Once we surmount all this noise, I have been patiently waiting to extend my initial discussion, so that we can venture into a discussion on the closely related, special relativity time dilation due to aberration topic.
[QUOTE=CraigS;745670]Yeah fair enough Phil, but I really don't think onlookers appreciate how much emotional effort is required to uphold a rigorous, unintuitive line of argument in these debates.
I have thought of that a few times Craig the number of times you post would make it difficult to do other things , do you work ?
phil
It also describes the abstract carriage of the electromagnetic force. As such, it also covers the full range of the EM spectrum .. not just the visible.
Cheers
Thanks Craig. I read something suggesting it applied outside visible range and realised I had somehow only thought of it as within or close to the visable spectrum..
Click on the gif in the article, there's an explanation as to what's going on there in the gif's description.
What the gif is explaining is that the velocity of light is a constant from either fleets perspective (communication between the ships), but that the apparent paths taken by the light beams from the perspective of the opposite fleet appears to take a diagonal path between the ships at a time which is also apparently longer than the actual communication time between the ships. The effect of time dilation in transverse motion. All due to the relative motion (inertial frames of reference) between the two fleets.
It's how you explain the reality of time dilation as an exercise in aberration.
You have a photon bouncing between two mirrors.
If the observer is stationary relative to the mirrors or the mirrors and the observer are moving at the same velocity, the observer will see photon hitting the surface of the mirrors at a 90 degree angle. The distance travelled by the photon from one mirror to the next is simply the spacing between the mirrors.
Suppose the observer is moving relative to the mirrors in a direction perpendicular to the direction of the photon in the rest frame. The observer moves a certain distance in the time it takes photon to travel from one mirror to the other. The observer therefore sees an oblique photon path instead of the photon path being perpendicular to the mirrors in the rest frame.
As the photon path is now oblique, the distance travelled by the photon is also longer. Since the speed of light is the same to all observers, the time taken for the photon to cross the mirrors relative to the moving observer is longer when compared to a stationary observer.
Note this form of time dilation is not directly related to cosmological time dilation.
Note this form of time dilation is not directly related to cosmological time dilation.
So then, this all is underpinned by this ...
(one of the seemingly most misunderstood experiments by certain folk, second only to the Sagnac Effect) ...
Originally Posted by sjastro
Note this form of time dilation is not directly related to cosmological time dilation.
So then, this all is underpinned by this ...
(one of the seemingly most misunderstood experiments by certain folk, second only to the Sagnac Effect) ...
(Just had to do this, so I could record the excellent YouTubes).
Cheers
At cosmological distances objects are accelerating away from the observer.
Hence we are not dealing with an inertial frame of reference.
Under these conditions SR (Lorentz) time dilation is not applicable.
Time dilation at cosmological distances is handled by the R-W metric.
At cosmological distances objects are accelerating away from the observer.
Hence we are not dealing with an inertial frame of reference.
Under these conditions SR (Lorentz) time dilation is not applicable.
Time dilation at cosmological distances is handled by the R-W metric.
Regards
Steven
Precisely, using the equation....
1+z=A(now)/A(then)
A being the cosmological scale factor. Now being at present and then being at some time in the past.
At cosmological distances objects are accelerating away from the observer.
Hence we are not dealing with an inertial frame of reference.
Under these conditions SR (Lorentz) time dilation is not applicable.
Time dilation at cosmological distances is handled by the R-W metric.
Regards
Steven
Right. So, in summary we have (I hope):
i) the "blinking out phenomenon" is explained by cosmological redshift, which is encapsulated in the R-W (FLRW) Metric solution, which is an accelerating universe model;
ii) the event horizon for a BH is based on gravitational redshift, as is time dilation within the grav. well;
iii) Lorentz time dilation is applicable for objects moving with respect to an inertial observation reference frame (eg: constantly expanding universe models, as distinct from acceleratingly expanding models);
iv) the Michelson Morley experiment (MMX) was designed to prove a cosmological aether, but resulted in disproof of a cosmological aether;
v) the results of the MMX experiment were eventually explained by Lorentz contraction/dilation, and was wrapped into special relativity.
i) the "blinking out phenomenon" is explained by cosmological redshift, which is encapsulated in the R-W (FLRW) Metric solution, which is an accelerating universe model;
When you apply Einstein's field equations with the cosmological constant to the R-W metric, you get a set of equations known as the Friedmann equations. The solutions provides various parameters for the Cosmological model for an accelerating Universe that includes the geometry of the Universe, a time dependant Hubble "Constant", density, pressure, etc.
Quote:
ii) the event horizon for a BH is based on gravitational redshift, as is time dilation within the grav. well;
Correct
Quote:
iii) Lorentz time dilation is applicable for objects moving with respect to an inertial observation reference frame (eg: constantly expanding universe models, as distinct from acceleratingly expanding models);
No. It doesn't apply to a constantly expanding Universe as the Universe is still accelerating in the observer's frame of reference. Einstein's field equations without the cosmological constant term is applied to the R-W metric. The R-W metric is consistent with a constant expanding Universe.
Quote:
iv) the Michelson Morley experiment (MMX) was designed to prove a cosmological aether, but resulted in disproof of a cosmological aether;
Correct.
Quote:
v) the results of the MMX experiment were eventually explained by Lorentz contraction/dilation, and was wrapped into special relativity.
Lorentz attempted to explain the MMX experiment by an ad hoc use of the Lorentz transformations but under the assumption that aether existed.
Einstein on the other hand mathematically derived the Lorentz transformation under the assumption that aether did not exist.
i) the "blinking out phenomenon" is explained by cosmological redshift, which is encapsulated in the R-W (FLRW) Metric solution, which is an accelerating universe model;
ii) the event horizon for a BH is based on gravitational redshift, as is time dilation within the grav. well;
iii) Lorentz time dilation is applicable for objects moving with respect to an inertial observation reference frame (eg: constantly expanding universe models, as distinct from acceleratingly expanding models);
The R-W metric is a solution to Einstein's field equations within a homogenous and isotropic spacetime which is either expanding or contracting. It's not necessarily an accelerating universe.
The EH for a BH is defined by the equation...
Rs = 2GM/c^2, where G is the gravitational constant and M the mass of the object. Rs is the Schwartzchild radius. You can work it out with gravitational redshift as part of the equation for this contains part of the derivation of the Schwarzchild metric...2GM/C^2r...where...
1+z= SQRT((1-(2GM/c^2 Rr)/1-(2GM/c^2 Rs))). R is analogous to the radius of the object or the radial coordinate of the source (the point on the surface of the sphere defining the radius from the centre. Or in this case, the distance from the receiver/detector (r) to the source (s)).
Lorentz time dilation occurs in flat (Minkowski) spacetimes in reference to the relative inertial frames of the objects in question. It's essentially relativistic doppler shift.
Last edited by renormalised; 20-07-2011 at 05:11 PM.
We have both stated our views on the question of redshift. You say you it can be calculated if you know the source, and I maintain that it cannot be determined in the absence of a spectrum, which a single photon is not. However, redshift is irrelevant to your original question the gist of which is:
Quote:
Originally Posted by CraigS
Ok all you relativists out thar .. he's a conundrum question I've been trying to wrap my mind around for a while … this has to do with cosmological event/particle horizons ...
Say there are two exo-galaxies out there, galaxy X and galaxy Y, where X is nearer to us than Y. Now with cosmic acceleration, there will be some last photon from either galaxy after which we will see nothing. Now, at the time X sends out its last photon, there will also be a Y photon passing by X. They both travel at the same speed, and thus they both reach us at the same time ....
So if we think of the entire universe consisting of galaxies of different ages, then this would mean that at one instant we will see our entire observable universe …. and in the next instant … all of it blinks out ??
There is some flaw here, but where is it … ??...
Answerers welcome.
Cheers
For the cosmological model postulated by CraigS it is possible the the two galaxies will blink out at the same time.
However, the entire universe can only blink out if Y is a photon from the galaxy furthest from us and X is a photon from the galaxy nearest to us and all galaxies are receding so fast that light cannot reach us. However some galaxies are not moving away from us. So the universe will not blink out all at once.
Further, CraigS did not stipulate that Y is a photon from the galaxy furthest from us and X is a photon from the galaxy nearest to us. So the question as stated was flawed.
For the cosmological model postulated by CraigS it is possible the the two galaxies will blink out at the same time.
However, the entire universe can only blink out if Y is a photon from the galaxy furthest from us and X is a photon from the galaxy nearest to us and all galaxies are receding so fast that light cannot reach us. However some galaxies are not moving away from us. So the universe will not blink out all at once.
This is clearly not correct. It violates Hubble's Law which states the recession velocity is a function of the proper distance of the galaxy to the observer. If galaxy Y has "just" blinked out it has done so because it has exited the Hubble sphere. Galaxy X which is closer to the observer is still inside the sphere and is therefore still observable.
This is applicable if galaxies X and Y are formed during a period when the acceleration of the Universe began and the expansion of the Universe is faster than the expansion of the Hubble sphere.
If on the other hand galaxies were formed during a period when the expansion of the early Universe may have been slightly decelerating, the Hubble sphere can expand faster than the expansion of the Universe. In this case those galaxies that are just beyond the Hubble sphere will eventually become visible. So we will never achieve a total and sudden blink out even if all galaxies were receding.
Quote:
Further, CraigS did not stipulate that Y is a photon from the galaxy furthest from us and X is a photon from the galaxy nearest to us. So the question as stated was flawed.
I must be missing something here. Photon Y is assumed to be emitted from galaxy Y and photon X is assumed to be emitted from galaxy X. Craig has clearly stipulated that galaxy X is closer than galaxy Y.
However, the entire universe can only blink out if Y is a photon from the galaxy furthest from us and X is a photon from the galaxy nearest to us and all galaxies are receding so fast that light cannot reach us. However some galaxies are not moving away from us. So the universe will not blink out all at once.
This is clearly not correct. It violates Hubble's Law which states the recession velocity is a function of the proper distance of the galaxy to the observer. If galaxy Y has "just" blinked out it has done so because it has exited the Hubble sphere. Galaxy X which is closer to the observer is still inside the sphere and is therefore still observable.
This is applicable if galaxies X and Y are formed during a period when the acceleration of the Universe began and the expansion of the Universe is faster than the expansion of the Hubble sphere.
If on the other hand galaxies were formed during a period when the expansion of the early Universe may have been slightly decelerating, the Hubble sphere can expand faster than the expansion of the Universe. In this case those galaxies that are just beyond the Hubble sphere will eventually become visible. So we will never achieve a total and sudden blink out even if all galaxies were receding.
I must be missing something here. Photon Y is assumed to be emitted from galaxy Y and photon X is assumed to be emitted from galaxy X. Craig has clearly stipulated that galaxy X is closer than galaxy Y.
What is clearly incorrect:
1) For the cosmological model postulated by CraigS it is possible the the two galaxies will blink out at the same time.
2) However, the entire universe can only blink out if Y is a photon from the galaxy furthest from us and X is a photon from the galaxy nearest to us and all galaxies are receding so fast that light cannot reach us.
3) However some galaxies are not moving away from us. So the universe will not blink out all at once.
You mention the Hubble sphere. As I understand Hubble sphere is the region of the Universe surrounding an observer beyond which objects recede from the observer at a rate greater than the speed of light, due to the expansion of the Universe.
There has been no empirical evidence of anything moving at a rate greater than the speed of light.
