Space-time is a single entity. Space does not flow.
How can time flow?
(1) "flow" is a word in the English language and has no direct relationship to physics. You need to be more qualitative/mathematical in your description of what it is that each does or does not do.
(2) why would one of the parts of a composite be necessarily constrained by the other part?
Space time really is a single entity, but that doesn't mean that time is not different from space. It is.
A car is a single entity. A car tire does not open and close. How can a car door open and close?
However, although your argument is faulty, in Minkowski's standard "block universe" interpretation time does not flow. Point particles are static lines in a 4D spacetime rather than points that move in 3D space as time flows.
I believe it's intended to be a metaphor. Some people may perhaps take the metaphor too literally :-(.
It may be more neutral to say that time progresses, but I don't actually recall seeing anyone write that way. Common usage, for better or worse, seems to use the verb "flow" to describe the same concept as I mean when I say "progressing".
Actually, space-time is a single invariant entity. ( I didn’t mention it earlier because I thought it was implied).
So, your car analogy is a total flop (it’s more for misleading than informing).
Now our car has two parts both of which are invariant. So, if space is invariant why does time change ( in day-today life, leave alone mathematical constructs like minskowiski model of space-time).
why does time 'progress' when space does not in our day today life.
You ask why do we have a psychological feeling of flowing time and not of flowing space? It's because we remember past and not the future, which ultimately comes from the second law of thermodynamics.
The car is a single invariant entity also (the car is a car whether it is moving or at rest). So I don't see in what way the analogy is either a flop or misleading.
The point is that the analogy illustrates a logical error in your original proposal. Your original proposal goes like this:
T is part of ST
S is also part of ST
S does not F
Therefore T does not F
This reasoning is clearly fallacious, as the example with the car shows. The fact that spacetime is invariant is irrelevant to the logical error you are making in the OP. You are making a simple logical error by asserting that something which applies to any one part of a whole must also apply to each part of the whole.
Do you mean: If I construct a coordinate system where 'I' remain at the same spatial coordinates along my entire worldline, then why does the spacetime coordinates of 'me' only change in the time component, and not the spatial components? This is almost tautological...
Maybe your question is how can we tell which is the time component, when starting at some arbitrary point in spacetime with a given metric? (I was asking this same question in another thread recently). We can always find which is the time component, either by using beams of light, or by using matter (assuming no tachyons). If you have a universe where you have 'empty' spacetime, you might have a problem. But since that is fairly trivial, it seems that in relativity, we always assume we can use a couple of beams of light to determine which component is the time component.
You have skipped this part:
Now our car has two parts both of which are invariant.
Can you give me an example (from physics or physical world) of a whole that consists of two parts. One part varies and the other does not. Still, the system as a whole is invariant?
The question is about "flowing", not invariance.
Furthermore, your fallacious argument was not that spacetime (the whole) does not flow and therefore time (a part) can not flow. Your argument was that space (a part) does not flow and therefore time (a different part) doesn't flow. The argument you are trying to present now has a different form.
If you would like to scrap your previous argument about time flowing and make a new one then we can certainly discuss that.
I think there is some misunderstanding
My original post was,
Space-time is a single entity. Space does not flow.
How can time flow?
It is implied here that space-time is invariant. If invariance is implied, then both the questions
1. space-time (the whole) does not flow, how can time (a part) flow?
2. space (a part) does not flow, how can time (a different part) flow?
The first thing you have to do is define exactly what you mean by "flow" and then how you propose to show how you would measure the flow of spacetime or space to demonstrate that they do not flow.
I think a better way to look at it is that the spacetime interval (dS^2) between two events is invariant, ie dS^2 = dR^2 - dT^2. The time interval (dT^2) between two events is not invariant and the spatial interval (dR^2) between two events is also not invariant.
If you define "not flowing" as invariant, then by your definition, spacetime does not flow, but time flows and space flows. The reason the spacetime interval is invariant, while its components are not, is because the changes in one component are compensated by changes in other components.
Take an ideal gas system. The temperature of the system is related to the volume and the pressure by T = PV. It is possible to change the two parts (P and V) while keeping the temperature of the system constant. We can also change the temperature and the volume while keeping the pressure constant and so on.
An electrical circuit has similar properties. The voltage of the system is related to the current and resistance by V+IR and it is possible to keep the current constant while varying the current (I) and the resistance (R). It is also possible to keep the current of the system constant while varying the resistance and the voltage and so on.
No, they don't follow. Invariance and flow have nothing to do with each other. If something represents a flow in all coordinate systems then it is an invariant flow. Similarly, if a quantity represents a flow in one reference frame, but not a flow in another reference frame then it is a variant flow. Both are possible.
In my opinion, if a covariant quantity describes a flow then it would be an "invariant flow". An example would be the four-current. On the other hand, if a non-covariant quantity describes a flow then it would be a "variant flow". An example would be the standard three-current.
What makes you think space doesnt not flow in the exact same sense as time. To your point it is a "single entity". the "flow" is c. And it applies equally to length & time.
I don't get what you mean here and it doesn't make sense to me. Can you expound on this a bit?
Sure, consider simultaneity. the distance between two points in space is dependent on the comparative motion to those points, and that distance would change as the comparative speed changes. This is the "flow". At rest with the "two points" the "flow is 100%" , at near c there is much less "flow" to distance.
So "flow" here is pretty much synonymous with contraction/dilation.
Surely "flow" of time wasn't referring to an accumulation of physical happenings, ala "time-line" / aging.
Practically speaking, length and time "flow" at c.
It still seems to me that you are just making up your own definition of "flow". It's not a terrible one, but I've not seen it before.
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