Binary pulsars vs. SR

[altergnostic]

Binary pulsars are often used to test predictions of GR, namely, the possibility of energy loss due to gravitational waves. But we never see any analysis of SR's predictions, although it is an extremely potential source of empirical data on time dilation due to velocity as well, since during the entire orbit the relative speed between earth-pulsar is variable.

Pulsars are near perfect, incredibly stable clocks (each pulse is a tic), and we can observe the doppler shift and isolate time dilation effects due to gravitaty and velocity. It turns out that there's no indication of time dilation due to speed independant of direction (or so it seems).

I've heard about this before but never came across actual data, until yesterday. Scroll down ro figure 5.

 

http://www.cv.nrao.edu/course/astr534/Pulsars.html

 

What do you make of this?

[elfmotat]

I don't know what you mean by "there's no time dilation." I don't see anything to indicate that in the figure you mention.

[Janus]

I don't know what you mean by "there's no time dilation." I don't see anything to indicate that in the figure you mention.

Agreed. The left figure shows the variation in observed period due to Dopper effect for a pulsar in a near perfectly circular orbit. This means that the orbital speed is constant, thus so would any time dilation due to orbital speed. In order to show whether or time dilation showed up in those observations, you would first have to know the Pulsar's proper rotation rate in its own frame, something we don't have direct knowledge of.

 

This leaves us with the right figure which deals with an highly eccentric orbit and thus a varying orbital speed and time dilation. So it would be theoretically possible to measure a difference between a classical Doppler shift observation and a Relativistic Doppler shift.

 

However, looking up the particulars of this pulsar, I've determined that the periapis velocity works out to ~350 km/sec an the apapis velocity to ~25 km/sec, or roughly 0.0012c and 0.00008c. This results in time dilation factors of 0.99999928 and 0.999999997 c or a clock rate difference between the two of 1.0000007.

So even if you were to plot both the classical and relativistic Doppler shifts together, the difference between the two at the scale of the figures shown would be too small to be able to tell them apart.

[altergnostic]

I didn't say "no time dilation", I meant no time dilation proportional to speed (magnitude) independent of direction (vector).

 

Agreed. The left figure shows the variation in observed period due to Dopper effect for a pulsar in a near perfectly circular orbit. This means that the orbital speed is constant, thus so would any time dilation due to orbital speed. In order to show whether or time dilation showed up in those observations, you would first have to know the Pulsar's proper rotation rate in its own frame, something we don't have direct knowledge of.

 

This leaves us with the right figure which deals with an highly eccentric orbit and thus a varying orbital speed and time dilation. So it would be theoretically possible to measure a difference between a classical Doppler shift observation and a Relativistic Doppler shift.

 

However, looking up the particulars of this pulsar, I've determined that the periapis velocity works out to ~350 km/sec an the apapis velocity to ~25 km/sec, or roughly 0.0012c and 0.00008c. This results in time dilation factors of 0.99999928 and 0.999999997 c or a clock rate difference between the two of 1.0000007.

So even if you were to plot both the classical and relativistic Doppler shifts together, the difference between the two at the scale of the figures shown would be too small to be able to tell them apart.

Wait, you are using orbital velocities, aren't you? Those are relative to the center of gravity. Shouldn't we use numbers relative to earth? I mean:

Set the conjunction alignments to v=0, since there's no motion away or towards the earth at these positions, and then compare the pulse period (time) for the receding and approaching halves of the orbit. Both should show a redshift due to relative velocity time dilation, but there's no indication of it (as far as I can see). Wouldn't this be the right approach?

[Janus]

I didn't say "no time dilation", I meant no time dilation proportional to speed (magnitude) independent of direction (vector).

 

 

Wait, you are using orbital velocities, aren't you? Those are relative to the center of gravity. Shouldn't we use numbers relative to earth? I mean:

Set the conjunction alignments to v=0, since there's no motion away or towards the earth at these positions, and then compare the pulse period (time) for the receding and approaching halves of the orbit. Both should show a redshift due to relative velocity time dilation, but there's no indication of it (as far as I can see). Wouldn't this be the right approach?

The effect of time dilation is so small you would not see it at the scale of the graphs shown.

 

Classical Doppler shift for the pulsar the first chart gives a factor of 0.999813368 for when the pulsar is receding and 1.000186702 when approaching.

 

Relativistic Doppler shift( which accounts for time dilation) gives values of 0.999813351 when receding and 1.000186684 when approaching. At the approach and recession speeds that are involved, this results in a very yery very small difference between the two approaches.

 

Oh, and no matter what the approach speed, you always get a blue shift, even with time dilation.

[altergnostic]

Oh, and no matter what the approach speed, you always get a blue shift, even with time dilation.

Wait, what? t=gt' implies a redshift for both halves of the orbit, since the in gamma is a magnitude not a vector, that's why it's dilated and not contracted, a blueshift would be a contraction. (I am talkng abou the isolated effects of linear velocity here).

[Janus]

Wait, what? t=gt' implies a redshift for both halves of the orbit, since the in gamma is a magnitude not a vector, that's why it's dilated and not contracted, a blueshift would be a contraction. (I am talkng abou the isolated effects of linear velocity here).

 

There's more to red or blue shift than just time dilation, there is also the effect of increasing or decreasing distance. When the source is receding, each successive wave takes a little longer to get to you, this stretches out the time between waves as you see them decreasing the observed frequency. When it is approaching, each successive wave takes less time to reach you, which compresses the waves an increases the observed frequency. The shortening of wavelength due to this always greater than any lengthening due to time dilation.

 

Relativistic Doppler shift is found by

 

Fo= sqrt((1+B)(1-B)) Fs

 

where

 

B = v/c

 

and v is positive when the source is coming towards you.

 

Thus for an object coming towards you at 0.9999 c, it has a time dilation factor of 0.01414 (time running as 1/71 yours), and you will see a blue shift by a factor of ~141

Edited February 4, 2013 by Janus

[altergnostic]

 

There's more to red or blue shift than just time dilation, there is also the effect of increasing or decreasing distance. When the source is receding, each successive wave takes a little longer to get to you, this stretches out the time between waves as you see them decreasing the observed frequency. When it is approaching, each successive wave takes less time to reach you, which compresses the waves an increases the observed frequency. The shortening of wavelength due to this always greater than any lengthening due to time dilation.

 

Relativistic Doppler shift is found by

 

Fo= sqrt((1+B)(1-B)) Fs

 

where

 

B = v/c

 

and v is positive when the source is coming towards you.

 

Thus for an object coming towards you at 0.9999 c, it has a time dilation factor of 0.01414 (time running as 1/71 yours), and you will see a blue shift by a factor of ~141

Yes, I get that. I thought you were talking about the effects of time dilation due to linear speed only, I know doppler causes both shifts. Anyhow, so basically we can't measure this system with enough precision to analyse this effect? Do you know of any binary system that does?

[Janus]

Yes, I get that. I thought you were talking about the effects of time dilation due to linear speed only, I know doppler causes both shifts. Anyhow, so basically we can't measure this system with enough precision to analyse this effect? Do you know of any binary system that does?

 

Well, with the first pulsar, which is in a circular orbit, precision isn't the issue.

 

The classical Doppler shift equation is

 

1/(1+B) where B is v/c and is positive while receding.

 

So if you want to work out the ratio between maximum blueshift and maximum redshift, you can assign B to be equal to the orbital velocity as a fraction of the speed of light and then do the following relationship:

 

(1/(1-B))/(1/(1+B)) = (1+B)(1-B)

 

Relativistic Doppler shift is

 

sqrt((1-B)(1+B)) Again with B being positive when receding.

 

Finding the Blue to red shift ratio like above, we get

 

sqrt((1+B)/(1-B))/sqrt((1-B)/(1+B))

 

sqrt(((1+B)/(1-B))/((1-B)(1+B)))

 

sqrt(((1+B)/(1-B))((1+B)(1-B)))

 

sqrt((1+B)²/(1-B)²)

 

(1+B)/(1-B)

 

The same ratio as with the Classical formula.

 

The upshot is that when we observe the pulse rate of said pulsar to measure the Red and Blue shift, what we measure alone can't tell us which formula is right, we would have to know the pulse rate as measured by someone at rest with respect the pulsar to do that.

 

This is why the second pulsar is a better candate for such a test, its eccentric orbit means its orbital speed changes and so would the time dilation. It would be theorectically possible to see a difference between a classical Doppler shift plot and a Relativistic one.

 

As to whether it is practical to measure such a difference depends of the accuracy of the measurements and how severe the orbital speed changes are. With the system shown, I don't know if the effect is large enough to be measured or not, because I don't have the measurement accuracy, I do know that it is to small to be seen on the given plot.

 

I'm not sure if there are any such systems where the difference would be very large. It would take some unusual cricumstances. You would likely have to have a pulsar orbiting a blackhole with a periapis that came in really close.

[altergnostic]

By your analysis on the circular orbit, relativistic and classical doppler yield the same number, but it's because you used orbital speed, and that requires that we know the rate in the pulsar's rest frame indeed, otherwise we are left in the dark.

But my idea was to set the nearest and farthest positions of the orbiter from the earth as v=0, since we are only interest in relative velocity in the x direction. By that token, a circular orbit's velocity varies just as well. Classically, the approaching and receding pulse rates should offset perfectly, but not relativistically, since linear relative velocity would slow down the pulse rate on both halves of the orbit - and that slowing down would range from 0 when v=0 to maximum when v=max.

 

What you did was a comparison of maximum positive to maximum negative velocity, and by that analysis both pulse rates should offset indeed, since time dilation due to linear velocity would decrease both sides' pulse rates by the same amount.

 

 

[Markus Hanke]

Binary pulsars are often used to test predictions of GR, namely, the possibility of energy loss due to gravitational waves. But we never see any analysis of SR's predictions, although it is an extremely potential source of empirical data on time dilation due to velocity as well, since during the entire orbit the relative speed between earth-pulsar is variable.

 

On what grounds do think it is permissible to use SR when analysing a binary pulsar system ? Surely you are aware that SR requires inertial reference frames.