What is the best frame of reference?

[nicknaq]

So I was studying some physics, and I keep encountering how many things depend on the frame of reference.
For example, kinetic energy and momentum.

My question is if there is an absolute frame of reference? Can we define one?

I remember reading somewhere that the absolute reference is the speed of light? Can someone explain whatever the answer is to me?

(this is my curiosity asking the question, not homework)

 

[K^2]

One of the postulates of General Relativity is that there is no absolute frame of reference. It's kind of an important one, and considered to be one of the standards for any other theory.

Speed of light is always a constant in all frames of reference, but it does not define a frame of reference. There is a lite cone transformation, but it's a bit of a complicated topic from relativity, and it doesn't change the answer.

Not all frames of reference are equal, however. There is a special class of these that are inertial. It is often convenient to choose an inertial frame of reference, because they are far easier to deal with. In an inertial frame of reference, energy and momentum are naturally conserved and the Newton's laws of motion hold without need to add fictitious forces. If you are dealing with relativity, in an inertial frame of reference you only need Special Relativity, which is far simpler than General Relativity.

Simplest example of a frame of reference that is not inertial is a rotating frame of reference. If you are inside a closed room and that room rotates, it appears that objects are acted on by some additional forces that seem to come from nowhere. There is the centrifugal force, pulling everything towards the outer edges of the room, and there is Coriolis force that makes thing move in a curve when they move towards/away from center. These are fictitious forces, because they are only there as a result of your coordinate system choice. But if things accelerate on their own under action of centrifugal force, the energy is not conserved. To fix that, you need to introduce an additional potential energy which is highest at the center of the room. That's called an effective potential. Same idea. It's only there because of a "bad" coordinate system choice.

Once you recognize that the room is actually rotating, however, and choose coordinate system that is not rotating with the room, you can describe all motion without these additional forces or potential.

If you know how to deal with these things, you can choose a coordinate system that's not inertial and work with it. You just have to be careful. And sometimes, this is a more convenient way to deal with it. If you are designing a space station that's going to generate artificial gravity by rotation, it's easier to go to a rotating frame of reference, so that the station is "still", and you just account for centrifugal and Coriolis effects in your design.

 

[D H]

First off, what does "best" mean? My definition: The best frame of reference for some problem is that frame that make my job of solving that problem least intractable. With that definition, there is no single "best frame of reference." What constitutes the "best" frame for one problem will be quite different than the "best" frame for some other problem.

Suppose the problem at hand is to model the Earth's weather. This problem is hard enough when done from the perspective of a frame that rotates with the Earth. Choose a non-rotating frame and, woo-boy, you have an intractable mess.

Suppose the problem at hand is to model the dynamics of the solar system. This problem is hard enough when done from the perspective of a non-rotating frame with origin at the solar system barycenter. Do this from the perspective of an Earth-fixed frame and you once again have an intractable problem. Its worse than intractable: That polar motion is unpredictable means you have just thrown out high accuracy and future predictability with this choice.

 

[Danger]

My opinion is that the only frame of reference that matters is my own.
I have friends, most of whom are PF members, who have issued challenges to my opinions. While I might disagree, I have to rely upon my personal experience in life for a final opinion. That experience might be diametrically opposed to that of others. If I had grown up in Uganda or the US or Egypt, I would not be the same person that I am today. (That might very well be a turn for the better, but I have to live with what I am.)

 

[Drakkith]

Is there a frame of reference that can be regarded as standing still in space? One that you can measure every other reference from?

 

[Danger]

Yes and no. It's always referenced to the observer.

 

[1MileCrash]

Is there a frame of reference that can be regarded as standing still in space? One that you can measure every other reference from?

No, because that would mean it would be possible to measure absolute motion, which violates SR.

It is impossible to measure motion relative to space. You can only measure motion relative to something else, because motion is only relative to something else.

Moving at a constant speed of any value and staying "still" are all the same thing, physically.

 

[Danger]

That is a much better response than mine, 1. I agree with you, but was too lazy to articulate what I meant. (Okay, laziness isn't the problem. There's a new episode of "Bones" on TV, so I post only during commercials.)

 

[D H]

No, because that would mean it would be possible to measure absolute motion, which violates SR.

An absolute frame (and hence absolute motion) does not violate SR. SR says that there is no need for an absolute frame of reference. It does not say that an absolute frame of reference does not exist.

 

[darkfrog]

One of the postulates of General Relativity is that there is no absolute frame of reference. It's kind of an important one, and considered to be one of the standards for any other theory.

Speed of light is always a constant in all frames of reference, but it does not define a frame of reference. There is a lite cone transformation, but it's a bit of a complicated topic from relativity, and it doesn't change the answer.

Not all frames of reference are equal, however. There is a special class of these that are inertial. It is often convenient to choose an inertial frame of reference, because they are far easier to deal with. In an inertial frame of reference, energy and momentum are naturally conserved and the Newton's laws of motion hold without need to add fictitious forces. If you are dealing with relativity, in an inertial frame of reference you only need Special Relativity, which is far simpler than General Relativity.

Simplest example of a frame of reference that is not inertial is a rotating frame of reference. If you are inside a closed room and that room rotates, it appears that objects are acted on by some additional forces that seem to come from nowhere. There is the centrifugal force, pulling everything towards the outer edges of the room, and there is Coriolis force that makes thing move in a curve when they move towards/away from center. These are fictitious forces, because they are only there as a result of your coordinate system choice. But if things accelerate on their own under action of centrifugal force, the energy is not conserved. To fix that, you need to introduce an additional potential energy which is highest at the center of the room. That's called an effective potential. Same idea. It's only there because of a "bad" coordinate system choice.

Once you recognize that the room is actually rotating, however, and choose coordinate system that is not rotating with the room, you can describe all motion without these additional forces or potential.

If you know how to deal with these things, you can choose a coordinate system that's not inertial and work with it. You just have to be careful. And sometimes, this is a more convenient way to deal with it. If you are designing a space station that's going to generate artificial gravity by rotation, it's easier to go to a rotating frame of reference, so that the station is "still", and you just account for centrifugal and Coriolis effects in your design.

What FOR is the room rotating measured against? IOW, if the people inside the room feel a force pulling them against the wall, they could deduce it is rotating but in relation to what? Isn't the space it is rotating in an absolute frame?

 

[Acuben]

I don't think there is absolute frame of reference. you would have to define it in each situations.
if it's for calculation, it seems like a useful "absolute frame of reference" (if you must make one, but it's probably not necessary) is location where inertia frame of reference does not change.
In another words useful absolute frame of reference is location where it does not accelerate.

It's just my opinion.

 

[1MileCrash]

An absolute frame (and hence absolute motion) does not violate SR. SR says that there is no need for an absolute frame of reference. It does not say that an absolute frame of reference does not exist.

My mistake.

I suppose my opinion that an absolute frame of reference doesn't exist is more of an innate conclusion of my own.

 

[Drakkith]

If the higher your velocity, the slower your clock runs, could you send a probe or something out, and from that probe launch other probes that accelerate away in all directions and then compare the timing of each clock with the clock on the original probe that didn't accelerate? If we are moving through space, would one of the probes show its clock as speeding up, or at least not slowed down as much as it should if we weren't moving through space? Does that make sense?

 

[K^2]

IOW, if the people inside the room feel a force pulling them against the wall, they could deduce it is rotating but in relation to what? Isn't the space it is rotating in an absolute frame?

First of all, you can't actually deduce that you are rotating. It's the most likely scenario, yes, but a super-massive ring just outside the room that is rotating at sufficient rate to cause gravitomagnetic Lorentz forces inside will provide you with all the same symptoms. You'll be pulled to the outer walls of the room by gravity, and you'll feel "Coriolis effect" when walking around due to Lorentz forces.

The fictitious forces due to accelerated frame are indistinguishable from the effects of gravity. That's one of the GR postulates, and that's what makes it all so much more interesting.

Of course, if you simply assume that the room is rotating, you'll still get all the right dynamics in the inertial frame, since the inertial frame is the same in both cases.

Finally, as far as absolute rotation... That's one of the problems with GR that Einstein himself didn't like. Ideally, we'd like to see all acceleration and rotation as relative to distant masses. That's the Mach's Principle. GR has absolute acceleration and absolute rotation instead. That suggests that there is something very fundamental that we still don't understand about the physics of space-time.