Relativity anyone? - RF Cafe Forums

If speeds in space one day get up to a significant fraction of the speed of light, will the usual Doppler radar solution: fractional frequency shift = twice the relative speed (expressed as a fraction of the speed of light) between the radar and the target still hold? Stated differently: is (Delta lambda)/lambda = 2v/c still valid?

Since there was no response to the Doppler question, how about the twin paradox? Do you believe the story that if one twin sets out on a long, very fast return trip, he/she will end up younger than the stay-home twin?

Greetings Jorrie:

It is not really a question of belief. Many experiments have been carried out using atomic clocks in aircraft, as wellas in space vehicles, that confirms absolutely the tenets of general relativity. As an example, the effects of both lower gravitation and relative speed are corrected for in the GPS system. A Google Search on the topic will yield a plethora of information on the topic.

Thanks for writing.

_________________
- Kirt Blattenberger
RF Cafe Progenitor & Webmaster

Hi Kirt,

Firstly, thanks for a great site and forum! Secondly, thanks for replying.

I'm actually a "converted relativist" and made the statement in my previous post only to try and extract some reaction! I agree with all that you said.

By the way, any ideas on my Doppler radar question? (I know engineers don't need relativity, but it's still intriguing!)

Jorrie

I've been idly sucking my thumb over the weekend thinking of this one, without much result.
One of the thoughts that wafted my way was: if we observe from earth using a spectrometer the collision betwixt two very large objects, super-suns (as found in colliding galaxies), occurring along our line of vision, one will be receding from us and have a red shift corresponding to say 60% of the VOL, and the other approaching it and us with a blue shift corresponding to 60% of the VOL.

Does that mean the relative velocity between them is 120% of the VOL?
If not, why not?

Relativistic velocities measured in the same inertial frame adds up as v = (v1/c+v2/c)/(1+v1v2/c^2). This means that if an observer riding with your "super-sun" A measures the velocity of "super-sun" B, the result will be 1.2c/1.36 = 0.882c. The reasoning behind the "relativistic addition of velocities" equation is rather complex and requires some knowledge of relativity.

Hope it helps.
Jorrie

Greetings Jorrie:

I thought you might be tweaking us a little in order to provoke a discussion.

The subject of relativistic speed addition brings to mind the old (well, it can't be too old) Einsteinian Commandment, "Thou shalt not add thine own speed directly to the speed of thine fellow traveler."

Since the relativistic addition of velocities is given by

V = v1+v2/sqrt (1+ (v1·v2/c²)),

it can be seen that when v1 and/or v2 are very small compared to c, the equation reduces to the Newtonian form of

V= v1 + v2 QED (always thought that QED thing looked scholarly).

_________________
- Kirt Blattenberger
RF Cafe Progenitor & Webmaster

Hi Kirt, a very nice Einstein Commandment!

To stick to it diligently, however, requires some care with the formula.

The equation that you gave [V = v1+v2/sqrt (1+ (v1·v2/c²))] 'sins' heavily. The one that I gave [v = (v1/c+v2/c)/(1+v1v2/c^2)] 'sins' lightly, but sin is sin!

Can anybody spot the two problems? Hint: relativistic addition of velocities cannot result in a velocity greater than c... And watch those units of measure!

Jorrie

To guard against loose ends in threads, I'm stitching this one up - the correct relativistic addition of velocities is:

v = (v1+v2)/(1+v1.v2/c^2),

where v, v1, v2 and c are in conventional SI units of m/s. The 'sin' in my original formula was units of measure. The r.h.s. implied that v1 and v2 were SI velocites, while the left hand implied velocity as a fraction of c, due to the lack of the division by c (not intended as a test, but a typo, I must confess).

You can read more on this and other special relativity formulae in a download from my website https://www.einsteins-theory-of-relativi ... ement.html

Jorrie

Greetings Jorrie:

I took the occasion of you posting your great Relativity 4 Engineers website URL to give you a little extra promotion by listing your site in the Recent Additions list on the RF Cafe homepage.

I have always had a big interest in relativity and used to do quite a bit of reading on it back when I had more time (that would be about 20 years ago). My own attempt at a Relativity page is pretty pathetic, but it will be vastly improved as I go about updating material.

Thanks for your contributions.

_________________
- Kirt Blattenberger
RF Cafe Progenitor & Webmaster

Hi Kirt

Thanks for the publicity. I was unsure on the issue of free 'advertising'. Relativity 4 Engineers contains a lot of free content and, as you perhaps spotted, no advertising other than promoting the ebook-to-be, which will be sold from another, more commercial website.

Keep up the good work! I will post interesting relativity and cosmology tidbits from time to time.

Regards, Jorrie

Hi Kirt

(Some hiccup on my side caused a double post!)

Regards, Jorrie