Friday 7 September 2012
New(?) Theory of Gravity
An epiphanic moment of realisation this pm. driving home from Peterhead.
Gravity is a relativistic effect.
It is due to inter-dimensional rotation into a 5th dimension.
(I am still unsure whether this should be, or could be, described as a 'pseudo'-dimension).
The well known effects of Length Contraction and Time Dilation are due to such inter-dimensional rotations as observed in bodies travelling at near light speeds.
Rotated into another dimension time and space become foreshortened causing the said effects.
Acceleration may be equated to gravity … or to centrifugal force; which may be considered a pseudo gravity.
Then we have the body on the edge of Einstein's rotating flat disc, experiencing both the pseudo gravity of centrifugal force AND the inter-dimensional rotation due to its tangential velocity (that which causes the time dilation and length contraction of the body).
It is but a small step there-from to say that another such body – on its own flat rotating disc would experience a similar effect and if those two forces were acting toward one another we have gravitational effects upon the two bodies in proportion to their inertial masses (remember - inertial mass = gravitational mass) and, being considered as motion on flat discs, inversely proportional to their displacement one from the other.
Or Newtons theory of Gravity.
As I say this only came to me this afternoon and the details need some more work but it seems to fit well with the rest of relativity, General relativity in this case, as the said foreshortening due to the inter-dimensional rotation fits with Einstein's space curvature explanation of gravity.
Of such things dreams are made ...
Saturday 24 March 2012
The Twin Paradox explained; what it is and how it works. Simples!
Twin Paradox
The Twin Paradox
This is possibly the most well known of all the supposed paradoxes associated with Special Relativity.
In 1911, Paul Langevin first proposed it as an attempt to visualise effects of a journey at near Light Speed, utilising the additional twist of making the subjects twins, thereby emphasising the paradoxical nature of the effect. It was the tale of a traveller taking a trip at a Lorentz Factor of ɣ = 100. He travels for one year of his time, stops and then reverses direction. On his return, the traveller will have aged two years, while 200 years have passed on Earth.
This, paradoxical effect of each seeing their sibling age more than him/her-self, is how I, and I think many others, first visualise Special Relativity; and right from the start it seemed obvious to me that there is nothing in the least paradoxical about each seeing the other age, anymore than it is paradoxical for two people separated by a distance to see that the other is much smaller.
We might even call it Relativistic Perspective.
There have been many attempts to explain why it is not a paradox and even to say that one twin does in fact age more than the other and to claim that that is the real paradox.
Yet, as so often happens, we find that when we take a step back; to dispense with assumption, presumption and biased thinking, we find that it is, as is generally the case with scientific truths, simple and easily explained.
We will now do just that.
First appearances indicate that we are looking at a two way process: i.e. the journey away and the return; or even that we should consider three parts: the journey, the turn around and the return.
Yet on close examination there are four states: travel at v, rest v=zero, return at -v, and finally rest v=zero, once more. Just those four and the transitions between them.
And if that were not complicated enough, each state can be viewed from three different perspectives: that of the outgoing twin; that of the home-alone twin, using his own measurements made with his own rulers and clocks; and the view of the outgoing twin's measurements, relayed to her sibling and transformed by the Lorentz transformations to take account of their relative velocities.
We will now examine each of those states from the three perspectives in order to demonstrate how it all fits together into one coherent whole.
Stage 1; Outward Bound.
Fig. 10
After 4 units of time have passed for each of the Twins, each being in an inertial Frame of Reference and therefore being subject to identical laws of physics, they will both agree that 4 units of Proper Time have passed along the black ct axis.
The third perspective is different though. For in this view the homebound twin will measure, by applying the Lorentz transformations, to the measurements of his travelling Twin, giving 5 units of time passing. But even so this rotated axis will be projected down onto the home Twin's ct axis and measure 4 units.
Stage 2; The Turnaround.
Fig. 11
The traveller now reduces speed and comes to a halt (let us say for the pedants who may read this that such accelerations and decelerations only take a day so will not show on these scales).
Having now come to a stop the rotation is zero degrees, with a relative velocity of zero there will be no requirement for Lorentz Transformation as those transformed units of time will be unchanged and equal with those measured directly by each twin.
Stage 3; Inward Bound.
Fig. 12
Now on the return journey the travellers time axis, as observed by the Stay-at-home Twin is rotated downwards to represent the relative velocity v = -0.6c.
Once again the black ct axis depicts what each of the Twins will measure within their own Inertial Frames of Reference; while the rotated ct' axis of the traveller's measurements, Transformed to be relative to the home-bound Twin, shows the ct' axis projected back onto the ct axis; 10 Lorentz units becoming equal to 8 Proper units.
Stage 4; The Arrival.
Fig. 13
Stage four, the Return, has two possible scenarios depending on whether the traveller slows down and comes back to rest by her sibling.
If she continues past her stay-at-home Twin the conditions described in Stage 3 will continue; giving the well know result that each Twin will calculate, via the Lorentz Transformations, that their sibling has aged differently.
However, if the Traveller returns to be stationary beside her Twin, then once again, the Lorentz Transformations become irrelevant, as they are once again in the same Inertial Frame of Reference and, with a relative velocity of zero, will measure the same times.
It is important to remember that these are not Proper Units. No they are Lorentz Units (where as stated above) 1 proper unit = ɣ Lorentz units.
Points to consider:
1. each twin may be considered to be stationary in Spacetime.
2. each, being within an Inertial Frame of Reference, will be subject to identical scientific laws and principles - courtesy of Einstein's First Postulate.
3. Therefore, the units of time and space will be the same in both Frames of Reference.
4. each twin will observe, only those measurements taken from the other twin's Frame of Reference, to be transformed, in order to make them relative to his/her own Frame of Reference.
5. such transformations, Lorentz Transformations, being a function of the velocity of one twin relative to the other will be the same for each twin.
6. therefore, such an effect will be reciprocal, and either twin could be considered to be the traveller.
7. the Lorentz factor, ɣ = 100, is that for a relative velocity of 0.9999c
8. the distances measured - 1 light-year/year (proper units) = 100 light-years/years (Lorentz units, when ɣ = 100)
Relativity is about transforming measurements from one Frame of Reference to make them Relative to another Frame of Reference. It is the transformation of measurements that exist at that one point in time; transforming them to make them relative to another, moving Frame of Reference at that same point in time.
That is it.
Just that.
And as the relative velocity is the same for each then the transformations will also be the same.
As defined by the Lorentz Transformations.
Note that we are dealing with a particular case here. We are not merely looking at measuring the path or size of a moving object. No, we are dealing with how measurements from one Frame of Reference may be represented relative to an observer in another Frame of Reference; one that is moving with a constant, non-rotational velocity, with respect to the first Frame of Reference.
So in the case of the twins it is how the measurements, taken with respect to one twin from within that twin's Frame of Reference, will be transformed from the perspective of the other twin as a function of the velocity between their Frames of Reference.
I.e. How will time and distance be affected such that those measurements will still conform with Einstein's two postulates.
Now, having said all that we can dispense with some of the more outrageous claims and conclusions that have been pinned on this particular donkey!
And those include:
1. that the Contraction/Dilation effects are physical changes undergone by the travelling Twin;
but: 1.1 they are only observed by a 'stationary' observer.
1.2 it is only the unit size and quantity that change. The Absolute magnitudes are unaltered.
1.3 that means that they would have to be an infinite number of different sizes at the same time to reflect their change in size with respect to every other body in Minkowski Spacetime.
2. One twin really does age differently from the other;
but: 2.1 that cannot be. Relativity is relative. Reciprocal. Each would measure the
other as having an equal relative velocity.
2.2 this would disprove the First Postulate and therefore Special Relativity!
3. The difference is caused by a lack of symmetry because only one twin accelerates;
but: 3.1 special Relativity makes no reference to acceleration. It is not in any such formula.
3.2 relative movement requires no knowledge of the cause of the movement.
3.3 like movement, acceleration is relative i.e. each accelerates relative to the other.
4. The difference is an effect of changing or reversing Frames of Reference;
but: 4.1 this is tied in with the idea that currently holds about the Relativity of simultaneity; that two events can only be observed as simultaneous by one, Privileged Frame of Reference.
4.2 a moving observer will experience a different simultaneity, yet all observers are, to their own view, stationary. And if two events are simultaneous to a stationary observer midway between those events, they must be simultaneous to any stationary observer midway between those events. It is only in another's Frame of Reference that they move, so they will be seen by others to have a different appreciation of Simultaneity, while holding the same simultaneity within their own purview, from their own stationary Frame of Reference. This is exactly the same description of Relative Simultaneity described by Einstein with his trains.
The Twin Paradox
This is possibly the most well known of all the supposed paradoxes associated with Special Relativity.
In 1911, Paul Langevin first proposed it as an attempt to visualise effects of a journey at near Light Speed, utilising the additional twist of making the subjects twins, thereby emphasising the paradoxical nature of the effect. It was the tale of a traveller taking a trip at a Lorentz Factor of ɣ = 100. He travels for one year of his time, stops and then reverses direction. On his return, the traveller will have aged two years, while 200 years have passed on Earth.
This, paradoxical effect of each seeing their sibling age more than him/her-self, is how I, and I think many others, first visualise Special Relativity; and right from the start it seemed obvious to me that there is nothing in the least paradoxical about each seeing the other age, anymore than it is paradoxical for two people separated by a distance to see that the other is much smaller.
We might even call it Relativistic Perspective.
There have been many attempts to explain why it is not a paradox and even to say that one twin does in fact age more than the other and to claim that that is the real paradox.
Yet, as so often happens, we find that when we take a step back; to dispense with assumption, presumption and biased thinking, we find that it is, as is generally the case with scientific truths, simple and easily explained.
We will now do just that.
First appearances indicate that we are looking at a two way process: i.e. the journey away and the return; or even that we should consider three parts: the journey, the turn around and the return.
Yet on close examination there are four states: travel at v, rest v=zero, return at -v, and finally rest v=zero, once more. Just those four and the transitions between them.
And if that were not complicated enough, each state can be viewed from three different perspectives: that of the outgoing twin; that of the home-alone twin, using his own measurements made with his own rulers and clocks; and the view of the outgoing twin's measurements, relayed to her sibling and transformed by the Lorentz transformations to take account of their relative velocities.
We will now examine each of those states from the three perspectives in order to demonstrate how it all fits together into one coherent whole.
Stage 1; Outward Bound.
Fig. 10
After 4 units of time have passed for each of the Twins, each being in an inertial Frame of Reference and therefore being subject to identical laws of physics, they will both agree that 4 units of Proper Time have passed along the black ct axis.
The third perspective is different though. For in this view the homebound twin will measure, by applying the Lorentz transformations, to the measurements of his travelling Twin, giving 5 units of time passing. But even so this rotated axis will be projected down onto the home Twin's ct axis and measure 4 units.
Stage 2; The Turnaround.
Fig. 11
The traveller now reduces speed and comes to a halt (let us say for the pedants who may read this that such accelerations and decelerations only take a day so will not show on these scales).
Having now come to a stop the rotation is zero degrees, with a relative velocity of zero there will be no requirement for Lorentz Transformation as those transformed units of time will be unchanged and equal with those measured directly by each twin.
Stage 3; Inward Bound.
Fig. 12
Now on the return journey the travellers time axis, as observed by the Stay-at-home Twin is rotated downwards to represent the relative velocity v = -0.6c.
Once again the black ct axis depicts what each of the Twins will measure within their own Inertial Frames of Reference; while the rotated ct' axis of the traveller's measurements, Transformed to be relative to the home-bound Twin, shows the ct' axis projected back onto the ct axis; 10 Lorentz units becoming equal to 8 Proper units.
Stage 4; The Arrival.
Fig. 13
Stage four, the Return, has two possible scenarios depending on whether the traveller slows down and comes back to rest by her sibling.
If she continues past her stay-at-home Twin the conditions described in Stage 3 will continue; giving the well know result that each Twin will calculate, via the Lorentz Transformations, that their sibling has aged differently.
However, if the Traveller returns to be stationary beside her Twin, then once again, the Lorentz Transformations become irrelevant, as they are once again in the same Inertial Frame of Reference and, with a relative velocity of zero, will measure the same times.
It is important to remember that these are not Proper Units. No they are Lorentz Units (where as stated above) 1 proper unit = ɣ Lorentz units.
Points to consider:
1. each twin may be considered to be stationary in Spacetime.
2. each, being within an Inertial Frame of Reference, will be subject to identical scientific laws and principles - courtesy of Einstein's First Postulate.
3. Therefore, the units of time and space will be the same in both Frames of Reference.
4. each twin will observe, only those measurements taken from the other twin's Frame of Reference, to be transformed, in order to make them relative to his/her own Frame of Reference.
5. such transformations, Lorentz Transformations, being a function of the velocity of one twin relative to the other will be the same for each twin.
6. therefore, such an effect will be reciprocal, and either twin could be considered to be the traveller.
7. the Lorentz factor, ɣ = 100, is that for a relative velocity of 0.9999c
8. the distances measured - 1 light-year/year (proper units) = 100 light-years/years (Lorentz units, when ɣ = 100)
Relativity is about transforming measurements from one Frame of Reference to make them Relative to another Frame of Reference. It is the transformation of measurements that exist at that one point in time; transforming them to make them relative to another, moving Frame of Reference at that same point in time.
That is it.
Just that.
And as the relative velocity is the same for each then the transformations will also be the same.
As defined by the Lorentz Transformations.
Note that we are dealing with a particular case here. We are not merely looking at measuring the path or size of a moving object. No, we are dealing with how measurements from one Frame of Reference may be represented relative to an observer in another Frame of Reference; one that is moving with a constant, non-rotational velocity, with respect to the first Frame of Reference.
So in the case of the twins it is how the measurements, taken with respect to one twin from within that twin's Frame of Reference, will be transformed from the perspective of the other twin as a function of the velocity between their Frames of Reference.
I.e. How will time and distance be affected such that those measurements will still conform with Einstein's two postulates.
Now, having said all that we can dispense with some of the more outrageous claims and conclusions that have been pinned on this particular donkey!
And those include:
1. that the Contraction/Dilation effects are physical changes undergone by the travelling Twin;
but: 1.1 they are only observed by a 'stationary' observer.
1.2 it is only the unit size and quantity that change. The Absolute magnitudes are unaltered.
1.3 that means that they would have to be an infinite number of different sizes at the same time to reflect their change in size with respect to every other body in Minkowski Spacetime.
2. One twin really does age differently from the other;
but: 2.1 that cannot be. Relativity is relative. Reciprocal. Each would measure the
other as having an equal relative velocity.
2.2 this would disprove the First Postulate and therefore Special Relativity!
3. The difference is caused by a lack of symmetry because only one twin accelerates;
but: 3.1 special Relativity makes no reference to acceleration. It is not in any such formula.
3.2 relative movement requires no knowledge of the cause of the movement.
3.3 like movement, acceleration is relative i.e. each accelerates relative to the other.
4. The difference is an effect of changing or reversing Frames of Reference;
but: 4.1 this is tied in with the idea that currently holds about the Relativity of simultaneity; that two events can only be observed as simultaneous by one, Privileged Frame of Reference.
4.2 a moving observer will experience a different simultaneity, yet all observers are, to their own view, stationary. And if two events are simultaneous to a stationary observer midway between those events, they must be simultaneous to any stationary observer midway between those events. It is only in another's Frame of Reference that they move, so they will be seen by others to have a different appreciation of Simultaneity, while holding the same simultaneity within their own purview, from their own stationary Frame of Reference. This is exactly the same description of Relative Simultaneity described by Einstein with his trains.
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