# Why Universe Appears to Have Only 1 Time and 3 Spatial Dimensions>

Discussion in 'Physics & Math' started by Spellbound, Sep 15, 2015.

1. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

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Let me ask again, more specifically:
What observable property, geometic or otherwise, does time have?

Also again, I am not denying the relativity's procedures for expressing events in another frame in terms of the variables of your frame. I am saying that in any one inertial frame time is just an index, not a dimension.

Also I think your
"The rate at which time proceeds at any point near a gravitational ..." reflects the false but wide spread idea of "time flowing."

What the gravitational field does is make two identical processes not complete simultaneosly, even if started simultaneously. The one in the weaker field completes before the one in the strong field does. Only processes making changes are observable, not time. Physics concerns observables, not fiction like time, that does not exist.

Last edited: Nov 23, 2015

3. ### danshawenValued Senior Member

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If you were an observer riding on the tips of the Hour, Minute, Second hands of an old style mechanical analog clock, EVERY ONE OF THOSE would register a different passage of time.

Proximity to a particle, an ATOM of bound energy, or a beam of light produces a different rate of time dilation, even if, by the principle of uncertainty, we are unable to measure the difference.

Last edited: Nov 23, 2015

5. ### Q-reeusValued Senior Member

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Might be time to point to a sensible answer to the original thread question: http://space.mit.edu/home/tegmark/dimensions.pdf
Basically, stable things like atoms and humans are impossible or at best hugely unlikely in anything other than (3+1)D spacetime.

7. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

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Yes, most things, even some atoms, do change. How does that fact show time is a dimention? (Instead of an index to the changed states)

Last edited: Nov 23, 2015
8. ### Q-reeusValued Senior Member

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In the formal mathematical sense, putting time on an 'equal footing' with spacial dimensions according to the invariant interval ds^2 = d(ct)^2 - dx^2 of SR and as generalized in GR, works.
I maybe agree with you that it's not really 'on an equal footing' for the obvious reason of a minus sign (which assignment is arbitrary dependent on the convention adopted).
I also think advocates of 'block universe' take the literal dimensionality of time too seriously and push it to imo an absurd conclusion. That the eternal future and all of the past are all existing 'out there' in some fixed 'eternal now'.

9. ### The GodValued Senior Member

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'Time' and philosophy comes into picture.....it is nothing but observing change...Its funny without knowing what the time is...we are able to talk about its contraction and dilation.

Anyways, one very simple question can be asked which is based on time dilation....the relative motion based time dilation gets capped at v = c, the term (Sqrt(1-v2/c2) ) becomes absurd if we take v > c.... This we accept as gospel truth and it may be.

But we do not limit ourselves at Rs (Schwarzchild radius) for Gravitational Time Dilation even though here also, SQRT(1-rs/r) becomes absurd...and we allow BH to form.

Why can we not add one more postulate to SR that..no inertial mass can have a volume less than the volume of Schwarzchilds Sphere....(kind of limiting things at Rs for spherical object). Small maths will yield that it violates SR when an object achives Rs. This will instantly scrap BH, singularity etc and will pave a way for fresh look on many cosmological observations.

Last edited: Nov 23, 2015
10. ### The GodValued Senior Member

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True, time cannot be dimension. But argument in this direction will yield nothing, the entire spacetime philosophy of 4D gets cranked up. We can freely move in 3D space but time movement is only in one direction, why this ? This does not make the system 4D, it makes the system 3D + Special Time Dimension, which looks fixed up. So we might as well call it (3D space + Time) geometry of universe, rather than 4D spacetime. In fact it is that way only, but got convoluted. That great looking statement by minkowski in his moment of glory, should not have been followed up, it should have been (3D + T) representation only..

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12. ### The GodValued Senior Member

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My passing argument is that if we are capped at c, then why not cap at Rs (Schwarzschild Radius)......absurdities called BH singularity will disappear....

13. ### FarsightValued Senior Member

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I agree with that. If you read the Einstein digital papers you can see Einstein referring to a gravitational field as a place where the speed of light varies. Nowadays people tend to say the "coordinate" speed of light varies. But whatever you call it, the moot point is at the event horizon it's zero. And it can't go lower than that.

14. ### QuarkHeadRemedial Math StudentValued Senior Member

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Ya know, you guys are drifting into metaphysics as a result of not being sufficiently precise in your use of terms.

Bottom line first: time is not a dimension. Why?

Suppose we inhabit a universe (n the most general and abstract meaning of the term) that can be modelled as a manifold $M$. Then by definition we will have a continuous invertible and structure preserving mapping from some open region $U \subseteq M$ onto some subset of $R^n$ like $h:U \to R^n$.

Now the value of the integer index $n$ defines the dimension of our manifold.

Then for the point $p \in M$ we will have the image n-tuple $h(p)=(u^1,u^2,...,u^n) \in R^n$.

And for each such image we will have a set of projections of the form $\pi^j:(u^1,u^2,....,u^n) \to u^j \in R$, a real number. Thus the composite $\pi^j \circ h$ defines a function $M \to R$ which is usually referred to as the coordinate $\pi^y \circ h = x^j$

And if for all $U \subseteq M$ that $h(U) \in R^4$ we can call this a spacetime manifold if and only if the following are satisfied......

1) We elect some $x^i = ct$ (where the RHS has the obvious meaning)

2) We insist on a metric such that $ct=x^4$ (say) carries different sign from the remaining coordinate functions.

So to reiterate the bottom line: the "dimension" of the space we inhabit is given by the integer $n$ in $M \to R^n$, and the "coordinates" of a point-event in spacetime are given by the real numbers $x^j$

15. ### SpellboundBannedValued Senior Member

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Length contraction is not an illusion.

16. ### SpellboundBannedValued Senior Member

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You got it!

For the translational kinetic energy, that is the kinetic energy associated with rectilinear motion, of a rigid body with constant mass

, whose center of mass is moving in a straight line with speed

, as seen above is equal to

Kinetic energy

17. ### BdSRegistered Senior Member

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Times "arrow/flow" is a product of all energy/mass moving on all scales in any/all directions in 3d space, not just 1 thing moving "1d"?

When analysing a single object 3d space and 1d time is totally valid, its the objects contribution to times now frame.

Last edited: Nov 23, 2015
18. ### SpellboundBannedValued Senior Member

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In other words danshawen, energy is carried by motion, which, as you say, requires time.

19. ### BdSRegistered Senior Member

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If everything was moving in the opposite direction, time would still be going forward not backwards. If we wanted to get everything to move backwards, we start applying a force in the opposite direction to everything thats moving, when we get to the point where everything stops, does all the mass & energy disappear/null?

20. ### SpellboundBannedValued Senior Member

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Only time ceases to exist at the speed of light in which case motion would become "null".

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22. ### BdSRegistered Senior Member

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Only in the frame of the object moving at c would time appear to cease, but the objects motion is still a contribution to the universes time or change of configuration.

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