Well, I don't buy it ;-) not the description, nor the math :-D the mathemagicians have made a dodo again ;-D
Read you first sentence above again.... lol....
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Read you first sentence above again.... lol....
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Not quite.... what happens if the coordinate system expands?
Let's say that the objects still stay four miles apart, but in space-time, those miles got "bigger".
You know, the way a can of tuna now is 5.5 ounces instead of 6 ounces? They kept the price the "same"...
Inflation deflates expansion.
I told you the concept was hard to grasp, but tonyEE nailed it when he mentioned the "coordinate system".
A coordinate system locates points in spacetime by assigning unique coordinates, to each point.
The 'metric' is a formula that converts the coordinates of two points into distances.
Understanding spacetime requires us to stop regarding 'distance' as an absolute, but as something which is determined by a metric which is changing with time.
It all results from the fact that spacetime is 'non-Euclidean'. An example of non-Euclidean geometry is the Earth's surface. We can use different 'metrics' to measure the distance between two points on the Earth's surface. For example, local mapmaking often ignores the curvature of the Earth, whereas airline flights and distances are based upon a 'Great Circle'. https://aerosavvy.com/great-circle-routes/#:~:text=The shortest route between any two points on,political borders (we don’t fly over certain countries).
Since the Earth is not flat, the "distance" between two points (such as Glasgow and New York) may differ depending on the metric used to measure it.
In a similar way, the "distance" between two points in spacetime depends on the metric used to measure it at a particular time.
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Figuring the "coordinate transformation", ie: your "metric", is fundamental to Physics work.
So what! Just because coordinates don't change doesn't mean squat. It still takes longer to get there. Why? Cuz "distance" is greater. Calling it "time" doesn't change the facts. What's moving? Well 'something' has to be... space or what is contained therin. This is definitely not a hard concept to grasp. They say psychologists enter their vocation firstly to help themselves figure it out.
oh...Sheesh!
just answer the syringe problem and we can call it even.
oh...Sheesh!
just answer the syringe problem and we can call it even.
The movement you need is on your shoulder (Nah, nah nah, nah nah, nah nah, nah nah). 😀
How can you measure that distance is "greater", or lesser, when the coordinate system, ie: the yardstick, changes accordingly so that four miles will still be for miles... whether the miles are shorter or longer?.
And it will still take you the SAME amount of time to get from one to another since you would still be doing the same velocity in your coordinate system.. ie: if you started at 400 mph, you would still be doing 400 mph. You would NO WAY of knowing that your definition of "mile" has changed. NONE.
You would need an independent (separate) coordinate system, and the concomitant transformation matrices, which MIGHT not be constant, to measure the change.
See? The point is that the means you use to measure is what's changing. That's the whole point of the claim. Your measurement does not change, your life experience and your world view do NOT change. Your own size is also changing, but you are not aware of it. You can not measure the change.
OK, Let's do a thought experiment. (*)
Say you have two objects, one in New York and another in Baltimore. You measure the shortest distance between them, on the surface of the Earth. For all intents and purposes that's a geodesic and because of the short distance (not much curvature) close to a straight line in x,y,z space dimensions.
Let's think that you only measure stuff with longitude and latitude. That is your coordinate system. Your GPS receiver broke. You do not have a changing altitude ( radius from the center of the Earth ) in your coordinate system. Actually, you have no concept of altitude, it's not in your "world view". ( Back to Flatland ).
Now, raise those two objects, STRAIGHT UP, 400 miles from New York and Baltimore. Their latitude and longitude have not changed, yet the distance between them is greater, even if you decide not to use a geodesic line and just use a straight x.y.x line.
So, from a latitude and longitude coordinate system the space between those two objects did not change, yet in a different coordinate system it got much longer. From your point of view, those objects did not move.
Several thought models of the expansion of the Universe think of an inflating multi-dimensional balloon, with our universe in on its surface and expanding. But because we can only measure on the surface of the balloon, and not see the other dimensions, we can NOT measure the expansion.
Please trust me on this one... or if not, go search for Physics Coordinate Transformation.... as I pointed out earlier, it's fundamental to Western European Empirical Physics.
(*) Have you read Flatland by Edwin Abbott Abbott?
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But the expansion of the universe is confined to a static coordinate state in which the positions of objects do not move relative to each other. However it's not hard to grasp the expansion increasing distance between them. I don't see the difficulty. A converse analogy would be all objects exponentially decreasing in size. My point is regardless what system you use, you don't need to do the math to grasp the concept.
Hmm... that's a contradiction right there.
Look, think a little about the thought experiment I gave you.
In some coordinate systems you can NOT measure change, for a given physical "thing", in others you can. It all hinges on whether the change keeps the coordinate system, metrics, invariant. Meaning that you CAN measure the change.
Riemann geometry.
The only way you can measure our space-time universe is changing size would be to step OUT from it and look at it from without. How are you gonna do that?
I got it all together now
With my very own disco clothes, hey
My shirt's half open to show you my chains
And the spoon fer up my nose
I am really something
That's what you'd probably say
So smoke your little smoke, drink your little drink
While I dance the night away
Now, think about it before you reply... gimme some time to crank up some tunes, I think the amps are warm now...
The disco folks all dressed up
Like they's fit to kill
I walk on in, see 'em there
I'm gonna give them all a thrill
When they see me comin'
They all steps aside
They has a fit while I commit
My social suicide
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I meant the positions of objects do not 'change', rather, relative to each other. Coordinates remain static. This is not difficult to visualize.
That's because you are in a two dimensional world and can not see (or measure or experience) the expansion that is happening in the 3rd dimension.
That was the whole point of my thought experiment....
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