A simple question about absolute time and Special Relativity

[quantum quack]

I do think I already have the correct understanding but I thought I would seek confirmation from others more versed in the nature of SRT.

 

The question is:

Is time absolute from a single reference frames perspective?

In that from a single frames perspective all time is absolute and only not so when considering the perspective of another observer who is travelling at relative velocity.

 

It is true that SRT states non-simultaneity exists when comparing two frames at relative v.

 

IS it also true that from the RF that is at rest all objects in it's frame of reference share an absolute time?

[Jay-qu]

SRT proved time was not absolute full stop... since theres no such thing as an absolute position i dont think you can have an absolute time

[Little Bang]

Time is one of the least absolute values in the universe.

[geistkiesel]

SRT proved time was not absolute full stop... since theres no such thing as an absolute position i dont think you can have an absolute time

 

Here you are in error Jay-qu.

 

Using a linear Sagnac effect device an absolute invariant point in space can determined with trivial ease.

 

Using three postulates of light only the eternally invariant point P is defined.

1. The speed of light is constant.
2. The motion of light is isotropic (light moves in a straight line until acted upon by an external force).
3. The motion of light is independent of the motion of the source of the light.

 

The figure below is not difficult to nterpret. The Sagnac effect device moving to the right with an as yet unknown velocity v (wrt point P), emits two photons, L and R, from the midpoint of the L and R clock/reflectors at each end of the moving inertial frame. The phyiscal midpoint mP moves to the right at velocity v.

 

The point P can be verified by at least three separate events in the complete round trip of the photons.

1. The photons are emitted at t = 0.
2. After moving a distance ct The L photons returns to P after reflection form clock/reflector L and after moving another distance ct.
3. The L and R photons return simultaneously to the phyhsical midpoint mP after moving for a complete round trip time of 2ct + t'.

t' is the time the photons move during the transit across the distance 2vt plus the distance the frame travels while the photon is underway. This distance is seen by both photons separated by their respective completed distance of ct. After the photons are emitted and the L photon has moved a distance ct (and arrived at the L clock reflector) the R photon is located adistance 2vt + vt' from the R reflector. After another distance travled of ct byoth photons the L photon is looking at the 2vt + vt' distance away from the physical midpoint of the L and R clock/reflectors, Here the R photon moving oppositely to L is located a distance 2vt + 2vt' from the oncoming mP. The L and R photons converge simultaneously at mP after a travel time of 2t + t'.

 

If one analyzes the figure with the detail required, they will see that during the time t' immediately after the L photon has reflected from L clock/reflector both the L and R photons are moving in the same direction to the right. This continues until the R photon reflects back to the direction of the invariant point P. This t' is the measured difference in time for the ropund trip of the photons wrt the condition where the frame is at rest wrt the stationary frame. This short duration deflection t' from perfect symmetry is what accounts for the different measured round trip travel times and is the measured proof of motion of the inertial frame versus a condition of rest for the inertial frame.

 

From the distance the light travels 2vt while the frame is underway, ct' we determine the time t' from ct' = 2vt + vt', where t' = t(2v)/(c - v), or in terms of velocity, v = ct'/(2t + t').

 

These data are not availabe for analyses prior to the completion of the round trip of the photons and therefore an observer on the movng frame has no data from which he may conclude, one way or the other, whether the frame is in motion or at rest wrt the stationary frame of reference.

 

 

Here, we assume the arrival times of the photons at L and R are embedded in the reflected signals which are not available for inspection until the reflected signals arrive at the midpoint mP after the completion of their round trip. On can see the difficulty in separating the signals such that an illusory loss of simultaneity can be claimed by eiother observer. The simultaneous arrival time as observed by the stationary observer cannot be rationalized away using a claim of nonexistent absolute tmes as perceived by the moving observer which can have only one solution. If the stationary observer measures the simultaneous arrival of the L and R photons where the mP is located (which can be determined from experiment) then there is no physical way in whch the moving observer can claim the event was not simultaneous. Similarly, if the stationary observer places clocks on the stationary frame (determined from experiment) at the point where the photons arrive at the L and R clocks on the moving frame, these clocks will show a definite sequential arrival of the photons at L and R that cannot be erased theoretically and have a substituted simultaneous arrival of photons measured.

 

Even were we to assume the moving clocks to be unsynchronized wrt the stationary frame the fact of time dilation and frame contraction will not hide the sequential arrival opf the photons wrt the moving frame clock measurements. This, of course, would negate any claim of time dilation and frame contraction.

 

The midpoint of the moving photons holds up to the point of reflection by the L photon. However, the point is still defined bhy the motion of the photons as the L photon returns to the point after reflecting back a distance ct. For the rather short spurts of time and distance considered here the isotropic motion, constancy of speed are maintained to any concevable resolutuion of measurement.

 

Notice that differences in observation by an observer moving with the inertial frame and an observer on the stationary frame are resolved by the measuremnt of t', which negates the concept that the moving and stationry observer will measure times of the events other than simultaneously.

 

The convergeance of the photons at the moving midpoint mP is simultaneous as it is when the frame is in the stationary condition. This makes it very difficult for the moving observer to claim any "loss of simultaneity, doesn't it?

 

If we assume the distance from mP to L and R each at 3000 meters we see the round trip time of flight for the photons in the stationary frame as 2x10^-5 sec. If the frame is moving in the L-to-R direction at 30 km/sec this will add a t' = 4.00040004 x10^-9 sec. In this time the frame will have moved in the order of 6 cm .

 

Geistkiesel

[Jay-qu]

wow, sorry bout that... but i believe with the expansion of space itself you cant have an absolute point

[Erasmus00]

Geistkiesel, if the distance between the mirrors in some frame is L, and the distance from one mirror to the point where the light beams reconverge is l, then what is frame invariant is l/L and not the point in space, per se. Also, I'm unfamiliar with phrase linear Sagnac frame, as the sagnac effect occurs in a rotating reference frame.

-Will

[infamous]

wow, sorry bout that... but i believe with the expansion of space itself you cant have an absolute point

 

Assuming that space is truly expanding I would have to agree with you Jay-qu. Isn't it frustrating how some will grasp at every opportunity to expound upon their pet theories.

[quantum quack]

Thanks guys, my question was really about how an observer will record the time or duration of any event in his universal reference frame in absolute terms.

Pretty naked stuff really.....and that it is only when we presume the perspective of a relative v observer that time becomes relative....

[geistkiesel]

Geistkiesel, if the distance between the mirrors in some frame is L, and the distance from one mirror to the point where the light beams reconverge is l, then what is frame invariant is l/L and not the point in space, per se. Also, I'm unfamiliar with phrase linear Sagnac frame, as the sagnac effect occurs in a rotating reference frame.

-Will

No Will, the physical frame moves wrt P that is and is not invariant. Look at it from the stationary frame3 and you will see what I mean. Google on Sagnac effect for a plethora of Sagnac descriptions. AE even suggested that "rotating frame" be unwrapped into a linear mode. Think about it Will, at what angle does rotating, or circular stop and linear begin? It certainy isn't a "delta function' interface.

 

I don't understand what youmean by "what is frame invariant is l/L?"

Thanks for the comments.

Geistkiesel

[Erasmus00]

No Will, the physical frame moves wrt P that is and is not invariant. Look at it from the stationary frame3 and you will see what I mean. Google on Sagnac effect for a plethora of Sagnac descriptions. AE even suggested that "rotating frame" be unwrapped into a linear mode. Think about it Will, at what angle does rotating, or circular stop and linear begin? It certainy isn't a "delta function' interface.

 

The Sagnac effect is ONLY observed in non-inertial reference frames. As such, Linear Sagnac makes no sense. If AE is Einstein, then you suggest Einstein thought the Sagnac effect would occur in a linear frame, and I'll need a source for that. If you want a mathematical treatment of the Sagnac effect in SR, let me know, and I'll provide. Now the sentence that ends in "that is and is not invariant" makes no sense. EDIT: I suppose in a non-inertial frame, an accelerating frame, you could have a linear sagnac effect, but that should hardly be surprising. You could even probably build a Sagnac accelerometer.

 

I don't understand what youmean by "what is frame invariant is l/L?"

Thanks for the comments.

Geistkiesel

 

You don't have an invariant point in space. Different observers will disagree about where the light reconverged. What you have is an invariant ratio. Lets say in some frame an obersver A measures the seperation beween mirrors L, in another frame an observer B measures L'. Now, A measures the light as reconverging a distance l from the end of the back mirror. B measures the light reconverging a distance l' from the end of the mirror. Then l/L=l'/L', for all reference frames. The point varies from observer to observer, but the ratio stays the same

-Will

[C1ay]

See Relativity, Chapter 8. In particular AE wrote in §6:

 

It is clear that this definition can be used to give an exact meaning not only to two events, but to as many events as we care to choose, and independently of the positions of the scenes of the events with respect to the body of reference 1 (here the railway embankment). We are thus led also to a definition of “time” in physics. For this purpose we suppose that clocks of identical construction are placed at the points A, B and C of the railway line (co-ordinate system), and that they are set in such a manner that the positions of their pointers are simultaneously (in the above sense) the same. Under these conditions we understand by the “time” of an event the reading (position of the hands) of that one of these clocks which is in the immediate vicinity (in space) of the event. In this manner a time-value is associated with every event which is essentially capable of observation.

 

This stipulation contains a further physical hypothesis, the validity of which will hardly be doubted without empirical evidence to the contrary. It has been assumed that all these clocks go at the same rate if they are of identical construction. Stated more exactly: When two clocks arranged at rest in different places of a reference-body are set in such a manner that a particular position of the pointers of the one clock is simultaneous (in the above sense) with the same position of the pointers of the other clock, then identical “settings” are always simultaneous (in the sense of the above definition).

[geistkiesel]

The Sagnac effect is ONLY observed in non-inertial reference frames. As such, Linear Sagnac makes no sense. If AE is Einstein, then you suggest Einstein thought the Sagnac effect would occur in a linear frame, and I'll need a source for that. If you want a mathematical treatment of the Sagnac effect in SR, let me know, and I'll provide. Now the sentence that ends in "that is and is not invariant" makes no sense. EDIT: I suppose in a non-inertial frame, an accelerating frame, you could have a linear sagnac effect, but that should hardly be surprising. You could even probably build a Sagnac accelerometer.

 

 

 

You don't have an invariant point in space. Different observers will disagree about where the light reconverged. What you have is an invariant ratio. Lets say in some frame an obersver A measures the seperation beween mirrors L, in another frame an observer B measures L'. Now, A measures the light as reconverging a distance l from the end of the back mirror. B measures the light reconverging a distance l' from the end of the mirror. Then l/L=l'/L', for all reference frames. The point varies from observer to observer, but the ratio stays the same

-Will

Will,

If the term, "Sagnac" biothers you then don't use the word. Look at the system and judge it on its own merits.Likewise, if you look closely you will see that there is no use of "L". It is the photons motion doing virtuallhy all the "measurements" here. This is an exercise in velocity analysis of photon activity.

 

You say two observers using your "L" get different results. There is no meaured L here. What about the times of arrival of the moving phiotons at L and R and mP?

 

I do not understand your use of 'observer' here. When the lights are emitted from a point that point is specifically andf definitively located, it is defined and updated by the continuing motion of the light (infact a single photon would work just as well, as would multiple photons emitted anti-parallel or at any angle wrt each other). The point P initially is the midpoint of the moving photons. No observer, on the frame or off, can perturb that point with their unique perspective. If you claim otherwise please indcate just how that occurs.

 

The fact that some observers disagree, has nothing to do with the invariance, that is spatial location of the point. If you say this I am at a loss to determine your justification. Which observer located where will disagree with another observerlocated where, regarding the location of P? What does an observer on the frame "see" that defines for him where the point is located? What data does the moving observer use to justify his measurement, rathyer his assessment?

 

 

Your use of the distance as "L" is interesting. If you look closely at the figure you will see that "L" does not appear. I am using the distance light travels in equal durations of time as the photons expand then reconverge at the phyisical midpoint of the L and R reflector clocks. There are clocks at L and R as well as relectors. When the lights arrive at the clocks the arrival time is noted and embedded in the reflecting signal, with a number, a time stamp if you will. This number does not evolve and appear different to dofferent observers, as this would be impossible under any analysis. Notice also that no observer makes any measurment of the trajectory of the photons until those photons reconverge at the physical midpoint which is moving wrt the sgtationary frame. Can you address your comments to these aspects please?

 

Try an anlysis like the following:

1. Will the photons arrive at L and R simultaneoulsy under any conditions? If so what are those conditions?
2. Will the photons arrive (converge) at the physical midpoint simultaneously under any conditions? If so what are those conditions?
   
   
3. Can the photons arrive at the L and R clocks simultaneously and not arrive at the phyiscal midpoint simultaneously? or
4. Can the photons arrive at the clocks sequentially and arricve at the midpoint mP simultaneously?
5. Can you determine if two observers, one on the embankkemt and one on the moving frame, can detect different arrival times of the photons at L and R and reconverge at different times at the physical midpopint?
6. Remember, the clocks give out a single number indicating the arrival times of the photons and embed this number in the reflected signal that can only be measured, or read, after arriving at the moving observers location co-located with the physical midpoint., ONLY!

 

I cannot understand why there is no analysis of the photons motion, their trajectory through space and time as defined by the figure.

 

Geistkiesel

[Little Bang]

C1ay, thats the first time I seen that (chapter 8) His analytical skills were impeecable.

[geistkiesel]

See Relativity, Chapter 8. In particular AE wrote in §6:

I can hardly disagree with this, but the question I have what does this have to do with the thread?

 

The clocks on the moving frame are assumed synchronized and moving as "one".

 

Geistkiesel

[Erasmus00]

 

 

Your use of the distance as "L" is interesting. If you look closely at the figure you will see that "L" does not appear.

 

You are correct, L doesn't appear in your diagram. I defined it in my post to show you what invariant you had discovered. Its not an absolute point in space, its an absolute ratio.

 

Different observers will see the midpoint at different points in space. For example, consider a frame A in which the mirror arrangement is at rest, and another frame B moving at a speed v with respect to the first frame. For simplicity, the origins of the two frames are aligned at time 0 which is also when the pulse of light is emitted.

 

An observer from A sees the light emited at a point xa=M (m for midpoint). An observer in frame B sees the light emited at a point xb = sqrt(1-v^2/c^2) * M. These are obviously not the same point. Similarly, A sees the light reconverge to xa=M, and B sees the light reconverge at xb = sqrt(1-v^2/c^2) * M.

-Will

[quantum quack]

Clay, Thanks for the clarification.

The relevance is that if we assume a frame as at rest then all rest points on that frame are simultaneously at rest as well. regardless of distance between those points.

Thus we have an enshrinement of absolute time but only to a particular rest frames' "universe". also all points with velocity in that universe are absolutely defined by that rest frames rest points

 

As far as non-simultaneousness betweeen relative frames is concerned this is also an obvious outcome given the nature of lights invariance and not really the topic of this thread.

 

The whole pont was to clarify the use of the definition of absolute time with regards to a rest frames' observer.

 

According to SRT relative v observers will observe non-simultaneous absolute time "universes" thus a relative velocity observers frame whilst also absolute to it-self is relative in time to the other observer.

 

I just wished to clarify this issue regards absolute and relative time...and thanks for the help.

 

To sum up, it means to me that an observer regardless of what v that observer may be deemed to be at by another observer will always experience absolute time regards to itself therefore relative time is only an extrapolation of what the observer will "presume " to be the observations of a relative v observer. [ by way of calculation using Lornenzian transforms.]

please feel free to correct me if you feel I am in error.... :)