Explanation Amplified: Time thought of as Relative Motion

[FrumiousBandersnatch]

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.

 

[Ohj1n37]

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.

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?

 

[FrumiousBandersnatch]

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?

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?

I don't see how that example is relevant to the earlier example of a car moving at 60mph relative to some object - perhaps you could explain?

p.s. Gravity doesn't push.

 

[Ohj1n37]

p.s. Gravity doesn't push.

Push, pull, fall however you would like to express it for right now.

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.

So you see the people on the planets experiencing more and less gravity as being in the same inertial frame? I see them on a different inertial frame. I was trying to find the discrepancy between our two view points. I am attempting to find out which one is correct and why. Now that I know the difference I will explain my view point and we can discuss.

In what way do you think the gravity of their respective planets is relevant?

Read through the entirety of this explanation before replying as it is all very important. The inertial frame is when an object can be considered not accelerating by either being at rest or moving at a constant velocity. 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.

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.

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.

So this begs the question why aren't the people on the planets in the example considered having different inertial frames?

 

[FrumiousBandersnatch]

So you see the people on the planets experiencing more and less gravity as being in the same inertial frame?

I didn't say that; I said it was possible. It really depends on details you didn't specify in the example.

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. Gravity is equivalent to acceleration.

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.

No. A car in uniform (inertial) motion at 60 mph is not accelerating, so it is not equivalent to gravity.

If the planet you were standing on disappeared, you would simply continue to follow its orbit (assuming it was orbiting). In classical (Newtonian) mechanics, when you stand on Earth, gravity pulls you down and the Earth's surface resists with an equal and opposite force; if both equal and opposite forces suddenly vanish, it has no net effect on your motion - you just become weightless. In General Relativity, there is no gravitational force, spacetime is curved by the planet's mass and you're accelerated by the planet surface; if the curvature of spacetime and the planet surface vanish, you simply find yourself in locally flat spacetime, no longer being accelerated - and you just become weightless.

In Newtonian gravity, the force of gravity on you is opposed by the reaction of the ground, so you can be (locally) inertial standing on a planet's surface; under GR gravity, you're being accelerated upwards by the ground, so you're non-inertial.

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 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.

If you're standing on the surface of a planet, you're not moving, whatever the strength of its gravity.

So this begs the question why aren't the people on the planets in the example considered having different inertial frames?

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.

Under GR gravity, which is not a force, people on the planet surface are being accelerated upwards by the ground, so they're not in inertial frames in the first place, so they can't share an inertial frame.

Caveat - this is my current understanding of the situations described; I'm not a physicist, and I would be happy to be corrected by an authoritative source.

 

[Ohj1n37]

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.

I have been looking up further information on this matter. And I have an example and questions in the hopes that I can better understand your view point. While I now understand (thanks to you, much appreciated) that gravity being an accelerative force and a car moving at a constant velocity are different, I am not sure why that affects one being considered movement that is applicable to inertial frames and the other not, other than by definition. Hopefully the example will bring clarity.

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? 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?

 

[FrumiousBandersnatch]

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?

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.

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?

Kind of - they are reference frames, used to compare the uniform (non-accelerating) motions of objects.

 

[Ohj1n37]

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.

Yes I agree and the movement causing them to fall is gravity. Maybe I am misunderstanding something, but please if you will help me with the following.

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.

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?

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?

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.

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. 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?

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?

 

[FrumiousBandersnatch]

Yes I agree and the movement causing them to fall is gravity.

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.

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?

No - inertial frames are only 'equivalent' when at rest with respect to each other, i.e. when they're the same 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?

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.

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.

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.

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?

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.

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?

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.

 

[Ohj1n37]

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.

Thank you and I apologize. That is one of my problems and I believe it adds to the misunderstanding.

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.

An apology for not being specific enough. Yes, I was referring to the objects being stationary with respect to the surface of the Earth.


After looking up more definitions I have found further mistakes in my use of terminology although not in my intended logic. I will answer each accordingly.

No - inertial frames are only 'equivalent' when at rest with respect to each other, i.e. when they're the same frame.

I can not say anything other than I have in some cases been using the term inertial frame incorrectly. I apologize and thank you for you're patience in sorting out this particular misunderstanding.

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 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.

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.

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.

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.

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.


Now that I have gotten the above hopefully sorted out, writing all this made me look back at where this tangential portion of the discussion came from and hopefully the following will sort that out,

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.

This seems to be a case of me not being specific enough and again I would like to thank FrumiousBandersnatch for being patient with me and helping me sort this out thus far.

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 could not find anything else wrong with what I said in this specific post. Please let me know if this is not true and why.

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.

The greater gravitational force should be increasing the total energy of Mercury relative to Earth which would be experiencing a lesser degree of gravitational force.

Edit: Yeah sorry, made some edits earlier that were not correct. Also took out a part that was not applicable. Should make sense now. In those edits I was confusing inertial and relativistic mass. I guess it's just frustrating that I am having trouble accurately expressing exactly what's in my head. Hopefully further discussion will bring it to light and help me finally figure out if it's right or wrong.

 

[Ohj1n37]

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.

 

[FrumiousBandersnatch]

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.

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 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.

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.

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.

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.

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 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'm not up to speed on the energy implications of orbital mechanics.

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.

I hear that relativistic mass is no longer considered a useful concept, and total energy should be preferred.

 

[Ohj1n37]

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.

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; in practice this means that the two objects appear to be stationary to one another. I am still confused by the definition to some degree and am unsure if there is a difference from something sharing the same frame and something being the 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.

Yes, this is similar to what I was saying in the post above, on how I see relativity from an absolute reference point. I would like to know your opinion on that post as the only person who takes the time to listen to me is my dad, but this is not his area of interest and he doesn't invest his own time into further understanding relativity.

I'm not up to speed on the energy implications of orbital mechanics.

Sadly I may have ran off sjastro. 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 from or closer to the maximum, (the speed of light) which in turn causes its motion to go through varying degrees of time dilation.

 

[FrumiousBandersnatch]

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.

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.

Yes, this is similar to what I was saying in the post above, on how I see relativity from an absolute reference point.

That's a contradiction in terms; there are no absolute reference points in relativity by definition.

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.

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.

 

[Ohj1n37]

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...

I understand that now. I just wanted to verify. Thank you for taking the time to explain that to me. I believe you have some teaching skills, at the least you seem patient.

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.

I more than likely do not use the terms correctly, but just because the terminology gets scrambled in my head doesn't mean the logic necessarily does. Take the following as an example,

Would you agree that two accelerating objects that also share the same speed would see each other as stationary? 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.

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?

That's a contradiction in terms; there are no absolute reference points in relativity by definition.

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.

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.

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.

 

[FrumiousBandersnatch]

Would you agree that two accelerating objects that also share the same speed would see each other as stationary?

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.

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.

Only if they were moving in the same direction. Velocity is speed in a particular direction.

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?

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 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 what you mean by an 'absolute reference point' or 'scale of motion' (speed?). As I said, there are no absolute reference points in 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.

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.

 

[Ohj1n37]

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.

Yep that's what I mean.

Only if they were moving in the same direction. Velocity is speed in a particular direction.

Agreed.

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.

Agreed.

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.

Here, I will quote the post I am talking about.

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.

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

 

[FrumiousBandersnatch]

Here, I will quote the post I am talking about.
...

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.

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

I appreciate the thought, but alternatives to GR aren't really my field of interest.

 

[sjastro]

Since the perihelion advance of Mercury’s orbit is under discussion, here is maths and the predicted value for the advance.
As in post #10 starting off with the Schwarzschild solution to Einstein’s vacuum equation.

ds² = c²(1-2MG/c²r)dt² - dr²/(1-2MG/c²r) - r²(dθ² + sin² θdϕ²)

Since Mercury exists in a planar orbit θ = π/2, dθ = 0 and sin² θ =1.
The equation reduces to;

ds² = c²(1-2MG/c²r)dt² - dr²/(1-2MG/c²r) - r²dϕ²

Let the geodesic path length increment ds be expressed as a path parameter dk which can be the proper time of a clock.
With ds = dk the equation becomes;

dk² = c²(1-2MG/c²r)dt² - dr²/(1-2MG/c²r) - r²dϕ²

Dividing by dk;

1 = c²(1-2MG/c²r)(dt/dk)² - (dr/dk)²/(1-2MG/c²r) - r²(dϕ/dk)² (A)

In solving the Einstein’s vacuum equations two mathematical relationships are derived.
dt/dk= a/(1-2MG/c²r) and r²(dϕ/dk)sin²θ = b
dt/dk is eliminated from (A) and using dr/dk = (dϕ/dk)(dr/dϕ) = (r²/b)(dr/dϕ)
(A) bcomes;

(b²/r⁴)(dr/dϕ)² = c²a² - (1 – 2MG/c²r)(1 + b²/r²) (B)

Making the substitution u = 1/r (B) becomes;

(du/dϕ)² = c²a²/ b² - (1/ b²)(1 - 2MGu/c²)(1 + b²u²)
= c²a²/ b² - (1/ b² + u² - 2MGu/c²b² - 2MGu³/c²)

This equation can be simplified by differentiation of both sides with respect to ϕ.

(du²/dϕ²)(du/dϕ) = -(u - MG/c²b² - 3MGu²/c²)(du/dϕ)

If du/dϕ =0 this corresponds to a circular orbit.
Since Mercury has an elliptical orbit divide both sides by du/dϕ.

du²/dϕ² + u = MG/c²b² + 3MGu²/c². (C)

This equation is Newton’s equation for an orbit without the 3MGu²/c² term.
du²/dϕ² + u = MG/c²b²
We can use Newtonian theory to obtain an approximate solution for (C).

u = MG/c²b²[1 + ecos(ϕ - ϕ₀)] is a solution for Newton’s equation.

e is the eccentricity of the orbit and ϕ and ϕ₀ are explained in the diagram where ϕ₀ is angle at which perihelion occurs.

Substituting this solution into second term in the right hand side of equation (C) gives;

du²/dϕ² + u = MG/c²b² + (3M³G³/c⁴b⁴)[1 + ecos(ϕ - ϕ₀)]²

An approximate solution for this equation is;

u = MG/c²b²[1 + ecos(ϕ - ϕ₀ -Δϕ)] where Δϕ = (3M³G³/c⁴b⁴)ϕ and higher order terms of MG/ c²b² are neglected as they are very small.

Note the comparison with the Newtonian solution u = MG/c²b²[1 + ecos(ϕ - ϕ₀)].
Δϕ = (3M³G³/c⁴b⁴)ϕ indicates Δϕ increases with ϕ and is regarded as a constantly increasing correction to ϕ₀ or the precession of the position of the perihelion of Mercury’s orbit.
Plugging in the values for M, G, c and b gives the prediction of Δϕ = 43” per century which compares well with the observed value of 42.98” per century.

 

[Ohj1n37]

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.

It doesn't matter what amount of motion (frame) you have, you are always somewhere within the minimum and maximum. So when I say something takes a long time I am referring to within the context of the minimum and maximum. That thing I am referring to takes a long time because it is closer to the maximum than whatever else I am talking about.

but the description of time dilation is circular and rather incoherent.

Is it commonly understood that time dilation is caused by a higher requirement of energy the closer something is to the speed of light? And if so why do people make all this fuss about frames, is it not easier just to focus on the object in question's speed relative to the speed of light and not worry about everything else?

I guess the point of the two above quotes is why are frames important? The absolute reference point is the minimum and maximum, zero and the speed of light. Isn't it more complicated to figure out how things move relative to each other rather than an absolute reference point?

I appreciate the thought, but alternatives to GR aren't really my field of interest.

Well the link was mainly about why general relativity is better at describing things than gravitoelectromagnetism. One of the comments spoke about how any idea with time dilation can account for Mercury's perihelion precession. He then goes on to say, but space time curvature is something that is harder to explain and that is what my post on this forum was talking about. I believe that space time curvature is misinterpreted time dilation phenomenon that alters the trajectory/wavelength/whatever of the time dilated object.

Since the perihelion advance of Mercury’s orbit is under discussion, here is maths and the predicted value for the advance.

Thank you sjastro. I am honestly trying to be polite like I try to do most of time, but math a lot simpler than that is beyond me as I have stated in the original posts and numerous times after that; maybe others will get something out of it. But now that you're here if you would like to could you please give your analysis in words and without math of the following quote, I would really appreciate it. I just want to get others' understanding on my ideas in ways that I can understand.

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.