Jump to content
Objectivism Online Forum

The Theory of Relativity

Rate this topic


Recommended Posts

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.

Sure you do! You see and feel at the same time, only with different organs.

And tbere is a clear physical explanation for why you need different sense organs for color and temperature. They may be properties of the same object, but they are different properties--different "full properties," to use your terminology--so it is no wonder we should perceive them with different organs. Even if you are talking about electromagnetic radiation that contains red visible light and radiant heat, there is an explanation for why we perceive them differently: we perceive the part of the radiation that falls on our retina as redness, and the part that meets our skin as heat. Can you give a similar physical explanation for perceiving time and space differently, if they are "components" of the same property? Note that we do NOT have different senses for perceiving space and time as is the case with color and temperature; rather, we measure space intervals with our eyes, our hands, and often even with our ears, our mind integrating the data received from the different senses into one consistent percept--and we do not perceive time intervals with our senses at all, but use our memory of past events to tell how far back they happened from the present.

In other words, our way of measuring space intervals is fundamentally different from our way of measuring time intervals. What fact of reality lies behind this fundamental difference?

Also, men can move freely between points in space within their limits, but they cannot for the lives of them move between points in time, except forward, in a strictly monotonous way. That sounds like another MAJOR fundamental difference, doesn't it? What is the explanation for that, if time and space are just components of the same property, merely broken down for easy perception?

The length of a spacetime interval, by the way, is exactly how long it takes to traverse it.

You'll have to elaborate on what exactly you mean by that, since as I hinted above, I don't think the idea of "time travel" makes any sense, and that is what you sound like you are talking about...

Link to comment
Share on other sites

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?

I'm not against geometric or mathematical methods for obtaining the right answer; one that is predictive. But, Newton knew that the geometry in and of itself was not the cause of gravity or motion. While Newton's mathematical methods depict gravity as an action occurring over a distance, he knew that there had to be some real something there that made gravity possible, he just couldn't figure out what that cause was. In Einstein's interpretation of his equations, he doesn't seek a cause, but rather says that the geometry is the cause -- i.e. that spacetime is curved under the influence of massive objects.

So it is not an issue that the mathematics work, just as there is not an issue with the mathematics of quantum mechanics. The issue comes down to what is the cause or even in some minds the idea that there is no cause and that it just happens. That is, curved spacetime and particle probabilities are not causes -- they are not real things that lead to those motions. What Objectivists are saying is that scientists ought to be searching for the cause and ought not to be reifying mathematics for their own sake, just because they are predictive.

For an historic example, the earth centered model of why the planets move the way they do was mathematically predictive, but it didn't get to the cause (in that context) that it was gravity that made it all work, which can only be found by taking the most massive object, the sun, as the geometric center of the solar system.

Link to comment
Share on other sites

Special relativity uses geometry as its tool, just as Newtonian physics did. Geometry allows the physicist to abstract from what in particular he is studying to the general laws which describe all motion.

General relativity attributes seemingly curved or accelerated motion to the curvature of space (note: not the same meaning as when one speaks of an object being curved) and the fact that straight-line, unaccelerated motion in a curved space seems curved or accelerated (which is true independent of Einstein's interpretation). Einstein argued that matter curves space - and it immediately follows that other objects moved through curved space in straight, unaccelerated motion, and that their apparent curved or accelerated motion is caused by the curvature of space, which is caused by the presence of matter.

Obviously, the interesting part is Einstein's argument that matter curves space, and that matter is therefore the cause of seemingly gravitational motion in a universe where gravitational motion does not exist (by observation - this is the part which has to be explained somehow). Obviously, it's a philosophically deep question. But treating the use of "curved" here the same as the use of "curved" when describing everyday objects only obscures the argument.

Link to comment
Share on other sites

Obviously, the interesting part is Einstein's argument that matter curves space, and that matter is therefore the cause of seemingly gravitational motion in a universe where gravitational motion does not exist (by observation - this is the part which has to be explained somehow). Obviously, it's a philosophically deep question. But treating the use of "curved" here the same as the use of "curved" when describing everyday objects only obscures the argument.

I understand Einstein's argument, but you seem to be using curved in a sense other than something being physically curved, which is the point of contention. I realize that from the frame of reference of earth a body that does not create acceleration in its own frame of reference -- i.e. a spaceship that is not firing its rockets -- will follow a curved path. Newton explained this in terms of a force, gravity, acting on the body leading to the curved path; Einstein said there is no force acting on it, it simply follows a curved path because spacetime is curved.

In the frame of reference of the spacecraft not firing its rockets, everything within the spaceship experiences free fall, and those within the spacecraft can say that no forces are acting on them, even though, by looking outside of the spacecraft they can see that they are all following a curved path. Einstein said that there are no forces acting on the spacecraft, that it is following the curvature of spacetime. But if one is not going to say that spacetime is really curved, then why are they following a curved path? Of course the curvature is in reference to the big bodies in their frame of reference; if they didn't look out of their spacecraft, then they wouldn't be aware of that curvature. So, I think from this perspective one would have to say that spacetime is a real thing and that it is really curved. But if spacetime is just a mathematical convenience -- i.e. an abstraction -- then there isn't a real thing that is curved, so one still has to account for the curved path in reference to large bodies -- i.e. planets. Why do they follow a curved path if there isn't really anything there that is actually curved?

Einstein's mathematics are more precise than Newtons, but if one is not going to take the idea of spacetime being a real thing and really being curved, then one has not found the cause of gravity. Very broadly I agree with Einstein in the sense that large bodies do something to that which is there surrounding them; but I take the position that there is a real something there -- i.e. it is not just an abstraction -- and that large bodies does something to it which leads to those curved motions. And we need to find out what that something is instead of reifying mathematics as being causative.

Link to comment
Share on other sites

As Einstein observed, objects in free fall (i.e., objects moving under the effect of gravitation and only under the effect of gravitation) experience no accelerations, no forces; yet we observe them accelerating as though forces were acting on them. This is an indisputable observation of fact (which you're not disputing).

As Einstein observed, a mathematical description of this phenomenon is that the trajectory of such an object moving in free fall is the trajectory of a locally straight yet globally curved line. Lines are locally straight and globally curved in curved spaces. Therefore a mathematical description of this phenomenon is that spacetime - the spatiotemporal relationships between entities - is curved.

Now let me invert your perspective. It is the general case that the spaces which mathematics deals with are curved. It is sometimes a useful special case to consider spaces which lack curvature.

We observe, with our naked eyes, no curvature of spacetime. But we know from mathematics that the general descriptions of spaces account for curved as well as noncurved spaces equally, treating noncurved spaces as a useful special case. And we know from observation that mathematics would suggest that spacetime is curved, and again mathematics suggests where to look to find evidence of this curvature - that is, bodies which have followed curved paths. And lo, we have found such bodies, moving in exactly the trajectories which the curvature explanation of free fall would have them move. Do we have evidence that space is noncurved? Actually, no. We have mountains of evidence that, in all contexts observable and knowable before the 20th century, that no curvature was ever observed or expected, because velocities had not yet become so high, and observations had not yet become so precise, and the theory of electromagnetism had not yet reached the point of contradiction with Newtonian physics.

Curvature of a space has nothing to do with the observed curvature of the surface of a body. Space is not a thing. Curvature means that locally straight lines are not globally straight - lines parallel here may not be parallel there, parallel trajectories a certain distance apart here may be farther apart or closer together there, etc.

Is this the correct explanation. That's a good question. Mathematically, it fits. The correspondence is there between free fall and locally straight yet globally curved lines. The theory based on this mathematical explanation of free fall has been very successful. The theory neglects to answer, of course, by what mechanism the presence of matter induces curvature of space, and that is a serious flaw. The quantitative description is there, but not the causitive description. However, the solution is not to look for things which are not there.

Link to comment
Share on other sites

Here's the kicker and the contradiction:

Curvature of a space has nothing to do with the observed curvature of the surface of a body. Space is not a thing.

<snip>

The theory neglects to answer, of course, by what mechanism the presence of matter induces curvature of space, and that is a serious flaw. The quantitative description is there, but not the causative description. However, the solution is not to look for things which are not there.

I mean, if space or even spacetime are not real physical things, then how can a massive body do something to it leading to curved trajectories?

As far as I know, I will grant you that the mathematics are accurate, as in predictive to the path a body in free fall with an velocity will take. I think it might also be predictive for a body with no velocity will take -- i.e. dropping, say, and apple.

But, there has to be some real thing there that leads to those motions. Otherwise, it is a total contradiction to Newton's laws of motion -- i.e. that a body in motion will follow a straight path unless acted upon by a force; and to date, I have not found a physicist who says that Newton was completely wrong. Maybe you are trying to say that by saying that objects follow a locally straight path but a globally curved path.

However, to fully hold the position that space or spacetime are curved, and that bodies in free fall naturally follow those curved paths with no forces acting on them, one would have to say that it is a real thing that leads to those pathways -- either a real space or a real spacetime that is really curved. And yet you are affirming a curved path but not affirming a real space or a real spacetime. And that is the contradiction.

That's why we must look for the something that is there leading to those curved pathways. The mathematical description is all good and well, and it works. But metaphysically and existentially, scientists ought to be looking for the something that is there leading to those observed motions. I don't know that one ought to leave it at: We observe things in free fall following a curved path, and here are the mathematics for that, and we are not concerned with what is actually there leading to those curved paths.

Newton explained those curved pathways via the attractive force of gravity. Einstein is trying to explain those curved pathways by saying space or spacetime is curved but without claiming that there is a real thing as space or spacetime -- and neither he nor his followers can have it both ways.

Link to comment
Share on other sites

We observe, with our naked eyes, no curvature of spacetime.

Don't you count the curved trajectory of objects tossed in Earth's gravitational field?

It seems to me that a system traveling through "curved space-time" near a massive object would experience an acceleration gradient that would be detectable, especially in extreme cases. Does Einstein posit that objects become "curve shaped" in order to cancel out the detectable aspects of the gradient?

Link to comment
Share on other sites

My point is not that the mathematics are accurate - they are, but that is a given.

My point is that the mathematics describing the kind of motion of a body undergoing free fall - always and everywhere locally straight, free from the effects of any force or acceleration (by observation and experiment), but globally curved, seemingly moving in accordance with force or acceleration (also by observation and experiment) - is the exact same mathematics which describes a curved space. The mathematics of curved spaces (rather, general spaces) perfectly describes the motion of bodies influenced only by gravity.

It is very difficult to make the case that there is something else there, undetectable thus far, which masquerades in the mathematics as a curved spacetime. A pervasive material permeating all of space and transmitting gravity is quite likely to have a very different mathematical description: incompatible with and contradictory to the mathematics of curved spaces. But there is as yet no proposed mathematical description of such a pervasive material, to my knowledge, so no comparisons can even be made.

Note that the mathematics describing an object undergoing force or acceleration in a noncurved (specialized space) are vastly different from the mathematics describing the global movement of an object experiencing only the effect of gravity, and the differences in the mathematics are to be found again represented in observation and experiment. In other words, curved spacetime (rather, general spacetime) without forces is a good description of gravity, i.e., in accordance with observation and experiment, while noncurved spacetime with forces is a poor description of gravity, essentially Newton's description, which is not in accordance with observation and experiment (namely, the observation that falling objects feel neither force nor acceleration).

The source of curvature in spacetime is, as asserted in Einstein's theory, material. This particular deduction from the mathematics has predicted very many astronomical discoveries, such as binary stars, pulsars, and black holes. By all accounts, general relativity is a very successful theory: its accurately describes the way bodies move in response to the presence of other moving bodies. It does leave unexplained the mechanism by which material effects curvature of spacetime, although the mathematical relationship between moving material and curvature of spacetime is completely specified. This lack of mechanism makes the theory suspect and difficult to swallow. But it does not change the fact that the assertion of a pervasive material permeating the universe is unable to account for the motion of material in the presence of moving material.

Link to comment
Share on other sites

The curved spacetime of general relativity doesn't need an explanation by some "real thing" (apart from the mass that causes the curvature) anymore than the 3-dimensional space of classical physics needs an explanation by some "real thing". It's only that we take the latter for granted, as we've in our life always experienced a 3-d space where Euclidean geometry applies accurately. We could as well ask: why has space just 3 dimensions? Why is its geometry Euclidean? We don't suppose that there is some "real thing" that causes this behavior, nevertheless it is part of reality, we never see a fourth or a fifth or whatever dimension, just the three we know. The desire to "explain" the curved geometry of GR is caused by the fact that it goes against our intuition, we think it's "obvious" that space is 3-dimensional and Euclidean and not curved and that time is an absolute, independent variable, but it is our intuition that is wrong, which is due to the fact that the direct effects of the curvature are not part of our everyday experience, as they are too small to be observed in daily life. So we tend to look for an explanation that describes the unintuitive theory in terms of the classical, intuitive theory with some extra factor added. Instead we should accept that reality isn't always in accordance with our intuition. In fact this is the same thing that makes Quantum Mechanics so difficult to understand, as we would like to rewrite it in classical terms that are in accordance with our intuition, which is doomed to failure, however.

Link to comment
Share on other sites

To say that physicists aren't concerned with the cause of why things are isn't really accurate. I believe that is what the current emergence of string theory is all about. It's the cause of all the four types of forces in the universe (gravitational, electromagnetic, strong, and weak forces). A good read is Briane Greene's "The Elegant Universe" (also a PBS Nova series)

Link to comment
Share on other sites

And tbere is a clear physical explanation for why you need different sense organs for color and temperature.... Can you give a similar physical explanation for perceiving time and space differently, if they are "components" of the same property? ... In other words, our way of measuring space intervals is fundamentally different from our way of measuring time intervals. What fact of reality lies behind this fundamental difference?

It is of course a fair question, and no I cannot offer a philosophical or metaphysical explanation of the nature of space and time and their relationship to our senses.

I do know, however, that treating space and time as fundamentally similar, as aspects of a whole instead of as wholes in themselves, has various advantages: it accounts for observation and experiment; it accounts for observation and experiment without the necessity of proposing new entities which there is no clear conception of, let alone evidence for; it accounts for observation and experiment without suggesting that extents and durations are somehow "fluid" in that physical extents and durations depend on how they are observed. Ether theories propose new entities into existence for which there is no evidence, and various popularizations of relativity suggest that extents and durations are fluid, but the actual relativity theory does neither.

Also, men can move freely between points in space within their limits, but they cannot for the lives of them move between points in time, except forward, in a strictly monotonous way. That sounds like another MAJOR fundamental difference, doesn't it? What is the explanation for that, if time and space are just components of the same property, merely broken down for easy perception?

In fact, the phrase "move between points" is not meaningful, neither on relativity theory nor on Galilean and Newtonian theory; the statement that "move between points" is not meaningful is part of the principle of Galilean relativity and is assumed in Newton's laws of physics, including his three universal laws of motion.

You'll have to elaborate on what exactly you mean by that, since as I hinted above, I don't think the idea of "time travel" makes any sense, and that is what you sound like you are talking about...

Your trajectory through spacetime (your "worldline") can be measured. The length along your trajectory between any two spacetime events on your trajectory is called "proper time," and it is the amount of time which passes for you as you move between those events along your trajectory. Another person taking a different trajectory through spacetime, such that the same two spacetime events are present on his trajectory as well (i.e. you two meet up at two distinct moments) will experience a different quantity of proper time.

The phenomenon is identical to that wherein you take a circular route between two cities and your friend takes the direct route: one of you will have traveled a shorter total distance.

Link to comment
Share on other sites

I have a question for you Relativity enthusiasts regarding motion and forces. When an object is in free fall, it is claimed that no forces are acting on it, that it, in a sense, is following the curvature of spacetime. I still think this means that one has to take spacetime as a real thing, but that is not my question in this post. If we take the complex roller coaster type of trajectory of, say, sending the Voyager spacecrafts to the outer reaches of the solar system by sending them by several of the planets in the process, I can understand, maybe, that they are following the curvature of spacetime, but they also speed up and slow down at various points along the trajectory. Doesn't there have to be a force acting on them for them to speed up or slow down?

I don't think one can claim that the Relativistic effects of being near a massive body accounts for this. In other words, time dilation wouldn't be all that great, so that one could not say that the speeding up or slowing down are simply due to the specetime effects of being near a massive body, because the bodies (the other planets) are just not massive enough for relativistic effects to be noticeable.

In other words, if the motion is caused by following the curvature of spacetime, and therefore no forces are acting on the spacecraft, then how does one account for the speeding up and slowing down?

Newton would say that in order to have any change in velocity -- a change in direction or speed -- that a force has to be acting on the object. Einstein, or at least his followers, claim that there are no forces acting on a body in free fall, and yet the velocity changes -- both direction and speed. If one says that it is due to a kind of downward sloping of spacetime, wouldn't there have to be a force in the downward direction to account for the change in speed?

Link to comment
Share on other sites

The feeling of standing on earth is the feeling of a force acting on you: the upward force of the Earth resisting your natural motion towards the Earth's center. The feeling of weightlessness is the feeling of nothing, i.e., of no forces acting on you. This of course has been tested repeatedly with instruments designed to identify and measure force. This phenomena of weightlessness is felt by astronauts hurtling through space from the Earth to the Moon, astronauts simply orbiting the Earth in the Shuttle, and astronauts in training on the Vomit Comet. When an object is in free fall, when it is moving in response to gravity and nothing else, no forces are felt. And yes, the Vomit Comet does move in a parabolic arc, first ascending and then descending for a period of 25 seconds, during which the occupants feel no forces. This is a real phenomena, tested and observed every day, and it requires an explanation. Newton's physics are inadequate to provide that explanation, because Newton considered gravity to act as a force and to be felt as a force. While Newton's physics do describe and predict the motions of objects to a high degree of accuracy when the objects move at low speeds with respect to each other, the same laws are inadequate to provide a correct physical explanation for the way gravity works.

Time dilation is not what causes curvature of spacetime. Conceptually, the two [mathematical] phenomena are completely unrelated. Dealing with space and time together as opposed to separately is done, mathematically, in flat geometry; curvature of a geometry is dealt with independently of the relation between space and time. High relative speeds have nothing to do with whether objects in free fall feel any forces acting on them.

Manifolds, Geodesics, Curvature and Local Flatness (General Relativity) - part of a FAQ on relativity theory, and (after skimming) seems to introduce well the concept of a locally flat and globally curved space. It is this phenomenon which accounts for motion which is always and everywhere locally constant and unaccelerated but which is globally accelerated (i.e., velocity changes). Recall that objects moving under the influence of only gravity do not feel any forces at all, and that an account of gravity which introduces forces is apparently wholly inadequate to explain gravitational motion. This is the (directly observable and testable) fact which led Einstein to hypothesize a curved spacetime.

Link to comment
Share on other sites

I am going round and round making the same points:

1. Free fall is, locally (at any and every instant), unaccelerated motion. That is, an object in free fall feels no forces whatever. Free fall is motion affected only by gravity. This fact comes from observation and experiment, and the observation and experiment can be performed by anyone anywhere.

2. Free fall is, globally (when two separate places or times are compared), seemingly accelerated motion. Again, this fact comes from observation and experiment.

3. Newtonian physics can account for this only by supposing that gravity somehow permeates through space by some physical mechanism, which remains undetected and undetectable - in such a way as to simultaneously affect the entire universe. The conclusion of this approach is that no equipment in free fall can measure the effect of gravity as a force on another object again in free fall, because the effect is canceled out, but that point 1 is false and appears true by obfuscation. Newtonian physics is a good approximation at low relative velocities, but breaks down at high relative velocities.

4. Einsteinian physics can account for this by taking point 1 at face value, but saying that point 2 is false and appears true by obfuscation, and explaining them by means of a curvature of spacetime. Curvature of spacetime seems a physical oddity, but it is far from a mathematical oddity. Einsteinian physics is, so far as we know, a perfect match at low and high relative velocities.

Newtonian physics accounts for all motions affected by gravity in one way, while Einsteinian physics accounts for it all in another way. Questions asking whether relativity account for this or that macro effect are pointless: yes it can.

Link to comment
Share on other sites

Newtonian physics accounts for all motions affected by gravity in one way, while Einsteinian physics accounts for it all in another way. Questions asking whether relativity account for this or that macro effect are pointless: yes it can.

The problem is that we observe an entity in free fall as accelerating (changing velocity), as when, say, a football is thrown up in an arc -- it starts off after leaving one's hand with a high speed, slows down at the top of the arc, and then speeds up as it falls to the ground. Newton accounted for this by saying that there is a constant force acting on the object, the football, as if, in effect, the earth is pulling down on the football. Einstein wants to say that the football is following the shortest path in fourspace (spacetime), that it is not really accelerating (not really changing velocity, direction, or speed).

In other words, there is an implication in Relativity that we don't really observe reality the way it really is.

Or let me ask that in the form of a question: If an object in free fall follows a geodesic of fourspace (the shortest path possible, following the curvature of spacetime), and this is taken as a straight line in fourspace (spacetime), is it slowing down or speeding up in fourspace? And if it is slowing down or speeding up in fourspace, doesn't that have to be accounted for with the idea that a force is acting on it? Let's say in the frame of reference of someone watching it from the earth.

Going back to my original question about the roller coaster ride of the Voyager spacecrafts (in our frame of reference), does Relativity really say that it followed a straight path with no acceleration whatsoever (no change in velocity, direction, or speed)? And again, if the answer to that question is yes, then that implies that we don't really observe reality the way it really is, because we most certainly observed the Voyager spacecrafts as following a very loop the loop trajectory. Is the claim that we observed it following a loop the loop trajectory not really observing what it is really doing (i.e. it is really following a straight, unaccelerated trajectory in spacetime)?

By the way, Newton did account for the fact of free fall by saying that everything in the spacecraft is being pulled equally (according to its mass) down towards a massive body, say the earth while the space shuttle is in orbit, and that it is all falling at the same rate.

Link to comment
Share on other sites

Yes, general relativity says that an object moving solely under the effect of gravitation experiences no forces whatever and does not undergo any acceleration whatever at any given instant in time. And yes, obviously, this contradicts the everyday observation that objects do seem to accelerate and do seem to experience a force when moving under the effect of gravitation. And again, this phenomenon is easily and straightforwardly accounted for by supposing that spacetime is curved and that the trajectories through spacetime of objects moving solely under the effect of gravitation are geodesics: at any point or time, perfectly straight, but the result (in terms of, say, one's velocity) of moving from point A to point B depends on how one moves. Spherical geometry shows an example of what happens to an orientation in space as it is dragged along a sphere:if one drags the arrow from the equator to the north pole, the arrow points in one direction, but if one first drags the arrow 90 degrees to the left around the equator and then to the north pole, the arrow points fully in another direction. As you can see, the orientation of the arrow depends on its path through space along the surface of the sphere. In a similar way, velocity is an orientation in spacetime, and the orientation of an object moving along a trajectory depends on that trajectory.

Newton accounted for the impossibility of observing local acceleration of an object moving in free fall by supposing that every gravitating object instantaneously and simultaneously affects the entirety of the universe ... and naturally did not offer a causal explanation, because such a proposition violates the principle that all of physics is local (that is, nearby objects affect nearby objects, and faraway objects affect each other only after time has passed so that whatever carries a force from one place to another has the time to carry it). In other words, Newton's explanation of why no acceleration could be detected was that the entirety of the universe was working against such detection. Einstein accounted for it more straightforwardly ... if one is comfortable with geometry in four dimensions and having curvature.

Link to comment
Share on other sites

  • 5 weeks later...
No... Lorentz derived them first. That's why! <_<

The co-ordinate transform named after Lorentz was first derived by Fitzgerald and it is usually called the Lorentz-Fitzgerald transformation in the literature. See http://www.tcd.ie/Physics/history/fitzgerald/

What is significant is the -manner- in which Einstein derived the equations of electrodynamics. He made two assumptions:

1. The speed of light in vacuo is constant and the same in every inertial frame of reference regardless of the motion of the light source.

2. The laws of physics are the same in all inertial frames of reference. Einstein later generalized this principle to all frames of reference in his General Theory of Relativity.

May I recommend reading -The Principle of Relativity (A collection of original papers on the special and general theory of relativity. Notes by A. Sommerfeld)- This is available from Dover in paperback ISBN 0-486-60081-5.

The first two papers in this collection are by H.A.Lorentz in which he derives differences in lengths and clock time between inertial frames. He derives his results based on the existence of the aether, a elastic substance which fills all of space and carries light waves.

Einstein derives the very same equations based on the two assumptions (given above) without assuming the existence of the aether. This is has famous 1905 paper -On the Electrodynamics of Moving Bodies-.

It turns out that Maxwell's Equations are Lorentz Invariant but Newton's laws of motion are not (they are Galilean Invariant). Einstein resolved the dissonance by restating the laws of mechanics in Lorentz Invariant form. Under this regime rest mass is invariant in all inertial frames, but measured mass (or relativistic mass) varies with the velocity of the body whose mass is being measured.

mass-relativistic = mass-rest/sqrt(1-v*v/c*c)

where v is the velocity of the body and c is the speed of light in vacuum (a constant).

In relativistic mechanics momentum is now defined to be:

momentum-relativistic = mass-rest*v/sqrt(1-v*v/c*c).

contrast this with classical momentum; mass*velocity where mass is assumed to be invariant in the classical regime.

This quantity is conserved in all interactions, so the conservation of momentum holds in the relativistic version of mechanics as well as in the classical

To see more on this I recommend: -Space Time Physics- by Taylor/Wheeler; W.H.Freeman & Co. 1963, 1966. There is a new edition put out in 1992, but I do not think it is as good. Newer is not necessarily better.

Or one can read Volume 1, Chapter 15 of the well known three volume collection of Richard Feynman's Lectures (Leighton and Sand)

For those who are not entirely happy with Einstein's theories (both special and general theory of relativity) please note:

1. they predict accurately in all cases where as classical physics fails under some circumstance.

2. they have not yet been empirically falsified.

3. special relativity + quantum theory gives quantum field theory which is the basis of the Standard Model, the most accurate physical theory every formulated. It deals with all phenomena except gravitation.

3. General Theory of Relativity accurate predicts gravitational phenomena in medium and weak strength gravitational fields. It predicts bending of light in the neighborhood of massive bodies, the gravitational red-shift and the precession of orbits planets, which Newton's law does not get quite right.

Enjoy! L'chayim.

ruveyn

Link to comment
Share on other sites

Namely?

The two postulates of Einstein's eletrodynamics.

1. The laws of physics are the same in all inertial reference frames. Physical laws do not depend an a particular or privileged frame of reference. (This is the principle of relativity).

2. The speed of light in free space (not within some lump of matter) is the same (a constant) when measured in any inertial reference frame and is independent of the motion of the source.

From these two assumptions Einstein inferred the same equations for electrodynamics as did Lorentz. Einstein's approach was simple and clean. Einstein derived additional results including the famous equation E = m*c^2.

Einstein's derivation of the Lorentz-Fitzgerald transformation was cleaner and simpler.

For a direct comparison of the approaches see -The Principle of Relativity- ISBN 0-486-60081-5 which is a collection of the early papers on the subject of relativity and electrodynamics. In particular see -Electromagnetic Phenomena in a System Moving With Any Velocity Less Than That of Light- (Lorentz, 1904 pp 11-34; and -On the Electrodynamics of Moving Bodies- (Einstein,1905, pp 37-65. For the derivation of the Famous Equation see -Does The Inertia Of a Body Depend Upon Its Energy Content?- (Einstein,1905, pp 69-71). Einstein gets the results -without- assuming the existence of a light carrying aether substance. Lorentz not only assumes the aether, but a pre-quantum theory of electrons which, in the long run, turns out not to be right. (A better atomic theory started with the work of Bohr in 1913, 9 years after Lorentz published). From an application of Occam's Razor, Einstein has the better approach. He does not assume aether nor does he assume any properties of electrons.

ruveyn

Link to comment
Share on other sites

From an application of Occam's Razor, Einstein has the better approach. He does not assume aether nor does he assume any properties of electrons.

Occam's Razor is for choosing between two theories that otherwise have equal merit. If one of the theories is philosophically flawed, that's a razor that cuts it out of contention well before Occam's one can be applied.

Link to comment
Share on other sites

Occam's Razor is for choosing between two theories that otherwise have equal merit. If one of the theories is philosophically flawed, that's a razor that cuts it out of contention well before Occam's one can be applied.

The merit of a physical theory lies in the predictions it makes. Good theories make correct predictions. Bad theories make incorrect predictions. Both of Einstein's relativity theories are well supported by experimental test and neither have been falsified by experiment. That is over 100 years for Special Theory and over 90 years for General Theory. Both theories have been tested vigorously and continue to be tested vigorously. Furthermore the special theory is one of the pillars of quantum field theory which is the gut of the Standard Model, far and away the most accurate physical theory ever produced.

As to the application of O.R., it was the comparison between Lorentz's aether based theory and Einstein's electrodynamics. Lorentz presumes the existence of light bearing aether which has never, ever been detected. The famous Michelson Morley experiment failed to show it and the Trouton Noble experiment failed to show it. More modern and sophisticated experiments fail to show it. So far no physical experiment or measurement has indicated the existence of the sort of aether that Lorentz assumed. Additionally, Lorentz assumed electrons which obeyed classical electrodynamic laws (pre-quantum laws). We know that this hypothesis is incorrect because under classical electrodynamics the atom would collapse in something like 10^-11 seconds, which clearly does not happen. So what is the score? For Lorentz, he assumes a quasi-solid elastic medium, never seen experimentally and a kind of electron whose existence is inconsistent with stable atoms. On Einstein's side, two straightforward assumptions, both of which -are- experimentally supported. Einstein gets to the co-ordinate transforms clean and straightforward. In that sense, Einstein's is the better theory. That and the fact it is an integral part and foundation of the best physical theory ever proposed (Standard Model).

Theories in physics are intellectual artifacts for predicting the outcome of experiments under specified conditions. When a theory makes a prediction falsified by experiment, then it is a -wrong theory-, all philosophical considerations aside. I am trying to dig up (unsuccessfully, so far) a quote from Lorentz indicating that he believed Einstein's approach was the better. When I find it, I will post it, with your kind permission. Einstein and H.A. Lorentz were dear friends and Einstein held Lorentz in the highest esteem. Lorentz admired Einstein's fresh and bold approach (Einstein was a kid in 1905, only 26 years old, and he carried a lot less baggage than did H.A. Lorentz). When Lorentz died, Einstein wrote a moving praise and epitaph to his departed friend.

I have a different take on physics theories than you do. I judge them on three grounds:

0. Mathematical consistency.

1. They predict correctly.

2. They lead to successful technology by way of applied science and engineering art.

Einstein's theories win big on all counts. A practical application? How about nuclear fission power generation? (E=mc^2) How about the GPS which is a clear triumph derived from the time corrections of both the Special and General theories of relativity. Virtually all of the technology produced since 1948 (the year Bell Labs came out with the transistor) have been consequences of quantum field theory which is partially based on Einstein's special relativity.

ruveyn

Link to comment
Share on other sites

Theories in physics are intellectual artifacts for predicting the outcome of experiments under specified conditions. When a theory makes a prediction falsified by experiment, then it is a -wrong theory-, all philosophical considerations aside.
Well you can view physics as being nothing more than an elaborate mathematical framework for making predictions if you like but the consequence is that physical theories no longer say anything about what reality is actually like. If you want to maintain that objects like electrons/quarks/etc dont really exist and are just convenient mathematical fictions then noone can prove you wrong, but it essentially removes all purpose from physics other than the creation of new technology, and it cant really be called a means of understanding the world anymore . A set of mathematical equations cant dictate their own interpretation: look at the many different ways of giving a physical interpretation of the quantum mechanics formalism for instance.

Other sciences such as biology/neuroscience/medicine are capable of creating theories which actually describe objects existing in the world rather than just giving a set of equations to predict things with, I'm not sure why you think physics cant do the same. Prediction is nice but it isnt everything - being able to explain a host of already known facts and tie them into a coherent framework is equally important. Look at the theory of evolution for instance: it has limited predictive power (compared to theories in physics), but that isnt really where its virtue lies.

Edited by eriatarka
Link to comment
Share on other sites

Well you can view physics as being nothing more than an elaborate mathematical framework for making predictions if you like but the consequence is that physical theories no longer say anything about what reality is actually like. If you want to maintain that objects like electrons/quarks/etc dont really exist and are just convenient mathematical fictions then noone can prove you wrong, but it essentially removes all purpose from physics other than the creation of new technology, and it cant really be called a means of understanding the world anymore . A set of mathematical equations cant dictate their own interpretation: look at the many different ways of giving a physical interpretation of the quantum mechanics formalism for instance.

In a pinch, I will take the reality of technology over the illusion of understanding. People who held the caloric theory of heat really believed they understood heat. They were wrong. People who believed that electric charge was a continuous fluid were wrong (that includes Ben Franklin, Michael Faraday and James Clerk Maxwell). They took the fluid notion so seriously that the first capacitors were called Leyden -jars- after the place at which they were invented. A good deal of what we call understanding is, in reality heuristic, and plausible metaphor. What is essential to our survival is that we understand reality at man scale, under the conditions in which our intelligence evolved. Einstein's goal of reading the Mind of the Old One, was a tad over the top. I would say the human race understands the world at man scale quite well. Proof: we survive. And we survived when we did not have fancy science too. Somehow the pyramids were built and ships sailed around the earth before we developed a comprehensive science of mechanics. Compasses were in use long before Oestead revealed the nature of magnetism.

If we want to really, really, really understand Reality we have to get resolution to Planck Length. Currently we are fifteen orders of magnitude from that goal with our best theories and technology. Do you think we will make it? I don't, at least not in the short or medium run. I think we will have to mutate until we have 30 pound brains to do that. But that does not bother me as long as our best theories guide the applied scientists and engineers well.

Given a choice between waiting for Understanding and finding my way to East Elbow, Wyoming using my GPS, I will use the GPS. Understanding will happen when it happens.

ruveyn

Link to comment
Share on other sites

In my philosophy class today, an interesting discussion occured when one of my classmates brought up the issue of Einstein's Theory of Relativity. He quoted a postulate developed by leading physicists which stated something to the effect of "If a beam of light was fired at a train while it was moving and the doors of the train opened via light sensory mechanics. To an observer inside the train, the doors would open simultaneously but, to an observer standing outside, they would be off-timed, and yet, this is not a contradiction. My teacher explained this as a proof of space being a relative concept of location between objects. How does this differ from primacy of conciousness or any other idea of subjectivism?

There is no contradiction and in fact this postulate has been validated and is absolutely true. Also space IS a "relative" concept in that space (that emptiness between planets, stars, etc...) is a relationship between those several objects. This, however, is not to say that any of these ideas are based on a "primacy of consciousness" or "subjectivism".

In order for it to be a contradiction it would have to both be and not be in the same respect. Being in a different inertial reference frame is obviously a differing "respect".

According to Taylor in his book Classical Mechanics, time dilation was first validated by B. Rossi and D. B. Hall in 1941. There was another experiment done in 1971 which came to the same conclusion using four synchronized atomic clocks. They were flown around the world in a plane and came back with a discrepancy (relative to a stationary clock at the U.S. Naval Observatory) of 273 +/- 7 ns which was in definite agreement with the predicted 275 +/- 21 ns. Not to leave you with the idea that there have only been these few experiments, I would note that GPS relies upon the theory of relativity to give you accurate location data. So the theory is absolutely right in that it correctly describes this ACTUAL phenomena of time dilation.

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
  • Recently Browsing   0 members

    • No registered users viewing this page.
×
×
  • Create New...