Relativity Question

[tar]

There is no objective way to say one frame is the real one.

 

Swansont,

 

Well perhaps there is. That is to say that we piece together what we have learned to build our model of the world.

 

When I see a truck 1/4 mile ahead on the highway, it looks very small. I can cover it with my thumb at arms length. I do not take this to mean that I should be able to hold the truck in my hand. Nor do I consider that covering it with my thumb, made it disappear.

 

Because of my knowledge of the world, having moved around in it, I have learned what is, and is not the case related to the apparent size of the truck and its "actual" size. Thus I am able to predict, that if I am going a few miles an hour faster than the truck, it will grow in size till it is big enough to actually contain a driver, which I know it must have behind the wheel. And sure enough, that happens.

 

When we measure the distance to a star we take into account its apparent movement against the "fixed" stars behind it, as we repeat the observation of the star 1/2 a year later from the other side of the Sun, and compare the views. We can take our knowledge of the whole situation, what we have found must be the size of the Earth, and its distance from the Sun, and the diameter of its orbit...hundreds, if not thousands or millions of observations and calculations, and observations, that "force" things to "have to be" the case for everything to fit together.

 

Thus, although there is no "preferred" frame of reference, if we take all the things we know "must" be the case and put them together, checking our findings and beliefs, from various hypothetical and/or real other frames of reference (thought, or actual "experiments") we can "build" a prediction, of "what is real" and actually the case.

 

Contradictions that arise, are not the fault of objective reality (which MUST be the case), but a sign that our model needs some adjustment, or that we are not looking at it the right way.

 

Thus, for various reasons, I would say "our" frame of reference, is not only a good one to use, but the only one we have, to use. And transformations and differential geometry and the mass=energy equivilancy, are excellent ways to "move around" in an existant universe, that fits together flawlessly.

 

Still, an "objective reality" that fits together flawlessly has to be the case. We experience it every day. Objectively speaking, the universe we experience IS the real one. (its the only one we have)

 

Regards, TAR2

[swansont]

Objectively speaking, the universe we experience IS the real one. (its the only one we have)

And what of someone living in a different frame of reference?

[J.C.MacSwell]

Frames generally speaking* do not have their own independent reality. We may shift around mathematically in the definitions of each, in both time and space...but we still exist...we are still "here" in the past, present or future of whichever frame you choose. (assuming the frame is physically legitimate)

 

They are all real in that sense.

 

*you can define a frame to exclude us, but in that sense the frame is just limited not our reality

Edited July 16, 2011 by J.C.MacSwell

[Janus]

How can there be real space contraction of the universe.[/font][/size]

 

The problem with that question is that it is a lot like the question, " If the world is round, how come the people on the underside don't fall off?" in that it is based on a presumption. The presumption of the quoted question deals with the nature of "down". The presumption of your question deals with the nature of time and space (and how its measured).

 

 

Now I'll explain what I mean.

 

Imagine that you have a point "a" located at a position with respect to the origin of a reference frame like this:

 

 

We have two axes, x and y. If you draw a line perpendicular to the x axis, it intersects with the x axis at xa which gives the distance of a from the origin in terms of x. a similar line drawn perpendicular to the y axis gives the distance of a from the origin in terms of y.

 

Okay. Now we superimpose a new reference frame on top the first with the same origin but tilted at 45 degrees. The axes are labeled x' and y' we draw lines perpendicular to the axes and intersecting with point "a" like we did before.

 

 

If we now rotate this whole image by 45 degree, we can more easily see how this new frame measures the position of with respect to the origin.

 

 

Note that if you were to draw a line between "a" and the origin, it would be the same length as it was in the first diagram, what has changed is the distance in terms from the axes.

 

To relate this to relativity we change the y and y' axes to t and t', the 45 degree tilt corresponds to the second frame of reference moving with a velocity with respect to the first, and the x axis is the distance as measured along the line of motion.

 

"a" and the origin represent events that occur at certain times. ta and t'a is the time difference between the event at the origin and the event marked a.

 

shown here are the measurement of "a" with respect to the axes according to both frames:

 

 

 

 

The time difference and the distance along the line of movement between the origin event and event a is different for the two frames. This corresponds to time dilation, length contraction, and the relativity of simultaneity). Again, the line joining the origin and "a" remains constant. This is known as the space-time interval. What changes between frames is the time and space components of the space-time interval.

 

These diagrams are for getting the general concept across and aren't proper space-time diagrams, so their utility is somewhat limited.

 

The point to all this is that any measurement you make is frame dependent and that measurement represents "reality" for that frame and that's all the reality that there is.

 

So from a reference frame moving with "with respect to the local region of the universe" ( I'll will not say moving with respect to the whole universe, because that actually has no meaning), the local universe does "really' contract. And from a reference frame moving at a different velocity, it will "really" contract differently and there is no contradiction in this.

 

It just comes down to thinking about time and space differently, just like accepting a round Earth required people to think differently about what "down" meant.

[Vilas Tamhane]

The problem with that question is that it is a lot like the question, " If the world is round, how come the people on the underside don't fall off?" in that it is based on a presumption. The presumption of the quoted question deals with the nature of "down". The presumption of your question deals with the nature of time and space (and how its measured).

 

 

Now I'll explain what I mean.

 

Imagine that you have a point "a" located at a position with respect to the origin of a reference frame like this:

 

 

We have two axes, x and y. If you draw a line perpendicular to the x axis, it intersects with the x axis at xa which gives the distance of a from the origin in terms of x. a similar line drawn perpendicular to the y axis gives the distance of a from the origin in terms of y.

 

Okay. Now we superimpose a new reference frame on top the first with the same origin but tilted at 45 degrees. The axes are labeled x' and y' we draw lines perpendicular to the axes and intersecting with point "a" like we did before.

 

 

If we now rotate this whole image by 45 degree, we can more easily see how this new frame measures the position of with respect to the origin.

 

 

Note that if you were to draw a line between "a" and the origin, it would be the same length as it was in the first diagram, what has changed is the distance in terms from the axes.

 

To relate this to relativity we change the y and y' axes to t and t', the 45 degree tilt corresponds to the second frame of reference moving with a velocity with respect to the first, and the x axis is the distance as measured along the line of motion.

 

"a" and the origin represent events that occur at certain times. ta and t'a is the time difference between the event at the origin and the event marked a.

 

shown here are the measurement of "a" with respect to the axes according to both frames:

 

 

 

 

The time difference and the distance along the line of movement between the origin event and event a is different for the two frames. This corresponds to time dilation, length contraction, and the relativity of simultaneity). Again, the line joining the origin and "a" remains constant. This is known as the space-time interval. What changes between frames is the time and space components of the space-time interval.

 

These diagrams are for getting the general concept across and aren't proper space-time diagrams, so their utility is somewhat limited.

 

The point to all this is that any measurement you make is frame dependent and that measurement represents "reality" for that frame and that's all the reality that there is.

 

So from a reference frame moving with "with respect to the local region of the universe" ( I'll will not say moving with respect to the whole universe, because that actually has no meaning), the local universe does "really' contract. And from a reference frame moving at a different velocity, it will "really" contract differently and there is no contradiction in this.

 

It just comes down to thinking about time and space differently, just like accepting a round Earth required people to think differently about what "down" meant.

 

Your explanation is as good as any can be. But I differ with your definition of reality. Any physical entity in the vector form is the reality which can never change by our selection of system of coordinates. Only components can change. This is not the case with space time diagram because of the addition of time as a coordinate. However existence of a vector is a physical reality and any coordinate system that changes this basic reality is necessarily wrong.

 

There cannot be any theory and associated mathematics based on coordinate system alone that has an ability to change basic quantities of nature. Any such theory, according to me, is grossly wrong.

 

In case we decide that reality depends on frame then we face many problems.

 

1. Length contraction is space contraction and we do not have any proof that space is some tangible entity which has capability of any dimensional change. Therefore the statement that space can contract is not good physics. If space can contract then it should be able to expand. What exactly this means?

 

2. For the traveller, the space contracts but at the same time the same space does not change for the observer in the rest frame. How can same space ‘really’ contract and remain unchanged at the same time?

 

3. For a rapidly moving train observer, wheels of moving cycle are elliptical (or rather every particle on the wheel moves in elliptical path. And this is not an apparent measurement but ‘real’ change. This is not possible.

 

4. There is nothing in physics that explains how any moving object can have influence on non moving objects. Is it ever possible that the wheels of a bicycle will become really oblong if I pass along it with greater speed in a car? The measurement is clearly apparent and not real. In the previous example, it is impossible that the distance between earth and Alpha c will ‘really’ contract. Any such measurement has to be apparent and if this is so then, in spite of the measurements of the traveller, he will have to travel the real distance that is measured in the rest frame.

[swansont]

Your explanation is as good as any can be. But I differ with your definition of reality. Any physical entity in the vector form is the reality which can never change by our selection of system of coordinates. Only components can change. This is not the case with space time diagram because of the addition of time as a coordinate. However existence of a vector is a physical reality and any coordinate system that changes this basic reality is necessarily wrong.

 

There cannot be any theory and associated mathematics based on coordinate system alone that has an ability to change basic quantities of nature. Any such theory, according to me, is grossly wrong.

 

In case we decide that reality depends on frame then we face many problems.

 

1. Length contraction is space contraction and we do not have any proof that space is some tangible entity which has capability of any dimensional change. Therefore the statement that space can contract is not good physics. If space can contract then it should be able to expand. What exactly this means?

 

Who is claiming that space is a tangible entity?

 

2. For the traveller, the space contracts but at the same time the same space does not change for the observer in the rest frame. How can same space ‘really’ contract and remain unchanged at the same time?

 

3. For a rapidly moving train observer, wheels of moving cycle are elliptical (or rather every particle on the wheel moves in elliptical path. And this is not an apparent measurement but ‘real’ change. This is not possible.

 

4. There is nothing in physics that explains how any moving object can have influence on non moving objects. Is it ever possible that the wheels of a bicycle will become really oblong if I pass along it with greater speed in a car? The measurement is clearly apparent and not real. In the previous example, it is impossible that the distance between earth and Alpha c will ‘really’ contract. Any such measurement has to be apparent and if this is so then, in spite of the measurements of the traveller, he will have to travel the real distance that is measured in the rest frame.

Repeating your statements does not make them any truer. If there is an objective true length, there must be a frame in which that length is measured. How do you tell if you are in that frame? You appear to be insisting that Galilean transforms are how nature behaves. Is there any physical evidence you can produce to confirm this? That it offends your sensibilities does not count.

[tar]

And what of someone living in a different frame of reference?

 

Swansont,

 

They see "our" universe, from their perspective. But once we meet them, they can make the transformation to our frame and we to theirs, and there will still be one objective universe that both we and the newly met "other framer" can and do consider "our" universe.

 

Regards, TAR2

 

The point to all this is that any measurement you make is frame dependent and that measurement represents "reality" for that frame and that's all the reality that there is.

 

Janus,

 

But included in that frame's reality is the ability to make the transformations to our reality, and any particle, field, object or motion, that exists in both frames can be "seen" in the other's frame, if the transformations are made.

 

If the imaginary frame does not account for everything that is "real" in the starting frame, if transformation into the imaginary frame and back, yields an impossible thing, then, as Vilas is arguing, the transformation was not done in a realistic way.

 

And the universe need not conform to our analogies. Our analogies are of it. And I for one, will challenge the completeness of our analogies, before I challenge the truth of the universe.

 

Regards, TAR2

[swansont]

Swansont,

 

They see "our" universe, from their perspective. But once we meet them, they can make the transformation to our frame and we to theirs, and there will still be one objective universe that both we and the newly met "other framer" can and do consider "our" universe.

 

Regards, TAR2

 

Why don't we have to consider it from theirs? Is there a physics-based reason that ours is preferred?

[tar]

Swansont,

 

We have to consider it from one place and time, inorder to have a frame to transform into another.

 

This starting frame is required, and the basis upon which we define any other.

 

Once we have defined the other, we can mentally exist there, put ourselves in its shoes, and even then consider IT the "starting" frame, and our frame "an other frame".

 

But I prefer our frame, because it is the one we have been experiencing the world and the universe from through our long history of experiments and theoretical exploration. It is the frame we have learned about, and the frame we understand the best.

 

Regards, TAR2

[J.C.MacSwell]

Swansont,

 

We have to consider it from one place and time, inorder to have a frame to transform into another.

 

This starting frame is required, and the basis upon which we define any other.

 

Once we have defined the other, we can mentally exist there, put ourselves in its shoes, and even then consider IT the "starting" frame, and our frame "an other frame".

 

But I prefer our frame, because it is the one we have been experiencing the world and the universe from through our long history of experiments and theoretical exploration. It is the frame we have learned about, and the frame we understand the best.

 

Regards, TAR2

 

Which frame would that be? I personally use a number of them everyday and would find it very inconvenient not to switch.

[StringJunky]

deleted. I answered my own question...there can be no preferred frame of reference.

 

In principle, would the 'correct' or 'ideal' frame(s) be the one(s) that are moving with the same velocity and in the same direction (so that they appear stationary with respect to each other) for measurement purposes?

Edited July 19, 2011 by StringJunky

[swansont]

Swansont,

 

We have to consider it from one place and time, inorder to have a frame to transform into another.

 

This starting frame is required, and the basis upon which we define any other.

 

Once we have defined the other, we can mentally exist there, put ourselves in its shoes, and even then consider IT the "starting" frame, and our frame "an other frame".

 

But I prefer our frame, because it is the one we have been experiencing the world and the universe from through our long history of experiments and theoretical exploration. It is the frame we have learned about, and the frame we understand the best.

 

Regards, TAR2

Emphasis added.

 

And that's the point. It's a preference. It is not mandated by the physics. There is no objective way to say one frame is correct.

[tar]

Swansont,

 

Not sure what your point is.

 

Physics is a human invention. A description of the rules and laws that the universe goes by, according to our view, and to increase our understanding, and give us the ability to predict what will happen if we move around in it and manipulate it. So we can know what will work and what will not.

 

The Physics of the universe don't have a point of view. Not any. Not a preferred frame or a unliked frame. No frame at all. You have to refer to it, to have a frame.

 

Regards, TAR2

[swansont]

Swansont,

 

Not sure what your point is.

 

Physics is a human invention. A description of the rules and laws that the universe goes by, according to our view, and to increase our understanding, and give us the ability to predict what will happen if we move around in it and manipulate it. So we can know what will work and what will not.

 

The Physics of the universe don't have a point of view. Not any. Not a preferred frame or a unliked frame. No frame at all. You have to refer to it, to have a frame.

 

Regards, TAR2

 

On the contrary, the laws of nature are not a human invention at all. They are a human discovery. But they are the same in any inertial frame of reference. Your preference for one frame is subjective, not objective.

[tar]

Swansont,

 

I agree, that Physics is a discovery of the Physics of the universe.

 

There are problems determining both the position and change in position over time, of an object, from the contradictory perspectives of two observers who themselves are changing their positions over time, in respect to each other and perhaps the object in question. But Vilas's and my contention is that the object must obey the laws of physics, and each observer must obey the laws of physics.

 

If the laws of Physics have predicted that light will take 4.5 years to get to Alpha Centuri, then an object traveling at .88C will take 5.114 years to get there. Whatever the traveler sees in her rear view mirror and through her windshield (gamma ray shield?) will conform to the physical laws of the universe. She cannot measure her progress through an already established distance at a speed greater than C. She will measure her speed at .88C, or else she has violated reality, or made a mistake. She in my imagination, will age right along with the rest of the universe, because she never leaves it. If we on Earth watch her on the trip out, she will appear to us as a redish or infrared or microwave image, and she will appear to be waving to us in slow motion and her trip out will appear to us to take a good portion of the 10.2 year round trip. But on the way back she will appear as a blueish or ultraviolet or x-ray image and appear to be waving at us at a fast rate, and we will time her trip back at only a couple years, or whatever the remainder of the 10.2 years is left, once we see her turn around.

 

Although see appears to us to be aging very slowly on the way out, and very quickly on the way back, she did 5 years worth of aging on the way out, and 5 years worth on the way back. If we count her waves, there will be 5 years worth on the way out, and 5 years worth on the way back. If she left here 27 years old, the immigration officer on Alpha Centuri will confirm her to be 32 and when she returns, our scientists will confirm she is 37.

 

The wierd thing happens when we observe the Centurian immigration officer signing the 32 year old's papers when we, (her twin) are 36.5 years old. But then again, not so weird, since we know it took the image 4.5 years to get to us.

 

Seems to all add up to me. Don't know where the laws of the universe say that she should return younger than her twin. That, in my imagination would break the laws.

 

Regards, TAR2

Edited July 20, 2011 by tar

[J.C.MacSwell]

Swansont,

 

I agree, that Physics is a discovery of the Physics of the universe.

 

There are problems determining both the position and change in position over time, of an object, from the contradictory perspectives of two observers who themselves are changing their positions over time, in respect to each other and perhaps the object in question. But Vilas's and my contention is that the object must obey the laws of physics, and each observer must obey the laws of physics.

 

If the laws of Physics have predicted that light will take 4.5 years to get to Alpha Centuri, then an object traveling at .88C will take 5.114 years to get there. Whatever the traveler sees in her rear view mirror and through her windshield (gamma ray shield?) will conform to the physical laws of the universe. She cannot measure her progress through an already established distance at a speed greater than C. She will measure her speed at .88C, or else she has violated reality, or made a mistake. She in my imagination, will age right along with the rest of the universe, because she never leaves it. If we on Earth watch her on the trip out, she will appear to us as a redish or infrared or microwave image, and she will appear to be waving to us in slow motion and her trip out will appear to us to take a good portion of the 10.2 year round trip. But on the way back she will appear as a blueish or ultraviolet or x-ray image and appear to be waving at us at a fast rate, and we will time her trip back at only a couple years, or whatever the remainder of the 10.2 years is left, once we see her turn around.

 

Although see appears to us to be aging very slowly on the way out, and very quickly on the way back, she did 5 years worth of aging on the way out, and 5 years worth on the way back. If we count her waves, there will be 5 years worth on the way out, and 5 years worth on the way back. If she left here 27 years old, the immigration officer on Alpha Centuri will confirm her to be 32 and when she returns, our scientists will confirm she is 37.

 

The wierd thing happens when we observe the Centurian immigration officer signing the 32 year old's papers when we, (her twin) are 36.5 years old. But then again, not so weird, since we know it took the image 4.5 years to get to us.

 

Seems to all add up to me. Don't know where the laws of the universe say that she should return younger than her twin. That, in my imagination would break the laws.

 

Regards, TAR2

 

Any elementary physics text that includes Special Relativity.

 

Sorry Tar, but it would only break your imaginary laws, your conjectures, not accepted physical laws. It is not simply a photon lag phenomena that physicists "forgot" to account for, or a 100 year old conspiracy to ignore it.

Edited July 20, 2011 by J.C.MacSwell

[DrRocket]

Swansont,

 

Not sure what your point is.

 

Physics is a human invention. A description of the rules and laws that the universe goes by, according to our view, and to increase our understanding, and give us the ability to predict what will happen if we move around in it and manipulate it. So we can know what will work and what will not.

 

The Physics of the universe don't have a point of view. Not any. Not a preferred frame or a unliked frame. No frame at all. You have to refer to it, to have a frame.

 

Regards, TAR2

 

Yes and no.

 

It is possible to formulate much of physics in a coordinate-free manner. That is the crux of Einstein's search for a description that is "generally covariant" and his success with the formulation of general relativity in terms of tensor fields on a manifold. It is also the heart of a geometrical treatment of special relativity in terms of the Minkowski metric and invariants, which can be applied in relativistic quantum theory or in the use of generalized coordinates in Hamiltonian or Lagrangian formulations of classical mechanics.

 

However, in order to correlate theory with actual measurements you have to impose at least a local reference frame at some juncture and crunch real numbers as reflected in that frame. Since physics is ultimately judged by the ability to predict the outcome of experiments, this cannot be avoided.

 

An agile mind can handle both situations and switch back and forth with alacrity. The scientifically illiterate can handle neither.

[tar]

I guess my mind is neither agile enough nor educated enough to get it.

 

I have read various descriptions and attempted to understand various formulae and always there are assumptions made that leave out realities that I have determined through the understand of other discoveries, need to be the case.

 

Perhaps I would be satisfied with my stupidity and ignorance if everything that Physicists said, actually made sense.

 

Most of it does, but some of it is contradictory, and thats where I draw the line.

 

I guess comprehending a vast universe and ones place in it, and ones relationship to it is in the end, a subjective, personal thing. My model does not have to satisfy anybody but me. It just has to be internally consistent, and fit reality.

 

For instance black holes that deform spacetime to such an extent that nothing, not even light can escape.

And this is proven by the discovery of structures that EMIT high energy radiation?

Edited July 20, 2011 by tar

[swansont]

I guess comprehending a vast universe and ones place in it, and ones relationship to it is in the end, a subjective, personal thing. My model does not have to satisfy anybody but me. It just has to be internally consistent, and fit reality.

 

The "fit reality" part is where you lose the luxury of it being a subjective personal thing.

[Vilas Tamhane]

The problem with that question is that it is a lot like the question, " If the world is round, how come the people on the underside don't fall off?" in that it is based on a presumption. The presumption of the quoted question deals with the nature of "down". The presumption of your question deals with the nature of time and space (and how its measured).

 

It just comes down to thinking about time and space differently, just like accepting a round Earth required people to think differently about what "down" meant.

 

In my last reply I did not say anything about common sense example you mentioned in your post, because it is a very difficult issue to deal with.

 

However unquestioned idea can lead to occult. How can we prevent it? There cannot be any doubt that common sense should not play any part in science. But we simply cannot get rid of it. Therefore the only way to test validity of the statement is by applying reason. Nobody can exclude reason in any of the human activities and this includes physics. In addition, reason and criticism always lead to new discoveries. Behind every logical objection there lies an unknown theory.

 

We should also apply our mind to possibility of a certain idea. In the case of length contraction it is clear that we are dealing with impossibility. You did not explain how length can ‘really’ contract differently for different inertial frames and how one frame can have influence on the matter in another frame.

 

It should be easy to disprove reality of the length contraction. In fact the statement that length contracts differently for different frames is itself a serious contradiction. In a moving frame, keep a ball of U235 and make its size just equal to the critical size. Observer in the moving frame will notice a bomb explosion but in the rest frame, critical size is not reached and so there will not be a bomb explosion. This is a paradox.

 

 

 

 

[swansont]

In my last reply I did not say anything about common sense example you mentioned in your post, because it is a very difficult issue to deal with.

 

However unquestioned idea can lead to occult. How can we prevent it? There cannot be any doubt that common sense should not play any part in science. But we simply cannot get rid of it. Therefore the only way to test validity of the statement is by applying reason. Nobody can exclude reason in any of the human activities and this includes physics. In addition, reason and criticism always lead to new discoveries. Behind every logical objection there lies an unknown theory.

 

When logic clashes with experimental results, it is the logic that is in error. You have a premise that is incorrect.

 

We should also apply our mind to possibility of a certain idea. In the case of length contraction it is clear that we are dealing with impossibility. You did not explain how length can ‘really’ contract differently for different inertial frames and how one frame can have influence on the matter in another frame.

 

Because this is a mis-statement of relativity. That's your error. At no point does relativity claim that one frame influences another. It says that measurements of (many) physical quantities are different in these frames.

 

This is similar to looking at a picture of a person from the front and another from the rear and saying "you changed." Did they really change? No, of course not. Walking behind you does not make your nose disappear. You merely changed your perspective. (The situation with relativity is more nuanced, of course; this is an analogy, not an example, and is meant to highlight the misuse of influence/cause)

 

 

It should be easy to disprove reality of the length contraction. In fact the statement that length contracts differently for different frames is itself a serious contradiction. In a moving frame, keep a ball of U235 and make its size just equal to the critical size. Observer in the moving frame will notice a bomb explosion but in the rest frame, critical size is not reached and so there will not be a bomb explosion. This is a paradox.

It's not a paradox, because the value of the density on one frame does not have to be the density as measured in another frame. Critical density is different for a sphere as for some other shape.

[Vilas Tamhane]

 

It's not a paradox, because the value of the density on one frame does not have to be the density as measured in another frame. Critical density is different for a sphere as for some other shape.

 

When the sphere of U235 has critical size, number of neutrons produced in the space of this material is more than those which escape the area enclosing the sphere. This way chain reaction can be sustained. For chain reaction to take place, only the number of atoms and area of the sphere enclosing this material are important. So I don’t know in what way density plays a part in the reaction.

 

 

[DrRocket]

It should be easy to disprove reality of the length contraction. In fact the statement that length contracts differently for different frames is itself a serious contradiction. In a moving frame, keep a ball of U235 and make its size just equal to the critical size. Observer in the moving frame will notice a bomb explosion but in the rest frame, critical size is not reached and so there will not be a bomb explosion. This is a paradox.

 

 

A paradox occurs when valid reasoning produces contradictory conclusions. Whan you have produced is not a paradox. It is just a mistake.

 

Any conclusion reached about a physical event, such as an explosion, in one reference frame is valid in any other reference frame. Events are invariant. What are not invariant are cooordinate dependent measurements such as time and length.

 

A nuclear chain reaction involves more than just spatial geometry -- a ratio of volume to surface area -- as you suggest. The retention of energy within the mass is a dynamic process and also involves time. You neglected to include the effect of variation in time measurements between reference frames in your analysis. This is more difficult, and demonstrates why calculations can be greatly simplified by choosing a convenient reference frame. But in any case the mass will either explode in all reference frames, or no explosion will occur in any reference frame.

 

No paradox. Just an incomplete analysis, a mistake.

[Janus]

Swansont,

 

I agree, that Physics is a discovery of the Physics of the universe.

 

There are problems determining both the position and change in position over time, of an object, from the contradictory perspectives of two observers who themselves are changing their positions over time, in respect to each other and perhaps the object in question. But Vilas's and my contention is that the object must obey the laws of physics, and each observer must obey the laws of physics.

 

If the laws of Physics have predicted that light will take 4.5 years to get to Alpha Centuri, then an object traveling at .88C will take 5.114 years to get there. Whatever the traveler sees in her rear view mirror and through her windshield (gamma ray shield?) will conform to the physical laws of the universe. She cannot measure her progress through an already established distance at a speed greater than C. She will measure her speed at .88C, or else she has violated reality, or made a mistake. She in my imagination, will age right along with the rest of the universe, because she never leaves it. If we on Earth watch her on the trip out, she will appear to us as a redish or infrared or microwave image, and she will appear to be waving to us in slow motion and her trip out will appear to us to take a good portion of the 10.2 year round trip. But on the way back she will appear as a blueish or ultraviolet or x-ray image and appear to be waving at us at a fast rate, and we will time her trip back at only a couple years, or whatever the remainder of the 10.2 years is left, once we see her turn around.

 

Although see appears to us to be aging very slowly on the way out, and very quickly on the way back, she did 5 years worth of aging on the way out, and 5 years worth on the way back. If we count her waves, there will be 5 years worth on the way out, and 5 years worth on the way back. If she left here 27 years old, the immigration officer on Alpha Centuri will confirm her to be 32 and when she returns, our scientists will confirm she is 37.

 

The wierd thing happens when we observe the Centurian immigration officer signing the 32 year old's papers when we, (her twin) are 36.5 years old. But then again, not so weird, since we know it took the image 4.5 years to get to us.

 

Seems to all add up to me. Don't know where the laws of the universe say that she should return younger than her twin. That, in my imagination would break the laws.

 

Regards, TAR2

 

We already went over this in page 1 of this thread. Watching from Earth, we will see 2.5 years worth of waves on the way out and 2.5 years of waves on the way back for a total of 5 yrs worth of waves.

 

In my last reply I did not say anything about common sense example you mentioned in your post, because it is a very difficult issue to deal with.

 

However unquestioned idea can lead to occult. How can we prevent it? There cannot be any doubt that common sense should not play any part in science. But we simply cannot get rid of it. Therefore the only way to test validity of the statement is by applying reason. Nobody can exclude reason in any of the human activities and this includes physics. In addition, reason and criticism always lead to new discoveries. Behind every logical objection there lies an unknown theory.

 

We should also apply our mind to possibility of a certain idea. In the case of length contraction it is clear that we are dealing with impossibility. You did not explain how length can ‘really’ contract differently for different inertial frames and how one frame can have influence on the matter in another frame.

 

 

 

You missed the whole point. Let's see if I can put it another way. What we measure as "reality" is just a projection of a "larger picture". Its like the 2 dimensional shadow made by a 3-D space. If the space rotates, the shadow changes.

 

Imagine there are two balls in that space each projecting its own shadow. The only way those balls interact with what we call "reality" is those shadows. Those shadows are the reality for us. If we change our orientation to the space and the "light", the relative positions of the shadows change. In our reality, they can change distance. That is the equivalent of us changing reference frames. Changing reference frames does not physically alter anything in that 3-D space, but it does alter the projection it makes on our reality.

 

Another way to look at it is to imagine a featureless plane. You are standing on the plane. There are two other objects on that plane. One is 1meter directly to the front of you and the other on meter directly to the right. You turn 45° to the right. Now one object is 0.707 meters in front of you and 0.707 meters to your right and the other is 0.707 meters in front of you and 0.707 meters to your left.

 

Replace the front-back direction with time,left-right with distance and the the objects with events, and you have a closer analogy to Relativity. As you turn (change reference frames), the events go from occurring at different times to occurring at the same time, and their distance from each other(left-right being the only measure of spacial separation) changes. The thing to keep in mind is that your whole reality is based on just the measurements made along those two axes. The events really do shift in time and distance. Someone facing in a different direction will measure a different time and distance separation for those events, and his measurements are just as much "reality" as yours.

[swansont]

When the sphere of U235 has critical size, number of neutrons produced in the space of this material is more than those which escape the area enclosing the sphere. This way chain reaction can be sustained. For chain reaction to take place, only the number of atoms and area of the sphere enclosing this material are important. So I don’t know in what way density plays a part in the reaction.

 

The number of atoms and the shape matter. Taken together, you can define a density (number per unit volume); a sphere has the smallest critical density. In the moving frame you will not see a supercritical volume. It will be critical as well.