Recent content by Grimble

Thank you gentle folk, one and all... What you are saying is what I was thinking - confirming that you have no simple mechanical explanation. What I understand from you is that it is due to time dilation and the nature of time - which no one has a good non circular definition for... I am happy...

Clock A and clock B are synchronised at event S. They have a relative velocity v. After time t each will calculate that the other's clock to take longer to tick than their own clock. That is each clock will run slow as observed from the other clock. As I understand it these are physical...

After much deliberation I can finally see and understand what you have all spent so much time and patience explaining to me! I can see that to observe the 2nd postulate; 'the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source or observer' a...

Very good so just where does hyperbolic geometry fit in?

So Minkowski made the connection between hyperbolic geometry and special relativity - so far, so good... So what then is the connection between Special Relativity, Minkowski space, Minkowski diagrams and hyperbolic geometry?

So How does that fit with the insistence on describing everything in terms of hyperbolic geometry?

The main difference in the two geometries is the number of dimensions, is it not? In Euclidean 3-space, a2+b2+c2 is invariant because there is no time component. So in Minkowski Spacetime the equivalent would be that a2+b2+c2 would be invariant at any single specific time. Similarly, in...

Well if it is not the same quantity then both equations are true... but cannot be equated - or even compared if ds represents different quantities? Or am I missing something here? The terms in these equations represent specific properties; I agree they are different things, but choosing a type...

YEs, but one is the aggregate length in 3 dimensions and the other in 4, so does ds represent the same quantity in each case?

I am finding this intriguing, you are opening up a whole new world to me. I have never understood, nor seen any indication of, hyperbolic geometry in relation to Minkowski Diagrams. Yes, I have seen the hyperbola in Minkowski's diagrams in his Space and Time Lecture but had no idea that that...

Calculate the length of what? As you have given the coordinate time - 1yr and thecoordinate distance - 1 ltyr, are you referring to the proper length or the length of the worldline? In any case ds2=−dt2+dx2+dy2+dz2 = -1 + 1 = 0.

I thought that might have been the case - but how did Einstein respond to his old teachers discovery with regard to his theory?

<Moderator’s note: forked from https://www.physicsforums.com/threads/proper-and-coordinate-times-re-the-twin-paradox.915212/page-13#post-6215675 > Thank you, that is very interesting and I can understand much of it. :smile: But can someone tell me if it was the application of hyperbolic...

Thank you, I have never come across hyperbolic geometry nor Lorentzian geometry for that matter. Is there any explanation of the differences between classical spacetime diagrams and Minkowski diagrams?

Hi Dale; I have been trying to work through what you say and most of it fits together very well, however, when you say I am unsure what you mean. As I understand it: So how does that make any sense? Unless you mean that x and ct are not the sides of a right angle triangle... in which case...