I Why isn't spacetime considered as true 4D?

[Akriel]

...and what is the difference between true 4D and the minkowski space?

To me, it would be much easier to see universe as a 4D and us humans just experiencing the dimension of time differently. In my mind i pictured the universe as a complete 4D structure which we humans experience in one present moment - in four specific coordinates - in the spacetime. Apparently this is not the case the scientists say. Can someone explain me why?

 

[Ibix]

You are misunderstanding something. Spacetime is a 4d entity. There is one direction that is different from the other three, which is the time-like one. But it really is 4d (or, at least, that is a popular interpretation of the maths).

I'm not sure what you mean by "true 4d", so I can't really answer your question. If you mean a Euclidean (i.e. flat Riemannian) 4d space then the difference between that and Minkowski (flat pseudo-Riemannian) spacetime is that there is a time-like direction in Minkowski spacetime, while all directions are interchangeable in a Euclidean (positive definite) space. There's no notion of time inherent in a Euclidean space.

 

[Akriel]

You are misunderstanding something. Spacetime is a 4d entity. There is one direction that is different from the other three, which is the time-like one. But it really is 4d (or, at least, that is a popular interpretation of the maths).

I'm not sure what you mean by "true 4d", so I can't really answer your question. If you mean a Euclidean (i.e. flat Riemannian) 4d space then the difference between that and Minkowski (flat pseudo-Riemannian) spacetime is that there is a time-like direction in Minkowski spacetime, while all directions are interchangeable in a Euclidean (positive definite) space. There's no notion of time inherent in a Euclidean space.

By "true 4D" i mean a complete 4D structure where none of the dimensions has any direction and are all every way equal to each other. Is that what you mean by euclidean space?

Why do we think that time has a direction in physics? I mean ofcourse, in our everyday life we see time having a very certain direction, but why do we see this as a property of time itself, instead of being an illusion created by our perspective in spacetime and causality? We do know that the one present moment is nothing but our personal experience of time, am i correct?

 

[The Bill]

Why do we think that time has a direction in physics? I mean ofcourse, in our everyday life we see time having a very certain direction, but why do we see this as a property of time itself, instead of being an illusion created by our perspective in spacetime and causality? We do know that the one present moment is nothing but our personal experience of time, am i correct?

Euclidean and Minkowski space have a different notion of "distance" between points. This notion of distance is called a metric. When we assume a spacetime with a Euclidean metric, we predict a spacetime that obeys Galileo's relativity. When we use the Minkowski metric, special relativity is the result.

Thus, the fact that special relativity agrees with local physics experiments in "flat" spacetime tells us that spacetime is locally much more Minkowski-like than Euclidean.

 

[Ibix]

Ultimately, because if you start from the assumption that spacetime is a pseudo-Riemannian manifold then you can make all sorts of testable predictions that agree with experiment. Historically, Einstein realized that he could resolve 50 years of headaches in electromagnetic theory if he assumed that the speed of light was the same in all inertial frames of reference. From there he derived the Lorentz transforms, and Minkowski pointed out that they were equivalent to a claim that spacetime is a Minkowski spacetime.

"The present moment" is largely a matter of convention in relativity. There are different ways to define it, and observers moving with respect to each other end up with different definitions of it even if they use the same procedure to define it.

I think that you were asking if "the present moment" is a slice of 4d spacetime. That is the usual interpretation, yes, but it is not the only possible one. @PeterDonis wrote an Insight on whether relativity requires the "block universe" model, concluding that the answer was no. Lorentz Ether Theory is the usual umbrella term for such interpretations.

 

[Akriel]

Ultimately, because if you start from the assumption that spacetime is a pseudo-Riemannian manifold then you can make all sorts of testable predictions that agree with experiment. Historically, Einstein realized that he could resolve 50 years of headaches in electromagnetic theory if he assumed that the speed of light was the same in all inertial frames of reference. From there he derived the Lorentz transforms, and Minkowski pointed out that they were equivalent to a claim that spacetime is a Minkowski spacetime.

"The present moment" is largely a matter of convention in relativity. There are different ways to define it, and observers moving with respect to each other end up with different definitions of it even if they use the same procedure to define it.

I think that you were asking if "the present moment" is a slice of 4d spacetime. That is the usual interpretation, yes, but it is not the only possible one. @PeterDonis wrote an Insight on whether relativity requires the "block universe" model, concluding that the answer was no. Lorentz Ether Theory is the usual umbrella term for such interpretations.

"because if you start from the assumption" what happens if we try the same experiements in a model which is otherwise the same than minkowski space but doesn't have the direction of time?

"The present moment" is largely a matter of" do we see the time in spacetime as an ongoing process or do we consider it (the whole spacetime in this case) as a complete 4D structure where every moment in the universe from the beginning to the end physically exist in time?

"if "the present moment" is a slice of 4d spacetime" ultimately why I am asking this is because i thought, that if the spacetime would exist as a complete structure (wether it has the direction of time or not), then wouldn't it mean that the beginning of the universe didn't happen 13,8 billion years ago, but instead the whole 4D structure of universe was born in one moment which cannot be defined in our dimension of time at all?

 

[Ibix]

"because if you start from the assumption" what happens if we try the same experiements in a model which is otherwise the same than minkowski space but doesn't have the direction of time?

You're describing a different universe that doesn't look like this one. It has four spatial dimensions and no time (unless you add one in some other way). Feel free to play around, but it's not our universe you are describing.

"The present moment" is largely a matter of" do we see the time in spacetime as an ongoing process or do we consider it (the whole spacetime in this case) as a complete 4D structure where every moment in the universe from the beginning to the end physically exist in time?

Up to you. That is a matter of interpretation for which we have no evidence, nor any theoretical approach to consider gathering evidence in the future, at our current level of understanding. Typically, physicists talk as if spacetime is a 4d structure, since it's the most straightforward way to interpret the maths. You are not required to take this approach, and (almost) all physicists will admit that "spacetime is 4d" is shorthand for "it is easiest for me to interpret spacetime as a 4d entity".

"if "the present moment" is a slice of 4d spacetime" ultimately why I am asking this is because i thought, that if the spacetime would exist as a complete structure (wether it has the direction of time or not), then wouldn't it mean that the beginning of the universe didn't happen 13,8 billion years ago, but instead the whole 4D structure of universe was born in one moment which cannot be defined in our dimension of time at all?

This is beyond our current understanding. I see what you're thinking, but there really isn't a way to phrase your question in scientific terms - there's nothing we can measure to test your hypothesis. You're into the realms of speculation here, and we don't really do that on Physics Forums.

In summary: we don't know. Wee may never know. It may not even be a meaningful question.

 

[Akriel]

You're describing a different universe that doesn't look like this one. It has four spatial dimensions and no time (unless you add one in some other way). Feel free to play around, but it's not our universe you are describing.

Up to you. That is a matter of interpretation for which we have no evidence, nor any theoretical approach to consider gathering evidence in the future, at our current level of understanding. Typically, physicists talk as if spacetime is a 4d structure, since it's the most straightforward way to interpret the maths. You are not required to take this approach, and (almost) all physicists will admit that "spacetime is 4d" is shorthand for "it is easiest for me to interpret spacetime as a 4d entity".

This is beyond our current understanding. I see what you're thinking, but there really isn't a way to phrase your question in scientific terms - there's nothing we can measure to test your hypothesis. You're into the realms of speculation here, and we don't really do that on Physics Forums.

In summary: we don't know. Wee may never know. It may not even be a meaningful question.

I see, okay. I don't want to push the general rules of physics forum. I found your answers very enlightening, thank you for your time and have a good night :)

 

[pervect]

...and what is the difference between true 4D and the minkowski space?

To me, it would be much easier to see universe as a 4D and us humans just experiencing the dimension of time differently. In my mind i pictured the universe as a complete 4D structure which we humans experience in one present moment - in four specific coordinates - in the spacetime. Apparently this is not the case the scientists say. Can someone explain me why?

I'm not sure what you mean by "true 4d". So I'm also not sure why you think the universe is, or isn't "true 4d", since I'm not sure precisely what that might mean.

Perhaps it's worthwhile explaining some of the differences between the 4-dimensional space time consisting of a separable 3 dimensional Euclidean subspace for the space-part with an independent time dimension, and Minkowskii space.

We can (and do) say that this 3+1 combination of space-time is a 4 dimensional manifold mathematically speaking - though I"m not going to try to give a precise defintion of "manifold", it would be too much of a digression and a bit too advanced, I think.

The difference between the 3+1 space-time manifold and Minkowskii space-time is in the geometry. Geometry can be viewed as being fundamentally based on some concept of "distance", which can be generalized to a concept called an "interval" when the word "distance" doesn't quite fit. The interval in the cases I'll talk about is always a real number. (I think this is usually true, but I'm not sure if I can quite claim it's ALWAYS true).

In the Euclidean 3-dimensional space, we have the concept of spatial distance, and a separate concept of time interval (that plays the role of a distance in the geometry) in the time dimension. So the combined space-time has two different sorts of intervals.

In Minkowskii space, there is only one interval, called the Lorentz interval, and not two separate notions of intervals. The square of the interval is positive for spatial distances, while it is negative for time intervals, and it's zero for light.

This brief explanation probably doesn't really quite explain exactly what the Lorentz interval is, but it may give you some idea of where to read more to find out more about Minkowskii space.

Note that in the Minkowskii space-time, the space intervals and the time intervals are considered not to be separate. For instance, if we have two points in Minkowskii space, some observers might say that the time-interval between them is zero (they are simultanieous) , so the interval between them has no time component, while other observers will say that the two points have a non-zero time interval (meaning they are not simultaneious). To compensate for the non-zero time part of the interval in this later case, the space interval changes as well. Operationally, the former concept is an example of "the relativity of simultaneity", while the later concept is an example of "length contraction".

Also note that the distances in an Euclidean space are always positive for any two points that are not identical. The Lorentz interval between two points can be positive, negative, or zero. We say that Euclidean 3-space is a Riemannian manifold, while we say that the 4-d space-time is a pseudo-Riemannian manifold, because the "distances" on which the later is based are not always positive, but can be negative or zero.

 

[vanhees71]

By "true 4D" i mean a complete 4D structure where none of the dimensions has any direction and are all every way equal to each other. Is that what you mean by euclidean space?

Why do we think that time has a direction in physics? I mean ofcourse, in our everyday life we see time having a very certain direction, but why do we see this as a property of time itself, instead of being an illusion created by our perspective in spacetime and causality? We do know that the one present moment is nothing but our personal experience of time, am i correct?

The reason that you have a pseudo-Euclidean (Minkowski) spacetime structure is that a purely Euclidean couldn't establish a causality structure. It's exactly this different sign of the temporal directions in the fundamental form of this 4D vector space (I don't know, why you come to the conclusion it's not "truely 4D" and what you want to say with this term) which enables to build up a causality structure, which you must have to do physics as we know it to begin with.

 

[Akriel]

In Minkowskii space, there is only one interval, called the Lorentz interval, and not two separate notions of intervals. The square of the interval is positive for spatial distances, while it is negative for time intervals, and it's zero for light.

How does the spatial dimensions squared being positive and time squared being negative work in practice? What does it mean in physical reality?

 

[Dale]

How does the spatial dimensions squared being positive and time squared being negative work in practice? What does it mean in physical reality?

It has many implications.

One is that mathematically there are three different kinds of intervals, called spacelike, timelike, and lightlike. Physically timelike intervals are measured by clocks, and spacelike intervals are measured by rods. From this, time dilation immediately falls out and has been experimentally confirmed.

Another is that particles can be separated into timelike and lightlike particles, with lightlike particles having 0 rest mass. This has also been experimentally confirmed.

Another is the causal structure mentioned above. If time had the same sign as the other dimensions then you could literally turn around and arrive in the past. This would be inconsistent with observation.

I am sure there are more, but this post is already long. Basically, all of this is chosen to match experimental evidence.

 

[Akriel]

It has many implications.

One is that mathematically there are three different kinds of intervals, called spacelike, timelike, and lightlike. Physically timelike intervals are measured by clocks, and spacelike intervals are measured by rods. From this, time dilation immediately falls out and has been experimentally confirmed.

Another is that particles can be separated into timelike and lightlike particles, with lightlike particles having 0 rest mass. This has also been experimentally confirmed.

Another is the causal structure mentioned above. If time had the same sign as the other dimensions then you could literally turn around and arrive in the past. This would be inconsistent with observation.

I am sure there are more, but this post is already long. Basically, all of this is chosen to match experimental evidence.

but i mean, what is a physicist saying when he says that spatial dimensions squared are positive, and time squared being negative? is it just to separate them from each other in calculations, or does this mean something in practice? what would it mean if it would be the opposite for example, so that the time squared would be positive and the spatial dimensions squared would be negative?

I'm asking because i don't understand the terms "positive" and "negative" in this context.

 

[Dale]

what is a physicist saying when he says that spatial dimensions squared are positive, and time squared being negative?

All of the things I mentioned above and more. It is one statement with a large number of implications.

what would it mean if it would be the opposite for example, so that the time squared would be positive and the spatial dimensions squared would be negative?

That doesn't make a difference, it is just a convention. Like calling the charge on an electron negative instead of positive. The important thing is just that they are different and that there are three with one sign and one with the opposite sign.

 

[Akriel]

All of the things I mentioned above and more. It is one statement with a large number of implications.

That doesn't make a difference, it is just a convention. Like calling the charge on an electron negative instead of positive. The important thing is just that they are different and that there are three with one sign and one with the opposite sign.

Okay, i think i got the answers i was searching for. thank you for your time :)

 

[The Bill]

Okay, i think i got the answers i was searching for. thank you for your time :)

Leonard Susskind explains the spacetime interval pretty well in his videos about special relativity, starting with this video:

Spoiler

 

[Demystifier]

By "true 4D" i mean a complete 4D structure where none of the dimensions has any direction and are all every way equal to each other. Is that what you mean by euclidean space?

Why do we think that time has a direction in physics? I mean ofcourse, in our everyday life we see time having a very certain direction, but why do we see this as a property of time itself, instead of being an illusion created by our perspective in spacetime and causality? We do know that the one present moment is nothing but our personal experience of time, am i correct?

Basically, you are asking why there is an arrow of time and no arrow of space, am I right? The theory of relativity alone cannot answer this question. A part of the answer lies in thermodynamics and statistical physics, but even that is not enough to explain our subjective experience of time. For a non-technical discussion of this see
http://fqxi.org/community/forum/topic/259

 

[vanhees71]

The thermodynamic arrow of time (i.e., the direction of time that leads to entropy production) is the same as the fundamental causality arrow of time, which you assume at the very beginning when doing physics usually without mentioning or thinking about it. The only important point with regard to relativity is that there you have to think a bit more about the question, whether there is a cauality structure describable by the spacetime model, and in fact it is. This is the reason for why the pseudometric of the spacetime manifold is of signature (1,3) (or equivalently (3,1) if you follow the east-coast convention).

 

[Demystifier]

The thermodynamic arrow of time (i.e., the direction of time that leads to entropy production) is the same as the fundamental causality arrow of time

Not exactly the same:
https://arxiv.org/abs/gr-qc/0403121

 

[Mark Harder]

It seems to me, naively I know, that the notion causality is intimately bound up with the notion of time. If event A precedes event B in time, then it's possible that A 'caused' B. If B occurs before A, then we can definitely say that A did not cause B. I don't know of any other way we can claim that 2 events are cause-and-effect, rather than simply correlated with each other (Correlation does not necessarily imply causation.) But suppose the timing of 2 events is so uncertain that we can't tell which one preceded the other. Doesn't the energy-time uncertainty principle imply that if the energy of a system is tightly constrained (by the requirement that energy be conserved, for example), then time can't be specified very precisely? Hence, there can be systems for which 2 events can't be separated by time. We can't really say which event preceded the other, therefore it's useless to speak of causality. I like to think of the absorption of a photon by an atom. In one event the photon is annihilated; and in the other, the atom's energy jumps to a higher state. The energy of the system is conserved, so its magnitude at any instant can't be specified sloppily. But this means that time for that system is distributed very broadly. In other words, one cannot tell whether the photon loses energy and 'then' the atom changes state or the other way 'round. It makes no sense to say the interaction with the photon causes the atom to change state.
Perhaps spontaneous particle-antiparticle creation in the vacuum represents an event of the opposite type. The lifetime of the particle pair is so short that the energy of the vacuum-particles system can't be specified very well, which is how mass-energy can appear out of nothing - and disappear before the legal violation is 'noticed'. Or, as I read somewhere, the mass-energy is 'borrowed' from the future for the short term.

 

[vanhees71]

The quibbles concerning the energy-time uncertainty relation and causality is answered by relativistic quantum field theory. It's by construction built up as a local microcausal quantum field theory, and further for interacting fields a particle interpretation in the "transient state", i.e., during the interaction/scattering process is very difficult or even impossible. That's why we usually consider cross sections, i.e., measures for transition rates from one asymptotic free states (usually 2 particles) to another asymptotic free state (usually several particles). The time ordering in the corresponding perturbative Green's functions is, thanks to the locality and microcausality of the models, Lorentz covariant as is the corresponding S-matrix which gives the transition rates between the asymptotic free states. So you take sufficiently long times before the collision to specify the asymptotic free in states and a sufficiently long time to specify asymptotic free out states, i.e., the time uncertainty due to the energy-time uncertainty relation is negligible.

 

[newjerseyrunner]

Three of the dimensions are different than the other. In math terms, it's not symmetrical. Three dimensions have two directions, time appears to only have one.

 

[PeterDonis]

In math terms, it's not symmetrical. Three dimensions have two directions, time appears to only have one.

That's not the difference if we're talking about the math; in the math, it's perfectly possible to model "motion in time" in both directions. The difference in the math is in the sign of the squared norm of vectors; timelike vectors have opposite sign to spacelike vectors. But that's just as true for past-pointing timelike vectors as it is for future-pointing timelike vectors.