Interesting. As I understand it, preferred frame is just another way of saying absolute frame, correct? Also if there exists preferred frames in the Universe, what is meant by “if the Universe has a preferred frame?”
And I assume Newton’s Theory of Gravity would be a theory with a preferred frame, right? And yes, I think the fact that there are solutions with preferred (absolute) frames might possibly have theological implications.
Not always. Preferred frames are frames where the laws of physics take their most natural form, usually mathematically represented as being simplest. Absolute frames are frames where one can take their measurement of time and space to be their true values. To wit, a theory can have many preferred frames, but only one absolute frame.
When we talk about preferred frames, the relevant theory is not Newton’s theory of gravity, but Newtonian mechanics. Newtonian mechanics has an infinite number of preferred frames, called inertial frames. Newtonian mechanics can be formulated in a way so that it has an absolute frame, but not necessarily so, in the sense that depending on how one formulates it, you can have (or not) absolute space. You always have absolute time in Newtonian mechanics.
As an example, a solution that has a preferred frame is a Universe with a single black hole. The frame that is at rest with respect to the black hole is preferred, but the theory of gravity that borne this solution has no preferred frame. A priori, this does not grant this solution an absolute frame.
Galileo and Newton came up with the concept of inertial frames of reference,
meaning non-accelerated frames of reference. They stated the fundamental principle of Newtonian Mechanics All inertial frames of reference are equivalent. The laws of mechanics may be derived in any inertial frame. There is no preferred inertial frame of reference.
I don’t recall seeing this in the ultimate book on Mechanics, namely, Goldstein…but for now I’ll accept it.
And then Einstein’s 1st postulation of Special Relativity:
All the Laws of Physics may be derived in any inertial frame. No law of physics
will distinguish any preferred reference frame
Before Einstein, Lorentz and Fitzgerald postulated that the speed of light is invariant in a vacuum ir-resepective of the inertial frame light was being measured. One can derive the Lorentz transformation from the approximation known as Classical Electromagnetism based on Maxwell’s equations. The Lorentz transformation became one of the pillars of Einstein’s special relativity.
Historically, the transformations were the result of attempts by Lorentz and others to explain how the speed of light was observed to be independent of the reference frame, and to understand the symmetries of the laws of electromagnetism. The Lorentz transformation is in accordance with Albert Einstein’s special relativity, but was derived first.
Inertial frames are subtle. Technically speaking, since we are on a planet that is rotating, we are in an accelerating frame. This is noticed by things like the centrifugal force at the equator and the corrioliss forces in various locations. These are called fictitious forces. Also there is gravity which creates forces too – wiki says gravity is a fictious force too – but that’s the first time I heard that!
To adjust for gravity, the “straight” lines have to be bent to create what are known as geodesics. So computing the speed of light in a gravitational field involves computing the distance along the geodesic, not a Euclidean straight line.
There is a small dissenting minority that believe inertial reference frames can be distinguished the variations in the measured the speed of light in refractive media of different inertial frames and possibly different locations in universe. Some in that group of dissenters are the neo-Lorentzians, in honor of Lorentz. I have sympathy for the neo-Lorenztian view.
The laws of mechanics may be derived in any inertial frame. There is no preferred inertial frame of reference.
There is no preferred inertial frame of reference among the family of inertial frames, but all of the inertial frames are preferred frames with respect to the collection of all frames. Newtonian mechanics has an infinite number of preferred frame.
This is a trivial fact that one should already understand from Freshman mechanics. If you’re already reading Goldstein without understanding this yet, you’re trying to run before knowing how to walk. As a classical mechanist, I also contest the view that Goldstein is the ultimate book on mechanics; it’s far from it…
This, again, is trivial to anyone who has taken even a single class on GR. I’m surprised that you haven’t heard of it, as you claimed that you’ve learned GR.
These are not the neo-Lorentzians, but a subset of people who are neo-Lorentzians.
Oh, I am not contesting that Goldstein is an excellent book, but it is written for general graduate students, not for specialists in classical mechanics. For example, you asked me before about the tautological one-form, which is absolutely crucial in understanding classical mechanics as a specialist, but is not covered in Goldstein.
There is no single book. One needs to go through series of books starting from beginning undergraduate (e.g. lots of books here, I don’t know what is good anymore), middle undergraduate level (e.g. Taylor), to graduate level (e.g. Goldstein), to specialist (e.g. Arnold). Do not skip, and do not try to run before you walk. If you do so, you will never learn anything. Not to be offensive, but from what you have been saying, you’re not ready for Goldstein yet.
I already took the graduate class and Goldstein was our textbook up through about 2/3 of the chapters. But, I’ve forgotten so much. The class was for Engineers working at the Applied Physics Lab, not pure physics undergrads.
The only time I saw the word one-form was in Bernard Shutz’s relativity.
That’s for sure. I was able to get through the exams well enough, but I can’t say I really understood. I knew enough to recognize template and canned problems and how to plug and chug, but I can’t say I understood.
Our discussion has been good in stimulating interest to go back and learn, really learn.
So Newton’s theory of gravity is his explanation of what gravity is, i.e., a force, and Newtonian Mechanics is the description of how gravity works, i.e., physical concepts and mathematical equations? And both are considered theories separate from each other?
@Jim Newtonian mechanics is his theory of motion, \vec{F} = m \vec{a}. It is a framework that tells you how bodies and forces interact with each other. Newtonian gravity is his prescription of what \vec{F} is for gravitational forces, that you can then plug into Newtonian mechanics. Newtonian gravity is a particular application of Newtonian mechanics.
If I’m not mistaken you are referring to Newtonian laws. As I understand it theory is usually defined as an explanation about phenomena. And laws and mechanisms are usually defined as descriptions about phenomena. In other words, theory is prescriptive, and laws and mechanisms are descriptive.
By that understanding Newton’s “theory” of gravity explains gravity as a force. Whereas Einstein’s “theory” of relativity explains gravity as a space-time continuum. However, it seems theory is also used in a broader sense that incorporates both prescriptive and descriptive into the term, i.e., not only “theories,” but also “laws” and “mechanisms.” Is that correct?
@Jim Correct, “laws” are descriptions about phenomena, while “theories” are explanations.
However, don’t put too much stock on words like “laws” or “theories” etc that physicists put in front of their phenomena, e.g. “Newton’s laws of motion” or “Einstein’s theory of general relativity”. Usually it’s more historical than anything.
For example, in the past we have “laws of conservation of energy”, but now we know that this “law” is actually a “theorem” (which is a completely different beast from “theory”). It is also common to hear Newtonian gravity being referred to as both Newton’s laws of gravity and Newton’s theory of gravity. We save those distinctions for the philosophers.
From what I can gather, Newton based his theory on absolute space. So would that be what you would consider a theory with preferred frames? It’s a little unclear to me since preferred frames and absolute space aren’t exactly synonymous. But it seems to me absolute space would entail preferred frames, wouldn’t it?
It seems to be a bit more complicated than that. Newton may have put forward the idea of absolute space, but Newtonian mechanics works just fine without one:
Obviously, the stars Newton referred to as fixed aren’t fixed. They are moving. I’m sure that if Newton were alive today he would agree that there is no absolute space in his model.
Yes, I agree. There certainly may be more to it when examined more carefully. Thinking more about the concept of absolute space, could it be that it’s more of a philosophical issue rather than an issue of physics?
From what I can tell, Einstein seems to have dismissed absolute space on the philosophical grounds of verificationism, a form of logical positivism. If so, that probably means that his assumption no longer holds since verificationism has been shown, among other things, to be self refuting, and is no longer considered a viable position among contemporary philosophers.
From what I can tell, Newton’s concept of absolute space seems to be based on theistic reasons and independent of physical existence. So in light of the demise of verificationism could it be that his argument for absolute space would possibly still be in the running?
Repeating my previous caveat, I am not a physicist so don’t take my posts as gospel. We are probably both hobbyists in this area of science, and being such we like to discuss the topic. With that said . . .
Defining a reference frame is certainly an issue in physics. Also, physicists have run tests to see if the laws of physics are different in different reference frames. I did find an interesting paper that combines these two topics:
They tested the isotropy of the speed of light in Earth’s frame of reference, and did not see any change within the detection limits of their instruments. It is also interesting that they used the cosmic microwave background as a way of describing Earth’s movement. Of course, they could have used any reference frames they wanted, but using the CMB sounds like a pretty nifty idea for standardizing reference frames.
It’s interesting how the CMBR seems to be used as somewhat of a global preferred inertial reference frame. I first read about this with the work of Mather and Smoot who were awarded the 2006 Nobel Prize for what they did.
I’m not real clear on what’s being said here. It seems to imply that because we haven’t come up with a means to measure the true values of time and space in the sense of a global, or universal frame, therefore, until such a time that we are able to measure the true value of such, we have to conclude that absolute space doesn’t exist. Am I understanding that correctly?
I have become convinced that there is no possibility of a global/universal frame. And thus we shall never be able to measure the true values of time and space, because such true values could not exist.