Expert: Philip A. Stahl - 4/2/2009

Question
QUESTION: Relativity says that an observer can be moving in any way and but it will always observe the same speed of light.

So if an observer moves at the speed of light does he still observe the same speed of light

ANSWER: Hello,

Yes, and you can work it out using the relative velocity formula:

thus,

u = (v1 + v2) /  [1 + v1*v2/ c^2]

(let v1 = c  and v2 = c)

u =  c + c/ [1 + c*c/ c^2]  =  2c/ (1 + c^2/c^2) =  2c/ 2  = c

So yes. If the observer moves at v1= c and the light is moving at v2 = c, then the observer still sees it moving at speed u = c.

---------- FOLLOW-UP ----------

QUESTION: I am a beginner in the field of relativity(I,m only 15) so can you please explain this relative velocity formula.

Can u tell me that if one writes a theory then how can he get it registered in his name.

ANSWER: Hello,

The "relative velocity formula" is actually an equation for the addition of velocities in a relativistic frame of reference - taking into account the result of the Michelson-Morley experiment (which you can google).

Assume an object in a system S', starts moving at the point x' = 0, at the time t' = 0. Assume it moves at constant velocity u' (relative to S').


S'
^
!
!
!  
!
!
!
!
!------------------!x', t'---> u' ------------>
x'= 0
(t' = 0)


Thus, from the diagram (admittedly not perfect) in the time t' it travels a distance, x'.

Thus, u' =  x'/t'


S
^
!
!
!  
!
!  
!
!
!
! !S'----------------!x', t'---> u' ------------>
!
!
!
!
!-------------------------------------------------->x


We now ask how fast the same object travels according to an observer at rest in the system S? This observer will see a velocity given by:

u = x/ t = (x' + vt')/ [t' + x' v/c^2] = x'/t' + v/ [1 + u'v/c^2}

= u' + v/ [1 + u'v/ c^2]

which is analogous to the formula I gave you.

Now, it should be noted here this is actually a simplified derivation. Not mentioned at all is the key Lorentz transformation used to get the component part of the equation.

Unfortunately, it is beyond the scope of this answer to go into this transformation, particularly as I am not sure how much you've already read on it (especially the Michelson-Morley experiment) and also how much algebra background you have.

My best recommendation is to try to get the book 'Relativity and Common Sense' by Hermann Bondi (Dover Publications) which is probably written at the level of an advanced high school student. If you get the book pay special attention to Chapter X, 'Coordinates and the Lorentz Transformation'.

In the meantime, you may find the material in these links to be useful:

http://ffden-2.phys.uaf.edu/212_fall2003.web.dir/Eddie_Trochim/Lorentztransform.

(Very good suggested exercise! But you need a lot of algebra skill!)



http://www.youtube.com/watch?v=202fU9qIVK4

(Lecture from Yale University Physics Dept. - but I strongly urge you to gety the above mentioned basic text *first*)

Hope this helps, but the main thing is to get hold of (general) physics texts that contain basic chapters on special relativity and read them, and try to get Bondi's book at the same time. After that you will be able to work the simple problem in the first link, and later, profit from the lecture in the 2nd link.



---------- FOLLOW-UP ----------

QUESTION: Can u tell me that if one writes a theory then how can he get it registered in his name.

U didnt giv the answer last time


Answer
Hello,

Theories, once created or proposed - and which stand the test of time, don't get registered in anyone's name. This is what happens with patents for new inventions. But a theory is not like that.

Generally, one doesn't begin with a theory anyway, but with a hypothesis, which amounts to a scientific guess.

A hypothesis provides a basis to improve on some existing theory (say General relativity) OR provide a new insight.

Say that Einstein's general relativity theory predicts 43" of arc for the change (advance) in Mercury's perihelion (closest point to the Sun in its orbit) per century.

But you come up with a new hypothesis that overturns this and predict 50". In effect, you are overturning Einstein's original theory with a new hypothesis of your own. BUT it must be subjected to multiple tests first, to see if that prediction is *real* and accurate.  Also what new model did you use to obtain the different (and in your mind, improved) result over Einstein's? All this must be known.

Here's how the process unfolds:

You have data, and accessory information which leads to some initial result which tests a particular hypothesis- say Einstein's theory of gravitation, and one of its predicted values 'x'. (e.g. the advance of the perihelion of Mercury due to General Relativity of 43 arcsec)

You then acquire better data (perhaps because of refined instruments, techniques ) and are led to a modified (improved prediction) result such that:

x’ = x + P(x) = 50 arcseconds

where x' (= 50 arecsec) denotes the improved prediction based perhaps on a better model that you possess or have worked out, with P(x) the process (acting on x) that allows it.

Later, more refined data become available, such that:

x” = x’  + P'(x + 1)

and so on, and so on and so forth.

Each x, x’, x” etc. being a successive approximation  (as a prediction from the ever improved hypotheses) to what the objective, genuine value should be.

And over years and after many tests you are led to the value of say x"" = 50.5 arcseconds.

After so many validations, and so many confirmations, you may then be ready to publish your work as a theory in a peer-reviewed physics journal.

This work is then read by all those who receive the journal and also by those who find it in libraries. If, after a while it passes the test of time, and there are no problems discovered (which will manifest in challenges to your hypothesis), you may be granted the honor of having proposed a new theory.

But one cannot simply "register" it in his name!

Of course, theories seldom remain as permanent fixtures. After all, Newton's theory of universal gravitation was later modified by Einstein's general theory of relativity. Bohr's simplified quantum theory was later overturned and modified by Schrodinger's wave mechanics (with the atom now seen as an ensemble of probability waves rather than a miniature solar system)

So, in the same way you may extend or modify an existing theory (or even hypothesis) someone may come along who extends or modifies what you have.

Hope this sheds some light!