A thought about visualizing space-time

[InquiringMind]

TL;DR

A thought about visualizing space-time.

I'm having difficulty getting my head around space-time, especially since it is not visible. I was wondering if it could be visualized as the universe being a liquid, all the objects in the universe displacing this liquid, and gravity being the pressure of the displaced liquid pushing back against the displacing object. Is that at all a reasonable analogy?

 

[phinds]

TL;DR Summary: A thought about visualizing time-space

I'm having difficulty getting my head around time-space, especially since it is not visible. I was wondering if it could be visualized as the universe being a liquid, all the objects in the universe displacing this liquid, and gravity being the pressure of the displaced liquid pushing back against the displacing object. Is that at all reasonable analogy?

No. Space-time is geometry, nothing more. It is not like a rubber sheet or a fluid or any other material thing. It is the geometrical construct in which things happen.

 

[renormalize]

Is that at all reasonable analogy?

Your idea is a variation of Le Sage's theory:
https://en.wikipedia.org/wiki/Le_Sage's_theory_of_gravitation
This approach to gravity is considered to be nonviable.

 

[Ibix]

You can draw helpful maps of spacetime in particular circumstances - Minkowski diagrams for flat spacetime, Kruskal diagrams for Schwarzschild spacetime, Penrose (aka conformal) diagrams for many symmetric spacetimes. There is no single visualisation, though, because spacetime is just the rules of geometry and they depend on the circumstances.

Note that any visualisation that neglects the curvature in timelike directions (including the infamous rubber sheet and, I'm afraid, the idea in the OP) is hopelessly misleading. It gives one a sense that one understands, but it illustrates the curvature of spatial planes only. Curvature in spatial planes is the cause of the difference between Newtonian and relativistic gravity (which is so tiny it took us 200-odd years to make precise enough measurements to notice), but is not the cause of gravity itself. That's all about the time-time component of the Einstein tensor.

 

[javisot]

TL;DR Summary: A thought about visualizing space-time.

I'm having difficulty getting my head around space-time, especially since it is not visible. I was wondering if it could be visualized as the universe being a liquid, all the objects in the universe displacing this liquid, and gravity being the pressure of the displaced liquid pushing back against the displacing object. Is that at all a reasonable analogy?

Some physicists use the analogy of a fluid, specifically a waterfall, to explain certain aspects of black holes. For example, Susskind in this video at first

But it's an analogy, not reality. Furthermore, it's an analogy used in the context of quantum gravity, not classical physics.

 

[Ibix]

But it's an analogy, not reality.

Just to add, it's also pretty specific to modelling gravity in a very narrow range of circumstances. I don't see how you can understand cosmological solutions with this analogy, and I'm not even sure black hole interiors make sense in those terms.

 

[PeroK]

TL;DR Summary: A thought about visualizing space-time.

I'm having difficulty getting my head around space-time, especially since it is not visible.

This is why you need mathematics. Roger Bacon (1220-1292) knew this 800 years ago!

Whoever then has the effrontery to study physics while neglecting mathematics should know from the start that he will never make his entry through the portals of wisdom.

 

[javisot]

Just to add, it's also pretty specific to modelling gravity in a very narrow range of circumstances. I don't see how you can understand cosmological solutions with this analogy, and I'm not even sure black hole interiors make sense in those terms.

Totally agree. For example, in the video we see that Susskind uses the analogy of the waterfall to describe what happens up to the edge of the waterfall (the event horizon), but the analogy ends there.

 

[Dale]

I think that the river analogy only works for Schwarzschild and Kerr spacetimes. Nothing else.

 

[jackjack2025]

This is why you need mathematics. Roger Bacon (1220-1292) knew this 800 years ago!

Whoever then has the effrontery to study physics while neglecting mathematics should know from the start that he will never make his entry through the portals of wisdom.

"effrontery" :)

OP, agree about the comments on maths above. But is it really not visible? I can see the regular 3 dimensions, and I can also see time passing, so 4 dimensions, and I can feel hot or cold, so 5 dimensions, I can see a spectrum of colours, so 6 dimensions, and so on. Not suggesting these are what everyone would consider dimensions, but we make a mathematical model. Which part of space-time is hard to visualise?

 

[PeroK]

Which part of space-time is hard to visualise?

Its four-dimensionality.

PS in fact, its curvilinear, non-Euclidean four-dimensionality.

 

[Ibix]

I can see the regular 3 dimensions, and I can also see time passing, so 4 dimensions,

How would you see if the three dimensions you are calling space are curved? Can you even define what it means for a 3d space to be curved without recourse to maths? And the point about relativity is that you have considerable freedom to pick your definition of space. Which one did you pick and why? Does the spatial slicing you picked allow you to cover all of spacetime, or did the choice you made limit you to some region? How would you answer these questions without maths?

Also note that your choice to think of it as space and time is throwing away some of your gauge freedoms. That's fine if you know what you are doing (the ADM formalism does exactly this), but did you know how you were limiting yourself? And how would you know without maths?

As I said in #4, there are specific visualisations for specific cases. But they are the product of someone who did know the maths.

and I can feel hot or cold, so 5 dimensions, I can see a spectrum of colours, so 6 dimensions,

These are not dimensions in the relevant sense. There is no meaning to rotating your coordinate system so that one of your spatial axes points partially in what you used to call the colour direction. But your spatial axes can point partially in the direction you used to call time - which was the insight that led Minkowski to propose a 4d manifold called spacetime as an implication of Einstein's maths.

 

[PeroK]

"effrontery" :)

That's from a quotation. The best word I ever used on PF was dilettanteism:

 

[jbriggs444]

"effrontery" :)

OP, agree about the comments on maths above. But is it really not visible? I can see the regular 3 dimensions, and I can also see time passing, so 4 dimensions, and I can feel hot or cold, so 5 dimensions, I can see a spectrum of colours, so 6 dimensions, and so on. Not suggesting these are what everyone would consider dimensions, but we make a mathematical model. Which part of space-time is hard to visualise?

Four dimensions of space and time, sure. We could agree to meet at 0 kilometers elevation, 0 degrees latitude, 0 degrees longitude (Null Island) on December 31, 2025. Four coordinate values to specify a position (an event) in space time.

If we try to add temperature as a fifth dimension, how can we arrange to rendezvous at 0 degrees Celsius?

If we try to add "color" as a sixth dimension (ignoring the extra dimensions for us trichromats) then how will we arrange to arrive at an agreed upon place on our color palette?

What units will we use to measure displacements in the red-temperature plane?

 

[Nugatory]

Which part of space-time is hard to visualise?

It's not easy to visualize a pseudo-Riemannian geometry, one in which the square of the distance between two physically separated points can be zero or negative.
It's not easy to visualize a four-dimensional space, one in which four straight lines come together at a point with each one at a right angles to the other three.
It's not easy to visualize intrinsic curvature in a space with more than two dimensions.

Spacetime is four-dimensional, intrinsically curved, and pseudo-Riemannian.

 

[jackjack2025]

That's from a quotation. The best word I ever used on PF was dilettanteism:

Love it

 

[jackjack2025]

Four dimensions of space and time, sure. We could agree to meet at 0 kilometers elevation, 0 degrees latitude, 0 degrees longitude (Null Island) on December 31, 2025. Four coordinate values to specify a position (an event) in space time.

If we try to add temperature as a fifth dimension, how can we arrange to rendezvous at 0 degrees Celsius?

If we try to add "color" as a sixth dimension (ignoring the extra dimensions for us trichromats) then how will we arrange to arrive at an agreed upon place on our color palette?

What units will we use to measure displacements in the red-temperature plane?

Just as we wait until December 31 2025, we also wait until the temperature is 0 degrees Celsius before we meet :)

As mentioned in my earlier post, I was not suggesting these as conventional dimensions, I was asking which part is hard to visualise.

Some good posts talking about the curved nature of space-time.

 

[Dale]

Which part of space-time is hard to visualise?

The curvature tensor has 20 independent components at each event in spacetime.

 

[jbriggs444]

Just as we wait until December 31 2025, we also wait until the temperature is 0 degrees Celsius before we meet :)

But if you wait, it is no longer guaranteed to be December 31 2025.

Perhaps the idea is that we can define have this six dimensional space where each point is a 6-tuple of $(x,y,z,t,\text{Temp},\text{Illumination})$. But our physical universe consists of the four dimensional sub-space where $\text{Temp}$ and $\text{Illumination}$ are the actual temperature and illumination at each 4-event.

But then we could not expect to have a rendezvous at any given 6-event. Only at those 6-events that happen lie within our 4 dimensional sub-space.

 

[jackjack2025]

But if you wait, it is no longer guaranteed to be December 31 2025.

Perhaps the idea is that we can define have this six dimensional space where each point is a 6-tuple of $(x,y,z,t,\text{Temp},\text{Illumination})$. But our physical universe consists of the four dimensional sub-space where $\text{Temp}$ and $\text{Illumination}$ are the actual temperature and illumination at each 4-event.

But then we could not expect to have a rendezvous at any given 6-event. Only at those 6-events that happen lie within our 4 dimensional sub-space.

Great point! But it is time that is the most 'difficult' dimension there isn't it? We could arrange a meeting at specific co-ordinates, with a specified temperature and where the sky is a certain shade of blue. There will be many such events, many shades of blue and varying temperatures. As you say, some events may not lie within the space, but lots will. But fixing a time makes it problematic. Time is a dimension unlike the standard 3 dimensions.

 

[Ibix]

But it is time that is the most 'difficult' dimension there isn't it?

What are you on about? The basic problem is you keep trying to bolt extra concepts onto something where they don't fit. Temperature is not a dimension. Temperature is a measure of average kinetic energy in the rest frame of the matter. As such it's some measure of part of the stress-energy tensor. It's already in the maths. Needlessly adding it again somewhere else does not make an already complicated topic simpler, and nor does it help visualise anything.

 

[Nugatory]

Time is a dimension unlike the standard 3 dimensions.

Yes, it is different. That difference comes from spacetime being pseudo-Riemannian not Riemannian, and appears when we write the metric tensor the way that you are assuming when you use the word “normal”. Color and temperature are different in a different way: they don’t enter into the metric tensor so don’t work as dimensions.

So the bad news is that you are demonstrating Bacon’s point.
The good news is that there’s a surprisingly gentle introduction to the necessary math here. (From the introduction:

GR can be summed up in two statements: 1) Spacetime is a curved pseudo-Riemannian manifold with a metric of signature (−+++). 2) The relationship between matter and the curvature of spacetime is contained in the equation$$R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}=8\pi T_{ \mu\nu}$$​

However, these statements are incomprehensible unless you sling the lingo. So that’s what we shall start doing.​

 

[jackjack2025]

Yes, it is different. That difference comes from spacetime being pseudo-Riemannian not Riemannian, and appears when we write the metric tensor the way that you are assuming when you use the word “normal”. Color and temperature are different in a different way: they don’t enter into the metric tensor so don’t work as dimensions.

So the bad news is that you are demonstrating Bacon’s point.
The good news is that there’s a surprisingly gentle introduction to the necessary math here. (From the introduction:

GR can be summed up in two statements: 1) Spacetime is a curved pseudo-Riemannian manifold with a metric of signature (−+++). 2) The relationship between matter and the curvature of spacetime is contained in the equation​

Rμν − 12Rgμν = 8πGTμν .​

However, these statements are incomprehensible unless you sling the lingo. So that’s what we shall start doing.​

Can I politely disagree without getting banned? :)

The difference does not come from spacetime being pseudo-Riemannian. The difference is fundamental. Riemannian geometry and manifolds are a mathematical construct. Brilliant as they are. Time is unlike the other 3 standard dimensions, which you agree with, I think.

Compared to the standard 3 dimensions of space, time is different, temperature is different, colour is different. And as you said, different in different ways. Agreed.

Perhaps my misunderstanding is that I don't really get why Space-Time is so hard to visualise because of the curvature. What is it about the curvature that doesn't provoke in mind a concept of curved space, and therefore curves we visualise in everyday life?

You can define space-time in the way you have, and that's fine. It isn't the only definition of space-time, but it may be the most accepted.

 

[PeroK]

The difference does not come from spacetime being pseudo-Riemannian. The difference is fundamental. Riemannian geometry and manifolds are a mathematical construct. Brilliant as they are. Time is unlike the other 3 standard dimensions, which you agree with, I think.

That was closer to the theory pre-relativity. That said, it was still clear that time was a dimension, which colour isn't. Much of elementary physics involves the relationship between spatial position and time.

Relativity changed this, as Minkowsi Spacetime unified the three spatial dimensions with the one time dimension into four-dimensional spacetime. Relative velocity, for example, can be modelled as a hyperbolic rotation of spacetime.

Proper time measures the length of the path through spacetime. That was another fundamental insight of relativity.

Compared to the standard 3 dimensions of space, time is different, temperature is different, colour is different. And as you said, different in different ways.

This misses the point of relativity entirely. Note that this is an academically motivated science forum. These things are not a matter of opinion. They are determined by the what mainstream science and mathematics have developed, and we in the 21st Century have inherited. Almost all technological innovation of the modern world is based on these ideas. Ideas that model colour as a dimension are nowhere to be found under this scientific regime.

 

[Dale]

I don't really get why Space-Time is so hard to visualise because of the curvature. What is it about the curvature that doesn't provoke in mind a concept of curved space, and therefore curves we visualise in everyday life?

You don’t get why it is hard to visualize something with 20 components at each event in spacetime?