# Inertial frame dependent on mass?

• mixinman7
In summary: I don't understand how you came up with this mangled definition when any number of good definitions can be found via Google or in any decent book on SR.It's called critical thinking - a seemingly rare skill among humans.
mixinman7
My question is: Is the inertial reference frame dependent on mass?

In re-reading materials on the topic of special relativity, I have noticed something that passed my attention previously. Within the inertial reference frame, the mass of test particles isn't necessarily dependent on how they will behave in relativity. An astronaut will float in a spacecraft as well as a drop of water will. However, the inertial reference frame varies depending on the total mass of the object. For example, a scrap bolt orbits the Earth closer than a spaceship when traveling at the same velocity. Likewise with the moon if it too traveled at that velocity. So the inertial reference frame depends on its mass if I am not mistaken. Does this mean that relativity must be considered in terms of mass, velocity and time?

The inertial reference frame is x$^{2}$-t$^{2}$ = x'$^{2}$-t'$^{2}$

Mass doesn't matter in these frames, however it does affect where the frame is located in an orbit. So, is the inertial reference frame dependent on mass? Can it be explained why, if not? If mass does effect the inertial reference frame, what might that effect be?

Thanks

mixinman7 said:
My question is: Is the inertial reference frame dependent on mass?

I'm at a loss to see where you came up with this misconception, so perhaps you should start at the beginning: what is an inertial reference frame?

Daverz said:
I'm at a loss to see where you came up with this misconception, so perhaps you should start at the beginning: what is an inertial reference frame?

The inertial reference frame is where a mass will maintain its velocity without being influenced by another force. From this, in an orbit an object like the moon or a man made satellite can maintain its velocity without another force.

I love that my description of reality is named a "misconception."

mixinman7 said:
Does this mean that relativity must be considered in terms of mass, velocity and time?

That's actually a very clever observation. There are papers where the quadratic form

$$(x,y,z,t) \ \mapsto \ x^2 + y^2 + z^2 - t^2$$

has been augmented to include mass (and even other terms)

$$(m,x,y,z,t) \ \mapsto \ m^2 + x^2 + y^2 + z^2 - t^2$$

I don't remember the authors' names and haven't really read the papers. In at least one case the author claimed a better match to experimental data. In any event, I'm not sure the papers had been peer-reviewed and if that is not the case they shouldn't be discussed here.

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mixinman7 said:
My question is: Is the inertial reference frame dependent on mass?
Mass is part of the 0,0 component of the stress energy tensor in the EFE, so I would say yes in GR. In SR they are not simply because the masses are explicitly assumed to be negligible, but your question seems to be a GR question.

Inertial frames are defined in SR and GR as observers traveling on non-spinning geodesics. In SR these are (Euclidean) straight lines, but when gravity is present they are generally not

mixinman7 said:
The inertial reference frame is where a mass

Any mass.

will maintain its velocity without being influenced by another force.

You've got the inertial part, but not the reference frame part. The mass is not a part of the reference frame. In your incomplete description, it's just a test particle for selecting inertial reference frames. Again, reference frames, inertial or otherwise, have no mass and are not dependent on any mass.

I don't understand how you came up with this mangled definition when any number of good definitions can be found via Google or in any decent book on SR.

From this, in an orbit an object like the moon or a man made satellite can maintain its velocity without another force.

If you want to consider gravitational fields, you can only talk about local inertial frames.

Daverz said:
...I don't understand how you came up with this mangled definition when any number of good definitions can be found via Google or in any decent book on SR...

It's called critical thinking - a seemingly rare skill among humans.

Daverz said:

I would appreciate this post being removed, or the thread. I got the answer I needed. Thanks for the responses.

Classically (Newtonian gravity), the radius of the orbit is not affected by the test object's mass, only the gravitating body's mass. What are you basing your statement of different orbits for different masses on?

Matterwave said:
Classically (Newtonian gravity), the radius of the orbit is not affected by the test object's mass, only the gravitating body's mass. What are you basing your statement of different orbits for different masses on?

This is a simple concept. The sun is very massive and far away from the earth. The moon is less massive, and closer to the earth. An orbiting man-made satellite is less massive, and closer to the earth. A bolt is less massive and closer to the earth. Velocity is a factor, so hold the velocity constant, and the mass determines the sustainable orbit.

I understand that my post may be confusing. It is conceptually based. I hope this helps

mixinman7 said:
The sun is very massive and far away from the earth. The moon is less massive, and closer to the earth. An orbiting man-made satellite is less massive, and closer to the earth. A bolt is less massive and closer to the earth.
The space station is more massive than a communications satellite but orbits closer to earth.

mixinman7 said:
This is a simple concept. The sun is very massive and far away from the earth. The moon is less massive, and closer to the earth. An orbiting man-made satellite is less massive, and closer to the earth. A bolt is less massive and closer to the earth. Velocity is a factor, so hold the velocity constant, and the mass determines the sustainable orbit.

I understand that my post may be confusing. It is conceptually based. I hope this helps

But you refer to accelerating objects. There are no inertial frames associated with accelerating objects.

An inertial frame is just a special type of (t,x,y,z) coordinate system that covers all of spacetime. Although there are no inertial frames associated with accelerating objects, an inertial frame can contain as many accelerating objects as we like - unless we are using a general relativistic description of gravity, in which case there are no global inertial frames.

atyy said:
But you refer to accelerating objects. There are no inertial frames associated with accelerating objects.

An inertial frame is just a special type of (t,x,y,z) coordinate system that covers all of spacetime. Although there are no inertial frames associated with accelerating objects, an inertial frame can contain as many accelerating objects as we like - unless we are using a general relativistic description of gravity, in which case there are no global inertial frames.

Free-fall frames are "inertial" frames in GR because gravity is no longer a force producing an acceleration but a curvature in the space-time.

I'm not sure what exactly the OP is trying to talk about though. If he wants to talk in the context of SR, or GR, or what. Newtonian mechanics has that, for a circular orbit:

$$r=\frac{GM}{v^2}$$

Which is only dependent on the gravitating mass and not the test mass. The radius of orbit is determined by the velocity of the test object and not its mass. There perhaps could be effects due to coupling of the gravitational fields (if the test mass is massive enough to give a non-negligible contribution to the field) in which case the radius of orbit may be dependent on the test mass, but I haven't analyzed that situation deeply, and I would expect the OP to provide that analysis since this is his thread.

Matterwave said:
I'm not sure what exactly the OP is trying to talk about though.

Me neither - it seems rather muddled.

DaleSpam said:
The space station is more massive than a communications satellite but orbits closer to earth.

The space station has to travel faster to orbit lower than a communication satellite. The space station can be seen http://spaceflight.nasa.gov/realdata/sightings/index.htmlhttp://spaceflight.nasa.gov/realdata/sightings/index.html , where as a communication satellite is in a fixed position that satellite dishes can be pointed at. If the velocities were equal, the space station would travel at a higher orbit.

Consider that two satellites can be equal in mass, but travel in higher and lower orbits. A satellite in geosynchronous orbit travels slower and is in a higher orbit than a lower orbiting satellite that scans the surface of the earth, such as is used for Google Earth images.

atyy said:
But you refer to accelerating objects. There are no inertial frames associated with accelerating objects.

An inertial frame is just a special type of (t,x,y,z) coordinate system that covers all of spacetime. Although there are no inertial frames associated with accelerating objects, an inertial frame can contain as many accelerating objects as we like - unless we are using a general relativistic description of gravity, in which case there are no global inertial frames.

I refer to accelerated objects, not accelerating objects. That said, I think your point is right on target. If I am not mistaken, you are pointing out that a more massive object must undergo an acceleration to obtain a different orbit where the final velocities are equal. That pretty much answers my question, "If mass does effect the inertial reference frame, what might that effect be?" The summarized answer would be 'different masses have different inertial reference frames.'

You are also pointing to the fact that inertial frames are just a coordinate system. I am not sure what this would explain other than what I described in the previous paragraph.

Please keep in mind I am still studying SR and GR. Thanks for the responses

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Matterwave said:
Free-fall frames are "inertial" frames in GR because gravity is no longer a force producing an acceleration but a curvature in the space-time.

OK, I should have said no global inertial frames. Already in Newtonian gravity, free fall frames are locally inertial.

I was thinking that there are no local Lorentzian inertial frames associated with 4-accelerated worldlines in GR, but the free-fall case is indeed more pertinent to a bolt orbiting the earth.

mixinman7 said:
I refer to accelerated objects, not accelerating objects. That said, I think your point is right on target. If I am not mistaken, you are pointing out that a more massive object must undergo an acceleration to obtain a different orbit where the final velocities are equal. That pretty much answers my question, "If mass does effect the inertial reference frame, what might that effect be?" The summarized answer would be 'different masses have different inertial reference frames.'

Well, actually what I said was not quite correct. As Matterwave pointed out, a freely-falling object like a bolt orbiting the Earth doesn't have a global inertial frame, but it does have a local inertial frame. However, the reason that freely-falling objects have local inertial frames is because objects with small but different masses fall at the same rate, and if they are nearby, share the same inertial frame. So in that sense, the inertial frame doesn't depend on mass.

mixinman7 said:
Consider that two satellites can be equal in mass, but travel in higher and lower orbits.

Which was Dale's point. The orbit is not dependent on the mass of the satellite. See also Matterwave's post.

'different masses have different inertial reference frames.'

Again, no. They do not.

Inertial reference frames are just a special class of coordinates on spacetime. If we want to describe the behavior of some mass, the choice of coordinate system is completely arbitrary. In the case of flat spacetime, inertial reference frames are global, and we can use any inertial reference frame to describe the behavior of some mass we are interested in.

In the case of some object moving in a gravitational field, we can only talk about local inertial frames (LIFs). We can construct LIFs in some neighborhood of the object, but their construction is not dependent on the mass or any other property of the object except where it is located in spacetime (assuming the object itself has a negligible gravitational field). In particular, we could construct an infinite number of such LIFs.

A LIF could have any number of physical things moving through it: photons, protons, neutrinos, marbles, bolts, pens, chickens... But the LIF can't be dependent on any mass moving through the LIF.

mixinman7 said:
I would appreciate this post being removed, or the thread. I got the answer I needed. Thanks for the responses.

What I was trying to get at was that your cockiness is not warranted by your present level of mastery of the material. Everyone has been a victim of the Dunning-Kruger effect at some point.

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mixinman7 said:
The space station has to travel faster to orbit lower than a communication satellite. ...
Consider that two satellites can be equal in mass, but travel in higher and lower orbits.
Given that you know this then I don't understand why you posted your post 12. It seems that you are already aware that your claims of post 12 are nonsense.

Daverz said:
...But the LIF can't be dependent on any mass moving through the LIF...

I think I understand now. The books I'm reading use illustrations to explain what inertia is, but the inertial reference frame in practice is an arbitrary math construct with no conceptual reality. So my expanding the illustrations that are not actually real is basically missing the point.

mixinman7 said:
I think I understand now. The books I'm reading use illustrations to explain what inertia is, but the inertial reference frame in practice is an arbitrary math construct with no conceptual reality. So my expanding the illustrations that are not actually real is basically missing the point.

Coordinates are not just a math construct, and they certainly have conceptual reality and tell us things about physical reality.

For example, a map of the Earth distills a lot of physical information about the Earth, and there are infinite number of valid ways to construct maps. But Nature doesn't "care" how we construct our maps.

In the case of spacetime, valid coordinate systems give us physical information about spacetime. A patch of spacetime can be thought of as an equivalence class of all the valid coordinate systems on that patch. Because they make the symmetries of spacetime apparent, the inertial reference frames are the most useful coordinate systems on flat spacetime. In a similar way, spherical coordinates are very useful for spherically symmetric physical situations.

Daverz said:
Coordinates are not just a math construct, and they certainly have conceptual reality and tell us things about physical reality...

Does a single inertial reference frame have conceptual meaning outside their use in math, or do you need a series of inertial reference frames to build a concept? What I meant in my previous post is that a single inertial reference frame is only useful for math, and a conceptual illustration of that inertial frame isn't accurate.

Does that sound agreeable?

mixinman7 said:
Does a single inertial reference frame have conceptual meaning outside their use in math, or do you need a series of inertial reference frames to build a concept? What I meant in my previous post is that a single inertial reference frame is only useful for math, and a conceptual illustration of that inertial frame isn't accurate.

Does that sound agreeable?

An inertial reference frame is something that could in principle be constructed, with rods, clocks and light signals in the usual example. See

pages 17-20.

mixinman7 said:
Does a single inertial reference frame have conceptual meaning outside their use in math, or do you need a series of inertial reference frames to build a concept? What I meant in my previous post is that a single inertial reference frame is only useful for math, and a conceptual illustration of that inertial frame isn't accurate.

Does that sound agreeable?

An inertial frame has more than a conceptual meaning. The conceptual reality of the inertial frame is at the heart of the construct of the universe.

According to the "Principle of Relativity" there is no inertial frame of reference in the universe that is any more special than any other frame.

The principle of relativity, which states that there is no preferred inertial reference frame, dates back to Galileo, and was incorporated into Newtonian Physics, and then grounded by Einstein as one of the postulates of Special Relativity.

Any and every mass body in the universe can be considered an inertial frame of reference. Any and every location in space can be considered an inertial frame.

This is somewhat of a mystery, as to why this is so. But to conclude that an inertial frame is mathematical nonsense, is totally ludicrous and ridiculous; and makes me question your level of understanding of physics.

If you take any Physics 101 class, this is the first thing that you learn. Also if you take a Modern Physics level 1 class, this is also the first thing that you learn. Did you ever take a physics class?? Because once the instructor gave you a test where you would have had to come to grips with this concept, you would never have questioned this again!

Sup_Principia said:
Did you ever take a physics class??

No. I took a conceptual physics course for my major, but it is not that type of physics course.

I understand the rod and clocks concept, but I was not thinking that is the meaning of an inertial frame of reference. That is about as far as I have gotten with that book. I'm still reading it when I get time, along with another book I own - "The collapse of special relativity" by michael strauss

mixinman7 said:
... That is about as far as I have gotten with that book. I'm still reading it when I get time, along with another book I own - "The collapse of special relativity" by michael strauss

See, this is the problem. You are reading "Contrarian" material without "first" understanding what mainstream physics have completely accepted for 100 years now.

My suggestion, learn what mainstream physics accepts, first. Then once you have understood that, then focus in on what you see as "Contrary" or an area that may require some additional clarity, that you would be able to provide; and that others could even contemplate or accept.

Best.

mixinman7 said:
"The collapse of special relativity" by michael strauss

Looks like garden variety anti-relativity crankery.

mixinman7 said:
Does a single inertial reference frame have conceptual meaning outside their use in math, or do you need a series of inertial reference frames to build a concept? What I meant in my previous post is that a single inertial reference frame is only useful for math, and a conceptual illustration of that inertial frame isn't accurate.

Does that sound agreeable?

An inertial frame is not an abstract math concept. It is simply the assignment of coordinates to events using stationary rigid measuring rods and clocks at rest, in such a way that the law of inertia claims validity. The theorems of Euclidean geometry apply to the laying out and fitting together of measuring rods at rest.

## 1. What is an inertial frame?

An inertial frame is a reference frame in which Newton's laws of motion hold true, meaning that an object at rest will remain at rest and an object in motion will continue in a straight line at a constant speed unless acted upon by an external force.

## 2. How does mass affect an inertial frame?

The mass of an object does not affect the inertial frame itself, but it does affect how the object behaves within the frame. Objects with greater mass require more force to accelerate and maintain their motion, while objects with less mass require less force.

## 3. Is an inertial frame dependent on the mass of the observer?

No, an inertial frame is not dependent on the mass of the observer. The laws of motion hold true for all observers in an inertial frame, regardless of their mass.

## 4. Can an object be in multiple inertial frames at the same time?

No, an object can only be in one inertial frame at a time. However, an object can transition between different inertial frames if it is subjected to external forces that cause it to accelerate or decelerate.

## 5. What is the significance of an inertial frame in physics?

Inertial frames are important in physics because they provide a consistent and universal reference point for measuring motion and forces. They allow for the accurate prediction and understanding of the behavior of objects in motion.

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