# Determinism & General Relativity: A Physics Primer

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In summary: TL;DR Summary:In summary, my friend believes that space time is a loaf of bread, and that you can slice it to show the future or past. This means all time is predetermined. He says that light stays at a constant speed, which means that the "other parts of the equation" time and mass and space, have to give. He's talking about the "block universe" concept, which you can now Google, since you have the name.
intravenous
TL;DR Summary
My friend believes that space time is a loaf of bread, and that you can slice it to show the future or past. This means all time is predetermined.
I know nothing about physics, to be clear. My friend was saying due to general relativity, the faster you move through space, the slower you move through time. Objects with a heavy mass (like a blackhole) can distort the fabric of space time and being near its gravitational pull means that you experience time slower than a twin back on earth might. He said that light stays at a constant speed, which means that the "other parts of the equation" time and mass and space, have to give. I've tried researching this equation and came up with time dilation, which doesn't sound like the same equation he mentioned.

Anyway, if time is a space loaf and it can be sliced forward or backward, does this mean the future is predetermined from a physics perspective? I'm just trying to understand where he's coming from, any response helps!

He's talking about the "block universe" concept, which you can now Google, since you have the name.

Demystifier, physika, russ_watters and 2 others
intravenous said:
TL;DR Summary: My friend believes that space time is a loaf of bread, and that you can slice it to show the future or past. This means all time is predetermined.

I'm just trying to understand where he's coming from

PeterDonis, topsquark and vanhees71
intravenous said:
This means all time is predetermined.
Next Tuesday is inevitable if that's what you mean by predetermined.

intravenous said:
TL;DR Summary: My friend believes that space time is a loaf of bread, and that you can slice it to show the future or past. This means all time is predetermined.

I'm just trying to understand where he's coming from
Ask him to give you a specific reference for where he got his claimed belief from. Then you can look at that reference yourself and evaluate it independently.

Any deterministic theory of physics implies that the future is completely determined by the state of things now. GR is deterministic and the "block universe" interpretation (which it sounds like your friend is talking about) is one of the more popular ways of describing it. Unfortunately, though, your friend is using a number of pop-sci concepts like "faster through space, slower through time" that are more helpful in making you think you understand the theory than they are in actually understanding it.

The important point to note is that quantum theory is not a deterministic theory and we have not been completely successful in combining quantum theory with general relativity. So there is no unified "physics perspective" on whether the universe is deterministic or not. We would probably lean towards "not", and the existence of deterministic chaos means that even if the universe were to turn out to be fundamentally deterministic it would not be practically possible to predict anything perfectly anyway.

topsquark, jbriggs444 and Dale
intravenous said:
TL;DR Summary: My friend believes that space time is a loaf of bread, and that you can slice it to show the future or past. This means all time is predetermined.

Anyway, if time is a space loaf and it can be sliced forward or backward, does this mean the future is predetermined from a physics perspective?

Yes. But there is no reason to believe spacetime must be like a loaf. That everything is predetermined and there is no free will. Many physicists believe it, many (probably most) don't. The thing is, whether you believe it or not, the physics is the same.

Mister T said:
everything is predetermined and there is no free will
Determinism and free will are not incompatible. Further, free will is not really a physics concept and discussion of it is really off topic in this forum.

vanhees71 and malawi_glenn
intravenous said:
Anyway, if time is a space loaf and it can be sliced forward or backward, does this mean the future is predetermined from a physics perspective? I'm just trying to understand where he's coming from, any response helps!

It seems to me this is all philosophy, unless you can think of an experiment to determine whether the universe is predetermined or not.

Also, of some interest, is the question whether Newtonian physics is deterministic, and if so, in what sense. Or the more general question - is there any theory of physics that can be definitevely regarded as being "non-deterministic".

But Newtonian physics is a good place to start - It's likely you understand Newtonian physics better than General Relativity.

For my personal opinion, which is based on my not-so-great understanding of initial value problems in physics (often called the Cauchy problem), GR may be less deterministic than Newtonian theorem in the sense you can envision situations where you know the initial values of everything at some surface that you think of as "now", as some instant in time, without having a unique solution for all time.

Specifically, see the "Billiard Ball paper", "Billiard balls in wormhole spacetimes with closed timelike curves: Classical theory.", Thorne, et al for an example of such a space-time, which contains a wormhole acting as a time machine.

jbriggs444
pervect said:
Also, of some interest, is the question whether Newtonian physics is deterministic
No. It is not. There are scenarios for which Newton's laws fail to be predictive.

Off the top of my head, one example is a dome on which a puck is free to slide. The dome has a height profile along the lines of ##h = 1-e^{-1/x^2}## for ##x \neq 0## and ##h = 1## for ##x = 1##. The puck is given an initial velocity that is just enough to reach the top and stop. It will arrive in finite time. It can depart at any time in any direction, consistent with the laws of Newtonian physics.

The basic problem here is that we have a function with all of its derivatives equal to zero at a point. But the function is not identically zero. The radius of convergence of its Taylor series is zero. It is not analytic at x=0.

We can write down a differential equation for the motion of a puck on the dome. But the boundary conditions at ##x=0, v=0, t=0## do not suffice to uniquely identify a solution to that differential equation.

There are also nasty situations with the three body problem involving pointlike objects. One of the objects can be ejected to infinity in finite time as I recall. John Baez spoke about this in one of his insight articles about problems with the continuum.

Edit: Failed recollection. It takes five particles.

https://math.ucr.edu/home/baez/continuum.pdf said:
5 or more particles, there are solutions where particles shoot off to infinity in a finite amount of time [79, 94].
You can chase reference 79 above
http://www.ams.org/notices/199505/saari-2.pdf said:
Even the suggestion that our familiar Newtonian inverse square force law might allow such a counter-intuitive behavior is so surprising that it is reasonable to wonder how such an esoteric sounding question was first raised. As we show in this brief survey, Xia’s result resolves a natural, fundamental problem raised by Poincaré and Painlevé about a century ago. The issue is to characterize the nature of “singularities” of n-body systems. Here, a singularity is a “time”value t = t∗ where analytic continuation of the solution fails

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Demystifier and dextercioby
PeterDonis said:
Determinism and free will are not incompatible. Further, free will is not really a physics concept and discussion of it is really off topic in this forum.
This depends very much on what you mean by "free will" which, as you say, is clearly outside the scope of physics. In contrast, I have an argument that establishes that even if QM is taken to exclude determinism, it may well still be true that there is no free will.

PAllen said:
I have an argument that establishes that even if QM is taken to exclude determinism, it may well still be true that there is no free will.
Which would also depend on what you mean by "free will" and would therefore also be outside the scope of physics.

PAllen
intravenous said:
if time is a space loaf and it can be sliced forward or backward, does this mean the future is predetermined from a physics perspective?
This is a philosophical topic, as has been mentioned above. The block universe (the loaf) is an interpretation of time that all events (points in spacetime) have equal ontological status, that the events are not divided into past/present/future or has happened, is happening, and will happen. The relativity-of-simultaneity that comes from Einstein's relativity theory suggests exactly that.
Under the view, there is no 'the future' to be 'predetermined', so the question is ill formed.

Under the contrasting view (presentism), all events are indeed divided into those three categories, in which case there is a preferred frame defined by all the events comprising the present. This view violates relativity, and is thus considered an alternate interpretation.
Under presentism, the question of determinism (I don't know how predeterminism differs) falls to one's choice of quantum mechanics interpretations, some of which are deterministic and some not.

PeterDonis said:
Which would also depend on what you mean by "free will" and would therefore also be outside the scope of physics.
There is a physics definition of free will which applies to, among other things, superdeterminism, a loophole in Bell's theorem where we lack the free will to perform measurements that would demonstrate probabilistic outcomes that are compatible with the principles of both counterfactual definiteness and locality.
They also use this definition of free will in descriptions of various delayed-choice experiments where the choice of what to measure is not free, but determined by the already-collapsed state of the system, thus eliminating the need to describe reverse-causality.

This kind of free will is probably not the kind the philosophers usually talk about.

Halc said:
The relativity-of-simultaneity that comes from Einstein's relativity theory suggests exactly that.
No, it doesn't. What it does suggest is that the three categories you describe, "past", "present", and "future", are not quite the same as they are assumed to be in pre-relativistic physics. The boundaries between these regions in relativity are the light cones, not a "simultaneity surface". And once you realize that, you realize that the arguments that are given for why relativity of simultaneity implies the block universe are not valid.

See this Insights article:

https://www.physicsforums.com/insights/block-universe-refuting-common-argument/

Halc said:
There is a physics definition of free will
The definition you refer to, since it applies to qubits as much as to people, is obviously not a candidate for a physics interpretation of what either ordinary people or philosophers mean by the term "free will", since both ordinary people and philosophers view free will as something that people have but qubits don't.

nasu, vanhees71 and phinds
intravenous said:
TL;DR Summary: My friend believes that space time is a loaf of bread, and that you can slice it
But is it fresh baked and tasty?

It's a 4D loaf of bread, and indeed you can introduce time slices to provide general invariant time parameters (at least locally) :-).

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