3 dimensions of space and 1 of time

[Altabeh]

In response to this, I've tried finding "re-definitions" of the word "force" as it applies to relativity. The search has come up fruitless. All definitions of a force as it relates to gravity are equivalent to every other definiton with the exception that gravity, like electromagnetism, and the strong and weak forces, is not a "contact force".

Gravity is an interacting force between matter and the fabric of spacetime but in GR it is not actually described in such a way that a curious reader is able to dig the straight meaning of "force" from the context at first glance. Simply gravity is treated like a "geometrical object" that is only observed through the changes in the shape of spacetime which we call it "curvature". In the Newtonian physics, this has a different facet to look through which is like you're now feeling something is pushing you down to the ground so the "gravitational force" exists and of course this has something to do with the fact that Newtonian theory is not a geometrized framework to work in but rather is a classical theory dealing with the ordinary implications of time, space, force and etc.

dx, you and Nabeshin seem to be taking similar, diplomatic approaches to the problem by trying to overlook semantics. I think this is a noble approach, but it also seems like a cop-out. In post #10, Nabeshin says, "Gravity does not even exist in GR. So it makes no sense to speak of it as a force." Then he says, "No mention of the word gravity is ever needed." In other words, let's not mention the ugly stepchild and pretend that everything's ok.

I've already encountered with Nabeshin's argument before though I'm a little bit uncomfortable with it! I think we can't say gravity does not exist in GR because then we have no curvature and nothing to talk about! Also in the reduction to the Newtonian mechanics, the gravity appears to exist apparently as an attractive force and if GR was free of such force, then this would seem to be a contradiction. We better say gravity does no longer have its classical meaning and rather it is now cast into a new form as the one we see in GR and is of course able to reveal itself as a force in some limited cases.

http://www.uoregon.edu/~struct/courseware/461/461_lectures/461_lecture4/461_lecture4.html says:
"A "force" is an action that changes, or tends to change, the state of motion of the body upon which it acts." In other words, a force does work, right? So, I'm wondering if the relevant question might be, "what has energy?"

Why are planets in orbit? Isn't it because of opposing forces? Isn't it similar to tying a ball at the end of a string and spinning it in a circle? Energy, thus force, is required to resist something, isn't it?

Why don't planets take a geodesic path right into the sun? Isn't it because they have their own agenda - their own energy - that is trying to go somewhere else but the gravity prevents them from leaving?

All these questions lie in the fact that you're a bit of a stranger to fresh arguments of GR! Gravity though has a force-like nature, is more efficiently replaced systematically by the curvature of spacetime and as soon as you find this as a really useful touchstone to measure the effects of gravitational fields on the fabric of spacetime, it turns out to be like an easy essay which is going to sit right with you line-by-line. But remember that sometimes we don't ask why; we just simply ask ourselves how are planets orbiting? This is because no one has any information as to what happened millions of years ago at the advent of planets and stars! This is what we see and GR Physics tries to find out what is behind all these motions!

AB

 

[Dale]

DaleSpam, you're suggesting that gravity can still be defined as a force

No, I am suggesting that it does not matter at this point and that you should be focusing on trying to understand the idea of worldlines and curved geometry.

Why don't planets take a geodesic path right into the sun? Isn't it because they have their own agenda - their own energy - that is trying to go somewhere else but the gravity prevents them from leaving?

This is a much more important question, and you have the tools to answer it. Remember the "local" definition of a geodesic? How can you apply that definition here? Keep in mind that we are talking about the geometry of spacetime and not just space.

 

[dx]

dx, you and Nabeshin seem to be taking similar, diplomatic approaches to the problem by trying to overlook semantics. I think this is a noble approach, but it also seems like a cop-out.

I don't see how its a cop-out. There are two ways that your question can be interpreted. One has to do with the difference between gravity and the other interactions, and this definitely is a meaningful question, since our description of gravity is distinctly different from our descriptions of the other three interactions. What you seem to worried about is the more naive question of "is gravity curvature of spacetime or is gravity a force?". This second question definitely does not make sense, and you don't even have to go to general relativity to see why; it can be illustrated in classical mechanics itself. Newton's description of motion involves the notion of 'force', and the phenomenon of gravity is represented in this description by the force F = GmM/r². But the actual content of Newton's theory is not the assertion "F = ma", with force, mass and acceleration defined seperately, but the assertion "the mathematical structure of second order differential equatoins applies to the phenomenon of motion". This mathematical structure can be 'viewed' in different ways, and some of these ways involve the idea of 'force' and some of them don't. For example, the lagrangian formulation of mechanics, which is mathematically isomorphic to Newton's viewpoint does not involve the idea of force. The dynamics in this viewpoint is represented by a function called the lagrangian, and gravity enteres in the form L =mv₁²/2 + Mv₂²/2 + GmM/|r₁ - r₂|. So it doesn't make sense to ask "is gravity a largangian or a force?", since they mean exactly the same thing. They are two ways of looking at the same mathematical structure, i.e. the structure of second order differential equations.

 

[Altabeh]

... which is mathematically isomorphic to Newton's viewpoint does not involve the idea of force. The dynamics in this viewpoint is represented by a function called the lagrangian, and gravity enteres in the form L =mv₁²/2 + Mv₂²/2 + GmM/|r₁ - r₂|. So it doesn't make sense to ask "is gravity a largangian or a force?", since they mean exactly the same thing. They are two ways of looking at the same mathematical structure, i.e. the structure of second order differential equations.

The Lagrangian approach leads to the idea of force for representing gravity via the fundamental formula

-\nabla L = \textbf{F}.

All is known to us from the Newtonian mechanics discussed in either way is that it has "gravity" defined as a force!

AB

 

[dx]

The Lagrangian approach leads to the idea of force for representing gravity via the fundamental formula

-\nabla L = \textbf{F}.

All is known to us from the Newtonian mechanics discussed in either way is that it has "gravity" defined as a force!

AB

That is simply a connection between the concepts of two equivalent descriptions of an underlying structure, which of course must exist (just like there is always a connection between the elements of two basis sets for the representaiton of a vector space). The point is that the notion of 'force' does not even have to be introduced. If mechanics were discovered historically in the lagrangian form, physics could have gone on just as well without ever using the word 'force' and simply talking about lagrangians.

 

[Altabeh]

That is simply a connection between the concepts of two equivalent descriptions of an underlying structure, which of course must exist (just like there is always a connection between the elements of two basis sets for the representaiton of a vector space). The point is that the notion of 'force' does not even have to be introduced. If mechanics were discovered historically in the lagrangian form, physics could have gone on just as well without ever using the word 'force' and simply talking about lagrangians.

Nevertheless there is such a word "force" and people have been keeping to fall into the habit of saying that since physics was born. The Lagrangian by itself can't be so much useful and that is the formulae like the one I gave, or the action formula, that let the theory blossom the applicative power of Lagrangians in physics!

AB

 

[dx]

The Lagrangian by itself can't be so much useful and that is the formulae like the one I gave, or the action formula, that let the theory blossom the applicative power of Lagrangians in physics!

AB

No, the formula that you gave really says nothing and is not needed in the application of lagrangians, let alone "let the theory blossom their applicative power". Also, the formula that you gave is actually wrong.

The fundamental equation of motion in the lagrangian formulation is (d/dt)(∂L/∂q') = ∂L/∂q. Only when we use the cartesian coordinates x, y, z can we think of ∂L/∂q as the vector quantity (F_x, F_y, F_z). For other generalized coordinates, ∂L/∂q does not even transform as a vector; it is a new type of object called a 1-form. So in fact the idea of force in the Newtonian sense has a limited domian of usefulness.

 

[Altabeh]

No, the formula that you gave really says nothing and is not needed in the application of lagrangians, let alone "let the theory blossom their applicative power". Also, the formula that you gave is actually wrong.

Please be careful when denying something that is already known to be true: I only made a typo and used a minus sign while this would have been a plus sign. This formula is not wrong at all and of course it is given in the Cartesian coordinates to lead to Newton's second law!

The fundamental equation of motion in the lagrangian formulation is (d/dt)(∂L/∂q') = ∂L/∂q. Only when we use the cartesian coordinates x, y, z can we think of ∂L/∂q as the vector quantity (F_x, F_y, F_z). For other generalized coordinates, ∂L/∂q does not even transform as a vector. It is a new type of object called a 1-form.

Who talked about "generalized coordinate system"? You and I, as I remember correctly, were talking about the Lagrangian approach to Newtonian mechanics and you gave in an early post the gravitational Lagrangian and I just said that you're wrong if you claim there is no such thing as "force" in the new approach! Again Lagrangian is just a key to many doors and until there we don't see a door, this key cannot come in handy! Period!

AB

 

[dx]

Please be careful when denying something that is already known to be true: I only made a typo and used a minus sign while this would have been a plus sign. This formula is not wrong at all and of course it is given in the Cartesian coordinates to lead to Newton's second law!

When I said it was wrong, what I meant was that it has a limited applicability, as I explained right after that statement.

You and I, as I remember correctly, were talking about the Lagrangian approach to Newtonian mechanics and you gave in an early post the gravitational Lagrangian and I just said that you're wrong if you claim there is no such thing as "force" in the new approach!

I don't know what you were talking about, but I was talking about the Lagrangian and the Newtonian approaches as two equivalent approaches to classical mechanics. One involves the concept of 'force', the other does not, and need not. The fact that 'force' and 'lagrangian' can be related, which is obvious, does not imply that the lagrangian formulation needs the idea of force.

 

[Altabeh]

When I said it was wrong, what I meant was that it has a limited applicability, as I explained right after that statement.

I really don't know what logic is behind the statement 'if a formula has "limited applicability" so it is worng'! Maybe the other users know!

I don't know what you were talking about, but I was talking about the Lagrangian and the Newtonian approaches as two equivalent approaches to classical mechanics. One involves the concept of 'force', the other does not, and need not. The fact that 'force' and 'lagrangian' can be related, which is obvious, does not imply that the lagrangian formulation needs the idea of force.

If you really don't, I don't see a reason to keep this going!

AB

 

[ia_]

Just for the sake of argument, I'm going to say that space is 3 dimensional, and time (although a useful convention) doesn't exist, because you can always substitute it out of your equations for any experiment by including your timekeeping device. i.e. A process does not take two seconds, a process occurs when the longer hand on my watch moves pi/15 radians clockwise.

Therefore when the minkowski metric, for instance, is written with a -, +, +, + signature, what this says is that space is 3 dimensional, and the negative sign on the extra entry is used for correlating the spatial configuration of your experiment to another referenced physical process (like the longer hand on your watch changing by pi/15 radians clockwise).

 

[Dale]

a process occurs when the longer hand on my watch moves pi/15 radians clockwise.

This statement is meaningless without time.

Btw, I would remind you about the prohibition against overly speculative posts. You agreed to the rules when you signed up for your PF account. Please review them. This forum is for the discussion of mainstream physics, not the discussion of personal pet theories. To my knowledge every single theory which is consistent with experiment uses time. If you have a peer-reviewed reference to the contrary then please cite it.

 

[Frame Dragger]

I just want to know how he thinks matter exists in a timeless universe. The only way I can imagine it would be an idealized crystal AT (impossible) Absolute Zero, and even that is just an approximation.
<s></s>

@ia: What theory are you selling? You're talking about motion out of time, but you've heard of "Minkowski", sooo... you're probably a kook. If not, you should know that's the STRONG impression you've made on me (and clearly DaleSpam who is a reasonable guy as far as I've seen).

 

[matheinste]

Just for the sake of argument, I'm going to say that space is 3 dimensional, and time (although a useful convention) doesn't exist, because you can always substitute it out of your equations for any experiment by including your timekeeping device. i.e. A process does not take two seconds, a process occurs when the longer hand on my watch moves pi/15 radians clockwise.

.

I have a digital clock. The man who sold it to me assured me that the clock mechanism had no moving parts. How would I "substitute it out of my equations" whatever that means. The mechanism has no spatial movement and so cannot be incorporated into one of the three spatial dimensions if that is what you are suggesting. But that makes no sense either. Perhaps you could explain in more detail what you mean.

Matheinste.

 

[ia_]

This statement is meaningless without time.

Btw, I would remind you about the prohibition against overly speculative posts. You agreed to the rules when you signed up for your PF account. Please review them. This forum is for the discussion of mainstream physics, not the discussion of personal pet theories. To my knowledge every single theory which is consistent with experiment uses time. If you have a peer-reviewed reference to the contrary then please cite it.

I am not advancing any theory of my own. It's amazing that you're threatening to ban me...

Perhaps you would be interested in reading some of the fqxi essay winners, by Julian Barbour (visiting physics professor at Oxford), Claus Kiefer (institute for theoretical physics at Univ of Köln), or Carlo Rovelli (univ of Marseille phy dept) http://www.fqxi.org/community/essay/winners/2008.1 I was expressing a simplified (and obviously less cogent) version of that argument. And matheinste, there's not really any difference between an analogue clock and a digital clock, but thanks.

 

[Frame Dragger]

I am not advancing any theory of my own. It's amazing that you're threatening to ban me...

Perhaps you would be interested in reading some of the fqxi essay winners, by Julian Barbour (visiting physics professor at Oxford), Claus Kiefer (institute for theoretical physics at Univ of Köln), or Carlo Rovelli (univ of Marseille phy dept) http://www.fqxi.org/community/essay/winners/2008.1 I was expressing a simplified (and obviously less cogent) version of that argument. And matheinste, there's not really any difference between an analogue clock and a digital clock, but thanks.

Ok, as there is no difference, why not humour us all and answer his question? Don't forget by the way, that the thoughts expressed in an Essay Contest may not have the rigour of those that would put forth in a peer-reviewed journal?

EDIT: @ia: btw, DaleSpam can't ban you directly, and if he's talking to you HERE, it means he probably didn't just REPORT you! In fact, he was trying to do you a favour, and your manner of showing gratitude proves the saying that no good deed goes unpunished.

 

[atyy]

I am not advancing any theory of my own. It's amazing that you're threatening to ban me...

Perhaps you would be interested in reading some of the fqxi essay winners, by Julian Barbour (visiting physics professor at Oxford), Claus Kiefer (institute for theoretical physics at Univ of Köln), or Carlo Rovelli (univ of Marseille phy dept) http://www.fqxi.org/community/essay/winners/2008.1 I was expressing a simplified (and obviously less cogent) version of that argument. And matheinste, there's not really any difference between an analogue clock and a digital clock, but thanks.

Yes, those came to mind when I saw your earlier post, but I wasn't sure, because it seemed quite different. I'm not sure that Rovelli or Barbour would agree, but I think it's not so much that time doesn't exist, rather that in Newtonian and special relativistic mechanics, it is possible to define time such that "motion looks simple". This is the view advanced in Misner, Thorne and Wheeler's "Gravitation", p23 and in Stephani's http://books.google.com/books?id=WAW-4nd-OeIC&dq=stephani+hans+relativity&source=gbs_navlinks_s, p5.

 

[brainstorm]

Whenever discussing dimensionality, the issue always seems to end up being whether dimensions are cognitive frameworks (a la Kant), or whether objective matter-energy is actually organized according to real dimensions that exist outside the mind.

Those who get sucked into this debate do because they can't comprehend the idea that all human perceptions, including those of physical matter-energy, are structured and defined by consciousness in order to perceive it.

That doesn't mean that nothing exists outside of consciousness. It means that nothing exists in the way that consciousness perceives it without applying conceptual frameworks like dimensionality, space, time, etc.

I suspect that some people will always insist that the reality of their perception IS the reality as it exists outside their perception. These people are in dire fear that if perception is subjective, they risk terrible consequences of losing their mind, grip on reality, etc.

The fact is, dimensions are applied and space-time is a conceptual framework for making sense of various matter-energy events in different contexts. I would guess that misinterpretation of one observational context in terms of another is the cause of most if not all shortcomings in knowledge.

Learning how to sort out the discrepancies caused by misapplied knowledge is probably the key to attaining truer knowledge, but in order to do that you have to overcome the insistence of everyone who has achieved some level of authority or expertise who is more interested in asserting what they know than figuring out how what they know might be misleading at one level, even while it may be enlightening on another.

 

[brainstorm]

Yes, those came to mind when I saw your earlier post, but I wasn't sure, because it seemed quite different. I'm not sure that Rovelli or Barbour would agree, but I think it's not so much that time doesn't exist, rather that in Newtonian and special relativistic mechanics, time is defined so that "motion looks simple". This is the view advanced in Misner, Thorne and Wheeler's "Gravitation", p23 and in Stephani's http://books.google.com/books?id=WAW-4nd-OeIC&dq=stephani+hans+relativity&source=gbs_navlinks_s p5.

How can time exist or not? Time is sequentiality. Matter and energy exist. Forces are relations between them. Time/sequentiality is a method of defining and measuring them. Don't mix up materiality with cognition. Yes our only access to materiality comes via cognition, but it is possible to sort out ideas from material things, imo.

 

[Frame Dragger]

Whenever discussing dimensionality, the issue always seems to end up being whether dimensions are cognitive frameworks (a la Kant), or whether objective matter-energy is actually organized according to real dimensions that exist outside the mind.

Those who get sucked into this debate do because they can't comprehend the idea that all human perceptions, including those of physical matter-energy, are structured and defined by consciousness in order to perceive it.

That doesn't mean that nothing exists outside of consciousness. It means that nothing exists in the way that consciousness perceives it without applying conceptual frameworks like dimensionality, space, time, etc.

I suspect that some people will always insist that the reality of their perception IS the reality as it exists outside their perception. These people are in dire fear that if perception is subjective, they risk terrible consequences of losing their mind, grip on reality, etc.

The fact is, dimensions are applied and space-time is a conceptual framework for making sense of various matter-energy events in different contexts. I would guess that misinterpretation of one observational context in terms of another is the cause of most if not all shortcomings in knowledge.

Learning how to sort out the discrepancies caused by misapplied knowledge is probably the key to attaining truer knowledge, but in order to do that you have to overcome the insistence of everyone who has achieved some level of authority or expertise who is more interested in asserting what they know than figuring out how what they know might be misleading at one level, even while it may be enlightening on another.

In short, some people can't resolve cognitive dissonance, nor can they accept that their senses are more about filtering irrelevant information for the sake of survival than anything else. Intellect aside (and yes, I know that's a BIG aside, but for now, please) we're not built to explore much outside of new hunting grounds. We see a tiny portion of the EM spectrum, hear a little bit in some mediums, feel vaguely, and ALL of this is subject to interpretation at the cellular level.

I'll have to see if the JAMA article is free, but there was a fun study recently which shows that cells in the retina respond to basic shapes which informs later processing in the brain. You're concieving what it is you see, before the signal even travels the optic nerve to the brain.

As you say, it's not an argument for Solopism, but an argument for ignorance beyond what can be proven in experiments, and perhaps the result that we'll end using technology based on principles we may not be capable of understanding in a way we find satisfactory (say, the way we understand a rock, or think we do).

 

[watty]

doesnt this thread go against the sticky rules in that its a discussion of someones theory?

 

[atyy]

How can time exist or not? Time is sequentiality. Matter and energy exist. Forces are relations between them. Time/sequentiality is a method of defining and measuring them. Don't mix up materiality with cognition. Yes our only access to materiality comes via cognition, but it is possible to sort out ideas from material things, imo.

When discussing general relativity, we are not discussing psychological time, nor thermodynamic time, nor several other times. We are discussing time as defined in general relativity, or as Nikolic suggests "pime"! http://www.fqxi.org/community/forum/topic/259

 

[brainstorm]

When discussing general relativity, we are not discussing psychological time, nor thermodynamic time, nor several other times. We are discussing time as defined in general relativity, or as Nikolic suggests "pime"! http://www.fqxi.org/community/forum/topic/259

If people could adequately bracket their discussion of time to limit their discussion to the context of GR or any other theory, there would never be any issue of whether time, space, or any other dimensionality exists outside of theory.

However, I don't know of anyone disciplined enough to separate their psychological or other personal experiences of time from their discussion of physics. Most physicists I know think that the physical realities described in their theories are the same physical realities they live in. Many wouldn't have any reason to do physics without this belief.

I guess the simplest way to put this problem is whether physics is a form of philosophy or something else. I would say of course it is, but too many scientists experience some kind of primal desire to distinguish themselves from philosophers, I think.

 

[bapowell]

I really hesitate to get involved in this discussion, but isn't the difference between physics and philosophy the fact that physics is an experimental science?

 

[brainstorm]

I really hesitate to get involved in this discussion, but isn't the difference between physics and philosophy the fact that physics is an experimental science?

I understand your hesitation, because I share it. It is potentially energy-draining and fruitless, depending who gets involved in the discussion and the attitude they take.

Still, it is a valid issue; one that has the potential to refine philisophical understanding of the relationship between disciplinarities.

I think the most fruitful basis for it is to establish what disciplinarity is and how distinct disciplines may relate to each other. From a relatively naive approach to classification, any discipline or other category of knowledge can be defined in mutual exclusion to other categories. This is naive because in reality, forms of knowledge labeled as distinct actually overlap and are related in their genealogy and conceptual bases.

So, to get into the logic of whether physics is an experimental science and philosophy isn't, you have to address the question of what constitutes experimentation and whether philosophy is devoid of it.

Likewise, to define physics or any other category of science as "not philosophy," you would have to define philosophy and demonstrate that physics or the other science is devoid of philosophical elements.

In practice, these are impossible and in fact physics exercises philosophical elements - and experimentation and empiricism can be viewed as philosophical methods of appropriating observation and interaction with material realities in the process of generating knowledge.

If you can understand all that, then it should not be too difficult to see how physics or any other science brings philisophically-derived concepts to bear on observations and even applies theoretically developed concepts and language to processes of perception and (empirical) observation to start with.

This is maybe a risky claim, but I would venture to say that science is applied philosophy in the same sense that technology and engineering is applied science.

 

[Dale]

I am not advancing any theory of my own. It's amazing that you're threatening to ban me...

Perhaps you would be interested in reading some of the fqxi essay winners, by Julian Barbour (visiting physics professor at Oxford), Claus Kiefer (institute for theoretical physics at Univ of Köln), or Carlo Rovelli (univ of Marseille phy dept) http://www.fqxi.org/community/essay/winners/2008.1 I was expressing a simplified (and obviously less cogent) version of that argument.

The fqxi is not a peer-reviewed source, it is an essay contest. Your continuing along this line is inappropriate, you have agreed to the rules and are deliberately ignoring them despite having been warned.

Btw, you did not adress the substance of my rebuttal. All of the words in bold already imply time. Your statement was nonsense (regardless of who you are imitating) without time.

 

[Dale]

Still, it is a valid issue; one that has the potential to refine philisophical understanding of the relationship between disciplinarities.

So take it to the philosophy forum.

This thread has now been thoroughly hijacked by ia_ and brainstorm and abandoned by the OP, it seems to have lost all useful purpose.

 

[brainstorm]

So take it to the philosophy forum.

This thread has now been thoroughly hijacked by ia_ and brainstorm and abandoned by the OP, it seems to have lost all useful purpose.

This topic is very relevant to this thread. The whole problem of discussing the existence of dimensionality, space, and time in the context of physics is that it is a philosophical physics issue. That was the point of the post.

Discussing what spacetime, space, time, dimensions, etc. are is absolutely a physics topic, but it is an impossible one without awareness that this is the philosophical side of physics.

There was no intent to hijack the thread, and it is the OP's responsibility to provide argumentation why or how this issue could avoid philosophical grounding issues, imo.

 

[Hoku]

Haven't abandoned the post, just busy this weekend. Bought a book, The Shape of Space by Jefferey Weeks and am reading through it before posting next.

ia_'s post made sense to me. Because of time dialation, two seconds is relative (twin paradox), right? So I think ia_ is saying that the important measurement is how far the clock hand moves. This is because 2-seconds is different for each twin but the both see the clock hand move the same amount, right? I think this is in line with Relativity?

Anyway, wish I could write more but I didn't even have time to write this. Gotta go...

 

[Dale]

This topic is very relevant to this thread. The whole problem of discussing the existence of dimensionality, space, and time in the context of physics is that it is a philosophical physics issue.

Philosophers can write reams of elegant prose and carefully disguise the tired old recycled arguments, and not a word of it changes the fact that theories that use time accurately predict the results of experiment. That is all that is expected of any scientific theory.

You may not realize it, but your and ia_'s anti-time ramblings are a dime a dozen here (sometimes on days like today we get two for the price of one). I have offered the same challenge to each that I now offer to you:

If time does not exist then show me a time-free theory of physics that both accurately predicts the results of experiments done to date and also suggests new experiments which have not yet been performed which could distinguish it experimentally from time-based theories. Until such a theory has been developed and experimentally validated it would appear that nature disagrees with your musings.

I have no doubt that you will fail to answer this challenge as have all of your predecessors.