Is spacetime just a mathematical trick or is it the actual physical reality?

[DoobleD]

While learning about SR, I encountered the famous Minkowski spacetime.

At first I thought it was just a useful mathematical trick, with no particular physical meaning. But reading more about it, it seems that this notion of spacetime is often (always?) regarded as the actual physical reality.

What makes one think spacetime is "real" ? Can we prove it ?

By real I mean that the intuitive notion we have that space is one concept and time is another different concept is wrong. So that there would not exist such thing as time, nor there would exist space. Only one thing would exist, spacetime. Which our brains instinctively interprets wrongly as two different and separate things. Kind of like with eletricity and magnetism being the same thing in reality, but perceived like two different things by us.

 

[Orodruin]

Mathematically, the unification of space and time reminds a lot about the unification of electricity and magnetism (in fact, this even becomes clearer in SR). Minkowski spacetime is a very good description of what we can observe and that is really all there is to a physical theory. Arguing that something is "real" or not is more of a philosophical question.

Edit: Regarding "physical meaning", I would ascribe physical meaning to anything which can make relevant quantitative precise predictions. You really cannot get more physically relevant than that.

 

[DoobleD]

Thanks for answering.

I deduce from your answer that while the spacetime concept works well, no proof shows the old concepts of separate space and time are not correct.

In EM for instance, I suppose one could say it is proven that eletricity and magnetism are not separate things, because depending of your frame of reference, either one or the other describes accurately the same physical phenomenon.

If something like that could be shown for space and time, I would then think "oh yeah, so space and time are actually the same thing, spacetime".

Also, I realize the question of the reality of spacetime is kind of useless for physics consideration.

 

[PeterDonis]

I suppose one could say it is proven that eletricity and magnetism are not separate things, because depending of your frame of reference, either one or the other describes accurately the same physical phenomenon.

If something like that could be shown for space and time, I would then think "oh yeah, so space and time are actually the same thing, spacetime".

Um, what do you think Minkowski spacetime is? It's exactly what you just described: depending on your frame of reference, different combinations of "space" and "time" describe the same physical phenomena. So the proof you seek is right in front of you.

 

[Hornbein]

Thanks for answering.

I deduce from your answer that while the spacetime concept works well, no proof shows the old concepts of separate space and time are not correct.

In EM for instance, I suppose one could say it is proven that eletricity and magnetism are not separate things, because depending of your frame of reference, either one or the other describes accurately the same physical phenomenon.

If something like that could be shown for space and time, I would then think "oh yeah, so space and time are actually the same thing, spacetime".

Also, I realize the question of the reality of spacetime is kind of useless for physics consideration.

It was long thought that space and time were independent. Not so. They are interdependent. There is plenty of proof.

One proof is the existence of magnetism. It is a direct result of this interdependence combined with electrical attraction/repulsion.

 

[russ_watters]

I deduce from your answer that while the spacetime concept works well, no proof shows the old concepts of separate space and time are not correct...

No, that's completely wrong. The "old concepts" were discarded precisely because they were shown to be wrong (that they don't work).

 

[Herman Trivilino]

At first I thought it was just a useful mathematical trick, with no particular physical meaning. But reading more about it, it seems that this notion of spacetime is often (always?) regarded as the actual physical reality.

You seem to go from one extreme to another, but neither reflects an understanding of the role of science. Spacetime is a model for the way nature behaves. It's value is in its utility. Scientists, technicians, and engineers can use it to get stuff done, and it works in the sense that they can use it to accomplish their tasks. It's a model.

 

[Dale]

What makes one think spacetime is "real" ?

Experiments:
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

 

[DoobleD]

Um, what do you think Minkowski spacetime is? It's exactly what you just described: depending on your frame of reference, different combinations of "space" and "time" describe the same physical phenomena. So the proof you seek is right in front of you.

Good point !

But, in EM theory, I can do the following : in a reference frame A, I can look at a force on a charge and say "this force is what I recognize as a magnetic force, F = qv x B", while another guy in a reference frame B can look at the same thing and say "this force is what I recognize as an electric force, F = qE".

Can a similar argument be made with space and time ? Can one guy in A say "oh yeah, this event is space" and another one in B say "oh yeah, this event is time" ?

As to answer what is my current, quite fragile, understanding of spacetime : spacetime is a four dimensionnal object (a "manifiold" ?), where the quantity (ct)^2 - x^2 - y^2 - z^2 is invariant under Lorentz transformation. And using four vector notation seems useful. That's basically all I know (I've read also that in GR, this spacetime has actually a curved geometry).

It was long thought that space and time were independent. Not so. They are interdependent. There is plenty of proof.

One proof is the existence of magnetism. It is a direct result of this interdependence combined with electrical attraction/repulsion.

Does the fact that space and time are interdependant proves that they are really the same thing ?

No, that's completely wrong. The "old concepts" were discarded precisely because they were shown to be wrong (that they don't work).

Could you show me or link me to something showing the old concepts are wrong (the mathematically simplest there is would be great :D) ?

EDIT : by old concepts I don't mean the old absolute time of course. I mean the concept that space and time are not quite the same physical thing (while they can vary depending of the reference frame, velocity, etc).

I have read that Einstein didn't believe Minkowski spacetime meant anything real at first. Then after a while he took it as the fundamental way nature is. (found something like that in the intro here for instance)

You seem to go from one extreme to another, but neither reflects an understanding of the role of science. Spacetime is a model for the way nature behaves. It's value is in its utility. Scientists, technicians, and engineers can use it to get stuff done, and it works in the sense that they can use it to accomplish their tasks. It's a model.

Don't get me wrong, I do recognize the utility of the model. I am only curious about the interpretation of it. I understand that interpreting a mathematical concept is useless for physics, I'm just being curious.

 

[russ_watters]

Could you show me or link me to something showing the old concepts are wrong (the mathematically simplest there is would be great :D) ?

Wikipedia has articles on both the histories of general and special relativity, which describe the failures of the previous theories, necessitating the development of the new ones. The articles are more narrative than mathematical, but the easiest math to understand was the constant speed of light: if light worked like a baseball or sound, every observer would measure it's speed to be the sum of its speed and his: c+v. When that was discovered to be wrong, it blew up the long held ideas of universal/constant space and time.

 

[DoobleD]

Wikipedia has articles on both the histories of general and special relativity, which describe the failures of the previous theories, necessitating the development of the new ones. The articles are more narrative than mathematical, but the easiest math to understand was the constant speed of light: if light worked like a baseball or sound, every observer would measure it's speed to be the sum of its speed and his: c+v. When that was discovered to be wrong, it blew up the long held ideas of universal/constant space and time.

Yes I see what you mean, I shouldn't have written "the old concepts". The old concepts of absolute time and length are wrong, that's proven. I should have written something like : the concepts of relative space and time after SR but before Minkowski spacetime. That is, the concepts that space and time are relative to the reference frame, but are still two separate things.

 

[russ_watters]

Yes I see what you mean, I shouldn't have written "the old concepts". The old concepts of absolute time and length are wrong, that's proven. I should have written something like : the concepts of relative space and time after SR but before Minkowski spacetime. That is, the concepts that space and time are relative to the reference frame, but are still two separate things.

I don't think there ever was an intervening idea/theory between SR and GR. SR didn't completely clean up the mess it made and the issues remained open for the short time until GR.

 

[DoobleD]

I don't think there ever was an intervening idea/theory between SR and GR. SR didn't completely clean up the mess it made and the issues remained open for the short time until GR.

As I understand it, Einstein published his paper on the now called Special Relativity in 1905. He did not however, invent the concept of spacetime. Spacetime has been developped by Minkowski a few years later, based on observations of SR. See for instance here. Eventually Minkowski spacetime became a framework for Einstein's GR, and also today is often used to teach SR.

SR is proven true, but SR can be understood without spacetime (that is, SR doesn't require space and time to be the same entity). Hence my question : is spacetime "real" / can it be proven that space and time are the same thing really (spacetime) ?

I phrased it very badly when I wrote "old concepts". I understand why SR is true and why for instance time is not absolute.

 

[DoobleD]

Maybe the only answer is that nobody knows if it's real or not, but everybody agrees that it's a useful concept to do physics...

 

[russ_watters]

Well again as Orodruin said above, "a useful concept to do physics" is everything that is expected of an idea/theory in science - that's as "real" as a theory/idea can be. I'm not sure what else there is to be said.

 

[Hornbein]

Does the fact that space and time are interdependant proves that they are really the same thing ?

No, but it shows they are not independent as was previously believed. You need to know one to know the other.

 

[Hornbein]

As I understand it, Einstein published his paper on the now called Special Relativity in 1905. He did not however, invent the concept of spacetime. Spacetime has been developped by Minkowski a few years later, based on observations of SR. See for instance here. Eventually Minkowski spacetime became a framework for Einstein's GR, and also today is often used to teach SR.

SR is proven true, but SR can be understood without spacetime (that is, SR doesn't require space and time to be the same entity). Hence my question : is spacetime "real" / can it be proven that space and time are the same thing really (spacetime) ?

I phrased it very badly when I wrote "old concepts". I understand why SR is true and why for instance time is not absolute.

Physics is (or rather, was) an applied science. The goal was to find mathematics that would predict what things would do. That was the criterion.

A physicist may simply fiddle around with formulas until he/she gets one that works. But more usually the physicist comes up with a simple model of what is going on, derives the math from that, and then determines whether or not it works.

There is no requirement that the model be correct. Isaac Newton declared his own model of gravity "absurd." It didn't matter: the math worked.

Sometimes bizarre models are later found out to be accurate. Other times they are replaced by other models.

Albert Einstein was outstanding in deriving a model and persuading others that his model was correct. His avoidance of mathematical abstraction was a big advantage to him in getting his theories accepted. He didn't like the Minkowski model at first, but later grew to appreciate its advantages. It made it much easier to do the math and to understand what is going on geometrically.

There is evidence that Minkowski came up with spacetime before 1905. But since he couldn't persuade anyone -- perhaps not even himself -- that it corresponded to reality, he didn't publish.

It bears repeating, Albert was especially good at showing that the math corresponded to reality. In the case of relativity that was the difficulty, not the mathematics.

 

[DoobleD]

I couldn't agree more with your last post Hornbein.

As I learned about spacetime only very recently, I wasn't sure there was or not a way one could show that this concept of spacetime is more correct than the concept of separate (but relative) space and time. For instance one could prove that relativistic mechanics is more correct/accurate than Newtonian mechanics. It seems, at least from that discussion here, that there is no such way spacetime can be shown to be more real/correct than relativistic space and time separately.

The implication is, for me, that I can chose to think of the world either way I want (namely, as relativistic but separate space and time, or, as spacetime). That of course is of no importance for the physics. It's just the way a human try to visualize things. In a way, the mathematics are always more correct than humain brain thinking, no matter the actual form of the mathematics.

So I can only conclude that, as several people implied above, my initial question is actually meaningless. Damn! :D

 

[Orodruin]

It seems, at least from that discussion here, that there is no such way spacetime can be shown to be more real/correct than relativistic space and time separately.

What do you mean by this? By construction, relativity deals with space-time, not space and time separately. What is one observer's time direction has a spatial component for another observer. Saying that they are different is exactly equivalent to saying that magnetic and electric fields are different.

 

[alw34]

I understand that interpreting a mathematical concept is useless for physics,

Not at all. It's especially useful when predictions don't match measurements. Then you need to change the model, but how? Physical insights, interpretations, are a key tool.

One of the greatest physicists said something like : Physical insights aren't just nice, they are essential.

... spacetime is a four dimensional object... in GR, this spacetime has actually a curved geometry).

Despite our apparent everyday senses, it turns out the speed of light is constant ['c'] for everyone while space and time are not the constants they appear to be. So we find that relative speed between observers affects their relative perceptions of time and distance.
Further, Einstein showed that gravity is a special curvature of space and time. Changes in gravitational potential also change the relative passage of time between different observers. So space, time, the speed of light and gravity are all related. For a practical application, you can read in Wikipedia, for example, how GPS position calculations must be corrected to account for all these 'real' effects between satellites and Earth to arrive at accurate outputs.

 

[PeterDonis]

Can one guy in A say "oh yeah, this event is space" and another one in B say "oh yeah, this event is time" ?

An event is a point in spacetime, so it doesn't have any extension in either space or time. But given a spacetime interval, i.e., a pair of events and a curve in spacetime connecting them, A might say that the interval is entirely "time", while B might say that it is a mixture of "time" and "space". Or A might say the interval is entirely "space" while B might say it is a mixture of "space" and "time". (It is not possible for the same interval to be entirely "time" to one observer and entirely "space" to another.)

 

[martinbn]

Since you are contrasting space-time on one hand and space and time (separately) on the other, and you are asking which is real, let me asky this. What is space and what is time separately? Because if you take relativity seriously they don't make sence! There is not such thing as space, there is space relative to a 3+1 split, but not space unconditional to anything.

 

[Hornbein]

Since you are contrasting space-time on one hand and space and time (separately) on the other, and you are asking which is real, let me asky this. What is space and what is time separately? Because if you take relativity seriously they don't make sence! There is not such thing as space, there is space relative to a 3+1 split, but not space unconditional to anything.

Yeah. It depends on what exactly you mean by "separate." They influence one another, so I say they are not separate. I feel that I CAN tell them apart, so in that sense they are separate. Some say that the distinction is lost inside a black hole, but since I hope never to find myself in such a situation I feel I can safely disregard that possibility.

 

[DoobleD]

Lots of answers, nice !

What do you mean by this? By construction, relativity deals with space-time, not space and time separately. What is one observer's time direction has a spatial component for another observer. Saying that they are different is exactly equivalent to saying that magnetic and electric fields are different.

That's a good question. Maybe I have a wrong view of SR ? Here is what I learned (from Prof. Shankar 4 lectures on SR) :

First, a derivation of the Lorentz transformation and its consequences on space (length contraction) and time (time dilation) and things like relativity of simultaneity. Then, the Lorentz invariance of (ct)^2 - x^2 - y^2 - z^2, and the use of four vector to derive four momentum and mass-energy equation.

In the first part of the lectures, it is never said that space and time are really the same thing. They are treated as relative to a reference frame, but there is still in one hand position and in the other hand time, two different concepts. Then Lorentz invariance and four vector are introduced. With those mathematical tools, time t (or ct) seems to be treated the same way x, y, z are treated. It is just another coordinate, of a four dimensional thing.

As I was quite blown by this, I search on Google for that concept, and I learned is called Minkowski spacetime (or simply "Minkowski space" sometimes), and with which it seems to be considered that space and time are the same thing, called spacetime. I also learned that this concept of spacetime has been invented after Einstein published his paper on SR. In other words, it does not seem essential for SR.

So here I am now, considering that a relativistic space and time is NOT the same thing as the concept of spacetime (four dimensional "object" -topology?- with time treated like space). Am I wrong to think this ?

Also, when I read papers from Minkowski, or when I read that Einstein did not at first really recognized the spacetime idea, well, that tells me they are different views of the world. Hence the original question I asked.

Maybe this is just overthinking, and one could say that the Minkowski spacetime is just a mathematical way of representing the relativistic space and time from SR and that's it...

Not at all. It's especially useful when predictions don't match measurements. Then you need to change the model, but how? Physical insights, interpretations, are a key tool.

One of the greatest physicists said something like : Physical insights aren't just nice, they are essential.
Despite our apparent everyday senses, it turns out the speed of light is constant ['c'] for everyone while space and time are not the constants they appear to be. So we find that relative speed between observers affects their relative perceptions of time and distance.
Further, Einstein showed that gravity is a special curvature of space and time. Changes in gravitational potential also change the relative passage of time between different observers. So space, time, the speed of light and gravity are all related. For a practical application, you can read in Wikipedia, for example, how GPS position calculations must be corrected to account for all these 'real' effects between satellites and Earth to arrive at accurate outputs.

Yes, again I have no doubt that the effects or SR are real. I totally trust SR. But SR is not the same thing as spacetime. At least, it wasn't designed using Minkowski spacetime.

An event is a point in spacetime, so it doesn't have any extension in either space or time. But given a spacetime interval, i.e., a pair of events and a curve in spacetime connecting them, A might say that the interval is entirely "time", while B might say that it is a mixture of "time" and "space". Or A might say the interval is entirely "space" while B might say it is a mixture of "space" and "time". (It is not possible for the same interval to be entirely "time" to one observer and entirely "space" to another.)

Thanks for answering that. Hm I don't really know what to conclude...In a way it seems space and time are the same thing, buuuut, not really, due to the fact you can't describe an event using either one or the other only...

Since you are contrasting space-time on one hand and space and time (separately) on the other, and you are asking which is real, let me asky this. What is space and what is time separately? Because if you take relativity seriously they don't make sence! There is not such thing as space, there is space relative to a 3+1 split, but not space unconditional to anything.

Hm yes what is space and what is time separately are tough questions...But does the fact that one exist with the other mean they are the same thing ?

They influence one another, so I say they are not separate. I feel that I CAN tell them apart, so in that sense they are separate.

I'd say and feel exactly the same way.

 

[DoobleD]

Experiments:
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

Experiments confirm SR, they do not confirm our world is a Minkowski spacetime where time is just like space. I distinguish those two things, SR and Minkowski spacetime. This might be wrong, from what everybody says.

 

[jbriggs444]

Experiments confirm SR, they do not confirm our world is a Minkowski spacetime where time is just like space. I distinguish those two things, SR and Minkowski spacetime. This might be wrong, from what everybody says.

What experimental predictions does the one make that the other does not?

 

[DoobleD]

What experimental predictions does the one make that the other does not?

None, of course. But why assume because SR is true, then Minkowski spacetime is an accurate view of the world ? SR can be derived without using Minkowski spacetime.

 

[jbriggs444]

If there is no experimental basis to distinguish it from some competing viewpoint then it's not a matter of science but only of preference.

 

[Orodruin]

I also learned that this concept of spacetime has been invented after Einstein published his paper on SR. In other words, it does not seem

This seems to imply that you think relativity was "done" after Einstein. While he did introduce it, our current understanding of relativity is far more advanced than what Einstein introduced in his 1905 paper.
In particular, when you go to GR, space-time is a fundamental concept and things such as the possibility of being able to define a global time at all are thrown out of the window.

 

[A.T.]

Experiments confirm SR, they do not confirm our world is a Minkowski spacetime where time is just like space. I distinguish those two things, SR and Minkowski spacetime. This might be wrong, from what everybody says.

No, you are right. Minkowski spacetime is one possible geometrical interpretation of SR, that was proposed after SR has been already published.

But note that in Minkowski spacetime, time is not "just like space", that why it is pseudo-Euclidean. There is another, less common geometrical interpretation of SR by Epstein, where proper time is more like another space dimension, and (coordinate)time is the Euclidean path integral.