Question regarding determinism

[Gothican]

Hello there!

I've been reading Brian Greene's book, 'The Fabric of the Cosmos', and I've stumbled upon a troublesome statement regarding determinism:
In the chapter about Einstein's conception of time, he discusses the determinism of spacetime and comes to the following conclusion; Imagine time-space as a loaf of bread, and the present time of each man in different places and velocities in space (relative to earth) as slices of the bread cut in different angles, (when the only restriction comes from the speed limit set by light, which translates into a limit on the rotational angle of 45 degrees).
Imagine the spacetime loaf sliced up into many various presents of observers situated in different distances from Earth (zero relative velocity). “Now, the collection of all these now-slices fills out a substantial region of the spacetime loaf. In fact, if space is infinite – if now-slices extended infinitely far – then the rotated now-slices can be centered arbitrarily far away, and hence their union sweeps through every point in the spacetime loaf.” -Brian Greene
But here I noticed a paradox, which is pretty disturbing – if there is a restriction on the slicing of the spacetime loaf (a 45 degree limit), then it is logically impossible for all the now-slices to “sweep through every point in the loaf”!
If Brian Greene is correct, then all of spacetime is determined before we actually “get there”. Is this correct?

Could anyone please explain to me this statement of his?

Thanks in advance,
Gothican.

 

[tiny-tim]

Welcome to PF!

Hi Gothican! Welcome to PF!

I think Greene is saying that, if you start at any spacetime point in the loaf, you can always find a slice which passes through that point …

where that slice cuts the "x-axis" is where a stationary observer would say that that spacetime point is in the present.

But it's not in our present, so it's not pre-determined for us.

(but i don't see what difference the 45º makes )

 

[Naty1]

Greene also points out : "Does Elvis exist right now? No...(Elvis) is not on my current time slice...not on my "current" list...(he) does not currently exist...reality embraces the past, present,future equally and the flow (of time) we envision ...is illusory..." (page 132) ?

Well,that IS Einstein's view, and that of physics in general...equations don't distinguish between past present and future...Greene also discusses how entropy affects the arrow of time...in about an other 30 pages or so...and all in all it requires a few readings to sort out the different perspectives...but I, for one, was still left with more questions than answers.

Wikipedia says:

...but defining time in a non-controversial manner applicable to all fields of study has consistently eluded the greatest scholars.

http://en.wikipedia.org/wiki/Time

So don't be surprised if you are not entirely comfortable with descriptions from Greene... nobody REALLY understands what time is...

But his book is a favorite of mine...

 

[matheinste]

Hello all.

I know the nature of time is the subject of much philosophical discussion but is it not the fact that for SR a working defintion is that time is what a clock measures.

Matheinste.

 

[Fredrik]

But here I noticed a paradox, which is pretty disturbing – if there is a restriction on the slicing of the spacetime loaf (a 45 degree limit), then it is logically impossible for all the now-slices to “sweep through every point in the loaf”!

I don't see how you came to that conclusion, but I can tell you that it's wrong.

If Brian Greene is correct, then all of spacetime is determined before we actually “get there”. Is this correct?

Yes, that's how special (and general) relativity describes spacetime, as a 4-dimensional "thing". However, that doesn't imply that what happens in spacetime is deterministic. The determinism in special relativistic classical mechanics doesn't really have anything to do with the "slicing" of spacetime into "slices" that different observers think of as "now". The determinism comes from the special relativistic version of Newton's second law, which implies that if you know the position and velocity of a particle at one time (and the force at all times), you can calculate the position at all times.

I know the nature of time is the subject of much philosophical discussion but is it not the fact that for SR a working defintion is that time is what a clock measures.

That's not enough. You need that operational definition and a mathematical definition. The operational definition should be thought of as a postulate that enables us to interpret mathematical calculations as predictions about the results of experiments. SR isn't defined by Einstein's postulates, or by the mathematics of Minkowski space. It's defined by the operational "definitions" that describe the connection between the mathematical model (Minkowski space) and the results of experiments. The operational definitions are the true postulates of the theory.

 

[Naty1]

Fredrik posts:

Yes, that's how special (and general) relativity describes spacetime, as a 4-dimensional "thing". However, that doesn't imply that what happens in spacetime is deterministic.

Insightful! Thanks...
a great way to interpret that equations don't distinguish between past ,present and future.

 

[Gothican]

I think that Fredrick managed to fully answer my question. thanks a lot!

(but i don't see what difference the 45º makes )

for this you should check out Wikipedia regarding light cones:
http://en.wikipedia.org/wiki/Light_cone"
and the Lorentz transformation for further reading:
http://en.wikipedia.org/wiki/Lorentz_transformation"