I haven't listened to the video yet - right now I am suffering from video overload syndrome - but I think it is important that people realise that the 4D space-time is NOT what most people imagine. Either time has to be multiplied by SQRT(-1) or the very definition of a space has to be extended by the inclusion of a 'metric'.
Without the metric a simple 4-D extrapolation of Pythagorus' theorem would give the wrong answers.
I suppose Einstein's ideas seem less plausible when you realise that the 'space' of space-time is a mathematical abstraction.
David
(2024-01-07, 12:28 PM)David001 Wrote: [ -> ]I haven't listened to the video yet - right now I am suffering from video overload syndrome - but I think it is important that people realise that the 4D space-time is NOT what most people imagine. Either time has to be multiplied by SQRT(-1) or the very definition of a space has to be extended by the inclusion of a 'metric'.
Without the metric a simple 4-D extrapolation of Pythagorus' theorem would give the wrong answers.
I suppose Einstein's ideas seem less plausible when you realise that the 'space' of space-time is a mathematical abstraction.
David
David, a metric is just a function that measures a distance between 2 points. It’s not a basic physical entity in itself.
Everybody is aware of the basic euclidean metric teached in primary school. In general relativity you use other definitions for the metric function that accounts for the curvature of spacetime.
(2024-01-07, 12:41 PM)sbu Wrote: [ -> ]David, a metric is just a function that measures a distance between 2 points. It’s not a basic physical entity in itself.
Everybody is aware of the basic euclidean metric teached in primary school. In general relativity you use other definitions for the metric function that accounts for the curvature of spacetime.
Yes, and my point is that in the context of talk about block universes etc, this difference is not made clear.
Mathematicians will always try to generalise concepts, but the resulting generalised concepts may be very counter-intuitive to others.
I'd bet 90% of those who refer to the concept of a block universe, have no idea that this thing exists in a generalised mathematical space.
David
(2024-01-07, 05:44 PM)David001 Wrote: [ -> ]Yes, and my point is that in the context of talk about block universes etc, this difference is not made clear.
Mathematicians will always try to generalise concepts, but the resulting generalised concepts may be very counter-intuitive to others.
I'd bet 90% of those who refer to the concept of a block universe, have no idea that this thing exists in a generalised mathematical space.
David
I’m not sure what you mean here. There are solutions to the Einstein field equations that theoretically allows for timetravel.
I guess that’s why it’s an interesting philosophical challenge for people like Raymond Tallis.
I’m not familiar with the idea of “block universes” - does it mean everything in “time” forever back and forever into the future exists at the same time?
(2024-01-07, 08:46 PM)sbu Wrote: [ -> ]I’m not familiar with the idea of “block universes” - does it mean everything in “time” forever back and forever into the future exists at the same time?
Surely you must be. There is the idea that the whole of the past (and maybe the future also) exists as a 4D entity - something a bit like the Akashic records I suppose. See this for example:
https://plus.maths.org/content/what-block-time
The idea mainly excites people because they don't realise that it isn't geometry simply extended to 4 dimensions. Ordinary geometry doesn't require a metric (because it would be an identity matrix). I don't mind mathematicians inventing a new kind of geometry if they find it useful, but I think telling non-mathematicians that space-time is 4-dimensional is actually fairly misleading.
David
(2024-01-07, 10:08 PM)David001 Wrote: [ -> ]Surely you must be. There is the idea that the whole of the past (and maybe the future also) exists as a 4D entity - something a bit like the Akashic records I suppose. See this for example:
https://plus.maths.org/content/what-block-time
The idea mainly excites people because they don't realise that it isn't geometry simply extended to 4 dimensions. Ordinary geometry doesn't require a metric (because it would be an identity matrix). I don't mind mathematicians inventing a new kind of geometry if they find it useful, but I think telling non-mathematicians that space-time is 4-dimensional is actually fairly misleading.
David
I’m well aware about the 4D structure of space time but I would be surprised if physicists really perceives time as an equivalent dimension to the spatial dimensions. In both quantum mechanics and thermodynamics the arrow of time points in one direction.
(2024-01-08, 03:53 PM)sbu Wrote: [ -> ]I’m well aware about the 4D structure of space time but I would be surprised if physicists really perceives time as an equivalent dimension to the spatial dimensions. In both quantum mechanics and thermodynamics the arrow of time points in one direction.
If the essence of time is in some way the necessary existence of change in our reality, then time could be analogous to a physical dimension that by design only allows excursion in one direction. This design of reality being anthropically necessitated by the fact that we couldn't exist otherwise.
(2024-01-08, 08:59 PM)nbtruthman Wrote: [ -> ]If the essence of time is in some way the necessary existence of change in our reality, then time could be analogous to a physical dimension that by design only allows excursion in one direction. This design of reality being anthropically necessitated by the fact that we couldn't exist otherwise.
Intuitively I think it must be in this way. (I’m sure Einstein privately must have thought the same 😂)
(2024-01-07, 10:08 PM)David001 Wrote: [ -> ]Surely you must be. There is the idea that the whole of the past (and maybe the future also) exists as a 4D entity - something a bit like the Akashic records I suppose. See this for example:
https://plus.maths.org/content/what-block-time
The idea mainly excites people because they don't realise that it isn't geometry simply extended to 4 dimensions. Ordinary geometry doesn't require a metric (because it would be an identity matrix). I don't mind mathematicians inventing a new kind of geometry if they find it useful, but I think telling non-mathematicians that space-time is 4-dimensional is actually fairly misleading.
David
I finally understand what you're saying. Here's the Schwarzschild metric, which is a solution for the gravitational field around stars, with the time component in bold. It bears the opposite sign compared to the almost identical radial component (the star is modeled as a sphere). So indeed, thinking of 4D spacetime as a simple generalization of 3D space can be somewhat misleading.
Schwarzschild metric