Visualizing spacetime

One of the insights of the general theory of relativity has been to change our understanding of the relationship between gravity and spacetime. We now say that mass has the effect of distorting spacetime and it is that distortion that causes other objects with mass to move in ways that formerly we used to describe as being acted upon by a gravitational force that could act at a distance.

But visualizing that distortion of spacetime and its effects is not easy because the distortions are not visible in the three spatial dimensions that we can ‘see’ and must be described mathematically.

However, this video makes a valiant effort.

1. John Morales says

Very nice, an explanation suitable for non-experts, and lots of eye candy.

(Right, right… visualisation!)

2. file thirteen says

One thing that I recently found enlightening was realising that the often touted “speed of light” is only tangentially related to light. In fact I surmise that the speed of electromagnetic radiation is wholly dependent on the rate that whatever medium it’s travelling through can transmit it (eg. 225 km/s for visible light through water). The so-called “speed of light” is actually a property (perhaps a fundamental property?) of spacetime itself*, the maximum rate at which that transmits, so electromagnetic radiation’s speed is limited to that when travelling through spacetime. And because we see light being propagated at that speed, we have called that transmission rate the speed of light. I presume nobody has yet provided any theory as to how and why that’s 300,000 km/s though? But anyway, I now think of the phrase “speed of light” as misleading, and I sometimes like to think of spacetime as the three-dimensional equivalent of a line of infinitely small dominoes. 😄

*Take with a grain of salt I guess. I’ve only checked with an AI to confirm that I have the right end of the stick here, but the current generation are somewhat notorious for telling you what you want to hear.

3. John Morales says

4. Rob Grigjanis says

Ho-hum. Just regurgitated pop-sci that’s been around for decades. If someone watched it and learned something new, I’d love to hear it.

file thirteen @2:

225 km/s for visible light through water

That’s 225,000 km/s, as opposed to 300,000 km/s in vacuum. If I go for a run and keep bashing into stuff, I slow down as well.

I presume nobody has yet provided any theory as to how and why that’s 300,000 km/s though?

No. There’s a whole lot of constants which we’ve measured but not ‘explained’.

5. John Morales says

As I understand (heh) it, the [speed of light] is a conceptual limit that happens to apply to the propagation of EM fields. But not just to them.

(A bit like π in math is thought of as having something to do with circles, instead of being all over the place)

If someone watched it and learned something new, I’d love to hear it.

Probably not on Mano’s comment blog, though. 🙂

Pretty obvious the target audience is not people who already know about this stuff, bowlerised by natural language as explanative metaphors may be.

Mano indirectly acknowledged this: “But visualizing that distortion of spacetime and its effects is not easy because the distortions are not visible in the three spatial dimensions that we can ‘see’ and must be described mathematically.

However, this video makes a valiant effort.”

6. John Morales says

[Rob, you allude to ‘c’ originally standing for ‘constant’, no?]

7. Rob Grigjanis says

The ‘c’ is from Latin celer, ‘swift’.

8. file thirteen says

@Rob #4:

If someone watched it and learned something new, I’d love to hear it.

That was the feeling I had as well

That’s 225,000 km/s, as opposed to 300,000 km/s in vacuum.

Lol, whoops! Didn’t mean to say light slowed down a thousand times in water!

If I go for a run and keep bashing into stuff

Do you do this often? 😄

9. Rob Grigjanis says

file thirteen @8:

Do you do this often?

Not any more. Photons don’t have dodgy knees and backs.

10. John Morales says

[Ta, Rob. Mislearned factoid, then. Fixed.]

[F13, air molecules are stuff, but I don’t recommend running in a vacuum]

11. Steve Morrison says

Technically, doesn’t c stand for celeritas, meaning “speed?”

12. Prax says

@file thirteen #2,

The so-called “speed of light” is actually a property (perhaps a fundamental property?) of spacetime itself*, the maximum rate at which that transmits, so electromagnetic radiation’s speed is limited to that when travelling through spacetime.

Pretty much, yes. Any particle with no rest mass travels at c when it’s not interacting with its surroundings, and photons happen to be such. Gravity waves also travel at c. Under the rules of relativistic transformation, c is also the fastest anything can travel without, from certain inertial reference frames, traveling backwards in time. So the existence of tachyons (FTL particles) would threaten our understanding of causality.

And because we see light being propagated at that speed, we have called that transmission rate the speed of light. I presume nobody has yet provided any theory as to how and why that’s 300,000 km/s though?

Currently, it’s simply a matter of definition; the meter is defined as 1/299,792,458 of the distance light travels in a vacuum in one second. Of course, that doesn’t explain why this distance matches the historical meter, which was defined as the length of a particular object, or as a certain multiple of the wavelength of a type of radiation. As Rob says, those facts follow from the particular values of various physical constants, such as Planck’s constant and the mass and charge of the electron. There are, saith Wikipedia, about twenty or thirty of these constants whose values are apparently independent of one another, and yeah, no one knows why they have the values they do. Fine-tuning advocates say “because God wanted it that way,” anthropic principle advocates often say “because we probably wouldn’t be here otherwise,” but that’s about it so far.

13. John Morales says

Gravity waves also travel at c. Under the rules of relativistic transformation, c is also the fastest anything can travel without, from certain inertial reference frames, traveling backwards in time.

More of an asymptote. Would need infinite energy to get there, no?

14. John Morales says

[to clarify, ≤ vs <]

15. file thirteen says

@Prax #12:

Thanks Prax, so c does seem to be a fundamental constant then, just of propagation through spacetime of massless particles instead, and like all the other fundamental constants we’ve defined, it isn’t helpful to ask why it has a particular value. Not a very intelligent question for me to ask in retrospect, but hey, can’t be afraid of asking questions if I want to get answers.

Btw then, since I’m into asking layperson questions, pardon me while I ask another. Although I’m aware evidence has been found that gravity waves exist, I’m aware the carrier particle for gravity (graviton) is only theorised, and if I understand correctly that’s because if it is real it’s too difficult (so far as anyone knows) to detect experimentally. My question is related to that: are we pretty sure the graviton must exist even if we can’t find it (because without a carrier particle how can there be gravity waves propagating through spacetime at c -- I’m presuming gravity waves travel at c too? Or hasn’t that been determined yet?), or are there theories in which there is no graviton, and if so, what do they have instead? Is it that they assert “gravity” is an outdated crutch and I should be thinking about the bending of spacetime rather than gravity?

16. Rob Grigjanis says

f13 @15: Yeah, gravitational waves travel at the speed of light. In regions of space which only differ slightly from a flat spacetime (which is most of space), Einstein’s field equations determine that the ‘bit’ which differs satisfies a wave equation with speed c. Observational data (from LIGO and other tools) backs that up.

As for gravitons: well, we quantize the classical em wave solutions to give massless spin-1 particles called photons. Why can’t we do the same for the classical gravitational wave, which would give us a spin-2 massless particle (the graviton)? Observing gravitons is a huge problem, as you point out. But most physicists accept its existence. It’s just that there’s no complete quantum theory of gravity which includes regions of spacetime with large curvature (e.g. near black holes).

Gravity is the bending of spacetime.

17. Mano Singham says

file thirteen @#15,

In science, when we find a theoretical framework that seems to work well in many contexts, we tend to extend it to other similar contexts even if those have not been well-tested, as long as they have not been seriously contradicted.

So where we once used to think of elementary particles as little blobs of matter, we transitioned to viewing them as quantized fields. That has worked well in describing those entities where we are able to quantize the fields. But with gravity, as Rob says in #16, the problem is that we do not have a theory of quantum gravity, at least not yet. But since we have no reason to think that gravity is an exception to the general pattern of quantized fields, we postulate the existence of the graviton and can even suggest some of its properties such as mass and spin based on general principles.

We could be wrong, of course. It may turn out that gravity is fundamentally different in a way such that there are properties of gravity that are incompatible with the framework of quantum fields. This is why testing of theories plays such fundamental role in science. It enables us to probe the consequences of theories.

18. file thirteen says

Rob & Mano, thanks