absolute space

Xgen

Registered Senior Member
I had not read GR books profoundly but I understand the basic idea - relative frames of reference and constant speed of light.

Is it possible to exist absolute space, as defined below?

absolute space - this is such a space and frame of reference in which all objects moves with the maximal allowed velocity - the speed of light.

what that means - imagine two frames K1 and K2 that moves one according to other with velocity of v. If now we rotate K2 such that it axes coinside with x,y and z axes of K1 so that only vx is different then zero, and start to move K2 in a direction opposite to vx with velocity (c-vx), in K2 K1 will moves with the speed of light. Since that is the maximal speed there exist only one such system of reference according to which all frames moves with a velocity equal ezactly to c.

an another explanation - imagine a point source of light, it irradiates photons in all directions, since according to a Frenel law (i dont remember exact definition) every point from the EM wave is a source of light, we can consider the following illustration - photons move in a 2D square lattice, after time of dt four new photons are irradiated in all four directions of the x and y axes, after time of 2dt every photon produces 4 new photons and so on:

X

X X X

X

when the number of directions is extrapolated to infinity is produced an absolute space, all photons in the world share one and the same frame of reference, am I correct? Also this space is immovable to all systems of reference.

Xgen said:
imagine two frames K1 and K2 that moves one according to other with velocity of v. If now we rotate K2 such that it axes coinside with x,y and z axes of K1 so that only vx is different then zero, and start to move K2 in a direction opposite to vx with velocity (c-vx), in K2 K1 will moves with the speed of light.

No K1 will not move with the velocity of light since in relativity you don't add just like that the velocities.

1000f,
yes you are right. But photons moves with the speed of light. So if we shoot one photon in a moment t at opposite to vx direction it will move with c in K1? So if we attach a frame of reference to this photon we will have K2.

Xgen said:
1000f,
yes you are right. But photons moves with the speed of light. So if we shoot one photon in a moment t at opposite to vx direction it will move with c in K1? So if we attach a frame of reference to this photon we will have K2.
No since you said that K2 moves at velocity v
Xgen said:
imagine two frames K1 and K2 that moves one according to other with velocity of v
and the photon has a velocity c in frame K1, so that the frame K2 cannot be attached to the photon.
BTW, the photon will also have velocity c in frame K2

No since you said that K2 moves at velocity v.

This was at the beggining. Then I accelerate K2 until it start to move with c.

But OK, I admit that I didn't put it well. Lets forget about K1 and K2. Lets just take one frame of reference attached to a photon and moving in all systems of reference with velocity c. I called this system of reference absolute space, the picture can be always reversed and it can be said that absolute space is immovable and everything else is moving with velocity c according to it.

Why I am discussing with you the absolute space? Well, imagine just for a second that there is absolute space. Then it is accualy possible to be invented a device that can allow us to navigate and to position ourselfs in the absolute space. This device is accualy so simple that I will explain it right now. I will call it PASD - Positioning in Absolute Space Device. It represents a source of spherical EM waves (i.e light photons emitted with equal number in all directions) put in a 4pi spherical photodetector which can very accurately measure the time interval between emition and absorbtion of the photon on the second sphere. In this way PASD can measure (since it moves with the frame of reference) not only the acceleration but and velocity and both in the absolute space.

There is only one problem - PASD produce pictures of velocity distributions in 4pi, say every moment between time interval dt which is very small. But if there is a rotation of the frame PASD should be rotated in the opposite direction in order to be taken the same points from the absolute space. In other words there is problems with rotation. But this problem can be solved.
(if it is not clear I will explain it more detaily later).

With PASD is possible for example to measure how fast is moving Earth around the Sun, how fast is moving solar system around galaxy center, how fast is moving the entire galaxy and so on. Its not needed to have anything except PASD (its not needed to see the stars for example).

do you know what a lorentz transformation is?

Xgen said:
Lets just take one frame of reference attached to a photon ...
I'm pretty sure that this is at best immensely impractical. Though I hold that this is not possible in principle. Call me close-minded an you will.

Xgen said:
With PASD is possible for example to measure how fast is moving Earth around the Sun, how fast is moving solar system around galaxy center, how fast is moving the entire galaxy and so on. Its not needed to have anything except PASD (its not needed to see the stars for example).
I didn't follow your PASD description very well. Can you attach a diagram?

do you know what a lorentz transformation is?

yes, what about it? /may be you are gonna tell me that a frame can not move with speed of c, because lorentz transformations become nonsense, but it is a fact that such frames exist (since there is particles that moves with the speed of light)/

I'm pretty sure that this is at best immensely impractical. Though I hold that this is not possible in principle. Call me close-minded an you will.

Prove it.

Below I had attach a diagram which help to demonstrate the principle behind PASD. There is a source of light S which emits at one moment two photons P1 and P2 moving in opposite directions. On some distance d from S there is two photo-absorbing plates which produce electricity when a photon falls on them. The entire devise moves with velocity v. Since the second plate is moving away from S and first is approaching it, P1 will be absorbed before P2. From the time interval between the emition and the absorbtion of both photons it can be determined the velocity of the system according to the frame of reference of the absolute space.

the PASD device explained before is extention of this one-dimensional illustration for the 3D case.

Xgen said:
Prove it.

Below I had attach a diagram which help to demonstrate the principle behind PASD. There is a source of light S which emits at one moment two photons P1 and P2 moving in opposite directions. On some distance d from S there is two photo-absorbing plates which produce electricity when a photon falls on them. The entire devise moves with velocity v. Since the second plate is moving away from S and first is approaching it, P1 will be absorbed before P2. From the time interval between the emition and the absorbtion of both photons it can be determined the velocity of the system according to the frame of reference of the absolute space.

the PASD device explained before is extention of this one-dimensional illustration for the 3D case.

But in the reference frame of your PASD, the two photons are emited at the same time, they have the same distance to pass so they will arrive at the same time.

Xgen said:
Prove it.

Below I had attach a diagram which help to demonstrate the principle behind PASD. There is a source of light S which emits at one moment two photons P1 and P2 moving in opposite directions. On some distance d from S there is two photo-absorbing plates which produce electricity when a photon falls on them. The entire devise moves with velocity v. Since the second plate is moving away from S and first is approaching it, P1 will be absorbed before P2. From the time interval between the emition and the absorbtion of both photons it can be determined the velocity of the system according to the frame of reference of the absolute space.

the PASD device explained before is extention of this one-dimensional illustration for the 3D case.

Hi XGen,
Such an experiment could indeed demonstrate the existence of an absolute reference frame.
However, if it were found that there was no time difference, that both absorptions occurred at the same time, what would your conclusion be?
What if both absorptions occurred at the same time no matter how you changed the motion of the apparatus between experiments?

In other words, until you do the experiment, you can't know whether it determines absolute velocity or not. The weight of evidence at the present times indicates that it would not.

Xgen said:
Prove it.
As has been pointed out by 1100f and Pete, you seem to be ignoring current experimental evidence. There is no way to prove anything (in the sense that I assume you mean to draw an absolute conclusion transcendent from a set of givens; one of the givens may be flawed). But, in principle, and in light of the evidence, I don't believe it is possible to have an inertial frame moving at the speed of light with respect to any other inertial frame. Can a massive body move at the speed of light with respect to any other massive body? What does inertia mean?

Xgen said:
With PASD is possible for example to measure how fast is moving Earth around the Sun, ...
I would like to hear your comments regarding a painfully frequently cited experiment: Michelson Morley Interferometer.

But in the reference frame of your PASD, the two photons are emited at the same time, they have the same distance to pass so they will arrive at the same time.

Yes, but there is such a frame of reference that do not moves. Since photons are moving with velocity c in all systems of references we can consider their movement in the stationary frame. In another words photons do not care in what system of reference they are, they do not care that apparatus is moving, that is because they exist in an absolute system of reference and that is the only frame that concept "distance" have a sense for the photons. And in even more simple words - velocity v of the frame do not influence photons and they can not be consider as existing in that system of reference.

Thus photons will not be absorbed at the same time. If v and d are small , the resolution of the device may not be enough to measure the time-shift of both photons. But lets make some calculations. If d is 1 meter and velocity v (which is sum of all velocities according to the absolute space) is 1% from c, then the first plate will shift vdt and P1 path will be cdt, and dt = d/(c+v), or 3,302614 nanosec instead than 3,335640 nanosecs for v = 0. The second photon P2 instead will delay and will be absorbed after time dt = 1.010101........ d/c = 100/99c = 3,369333 nanosecs, the difference betwen absorbtion of both photons will be 3,369333 - 3,302614 = 0,066719 nanosecs, whic corresponds to a counter with frequency 1498823423,6 Hz , approx 1.5 GHz. I think that the real resolution should be at least 20 times more , say 30 GHz.
I hope CPUs will become fast enough soon .

The another solution is to make the device bigger. If d is 100 meters, the counter frequency from 3 GHz will be enough (one overclocked Pentium IV may be .

However, if it were found that there was no time difference, that both absorptions occurred at the same time, what would your conclusion be?

My conclusion will be that experimental detector is not precise enough.

In other words, until you do the experiment, you can't know whether it determines absolute velocity or not. The weight of evidence at the present times indicates that it would not.

What evidence you are talking about? All modern knoledge , including GR and QM, are in consensus that speed of light is a fundamental constant - the maximal speed in nature. Everything else is interpretation.

I would like to hear your comments regarding a painfully frequently cited experiment: Michelson Morley Interferometer.

Michelson and Morley discovered that velocity of light is equal in all directions. But I dont think that it means that absolute space do not exist, just the opposite. The ether they were searching for was wrongly imagined as some kind of gas. This is poor mechanical interpretation. The ether is the space-time continuum by itself. It do not move with Earth and there is no way to influence the speed of light. The experiment shouldn't have been directed to measuring speed of light but rather the times for absorption (which however can not happen with interferometer).

I will illustrate where is the problem in Michelson-Morley experiment. Maybe i misunderstand it but lets return to the PASD figure that i posted before. If we have not absorbing but reflecting plates and measure the time both photon reach again the middle point it is obvious that they will return at the same time. I dont know if it is the case with Michelson-Morley experiment, but since it was not directed to detecting time-shifts relative to the absolute space i can not further comment it.

Also, a frame of reference is a mathematical abstraction. It is not necessary to be bounded to a massive body. Photons are moving with a constant speed and are the best choice for inertial frame of reference (since inertial means non-accelerating I believe). Acceleration is a property of massive bodies not to photons.

Xgen said:
Yes, but there is such a frame of reference that do not moves.
There are an infinite number of reference frame that do not move. Each reference frame is not moving with respect to itself and with respect to other reference frames thet do not move with respect to it. However for each such reference frame, there exists other moving reference frames. These reference frames are moving with respect to those moving reference frames.

Quantum Quack said:
Since photons are moving with velocity c in all systems of references we can consider their movement in the stationary frame. In another words photons do not care in what system of reference they are, they do not care that apparatus is moving, that is because they exist in an absolute system of reference and that is the only frame that concept "distance" have a sense for the photons. And in even more simple words - velocity v of the frame do not influence photons and they can not be consider as existing in that system of reference.
No, the concept of distance exists in all reference frame. There is no absolute reference frame. If photons exist in a reference frame, they exist in all reference frames.

Quantum Quack said:
Thus photons will not be absorbed at the same time.
You are right, and I see that finally you appear to agree with the theory of relativity, that in one frame two events are simultaneous and in another one they are not.

Quantum Quack said:
If v and d are small , the resolution of the device may not be enough to measure the time-shift of both photons. But lets make some calculations. If d is 1 meter and velocity v (which is sum of all velocities according to the absolute space) is 1% from c, then the first plate will shift vdt and P1 path will be cdt, and dt = d/(c+v), or 3,302614 nanosec instead than 3,335640 nanosecs for v = 0. The second photon P2 instead will delay and will be absorbed after time dt = 1.010101........ d/c = 100/99c = 3,369333 nanosecs, the difference betwen absorbtion of both photons will be 3,369333 - 3,302614 = 0,066719 nanosecs, whic corresponds to a counter with frequency 1498823423,6 Hz , approx 1.5 GHz. I think that the real resolution should be at least 20 times more , say 30 GHz.
I hope CPUs will become fast enough soon .

The another solution is to make the device bigger. If d is 100 meters, the counter frequency from 3 GHz will be enough (one overclocked Pentium IV may be .

However, if it were found that there was no time difference, that both absorptions occurred at the same time, what would your conclusion be?

My conclusion will be that experimental detector is not precise enough.
MM experiments is much more prcise than your experiments. Eve 1% of c is almost not detectable by your experiment

What evidence you are talking about? All modern knoledge , including GR and QM, are in consensus that speed of light is a fundamental constant - the maximal speed in nature. Everything else is interpretation.

Quantum Quack said:
Michelson and Morley discovered that velocity of light is equal in all directions. But I dont think that it means that absolute space do not exist, just the opposite. The ether they were searching for was wrongly imagined as some kind of gas. This is poor mechanical interpretation. The ether is the space-time continuum by itself. It do not move with Earth and there is no way to influence the speed of light. The experiment shouldn't have been directed to measuring speed of light but rather the times for absorption (which however can not happen with interferometer).

I will illustrate where is the problem in Michelson-Morley experiment. Maybe i misunderstand it but lets return to the PASD figure that i posted before. If we have not absorbing but reflecting plates and measure the time both photon reach again the middle point it is obvious that they will return at the same time. I dont know if it is the case with Michelson-Morley experiment, but since it was not directed to detecting time-shifts relative to the absolute space i can not further comment it.
You are exactly describing the MM experiment, which was,btw, directed to detecting time shifts relative to the absolute space.

Quantum Quack said:
Also, a frame of reference is a mathematical abstraction. It is not necessary to be bounded to a massive body. Photons are moving with a constant speed and are the best choice for inertial frame of reference (since inertial means non-accelerating I believe). Acceleration is a property of massive bodies not to photons.
Nobody said that a reference frame is to be bounded to massive bodies.

Xgen said:
... photons ... do not care in what system of reference they are, ... because they exist in an absolute system of reference ...
Your reason for the apathy of photons is incorrect according to the most commonly accepted theories and experimental results. Photons "don't care" because, in terms of the theory, they have a scalar speed field that is locally invariant under a Lorentz transformation. An absolute system of reference implies quite the opposite.

Xgen said:
... that is the only frame that concept "distance" have a sense for the photons.
There are two types of distance. The pre-Einsteinian refers to spatial displacement. This can be measured quite readilly for a beam of light in any local inertial frame. The other is proper distance, which came into being with Einsteinian relativity. This is <i>always</i> zero for light. Incidently, the proper distance is what would be measured in the "photon's rest frame," in a crude way of thinking. But, a photon <i>does not even have</i> a rest frame.

Xgen said:
... velocity v of the frame do not influence photons and they can not be consider as existing in that system of reference.
In <i>what</i> system of reference?

Xgen said:
... photons will not be absorbed at the same time.
In the frame that observes your P-whatever moving at a non-trivial velocity I agree. But, regardless of the velocity, if it is transformed away (that is, if observations are made while traveling with this P-whatever), then the photons will be absorbed at the same time.

BTW, by photons here, I'm referring to semiclassical "chunks" of light for which uncertainties are insignificant WRT technical limitations. I'm assuming that you intend the same basic meaning. Correct me if I'm misinterpretting you.

Xgen said:
All modern knoledge , including GR and QM, are in consensus that speed of light is a fundamental constant - the maximal speed in nature. Everything else is interpretation.
The maximal speed in nature is an interpretation. The fundamental concept in relativity behind c is the <i>invariance</i>, not the <i>maximization</i>.

Xgen said:
Michelson and Morley discovered that velocity of light is equal in all directions. But I dont think that it means that absolute space do not exist, just the opposite. ... The ether is the space-time continuum by itself. It do not move with Earth
If it does not move with Earth, then how could the MM experiment yield a null result? How could the speed of the light beams be equal in all directions WRT Earth while the Earth moves WRT the medium? Are you referring to Lorentz' idea of contraction due to motion through the ether? I don't really want to get into that, but it presents problems.

Xgen said:
The experiment shouldn't have been directed to measuring speed of light but rather the times for absorption (which however can not happen with interferometer).
Why would the times for absorption be affected? I obviously don't understand at all your point behind this P-whatever.

Xgen said:
... lets return to the PASD figure that i posted before. If we have not absorbing but reflecting plates and measure the time both photon reach again the middle point it is obvious that they will return at the same time.
It is obvious to me that this is true in the rest frame of the PASD, but that this is false in any frame that is moving WRT the PASD in the same direction.

Xgen said:
... a frame of reference is a mathematical abstraction. It is not necessary to be bounded to a massive body. Photons are moving with a constant speed and are the best choice for inertial frame of reference (since inertial means non-accelerating I believe). Acceleration is a property of massive bodies not to photons.
A frame of reference is quite general, yes. A physically useful frame of reference should be <i>inertial</i>. One aspect of this type of frame is, as you have said, that it is not accelerating. But, you are ignoring the other aspect, which can be seen by either considering that

a) Inertial frames are those that can be considered at rest WRT a particle with proper mass and thusly, all such particles within the frame have locally timelike geodesics.

b) A photon has an infinite proper acceleration, as can be seen by extrapolating accelerated constant position hyperbolae to the origin.

It is necessary to be bounded to a massive body for the sake of any experiment that I can coneive, and certainly for the sake of the PASD, which I can only assume to be a massive body if it is to contain an over-clocked computer processor.

1100f said:
Nobody said that a reference frame is to be bounded to massive bodies.
I'm sort of guilty of this vile infraction. I did say that <i>inertial</i> frames must contain all of the worldlines of massive bodies as locally timelike geodesics, in so many words.

errandir said:
In the frame that observes your P-whatever moving at a non-trivial velocity I agree. But, regardless of the velocity, if it is transformed away (that is, if observations are made while traveling with this P-whatever), then the photons will be absorbed at the same time.

No. Photons will not be absorbed at same time in ANY frame of reference, except the frame that is immovable according to the absolute space, or where the velocity in the absolute space v is 0. Accualy my definition for absolute space and reference was incorect it must be defined in that way:

absolute space and reference - it is the reference in which both photons are absorbed at the same time

You say "observations are made". It is very slicky explained you know. I will repeat what I had posted the last time. See diagram. If the device is on a inertial frame of reference moving with a velocity v according to the absolute space, they will be absorbed at different times but if they was reflected they will reach the middle point S at the same time, so if there is an observer there he will see both events as simultaneous.

MM experiments is much more prcise than your experiments. Eve 1% of c is almost not detectable by your experiment.

MM experiment had not been directed at detecting time-shifts but measurement of velocity of light. They had though that velocity in the direction of movement would be c+v and opposite to it c-v. Their interfometer is very inpractical for the measurement of the time-shifts that PASD measure, becose interference happens when two waves overlaps, or sayed in another words when are in the same place at the same time. This means that both photons should be also putted in the same place at the same time. But this make functioning of entire device senseless. I will let you figure out why.

Something more. All the calculations that should be made with PASD should be localy-distributed. What that means. Suppose that two analogus cables connect both plates with a computer that makes the calculations, and let this computer be in the center of the room. Both photons will be absorbed at different times but now signal from P1 will have to travel in the same direction as v and will delay, so the absorbtion will be reported later, and in reverse, the absorbtion time of P2 will arive sooner and the entire device will not function correctly. Thus only digital information containing localy calculated absorbtion time should be transported through the cables.

Also my experiment is not imprecise. It can be maded as precise as it is needed. There is many practical ways to be realized. Velocity can be measured with enormous precision.

errandir said:
If it does not move with Earth, then how could the MM experiment yield a null result? How could the speed of the light beams be equal in all directions WRT Earth while the Earth moves WRT the medium? Are you referring to Lorentz' idea of contraction due to motion through the ether? I don't really want to get into that, but it presents problems.

I just explained that.

Your reason for the apathy of photons is incorrect according to the most commonly accepted theories and experimental results. Photons "don't care" because, in terms of the theory, they have a scalar speed field that is locally invariant under a Lorentz transformation. An absolute system of reference implies quite the opposite.

OK, I admit that I didn't formulate the concept of absolute space correct. I think that "exist in a frame of reference" and "be in a frame of reference" can be sayed for all objects that are moving with this frame when it moves with constant velocity v or accelerates with a. But photons are moving in the absolute space and do not care or know about the velocity v. So you can describe then in any frame of reference if you want, but this is not practical.

errandir said:
A frame of reference is quite general, yes. A physically useful frame of reference should be inertial. One aspect of this type of frame is, as you have said, that it is not accelerating. But, you are ignoring the other aspect, which can be seen by either considering that

a) Inertial frames are those that can be considered at rest WRT a particle with proper mass and thusly, all such particles within the frame have locally timelike geodesics.

b) A photon has an infinite proper acceleration, as can be seen by extrapolating accelerated constant position hyperbolae to the origin.

I didn't understand that.

I see that you are perplexed how a frame of reference can move with the speed of light. Well, accualy I can prove that if space and time steps are taken small enough everything moves with the speed of light, even massive particles. Mass is a global concept, in microworld this concept has lower-limit for application (take Heizenberg inequality if you like).

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Xgen said:
No. Photons will not be absorbed at same time in ANY frame of reference, except the frame that is immovable according to the absolute space, or where the velocity in the absolute space v is 0. Accualy my definition for absolute space and reference was incorect it must be defined in that way:

absolute space and reference - it is the reference in which both photons are absorbed at the same time

If we take two devices like yours, and one device will move wrt the other, you can see that in the reference frame associated with the first one, you will find that the two photons will arrive at the same time, since they start in the middle of the device, they have the same distance to go and they have the same velocity.
However, if you go to the second device, in its reference frame, the two photons start in the middle, they will have the same distance to go and the same velocity. There is no absolute reference frame, or absolute frame.

Xgen said:
MM experiment had not been directed at detecting time-shifts but measurement of velocity of light. They had though that velocity in the direction of movement would be c+v and opposite to it c-v. Their interfometer is very inpractical for the measurement of the time-shifts that PASD measure,
The time-shift is exactly what the interferometer measures.

Xgen said:
OK, I admit that I didn't formulate the concept of absolute space correct.
Because you just showed that there is no such thing.

Xgen said:
I think that "exist in a frame of reference" and "be in a frame of reference" can be sayed for all objects that are moving with this frame when it moves with constant velocity v or accelerates with a. But photons are moving in the absolute space and do not care or know about the velocity v. So you can describe then in any frame of reference if you want, but this is not practical.
I think you just don't understand what a reference frame is.

If we take two devices like yours, and one device will move wrt the other, you can see that in the reference frame associated with the first one, you will find that the two photons will arrive at the same time, since they start in the middle of the device, they have the same distance to go and they have the same velocity.

Plates are moving with velocity v. But photons are not affected from this movement. So they will reach both plates in different times because plates had changed theirs positions. They would return in the middle at the same time if they was reflected, but will not be absorbed at the same time in ANY frame of reference.

Please, dont make me explain it again.

Xgen said:
Plates are moving with velocity v. But photons are not affected from this movement. So they will reach both plates in different times because plates had changed theirs positions. They would return in the middle at the same time if they was reflected, but will not be absorbed at the same time in ANY frame of reference.

Please, dont make me explain it again.
So do you say that photons do not go with velocity c in all reference frames?

errandir said:
Xgen said:
... lets return to the PASD figure that i posted before. If we have not absorbing but reflecting plates and measure the time both photon reach again the middle point it is obvious that they will return at the same time.
It is obvious to me that this is true in the rest frame of the PASD, but that this is false in any frame that is moving WRT the PASD in the same direction.
I just wanted to say that my respons to this was stupid. It is obvious that they will return at the same time in any inertial frame. I agree with you.

I am reading through your post, Xgen, and will respond when I figure out what you are saying.

Xgen said:
If the device is on a inertial frame of reference moving with a velocity v according to the absolute space, they will be absorbed at different times but if they was reflected they will reach the middle point S at the same time, so if there is an observer there he will see both events as simultaneous.
I agree with this (now). I was being stupid earlier.

Xgen said:
MM experiment had not been directed at detecting time-shifts but measurement of velocity of light. They had though that velocity in the direction of movement would be c+v and opposite to it c-v.
Actually, the velocity of light was accepted as some round-about value, and they <i>were</i> trying to detect time-shifts (well, equivalently, they were trying to detect phase shifts indirectly by determining the shift in a fringe pattern). You are forgetting about the perpendicular leg of the apparatus.

Consider this simple algebraic example that presumes an ether:

L is the length of the leg in question
c is some value (with dimensions of speed) that is assumed >> v
v is the speed of the apparatus WRT the ether
&theta; is the angle that the leg in question makes with the direction of motion through the ether
t is the round-trip time of flight of the light in the leg

t = (2L/c)[1-(v/c)<sup>2</sup>cos<sup>2</sup>&theta;]

So, for two legs perpendicular to each other, the time of flight difference &Delta;t is:

&Delta;t = t<sub>2</sub> - t<sub>1</sub> = (2L<sub>2</sub>/c)[1-(v/c)<sup>2</sup>cos<sup>2</sup>&theta;<sub>2</sub>] - (2L<sub>1</sub>/c)[1-(v/c)<sup>2</sup>cos<sup>2</sup>&theta;<sub>1</sub>]

Assuming for the time being that L is invariant and equal for both legs and that the legs are perpendicular gives:

&Delta;t = (2L/c){[1-(v/c)<sup>2</sup>cos<sup>2</sup>&theta;] - [1-(v/c)<sup>2</sup>cos<sup>2</sup>(&theta; + &pi;/2)]} = (2L/c){[1-(v/c)<sup>2</sup>cos<sup>2</sup>&theta;] - [1-(v/c)<sup>2</sup>sin<sup>2</sup>&theta;]}

This can be pushed around to show that some sin<sup>2</sup> + cos<sup>2</sup> = 1, but, ultimately, a dependence on &theta; remains. This is precisely what Michelson and Morley used as a theoretical basis for comparison. They rotated there apparatus 360<sup>o</sup> and performed the experiment at different times of the day and in different seasons. They recieved a null result. The experiment was performed several more times with a trend in increasing accuracy and a correlated certainty of the null result. Of course, if you know your history of late 19th century science, you know that Lorentz proposed a seemingly reasonable suggestion that would save the ether. Well, that's another story.

Xgen said:
Their interfometer is very inpractical for the measurement of the time-shifts that PASD measure, becose interference happens when two waves overlaps, or sayed in another words when are in the same place at the same time. This means that both photons should be also putted in the same place at the same time. But this make functioning of entire device senseless.
I think considering light in terms of photons makes this device impractical/senseless from the start. This device relies on the wave nature of light and disregards the particle nature. Is this a reason why you have a problem with the device?

Xgen said:
Something more. All the calculations that should be made with PASD should be localy-distributed. What that means. ...
Yes, I believe I see what you're saying, and I totally agree with you on this point. I would certainly be interested in the results of your experiment. It seems that it is a quite reasonable one to conduct at the current stage of technology, and I wonder if it has not already been done. Have you done a literature search?

Xgen said:
I see that you are perplexed how a frame of reference can move with the speed of light.
Not exactly. I just don't think that any frame of reference <i>relevant to the PASD</i> can be such a frame. I have already explained why I feel this way.

Xgen said:
Well, accualy I can prove that if space and time steps are taken small enough everything moves with the speed of light, even massive particles. Mass is a global concept, in microworld this concept has lower-limit for application (take Heizenberg inequality if you like).
You can <i>prove</i> it? I don't see how an <i>interpretation</i> of the HUP proves anything, much less that everything moves at the speed of light or any other speed for that matter. I am no expert in QM, though, so, perhaps you would be willing to help me out with this?