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It is only equivalent if the car is accelerating, i.e. in a non-inertial or accelerated frame, with respect to the object. But if, as in your example, the car is going at 60mph relative to some object, it is not accelerating and so is not in an accelerated frame with respect to that object. So the object doesn't see the car as an accelerated frame of reference but as an inertial frame of reference, and the car also sees the object as an inertial frame of reference.The main point of the above is that if gravity can be considered an accelerative force why can't being in a gravitational field be like being in the car in the example?
It is only equivalent if the car is accelerating, i.e. in a non-inertial or accelerated frame, with respect to the object. But if, as in your example, the car is going at 60mph relative to some object, it is not accelerating and so is not in an accelerated frame with respect to that object. So the object doesn't see the car as an accelerated frame of reference but as an inertial frame of reference, and the car also sees the object as an inertial frame of reference.
Two people share an inertial reference frame if they are stationary with respect to each other (co-moving) and not accelerating. However, an object in orbit is accelerating, i.e. in a non-inertial frame. As I understand it, objects comoving in a shared orbit can be seen as sharing a local inertial frame, e.g. objects inside the ISS, so it's possible the people in the situation you describe could be seen that way. In what way do you think the gravity of their respective planets is relevant?Here's an example illustrating the point further,
Two planets are orbiting a star in the same orbital path one after the other at the same speed. Do not worry about how they would affect each other's orbit or gravity this is just for the example. One planet has more mass than the other planet. This would mean the planet with more mass has a greater gravitational field than the planet with less mass. Now lets say there are two people one on each planet. Both people are stationary on their own planet and are located on their respective planets in a way that the gravity of each of their planets is pushing them both the same direction. The person on the planet with more mass experiences greater gravity and therefore experiences a greater accelerative force than that of the person on the planet with less mass. Are both persons in the same inertial frame or are they on different inertial frames? Why?
p.s. Gravity doesn't push.
However, an object in orbit is accelerating, i.e. in a non-inertial frame. As I understand it, objects comoving in a shared orbit can be seen as sharing a local inertial frame, e.g. objects inside the ISS, so it's possible the people in the situation you describe could be seen that way.
In what way do you think the gravity of their respective planets is relevant?
I didn't say that; I said it was possible. It really depends on details you didn't specify in the example.So you see the people on the planets experiencing more and less gravity as being in the same inertial frame?
No. Gravity is equivalent to acceleration.How I see it is gravity can be thought of as a constant velocity as it is constantly moving the people in this example onto their own planet.
No. A car in uniform (inertial) motion at 60 mph is not accelerating, so it is not equivalent to gravity.In the car example the car moving sixty miles per hour would be likened to each planet's gravitational field. If one were to instantly remove the moving car the person in the car would be sent skidding down the road. In a similar manner if one were to instantly remove one of the planets the person would be sent jettisoning off into space.
The person in the car is only experiencing more movement than a stationary object outside the car because you've defined that object as your stationary reference frame. If you define the car as your stationary frame, the object experiences more movement than the car. There is no absolute movement, it's all relative.In the car example everything in the car with the person is also moving the speed of the car and is therefore in the their inertial frame, but everything outside the car not moving the car's speed is not in the car's inertial frame. Likewise with the planets the only difference between either person's movement is the strength of gravitational field. This is like how the person in the car is experiencing more movement than a stationary object outside the car. The person on the planet with more mass experiences a greater gravitational force and therefore more movement than the person on the planet with less mass.
The criteria for sharing inertial frame is that they are comoving and not accelerating. Under Newtonian gravity, this will not be the case if the planets are moving at different velocities or rotating, or orbiting a star; or if the people are moving on the surface of their respective planets. So if circumstances are arranged just right, it's possible that you could consider them to share an inertial frame, but it's extremely unlikely. The gravity of their respective planets is not relevant in itself.So this begs the question why aren't the people on the planets in the example considered having different inertial frames?
No. Gravity is equivalent to acceleration.
No. A car in uniform (inertial) motion at 60 mph is not accelerating, so it is not equivalent to gravity.
A free-falling lift and its occupant would be inertial with respect to each other - inside the lift the occupant is comoving and there would be no sense of acceleration. However, free-falling involves acceleration, so from an external viewpoint, they would share the same acceleration with respect to the Earth, i.e. the acceleration due to gravity (on Earth 9.8m/s²). So whether they can be said to share an inertial frame is context-dependent. Inside the ISS, the astronauts and the objects around them are often in uniform (non-accelerated) motion with respect to each other and the ISS, so they can be treated as inertial, but the ISS and its contents as a whole are accelerating in Earth orbit, so they're non-inertial with respect to the larger context.If an elevator were to break at a very high floor and free fall due to gravity would an object in the elevator not experience the same velocity as the elevator? Would this not mean it was in the same inertial frame as the elevator because it was experiencing the same velocity?
Kind of - they are reference frames, used to compare the uniform (non-accelerating) motions of objects.Are not frames a simplification of motion, meaning that they are used to cancel out the velocities of objects that are experiencing the same amounts of velocity at any given moment?
A free-falling lift and its occupant would be inertial with respect to each other - inside the lift the occupant is comoving and there would be no sense of acceleration.
However, free-falling involves acceleration, so from an external viewpoint, they would share the same acceleration with respect to the Earth, i.e. the acceleration due to gravity (on Earth 9.8m/s²). So whether they can be said to share an inertial frame is context-dependent.
The main point of the above is that if gravity can be considered an accelerative force why can't being in a gravitational field be like being in the car in the example?
It is only equivalent if the car is accelerating, i.e. in a non-inertial or accelerated frame, with respect to the object.
It's not a 'movement', it's a force (or pseudo-force) that causes them to fall. Using appropriate terminology is important if you want to be understood.Yes I agree and the movement causing them to fall is gravity.
No - inertial frames are only 'equivalent' when at rest with respect to each other, i.e. when they're the same frame.Are not all inertial frames considered equivalent; meaning regardless of acceleration or constant velocity, as long as in that point in time the objects being considered have the same amount of movement?
That depends what the object is stationary with respect to. If it's stationary with respect to the lift or the car, it's in the same inertial frame. If it's stationary with respect to the surface of the Earth, it's clearly in a different frame.Would not the elevator and the person in it be in the same inertial frame, but in a different one than a stationary object outside the elevator, just as a moving a car and the person in it would be in the same inertial frame, but in a different one than a stationary object outside the car?
If the car is accelerating it is not inertial and neither is the occupant. It is not the same situation as being in a free-falling lift (or in orbit) where you are weightless inside the car or spacecraft.What I was saying with the car example is that being in a moving car whether it be moving at a constant velocity or accelerating you are in the same inertial frame as the car.
Strictly speaking, if you're on a planet, you're being accelerated, so you're not inertial. In practice, for local contexts, when people are stationary with respect to each other, you can treat them as being in the same inertial frame.Likewise if you are on a planet with multiple people you are in the same inertial frame with those people because you all are affected by the same amount of gravitational force (for the sake of simplicity not worrying about the movement of the celestial bodies' motion the people also share) . Is this not correct? Why?
I don't know what you mean by 'equivalent' in this context. How can all inertial frames be equivalent when they're all different by definition? Every inertial frame is in uniform motion with respect to every other inertial frame.The big question is that from what I have thought and now have read all inertial frames are considered equivalent as I said earlier in this post. Am I misunderstanding this?
It's not a 'movement', it's a force (or pseudo-force) that causes them to fall. Using appropriate terminology is important if you want to be understood.
That depends what the object is stationary with respect to. If it's stationary with respect to the lift or the car, it's in the same inertial frame. If it's stationary with respect to the surface of the Earth, it's clearly in a different frame.
No - inertial frames are only 'equivalent' when at rest with respect to each other, i.e. when they're the same frame.
If the car is accelerating it is not inertial and neither is the occupant. It is not the same situation as being in a free-falling lift (or in orbit) where you are weightless inside the car or spacecraft.
Strictly speaking, if you're on a planet, you're being accelerated, so you're not inertial. In practice, for local contexts, when people are stationary with respect to each other, you can treat them as being in the same inertial frame.
I don't know what you mean by 'equivalent' in this context. How can all inertial frames be equivalent when they're all different by definition? Every inertial frame is in uniform motion with respect to every other inertial frame.
Gravity does not increase relativistic mass and you wouldn’t be making such statements if you were familiar with the maths and physics.
Relativistic mass is a product of inertial frames in motion which by definition are not accelerated frames hence are gravity free.
I would imagine that as Mercury enters the part of its orbit that is closest to the Sun it would experience a great deal of relativistic mass due to the strength of the Sun's gravity at that proximity. This is one of the main points of the original post. Gravity increases relativistic mass because it too is a force that moves an object in a given direction.
Car and its passenger can be considered to share an inertial frame in a local context, i.e. ignoring gravity and the bigger picture (e.g. planetary rotation, etc), if they're not accelerating.What I was trying to express is that both the person and the car shared the same amount of force and the person and the elevator shared the same amount of force. Hopefully this is the correct terminology, but I believe this means that each object shares the same frame as their respective occupant.
As I understand it, if they're experiencing the same acceleration due to gravity, they're not inertial - but taken in a local context, and ignoring gravity, they could be said to share an inertial frame if they're stationary with respect to each other. It's not strictly correct, but it probably makes teaching physics easier.What I was trying to express is that since all the people are on the same planet they all share more or less the same amount of gravitational force if they were at or near the same level of elevation. Again I would guess the terminology would be that they are sharing the same frame if they are all stationary with respect to the Earth, correct me if I am wrong.
The two contexts are different in that in the local context of a free-falling lift, there are no measurable forces or pseudo-forces acting from a local (inside the lift) viewpoint, so it's reasonable to treat them as sharing a local inertial frame. For the car example, both the car and the occupant experience the acceleration due to gravity, so, strictly speaking, they can't occupy an inertial frame.This is my misunderstanding of a definition. What I was trying to express in this case is that the person and elevator are moving with the same force as each other and therefore don't appear to be moving with respect to each other, like the person and car are moving with the same force as each other and therefore don't appear to be moving with respect to each other.
I suppose if Mercury's velocity increases or decreases with respect to Earth, it will gain or lose kinetic energy and so its will mass increase or decrease; presumably, as it gets closer to and further from the sun, its potential energy with change too.What I was trying to express is that to us as a viewer from Earth as Mercury get's closer to the Sun it would experience a greater gravitational force causing its movement to increase and this would cause further movement to require more energy.
Or in my attempt to use proper terminology. With Earth being the inertial frame of reference edit: the frame of reference?, as Mercury moves closer to the Sun it experiences a greater gravitational force, this further accelerates it and therefore increases its relativistic mass.
I hear that relativistic mass is no longer considered a useful concept, and total energy should be preferred.The following definition of relativistic mass seems to agree with what I was attempting to express.
According to the concept of mass–energy equivalence, the rest mass and relativistic mass are equivalent to the rest energy and total energy of the body, respectively.
Car and its passenger can be considered to share an inertial frame in a local context, i.e. ignoring gravity and the bigger picture (e.g. planetary rotation, etc), if they're not accelerating.
As I understand it, if they're experiencing the same acceleration due to gravity, they're not inertial - but taken in a local context, and ignoring gravity, they could be said to share an inertial frame if they're stationary with respect to each other. It's not strictly correct, but it probably makes teaching physics easier.
The two contexts are different in that in the local context of a free-falling lift, there are no measurable forces or pseudo-forces acting from a local (inside the lift) viewpoint, so it's reasonable to treat them as sharing a local inertial frame. For the car example, both the car and the occupant experience the acceleration due to gravity, so, strictly speaking, they can't occupy an inertial frame.
I suppose if Mercury's velocity increases or decreases with respect to Earth, it will gain or lose kinetic energy and so its will mass increase or decrease; presumably, as it gets closer to and further from the sun, its potential energy with change too.
I hear that relativistic mass is no longer considered a useful concept, and total energy should be preferred.
I'm not up to speed on the energy implications of orbital mechanics.
An inertial frame is a coordinate system that is not accelerating; IOW, the physics of a system in an inertial frame has no causes external to the system, i.e. no forces or pseudo-forces affect the system context. This is why the system of lift and occupant in free-fall can be considered as an inertial frame, but strictly speaking, the car and its occupant cannot. I've tried to explain it several times, but clearly not well enough - as I said, I'm not a physicist, nor am I a teacher...The idea I am attempting to express is that whether two objects are accelerating or are at a constant velocity if their acceleration and speed, or velocity are the same respectively, meaning if two objects share the same acceleration and speed or if two objects share the same velocity, then they share the same amount of movement or total energy; meaning they appear to be stationary to one another. I am unsure if there is a difference from something sharing the same frame and something being the inertial frame of reference.
That's a contradiction in terms; there are no absolute reference points in relativity by definition.Yes, this is similar to what I was saying in the post above, on how I see relativity from an absolute reference point.
Both gravity and speed do cause time dilation if that's what you mean, but the effects are extremely small unless travelling at a significant fraction of light speed, which is clearly not the case with Mercury.Basically I see the dip in space time as not modeling gravity, but modeling the altered trajectory of the planet at the point in space. The gravitational field dynamically alters the total energy, motion, however you want to put it of the planet. As the planet enters different parts of the Sun's gravitational field its total energy gets further and closer to the maximum, (the speed of light) which in turn causes its motion to go through varying degrees of time dilation.
An inertial frame is a coordinate system that is not accelerating; IOW, the physics of a system in an inertial frame has no causes external to the system, i.e. no forces or pseudo-forces affect the system context. This is why the system of lift and occupant in free-fall can be considered as an inertial frame, but strictly speaking, the car and its occupant cannot. I've tried to explain it several times, but clearly not well enough - as I said, I'm not a physicist, nor am I a teacher...
Not only is your terminology confusing, but your usage suggests you don't understand the distinction (or the importance of clearly distinguishing) between movement, speed, velocity, and acceleration.
That's a contradiction in terms; there are no absolute reference points in relativity by definition.
Both gravity and speed do cause time dilation if that's what you mean, but the effects are extremely small unless travelling at a significant fraction of light speed, which is clearly not the case with Mercury.
Acceleration is the rate of change of speed, so it isn't correct to say they share the same speed. But I see what you mean, and two such objects would only see each other as stationary if they were accelerating at the same rate, in the same direction, having started stationary relative to each other.Would you agree that two accelerating objects that also share the same speed would see each other as stationary?
Only if they were moving in the same direction. Velocity is speed in a particular direction.While not the same would you agree that two objects moving at the same speed and constant velocity would see each other as stationary? This is what I wanted to point out, while not the same, the observational result is the same.
They're ambiguous; when I'm driving down the motorway at 70mph or accelerating from the lights, the car appears to be moving pretty fast relative to the scenery. But it's true that when you're attached to a moving object you are stationary with respect to that object.If you are in a car moving and the car is moving a constant velocity the car appears stationary to you. If you are in a car and it is accelerating that car appears stationary to you. Are these statements not correct?
I don't know what you mean by an 'absolute reference point' or 'scale of motion' (speed?). As I said, there are no absolute reference points in relativity.I explained in that post that while it seems contradictory it is not. Perhaps if you read it again you could tell me why it is contradictory if you still believe it so. It is a few posts above this one. I did not quote you in that post. Note the absolute reference point is the scale of motion, the minimum and maximum.
I don't know the details of Mercury's precession, beyond that it is anomalous under Newtonian gravity and the anomaly is largely due to gravitoelectric effects described by General Relativity.Yes, but in Mercury's case it was the not factoring in time dilation that caused the incorrect calculations of its perihelion shift. The warping of space time that causes the discrepancy in the calculations is actually Mercury's angular momentum being altered by entering different strengths of the Sun's gravitational field. To my understanding it takes a long time for this to become noticeable and even then it is not much of a difference, but perhaps I am incorrect on that point, I am not too great with numbers either.
Acceleration is the rate of change of speed, so it isn't correct to say they share the same speed. But I see what you mean, and two such objects would only see each other as stationary if they were accelerating at the same rate, in the same direction, having started stationary relative to each other.
Only if they were moving in the same direction. Velocity is speed in a particular direction.
They're ambiguous; when I'm driving down the motorway at 70mph or accelerating from the lights, the car appears to be moving pretty fast relative to the scenery. But it's true that when you're attached to a moving object you are stationary with respect to that object.
I don't know what you mean by an 'absolute reference point' or 'scale of motion' (speed?). As I said, there are no absolute reference points in relativity.
It has been irking me something greatly now knowing at least one of the reasons why I am not finding any traction in my search for someone who can understand my idea. I have been misusing terminology and this while frustrating and annoying is enlightening because now hopefully progress may be able to be made. I have found it interesting because I seem to have trouble with the terminology because I see relativity from a different way than the people I have encountered. I understand relativity from an absolute reference point. I am here to explain why that’s not contradictory even though it seems like it is.
First step of understanding relativity from an absolute point of view is to not think in frames, disregard direction totally, and see everything’s motion as a value in between a minimum and a maximum. The minimum can be zero and the maximum will be the speed of light.
Next step is that motion is additive, but due to the minimum and maximum is altered and is therefore not totally linear. The more motion something has the more energy it requires to increase further motion. In this way motion can never reach the maximum.
Final step, what does this have to do with time dilation? If a being on a planet that is moving near the maximum were to take a walk in a park it’s going to take a really long time. This is because the being’s motion already starts at near the maximum and will be slowed greatly. The thing is that the being will not even know it’s taking them a really long time because everything that is on the planet is also near the maximum and moves at the same pace as it does. And that is what causes time dilation.
So ultimately from my perspective it doesn’t matter what is causing the increase in motion. If an object’s motion is being increased it requires more energy to further increase its movement meaning it has gotten closer to the maximum. The consequence of this is time dilation. Let me know what you think. If there are any problems please point them out and explain why.
I don't know the details of Mercury's precession, beyond that it is anomalous under Newtonian gravity and the anomaly is largely due to gravitoelectric effects described by General Relativity.
It's still not clear to me what you mean by an 'absolute point of view'. The rest of the post is a rough description of relativity, but the description of time dilation is circular and rather incoherent. Simply adding 'And that is what causes time dilation' doesn't change assertion into explanation.Here, I will quote the post I am talking about.
...
I appreciate the thought, but alternatives to GR aren't really my field of interest.I stumbled upon this when talking on this thread earlier. It may be something you find interesting. I think the comment near the top that Robert Shuler makes is especially interesting in the context of our discussion.
https://www.researchgate.net/post/M...ive_to_Einsteins_theory_of_general_relativity
It's still not clear to me what you mean by an 'absolute point of view'.
Note the absolute reference point is the scale of motion, the minimum and maximum.
but the description of time dilation is circular and rather incoherent.
I appreciate the thought, but alternatives to GR aren't really my field of interest.
Since the perihelion advance of Mercury’s orbit is under discussion, here is maths and the predicted value for the advance.
It has been irking me something greatly now knowing at least one of the reasons why I am not finding any traction in my search for someone who can understand my idea. I have been misusing terminology and this while frustrating and annoying is enlightening because now hopefully progress may be able to be made. I have found it interesting because I seem to have trouble with the terminology because I see relativity from a different way than the people I have encountered. I understand relativity from an absolute reference point. I am here to explain why that’s not contradictory even though it seems like it is.
First step of understanding relativity from an absolute point of view is to not think in frames, disregard direction totally, and see everything’s motion as a value in between a minimum and a maximum. The minimum can be zero and the maximum will be the speed of light.
Next step is that motion is additive, but due to the minimum and maximum is altered and is therefore not totally linear. The more motion something has the more energy it requires to increase further motion. In this way motion can never reach the maximum.
Final step, what does this have to do with time dilation? If a being on a planet that is moving near the maximum were to take a walk in a park it’s going to take a really long time. This is because the being’s motion already starts at near the maximum and will be slowed greatly. The thing is that the being will not even know it’s taking them a really long time because everything that is on the planet is also near the maximum and moves at the same pace as it does. And that is what causes time dilation.
So ultimately from my perspective it doesn’t matter what is causing the increase in motion. If an object’s motion is being increased it requires more energy to further increase its movement meaning it has gotten closer to the maximum. The consequence of this is time dilation. Let me know what you think. If there are any problems please point them out and explain why.
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