Time is a dimension, but not like space

I would really appreciate if people writing these types of articles first give rigorous and unique definitions of space and time.

Something like (from Wikipedia):

> In the presence of gravity spacetime is described by a curved 4-dimensional manifold for which the tangent space to any point is a 4-dimensional Minkowski space.

Perhaps? A good way to lose 99% of the readers before the end of the first sentence.

Just represent it in a 4x4 multidimensional array that corresponds to the metric tensor.

Yes, that will really pull in the laymen...

Reminds me of the mathematician who was asked how he mentally visualizes a 4 dimensional space.

"I simply imagine an n-dimensional space, and then set n to 4"

>>> After Hilbert was told that a student in his class had dropped mathematics in order to become a poet, he is reported to have said "Good--he did not have enough imagination to become a mathematician"

https://scienceworld.wolfram.com/biography/Hilbert.html

Reminds me of Geoffrey Hinton who, when asked how to imagine a 14-dimensional space, said: “imagine a 3-dimensional space, and say ‘fourteen’ very loudly”

I'm a huge fan of providing laymen explanations. And at some point if you _actually_ want to understand you have to stop using those and pickup and understand the math.

http://therisingsea.org/post/mast30026/

Has a good introduction to space, and the notion of a manifold, and what a Minkowski space is.

Time: a separation between individual events that can be crossed by cause and effect.

Space: a separation between individual events that cannot be crossed by cause and effect.

"Individual event" is meant in the familiar sense, like a "bang" from a gun, or your birthday party.

This is great, can't believe I haven't heard it before.

That's in the article on Minkowski space. It's actually a good summary, with a hyperlink to manifold.

Here's the introduction to the "spacetime" page:

> In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive where and when events occur.

My favourite explanation (which IIRC is in a book by Brian Greene) is that you can think that everything always moves at the speed of light in a 4D spacetime. That way, if you stand still, you're moving only along time, and as you tilt your velocity vector more and more toward the space dimensions you have to travel more slowly along the time dimension. At the limit you are moving at the speed of light along some space axis and technically your time is "frozen".

As per Kant:

Time: inner sense, intuition of continuity, unity

Space: outer sense, intuition of objects

Its a bit more complex but that’s a basic summary from the guy who came up with the “space and time” thing. Read the “Transcendental Aesthetic” in the Critique of Pure Reason for more.

Or as I tell people, kidding on the square, we're trapped in a time machine hurtling us into the future at the rate of one minute every sixty seconds! It is important you say that last bit in a panicked, breathless voice.

My God, that means every three hundred sixty-five days or so, we'll have gone forward a year!

But then it gets weird and the time axis changes scale relative to other elements in space.

Thee is no „Stillstand“, you can’t stand still relative to anything in the universe.

That's a solid burn, suggesting that nobody else came to their party

Hm. That’s a possibility. As I understand it though, an infinitely massive object would not move in space, and would experience time at the absolute rate of one second per second.

Although that sounds theoretically impossible, I would remind you that somehow the opposite seems to be possible (a particle with zero mass that moves through time at a rate of zero seconds per second), despite that not making a lot of sense to a layperson.

Footnote: Talking about time in seconds makes very little sense here because our notion of time is so heavily linked to how light moves through space, but hopefully my point is clear. Maybe someone has a better unit we could use to measure time independently of space?

For an observer, maybe

There is no absolute frame.

Some of the answers at https://physics.stackexchange.com/q/33840 explain why "everything always moves at the speed of light in a 4D spacetime" is a statement that, at best, has no content.

Your point is clear. As far as can wrap my head around those theoretical concepts: An infinitely heavy object can’t move in space because there isn’t any space left to move. I would say that this object would have concentrated all mass in one point, no space left to move. No observer left to measure. I would also say that there can’t be two or more infinite masses at the same time, or they would move (at the speed of c (?) But that would have additional implications on mass and time) to the point between them.

But back to observable reality: let’s say you fall into a dark place where the time stands still and that means you are not moving, from an outside observer you are still moving relative to the space outside your black hole. Let’s say the observer fall on his way to your black hole into another black hole and experience the same phenomenon like you, from a third observers perspective everyone is moving.

Ok, but almost nobody is going to read an article that requires you to work through 21 lectures, 9 tutorials, and 3 assignments first. It'd be great if they did, and it'd be nice to give the link for interested people, but otherwise it is just making the subject inaccessible to almost everyone.