Who Truly Experiences Slower Time in the Paradox of Time Dilation?

[swerdna]

BTW, there is a very pedantic construction. We don't start by assuming frames to be either stationary or in motion relative to each other. A frame is just a coordinate system for space and time. An inertial frame is a coordinate system in which eg. Maxwell's equations take their standard form. Then one only talks about whether things (like a car, but not a whole frame) are stationary or moving relative to a frame. Consider a thing P that is stationary in inertial frame X, but moving in frame Y. We can assign a velocity to frame X relative to frame Y by saying that it is the velocity of P in frame Y, where P is any thing that is stationary in frame X. In this way, we can define the velocity of a frame X relative to itself by saying that it is the velocity of P in frame X, where P is any thing that is stationary in frame X.

Sorry but I can’t see all that as being anything but obfuscation.

All inertial frames have to be in motion relative to all other inertial frames. If they aren’t they are essentially the same inertial frame. If this is wrong please explain precisely why (non-mathematically).

How a thing can be relative to itself?

 

[atyy]

Sorry but I can’t see all that as being anything but obfuscation.

All inertial frames have to be in motion relative to all other inertial frames. If they aren’t they are essentially the same inertial frame. If this is wrong please explain precisely why (non-mathematically).

How a thing can be relative to itself?

An inertial frame is defined as just a coordinate system in which Maxwell's equations have their standard form. First we define one inertial frame X. Using that frame we find an object P that is stationary. Now we find all possible inertial frames, ie. all coordinate systems in which Maxwell's equations have their standard form. To find out whether any particular inertial frame K is the same or different from X, we ask whether P is stationary in K. If P is stationary in K, then it is the same inertial frame as X. If P is not stationary in K, then it is a different inertial frame from X.

Notice that in the above I did not make use of any concept of one frame moving relative to itself or to another frame. We only have the concept of an object moving relative to a frame.

Now, to define the concept of one inertial frame moving relative to another inertial frame, we define the velocity of inertial frame X relative to inertial frame Y as the velocity of object P in frame Y, where P is any object that is stationary in frame X.

 

[atyy]

All inertial frames have to be in motion relative to all other inertial frames. If they aren’t they are essentially the same inertial frame. If this is wrong please explain precisely why (non-mathematically).

BTW, this is correct. But this is not "absolute", because "absolute means "relative to all inertial frames", not "relative to all other inertial frames".

 

[swerdna]

An inertial frame is defined as just a coordinate system in which Maxwell's equations have their standard form. First we define one inertial frame X. Using that frame we find an object P that is stationary. Now we find all possible inertial frames, ie. all coordinate systems in which Maxwell's equations have their standard form. To find out whether any particular inertial frame K is the same or different from X, we ask whether P is stationary in K. If P is stationary in K, then it is the same inertial frame as X. If P is not stationary in K, then it is a different inertial frame from X.

Notice that in the above I did not make use of any concept of one frame moving relative to itself or to another frame. We only have the concept of an object moving relative to a frame.

Now, to define the concept of one inertial frame moving relative to another inertial frame, we define the velocity of inertial frame X relative to inertial frame Y as the velocity of object P in frame Y, where P is any object that is stationary in frame X.

In the piece I’ve bolded - Do you mean object P is stationary relative to frame X? Given frame X is defined by object P (not the other way around) isn’t this essentially the same as saying “a thing is stationary relative to itself”? How can a thing be relative to itself?

 

[swerdna]

BTW, this is correct. But this is not "absolute", because "absolute means "relative to all inertial frames", not "relative to all other inertial frames".

I would happily accept this as being true if you can explain how a thing can be stationary relative to itsef let alone just relative to itselff.

 

[atyy]

In the piece I’ve bolded - Do you mean object P is stationary relative to frame X? Given frame X is defined by object P (not the other way around) isn’t this essentially the same as saying “a thing is stationary relative to itself”? How can a thing be relative to itself?

A frame is a coordinate system, ie. a notional system of rulers and clocks. P need not be any notional ruler or clock - it is a real object like a car. So P is stationary relative to the frame, not to itself (because I haven't defined that yet).

 

[atyy]

In the piece I’ve bolded - Do you mean object P is stationary relative to frame X? Given frame X is defined by object P (not the other way around) isn’t this essentially the same as saying “a thing is stationary relative to itself”? How can a thing be relative to itself?

Also, a frame is not defined by object P. It is defined by Maxwell's equations having their standard form.

 

[swerdna]

A frame is a coordinate system, ie. a notional system of rulers and clocks. P need not be any notional ruler or clock - it is a real object like a car. So P is stationary relative to the frame, not to itself (because I haven't defined that yet).

Unless this is a game of “let’s pretend” I can’t accept that any notion of a frame is valid unless it’s defined by something that is real.

Really don’t like being so repetitive but I think this question is very important to the whole issue - How can a thing be relative to itself?

I don’t see how it can be so given you keep using the term please explain why you think it’s valid to do so.

 

[swerdna]

Also, a frame is not defined by object P. It is defined by Maxwell's equations having their standard form.

Equations don’t create reality.

 

[atyy]

Unless this is a game of “let’s pretend” I can’t accept that any notion of a frame is valid unless it’s defined by something that is real.

Really don’t like being so repetitive but I think this question is very important to the whole issue - How can a thing be relative to itself?

I don’t see how it can be so given you keep using the term please explain why you think it’s valid to do so.

Equations don’t create reality.

Do either of these work for you?

An inertial frame is a method of assigning distances and times to objects such that the speed of light is the same in all directions.

An inertial frame is a method of assigning distances and times to objects such that Newton's third law holds for for slow speeds.

 

[swerdna]

Do either of these work for you?

An inertial frame is a method of assigning distances and times to objects such that the speed of light is the same in all directions.

An inertial frame is a method of assigning distances and times to objects such that Newton's third law holds for for slow speeds.

This works for me . . .

Inertial frames are a method of defining whether things are moving relative to other things or not at a particular time.

Have to take a break right now.

 

[atyy]

This works for me . . .

Inertial frames are a method of defining whether things are moving relative to other things or not at a particular time.

Have to take a break right now.

That doesn't work for me. I think if one uses that definition, one could end up in the Rindler frame, which is non-inertial.

BTW, the one about Newton's third law holding is the way an inertial frame is defined in Newtonian physics. So I imagine it'd be acceptable to anyone who accepts Newtonian physics.

 

[swerdna]

That doesn't work for me. I think if one uses that definition, one could end up in the Rindler frame, which is non-inertial.

BTW, the one about Newton's third law holding is the way an inertial frame is defined in Newtonian physics. So I imagine it'd be acceptable to anyone who accepts Newtonian physics.

For my purposes I don’t see that it matters if a frame is inertial or not.

 

[atyy]

For my purposes I don’t see that it matters if a frame is inertial or not.

Most of the traditional ways of talking about special relativity require inertial frames, including the short hand statement that "acceleration is absolute", or that "constant velocity is relative".

What is your purpose?

 

[swerdna]

Most of the traditional ways of talking about special relativity require inertial frames, including the short hand statement that "acceleration is absolute", or that "constant velocity is relative".

What is your purpose?

I have trouble accepting that it’s valid for Relativity to arbitrarily define that any particular frame (and therefore thing) is stationary. My first purpose is to hold up to scrutiny my own current understand and acceptance of how motion is defined.

Today I’ve questioned if a thing can be relative to itself and if statements like “a thing is stationary relative to itself” are valid. From my current knowledge and understanding I have to conclude that such statements aren’t valid and therefore I can‘t accept them. If I‘m wrong in this I‘m happy to be corrected with credible evidence to the contrary.

In this process I can’t accept any argument that requires my prior acceptance that Relativity is valid. If Relativity is allowed to be it’s own witness, judge and jury the verdict will always be in favour of Relativity.

 

[atyy]

I have trouble accepting that it’s valid for Relativity to arbitrarily define that any particular frame (and therefore thing) is stationary. My first purpose is to hold up to scrutiny my own current understand and acceptance of how motion is defined.

Relativity does allow a particular frame to be stationary. But it is not necessary for relativity. Relativity requires that a frame can be defined in which an object is stationary. This is also true of Newtonian physics.

Today I’ve questioned if a thing can be relative to itself and if statements like “a thing is stationary relative to itself” are valid. From my current knowledge and understanding I have to conclude that such statements aren’t valid and therefore I can‘t accept them. If I‘m wrong in this I‘m happy to be corrected with credible evidence to the contrary.

I think you are wrong, but again, relativity allows the idea that a thing is stationary relative to itself, but it does not require it. Relativity requires that a thing can be stationary relative to a frame. This is also true of Newtonian physics.

In this process I can’t accept any argument that requires my prior acceptance that Relativity is valid. If Relativity is allowed to be it’s own witness, judge and jury the verdict will always be in favour of Relativity.

I don't agree with this. I think the process should be to ask: (i) Is relativity a coherent mathematical theory? (ii) What experimental procedures does relativity say correspond to what mathematical operations? (iii) Are the results of real experiments consistent with relativity? But I think your approach is fun, so let's see where it goes.

Do you accept Newtonian physics? If you do, and all you are questioning is the "Principle of Relativity", then why don't we discuss it in that context, since the Principle of Relativity also holds in Newtonian physics. The "Principle of Relativity" states (i) A frame is a method of assigning positions and times to events (ii) There is a preferred class of frames, which we will call inertial frames (iii) An inertial frame is a frame in which the laws of physics look "pretty" (iv) The laws of physics are equally pretty in every inertial frame.

The prettiness of the laws of physics is the crucial point of the Principle of Relativity, not that an object can be arbitrarily called stationary. I hope you at least accept that an object can be moving at constant velocity in an inertial frame?

 

[swerdna]

Relativity does allow a particular frame to be stationary. But it is not necessary for relativity. Relativity requires that a frame can be defined in which an object is stationary. This is also true of Newtonian physics.



I think you are wrong, but again, relativity allows the idea that a thing is stationary relative to itself, but it does not require it. Relativity requires that a thing can be stationary relative to a frame. This is also true of Newtonian physics.



I don't agree with this. I think the process should be to ask: (i) Is relativity a coherent mathematical theory? (ii) What experimental procedures does relativity say correspond to what mathematical operations? (iii) Are the results of real experiments consistent with relativity? But I think your approach is fun, so let's see where it goes.

Do you accept Newtonian physics? If you do, and all you are questioning is the "Principle of Relativity", then why don't we discuss it in that context, since the Principle of Relativity also holds in Newtonian physics. The "Principle of Relativity" states (i) A frame is a method of assigning positions and times to events (ii) There is a preferred class of frames, which we will call inertial frames (iii) An inertial frame is a frame in which the laws of physics look "pretty" (iv) The laws of physics are equally pretty in every inertial frame.

The prettiness of the laws of physics is the crucial point of the Principle of Relativity, not that an object can be arbitrarily called stationary. I hope you at least accept that an object can be moving at constant velocity in an inertial frame?

I don’t have any spare time right now and will be traveling all next week so may be some time before I can continue with this. I also want to bone-up on Newton. Thanks for giving me your help and time.

 

[swerdna]

Relativity does allow a particular frame to be stationary. But it is not necessary for relativity. Relativity requires that a frame can be defined in which an object is stationary. This is also true of Newtonian physics.

I think you are wrong, but again, relativity allows the idea that a thing is stationary relative to itself, but it does not require it. Relativity requires that a thing can be stationary relative to a frame. This is also true of Newtonian physics.

A quick reply before I leave on my travels - Real things that don’t move relative to each other define a frame in a real sense. To say a thing can be relative to a frame is therefore merely saying things can be stationary relative to other things. This has nothing to do with things being able to be relative to themselves. A concept of a frame without things is an abstract concept that has no basis in reality. Bit like a god.

I ask again- How can a thing be relative to itself? (in the real universe)

 

[matheinste]

Hello swerdna.

A thing can be equal to itself and equality is an equivalence relation.

A thing can be the same size as itself. The same size as is an equivalence relation.

So why cannot moving at the same speed as itself not be an equivalence relation.

Matheinste.

 

[swerdna]

Hello swerdna.

A thing can be equal to itself and equality is an equivalence relation.

A thing can be the same size as itself. The same size as is an equivalence relation.

So why cannot moving at the same speed as itself not be an equivalence relation.

Matheinste.

A thing is NOT equivalent to itself. A thing IS itself.

 

[atyy]

A quick reply before I leave on my travels - Real things that don’t move relative to each other define a frame in a real sense. To say a thing can be relative to a frame is therefore merely saying things can be stationary relative to other things. This has nothing to do with things being able to be relative to themselves. A concept of a frame without things is an abstract concept that has no basis in reality. Bit like a god.

I ask again- How can a thing be relative to itself? (in the real universe)

I believe that in keeping with you philosophy of "real things" only, your definition is insufficiently real. How can you define "don’t move relative to each other"? Suppose you want to say an object A is moving or not moving in some relative sense, is there always an object B at the exact location or sufficiently near A for you to compare A relative to B? It seems like you are assuming "don't move relative to each other" is "real".

How about using only "real things" - real "events" like lightning striking a tree. A frame is then just a method of assigning 4 numbers, 4 coordinates (a,b,c,d) to each event. If we arbitrarily call coordinate (a) "time", and coordinates (b,c,d) "space", then we can define "movement". This is arbitrary, and is just a naming convention. If in one convention an object is moving, we can always choose another convention in which the same object is not moving.

Nothing deep. Suppose "The rain falls down" is true, and now we redefine "down" to be "up", then "The rain falls up" will now be true. Or if "I am here" is true, and now we redefine "here" to be "there", then "I am there" will be true. It's just a silly naming game. Similarly, "moving" or "not moving" is just a silly naming game. This silly naming game is not the heart of the "Principle of Relativity", but it is needed for it.

 

[matheinste]

Hello swerdna.

Look up equivalence relation. Equality is very often used as an example of an equivalence relation

Matheinste.

 

[atyy]

A quick reply before I leave on my travels - Real things that don’t move relative to each other define a frame in a real sense. To say a thing can be relative to a frame is therefore merely saying things can be stationary relative to other things. This has nothing to do with things being able to be relative to themselves. A concept of a frame without things is an abstract concept that has no basis in reality. Bit like a god.

Another reason for not using your definition of a frame is that Newton's laws for the solar system written in the form "GMm/r²=ma" only apply in an inertial frame. But there is no object in the solar system that is stationary in an inertial frame - the planets and the sun are all accelerating relative to an inertial frame because gravity acts on each of them. If we use your definition, we cannot define an inertial frame to apply Newton's law of gravitation and 2nd law of mechanics to the solar system.

I ask again- How can a thing be relative to itself? (in the real universe)

Relativity allows this, but doesn't need it, so I won't use it, since it is under dispute. Relativity only requires that an object can move or be stationary relative to a frame. (However I see that matheinste is addressing this query of yours in a very correct way.)

BTW, I am going back and forth between Newtonian physics and special relativity since the Principle of Relativity holds in both theories. The only difference between the two theories with respect to the Principle of Relativity is what they define to be "pretty".

 

[p764rds]

What, you mean like a simulation? Not necessarily... the appeal of simulating things on the computer is that you can program in any physical laws you want. You could make your virtual world follow the laws of relativity if you want, or you could make it follow the laws of nonrelativistic mechanics (but then you'd run into trouble with Maxwell's equations, if EM fields existed in your virtual world).

Sorry to be out of step with the 'self frame theme' (can't see the point or understand it, personally).

Can anyone throw light on this puzzle that is denying me sleep:
Lets say I make a 3d space (cube, 1 billion miles) in a computer memory that obeys Maxwells laws using algorithms that I programmed in.

I run an einsteins train simulation (using simulated lightning strikes on a shape that looks like a train) and find everything runs as it does in the real universe. The observer on the simulated platform has a different view of simultaneity than the observer on the simulated train. So I say everything is as it should be in a simulation.
BUT, I designed the cubic 3D space myself and you then tell me its not a fixed reference frame?.

I am confused. Surely there is an absolute frame here (I made it myself!) - but in this forum we would say no, no, no there is no absolute frame of reference. Listen, I designed it, I know there is one - its a cube of sides 1 billion miles. As I say I am confused, there is something deeper going on here. It seems (to me) there are two things here, relativity after maxwell and light speed giving me embedded frames but built on an absolute frame that constructed the basic 3D space. Isn't it algorithmiclly manipulated space sitting on top of the basic flat cubic space?

 

[matheinste]

Sorry to be out of step with the 'self frame theme' (can't see the point or understand it, personally).

Can anyone throw light on this puzzle that is denying me sleep:
Lets say I make a 3d space (cube, 1 billion miles) in a computer memory that obeys Maxwells laws using algorithms that I programmed in.

I run an einsteins train simulation (using simulated lightning strikes on a shape that looks like a train) and find everything runs as it does in the real universe. The observer on the simulated platform has a different view of simultaneity than the observer on the simulated train. So I say everything is as it should be in a simulation.
BUT, I designed the cubic 3D space myself and you then tell me its not a fixed reference frame?.

I am confused. Surely there is an absolute frame here (I made it myself!) - but in this forum we would say no, no, no there is no absolute frame of reference. Listen, I designed it, I know there is one - its a cube of sides 1 billion miles. As I say I am confused, there is something deeper going on here. It seems (to me) there are two things here, relativity after maxwell and light speed giving me embedded frames but built on an absolute frame that constructed the basic 3D space. Isn't it algorithmiclly manipulated space sitting on top of the basic flat cubic space?

How many 3D spaces have you in your model. For the train/embankment scenario in the real world, two are directly involved, one for the train observer and one for embankment observer. For a model of the universe an infinite number are portentially involved, one for each potential observer. You can choose to model in any frame you wish and will get the correct answers, but you will also get the correct answers from any other frame you wish to model in. I am not a software man but I do know that computers can mimic physical situations if correctly programmed, it is only the application of the laws of mathematics and physics. What a computer does is what it is told and if the results do not agree with the physical situation we cannot alter physical laws to accommodate it. You say that the model predicts the expected relativistic effects and, if that is so, it is probably OK. I suspect, however it is not the computer itself saying there is an absolute frame, but your interpretation of the situation. You may have chosen one frame out of the two that are directly involved ( and out of the infinite number from which you could have chosen). This does not make it absolute in the sense that there is something about it that makes it stand out from all other inertial frames.

The search for an absolute frame, and the inability to find one, was the spur for Einstein's relativity.

Matheinste

 

[granpa]

However, special relativity claims that as a body approaches light speed, time (for that body) slows down. But this seems to contradict the postulate that motion is always relative.

not if you take relativity of simultaneity into account. the best way to learn to understand relativity of simultaneity is to learn to draw a spacetime diagram.