Absolute motion's point of reference

[yoelhalb]

Once again you seem not to understand the basic meaning of "acceleration"! Any change in speed or direction is acceleration, it doesn't matter whether the reason for this change in direction is something "internal" like firing a rocket or "external" like the wind or water applying a force on the object.

What I called here acceleration I mean experiencing g-force.
Here nobody will encounter any g-force and both of them will claim rest, so again when they are reunited who is younger?.

In this case spacetime is curved so no coordinate system covering each object's entire path can qualify as "inertial", and again there is no requirement that time dilation work the same way in a non-inertial frame. So even if you define a non-inertial coordinate system where object A is at rest throughout the journey while object B moves away and then returns, there's no reason to predict that B ages more slowly throughout the journey in this non-inertial coordinate system, it's only in inertial coordinate systems that objects in motion always age more slowly than objects at rest.

So you actually claim that when Einstein proposed that the universe is round then he disregarded special relativity entirely.
Actually even if we will claim the universe to be flat, still there can never be a true inertial frame of reference, since any two objects always exert some gravity on each other.
What do you say to that?.
So all the brilliant minds on the planet for the last 100 years had dealt with something that can't exist.

If they're far apart there doesn't have to be any frame-independent truth about which is younger. Again, in relativity there is no frame-independent notion of a "given time", different frames have different definitions of which sets of events occur at the "same time" and which occur at "different times" (i.e. whether a given pair of events are assigned the same time-coordinate or different time-coordinates), so two events that happened at the same time in one frame can have happened at different times in another frame (unless both events happened at both the same place and the same time in one frame, in which case all frames agree the events happened at the same place and time). Did you look at the link I gave you on the "relativity of simultaneity"? Here is another one: http://www.pitt.edu/~jdnorton/Goodies/rel_of_sim/index.html

It is clear to all of us that if the twin are meeting together then there is only one who is younger, even though they may use different space time coordinates.
Now let's imagine we are putting a sheet of paper between the twin, still only one of them is younger.
Now let us make tichker the paper till it is getting a wall, still only one of them is younger.
So let us make it thicker and thicker till it spans many light years, is there any point when we can start claiming that it can be possible that both are younger?
To illustrate that even further, let's instead of paper and a wall fill the gap with people, on which two persons can we claim that he and his immediate neighbor are both younger?.
Since there is no such thing, we can't claim it on any persons in the universe.

 

[JesseM]

What I called here acceleration I mean experiencing g-force.
Here nobody will encounter any g-force and both of them will claim rest, so again when they are reunited who is younger?.

Yes, anytime you change speed or direction you experience a G-force, regardless of the cause. You really should try to learn basic Newtonian physics before you try to challenge relativity!

So you actually claim that when Einstein proposed that the universe is round then he disregarded special relativity entirely.

This proposal was made in the context of his theory of "general relativity" in which spacetime is curved, not special relativity where spacetime is flat. However, according to the equivalence principle we can still say that the laws of special relativity still work "locally" in an arbitrarily small region of curved spacetime, you can define a "locally inertial frame" in such a small region.

Actually even if we will claim the universe to be flat there can never be a true inertial frame of reference, since any teo objects always exert some gravity on each other.
What do you say to that?.
So all the brilliant minds on the planet for the last 100 years had dealt with something that can't exist.

In physics successful theories are rarely shown to be completely wrong, instead they are usually shown to be a limiting case of some more accurate theory (do you understand the calculus notion of a limit?) For example, Newtonian physics is still very useful in many scenarios, and it's possible to show that it is a very accurate approximation to both special relativity and general relativity in the appropriate limits (for example, the relative velocities being very small compared to c). Likewise, as I mentioned above SR can be understood as the limit case of GR as the size of the region of spacetime being considered becomes very small (so 'tidal effects' which depend on curvature become very small as well).

But yes, everyone understands that SR is not the most accurate known theory for calculating elapsed time on various clocks, GR is.

It is clear to all of us that if the twin are meeting together then there is only one who is younger, even though they may use different space time coordinates.

Yes, if we idealize the twins as point particles and suppose they meet at the same precise point of spacetime, then all frames agree on their ages when they meet.

Now let's imagine we are putting a sheet of paper between the twin, still only one of them is younger.

If there is any finite distance between them, then different frames can disagree on the precise difference in their ages, although it may still be the case that all frames agree one is younger (but perhaps one frame will say the younger twin is younger by 457902910335298.3 nanoseconds while another will say the younger twin is younger by 457902910335298.2 nanoseconds)

A geometric analogy may help. Suppose we have two curves on a flat 2D wall which meet at one point P1, move apart, and then meet again at another point P2. If different observers have different definitions of which direction along the wall is "vertical" and which is "horizontal", they may disagree on the vertical and horizontal distances between P1 and P2, but they will all agree on the length of each curve between P1 and P2 (i.e. the distance an ant would measure if he walked along each curve from P1 to P2.

On the other hand, suppose both curves travel through P1 on the wall, but while the first curve also travels through P2, the second curve gets very close to P2 but never actually touches the first curve, after P2 it just remains parallel to the first curve but never quite touches it. And suppose we again imagine different observers with different definitions of which direction on the wall is "vertical" and which is "horizontal" (or what direction the y-axis and x-axis of their cartesian coordinate systems lie, if you prefer), then they will have different answers to the question "what point P3 on the second curve is at exactly the same vertical height as P2 on the first curve"? And so they will also disagree on the question "exactly what is the difference between the distance an ant must travel from P1 to P2 on the first curve and the distance an ant must travel from P1 to P3 (the point at the same vertical height as P2) on the second curve?" If the second curve gets very close to P2 and the different observer' vertical axes are not at too great an angle relative to one another (not more than 90 degrees, say) then the disagreement about ant-travel-distance to get to the same vertical height as P2 may not be too great, but there will still be some small difference.

It's almost exactly the same story in relativity. If you have one pointlike twin whose worldline goes between events E1 and E2, and another twin whose worldline goes through E1 and gets very very close to E2 but never actually crosses the worldline of the first twin again, then different frames disagree about what event E3 on the worldline of the second twin happens "at the same time" as E2 on the worldline of the first twin (i.e. they disagree about what E3 is at the 'same height on the time axis' as E2). And just as all frames in the geometric example agree about the distance along a curve (as traveled by an ant) between any two specific points on that curve, so all frames in relativity agree about the elapsed time on any worldline between any two events on that worldline. So all frames agree how much the first twin ages between E1 and E2, but since "E3" is defined to be the event that occurred at the same time as E2 and different frames disagree about which event this is, they will get different answers to the question "how much does the second twin age between event E1 and E3"? The difference may be slight if the second twin is very close to E2 (say, only a paper-thin separation between them) but it's not zero.

 

[Dale]

Surely you are right that since there is an established way to present an argument I have to adhere to it, so can you please show me where I can see more on those diagrams.

Here is a good place to learn about free-body diagrams:
http://www.physicsclassroom.com/class/newtlaws/u2l2c.cfm#1

If you are not already familiar with them then I would recommend learning Newtonian mechanics before tackling relativity. You need to understand basic concepts like force, energy, acceleration, and velocity before relativity.

What I am saying about internal force, I mean the usual force that a horse pulls a buggy with,

So your concern is indeed the one I identified way back in https://www.physicsforums.com/showpost.php?p=2927641&postcount=73". It would help if you would clarify such things right away; in this case it would have saved more than 30 posts.

Usually a horse pulls a buggy using a rigid rod which is called a tongue, this enables the horse to push the buggy backwards as well as pull it forwards, it also allows the horse to stop which is usually convenient feature once the buggy has reached its destination. However, for the sake of argument, let's suppose that we had a bad buggy designer who replaced the usual rigid tongue with a rope. In such a case the buggy would only function correctly when the tension in the rope is positive. So let's analyze the tension:

In an inertial frame there are three forces acting on the buggy, the normal force, N, the weight, mg, and the tension, T. Assuming that the ground is level N=-mg and therefore the sum of the forces on the buggy is equal to the tension (f=N+mg+T=T). So, by Newton's second law (f=ma) we easily derive T=ma. Note, the tension is NOT a function of the velocity, v, but only of the acceleration, a. Therefore, even with a poorly-designed buggy, as long as the buggy is accelerating in the positive direction there will be positive tension, and it does not matter if the velocity is positive or negative.

Your key point does not hold up to scrutiny. This has nothing to do with relativity, it is basic, first-semester Newtonian mechanics.

 

[ghwellsjr]

Imagine two trains are moving in opposite directions coming from different locations, then they meet together, and continue their motion, this does not need any acceleration, and according to relativity every one might claim resting (but not according to regular physics in which you would find a reference to the some absolute point).
So every one claims to be at rest and the other trains clock to slow down.
Now the train who was moving backs up and they reunite, who of them is younger?.

OK, we have two trains moving towards each other and when they meet, (without stopping or slowing down) an observer in each train starts a stopwatch. Now they "continue their motion" but now they will be moving apart. After some time, one of the trains "backs up and they reunite". At this point, the two observers stop their stopwatches and now the one in the train that backed up is the one with less elapsed time. If the two observers were the same age when they first met, the one in the train that backed up is the one that will be younger when they meet the second time.

This is what actually happens. You can analyze this "according to relativity" or you can analyze it "according to regular physics in which you would find a reference to the some absolute point" or you can actually perform the experiment, you will get the same answer in all three cases, correct?

Now, I want to point out an example of something that is extremely irritating and confusing in all your posts. Look at this phrase:

"according to regular physics in which you would find a reference to the some absolute point"

I don't know what you mean by this because it isn't correct English. I will fix it three possible ways:

1) "according to regular physics in which you would find a reference to some absolute point"

2) "according to regular physics in which you would find a reference to the absolute point"

3) "according to regular physics in which you would find a reference to the same absolute point"

When somebody reads this, it is impossible to know which way you meant it to be or even if you meant it a fourth way. You may be saving a little bit of time by not proof-reading your posts before you post them and by not rereading them and editing them after you post them, but you are wasting everyone else's time when you do this. We're trying to help you understand something that you need help on. Please help us help you by proof-reading and editing your posts to get rid of the incorrect English.

Now I would like to ask you which of the three corrections did you mean or are they all incorrect?

 

[ghwellsjr]

Let's put it different, is it possible for to have two people in linear motion without any acceleration or no?.
If no then we don't need relativity, since we always know who is moving.
If yes then in this situation when they reunite who is younger?.

OK, let's work on the first sentence (correcting the typo):

I think you mean: "Let's put it differently, is it possible to have two people in linear motion without any acceleration?"

To me, when someone says that a person is in linear motion, I think that means the person is traveling in a straight line at a constant speed. This means no acceleration. But, I don't know, maybe you mean this person is traveling in a straight line at a varying speed. That would mean there was acceleration. But now you want to ask about two people in linear motion. I'm wondering, what does he mean? Does he mean they are traveling together in a straight line, with or without acceleration? Or does he mean they are traveling in the same straight line but one is in front of the other one and maybe he means they are traveling at the same constant speed or maybe he means one of them is changing his speed while the other is at a constant speed or maybe they're both changing their speeds? Or does he mean they are traveling in the same straight line but they are going in opposite directions coming towards each other or maybe they are traveling in the same straight line but going away from each other, and again, maybe one of them maintains a constant speed or maybe both of them are maintaining a constant speed? Maybe one of them reverses direction. Maybe both of them reverse direction. Or does he mean that they are both on different straight lines going at an angle to each other, etc, etc, etc, etc? It never ends, I don't know what you are asking but I think the answer could be either yes or no.

OK, now let's work on the second sentence:

"If no then we don't need relativity, since we always know who is moving."

I'm trying really hard to understand why you would make this statement in response to a "no" answer to the first question. Why would no acceleration mean that you know which of the two people is moving? This could only make sense if one of the people was not moving, but you said that we had two people in motion. I have absolutely no idea what you are thinking of here. Beyond that, I don't understand why you think that knowing who is moving draws you to the conclusion that you don't need relativity. You don't need relativity in any situation. You can analyze any problem with the concept of an absolute reference frame if you want to. I just don't follow your thought process here.

Now for the last sentence:

"If yes then in this situation when they reunite who is younger?"

Now this question has a lot of assumptions that should have been stated earlier before anyone can possibly answer this question. The word "reunite" means that they were at one time united and then they separated by some undefined process and then they came back together by another undefined process. And no one can answer the question about who is younger until and unless you specify their ages at the time they were first united. Maybe you think it is obvious that they were the same age but unless you specifically say so, there is no way to answer this question. There is also no way to answer this question until you specify how the two people move from the first time they are united until they reunite.

The fact that you persist in asking these ill-formed questions over and over again means either that you are too lazy to ask a coherent question or your present understanding of physics is so limited that you don't know that your questions don't make any sense. So which is it: are you lazy or are you ignorant or is there another explanation I haven't considered?

 

[Passionflower]

Imagine two trains are moving in opposite directions coming from different locations, then they meet together, and continue their motion, this does not need any acceleration, and according to relativity every one might claim resting (but not according to regular physics in which you would find a reference to the some absolute point).

Regular physics? So you think relativity is not regular physics?

I wonder what your point is yoelhalb? Are you questioning the validity of relativity or do you try to understand it? If it is the former you are wasting everybody's time.

 

[yoelhalb]

Yes, anytime you change speed or direction you experience a G-force, regardless of the cause. You really should try to learn basic Newtonian physics before you try to challenge relativity!

Again my story is when there is sudden change such as the wind carries along the ship in which case the slope of the velocity will always be 0 and accordingly the g-force formula gives that the g-force will be 0.
(Yet I have no way of writing such velocity as a function, the only thing I would see on a graph is, that the slope will always be 0, but maybe you have a way to get the acceleration, if so then please let me know)

But anyway isn't it possible that both are encountering g-force?.
Let's take an example, two twins A and B, A takes of with a rocket while in the same time B accelerates in its car on a road to his house, later the rocket turns around but in the same time his brother on Earth also made a u-turn, now when they reunite who is younger?.
(here both are claiming that the other one has moved and that he did only local acceleration or rotation, if you are for example now rotating on your axis do you start traveling?).

Want another example for the twin paradox (without any acceleration or rotation), here it is.
Suppose A and B and C are already in uniform motion, A is traveling to the left direction according to B's perspective on a rate of 100 m/s, and A claims that B moves to the right with a rate of 100 m/s.
Yet initially B sees A coming from the right, and when A passes B they both see that they are exactly the same age.
Then when A is already to the left of B, then we see that C is coming from the left with a linear motion of 200 m/s, (again C claims to be at rest).
Now when C passes A they both see that they are also the same age, C proceeds now to B.
So when C will meet B who will be younger?.

This proposal was made in the context of his theory of "general relativity" in which spacetime is curved, not special relativity where spacetime is flat. However, according to the http://www.einstein-online.info/spotlights/equivalence_principle we can still say that the laws of special relativity still work "locally" in an arbitrarily small region of curved spacetime, you can define a "locally inertial frame" in such a small region.

In physics successful theories are rarely shown to be completely wrong, instead they are usually shown to be a limiting case of some more accurate theory (do you understand the calculus notion of a limit?) For example, Newtonian physics is still very useful in many scenarios, and it's possible to show that it is a very accurate approximation to both special relativity and general relativity in the appropriate limits (for example, the relative velocities being very small compared to c). Likewise, as I mentioned above SR can be understood as the limit case of GR as the size of the region of spacetime being considered becomes very small (so 'tidal effects' which depend on curvature become very small as well).

But yes, everyone understands that SR is not the most accurate known theory for calculating elapsed time on various clocks, GR is.

So if it is possible to make an inertial frame on a small scale when the affects of the curve will be small, don't you think that the same can be said on a curve as big as the entire universe?.
And what if the universe expands to trillion times larger?, would not be the curve and the g-force getting even smaller?.
So there must be some size that when the universe will become that size, then we should be able to claim that both of them are in inertial frame of reference, now in this case when they will reunite who of them will be younger?.
(Actually according to Galileo and his ship, even the curve of Earth is small enough that a moving object should be able to claim rest).

Yes, if we idealize the twins as point particles and suppose they meet at the same precise point of spacetime, then all frames agree on their ages when they meet.

If there is any finite distance between them, then different frames can disagree on the precise difference in their ages, although it may still be the case that all frames agree one is younger (but perhaps one frame will say the younger twin is younger by 457902910335298.3 nanoseconds while another will say the younger twin is younger by 457902910335298.2 nanoseconds)

A geometric analogy may help. Suppose we have two curves on a flat 2D wall which meet at one point P1, move apart, and then meet again at another point P2. If different observers have different definitions of which direction along the wall is "vertical" and which is "horizontal", they may disagree on the vertical and horizontal distances between P1 and P2, but they will all agree on the length of each curve between P1 and P2 (i.e. the distance an ant would measure if he walked along each curve from P1 to P2.

On the other hand, suppose both curves travel through P1 on the wall, but while the first curve also travels through P2, the second curve gets very close to P2 but never actually touches the first curve, after P2 it just remains parallel to the first curve but never quite touches it. And suppose we again imagine different observers with different definitions of which direction on the wall is "vertical" and which is "horizontal" (or what direction the y-axis and x-axis of their cartesian coordinate systems lie, if you prefer), then they will have different answers to the question "what point P3 on the second curve is at exactly the same vertical height as P2 on the first curve"? And so they will also disagree on the question "exactly what is the difference between the distance an ant must travel from P1 to P2 on the first curve and the distance an ant must travel from P1 to P3 (the point at the same vertical height as P2) on the second curve?" If the second curve gets very close to P2 and the different observer' vertical axes are not at too great an angle relative to one another (not more than 90 degrees, say) then the disagreement about ant-travel-distance to get to the same vertical height as P2 may not be too great, but there will still be some small difference.

It's almost exactly the same story in relativity. If you have one pointlike twin whose worldline goes between events E1 and E2, and another twin whose worldline goes through E1 and gets very very close to E2 but never actually crosses the worldline of the first twin again, then different frames disagree about what event E3 on the worldline of the second twin happens "at the same time" as E2 on the worldline of the first twin (i.e. they disagree about what E3 is at the 'same height on the time axis' as E2). And just as all frames in the geometric example agree about the distance along a curve (as traveled by an ant) between any two specific points on that curve, so all frames in relativity agree about the elapsed time on any worldline between any two events on that worldline. So all frames agree how much the first twin ages between E1 and E2, but since "E3" is defined to be the event that occurred at the same time as E2 and different frames disagree about which event this is, they will get different answers to the question "how much does the second twin age between event E1 and E3"? The difference may be slight if the second twin is very close to E2 (say, only a paper-thin separation between them) but it's not zero.

Again how can you say that both can be younger, if A < B then it cannot be that B < A.
and you can also not claim that since their clocks are differenet they can both claim younger, as this is like two people on different timezones claiming that both can be younger, or like saying that twin here in our example can both claim each other to be dead, or to say that we can claim that both are on the left side of each other.
And you can also not claim anyone of them to be in the past since "past" means what is no longer there.

But if you want proof, I will do the proof again (and show that thiw is not answered by your claim).
Imagine we fill the gap with people, since all the people claim each other resting there clocks must be synchronized.
To prove this even farther we can have someone accelrating over the entire length of the row of people, since all people will claim to accelrate with the same rate so they know exactly how muce his clock got slower, so they now have proof that their clcoks are synchronized.
since this can be extanded to any length, there is clearly no such claim that two people can be younger at the same time.

And this is actually my answer to the relativity of simultaneous.
Einstein had never prooved that what it is simultaneous in one frame of refrence does not have to be simultaneous in anther frame.
What he had proved is, That what it APPEARS to be simultaneous in one frame, does not have to APPEAR simultaneous in another frame, and this we know without him.
But Einstein's claim that since both frames are equely valid according to relativity, then it follows that what it is simultaneous in one frame of refrence does not have to be simultaneous in anther frame.
However I am just wondering on that, even if there would be no proof against relativity, it is still just a logical hypotesis, so why had Einstein choosen the more paradoxial relativity over the more straightforward hypotesis that simultaneous event are simultaneous every where?.

 

[Dale]

Again how can you say that both can be younger, if A < B then it cannot be that B < A.

That is not what we are saying. We are saying that if A<B then it is still possible that B'<A'. A is not the same as A' and B is not the same as B'

Einstein had never prooved that what it is simultaneous in one frame of refrence does not have to be simultaneous in anther frame.
What he had proved is, That what it APPEARS to be simultaneous in one frame, does not have to APPEAR simultaneous in another frame, and this we know without him.

No, this is a basic misunderstanding of SR that is, unfortunately, fostered by the whole "thought experiment" approach to teaching SR. The SR effects of time dilation, length contraction, and relativity of simultaneity are NOT "appearances" or "optical illusions" due to the finite speed of light. They are what remains after correctly accounting for the finite speed of light and removing that confounding effect.

 

[yoelhalb]

That is not what we are saying. We are saying that if A<B then it is still possible that B'<A'. A is not the same as A' and B is not the same as B', so the .

Again so two people in different timezones on Earth can claim to be younger?.
Had you seen my proof?, (actually the post you are reffering to has more proof in the beginning of it).

No, this is a basic misunderstanding of SR that is, unfortunately, fostered by the whole "thought experiment" approach to teaching SR. The SR effects of time dilation, length contraction, and relativity of simultaneity are NOT "appearances" or "optical illusions" due to the finite speed of light. They are what remains after correctly accounting for the finite speed of light and removing that confounding effect.

Again what I say is that it is based on the claim that the principle of relativity must be true.
(Now read again my question at the end of the post).

 

[LBrandt]

I have been following this thread, and I'm totally lost. Can someone (other than Yoelhalb) state briefly what Yoelhalb contends or what he is asking?

 

[Dale]

Again so two people in different timezones on Earth can claim to be younger?.

Yes, if they are also going at different velocities.

Again what I say is that it is based on the claim that the principle of relativity must be true.

Which is thus far supported by the evidence: http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

Btw, I am curious to read your reply to the horse and buggy analysis and see what new folly you will introduce.

 

[ghwellsjr]

Let's take an example, two twins A and B, A takes of with a rocket while in the same time B accelerates in its car on a road to his house, later the rocket turns around but in the same time his brother on Earth also made a u-turn, now when they reunite who is younger?.
(here both are claiming that the other one has moved and that he did only local acceleration or rotation, if you are for example now rotating on your axis do you start traveling?).

Want another example for the twin paradox (without any acceleration or rotation), here it is.
Suppose A and B and C are already in uniform motion, A is traveling to the left direction according to B's perspective on a rate of 100 m/s, and A claims that B moves to the right with a rate of 100 m/s.
Yet initially B sees A coming from the right, and when A passes B they both see that they are exactly the same age.
Then when A is already to the left of B, then we see that C is coming from the left with a linear motion of 200 m/s, (again C claims to be at rest).
Now when C passes A they both see that they are also the same age, C proceeds now to B.
So when C will meet B who will be younger?.

Here you have provided two more ill-formed examples.

I'm going to interpret the first one as I think you mean: Two twins start together in the same place and are the same age. Twin A takes off in a rocket at 1000 kilometers per hour while his brother, Twin B, takes off in his car at 100 kilometers per hour. After a while, they both turn around and travel back toward their starting point at the same speeds. When they meet, Twin A will be younger because he was traveling at a higher speed than his twin during the same intervals of time.

Now the second one is even more ill-formed because you haven't specified the frame in which C is traveling. But it doesn't matter as long as we assume that C is traveling to the right at 200 m/s with respect to either A or B. In either case, C will be younger than B when they meet.

One of your problems is that you keep thinking that it is permissible to analyze part of the situation from the perspective of one observer and another part from the perspective of another observer. You need to specify the situation from one frame of reference, it doesn't matter which one and then analyze the problem from one frame of reference (either the same one or a different one, you will get the same answer, but I always like to take the simplest frame of reference).

For example, in your second example, if we use the frame of reference in which B is at rest, A will be traveling to the left at 100 m/s and we assume that C will be traveling to the right at 200 m/s. So, because B is at rest during the entire time and A and C are traveling, they are the ones that age more slowly and so C ends up younger than B.

If you meant that C was traveling to the right at 200 m/s with respect to A instead of B, we will have to do some calculation to determine C's speed in B's frame of reference but we will still come to the conclusion that C is younger than B because B has been at rest the whole time.

If on the other hand, we use the frame of reference in which A is at rest and B is traveling to the right at 100 m/s and assume now that C is traveling to the right at 200 m/s with respect to A, it will not be as obvious whether C or B is younger when they meet because both of them are traveling. So that is why I prefer to analyze the problem in the frame of reference that is easiest to do the calculations.

By the way, thanks very much for improving you spelling and grammar.

 

[ghwellsjr]

I have been following this thread, and I'm totally lost. Can someone (other than Yoelhalb) state briefly what Yoelhalb contends or what he is asking?

Yoelhalb has a misunderstanding of the theory of Special Relativity. He thinks that it is permissible to look at different parts (observers) of a scenario from different frames of reference at the same time and see contradictions. He thinks that if we assume an absolute reference frame, then all the contradictions will vanish, which is true, but that is exactly the same as using just one frame of reference within Special Relativity. He hasn't yet come to terms with the problem of knowing which absolute reference frame to use. If he will propose one, then I will ask him what happens if we propose a different absolute reference frame that is traveling at some speed with respect to the one he is proposing. Maybe then, the light will come on and he will see that there is no difference between believing that there exists one absolute reference frame and believing in Special Relativity, because we can't know which is the correct absolute reference frame and assuming a different one is exactly the same as using a different reference frame in Special Relativity.

 

[JesseM]

Again my story is when there is sudden change such as the wind carries along the ship in which case the slope of the velocity will always be 0 and accordingly the g-force formula gives that the g-force will be 0.

No, velocity is a vector which has components on all three spatial axes x-y-z, like v = [v_x, v_y, v_z], therefore even if the magnitude of the velocity vector (i.e. the speed, given by $$\sqrt{v_x^2 + v_y^2 + v_z^2}$$) stays constant, if there is any change in the direction of the velocity vector (i.e. individual components like v_x are changing even though the total magnitude of $$\sqrt{v_x^2 + v_y^2 + v_z^2}$$ is constant) that means the acceleration vector (given by a = [dv_x/dt, dv_y/dt, dv_z/dt]) will be nonzero and you will experience G-forces. For example, if you are sitting on the edge of a spinning disc, then even if the disc is spinning at a constant rate so you are traveling in a circle at constant speed, you will still experience a G-force that seems to push in the outward direction, this "fictitious force" (i.e. apparent force experienced by an accelerating observer which is really just due to his own inertia) is known as the centrifugal force. The only way to avoid experiencing G-forces is to travel at constant speed and in a constant direction, i.e. traveling in a straight line forever.

But anyway isn't it possible that both are encountering g-force?.
Let's take an example, two twins A and B, A takes of with a rocket while in the same time B accelerates in its car on a road to his house, later the rocket turns around but in the same time his brother on Earth also made a u-turn, now when they reunite who is younger?.
(here both are claiming that the other one has moved and that he did only local acceleration or rotation, if you are for example now rotating on your axis do you start traveling?).

If both have changing velocity, then if you know each one's speed as a function of time v(t) in some inertial frame, and you know the times t₀ and t₁ when they departed from one another and then reunited, you can calculate how much each one ages between meetings using the integral:

$$\int_{t_0}^{t_1} \sqrt{1 - v(t)^2/c^2} \, dt$$

SR says that if an object is traveling at constant speed v for a time interval of $$\Delta t$$, then the object will age by $$\Delta t \sqrt{1 - v^2/c^2}$$ during that time interval (the time dilation formula), so if you're familiar with the basic idea of integrals in calculus you can see this one is essentially breaking up the path into a bunch of "infinitesimal" time intervals with length dt and calculating the sum of the aging on each one.

Want another example for the twin paradox (without any acceleration or rotation), here it is.
Suppose A and B and C are already in uniform motion, A is traveling to the left direction according to B's perspective on a rate of 100 m/s, and A claims that B moves to the right with a rate of 100 m/s.
Yet initially B sees A coming from the right, and when A passes B they both see that they are exactly the same age.
Then when A is already to the left of B, then we see that C is coming from the left with a linear motion of 200 m/s, (again C claims to be at rest).
Now when C passes A they both see that they are also the same age, C proceeds now to B.
So when C will meet B who will be younger?.

C will be younger. You can derive this in any frame you like (A's frame, B's frame, or C's frame) by taking into account the way the moving clocks are running slower in that frame, and also taking into account the definition of simultaneity in that frame. For example, say that in B's frame, A is moving at 0.6c to the left and C is moving at 0.6c to the right, and A and B's clocks both read 0 when A passes B, and the event of C passing A happens at t=10 years in B's frame (simultaneous with B's own clock reading 10 years), while the event of C passing B happens at t=20 years (simultaneous with B's clock reading 20 years). In this case since A is traveling at 0.6c, in B's frame A's clock is slowed down by a factor of $$\sqrt{1 - 0.6^2}$$ = 0.8, so at t=10 years A's clock only reads a time of 8 years, and by assumption C's clock also reads 8 years when he passes A at this moment. In B's frame C is moving at the same speed and so his clock is running slow by the same factor of 0.8, so 10 years later when he passes B his clock has only ticked forward by 8 more years, so it reads 8 + 8 = 16 years at that moment. And 10 years before C passed A (at t=0 when A was passing B), C's clock only read 8 years less, i.e. 8 - 8 =0 years, so in this frame the event of A passing B when both their clocks read 0 seconds was simultaneous with C's own clock reading 0 years.

But now if we switch to C's own rest frame, he has a different definition of simultaneity, it's no longer true that C's clock read 0 years simultaneously with A passing B. Instead, in this frame the event of A passing B is simultaneous with C's clock reading -9 years. At this moment in C's frame, A and B are at a distance of 15 light-years from C (I can show how I got these numbers using the Lorentz transformation if you like). And if A is moving at 0.6c to the left in B's frame, and B is moving at 0.6c to the left in C's frame, then using the velocity addition formula A must have a speed of (0.6c + 0.6c)/(1 + 0.6*0.6) = 0.88235c in C's frame. So, starting from 15 light-years away A will take a time of 15/0.88235 = 17 years to reach C in this frame, when C's clock will read -9 + 17 = 8 years. And A's clock started from 0 when A was 15 light-years away, then over the course of those 17 years A's clock was running slow by a factor of $$\sqrt{1 - 0.88235^2}$$ = 0.4706 in C's frame, so A's clock should read 17*0.4706 = 8 years when A meets C. So you can see that in C's frame we predict that when C passes A, both their clocks read 8 years, same as what we predicted when we used B's frame before. Likewise, in C's frame B's clock started from 0 when B was at a distance of 15 light-years (when C's clock read -9 years), and B is traveling towards C at 0.6c, so B should take a time of 15/0.6 = 25 years to reach C in this frame, meaning C's own clock reads -9 + 25 = 16 years when they meet, and B's clock is running slow by a factor of 0.8 so in these 25 years his clock ticks forward by 25*0.8 = 20 years. So in C's frame we get the prediction that C's clock reads 16 years and B's clock reads 20 years when they meet, exactly the same prediction we got in B's frame.

So if it is possible to make an inertial frame on a small scale when the affects of the curve will be small, don't you think that the same can be said on a curve as big as the entire universe?.

No. Think about an analogy with spatial coordinate systems--just as it's true that a small region of spacetime is approximately like SR, it's true that a small region of the surface of a big sphere looks approximately like a flat 2D plane, so to a good approximation the laws of Euclidean geometry can be expected to hold for shapes and lines drawn on a small patch of a giant sphere. For example, the sum of the angles of a triangle drawn on such a small patch will add up to about 180 degrees. But does that mean that if the sphere is huge enough, then shapes which cover significant regions of the entire sphere will obey the laws of Euclidean geometry? No, for example on any sphere we can draw an equilateral triangle covering up 1/8 of the sphere's surface (1/4 of a hemisphere) such that all three angles are right angles (as seen in a small patch centered on each corner), so the sum of the angles is 90 + 90 + 90 = 270, which is impossible in Euclidean geometry. This page has a diagram:

Other laws of Euclidean geometry break down when you look at shapes and lines covering large proportions of the surface, for example the closest analogue to a "straight line" on a sphere is a great circle (like the equator or a line of longitude on a globe), and you can draw two great circles which are at one point "parallel" to one another in the sense that you can draw another great circle which is "orthogonal" to both, i.e. it meets both at a right angle (like two lines of longitude which are orthogonal to the equator), yet these great circles will later cross (like two lines of longitude crossing at the pole). In Euclidean geometry, if two straight lines are "parallel" in the sense that you can find a third line that's orthogonal to them both, then they can never cross.

And what if the universe expands to trillion times larger?, would not be the curve and the g-force getting even smaller?.

The condition needed for SR to work approximately is not that "g-force" becomes small (even in SR an accelerating observer experiences G-force, and in GR an observer in freefall experiences no G-force), it's that tidal forces become small (the article on the equivalence principle I gave you has an animated diagram at the bottom showing one example of tidal force: the fact that two objects dropped straight 'down' on what seem to be parallel paths will nevertheless get closer together over time). The extent to which tidal forces are measurable depends both on the spatial size of the region you're looking at, and the window of time in which you make your measurements (i.e. the total 'size' of the region of spacetime on which the measurements are made), even with weak curvature the effects are more easily measurable if you expand the spatial or temporal extent of your measurements. As for "what if the universe expands to trillion times larger", that would just mean that if you want to talk about a situation where one twin circumnavigates the entire universe, the size of the spacetime region covering his entire path would have to become about a trillion times larger too. Again think of the analogy with geometry on a sphere--to see departures from Euclidean rules on a patch of the sphere, what matters is not the absolute size of the patch, but rather the proportion of the sphere's entire surface taken up by the patch.

Again how can you say that both can be younger, if A < B then it cannot be that B < A.

But in relativity there is no way to say "A < B" or "B < A" in an absolute way unless you are comparing ages at a single point in spacetime--if you're not, then you can only compare their ages in a frame-dependent way. There is no contradiction between the statement "in B's rest frame, A < B" and the statement "in A's rest frame, B < A", the two frames just define simultaneity differently. Again think of geometry--if we have a wall with two dots A and B on it, and you and I both use chalk to draw a different set of x-y coordinate axes on the wall, with your x-y axes rotated relative to mine, then there is no contradiction in the statement "in my coordinate system, A has a smaller y-coordinate than B" and "in your coordinate system, B has a smaller y-coordinate than A". Well, in relativity time is treated a lot like another spatial direction, one frame can have a time axis rotated relative to the other, so we can say "in frame #1, event A has a smaller t-coordinate than B" and "in frame #2, event B has a smaller t-coordinate than A".

And you can also not claim anyone of them to be in the past since "past" means what is no longer there.

Now you're getting metaphysical! Like I said, relativity treats time much like a spatial dimension, "past" just means "at an earlier time-coordinate", so different frames can disagree about whether an event B lies in the "past" of event A or not. Of course, because of the finite speed of light, judgments about time-coordinates of events off my own worldline can only be made in retrospect anyway--for example, if in 2010 I see the light from an event A at a position 8 light-years away in my frame, and in 2012 I see the light from an event B at a position 10 light-years away in my frame, I can say that in my frame they both happened "simultaneously" in 2002 even though I wasn't aware of them until later. Someone in a different frame who also subtracts the distance in light-years from the time in years when he saw them may conclude that A happened in the past of B, and someone in a third frame may conclude B happened in the past of A, but none of us were aware of them until they were both in our own past (i.e. our own past light cone...and if an event X lies in the past light cone of another event Y, then in that case all inertial frames do agree that X happened in the past of Y).

Imagine we fill the gap with people, since all the people claim each other resting there clocks must be synchronized.

"synchronized" has no frame-independent meaning in SR. If you have two rows of clocks, with all the clocks in row A at rest and synchronized relative to one another and all the clocks in row B at rest and synchronized relative to one another, then if row A is in motion relative to row B, row A will judge that all the clocks in row B are out-of-sync and row B will judge that all the clocks in row A are out-of-sync. I drew up some detailed illustrations of this in this thread, you might want to check those out.

To prove this even farther we can have someone accelrating over the entire length of the row of people, since all people will claim to accelrate with the same rate so they know exactly how muce his clock got slower, so they now have proof that their clcoks are synchronized.

I don't understand what you mean here. If the guy is accelerating, then the rate at which his clock is running will be constantly changing, since the rate a clock ticks is a function of the clock's speed and acceleration means his speed is changing. My diagrams on the other thread show how, since the two rows of clocks A and B are moving at constant speed relative to one another, each individual clock in A (like the one with the red hand) is running slow as measured by the clocks in B, and each individual clock in B is running slow as measured by the clocks in A. There's no paradox there once you take into account the relativity of simultaneity.

And this is actually my answer to the relativity of simultaneous.
Einstein had never prooved that what it is simultaneous in one frame of refrence does not have to be simultaneous in anther frame.
What he had proved is, That what it APPEARS to be simultaneous in one frame, does not have to APPEAR simultaneous in another frame, and this we know without him.
But Einstein's claim that since both frames are equely valid according to relativity, then it follows that what it is simultaneous in one frame of refrence does not have to be simultaneous in anther frame.

As a metaphysical hypothesis you are free to believe that one frame's definition of simultaneity is "correct" in a metaphysical sense and the other frames' definitions are "incorrect". However, as long as all the fundamental laws of physics obey Lorentz-symmetric equations, so the equations in one inertial frame are the same as in any other, then any experiment you do that's confined to a windowless chamber (so you don't have any external landmarks to look at) will give the same results regardless of whether you are at rest in inertial frame #1 or inertial frame #2, so there's no experimental reason to pick out anyone frame as "preferred" by the laws of nature, and thus it must forever remain a mystery to you which frame is "metaphysically preferred" in the sense that its definition of simultaneity is metaphysically correct. Philosophically I think it's lot simpler to apply razor[/url] and eliminate the notion of a "true" definition of simultaneity, instead adopting an eternalist philosophy of time where events at all points in time are equally "real", but if you prefer the presentist philosophy of time where there is an absolute present and events not in the present have objectively "ceased to exist", nothing in relativity will contradict you as long as it's a purely metaphysical hypothesis without any physical implications about the results of actual experiments.

However I am just wondering on that, even if there would be no proof against relativity, it is still just a logical hypotesis, so why had Einstein choosen the more paradoxial relativity over the more straightforward hypotesis that simultaneous event are simultaneous every where?.

Basically, he picked it so that the laws of electromagnetism could work in every inertial frame as opposed to just a preferred "ether" frame (since Maxwell's laws say that electromagnetic waves always move at c, but the only way for different frames to agree that all electromagnetic waves move at the same speed is for them to have different definitions of simultaneity, as shown for example by the train thought-experiment). In part he may have been inspired by the failure of various experiments (like the Michelson-Morley experiment) to find a preferred ether frame, and subsequent experiments have consistently supported the idea that the fundamental laws of physics obey Lorentz-invariant equations.

 

[Dale]

Yoelhalb has a misunderstanding of the theory of Special Relativity.

He also has a misunderstanding of Newtonian mechanics.

 

[Mentz114]

However I am just wondering on that, even if there would be no proof against relativity, it is still just a logical hypothesis, so why has Einstein choosen the more paradoxial relativity over the more straightforward hypothesis that simultaneous event are simultaneous every where?.

You've got it the wrong way round - you have put the cart before the horse.

There is no natural concept of simultaneity of events that are not close together.
The rules of SR are such that paradoxes do not occur, and none have been demonstrated, so the SR convention appears to be the least paradoxical.

 

[yoelhalb]

But anyway isn't it possible that both are encountering g-force?.
Let's take an example, two twins A and B, A takes of with a rocket while in the same time B accelerates in its car on a road to his house, later the rocket turns around but in the same time his brother on Earth also made a u-turn, now when they reunite who is younger?.
(here both are claiming that the other one has moved and that he did only local acceleration or rotation, if you are for example now rotating on your axis do you start traveling?).

If both have changing velocity, then if you know each one's speed as a function of time v(t) in some inertial frame, and you know the times t₀ and t₁ when they departed from one another and then reunited, you can calculate how much each one ages between meetings using the integral:

$$\int_{t_0}^{t_1} \sqrt{1 - v(t)^2/c^2} \, dt$$

SR says that if an object is traveling at constant speed v for a time interval of $$\Delta t$$, then the object will age by $$\Delta t \sqrt{1 - v^2/c^2}$$ during that time interval (the time dilation formula), so if you're familiar with the basic idea of integrals in calculus you can see this one is essentially breaking up the path into a bunch of "infinitesimal" time intervals with length dt and calculating the sum of the aging on each one.

Let me explain myself again.
There is a known paradox called the twin paradox, and there is basically two answers on it, 1) that the subject moving must rotate in order to get back, 2) that the subject has to accelerate and decelerate when starting and ending the motion.
We have to understand the answers, since even if you rotate now on your axis it does not causes you any motion and you will not start to move to the moon, and the same is with acceleration.
I also don't believe that two persons in linear motion, none of them may turn their head for a while, and if one of them is doing so he can no longer claim resting, obviously this doesn't make sense.
I have two ways to interpret the answers, let's take a look on both ways.
But first let me define the situation as I view it.
A takes up in a rocket accelerating, then he stops accelerating and continues in linear motion,
after a while he makes a u-turn and then continues with linear motion till he is getting close to earth, and he decelerates till he is coming to full stop.

Now let us see both ways to interpret the answers why A must be the one who is younger.
i) That since the twin in motion is anyway younger just because of the acceleration and rotation then we already know that he is younger, even if we should agree that in the time he was in uniform motion he might claim rest, since the period of time that he spent accelerating and decelerating and rotating outweighs the uniform motion.
However I don't think this is right, consider if the acceleration and rotation took only five minutes, and the uniform motion took thousands of years.
ii) That since that as soon that he rotated the gap between A and B started to decrease, then in evidence based science it clearly shows that A (in the rocket) is the one who is moving and the other twin is at rest, (and similar to that we can explain with acceleration).
So now my question is, since rotation does not mean any motion and here we claim to move only because in this case the rotation had proved that he moves, so what if both are rotating in the same second, now there is no longer any evidence who of then caused the gap to decrease, and if one of them or both of them.
This was my original question, and I don't see how your answer relates to this.

But anyway if my interpretation of the answers on the twin paradox is right, then CONGRATULATIONS! welcome to experiment based science where every object has to rotate in order to see if he is actually at rest.
Yet this will not work in cases where the motion is due to external forces such as the wind or water, but since we already saw that uniform motion might still be proved moving, we have no reason to say here differently, and we actually might come up with an experiment that will suite external forces as well.

By the way I am still not understanding the twin paradox answer that claims that because of acceleration A must be younger.
My question on that is, is it possible to be in uniform motion without acceleration or no?.
If it is possible, (actually if it is a constant very small acceleration, it can be neglected to 0 just as we do with gravity), then why can't A also do the same and be in uniform motion without acceleration?.
And if it is not possible, then how can uniform motion and the principle of relativity be for real? is it just a science fiction?.

The condition needed for SR to work approximately is not that "g-force" becomes small (even in SR an accelerating observer experiences G-force, and in GR an observer in freefall experiences no G-force), it's that tidal forces become small (the article on the equivalence principle I gave you has an animated diagram at the bottom showing one example of tidal force: the fact that two objects dropped straight 'down' on what seem to be parallel paths will nevertheless get closer together over time). The extent to which tidal forces are measurable depends both on the spatial size of the region you're looking at, and the window of time in which you make your measurements (i.e. the total 'size' of the region of spacetime on which the measurements are made), even with weak curvature the effects are more easily measurable if you expand the spatial or temporal extent of your measurements. As for "what if the universe expands to trillion times larger", that would just mean that if you want to talk about a situation where one twin circumnavigates the entire universe, the size of the spacetime region covering his entire path would have to become about a trillion times larger too. Again think of the analogy with geometry on a sphere--to see departures from Euclidean rules on a patch of the sphere, what matters is not the absolute size of the patch, but rather the proportion of the sphere's entire surface taken up by the patch.

Can you explain me why?, since the principle of relativity says that there is no absolute point of reference and any object can claim rest and that every one else is moving, then what is different curved motion then linear motion?, both of them can still claim rest and claim that the other one is the one who moves with the curved motion.
If the condition would be that there should no g-force I Would be able to understand, take for example an accelerating object claiming to at rest and every body else accelerating, then he is actually predicting that he should not feel any g-force while every body should, and since this does not agree with observation then he is clearly disproved.
(Although I still do not understand, since if there is no absolute point of reference then how can he actually be wrong?).
But if the condition for SR is no tidal-force then why can't he be resting?.
Actually if we deal with a small region only, I would not considered the twin paradox to be a real question, and since I am seeing it is I think that it contradicts what you are writing here.

Also I have another question, since an accelerating object cannot claim to be at rest, since as I already explained this goes against observation since he feels g-force and nobody else feels, so we need to have some point of reference.
And since we cannot claim a specific point of reference for an accelerating object, since that if we are to claim that and since the accelerating object have proof for that - as he is experiencing g-force -, then our only option is to say that all inertial frames of reference are equally valid for that.
But now as you claim that there is almost no inertial frame of reference, so then what is the frame of reference for an accelerating object.
Even more the question applies anywhere and everywhere, since gravity is actually acceleration and every object under gravity is accelerating, (yet we might rest on the Earth but Earth itself together with all objects must also be accelerating), and as such every object in the current universe needs a point of reference but there is nothing.
Actually you cannot even use an inertial frame in a small region of spacetime as the point of reference, since after all there is gravity even if it is vary week, and as such the object claiming to be be in an inertial state is actually moving even though the motion is vary small.
So we are actually back on the same place that we were before relativity.

But in relativity there is no way to say "A < B" or "B < A" in an absolute way unless you are comparing ages at a single point in spacetime--if you're not, then you can only compare their ages in a frame-dependent way. There is no contradiction between the statement "in B's rest frame, A < B" and the statement "in A's rest frame, B < A", the two frames just define simultaneity differently. Again think of geometry--if we have a wall with two dots A and B on it, and you and I both use chalk to draw a different set of x-y coordinate axes on the wall, with your x-y axes rotated relative to mine, then there is no contradiction in the statement "in my coordinate system, A has a smaller y-coordinate than B" and "in your coordinate system, B has a smaller y-coordinate than A". Well, in relativity time is treated a lot like another spatial direction, one frame can have a time axis rotated relative to the other, so we can say "in frame #1, event A has a smaller t-coordinate than B" and "in frame #2, event B has a smaller t-coordinate than A".

Now you're getting metaphysical! Like I said, relativity treats time much like a spatial dimension, "past" just means "at an earlier time-coordinate", so different frames can disagree about whether an event B lies in the "past" of event A or not. Of course, because of the finite speed of light, judgments about time-coordinates of events off my own worldline can only be made in retrospect anyway--for example, if in 2010 I see the light from an event A at a position 8 light-years away in my frame, and in 2012 I see the light from an event B at a position 10 light-years away in my frame, I can say that in my frame they both happened "simultaneously" in 2002 even though I wasn't aware of them until later. Someone in a different frame who also subtracts the distance in light-years from the time in years when he saw them may conclude that A happened in the past of B, and someone in a third frame may conclude B happened in the past of A, but none of us were aware of them until they were both in our own past (i.e. our own past light cone...and if an event X lies in the past light cone of another event Y, then in that case all inertial frames do agree that X happened in the past of Y).

As a metaphysical hypothesis you are free to believe that one frame's definition of simultaneity is "correct" in a metaphysical sense and the other frames' definitions are "incorrect". However, as long as all the fundamental laws of physics obey Lorentz-symmetric equations, so the equations in one inertial frame are the same as in any other, then any experiment you do that's confined to a windowless chamber (so you don't have any external landmarks to look at) will give the same results regardless of whether you are at rest in inertial frame #1 or inertial frame #2, so there's no experimental reason to pick out anyone frame as "preferred" by the laws of nature, and thus it must forever remain a mystery to you which frame is "metaphysically preferred" in the sense that its definition of simultaneity is metaphysically correct. Philosophically I think it's lot simpler to apply razor[/url] and eliminate the notion of a "true" definition of simultaneity, instead adopting an eternalist philosophy of time where events at all points in time are equally "real", but if you prefer the presentist philosophy of time where there is an absolute present and events not in the present have objectively "ceased to exist", nothing in relativity will contradict you as long as it's a purely metaphysical hypothesis without any physical implications about the results of actual experiments.

I will try to explain again my question and I hope you will understand it.
What I understand from your words is that two different frames have two different time coordinates that don't have to correspond to each other.
Now what I ask is, for any point in the time coordinate of A, is there a corresponding coordinate of B's time frame?
If there is, then let's take the value of B's clock on that particular event and compare it to the corresponding time event in A.
And if there is no corresponding event, so there is actually no relation at all between the frames, then how can they coexist in the universe? and how did they meet together on the first hand?, since there is no corresponding event between the frames.
(Think about what I am asking, thanks).

Here is another way to look at it, current research with quantum mechanics show that it possible to send information via quantum mechanics instantaneously over the entire universe even faster then the speed of light.
This is done by splitting a particle, and it dates back to an argument between Einstein and Bohr on quantum mechanics, based on a thought experiment on a particle that has been split.
Now if this technology succeeds, we can use it to get the twins current age, then who of them will be younger?.

Also according to what I have written earlier, that acceleration means absolute motion, so an accelerating object cannot use its own frame to consider what is simultaneous, so which frame do he have to use?.

I don't understand what you mean here. If the guy is accelerating, then the rate at which his clock is running will be constantly changing, since the rate a clock ticks is a function of the clock's speed and acceleration means his speed is changing. My diagrams on the other thread show how, since the two rows of clocks A and B are moving at constant speed relative to one another, each individual clock in A (like the one with the red hand) is running slow as measured by the clocks in B, and each individual clock in B is running slow as measured by the clocks in A. There's no paradox there once you take into account the relativity of simultaneity.

I don't know so well the formulas, but I believe that if an object A accelerates with a constant acceleration, and started with a velocity of 0, then it should be easy to figure out at any time how much A's clock slowed down since he started accelerating based on A's current velocity.
If this is true we can use this to synchronize the clocks over the entire universe, and also to figure out what the clock of the twin shows even if the two twins will never meet.

Basically, he picked it so that the laws of electromagnetism could work in every inertial frame as opposed to just a preferred "ether" frame (since Maxwell's laws say that electromagnetic waves always move at c, but the only way for different frames to agree that all electromagnetic waves move at the same speed is for them to have different definitions of simultaneity, as shown for example by the train thought-experiment). In part he may have been inspired by the failure of various experiments (like the Michelson-Morley experiment) to find a preferred ether frame, and subsequent experiments have consistently supported the idea that the fundamental laws of physics obey Lorentz-invariant equations.

So according to what you write he had not succeeded anyway, since SR is possible only on a small scale, and I don't believe this this is what he tried to answer, (unless we say that Einstein actually forgot that there should be gravity all around).

BUT HERE I WOULD LIKE TO GIVE DIRECT PROOF AGAINST THE PRINCIPLE OF RELATIVITY.
And I am very interested to see if there is an answer on that.

A) Light experiment --
Here is an experiment that can prove directly who is moving, even without any clocks.
Consider we have a laser beam and a mirror just against it, so it should reflect the light, like this,
___ (mirror)

. (light)
(I am using a laser beam since it always goes straight, but you can use regular light as long you have a way that the mirror should only detect the light that goes in a straight line upwards and not diagonal).
The mirror and the light should be far away so that light should take some time before it arrives at the mirror, (maybe it can't be done with current technology but it will surely be one day).
Now let's consider this arrangement is on ship (or similar) and is moving in a uniform motion.
Now if the ship moves, then the light will never get to the mirror (assuming the ship is moving with an appropriate speed), since the mirror has been moved away from the laser beam that is going straight only.
So if the light arrives at the mirror then every body most agree that it is at rest, and if the light does not arrive then it is clear then it is moving, and no debate on that.
(You can actually make a joint experiment, in which two objects in uniform motion according to each other, are using the same laser beam to see to which mirror of them it will arrive).

B) Constant speed of light --
According to the special relativity it follows that the speed of light will not always be constant, listen why.
Assume A and B move away with a uniform motion and a light ray (L) goes to right of them,
A<------->B<------------>L
A claims that he is at rest and B's time slows down, that's fine.
But B claims that he is at rest, and if so A clearly sees the light more then c.
(You might want to resort to the velocity formula, but it cannot work here as you shall see).
Let's assume for a moment that the time of B and of A will stay the same (and we will ignore for a moment time dilation), in other words t_B = t_A.
Now we can use simple addition to add the velocities because, V₁ = s₁/t and V₂ = s₂ /t, so you can just add both velocities.
Now if we add the velocity that A moves ( from B's perspective ) together with c the speed of light, we clearly get more then the speed of light, and in other words from B's perspective A sees the light to go faster then the speed of light, some thing that is impossible according to special relativity.
And since according to B, A's clock will slow down, the situation will get even worse, since that means that according to B, A will see the light moving even faster.
(The velocity formula however might still work when both velocities are in the same direction).
Since this cannot be true this actually shows that B cannot claim to be the point of reference (or you might claim that B does not have to explain how A sees the light, but if say this then you can let go the whole time dilation which is based only on how one frame of reference sees the light according to the other frame of reference).
(you can also not invent that B will claim A's clock to go faster, because then there will be a problem when the light is going to the left).

 

[Mentz114]

Here is another way to look at it, current research with quantum mechanics show that it possible to send information via quantum mechanics instantaneously over the entire universe even faster then the speed of light.
This is done by splitting a particle, and it dates back to an argument between Einstein and Bohr on quantum mechanics, based on a thought experiment on a particle that has been split.
Now if this technology succeeds, we can use it to get the twins current age, then who of them will be younger?.

Nonsense. Information cannot be transmitted at greater than the speed of light, and quantum mechanics makes no claim to the contrary. You are getting desperate because there's no foundation to your arguments.

You really should try to learn more about relativity. There is no 'twin paradox' and if you knew what a worldline and a proper interval was you'd understand that.

Now if we add the velocity that A moves ( from B's perspective ) together with c the speed of light, we clearly get more then the speed of light, and in other words from B's perspective A sees the light to go faster then the speed of light, some thing that is impossible according to special relativity.
And since according to B, A's clock will slow down, the situation will get even worse, since that means that according to B, A will see the light moving even faster.
(The velocity formula however might still work when both velocities are in the same direction).
Since this cannot be true this actually shows that B cannot claim to be the point of reference (or you might claim that B does not have to explain how A sees the light, but if say this then you can let go the whole time dilation which is based only on how one frame of reference sees the light according to the other frame of reference).
(you can also not invent that B will claim A's clock to go faster, because then there will be a problem when the light is going to the left).

What total garbage.

BUT HERE I WOULD LIKE TO GIVE DIRECT PROOF AGAINST THE PRINCIPLE OF RELATIVITY.
And I am very interested to see if there is an answer on that.

It's nonsense and doesn't deserve any reply, which you would ignore in any case.

A) Light experiment --
Here is an experiment that can prove directly who is moving, even without any clocks.
Consider we have a laser beam and a mirror just against it, so it should reflect the light, like this,
___ (mirror)

. (light)
(I am using a laser beam since it always goes straight, but you can use regular light as long you have a way that the mirror should only detect the light that goes in a straight line upwards and not diagonal).
The mirror and the light should be far away so that light should take some time before it arrives at the mirror, (maybe it can't be done with current technology but it will surely be one day).
Now let's consider this arrangement is on ship (or similar) and is moving in a uniform motion.
Now if the ship moves, then the light will never get to the mirror (assuming the ship is moving with an appropriate speed), since the mirror has been moved away from the laser beam that is going straight only.
So if the light arrives at the mirror then every body most agree that it is at rest, and if the light does not arrive then it is clear then it is moving, and no debate on that.
(You can actually make a joint experiment, in which two objects in uniform motion according to each other, are using the same laser beam to see to which mirror of them it will arrive).

The section I've bolded shows you are completely at sea. Are you saying that a material body can outrun a beam of light ? You don't seem to understand the very basics of relativity ( or anything else for that matter ).

I think you ought to be banned for wasting everybody's time with rubbish like this.

After all the efforts to help you, you come back with this !

 

[yoelhalb]

Here is another light experiment.
Consider A and B are in a linear motion next to a wall, and the wall has an hole.
Now consider we are putting on a light for a second and turn it off right away, the light will shine out from the hole perpendicular to the linear motion (so we cannot say that space has contracted).
The light travels for a while, and it is then being reflected by a mirror to A and B.
Now if the clock of anyone of them has been slowed down, then he would see the light going faster then c.

 

[yoelhalb]

Nonsense. Information cannot be transmitted at greater than the speed of light, and quantum mechanics makes no claim to the contrary. You are getting desperate because there's no foundation to your arguments.

You really should try to learn more about relativity. There is no 'twin paradox' and if you knew what a worldline and a proper interval was you'd understand that.



What total garbage.



It's nonsense and doesn't deserve any reply, which you would ignore in any case.



The section I've bolded shows you are completely at sea. Are you saying that a material body can outrun a beam of light ? You don't seem to understand the very basics of relativity ( or anything else for that matter ).

I think you ought to be banned for wasting everybody's time with rubbish like this.

After all the efforts to help you, you come back with this !

Is this a religion?.
Actually can you explain how the clocks are being affected by the light? is this action at a distance?.
And what happens if it is dark and there is no light? will the clocks behave differently?.

 

[George Jones]

I have closed this thread.

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