[PeterJ]

ajb, on 29 January 2012 - 03:52 PM, said:

You don't exactly ignore it, it is a fundamental result of special relativity.

Erm. Sorry, but what is a fundamental result? The fact that we cannot say anything about time for photons?

[ajb]

PeterJ, on 30 January 2012 - 10:58 AM, said:

Erm. Sorry, but what is a fundamental result? The fact that we cannot say anything about time for photons?

It is a result, or maybe rather a postulate depending on how you approach the subject, that there are no inertial frames of reference in which the speed of light is not measured to be c. This means we cannot talk about "time as measured by a photon" or similar statements.

[PeterJ]

I'm afraid I can't see why we have to decide on this issue on the basis of a theory that has nothing to say about it.

If photons are out of time then is this not interesting enough to talk about?

[swansont]

PeterJ, on 30 January 2012 - 11:46 AM, said:

I'm afraid I can't see why we have to decide on this issue on the basis of a theory that has nothing to say about it.

If photons are out of time then is this not interesting enough to talk about?

To talk about it, we need a model. We don't have one. We can only discuss how photons behave in the frames of reference we can be in, because that's the model we have.

[PeterJ]

Okay. I see what you're saying. Physics will never have anything to say about this. It's another of those interesting philosophical problem beyond the reach of science, to be discussed on a different forum.

But surely if this is the case then it means that I was right to start with, that from the photons perspective it is timeless or outside time, and this would be the reason why we cannot talk about it in terms of our Minkowskian model. No?

[ajb]

PeterJ, on 30 January 2012 - 12:38 PM, said:

But surely if this is the case then it means that I was right to start with, that from the photons perspective it is timeless or outside time, and this would be the reason why we cannot talk about it in terms of our Minkowskian model. No?

Define what you mean by "timeless".

If it is a statement like: the affine parameter describing a null geodesic cannot by an affine reparametrisation be understood as the time measured by a standard clock moving along the null geodesic, then yes, photons are timeless.

The problem is that the space-time interval for null geodesics, that is the paths of light is always zero. This messes things up.

For a time-like geodesics, that is the paths of massive particles moving in just a gravitational field (or no field) one can reparametrise things so that the parameter describing the geodesic is the local time as measure by some clock following that geodesic. One can talk about time as "felt" by any massive test particle.

[PeterJ]

Right. Got that. I think we are just differing on the words.

Is the space-time interval zero? I thought that as one parameter went to zero the other went to infinity.

[ajb]

along some path.

For null geodesics this is always zero. So you cannot use s (or - s) to parametrise a null geodesic.

[DrRocket]

ajb, on 30 January 2012 - 01:57 PM, said:

For a time-like geodesics, that is the paths of massive particles moving in just a gravitational field (or no field) one can reparametrise things so that the parameter describing the geodesic is the local time as measure by some clock following that geodesic. One can talk about time as "felt" by any massive test particle.

In fact the parameter required in this instance is just arc length, with respect to the natural metric of spacetime. So what is involved is just the usual trick of parameterizing a curve by arc length. So, one can say that for a timelike curve the length of the curve is the propertime associated with that world line.

This in fact applies to any time-like curve in spacetime, whether or not it is a geodesic. If one also notes that with a metric of signature +,-,-,- that geodesics actually maximize arc length (quite different from the Riemannian case) one has a quick resolution of the "twin paradox" (the "non-traveling twin" has a world line that is a geodesic while the traveling twin has a non-geodesic world line, so the non-traveling twin's world line has the greater proper time).

I guess you might stretch this to say that the proper time associated with any segment of a null geodesic is zero, but I don't know that you get anything useful out of that stretch.

This post has been edited by DrRocket: 30 January 2012 - 06:57 PM

[ajb]

DrRocket, on 30 January 2012 - 06:54 PM, said:

This in fact applies to any time-like curve in spacetime, whether or not it is a geodesic.

Yes, of course.

DrRocket, on 30 January 2012 - 06:54 PM, said:

I guess you might stretch this to say that the proper time associated with any segment of a null geodesic is zero, but I don't know that you get anything useful out of that stretch.

I doubt this is a useful concept, but is as close to "photons being timeless" as I think we can get.

[Widdekind]

DrRocket, on 30 January 2012 - 06:54 PM, said:

This in fact applies to any time-like curve in spacetime, whether or not it is a geodesic. If one also notes that with a metric of signature +,-,-,- that geodesics actually maximize arc length (quite different from the Riemannian case) one has a quick resolution of the "twin paradox" (the "non-traveling twin" has a world line that is a geodesic while the traveling twin has a non-geodesic world line, so the non-traveling twin's world line has the greater proper time)

Vaguely, the application of "rocket thrusters", by the traveling twin, somehow "drives them against the grain of space-time", so that they are "shoved along a short-cut" through space-time ?? Somehow the artificial force "cut corners off" the would-have-been geodesic arc-length-path ??

Vaguely, I intuit "maximizing arc-length" as "maximizing proper time" as implying that, in the absence of artificial forces, particles "lackadaisically take their time" through space-time ??

This post has been edited by Widdekind: 6 February 2012 - 09:27 PM

[khaled]

I'm not really good in physics, but when you said that "photons are timeless"

.. feels like "From the moment a photon was born, it traveled observing everything else halt"

This post has been edited by khaled: 6 February 2012 - 10:36 PM