# Is Space-Time a Physical Entity or a Mathematical Model?

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True but Tim is comparing mathematical models. Yet ignoring how those models define and use the term dimension. It is a mathematical convenience. How else does one describe or even define reality except via relations/interactions/quantites ?

m

Edited by Mordred

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Perhaps Physicists sometimes forget this as well?

In order to mathematically guarantee the calculus of differential geometry on manifolds you have to restrict them to finite subsets of Rn, otherwise you cannot generate the necessary neigherbourhoods.

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Oh I imagine some do lol. Either way the only way to agree on reality is to agree on how to define reality. Which subsequently requires agreed on relations and definitions. Which invariently will require agreed upon measurements.

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Measurements are good.

Physicists should never be afraid of getting their hands dirty.

Edited by studiot

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lol I would say measurements are required. Unfortunately there is no way to measure Lorentz ether. So why believe it better represents reality.

Edited by Mordred

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Because my definition of reality follows English in including abstract nouns.

It exists because we have invented it.

It has, however, less merit than caloric which enjoys at least some use in thermodynamics, but can be equally falsified in other uses.

The fictitious current in electric circuit theory has more use and is self consistent.

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It exists because we have invented it.

Action is a good example, we can describe all kinematic interactions via action.

Does this make action real?

We can measure,model and mathematically describe action. Yet we invented the model

Your all familiar with Newtons Mechanics

$\overrightarrow{f}=m\overrightarrow{a}=m\ddot{\overrightarrow{r}}$

Instead of looking at initial position and velocity, look at the initial position and final position and connect the with two paths. (Doesn't necessarily need to be straight lines) Assign those points $\overrightarrow{r}(t_1),\overrightarrow{r}(t_2)$ The path taken can be determined by action.

Were just simplifying and using radius as a coordinate

action =$S=\int^{t_2}_{t_1}$$(KE-PE)dt$

You can find the details on the last equation at Feyman lectures.

http://feynmanlectures.caltech.edu/II_19.html

relativistic motion for an electromagnetic field for Newton potential ie a particle moving in a weak uniform gravitational field

$\mathcal{L}=-m_o c\sqrt{1-1-v^2/c^2}-q(\phi-v*A$

For a particle moving in a vertical path in a gravity field then

$PE=1/2m\dot{x}^2$ the kinetic term for a particle $ke=1/2m\dot{x}$

gives with the above situation\

$\mathcal{L}=1/2\dot{x}^2+1/2m\dot{z}^2-mgz$

However that is in weak gravity fields. Without going through all the solutions there is a sort of a master equation very close in some regards to a GUT for motion lol.

$\stackrel{Action}{\overbrace{\mathcal{L}}} \sim \stackrel{relativity}{\overbrace{\mathbb{R}}}- \stackrel{Maxwell}{\overbrace{1/4F_{\mu\nu}F^{\mu\nu}}}+\stackrel{Dirac}{\overbrace{i \overline{\psi}\gamma_\mu\psi}}+\stackrel{Higg's}{\overbrace{\mid D_\mu h\mid-V\mid h\mid}} +\stackrel{Yugawa-coupling}{\overbrace{h\overline{\psi}\psi}}$

Quite handy in that we can describe all field and kinematic motion under action but does this mean Action is real?

Edited by Mordred

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No.

I.o.w. you don't agree there can be no non-inertial motion without the existence of an ether.

I.o.w. non-inertial motion does not need an ether to exist. Thanks.

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Hi Mordred, sorry I can't cut and paste on this pesky pc so I refer to line 6 of your post#232

Your position points define a displacement, and these do not have to be 'real' in the sense used in the Principle of Virtual Displacements.

In fact that is really the idea behind the calculus of variations.

All non extremal displacements and actions are, in a sense, virtual.

The other plus point for the POVD is that it works with both linear and non linear, Newtonian and non Newtonian mechanics.

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Th discussion lately has been one of reality. The OP, however, has taken this one step further. Not a question of reality, but a question of a physical existence.

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Hi Mordred, sorry I can't cut and paste on this pesky pc so I refer to line 6 of your post#232

Your position points define a displacement, and these do not have to be 'real' in the sense used in the Principle of Virtual Displacements.

In fact that is really the idea behind the calculus of variations.

All non extremal displacements and actions are, in a sense, virtual.

The other plus point for the POVD is that it works with both linear and non linear, Newtonian and non Newtonian mechanics.

Yes virtual Displacement is handy, its usually a first order aporoximation of infinitesimals. Though if you maintain your constraints can become a second order approximation.

Its too bad a lot of people don't recognize how truly useful virtual displacement is. Particularly in simplifying complex problems. However your right in that a displacement does not necessarily need to be real under virtual displacements.

Certainly relates to the difference between Lorentz and GR. I know you understand what I am stating by that but I doubt other readers will.

Th discussion lately has been one of reality. The OP, however, has taken this one step further. Not a question of reality, but a question of a physical existence.

Well that gets complex considering quantum mechanics show that Newtonian physics, the Lorentz transformations and even GR are merely approximations. That merely reflect our perception of reality.

When you get right down to it every model discussed in this thread revolves around reality yet none accurately describe reality. This would include the ether itself. On a macro level assuming one could measure it. It may appear as a matter field. Yet under a quantum level class of observers would appear completely different.

When you get right down to it particles themselves let alone waveforms are abstractions. We model reality under a class of observers. That doesn't define reality. Physical existance ie physical properties also involve class of observers. Any measurable property exists to that observer.

Edited by Mordred

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Well that gets complex considering quantum mechanics show that Newtonian physics, the Lorentz transformations and even GR are merely approximations. That merely reflect our perception of reality.

That was my point earlier. If they are known to be approximations, how can they be a physical reality?

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You still haven't defined reality Tim.

[..]

That's right; how would you define reality? I'm not a dictionary.

In the end, words are defined by their usage and context.

Quite frankly nothing is solid, everything is nothing more than attractive/repulsive field excitations to field interactions and interferance.

[..]

And what do those "fields" consist of? Are those fields just made of mathematics, merely imaginations of our minds, or are they something substantial of nature according to you?

[..]

Please stop misquoting my posts by the way. You obviously refuse to see my arguments as you never address them. In particular adherence to basic math and definitions when discussing mathematical models such as Lorentz ether. [..]

Lorentz Ether is a mathematical model [..]

And where did I misquote any post of yours?? Anyway, it's a huge misconception to call Lorentz Ether a "mathematical model". Except if it's a mis-definition of the word "mathematical". Maybe you call radio waves and air molecules "mathematical models"??

That was my point earlier. If they are known to be approximations, how can they be a physical reality?

Exactly! Not sure if it is what you meant, but physical realty doesn't depend on our mathematical approximations.

I.o.w. there can be no non-inertial motion without the existence of an ether?

You mean, a (meta)physical entity such as an ether? Einstein tried to get rid of that concept by means of Mach's principle, but that didn't work as he explained. Others replaced "ether" by other words such as "fields" and "the vacuum", which are conceptually slightly different; but mere empty nothingness fails to explain inertia and related things such as clock retardation. Maybe you have an idea?

True but Tim is comparing mathematical models.[..]

No, mathematical models are not metaphysics in my book.

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Tim88

Maybe you call radio waves and air molecules "mathematical models"??

You mean, a (meta)physical entity such as an ether? Einstein tried to get rid of that concept by means of Mach's principle, but that didn't work as he explained

Do you also consider phlogiston real, just because famous people for at least 1500 years proclaimed it so?

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You are discussing 3d space vs 4d space. Yet ignore the literal meaning of dimension. If thats your idea of metaphysics ie no agreed upon definitions in any regard. You can keep it. As it becomes useless.

Too bad you can't understand such a basic concept as agreed upon definitions instead of willy nilly its whatever I feel that terminology means.

Lorentz ether is a mathematical model with zero measurable support.

So how can you possibly discuss that model even in metaphysics without discussing the math behind it?

You can't even use the definitions of key terminology within metaphysics.

example presentism

The majority of this thread has been an effort to get you to distinquish and clarify your terminology rather than the subject itself. So we can all work with identical meanings and cannotations. I've lost count on how many wasted pages of posts we've had to get you to use the proper terminology so any reader can join in without having to retranslate your personal definitions.

yeesh

That's right; how would you define reality? I'm not a dictionary.

In the end, words are defined by their usage and context.

Can you not google the terminology? All persons in any discussion to be meaningful must use the same definitions metaphysics or not.

And what do those "fields" consist of? Are those fields just made of mathematics, merely imaginations of our minds, or are they something substantial of nature according to you?

Did you not read the recent discussion Studiot and I had on virtual force as opposed to real force? Under time treatments?

You mean, a (meta)physical entity such as an ether? Einstein tried to get rid of that concept by means of Mach's principle, but that didn't work as he explained. Others replaced "ether" by other words such as "fields" and "the vacuum", which are conceptually slightly different; but mere empty nothingness fails to explain inertia and related things such as clock retardation. Maybe you have an idea?

What is the key differences of a static matter (ether) that doesn't interact, to a static field ? Nothing except mathematical relations.

A field is simply a collection of objects it doesn't matter what those objects are. It could be a collection of events, vectors, spinors etc. The objects can be mathematical or any everyday object such as a bag full of oranges.

The key distinction is when you specify a matter field you are referring to a specific type of field.

In the case of ether, one that doesn't behave in the same manner as any matter we observe it has no matching particle form under any SM particle.

Matter particles being fermionic but ether matches statistics of a boson with spin zero characteristics (static, uncharged).

Which quite frankly those characteristics is similar to the Higg's field which is not a fermionic matter field.

This knowledge was after Einstein, Lorentz etc. They only knew about electrons and protons. They didn't have our current knowledge of SM particles. They didn't even know about the neutron.

That wasn't discovered until 1932. The strong force wasn't even explained until after 1970. Before then we didn't even know how the nucleus held together in atoms. Let alone quarks/gluons etc. For that matter during Lorentz's time the only known fundamental particles were the electron,photon and proton.

James Chadwick and E.S. Bieler didn't propose the strong force until 1921

No, mathematical models are not metaphysics in my book.

Then why do they call it meta (physics). When physics is mathematical models describing reality? yet doesn't define reality

Maybe they should rename it meta whatever I feel like

Edited by Mordred

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Does something require embodiment to be real and part of reality?

Consider this example.

I pick up something and pull on it.

It stretches some.

Then I let go.

It returns to its original size.

I pull on it some more (a bit harder this time).

It stretches further and again returns to original condition upon release.

This is called elasticity.

So does elasticity exist? It elasticity real?

So

Can I weigh it?

Can I see it?

Can I smell, taste, feel, etc it?

Well actually none of these.

Yet I maintain that elasticity is real and that any system of definition that is unable to cope with this simple example of abstract existence is seriously deficient.

We deal with many far more subtle effects in our encounters with reality than this so we need a sophisticated definition to cope with with all the vagaries and ramifications.

Edited by studiot

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They are measurable quantities that more than one observer can agree upon under a standardized agreed upon format and definitions.

I would consider that real to the best of our ability.

To avoid confusion you don't measure math. Math does the measuring.

Edited by Mordred

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... mere empty nothingness fails to explain inertia and related things such as clock retardation.

Clock retardation (time dilation) follows from relativity of simultaneity: different 3D cuts through 4D spacetime.

You don't need a kind of ether to produce or explain time dilation.

Do you think ether is NEEDED to produce relativity of simultaneity?

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Does something require embodiment to be real and part of reality?

Consider this example.

I pick up something and pull on it.

It stretches some.

Then I let go.

It returns to its original size.

I pull on it some more (a bit harder this time).

It stretches further and again returns to original condition upon release.

This is called elasticity.

So does elasticity exist? It elasticity real?

So

Can I weigh it?

Can I see it?

Can I smell, taste, feel, etc it?

Well actually none of these.

Yet I maintain that elasticity is real and that any system of definition that is unable to cope with this simple example of abstract existence is seriously deficient.

We deal with many far more subtle effects in our encounters with reality than this so we need a sophisticated definition to cope with with all the vagaries and ramifications.

This is a nice analogy but a bit misguided in my opinion. If we corelate this analogy to the subject at hand, I presume we have to assume that elasticity is analogous to curvature of space time. Therefore spacetime is the rubber toy being exposed to elasticity and spacetime curvature is the elasticity. I wouldn't attempt to argue wether elasticity or curvature is a "physical thing" By all means both of these phenomena I would concider "real" but we also concluded in many threads that "real" is such a subjective term that it doesnt make sense to use it in this context.

Now, as for the title of the thread (the question at hand) do we have a solid definition of "physical" ? We can safely assume that "mathematical model" is a well defined and simple concept - its a measuring tool. As for "physical", previous threads shown that its not a simple task to define it In fact I don't think anynody has, its more of a semantics game. If we define "physical" as something which has to have mass, energy, volume or charge than things like spacetime or the 4 forces cannot be considered physical. Yet in my opinion they are - semantics again. So in order to answer if spacetime is a physical thing and/or just a mathematical model we need to define "physical"

Although I've read and watched numerous media on this subject since I've come to this forum 6 months ago, I cannot find a clearcut answer. For me it remains an intuitive answer (which doesnt satisfy me btw) - "if it bends, its a physical thing"

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Physical is tricky to define. You can have a physical property such a length, width, height color, smell etc. Or physical relations.

ie force,strain, torque. voltage etc.

Physical doesn't mean exclusively materialistic. Simple relations or measurable properties are physical even if virtual or quasi. Ie phonons.

Unfortunately its a common misconception to equate materialistic with the term physical.

Edited by Mordred

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Physical is tricky to define. You can have a physical property such a length, width, height color, smell etc. Or physical relations.

ie force,strain, torque. voltage etc.

Physical doesn't mean materialistic.

I agree. Thats why it is futile to answer the title question of this thread. Or better yet, its not futile, its a badly stated question. Edited by koti

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I agree. Thats why it is futile to answer the title question if this thread.

I absolutely agree on that lol. Thats why I've been stressing the importance of definitions of the terminology used 😉

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I absolutely agree on that lol. Thats why I've been stressing the importance of definitions of the terminology used 😉

But if it bends it be real ain't it?

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If more than one person agrees it bends via measurement I would say yes. After all you have to seperate illusions

Ie visual perception. A mirage is a measurable effect. Just as objects appearing smaller at distance is a "real effect"

Edited by Mordred

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A mirage is a measurable effect.

And there goes the elusive moment when we had it figured out