on the results of the MM experiment of 1887, it was apparent that the speed of light appears constant in any frame of reference. Using simple geometry and algebra, Einstein looked at the round trip time of light in a moving system, from point A to B in the direction of motion, and then from point B to A against the direction of motion. The round trip time is larger than the round trip time if points A and B are at rest, so he surmised that the distance between A and B must contract when they are in motion, to cancel out the time difference. The equation for this shortening is the same as the Lorentz transformation equation. Recognizing this, he believed his results were a confirmation of a universal law.

Then he did the same type of calculation using points A and B moving side-by-side, and found that while the distance between A and B is the same as when they are at rest, the zig-zag path resulting from motion made the distance traveled by light slightly longer. He calculated how much longer and came up with the Lorentz equation again, which is 1/sqrt(1 - v^2/c^2). He then surmised that time dilation occurs in accordance with the Lorentz equation.

There are a few adjustments he has to make after that, in which time must be dependent on distance in the direction of motion, and vice versa. These adjustments are what make "everything relative" as he said, and make it impossible to discover how fast you are travelling with respect to stationary system. In fact, the math makes the notion of a stationary system meaningless, except as an system can be considered stationary when describing a system in motion relative to it.

There is a problem in SR, that the O'ists here seem to sense intuitively. This is what's referred to as "arrogance" (or "vanity") by those who take the "just so" attitude towards scientific theories that are mathematically consistent with nature. The problem with SR is that there is no philosophic foundation for why length contracts or time dilates, other than "the math works out that way. This is a clue that the theory is probably missing something fundamental. I believe when that something is found, a lot of pieces will fall into place.

Edited April 16, 2008 by agrippa1

[y_feldblum]

The problem with SR is that there is no philosophic foundation for why length contracts or time dilates, other than "the math works out that way.

There is. Not a priori, of course. But when one understands that Newtonian physics treats time as completely separable from the three dimensions of space while Einsteinian physics treats time and the three dimensions of space as four dimensions, and that Einsteinian physics more accurately describes observed phenomena and more accurately predicts phenomena than does Newtonian physics because Einsteinian physics treats time and space as four dimensions (that is the root difference and, fundamentally, the only difference between the two theories), one is led to the conclusion that the treatment of time and space as four dimensions is justified and mandated philosophically.

Length does not contract and time does not dilate. The measurement of length and the measurement of time depend on the velocity relationship between observer and observed, but the combination of length and time ("timelength" taken as a whole) does not depend on the velocity relationship between observer and observed, because it is a "whole" property (as opposed to length and time taken individually, which are component parts of timelength).

The math does not state that entities depend on how fast they are going. The math states that entities are what they are, that a ruler of length 4in will always be of length 4in, that a trip of duration 1yr will always have duration 1yr.

Edited April 16, 2008 by y_feldblum

[agrippa1]

There is. Not a priori, of course. But when one understands that Newtonian physics treats time as completely separable from the three dimensions of space while Einsteinian physics treats time and the three dimensions of space as four dimensions, and that Einsteinian physics more accurately describes observed phenomena and more accurately predicts phenomena than does Newtonian physics because Einsteinian physics treats time and space as four dimensions (that is the root difference and, fundamentally, the only difference between the two theories), one is led to the conclusion that the treatment of time and space as four dimensions is justified and mandated philosophically.

Every theory more accurately reflects reality than its predecessor. That is the nature of science and discovery. "More accurate" does not equate to "true," and history teaches us that every theory is fallible, except, of course, the one we currently hold to be true.

[y_feldblum]

The point was that there is a single root point of difference between the mathematical framework of Newtonian physics and the framework of Einsteinian physics. The single root point of difference is in whether time and space (i.e., extents and durations) are to be treated mathematically as fundamentally distinct or as fundamentally similar and integrated.

From all the evidence available, the mathematical framework of Einsteinian physics is correct and true, while the framework of Newtonian physics is a very close approximation under the conditions considered normal at the time of its development. The difference between these two frameworks in the field is due solely and entirely to the single root point of difference identified above.

The implication is: the single root point of difference between the mathematical frameworks must be abstracted to become the single root point of difference between the philosophical justifications. In other words, Newton's mathematical framework treated time and space as fundamentally distinct: so too did his philosophical framework; Einstein's mathematical framework treats time and space as fundamentally similar and integrated: so too does his philosophical framework. Einstein's philosophical framework, which treats time and space as fundamentally similar and integrated, is justified ultimately by the evidence of the senses.

[poignant1]

...it asserts that partial observations of interrelated aspects of an entity depend on the relationship between entity and observer, but full observations of the actual properties of an entity do not so depend, as philosophically expected.

That there says quite plenty, and serves to clinch the subject, verily.

[Capitalism Forever]

The point was that there is a single root point of difference between the mathematical framework of Newtonian physics and the framework of Einsteinian physics. The single root point of difference is in whether time and space (i.e., extents and durations) are to be treated mathematically as fundamentally distinct or as fundamentally similar and integrated.

From all the evidence available, the mathematical framework of Einsteinian physics is correct and true, while the framework of Newtonian physics is a very close approximation under the conditions considered normal at the time of its development. The difference between these two frameworks in the field is due solely and entirely to the single root point of difference identified above.

The implication is: the single root point of difference between the mathematical frameworks must be abstracted to become the single root point of difference between the philosophical justifications. In other words, Newton's mathematical framework treated time and space as fundamentally distinct: so too did his philosophical framework; Einstein's mathematical framework treats time and space as fundamentally similar and integrated: so too does his philosophical framework. Einstein's philosophical framework, which treats time and space as fundamentally similar and integrated, is justified ultimately by the evidence of the senses.

So the explanation is that the spacetime interval is a real property of entities, while the intervals we perceive--length and time intervals--are not real? But if it is so, what is the explanation for us perceiving length and time intervals, rather than the real property, which is the spacetime interval?

[y_feldblum]

Extent and duration are components of timelength and so are perceived independently.

Extent in the forward direction and extent in the right direction are, likewise, components of distance and so are perceived independently. A single displacement (directed distance) may be specified by "3 steps forward and four steps right", if one is facing a certain way, and "five steps right" if one is facing another way.

[Thomas M. Miovas Jr.]

Actually, there is no time or space as one usually has it presented due to the influence of Kant onto modern physics. Time and space are not epistemological fundamentals, nor are they metaphysical fundamentals. That is, neither time nor space are things or substances. Time and space are a conceptualization of entities and their actions. In other words, entities (that we perceive) and what they do are the epistemological fundamentals. There is no time stuff and there is no space stuff. An entity, when it moves, does not need time and it does not need space; these are not substances that are needed for there to be movement. It is only figuratively speaking that one could say, "I don't have time to get to Philadelphia by nine o'clock."

I think it was Augustine who conceptualized time as something that was needed for things to happen; like God made just enough time so that events could happen. But he was starting in mid-stream, as most intrincisist do, taking a concept and reifying it into a thing -- like Plato's Forms. So, to put it another way, neither time nor space are Forms, because there are no Forms.

The concept of space is developed by observing that one entity is here while another is over there -- it's like distance, but in three dimensions: forward and back, up and down, left and right. But we do not observe space, we observe entities. Likewise, there is not time as a substance, time is a measure of motion -- it is a conceptualized relationship between one moving entity and another moving entity. Aristotle said that time was based on before and after, such as I toss a ball at the wall, but the dog got it before it hit the wall, and I yelled at the dog for messing up my game after I tossed the ball.

Einstein got it right in a sense, because he always used something moving in order to demonstrate what he was saying about time, but he got it wrong when he said that space-time was an actual existing stuff that can be twisted and bend and distorted.

So, there is no space-time as a substance that is out there in the universe; and gravity does not distort space-time, and relative motion does not distort space-time -- because there is no space-time as a real entity out there in reality apart from man's conceptualizations of entities and their actions.

[agrippa1]

The point was that there is a single root point of difference between the mathematical framework of Newtonian physics and the framework of Einsteinian physics. The single root point of difference is in whether time and space (i.e., extents and durations) are to be treated mathematically as fundamentally distinct or as fundamentally similar and integrated.

Is there a metaphysical order to time, distance, direction and velocity?

That is, are any of these derived from any other?

[Capitalism Forever]

Extent and duration are components of timelength and so are perceived independently.

Extent in the forward direction and extent in the right direction are, likewise, components of distance and so are perceived independently. A single displacement (directed distance) may be specified by "3 steps forward and four steps right", if one is facing a certain way, and "five steps right" if one is facing another way.

But we do not perceive the x, y, z intervals, we just perceive the length sqrt(x^2 + y^2 + z^2). The coordinates x, y, and z are something we derive indirectly from our perceptions. With the spacetime interval, it is the other way round: we perceive lengths and time intervals, and we have to compute the spacetime interval indirectly from those observations. If you have a ruler of a certain length, you can point out objects of the same length without any need to use your conceptual faculty to decide whether they really are the same length--but you cannot do this with a spacetime interval. Why this difference?

[poignant1]

Actually, there is no time or space as one usually has it presented ...

Einstein ... got it wrong when he said that space-time was an actual existing stuff that can be twisted and bend and distorted.

That sounds correct, all that was stated in that post. Now I ask this out of idle curiosity only, because I've said that I already grok relativity fine. Gravitational fields do indeed exist?? It's surely just a wording choice, and not a snag for me either way. If there's no space-time stuff then there must be this "field" dynamic and its attendant action-at-a-distance -- a notion which steadfast relativists are often heard to deride.

'Care to comment?

[y_feldblum]

But we do not perceive the x, y, z intervals, we just perceive the length sqrt(x^2 + y^2 + z^2). The coordinates x, y, and z are something we derive indirectly from our perceptions. With the spacetime interval, it is the other way round: we perceive lengths and time intervals, and we have to compute the spacetime interval indirectly from those observations. If you have a ruler of a certain length, you can point out objects of the same length without any need to use your conceptual faculty to decide whether they really are the same length--but you cannot do this with a spacetime interval. Why this difference?

That is how sense-perception works. A single full property of an entity is broken down into its component parts, which are more easily perceived. This approach is accurate to whatever degree any animal requires.

You see redness and you feel hotness; you do not see or feel both at once.

The length of a spacetime interval, by the way, is exactly how long it takes to traverse it. It can be measured directly with a clock and a transportation device capable of accelerating, steering, and keeping up a life support system. Or, we may send particles which tend to undergo decay along a spacetime interval and count how many decayed in transit.

[Thomas M. Miovas Jr.]

Gravitational fields do indeed exist?? It's surely just a wording choice, and not a snag for me either way. If there's no space-time stuff then there must be this "field" dynamic and its attendant action-at-a-distance -- a notion which steadfast relativists are often heard to deride.

I thought I mentioned this earlier in the thread, but maybe it was another thread. Gravitational fields, electric fields, and magnetic fields are conceptualizations of the force that would be acting on a unit particle in a certain volume surrounding the source. Saying something like, "The gravitational field of the earth exerts a force on the moon" is using the concept of "gravitational field" as if the field is the thing acting on the moon; but it is really a conceptualization that a force of a certain amount would be acting on the moon at a certain distance from the earth. The question is: What is exerting the force? If the field is a conceptualization of the force, then what is there that is imparting the force at those distances?

Mathematically, because Newton could not identify the thing acting, it comes across as an action at a distance, but he himself rejected that idea. He conceptualized what the force would be at a given distance, but he didn't know the cause of the force. That was something later scientists ought to have been trying to discover. But because mathematics became reified, the action at a distance mis-conceptualization stuck.

In other words, there is some real something there that is imparting the force, and it is up to scientists to discover what that real something is.

In my conception of what is going on, the earth, the magnet, or the charged matter does something to that which is there in a certain volume surrounding the source, and then that which is there acts on the moon, the iron, or the charged matter that is not right there at the source location. There is no action at a distance, but rather there is a real something there that is active in some way, and that activity or change imparts a force onto the moon, the magnet, or the charged matter. That is, there are no disembodied forces.

Einstein tried to say that space-time became distorted and things just follow the curvature of space-time instead of going in a straight line, but that requires conceiving of space-time as a real substance or stuff, which I reject.

[y_feldblum]

Thomas, the part about fields is correct. A field is a double abstraction from actual physical forces. One might say that the Earth exerts a specific quantity of force f on the Moon, which is a certain distance d away from the Earth and is of a certain mass m. If one abstracts away from the specific distance and the specific mass, the concept is a field: the Earth will exert some force on an object given its distance away from the Earth - but omitting the the particular distance - and given its mass - but omitting the particular mass. The field is a very powerful mathematical tool. Whereas to describe a force exerted by one gravitating body on another, one had first to describe each body and the distance between them, to describe a field exerted by one gravitating body, one need only consider that gravitating body. In essence, the tool allows the physicist to abstract away from the second body and to focus only on the first body alone. The physicist can analyze the shape of a body and in a first step decode its impact on the field the body exerts, keeping in mind that the field is a mathematical abstraction and not actual stuff, and then in a second step decode how the shape of the field exerts actual, physical forces on other bodies of whatever mass they are and in whatever location they are; without fields, the calculations of the actual forces would be made more far complicated.

Einstein observed that objects under the influence of gravity are always in free fall if there is nothing obstructing the effects of gravity. Such objects under the influence of gravity do not feel the influence of gravity. They do not feel force; neither do they feel acceleration. Falling feels exactly like not moving at all, or moving in a straight line without accelerating - even though, clearly, that is not the impression one gets from observing another person falling. (This is an observed fact.) Einstein went for the conclusion that falling is moving in a straight line through spacetime. The way to explain this conclusion, according to Einstein, is to consider space as curved (in a highly mathematical sense - not in the sense of an object being curved) wherever there is mass. Is his conclusion correct? It is extremely odd, to say the least. However, his general theory follows from accepting the observation that free fall feels like constant motion and going to the conclusion that free fall is constant motion, in accordance with observation.

[poignant1]

In my earlier post I made a wording mistake where I said,

...The sum total of causations converging on a particular time and place dictate what occurs there and then. Each time-place combo is therefore a unique station (or platform), and cannot be a peer or slave to any other/greater realm. ...

Replace or qualify the term "time-place combo" with "material thing on an apparent trajectory". Relativity isn't really for characterizing hypothetical intangible vantages, but only actual material 'landmarks', which I term "platforms" because they are places from which observations will be made (by machines, by molecules, by humans, etc.)

Relativity explains reality. It isn't so much about fantasy!

[y_feldblum]

Why the hostility to the deep focus on geometrical methods in Einstein's theory, especially considering there exists the same deep focus on geometrical methods in Newton's theory?