# Change without time

It is claimed in The Grand Design that during the early period of inflation when the universe was at the quantum scale, our time dimension behaved like a spatial dimension. But without time, there can be no change, because change is something that occurs over time. Inflation is a change, and hence there would be no way for inflation to occur in the first place, and inflation is necessary in order for the timelike dimension to curl in a way that makes it start acting timelike. In other words, this seems to be a contradiction. Please explain or direct me to a specific explanation.

Dale
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But without time, there can be no change, because change is something that occurs over time.
This is not correct. You can have change wrt time (d/dt) but you can also have change wrt space (d/dx).

That said, The Grand Design is a pop-sci book, not mainstream scientific literature. Physicists writing pop-sci books often make ambiguous statements that try to convey highly technical material in a overly simplified manner.

It is claimed in The Grand Design that during the early period of inflation when the universe was at the quantum scale, our time dimension behaved like a spatial dimension. But without time, there can be no change, because change is something that occurs over time. Inflation is a change, and hence there would be no way for inflation to occur in the first place, and inflation is necessary in order for the timelike dimension to curl in a way that makes it start acting timelike. In other words, this seems to be a contradiction. Please explain or direct me to a specific explanation.

I agree with that: an inflation over distance without the existence of a time dimension appears to imply no change over a time dimension - a "frozen" universe. Thus no physical change (= a change over time) of the universe.
But perhaps they mean something else (if so, what?).

Dale
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Thus no physical change (= a change over time) of the universe.
Simply because you arbitrarily choose to label d/dt as a "physical change" and d/dx as a non-"physical change" does not alter the results of any experiments in the least. According to you Maxwell's equations and the Einstein field equations and QM are highly successful physical theories that are all full of non-"physical changes".

[..]According to you Maxwell's equations and the Einstein field equations and QM are highly successful physical theories that are all full of non-"physical changes".
No. Since Newton* and even before, theories of physics are "mathematical physics": mathematical descriptions that allow to make predictions about observations of physical phenomena.

Note that I followed the OP's formulation in my answer; debating words instead of trying to answer his question is not very helpful.

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Dale
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theories of physics are "mathematical physics": mathematical descriptions that allow to make predictions about observations of physical phenomena.
Most of which involve what you arbitrarily deem non-"physical changes" in the course of making said predictions.

Note that I followed the OP's formulation in my answer; debating words instead of trying to answer his question is not very helpful
The OP's formulation is wrong, as is yours. d/dt is not the only change in physics. Correcting errors is helpful, even if it is not appreciated.

[..] The OP's formulation is wrong, as is yours. [..]
I'm pretty sure that most people will disagree with your formulation which confounds mathematical relationships with physical changes. But instead of entertaining debates about words, do you have any useful answer to the OP's question?

Dale
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I'm pretty sure that most people will disagree with your formulation
I call BS on this. I challenge you to find a mainstream scientific reference that supports the idea that only d/dt can be considered a "physical change" let alone one that supports the claim that most people agree with that idea. I have not come across either type of claim in my studies.

But instead of entertaining debates about words, do you have any useful answer to the OP's question?
Yes, see post 2 where I provided both the correction and a useful answer.

ghwellsjr
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Didn't we just have this conversation less than a month ago?

Yes, we did, starting with post #37 (page 3) on this locked thread:

And I'll repeat my comment from post #82:

Maxwell's equations contain two spatial derivatives, the curl and the divergence, which are vector operators, along with the gradient which calculate changes in vector fields that do not involve time. Wikipedia says the gradient "Measures the rate and direction of change in a scalar field". Maybe you should edit the wikipedia article so the world can be in line with your opinion.​

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Dale
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Didn't we just have this conversation less than a month ago?
Yes, and harrylin was unable to justify his position then either.

DrGreg
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When I was first taught differentiation, many decades ago, I was taught that the symbol "df/dx" could be described in words as "the rate of change of f with respect to x". That was standard terminology then as I believe it still is now.

Even outside the technical language of maths and physics, it's quite normal in everyday speech to talk about, say, the change in temperature between the south and the north, or a change in height between a valley and a hill.

Gentleman, the math is just as irrelevant as the English or the Ukranian. It is simply a language used for describing reality. Let us not become bogged down in differences of arbitrary word definitions. I am seeking a better understanding of the actual process, not a better understanding of the definition of the word we call derivative...so please refrain from such trivial arguments and let us focus on the actual question.

This is not correct. You can have change wrt time (d/dt) but you can also have change wrt space (d/dx).

Ok, fair enough. It is true that change can be measured (mathematically) with respect to any dimension, but your observation leaves much to the imagination with respect to my question.

It seems that you are saying the the inflationary changes of the three spatial dimensions can be measured relative to the fourth dimension. Moreover, the meaning of the fourth dimension changes from being spacelike to timelike with respect to itself.

From an intuitive perspective, the difference between a spacelike and a timelike dimension is that energy is constant relative to the timelike dimension (ie, energy is conserved), whereas energy is non-uniformly distributed throughout the spatial dimensions.

Thus, if the timelike dimension originally behaved like a spacelike dimension, then I assume it is implied that there was no conservation of energy during the initial phase of the big bang...and as the fourth dimension becomes more timelike, this is really just saying that conservation of energy gradually starts to apply.

Yes? No?

Yes, and harrylin was unable to justify his position then either.

Wrong again: I feel no desire to start a dog fight in what should be a polite exchange of opinions. In both this and the other thread a debate about words is totally irrelevant and distracts from the subject at hand - it's a form of trolling.

Harald

When I was first taught differentiation, many decades ago, I was taught that the symbol "df/dx" could be described in words as "the rate of change of f with respect to x". That was standard terminology then as I believe it still is now.
Yes that is rather standard in mathematics, but surely irrelevant for the discussion here.
Even outside the technical language of maths and physics, it's quite normal in everyday speech to talk about, say, the change in temperature between the south and the north, or a change in height between a valley and a hill.
Not that it matters here but I have never heard anyone say such things in everyday speech; evidently I don't meet the people that you meet (nor does the dictionary know of it). :tongue2:

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[..] It seems that you are saying the the inflationary changes of the three spatial dimensions can be measured relative to the fourth dimension. Moreover, the meaning of the fourth dimension changes from being spacelike to timelike with respect to itself.

From an intuitive perspective, the difference between a spacelike and a timelike dimension is that energy is constant relative to the timelike dimension (ie, energy is conserved), whereas energy is non-uniformly distributed throughout the spatial dimensions.

Thus, if the timelike dimension originally behaved like a spacelike dimension, then I assume it is implied that there was no conservation of energy during the initial phase of the big bang...and as the fourth dimension becomes more timelike, this is really just saying that conservation of energy gradually starts to apply.

Yes? No?
My intuition seems to work differently from yours, for how can you think of "originally behaved" and "during", if there was no time to do the "during" in, nor for an "initial phase"?

From an intuitive perspective, the difference between a spacelike and a timelike dimension is that energy is constant relative to the timelike dimension (ie, energy is conserved), whereas energy is non-uniformly distributed throughout the spatial dimensions.

Although superficially it may look like what you say, this differentiation is not correct. Conservation of a physical quatity is expressed in terms of a continuity equation, where time and space enter on a nearly equal footing. The change of the quanity in question involves both space and time in like manner.

$$\frac{\partial \phi_x}{\partial x} + \frac{\partial \phi_y}{\partial y} + \frac{\partial \phi_z}{\partial z} - \frac{\partial \rho}{\partial t} = 0$$

$\rho$ and $\phi$ form a spacetime vector $(\rho, \phi)$.

"Energy conservation" implicitly assumes there is no flow of energy to or from the system evolving over time, automatically precluding changes with repsect to spatial displacement. The complete expression involves momentum terms and changes over space.

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My intuition seems to work differently from yours, for how can you think of "originally behaved" and "during", if there was no time to do the "during" in, nor for an "initial phase"?

These words are simply used in the English language to express relationships between events through the fourth dimension. Whether or not this dimension haves in a timelike or spacelike manner is irrelevant because we have no other word or tense to use, and it would only lead to more confusion if I tried to omit them.

Although superficially it may look like what you say, this differentiation is not correct. Conservation of a physical quatity is expressed in terms of a continuity equation, where time and space enter on a nearly equal footing. The change of the quanity in question involves both space and time in like manner.

$$\frac{\partial \phi_x}{\partial x} + \frac{\partial \phi_y}{\partial y} + \frac{\partial \phi_z}{\partial z} + \frac{\partial \rho}{\partial t} = 0$$

$\rho$ and $\phi$ form a spacetime vector $(\rho, \phi)$.

Ok...I get what you are saying...basically, the scale factor on the time dimension is so much bigger that it creates the appearance of energy being constant over time as particles bounce around in space, but in reality they can also bounce around in time causing the total amount of energy (as measured at any time) to fluctuate some small amount, but its just not as noticeable.

In that case it seems that the difference between these dimensions is that the scale factor on the time dimensions is so much more significant. When it is said that the fourth dimension behaved like a spatial dimension during the early phase of the singularity is this really saying that all four dimensions were treated with equal weighting in the "continuity equation"?

Ok...I get what you are saying...basically, the scale factor on the time dimension is so much bigger that it creates the appearance of energy being constant over time as particles bounce around in space, but in reality they can also bounce around in time causing the total amount of energy (as measured at any time) to fluctuate some small amount, but its just not as noticeable.

Look at it this way. I mark off a particular volume of space. Over time, the amount of energy in this volume will be lumpy. Mark off a region in a busy intersection and it will very lumpy. So the same argument applies to lumpy changes over space as time. I don't know what scaling has to do with it. The phenomena would be the same, in either case.

When it is said that the fourth dimension behaved like a spatial dimension during the early phase of the singularity is this really saying that all four dimensions were treated with equal weighting in the "continuity equation"?

Sorry. I don't know what author claimed this behavior, or why.

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These words are simply used in the English language to express relationships between events through the fourth dimension. Whether or not this dimension haves in a timelike or spacelike manner is irrelevant because we have no other word or tense to use, and it would only lead to more confusion if I tried to omit them.
Then you completely lost me, as you stressed that nothing can happen in a universe without a time-like dimension. Never mind, I'll watch this thread to see if someone can clarify in what way time can behave like a spatial dimension (or, probably more like a spatial dimension than is currently the case). :tongue2:

It is claimed in The Grand Design that during the early period of inflation when the universe was at the quantum scale, our time dimension behaved like a spatial dimension. But without time, there can be no change, because change is something that occurs over time. Inflation is a change, and hence there would be no way for inflation to occur in the first place, and inflation is necessary in order for the timelike dimension to curl in a way that makes it start acting timelike. In other words, this seems to be a contradiction. Please explain or direct me to a specific explanation.

The Grand Design is by Hawking, and I know that Hawking uses the Wick rotation. He calls it "imaginary time." So I think that is what he was talking about. I'm not the one to ask about the meaning of this, perhaps someone else can explain. But I get the impression that the point of the Wick rotation is to get rid of the peculiar qualities of the time dimension so it behaves like the three spatial dimensions.

Dale
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Wrong again: I feel no desire to start a dog fight in what should be a polite exchange of opinions. In both this and the other thread a debate about words is totally irrelevant and distracts from the subject at hand - it's a form of trolling.
Asking someone to provide a mainstream scientific reference for a stated position is hardly trolling and is always acceptable. On this forum when you make non-scientific claims you should expect to have them challenged.

While it is true that this is a semantic debate, the fact is that your definition is not the one used scientifically. You are, however, incorrect that it is distracting from the subject at hand. The OP shares the same mistaken idea as you do, so it is important to teach him the correct scientific definition so that he can better understand and communicate in the future.

Dale
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Let us not become bogged down in differences of arbitrary word definitions. I am seeking a better understanding of the actual process, not a better understanding of the definition of the word we call derivative...so please refrain from such trivial arguments and let us focus on the actual question.
Fair enough, as long as you understand that in physics "change" is not limited only to things that change wrt time.

Moreover, the meaning of the fourth dimension changes from being spacelike to timelike with respect to itself.
I am not sure of this. I know that the FLRW metric does not change from timelike to spacelike nor vice versa, so I don't know what metric Hawking was refering to here. However, my understanding is that the signature is an invariant of the manifold, so I don't think it is possible for a (++++) manifold to evolve into the (-+++) manifold that we see today.

Unfortunately, as is common with pop-sci books, they are sloppy enough that a careful reader can come away with mistaken impressions. Unless someone knows what metric he was refering to then I suspect it is simply a misunderstanding of Hawking's intent.

Thus, if the timelike dimension originally behaved like a spacelike dimension, then I assume it is implied that there was no conservation of energy during the initial phase of the big bang.
Energy is not generally conserved in non-static spacetimes like the FLRW metric. There is a FAQ on the topic in the Cosmology forum:

and another one by Baez:
http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

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Asking someone to provide a mainstream scientific reference for a stated position is hardly trolling and is always acceptable. On this forum when you make non-scientific claims you should expect to have them challenged.

While it is true that this is a semantic debate, the fact is that your definition is not the one used scientifically. You are, however, incorrect that it is distracting from the subject at hand. The OP shares the same mistaken idea as you do, so it is important to teach him the correct scientific definition so that he can better understand and communicate in the future.
That is what is meant with trolling: such non-scientific, semantic allegations as you make don't need challenging as they are off-topic. See also: http://en.wikipedia.org/wiki/Troll_(Internet)

However, my understanding is that the signature is an invariant of the manifold, so I don't think it is possible for a (++++) manifold to evolve into the (-+++) manifold that we see today.

DaleSpam, you may be confusing metric with manifold.

Dale
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DaleSpam, you may be confusing metric with manifold.
That could be. There is a signature for a metric and for a manifold, and I think they are both closely related and both are invariants. It is hard to know without an exact metric to discuss.

Dale
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That is what is meant with trolling: such non-scientific, semantic allegations as you make don't need challenging as they are off-topic. See also: http://en.wikipedia.org/wiki/Troll_(Internet)
You are guilty of perpetuating this line of conversation just as much as I am. You could also stop it simply by ceasing to repeat statements that you know are non-scientific.

Btw, it is absurd to call this off-topic since it is not only part of the OP it is actually the title of the thread. Semantic or not, it is on topic.

spacelike nor vice versa, so I don't know what metric Hawking was refering to here. However, my understanding is that the signature is an invariant of the manifold, so I don't think it is possible for a (++++) manifold to evolve into the (-+++) manifold that we see today.

I think Patrick probably identified what he was talking about here with the Wick rotation. I've never heard of it before, but the Wikipedia description sounds related...

Unless someone knows what metric he was refering to then I suspect it is simply a misunderstanding of Hawking's intent.

To quote Hawking,

"Although Einstein's general theory of relativity unified time and space as space-time and involved a certain mixing of space and time, time was still different from space, and either had a beginning and an end or else went on forever. However, once we add the effects of quantum theory to the theory of relativity, in extreme cases warpage can occur to such a great extent that time behaves like another dimension of space.

In the early universe -- when the universe was small enough to be governed by both general relativity and quantum theory -- there were effectively four dimensions of space and none of time.

That means that when we speak of the beginning of the universe, we are skirting the subtle issue that as we look backward toward the very early universe, time as we know it does not exist! We must accept that our usual ideas of space and time do not apply to the very early universe.

The realization that time can behave like another direction of space means that one can get rid of the problem of time having a beginning, in a similar way in which we got rid of the edge of the world problem. Suppose the beginning of the universe was like the South Pole of the Earth with degrees of latitude plating the role of time. As one moves north, the circles of constant latitude, represening the size of the universe, would expand. The universe would start as a point at the South Pole, but the South Pole is much like any other point. To ask what happened before the beginning of thew universe would become a meaningless question, because there is nothing south of the South pole. In this picture space-time has no boundary -- the same laws of nature hold at the South Pole as in other places. In an analogous manner, when one combines the general theory of relativity with quantum theory, the question of what happened before the beginning of the universe is rendered meaningless. This idea that histories should be closed surfaces without boundary is called the no-boundary condition.

The realization that time behaves like space presents a new alternative. IT removes the age-old objection to the universe having a beginning, but also means that the beginning of the universe was governed by the laws of science and doesn't need to be set in motion by some god." (page 134)

Energy is not generally conserved in non-static spacetimes like the FLRW metric. There is a FAQ on the topic in the Cosmology forum:

and another one by Baez:
http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

Hawking seems to disagree with this as well...

"If the total energy of the universe must always remain zero, and it costs energy to create a body, how can a whole universe be created from nothing? Because gravity is attractive, gravitational energy is negative: one has to do work to separate a gravitationally bound system, such as the earth and moon. This negative energy can balance the positive energy needed to create matter...bodies such as stars or black holes cannot just appear out of nothing. But a whole universe can.

Because gravity shapes space and time, it allows space-time to be locally stable but globally unstable. On the scale of the entire universe, the positive energy of the matter can be balanced by the negative gravitational energy, and so there is no restriction on the creation of whole universes. Because there is a law like gravity, the universe can and will create itself from nothing" (p180)

I think Patrick probably identified what he was talking about here with the Wick rotation. I've never heard of it before, but the Wikipedia description sounds related...

To quote Hawking,

"Although Einstein's general theory of relativity unified time and space as space-time and involved a certain mixing of space and time, time was still different from space, and either had a beginning and an end or else went on forever. However, once we add the effects of quantum theory to the theory of relativity, in extreme cases warpage can occur to such a great extent that time behaves like another dimension of space.

In the early universe -- when the universe was small enough to be governed by both general relativity and quantum theory -- there were effectively four dimensions of space and none of time.

That means that when we speak of the beginning of the universe, we are skirting the subtle issue that as we look backward toward the very early universe, time as we know it does not exist! We must accept that our usual ideas of space and time do not apply to the very early universe.

The realization that time can behave like another direction of space means that one can get rid of the problem of time having a beginning, in a similar way in which we got rid of the edge of the world problem. Suppose the beginning of the universe was like the South Pole of the Earth with degrees of latitude plating the role of time. As one moves north, the circles of constant latitude, represening the size of the universe, would expand. The universe would start as a point at the South Pole, but the South Pole is much like any other point. To ask what happened before the beginning of thew universe would become a meaningless question, because there is nothing south of the South pole. In this picture space-time has no boundary -- the same laws of nature hold at the South Pole as in other places. In an analogous manner, when one combines the general theory of relativity with quantum theory, the question of what happened before the beginning of the universe is rendered meaningless. This idea that histories should be closed surfaces without boundary is called the no-boundary condition.

The realization that time behaves like space presents a new alternative. IT removes the age-old objection to the universe having a beginning, but also means that the beginning of the universe was governed by the laws of science and doesn't need to be set in motion by some god." (page 134) [..]

Thanks!
Hmm.. that sounds like pure nonsense to me (and apparently incited by religious considerations); but at least it clarifies your original statement, for he does not really claim that there was no time at all.

But "nothing south of the South pole" looks a bit misleading to me; instead, does by any chance Hawkins also speculate what happens if you go around the "South Pole" of spatial time, or why this cannot be done if indeed time behaves like space at that "South Pole"?

Thanks!
Hmm.. that sounds like pure nonsense to me (and apparently incited by religious considerations); but at least it clarifies your original statement, for he does not really claim that there was no time at all.

But "nothing south of the South pole" looks a bit misleading to me; instead, does by any chance Hawkins also speculate what happens if you go around the "South Pole" of spatial time, or why this cannot be done if indeed time behaves like space at that "South Pole"?

Well I don't know, but I did attend Prof Hawking's lecture and the impression I got is that it has to do with uncertainty. Traditionally the view is -- a view I never understood, by the way -- is that there is uncertainty in the spatial dimensions but not the time dimension. To me this seems to be a matter of convenience: you have to have something certain to start with, otherwise the math becomes complicated and possibly ill-defined.

At any rate, if you consider time as also uncertain -- if you like, consider it a spatial dimension -- then there is no precise instant of the birth of the Universe, and this could make a difference. There is then no unique South Pole, no time zero, rather an infinity of starting points. That seems reasonable to me.

My view -- whatever that may be worth -- is that once you have uncertainty in three dimensions then you have uncertainty in the fourth as well, but mathematically it simply isn't worth the trouble of dealing with. A great deal of math is based on the assumption that time is well-behaved at very small scales, so if you doubt that assumption then a great deal of math is excluded.

Feynman and Kac had a shot at how time could emerge from a random process, but it seems like a halfhearted, unphysical, and unsatisfying effort that never caught on. There isn't much data about very small subquantum scales so you are just guessing in the dark as to what is happening; maybe it is better to leave this one for the future. I was tempted to take a shot at it, but thought "if Feynman and Kac couldn't do it, then I can't do it." If anyone is interested I can give more detail. Maybe I should have a look at what Professor Hawking did, but I probably wouldn't be able to understand it.

Dale
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To quote Hawking, ...
It seems like pretty typical pop-sci language. Very flowery and sweeping, but also quite vague. It might be that he is describing the possible breakdown of the manifold structure at small scales, but it is too vague to know for sure. If I were you I wouldn't waste any more time trying to puzzle it out, you would be better off watching the Susskind lectures on GR or reading Sean Carrolls lecture notes or even reading Wikipedia entries.

It seems like pretty typical pop-sci language. Very flowery and sweeping, but also quite vague. It might be that he is describing the possible breakdown of the manifold structure at small scales, but it is too vague to know for sure. If I were you I wouldn't waste any more time trying to puzzle it out, you would be better off watching the Susskind lectures on GR or reading Sean Carrolls lecture notes or even reading Wikipedia entries.

None of the other references I have read on GR have mentioned how/why time should behave like a spatial dimension when the universe was small. Are you recommending these sources because they specifically deal with this issue, or because they are just good resources for GR in general?

There are some places in his book where he clarifies to say "not everyone agrees with me here.." but on these subjects, he is very matter of fact and states them as if its simply common knowledge among physicists. Is Hawking the only one who has these beliefs?

Dale
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None of the other references I have read on GR have mentioned how/why time should behave like a spatial dimension when the universe was small. Are you recommending these sources because they specifically deal with this issue, or because they are just good resources for GR in general?
The references I recommended are just good references in general, and much clearer than this one. Nothing I have read mentioned this either, which is primarily the reason I wouldn't waste my time on it.

There are some places in his book where he clarifies to say "not everyone agrees with me here.." but on these subjects, he is very matter of fact and states them as if its simply common knowledge among physicists. Is Hawking the only one who has these beliefs?
Unfortunately, the wording is so vague that I can't even tell what the beliefs are, let alone whether other physicists agree.