Doubts in special theory of relativity

[Fredrik]

I have a problem.. I cannot understand space-time diagrams.

The idea is extremely simple. The diagram shows the assignments of coordinates made by an inertial coordinate system. Each point represents the coordinates of an event. A curve in the diagram represents the motion of a point particle (or something that for our present purposes can be thought of as being point-like). If the curve is a straight line, the particle has a constant velocity. If it's a vertical straight line, the velocity is zero. The more it deviates from being vertical, the bigger the speed. The units on the axes are chosen so that a straight line drawn at 45 degrees represents motion at the speed of light. A curved line represents the motion of an accelerating particle.

The only thing that's a bit tricky is how to figure out how to draw the simultaneity lines of an observer whose motion is drawn in the diagram. A simultaneity line is a set of points that the observer's comoving inertial coordinate system assigns the same time coordinate. How to do this is explained in all the books that mention spacetime diagrams. Once you understand this, you will find it easy to understand all of the standard problems in SR.

 

[ghwellsjr]

How can we explain Time dilation through Doppler effect?

Yes, I do that at the beginning of the thread I just linked you to. Also, try this thread, down around post #7.

 

[Dale]

By this he means that If the clocks satisfy this simultaneous considerations,then these clocks go at the same rate.(my words)

Nowhere in any of the quoted material did he ever use the word "rate". You are making an incorrect inference from what he said to something entirely different.

One problem is that natural language is inherently imprecise, and translations between natural languages are even more imprecise. To precisely discuss these concepts it is important to use math. Mathematically, it is easy to come up with transformations which have time dilation but not relativity of simultaneity and vice versa. What that shows is that you cannot derive one from the other.

 

[ash64449]

Nowhere in any of the quoted material did he ever use the word "rate". You are making an incorrect inference from what he said to something entirely different.

One problem is that natural language is inherently imprecise, and translations between natural languages are even more imprecise. To precisely discuss these concepts it is important to use math. Mathematically, it is easy to come up with transformations which have time dilation but not relativity of simultaneity and vice versa. What that shows is that you cannot derive one from the other.

please read the pdf book that i earliar said. It explained relativity of simultaneity to explain that time go at different rates. Please look at it. And you see by reading that book that i am making incorrect conclusion,please tell me what i was wrongly understood by reading that book.

 

[ash64449]

Nowhere in any of the quoted material did he ever use the word "rate". You are making an incorrect inference from what he said to something entirely different.

One problem is that natural language is inherently imprecise, and translations between natural languages are even more imprecise. To precisely discuss these concepts it is important to use math. Mathematically, it is easy to come up with transformations which have time dilation but not relativity of simultaneity and vice versa. What that shows is that you cannot derive one from the other.

but i am not good in math. Please explain it to me in other ways other than math. To understand relativity,higher algebra is required. I haven't reach that class yet. But i do really want to understand relativity now..

 

[Fredrik]

but i am not good in math. Please explain it to me in other ways other than math. To understand relativity,higher algebra is required. I haven't reach that class yet. But i do really want to understand relativity now..

Actually, the algebra is very simple. But there's an even easier alternative, and that is to use spacetime diagrams. So you should start working on understanding them right now.

Note that SR is unique in physics in that it's possible to understand the essentials by talking about pictures that involve nothing but straight lines. There's no other theory that can be even partially understood without a significant amount of math.

 

[ghwellsjr]

By this he means that If the clocks satisfy this simultaneous considerations,then these clocks go at the same rate.(my words

Nowhere in any of the quoted material did he ever use the word "rate". You are making an incorrect inference from what he said to something entirely different.

Yes he did. Right in the middle of section 4 of his 1905 paper, he said:

What is the rate of this clock, when viewed from the stationary system?

Ash64449 later stated:

note this chapter explain why two clocks are not synchronous.i.e it shows clocks on stationary observer and clocks of moving observer relative to stationary system do not go at the same rate.

He may be coming to the correct conclusion for the wrong reason but it sounds like he has learned that a moving clock ticks at a different (slower) rate in a particular frame than a stationary one (or than the Coordinate Time of the frame) but what I think he is having trouble with is that in the rest frame of that moving clock, the previously stationary clock is now ticking at a slower rate than the previously moving clock (or than the Coordinate Time of the previously moving clock's rest frame).

I thought ash finally understood this point in post #32 from what you said in post #30 but apparently not.

 

[Dale]

please read the pdf book that i earliar said. It explained relativity of simultaneity to explain that time go at different rates. Please look at it. And you see by reading that book that i am making incorrect conclusion,please tell me what i was wrongly understood by reading that book.

I have read that book multiple times as well as the 1905 paper. They simply do not support your claims.

You claim that relativity of simultaneity (different frames disagree on which events are simultaneous) implies time dilation (moving clocks run slow). That is simply not correct. The texts you refer to never make that claim, and in fact do not even discuss the rate of clocks in the sections you mention.

Here is a post where I provided a mathematical counterexample to a similar claim made by another poster. This transform proves that relativity of simultaneity does NOT imply time dilation: https://www.physicsforums.com/showpost.php?p=3751522&postcount=2

 

[ash64449]

Yes he did. Right in the middle of section 4 of his 1905 paper, he said:


Ash64449 later stated:

He may be coming to the correct conclusion for the wrong reason but it sounds like he has learned that a moving clock ticks at a different (slower) rate in a particular frame than a stationary one (or than the Coordinate Time of the frame) but what I think he is having trouble with is that in the rest frame of that moving clock, the previously stationary clock is now ticking at a slower rate than the previously moving clock (or than the Coordinate Time of the previously moving clock's rest frame).

I thought ash finally understood this point in post #32 from what you said in post #30 but apparently not.

yes. You are right.i understood.thank you!

 

[ghwellsjr]

Still i am curious you see. What i mean is that time beat slower to the one who is moving relative to someone who is not.(just an example) Events that take place to that someone who is not moving takes place to the one who is moving relative to someone.(no additional events takes place) Since time dilates to that observer who is moving,What will happen to the events according to him when compared to the one who is not moving?

Events are assigned coordinates according to an arbitrarily chosen Inertial Reference Frame (IRF). You use the Lorentz Transformation process to re-assign coordinates to a second IRF moving with respect to the original one. You should think in terms of IRF's--not observers. When we say an observer's frame or according to an observer, we simply mean an IRF in which the observer is at rest. But all observers, clocks and other objects are in all IRF's as well as all events. If you do this it this way, Time Dilation happens automatically, as well as all the other aspects of SR.

 

[ash64449]

I have read that book multiple times as well as the 1905 paper. They simply do not support your claims.

You claim that relativity of simultaneity (different frames disagree on which events are simultaneous) implies time dilation (moving clocks run slow). That is simply not correct. The texts you refer to never make that claim, and in fact do not even discuss the rate of clocks in the sections you mention.

Here is a post where I provided a mathematical counterexample to a similar claim made by another poster. This transform proves that relativity of simultaneity does NOT imply time dilation: https://www.physicsforums.com/showpost.php?p=3751522&postcount=2

I understood daleSpam. Relativity of simultaneity will occur with length contraction or time dilation or not occur or relativity of simultaneity will be there but no length contraction or time dilation.

 

[Dale]

Yes he did. Right in the middle of section 4 of his 1905 paper, he said

Yes, I know that he discussed it elsewhere in those texts, but not in the quoted material.

The problem here is that ash64449 is making the illogical inference RoS \rightarrow TD where RoS is the relativity of simultaneity and TD is time dilation. By starting with this false premise he arrives at a false conclusion which is directly contradicted by Einstein. The correct inference, the one that Einstein proves, is (PoR,C) \rightarrow (TD,LC,RoS) where PoR is the principle of relativity, C is the invariance of c, and LC is length contraction. If ash64449 were to start with this correct premise then he could not arrive at his false conclusion.

 

[ash64449]

Events are assigned coordinates according to an arbitrarily chosen Inertial Reference Frame (IRF). You use the Lorentz Transformation process to re-assign coordinates to a second IRF moving with respect to the original one. You should think in terms of IRF's--not observers. When we say an observer's frame or according to an observer, we simply mean an IRF in which the observer is at rest. But all observers, clocks and other objects are in all IRF's as well as all events. If you do this it this way, Time Dilation happens automatically, as well as all the other aspects of SR.

let there be two observers. Both of them big distance apart. Let two lightning strike at a place at the same time. For both observer's both events will be simultaneous but won't 'Time' of an event change?

Well if we use co-ordinate system and make use of time axis,since they are distance apart,Both observer's will not have same time co-ordinate.So 'time' of events for them is different right?

 

[ash64449]

Yes, I know that he discussed it elsewhere in those texts, but not in the quoted material.

The problem here is that ash64449 is making the illogical inference RoS \rightarrow TD where RoS is the relativity of simultaneity and TD is time dilation. By starting with this false premise he arrives at a false conclusion which is directly contradicted by Einstein. The correct inference, the one that Einstein proves, is (PoR,C) \rightarrow (TD,LC,RoS) where PoR is the principle of relativity, C is the invariance of c, and LC is length contraction. If ash64449 were to start with this correct premise then he could not arrive at his false conclusion.

Yes DaleSpam,I understood. Will PoR and C will always make simultaneous events not simultaneous and vice-versa in all cases?

 

[Dale]

Yes DaleSpam,I understood. Will PoR and C will always make simultaneous events not simultaneous and vice-versa in all cases?

Yes. The principle of relativity (PoR) and the invariance of c (C) imply the Lorentz transform, which has the relativity of simultaneity (RoS).

 

[ash64449]

Yes. The principle of relativity (PoR) and the invariance of c (C) imply the Lorentz transform, which has the relativity of simultaneity (RoS).

What about the 'time' of the event?

 

[ash64449]

Yes. The principle of relativity (PoR) and the invariance of c (C) imply the Lorentz transform, which has the relativity of simultaneity (RoS).

Thank you DaleSpam for all this.If you guys were not there,i would have thought like this forever! Still i think there is some loopholes in my understanding! I will clear it from further discussion here!

 

[ghwellsjr]

Events are assigned coordinates according to an arbitrarily chosen Inertial Reference Frame (IRF). You use the Lorentz Transformation process to re-assign coordinates to a second IRF moving with respect to the original one. You should think in terms of IRF's--not observers. When we say an observer's frame or according to an observer, we simply mean an IRF in which the observer is at rest. But all observers, clocks and other objects are in all IRF's as well as all events. If you do this it this way, Time Dilation happens automatically, as well as all the other aspects of SR.

let there be two observers. Both of them big distance apart. Let two lightning strike at a place at the same time. For both observer's both events will be simultaneous but won't 'Time' of an event change?

Well if we use co-ordinate system and make use of time axis,since they are distance apart,Both observer's will not have same time co-ordinate.So 'time' of events for them is different right?

The simultaneity of two events a distance apart has nothing to do with any observers. It only has to do with the selected Inertial Reference Frame. If you have an IRF in which two lightning strikes occur at the same time and you have two observers who are also separated from the lightning strikes and from each other, they will not be able to tell that the lightning strikes are simultaneous because they don't know which IRF you are using. When they see the lightning strikes some time later, they may see them at different times according to their own clocks (even if they are synchronized). In another IRF moving with respect to the first one, the lightning strikes may not be simultaneous but it won't affect what the two observers see.

 

[ash64449]

The simultaneity of two events a distance apart has nothing to do with any observers. It only has to do with the selected Inertial Reference Frame. If you have an IRF in which two lightning strikes occur at the same time and you have two observers who are also separated from the lightning strikes and from each other, they will not be able to tell that the lightning strikes are simultaneous because they don't know which IRF you are using. When they see the lightning strikes some time later, they may see them at different times according to their own clocks (even if they are synchronized). In another IRF moving with respect to the first one, the lightning strikes may not be simultaneous but it won't affect what the two observers see.

I know that simultaneous events will be same for them! I just asked whether there will be change in 'time' of the event. you gave me the answer through this quote:

When they see the lightning strikes some time later, they may see them at different times according to their own clocks (even if they are synchronized).

 

[ghwellsjr]

Yes he did. Right in the middle of section 4 of his 1905 paper, he said

Yes, I know that he discussed it elsewhere in those texts, but not in the quoted material.

OK, I see what you mean. Thanks for clarifying.

 

[Dale]

What about the 'time' of the event?

I am not sure what you are asking. The time transforms according to the Lorentz transform t'=\gamma(t-vx/c^2). The γ represents time dilation and the term with x represents relativity of simultaneity, so both effects are present.

 

[ash64449]

I am not sure what you are asking. The time transforms according to the Lorentz transform t'=\gamma(t-vx/c^2). The γ represents time dilation and the term with x represents relativity of simultaneity, so both effects are present.

i didn't ask that. Gh answered that to me. Time of event is different according to location of the observer. See gh's comment.

 

[Samshorn]

Here is a post where I provided a mathematical counterexample to a similar claim made by another poster. This transform proves that relativity of simultaneity does NOT imply time dilation: https://www.physicsforums.com/showpost.php?p=3751522&postcount=2

That post says "Here is a transform which has the relativity of simultaneity, but not length contraction or time dilation: t′=t−vx, x′=x−vt. " Actually I think that transformation does entail some time dilation, although not reciprocal. A clock at rest in the primed coordinates would run slow by a factor of 1-v^2 relative to the unprimed coordinates. On the other hand, a clock at rest in the (unique) unprimed coordinates has no dilation relative to the primed coordinates.

 

[jambaugh]

y,,,
the problem; According to both SR and Galileo's theory of relativity, the meaning of rest and uniform motion has no meaning. Everything is relative. It is because an object in rest would be in motion relative to something else.As a result we cannot say one is moving uniformly or he is at rest.

Ahhh, I see what your problem is. You are thinking relativism implies nihilism.

You cannot identify your motion as you consider yourself as rest even though you are moving uniformly. But in actual sense he is moving. But he thinks that he is at rest. So it becomes a fact that one cannot identify who is moving who is not. But when we compare with the light,We can understand that we are moving! This is contradicting.. Is this the thing you were trying to explain?
OR are you telling that Maxwell's theory appear to contradict Galileo's theory of relativity?

It would help you to understand if you started with even earlier forms of relativity. Position is relative. Neither you nor a an electron has an x,y and z coordinate encoded in their state of being. You cannot look at a particle by itself and give its position. Position is relative to an arbitrary choice of origin. This doesn't mean position is meaningless and nothing exists anywhere. It means position is relative, that position is not a property of a specific object bur rather that relative position is a relationship between objects. You see this in the fact that e.g. longitude is defined relative to an arbitrary point on the Earth chosen for historic reasons, namely Greenwich England. What's so special about Greenwich that it have longitude 0?!

Similarly, orientation is relative. I would be quite parochial to laugh at the Indonesians for all being upside down, or insisting that the Earth was flat because "up" would be meaningless if it was relative. But "up" is a relative term and if I'm floating freely in space up is merely the direction my head is pointing.

A relativity principle states that a quantity we formerly thought was absolute, and a property of the object alone is in fact relative and a property of the objects relationship to other objects. The condition of "poverty" in the US today is relative to the mean standard of living and someone living in Haiti, or someone living in the middle ages, would consider themselves quite well off if they had the wealth possessed by most people living below the "poverty line". This doesn't mean those people should "shut up and quit whining". Their poverty is not meaningless.

Note also electrical potential is relative, you never say a given point in a circuit is "at x volts" but rather either "at x volts relative to ground" or that there is "x voltage difference between two points".

Motion, like position and orientation is a relative property, a property not of an object itself but a relationship between objects. This is not because the authorities in science declare it but is based on a firm meta-principle of science. For something to have meaning we must be able to empirically observe it. There is no way to observe if an object is "really stationary" or "actually moving" in and of itself. You can only observe relative motion, "the object is moving toward the North star" or "away from the Earth" or "not at all relative to this other object". (Mind you, it might be otherwise, it is conceivable. However combining this meta-principle with the actual empirical observations of countless experiments and we have relativistic theories as our best paradigm as valued by their matching with empirical observation. Before you try to contradict this you best be sure you can correctly conceptualize the relativity principles. Until you do you cannot understand them well enough to raise a valid objection.)

You bring up EM and light which is good. It was exactly this issue which required we revise Galilean relativity and led Einstein to invoke SR. If you look at Maxwell's equations they are Lorentz invariant. Choosing a non-relativistic mindset you could then argue that where Maxwell's Equations are valid for a stationary observer, they predict the speed of light in all directions as c=\sqrt{\mu\epsilon}. But for a moving observer in this absolute setting, the stationary equations are invalid. As in the absolute setting the moving observer should see light traveling in his direction of motion moving more slowly relative to him in his direction of motion and faster away from him.

This means either you have to modify the equations, (specifically promote the permeability and permittivity constants to tensor variables) in order to have the truly non-relativistic absolute state of motion you suggest, wherein we can judge our motion relative to light moves near us, or you have to change the relativity group from Galilean to Lorentz.

We do not see such absolute motion. That was the famous Michelson-Morley experiment. The first attempts to resolve its null result is the invocation of an aether which defines the local absolute frame but which upon examination becomes fundamentally unobservable.

You are having a hard time accepting the relativity of motion. That is your problem not a problem with the theories of relativity. I understand it, you have a strong intuition which is blocking the notion. Understand that your intuition is itself not absolute but something you train by repeated examination of facts. You have two choices. You can ossify your intuition as it is and be yet another "flat earther" insisting that empirical facts "must be wrong" because they don't fit into your world picture or you can adopt a bit of humility and reign in your hubris and re-examine your world picture. Actually get out there and study the debates of these very same questions in the history of physics. See how they have been asked and answered (repeatedly), and "do the math". Learn the details of SR and work out the Lorentz transformation for many example problems. I especially thing it is clarifying to work out Lorentz transformations using hyperbolic trig and pseudo-rotation matrices. It helps retrain the intuition to see the analogy of Lorentz space-time pseudo-rotations to coordinate rotations. You'll find legion's of posts and threads here in this forum.

 

[ash64449]

Ahhh, I see what your problem is. You are thinking relativism implies nihilism.


It would help you to understand if you started with even earlier forms of relativity. Position is relative. Neither you nor a an electron has an x,y and z coordinate encoded in their state of being. You cannot look at a particle by itself and give its position. Position is relative to an arbitrary choice of origin. This doesn't mean position is meaningless and nothing exists anywhere. It means position is relative, that position is not a property of a specific object bur rather that relative position is a relationship between objects. You see this in the fact that e.g. longitude is defined relative to an arbitrary point on the Earth chosen for historic reasons, namely Greenwich England. What's so special about Greenwich that it have longitude 0?!

Similarly, orientation is relative. I would be quite parochial to laugh at the Indonesians for all being upside down, or insisting that the Earth was flat because "up" would be meaningless if it was relative. But "up" is a relative term and if I'm floating freely in space up is merely the direction my head is pointing.

A relativity principle states that a quantity we formerly thought was absolute, and a property of the object alone is in fact relative and a property of the objects relationship to other objects. The condition of "poverty" in the US today is relative to the mean standard of living and someone living in Haiti, or someone living in the middle ages, would consider themselves quite well off if they had the wealth possessed by most people living below the "poverty line". This doesn't mean those people should "shut up and quit whining". Their poverty is not meaningless.

Note also electrical potential is relative, you never say a given point in a circuit is "at x volts" but rather either "at x volts relative to ground" or that there is "x voltage difference between two points".

Motion, like position and orientation is a relative property, a property not of an object itself but a relationship between objects. This is not because the authorities in science declare it but is based on a firm meta-principle of science. For something to have meaning we must be able to empirically observe it. There is no way to observe if an object is "really stationary" or "actually moving" in and of itself. You can only observe relative motion, "the object is moving toward the North star" or "away from the Earth" or "not at all relative to this other object". (Mind you, it might be otherwise, it is conceivable. However combining this meta-principle with the actual empirical observations of countless experiments and we have relativistic theories as our best paradigm as valued by their matching with empirical observation. Before you try to contradict this you best be sure you can correctly conceptualize the relativity principles. Until you do you cannot understand them well enough to raise a valid objection.)

You bring up EM and light which is good. It was exactly this issue which required we revise Galilean relativity and led Einstein to invoke SR. If you look at Maxwell's equations they are Lorentz invariant. Choosing a non-relativistic mindset you could then argue that where Maxwell's Equations are valid for a stationary observer, they predict the speed of light in all directions as c=\sqrt{\mu\epsilon}. But for a moving observer in this absolute setting, the stationary equations are invalid. As in the absolute setting the moving observer should see light traveling in his direction of motion moving more slowly relative to him in his direction of motion and faster away from him.

This means either you have to modify the equations, (specifically promote the permeability and permittivity constants to tensor variables) in order to have the truly non-relativistic absolute state of motion you suggest, wherein we can judge our motion relative to light moves near us, or you have to change the relativity group from Galilean to Lorentz.

We do not see such absolute motion. That was the famous Michelson-Morley experiment. The first attempts to resolve its null result is the invocation of an aether which defines the local absolute frame but which upon examination becomes fundamentally unobservable.

You are having a hard time accepting the relativity of motion. That is your problem not a problem with the theories of relativity. I understand it, you have a strong intuition which is blocking the notion. Understand that your intuition is itself not absolute but something you train by repeated examination of facts. You have two choices. You can ossify your intuition as it is and be yet another "flat earther" insisting that empirical facts "must be wrong" because they don't fit into your world picture or you can adopt a bit of humility and reign in your hubris and re-examine your world picture. Actually get out there and study the debates of these very same questions in the history of physics. See how they have been asked and answered (repeatedly), and "do the math". Learn the details of SR and work out the Lorentz transformation for many example problems. I especially thing it is clarifying to work out Lorentz transformations using hyperbolic trig and pseudo-rotation matrices. It helps retrain the intuition to see the analogy of Lorentz space-time pseudo-rotations to coordinate rotations. You'll find legion's of posts and threads here in this forum.

Actually,i understood my mistake. I did know this earlier but i lost that point when i started the thread.

c=\sqrt{\mu\epsilon}.

Is this equation true. Because i found this:http://www.phys.unsw.edu.au/einsteinlight/jw/module3_Maxwell.htm

 

[vanhees71]

It should read c=c_{\text{vac}}/\sqrt{\epsilon \mu}.

Further be careful with the integral form of Maxwell's equations on the website you linked to. They are only correct if in the definition of the electric and magnetic fluxes you use areas that are at rest in the considered frame of reference. The differential form is correct, and you can derive the integral form from them.

 

[ash64449]

It should read c=c_{\text{vac}}/\sqrt{\epsilon \mu}.

Further be careful with the integral form of Maxwell's equations on the website you linked to. They are only correct if in the definition of the electric and magnetic fluxes you use areas that are at rest in the considered frame of reference. The differential form is correct, and you can derive the integral form from them.

So it is better to use the other one. Right?

 

[jambaugh]

Actually,i understood my mistake. I did know this earlier but i lost that point when i started the thread.

c=\sqrt{\mu\epsilon}.

Is this equation true. Because i found this:http://www.phys.unsw.edu.au/einsteinlight/jw/module3_Maxwell.htm

Oops, my bad, I forgot to take the reciprocal. Yea, didn't catch up with replies when I composed my post so if I'm off mark just ignore it. Glad you've reached clarity.

 

[altsci2]

The key to understand SR

The key to understand SR is in 4-dimensional geometry.
Firstly, SR is a mathematical tool of theoretical physics. It uses 4-d coordinate system and produces correct numerical description of physical reality. There is no need of 3-d “frame” and physical clocks everywhere. But SR does not exist without 4-d coordinate system and the metric tensor. There is no metric tensor in the physical frame. The original Einstein’s presentation of SR is primitive. The use of metric tensor in it is implicit. It is replaced by the use of only Lorentz Transformations (LT) of coordinates. In geometry the transformation of coordinates is arbitrary.
Secondly, in a sense, SR is not a physical theory. It is a mathematical improvement in numerical description of physical reality. The physical consequences came from the old physical laws (Maxwell Equations, Newton’s Dynamics) upon using the correct math. The use of 3-d vectors and tensors with time as a parameter is in general logically inconsistent (in some cases like Maxwell’s Equations it is consistent), while the use of 4-d vectors and tensors is logically consistent in general.
Thirdly, SR provides deeper understanding of Newton’s “Absolute Space” and “Absolute Time” only in a form of “Absolute Space-Time” (notice that the concepts “space” and “time” separately became indefinite in SR). This Absolute Space-Time provides a reference for rotation and any acceleration.

 

[Mentz114]

The key to understand SR is in 4-dimensional geometry.

It might not be the key, but it helps a lot.

Thirdly, SR provides deeper understanding of Newton’s “Absolute Space” and “Absolute Time” only in a form of “Absolute Space-Time” (notice that the concepts “space” and “time” separately became indefinite in SR). This Absolute Space-Time provides a reference for rotation and any acceleration.

'Absolute Space-Time' ( your capitals) is not required to define acceleration nor rotation.