Beyond c if time goes positive does V decrease?

1. Dec 14, 2004

Royce

I am not a physicist nor a mathematician. I am not familiar with Einstein's actual equations so I don't know. This is simply a thought in the form of a question.

Photons and electromagnetic waves travel at c. At the speed of light time goes to 0 (zero); also, time is negative in the equations so as objects approach c time goes positive approaching 0.

Now in a strictly mathematical exercise if we vary time beyond 0, it goes positive. My question is: If we continue varying time more positive beyond zero does velocity then decrease toward 0?

Richard Fynman said that a positron is indistinguishable from an electron traveling backward in time. Wouldn't this be positive time as beyond, or the other side of the 0 time of c?

The implication is that there could be something beyond c from our relative view. Time would then be positive and velocity would decrease as time approached +1. We think that our universe is made up of matter. Could antimatter be normal matter with positive time on the other side of the zero time limit in the equations that set c to the value that we observe in our universe?

I realize that this may be hard to follow and disorganized. I haven't had time to really get my thoughts straight on this yet, so please bear with me.

2. Dec 14, 2004

Garth

A little equation Royce.

The Special Relativity 4 dimension version of Pythagoras' equation gives you what is called the 'metric'.

dtau2 = dt2 - {dx2 + dy2 + dz2}/c2

One observer A follows another B moving relatively to her. tau is the time recorded by the moving observer B, where t, x, y and z are the 1 time and 3 space coordinates of B's events recorded by A. (Note you can reverse the observers)
If you divide by dt2 and notice that {dx2 + dy2 + dz2}/dt2 is v2 where v is B's velocity measured by A, in A's 'frame of reference', then you get
(dtau/dt)2 = 1 - (v/c)2
where dtau/dt is the rate of moving B's clock measured by A.

Notice that, as v increases, B's clock (tau) appears to run more slowly than A's, as measured by A. As v approaches and eventually equals c, B's clock appears to stop, although v = c is not possible for massive objects, only massless ones such as photons. If v is greater than c then B's clock does not in fact go backwards, "time is negative", but rather it becomes imaginary. Remember all the squares in the metric? Take the square root of a negative number and you get an imaginary one.

In the metric, if v is greater than c, the positive terms become negative and vice versa. The properties of space and the properties of time are exchanged!

So although Feynman's positrons might be electrons going backwards in time, they are not going faster than light. I believe he also said that all the electrons in the universe could be the same electron/positron going backwards and forwards in time between the beginning and the end of the universe! (However I don't think there is enough antimatter in the universe for that to be true!)

I hope this helps, Garth

Last edited: Dec 14, 2004
3. Dec 15, 2004

Royce

Thanks, Garth. Yes it helps a great deal. I still have a question ,however, most if not all of the sources that I have read about Relativity say that time has a negative sign in Einstein's equations. Where does this come from?

I know that nothing can go move faster than c and nothing with mass can move at c. I thought that a positron would moved slower than c at the same relative v but in + time. The reasoning was that if it were a simple inverse relationship v would approach c as time or tau in this case approached 0 from either direction, -t going positive and +t going negative in direction.

This is not the case apparently as you have shown so so much for that brain f**t.

Thanks, again.

4. Dec 15, 2004

Garth

My equation
dtau2 = dt2 - {dx2 + dy2 + dz2}/c2
which is written in time-squared units
could equally well be written
ds2 = dx2 + dy2 + dz2 - c2dt2
in space-squared units.
Now the time term is subtracted and may be thought of as negative, but it is really the time2 term that is negative, so time is 'imaginary' in these units.
One way to think of this is to say SR treats time as a dimension like the space dimensions, but it is not exactly the same; its relationship to the space dimensions is mathematically the same as the relationship of the imaginary numbers to the real numbers.

Garth

5. Dec 15, 2004

Royce

Thanks again, Garth. I guess that means I have to forget the whole idea. I guess that is where imaginary time that I've been reading about come from.

6. Dec 15, 2004

Garth

In Minkowski space of SR time and space have this relationship with each other, as the imaginary numbers to the real; however in efforts to confront the original causality problem Stephen Hawking and others have conjectured that in the initial planck time of the BB Minkowski space with the metric above becomes ordinary Euclidean space and the negative sign become positive. Thus the time in this 'instant' is imaginarywrt our own time.
They use this in their "The only initial condition is there is no initial condition" hypothesis where the original singularity becomes like the North Pole, keep going back in time and you'll end up coming forward again like going north over the North Pole.

Garth

7. Dec 15, 2004

Royce

Okay, Now a question a bit off subject. Does tau going to 0 act as the limit to c and set the velocity of light?

8. Dec 15, 2004

Garth

The limit to v is set by the 4-momentum equation,
Pa = mdxa/dtau
as v increases Pa increases, it gets 'harder to push' and the total energy or 'relativistic mass' of the object goes to infinity as v -> c.

As photons are considered massless (but see the thread discussing whether this is true or not), light has to travel at this velocity c.

Garth

Last edited: Dec 15, 2004
9. Dec 16, 2004

Royce

Thank you, Garth for answering all my questions in such a clear manner. I can't think of any more at the moment; but, I will be back.