What Causes the Shapiro Time Delay in Radar Signals?

[Jorrie]

We start with the classic Keplerian equation for the orbital period

(Eq 1) T = 2 \pi \sqrt{\frac{R^3}{G M} }

You then applied gravitational and velocity time dilation to get

(Eq 10) T_p = \frac{2 \pi R }{c}\sqrt{(\frac{R c^2}{G M}-3)}

Your result is correct for a circular orbit and I think the steps are correct too. The only non-rigorous part is the 'leap of faith' that one can in fact take the Keplerian period, apply time dilations and get the relativistic period. This only works for perfectly circular orbits in Schwarzschild geometry (other orbits have to deal with spatial curvature too), so it by no means a general truth and should be used with care.

-J

 

[Canticle]

Hi Guys
I've been really interested reading your posts, and wating to see what happens when you feed in some quantitive experimental evidence on actual 'Shapiro' delays. The problem is there are discrepancies, and wrestling with relativity or, I had to smile, slowing down the speed of light, won't solve them. The first, Venus, result was 200ms, fine just for a curved track. The later Jupiter one didn't quite seem to work, but did when a vector for Jupiter was adden in. So that was ok then! Was it!?
But now we're doing it in deep space we might of course expect the delays to run into minutes perhaps, or even hours!
Think again. How about months. Do your homework on systems like B1600+434.
I came at this problem from another angle, sorting a beautifully simple unification theory that worked apart from throwing up a couple of bizarre predictions. This was one. In fact they both panned out!
Unfortunately physicists won't respond or read it. Even journal editors! I think they're still arguing with Capernicus, or too busy tied up with string theory and doing maths I expect. Shame. could have saved them so much work.
I might get a webpost organised some time so keep a look out.
Canticle

 

[Canticle]

The speed of light is 'c' because it's entirey constant guys. Gravity red shifts it but doesn't slow it down. Yes of course there's a paradox in the Shapiro delay, giving inconsistent results with galactic lensing, just like the time paradox in special relativity.
I'm told there's now an answer to these, ('these'?) but it's still being worked on. Hmm. Watch this space I suppose.
C

 

[Mentz114]

just like the time paradox in special relativity.

What time paradox ? I must have missed something because I've not heard of any such paradox.

 

[yuiop]

Yes of course there's a paradox in the Shapiro delay,

What paradox in Shapiro delay? I must have missed something too.

GR predicts that the coordinate speed of light slows down according to :

c ' = c \left( 1- \frac{2GM}{R c^2} \right)

and that is exactly what Shapiro (and others) measured in an actual experiments.

The greater the mass M and the smaller the distance R from the mass the greater the slow down or delay.

George Jones posted this nice derivation a long time ago https://www.physicsforums.com/showpost.php?p=928277&postcount=19 for the round trip time (\tau) taken for a photon to travel from the location (R) of the observer, down to a mirror located at (r_m) and then back up the to the observer, as measured by the wristwatch of the observer:

\tau = \sqrt{1-\frac{2GM}{R c^2}} \left( \frac{4GM}{c^3} \ln \left( \frac{R - 2GM/c^2}{r_m -2GM/c^2} \right) + \frac{2(R-r_m)}{c} \right)

I have added G and c constants to try and get the correct units for time. Could someone check that?

 

[Canticle]

Do your homework guys. There's always been a paradox in SR, and Einstein himself said it wouldn't work with the (quantum field) ether. Just google it. Simply; the light from the car approaching you leaves it's headlights at light speed in the cars reference frame, but also crosses the space to you at light speed, no matter what speed he's doing. And of course it's still doing exactly light speed when you measure it, no matter what speed and direction you're doing.
Nice sums on Shapiro delay Kev, but sums mean nothing till you use them. Throw some numbers at it. The delay Irwin S got from Venus was just measurable, Jupiter, later was also in Msec's but had to have extra factors for the planets vector and 'time dilation' (related to the SR paradox) added into make it work.
For any normal galaxy lensing case the delay would of course be massive by comparison, perhaps many days. So would you agree if we were talking years it might be a paradox?
check out GRB 070201 etc. You'll find many comments that gravity must be slowing down the light etc! In the physics I use it just red shifts it!
We humans are excellent at ignoring things, putting insoluable problems and paradoxes to the back of our minds and forgetting them. There are loads in Physics, including that relativity and quantum mechanics don't fit. If you want to check them out read something like Penrose's 'Road to Reality'.
But think about this, if you had the answer, would you think the human race and physicists in particular, were ready for it yet?
..Tricky! What do you think.

 

[Dale]

Canticle, this forum may not be a good fit for you. This is for interested students of relativity, not for people espousing personal theories or objecting to the mainstream ones (see the second sticky at the top of the forum). There are plenty of other places on the internet for that.

The experimental support for SR is overwhelming (see the first sticky at the top of the forum), and it is logically completely self-consistent.

 

[Canticle]

Hmm, Interesting view DaleSpam. I thought my views WERE mainstream! Let's see;
1. I disagreed with Mendocino about light propogation being slower near massive objects.
2. I agreed with Einsteins comments that SR needs changing if there's 'directional' ether.
3. I reminded us of the well known but oft forgotten basic light paradox in relativity.
4. And SR is also only 'self consistent' once we've accepted this and the twins paradox.
5. But there's no question about the results (as far as they go) for SR, or the formulae, which was actually Fresnels from 1818 and always did work fine.
6. I pointed out cosmologists have found 'Shapiro' delays way over those attributable to the curved path of his original theory, and identified them.

Now, none of the above takes genius, ..and I assume there's no objection to them? Someone here seems to be thinking and looking clearly at established solid facts and observations, rather like Galileo, and others seem happier to settle for something less, rather like the church of Galileo's day.
Or should I be under house arrest Dalespam?

 

[Mentz114]

Canticle,

you are misusing the word 'paradox'.

3. I reminded us of the well known but oft forgotten basic light paradox in relativity.
4. And SR is also only 'self consistent' once we've accepted this and the twins paradox.

Utter nonsense. You don't know the meaning of the words you use. Self-consistent means there are no paradoxes. You seem to think that anything that does not fit your flawed intuition is a 'paradox'.

 

[Dale]

Or should I be under house arrest Dalespam?

 

[Canticle]

Wow, didn't know there were professors about who still taught that stuff! You should find stacks of up simple to date paradox stuff on wikipedia, try something like physical paradox, or read some eminent physicists (I referred to Roger Penrose - quote goes something like; "..there are obviously some things fundamentally wrong with our understanding.." etc. or try Lee Smolin if you prefer.
The key thing about 'self consistent' is that anything can be self consistent if you amend 'reality' to accept paradox (defined as the Oxford dictionary). If you'd like a fun example of the paradox try this one.
http://math.ucr.edu/home/baez/physics/Relativity/SR/barn_pole.html
But now I've joined Galileo under house arrest by the Vatican police I'll reject all past claims and admit the sun still goes round the earth, not vice versa, and the Earth's still flat.
I have my answer, as I guessed, ..not ready for it yet. Hey Ho!

 

[Mentz114]

Wow, didn't know there were professors about who still taught that stuff! You should find stacks of up simple to date paradox stuff on wikipedia, try something like physical paradox, or read some eminent physicists (I referred to Roger Penrose - quote goes something like; "..there are obviously some things fundamentally wrong with our understanding.." etc. or try Lee Smolin if you prefer.
The key thing about 'self consistent' is that anything can be self consistent if you amend 'reality' to accept paradox (defined as the Oxford dictionary). If you'd like a fun example of the paradox try this one.
http://math.ucr.edu/home/baez/physics/Relativity/SR/barn_pole.html
But now I've joined Galileo under house arrest by the Vatican police I'll reject all past claims and admit the sun still goes round the earth, not vice versa, and the Earth's still flat.
I have my answer, as I guessed, ..not ready for it yet. Hey Ho!

I presume you got your physics education by reading Wiki pages and popular science books.

It's a pity you can't actually understand anything they say. Have you ever read an actual book ?

Your reference to the Baez page is just laughable since he demonstrates there's no paradox !

Safe again -- either way you look at it, provided you remember that simultaneity is not a constant of physics.

Please go away and be stupid somewhere else.

 

[Canticle]

Oooh! hurtful! I'd believe you were missing the point on purpose, except for the amazing capacity many humans have for self delusion. - And the tendency people have to judge others by their own standards. Very telling!
(And still only 'denial' about the 2yr.+ 'Shapiro' lensing delays in cosmology).
Consider; Relativity and QFT never will come together if that's as broadly as we can think. But I suppose some are perfectly happy with that.
I'm off to a site more suitable for grown ups.