@Alan McDougall,
hi Alan McDougall
it all depends upon how we interpret GR. Gr is open to more than one interpretation.
Suppose we consider the case of an accelerating particle in the LHC. We could say that the particle enters a different time zone relative to ourselves, and one in which that time zone is much slower than ours. We might witness for example that the particle does not decay as we 'observe' it, when we know that by probability that it almost certainly should have. Thus demonstrating that the interpretation that time has slowed down for the particle is consistent with what we observe. Time slowed down relative to our frame of reference at least, and so therefore time did indeed slow down.
But there is another interpretation. The particle in the accelerator has taken a spacetime short cut in terms of time. Time has not slowed down for the particle at all, what has happened is that the particle has taken a spacetime journey which is shorter in terms of time than our spacetime journey. Therefore it hasn't violated the probability of its half life decay at all. Time could be the same as us for the accelerated particle, but it has taken a shortcut and therefore hasn't experienced enough time to expect its decay.
This is counter intuitive for us, because
spatially the particle is racing around a loop, so in what possible sense could it be a shortcut? Its a longer journey spatially. But thats because we subjectively see a linear relationship between time and space using velocity on the one hand, and also we are used to euclidean geometry generally. In different purely
spatial geometries for example, a straight line between two points as viewed from outside the alternative geometry using a euclidean geometry is not actually the shortest route spatially
within the alternative geometry.
In GR theory the geodesic is very important. It replaces the straight line constant velocity as a geodesic in newtonian mechanics. Consider an orbit around a large mass. The orbit being a geodesic. Now consider a complete circuit returning to point A. Suppose two observers within that orbit, (geodesic), were to seperate. X follows the orbit and Y takes a different spatial path, but they meet up again at the seperation point A. In GR they have taken two completely different spacetime journeys, journeys in non euclidean spacetime. There is no reason generally in GR why they should agree that either spatially or in time that their spatial and time measurements of the journeys should be the same for each other. BUT if they return to the same point A and also to the same geodesic time frame, then they will both agree that the predictions for each other (if they have the information for each others journeys) will match. X will not have experienced any acceleration at all, because the spacetime path was a geodesic.
The thing about GR geodesics is that generally/locally they are the spacetime paths of
longest time. That is counter intuitive to us because 4d spacetime is counter intuitive and so is non euclidean geometry. Deviate from a geodesic (using acceleration) and generally you take a short cut in time. The particle in the accelerator is doing that but the situation is more complex to study because on the surface of the earth we are not following a geodesic either. Nevertheless the particle can be interpreted to have taken a 'time element' spacetime shortcut relative to ourselves, and time did not need to slow down for it to explain its non decay as viewed in our time.
Suppose two people meet up at mount olympus and take different journeys to alice springs and back again. One arrives before the other and waits a week. They could interpret it as
a you travelled at exactly the same speed but you took the longer journey spatially.
b you travelled at a different speed to me, but took an equally long journey spatially.
c combinations of a and b.
With GR we have an extra posiibility that can be interpreted in at least two different ways.
d1 lets compare watches. Your clock reads less time than mine, so whether you took a longer spatial journey or not, we know that you took a shorter journey through time.
d2 lets compare watches. Your clock reads less time than mine, so whether you took a longer spatial journey or not, we know that time slowed down for you.
To understand the reason for the difference of a week, we have to combine a,b, and d1. Or a,b, and d2.
Now the mathematics for d1 and d2 are identical, ie GR ...... but the
interpretation is different. Both make sense.
We can say that time slows down for an accelerated object or that an accelerated object takes a shortcut through time. (just as we can use the term shortcut to describe the shorter spatial journey compared to the longer spatial journey)
We could equally say in the the classical case without GR, that the person who arrived back first entered a space zone where space got shorter. But that would be a non euclidean counter intuitive possibilty for human understanding. It would also be a mathematical nightmare
.... in GR however we can interpret it as the traveller entered a space zone that was shorter(or longer), just as we can for time, but we have to combine the two using GR mathematics.
This effect is most notably concieved of with respect to interstellar travel. On the face of it, travel close to the speed of light and it will still take 4 years or so to reach the next star. But using the time zone interpretation, it won't take four years for the traveller it will take much less time. This is a time zone biased interpretation. But we could also say that the traveller enters a shorter space zone, so the distance is less and that also explains why the traveller can get there in under four years of their time. Of course to accurately get the right answer we must combine the two.
But alternatively we don't have to interpret space or time changing for the traveller, we can say that the acceleration and velocity enables the traveller to move through spacetime. Its just the nature of travelling through non euclidean spacetime, and their space and time experience does not change with respect to themselves. A second is still a second, a metre is still a metre, a measured/predicted half life remains the same. Who is to say that they aren't?
I hasten to add that i am not advocating one interpretation over the other. I am open minded and exploring possible consequences. I have to rush off for the weekend .... but the differences in interpretation could relate to whether we consider time to be physical or not.
It also potentially gives the possibility that physical measurements can be of different categories. Virtual and classical comparisons, where the logic of virtually compared measurements is not classical but that they will become classical in summation if the comparisons are made between identical spacetime frames.