The Eternal Perspective of Photons: A Scientific Exploration

[pervect]

\eta_{\mu\nu} p^{\mu} q^{\nu}=p_t q_t - p_x q_x - p_y q_y -p_z q_z = (1)(1)-(1)(-1)-(0)(0)-(0)(0)=2... so p is not Minkowski-orthogonal to q. [In your required equation, (-a+b=0) means of course a=b ].

You're right, I was quite confused.

I was ultimately interested in defining a coordinate system. It looks like the right way to do it is to say that given a plane defined by two space-like vectors x and y (and their linear combinations) that there are two unique (except for their magnitude) null vectors perpendicular to that plane (for example z+t and z-t for the x-y plane), and that these 4 vectors (two space-like and two null) span the space-time and can thus serve as a coordinate system.

Hopefully I got it right this time around (I've seen null coordinates used, but I haven't used them much personally).

 

[JesseM]

Let's see if I can get latex to work:

<br /> \nu&#039; = \nu \sqrt{ \frac{1-u/c}{1+u/c}}<br />

That's your run of the mill doppler shift. We have our base frame which represents normal reality. Our test frame is u relative to our frame. We have a laser mounted on our base frame shooting light in the direction of our test frame. If you take the limit of u to c, the frequency of the light in the laser beam goes to zero. The constant c is still c in the limit. However, my point is there is nothing too go at c. The phase is still technically changing at 3x10^8m/s in the limiting frame, but the wavelength is infinitly long.

This is if you take the limit where the velocity of the frame relative to the emitter is approaching c but the light wave is moving at c in every frame. But getting back to the point I made in my last post, why couldn't you also take the limit as the velocity of the frame relative to the emitter is approaching c, and the velocity of the wave being emitted is also approaching c (while its frequency remains constant)? This is a different way of trying to decide what the wavelength of an electromagnetic wave moving at c relative to the emitter should be in a "limiting frame" which is itself moving at c relative to the emitter. Since you get different answers depending on how you calculate the limit, this shows that there is no well-defined limit here.

edit: sorry, I think I messed up there...regardless of how fast the wave is moving, if the relative velocity between you and the emitter is approaching c, then the time between ticks of the emitter's clock should be approaching zero and therefore the frequency should be approaching zero as well. So frequency is not one of the quantities that will fail to have a well-defined-limit in the "limiting frame".

 

[caroso]

Good you're discussing this and making hypothesis, who knows one day man can be "teletransported" or faxed (I doubt cos is too much information and nobody would want to be exterminated in the process or be duplicated like Jet Li -in that science fiction movie-) but if that is improbable and not impossible, in that future nobody would have to bear radical statements like "It is definitely a mistake to import the baggage of frames of reference applicable to a massive observer to a photon - 3 space + 1 time does not work." You'll see, if Eliah ever traveled in a charriot of fire, HE HAD TO BE TRANSFORMED INTO LIGHT, can you imagine the phosphorus-chrononaut? Of course, I'm just using the Greek word for light as an example to trigger the imagination. If some people already think about impossibilities, it will be impossible for them, that's a fact.