Modes of Time

[Magic Man]

Fair enough. I believe you - you have trouble imagining infinite things or nothings. Do you believe me - that I have no trouble with "infinite", but can't do "finite"? I figure we are each the ultimate authorities on the workings of our own minds.

I'm not trying to tell you what you think or don't think. I'm just saying you're weird.

 

[Alceste]

I'm not trying to tell you what you think or don't think. I'm just saying you're weird.

No way - I'm normal. It's all the rest of you who are weird.

 

[themadhair]

Calculate phenomena.....like what?

Are you being serious? When experiments are performed to test GR what do you think they studying? The phenomena of light and matter and their respective motions. What else do you think those experiments do???

A metric of spacetime.

A metric describing the phenomena of light and matter rather. Because, and correct me if I am wrong here, but what experiment done to verify this metric didn’t observe phenomena? None?

And it's not flat no matter what coordinate system you choose to represent it in.

I never claimed it wasn’t Mr Spinkles.

Its curvature is specified by the spacetime metric tensor, g which essentially gives us rules for calculating distances and so forth between events A and B, which are points in spacetime by definition.

Defining it so doesn’t make it so. Especially when the experimental evidence to hand is testing phenomena within spacetime.

Now, you can argue that, actually, there is some higher space that is the "real" spacetime, and it is indeed flat....

That’s not what I’m arguing. It would be an example illustrating the difference between a metric measuring spacetime and a metric measuring the geometry of phenomena within that spacetime.

but if it is above and beyond the 3 spatial and 1 time coordinate physicists know and love, and we can't measure it, its very existence is mere speculation, much less its flatness vs. its curvature.

Last I checked the 3+1 spacetime hasn’t been measured either. Phenomena within it have been measured, but not the spacetime itself.

Meanwhile, we do need words to describe the 4D space we can actually measure and that word is "spacetime" and it is a curved space.

If you are doing this then you are defining spacetime to be the geometrical set in which light and matter move through. Fair enough but that is different that defining spacetime to be the points (t,x,y,z) and then claiming it is curved on the basis of observing and measuring phenomena within that set.

No no, the metric metric in tensor form is an abstract object, just like a vector in its abstract form, it is its own, independent thing and unaffected no matter what coordinate system you choose.

Exactly which part of the following do you disagree with?:
Different coordinate systems give different metrics though, but these metrics should be [/u]isomorphic to each other. You want to disagree in this point with then fine – but you will be disagreeing with a well known fact of metric spaces.

Like a vector, only its representation changes when you express it explicitly in terms of a chosen coordinate system.

That’s what isomorphic means here….

The abstract metric tells you the curvature of space,

Or rather the curvature of the phenomena’s geometry.

However, you could say the same thing about light itself.
…
So you could say there really is no such thing as the EM field, and therefore no light, it is all just charges interacting with each other, and the mathematics of the EM field is just a trick to capture this interaction.

This analogy isn’t really capturing what is going on here. I don’t have a problem that the EM field exists, and the equations represent the EM interactions through that field, etc. – I don’t buy the next step which is to equate the EM field with spacetime. That’s the step that I don’t as being justified – particularly when spacetime is previously defined in manner independent of the phenomena within it being measured.

But one picture is useful and predictive and the other is not.

This isn’t the case. None of the predictions you can make with GR require extrapolating spacetime further than is justifiable. Not even gravity waves.

The idea that the set of points (t,x,y,z) is the spacetime of the phenomena represented by the metrics seems intuitive – but what evidence is there really that this is so? Galilean relativity was intuitive too until GR came along.

 

[Alceste]

This analogy isn’t really capturing what is going on here. I don’t have a problem that the EM field exists, and the equations represent the EM interactions through that field, etc. – I don’t buy the next step which is to equate the EM field with spacetime.

LOL - you mean this is all just a semantic disagreement? Wow!

 

[Mr Spinkles]

Are you being serious? When experiments are performed to test GR what do you think they studying? The phenomena of light and matter and their respective motions. What else do you think those experiments do???

Okay, their respective motions.....through what, and what are the coordinates used to measure this?

If you are doing this then you are defining spacetime to be the geometrical set in which light and matter move through. Fair enough but that is different that defining spacetime to be the points (t,x,y,z) ...

The points (t,x,y,z) is the definition of spacetime. This must be the source of our mutual confusion. The "spacetime interval" for example is defined in terms of t,x,y,z.

 

[themadhair]

Okay, their respective motions.....through what, and what are the coordinates used to measure this?

And I thought the disproof of the ether had been done ; ). What the medium is doesn’t matter since the metrics are not measuring them – they are measuring phenomena and not the medium. I don’t understand your question of what the coordinates are – this is relativity after all. You can use almost any coordinate system and it will give the same result (up to isomorphism).

The points (t,x,y,z) is the definition of spacetime.

And this isn’t what the metrics are measuring. This is defining the conclusion in the absence of evidence for that conclusion.

LOL - you mean this is all just a semantic disagreement? Wow!

I think claiming that ‘spacetime’ is equivalent to the geometry of the phenomenon we have constructed the equations of GR to model is pulling a fast one. It is a leap that has been made with no evidence to justify it, however intuitive it seems.

 

[ManTimeForgot]

Ok. Nerds pay attention. As a mediator between the world of Nerd and People who can't think in 4 different ways at once I will show you what all the people here are actually asking for when they want an explanation of "what Spacetime is" & that explanation should not ever contain "math" or "abstract concepts" as a general rule.

Spacetime boils down to just a different way of looking at the world. In practice it means you think of time as being like spatial dimensions (length, width, and depth): having a range/set of possible values. It means that in order for the universe to "figure out" how things are going to happen you have to consider Time as having a "range of possible values" like a spatial dimension (with the past going into the future and vice versa; don't think too hard on that it will hurt your brain).

MTF

 

[Mr Spinkles]

The points (t,x,y,z) is the definition of spacetime.

And this isn’t what the metrics are measuring.

The metric is a measure of curvature. The curvature of (t,x,y,z). Which is "spacetime" by definition.

It is true that to measure any point in space(time) you have to put something physical at that point and measure it. (Is this roughly what you mean when you say, "we aren't measuring 'spacetime', we are measuring 'the phenomenon'"?) This is not a new difficulty for curved spacetime or even for regular old flat 3D space, in order to measure that you have to do the same thing. The spacetime defined by physicists IS the one that we can measure (at least indirectly) by definition. If you have a different definition of "spacetime" that cannot be measured by measuring "phenomena", then fair enough, but that's a separate thing from the standard definition.

(And sorry for not getting back to you for a while.)

 

[Mr Spinkles]

And I thought the disproof of the ether had been done ; ). What the medium is doesn’t matter since the metrics are not measuring them – they are measuring phenomena and not the medium. I don’t understand your question of what the coordinates are – this is relativity after all. You can use almost any coordinate system and it will give the same result (up to isomorphism).

Well, yes and no...I should have said "dimensions" instead of coordinates. Of course I am not talking about an ether or a medium. What I was driving at is this: your coordinates must be reducible to physical measurements that can actually be carried out, using 4 dimensions--3 spatial and 1 temporal. That is "spacetime" by definition. The 3 spatial dimensions are "space" by definition. Lengths in space are determined by the metric, which (as you know) depends on the physical details of the system under consideration, not on our choice of coordinate system. A curved metric implies curved space, by definition, no matter what particular coordinate axes you choose.

And again, yes technically we measure a "phenomenon" (like the time and space coordinates of an event, such as a photon from a laser arriving at a mirror). We infer things about time and space by measuring such phenomena. As I said above, this is not a new difficulty introduced by curved space. Even for flat Euclidean space, I could say, actually, we never really established it was flat, since we've never measured it. All this time, we've only measured "phenomena" using rulers and protractors. It seems that according to your definition, "space" (whether flat or otherwise) is immeasurable. We can set this eternally immeasurable "space" and all speculations about it aside, forever, since no measurement could resolve any disputes about it. Let's talk about things we can actually measure.....like the conventional definition of "space", which is *defined* by things we can actually measure ("phenomena").

 

[themadhair]

The points (t,x,y,z) is the definition of spacetime.

Let's talk about things we can actually measure.....like the conventional definition of "space", which is *defined* by things we can actually measure ("phenomena").

Please tell me you can see the problem with the above two comments, and why they are not consistent?

Even for flat Euclidean space, I could say, actually, we never really established it was flat, since we've never measured it. All this time, we've only measured "phenomena" using rulers and protractors. It seems that according to your definition, "space" (whether flat or otherwise) is immeasurable.

I understand that, but I’m arguing this on the basis of the definition of spacetime that you provided. What I am doing is pointing out that the equivocation being made with the geometry of phenomena (as measured by the metrics) and the geometry of spacetime hasn’t been justified beyond merely asserting it.

If you have a different definition of "spacetime" that cannot be measured by measuring "phenomena", then fair enough, but that's a separate thing from the standard definition.

You defined space time as the points (t,x,y,z). How can you make the claim that the geometry of phenomena within that spacetime have the same geometry of that spacetime? That seems to be mere assertion to me. I agree with the definition you provided, but it is you who is adding more conditions to that definition here.

Had a bit of RF sabbatical, so apologies for the delay.