In the latest edition of Modern Physics, a paper by Prof. M Gardner (Oxon) highlighting the many problems with the standard model of cosmology has seen a fundamental re-examination of Einsteins' theories with some surprising results!
Imagine a 1 metre long stick traveling through space, on a straight line co-linear with the stick.
A plate with a one metre diameter hole is also moving though space, perpendicular to the stick (see attached diagram)
We idealise the experiment by assuming both the plate and stick have zero thickness. Both the plate and the stick are on a precise collision course, so at the same instant the centre of the stick will be at the same location as the centre of the hole i.e. they will coincide.
Assume the stick is traveling so fast, that, as special relativity predicts, it is Lorentz contracted by a factor of 10, so that in this inertial frame its length is just 10 centimetres. As a result it will easily pass through the rising plate (the speed of which is immaterial).
Now consider the situation from the metre long stick's inertial reference frame.
The plate is moving in from the opposite horizontal direction, so its hole is Lorentz contracted by a factor of 10. There is no way the 10 centimetre hole can move up past the metre stick without collision.
The two situations are not equivalent, and thus the fundamental assumption of special relativity is violated.
It is ironic that Einstein being so fond of "gendankenexperiments" did not see the logical flaw in his theory. This collapse in Special relativity will soon appear in Reviews of Modern Physics, the full impact of this has yet to reach the popular press.
Last edited by Peter Ward; 20-12-2010 at 11:38 PM.
Is there a distinction here between 'is contracted' and 'appears to be contracted'?
As a general question. What happens when 2 intertial frames 'meet' or 'intersect'? Do they become the same for that instant? Or are they still different due to differences in their direction of momentum.
Is there a distinction here between 'is contracted' and 'appears to be contracted'?
As a general question. What happens when 2 intertial frames 'meet' or 'intersect'? Do they become the same for that instant? Or are they still different due to differences in their direction of momentum.
Lorentz contraction is real. The two objects are on a collision course.
The hole in the plate will only be Lorentz contracted by a factor of 10 if it is stationary. In other words in the stick's frame of reference, the plate will move past the stick. The plate (and the hole) are parallel to the direction of motion of the stick. From the sticks frame of reference the hole is moving in the direction of motion hence contraction of the hole is observed.
However in a collision scenario clearly the stick (or plate) is now travelling in an oblique pathway relative to the other. The plate is now no longer parallel to the direction of motion of the stick. Hence the plate and the hole do not undergoe contraction.
The report of the death of SR is rather premature.
However in a collision scenario clearly the stick (or plate) is now travelling in an oblique pathway relative to the other. The plate is now no longer parallel to the direction of motion of the stick. Hence the plate and the hole do not undergoe contraction.
Is this because the plate and the stick motions are perpendicular to eachother?
If so, what if the motions were say, a little less than 90 degrees ?
Is this because the plate and the stick motions are perpendicular to eachother?
If so, what if the motions were say, a little less than 90 degrees ?
If the motions of the stick and the plate are not in parallel planes (any angle between the planes other than 0 or 180 degrees), then the plate will follow an obique path relative to the stick.
The angle of the path relative to the stick (or plate) is also a function of the velocities of the stick and plate.
For example in a stationary observer's frame of reference if the plate and stick are moving at the same velocity in perpendicular directions, then the plate will collide with the stick at a 45 degree angle in the stick's frame of reference.
Quote:
Would the hole ever appear to be elliptical ?
Cheers
Lorentz contraction can only occur if the length of the body is parallel to the direction of motion.
In this condition the hole will be elliptical as it is being contracted in the one direction.
Ok. I think I get this with a slight variation.
(I may not have this quite right, yet so please bear with me for a bit)....
I thought that the contraction occurs in any component of an object's dimensions, which lies parallel to the direction of travel at the moment of measurement. (Ie: where this component intersects the other's 'hypersurface of simultaneity').
(This incidentally, I think, is associated with the twins paradox).
I've attached a pdf showing two sticks moving off at the same speed in opposite directions. Check out the B stick. Where the ends of the B stick intersect A stick's hypersurface you can see the length has contracted from one unit, to less than one unit.
So, from this diagram, the length contraction happens if the direction of travel is in opposite directions, but happens to the component of the stick's dimension, which lies parallel to the direction of travel.
The same reason explains the hole shape as being elliptical. (Incidentally, if it was elliptically contracted, the stick would fit thru the long axis in the other scenario, would it ?)
Ok. I think I get this with a slight variation.
(I may not have this quite right, yet so please bear with me for a bit)....
I thought that the contraction occurs in any component of an object's dimensions, which lies parallel to the direction of travel at the moment of measurement. (Ie: where this component intersects the other's 'hypersurface of simultaneity').
That's correct. Consider a rod travelling along the direction of the length of the rod.
The rod undergoes length contraction. The diameter of the rod which is a dimension perpendicular to the direction of motion remains unaltered.
Quote:
I've attached a pdf showing two sticks moving off at the same speed in opposite directions. Check out the B stick. Where the ends of the B stick intersect A stick's hypersurface you can see the length has contracted from one unit, to less than one unit.
So, from this diagram, the length contraction happens if the direction of travel is in opposite directions, but happens to the component of the stick's dimension, which lies parallel to the direction of travel.
The pdf is showing 2 Minkowski diagrams. The length contraction is based on the stationary observer's frame of reference.
In the stationary frame of reference the time and spatial axes are perpendicular or orthogonal. In the sticks frame of refernece which is moving relative to the stationary observer the axes are rotated and are now less than 90 degrees to each other. The faster the stick moves the greater the rotation of the axes. The lines intersecting the ends of the sticks are parallel to the rotated time axis. Since the lines run parallel to the time axes the ends have been simultaneously measured. The sticks are located over the rotated spatial axis.
The projection of the lines onto the rotated spatial axis gives the contracted length.
That's correct. Consider a rod travelling along the direction of the length of the rod.
The rod undergoes length contraction. The diameter of the rod which is a dimension perpendicular to the direction of motion remains unaltered.
The pdf is showing 2 Minkowski diagrams. The length contraction is based on the stationary observer's frame of reference.
In the stationary frame of reference the time and spatial axes are perpendicular or orthogonal. In the sticks frame of refernece which is moving relative to the stationary observer the axes are rotated and are now less than 90 degrees to each other. The faster the stick moves the greater the rotation of the axes. The lines intersecting the ends of the sticks are parallel to the rotated time axis. Since the lines run parallel to the time axes the ends have been simultaneously measured. The sticks are located over the rotated spatial axis.
The projection of the lines onto the rotated spatial axis gives the contracted length.
Regards
Steven
Cool. Thanks Steven.
I think I'm getting the knack of this !!
I find these spacetime diagrams really help out.
The ones they use to describe black holes are really cool, also.
They can explain lots of things on the one diagram.
The original premise is meaningless as a macroscopic stick or hole cannot travel at near light speed. To use this as a basis for debunking any theory is also meaningless. At best it gives insights what could happen in reality.
Consider this conundrum. If you were a photon you would travel across the known Universe in an instant. Or due to time dilation that would be your experience. Or sadly you could arrive at some astrophotographers sensor and you journey would come to an abrupt halt and you would be turned into an electron in some prison called a CCD until you are shuttled down and 'counted' and then discarded. Your freedom to roam the Universe gone forever as you are then stuck with all the other electrons in the copper conductor and now just one of the crowd! A truely sad end to a magnificent flight of fancy!
Then again, you might end up in some Astronomer's eye .. then his brain .. … and then as part of some twisted fantasy involving all sorts of mythical beings as an attempt to explain where it came from in the first place !
If you were a photon you would travel across the known Universe in an instant.
Bert
so, since the age of the universe to any (free) photon is essentially instantaneous, they cant die of old age, they last for ever (to the universe), so in the "end", the universe will be full of just photons?.
Then again, you might end up in some Astronomer's eye .. then his brain .. … and then as part of some twisted fantasy involving all sorts of mythical beings as an attempt to explain where it came from in the first place !
Poor little photon !!
Cheers
Yep, the photon would be caught in a nightmare, an universe of insanity!!!
(apologies to Martin Gardner, Scientific American April 1st edition)
