# Models for making sense of relativity - physical space vs physical spacetime

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Tim88

A geometric method for solving such applied mathematical questions would likely be of interest in either the relativity forum or in the homework forum. It will be of no interest here, except if that method provides a different explanation for the car example than the two models of reality already under discussion.

OK so you don't want another model when offered, despite asking for one.

But you cannot keep claiming that other models do not exist.

Over and out.

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Who said anything about SM particles involvement in the stress tensor being an alternative view to GR.?

That is precisely what GR describes...

As far as block universes. There is two main models. "block universe" and "evolving block universe". The first is problematic as it requires reversible processes. The second fixes this using tangent bundle worldlines. However you still run into the "presentism vs eternal arguments".

the block universe models would just serve to add distraction.

I really don't understand why people can't see the stress tensor involvement in the Einstein field equations. How the stress tensor correlates pressure/mass density to determine the metric tensor.

The Lorentz group SO(3.1) includes all the SM particles under SO(2)×U (1).

So all dynamics not involving supersymmetric particles and the Higgs field is described under the SO(3)×SO(2)×U (1). This includes their thermodynamic influences via their corresponding equations of state.

However this is probably best done by a worked example. To save some time I'll post an example of just matter with an equation of state w=0. pressureless.

Radiation and lambda have different pressure relations.

As I mentioned equations of state...

here is another workup I did on another thread.

$DU=pdV$.

First take the first law of thermodynamics.

$dU=dW=dQ$

U is internal energy W =work.

As we dont need heat transfer Q we write this as $DW=Fdr=pdV$

Which leads to $dU=-pdV.$. Which is the first law of thermodynamics for an ideal gas.

$U=\rho V$

$\dot{U}=\dot{\rho}V+{\rho}\dot{V}=-p\dot{V}$

$V\propto r^3$

$\frac{\dot{V}}{V}=3\frac{\dot{r}}{r}$

$\dot{\rho}=-3(\rho+p)\frac{\dot{r}}{r}$

We will use the last formula for both radiation and matter.

Assuming density of matter

$\rho=\frac{M}{\frac{4}{3}\pi r^3}$

$\rho=\frac{dp}{dr}\dot{r}=-3\rho \frac{\dot{r}}{r}$

Using the above equation the pressure due to matter gives an Eos of Pressure=0. Which makes sense as matter doesn't exert a lot of kinetic energy/momentum.

For radiation we will need some further formulas. Visualize a wavelength as a vibration on a string.

$L=\frac{N\lambda}{2}$

As we're dealing with relativistic particles

$c=f\lambda=f\frac{2L}{N}$

substitute $f=\frac{n}{2L}c$ into Plancks formula

$U=\hbar w=hf$

$U=\frac{Nhc}{2}\frac{1}{L}\propto V^{-\frac{1}{3}}$

Using

$dU=-pdV$

using

$p=-\frac{dU}{dV}=\frac{1}{3}\frac{U}{V}$

As well as

$\rho=\frac{U}{V}$

$p=1/3\rho$ for ultra relativistic radiation.

Those are examples of how the first law of thermodynamics fit within the equations of state. There is more intensive formulas involved. In particular the Bose-Einstein statistics and Fermi-Dirac statistics

What the above correlates to is particle degrees of freedom.

One can calculate how much influence any particle with known properties influence the temperature... pressure... expansion relations. Provided one knows the correct correlations to the Einstein field equations.

(the above can and does affect geodesic equations. Which in turn can and does affect redshift to distance calculations)

So to that end a sample of how to define a geodesic may be handy.

For that Im going to cheat again and use a previous post...

in the presence of matter or when matter is not too distant physical distances between two points change. For example an approximately static distribution of matter in region D. Can be replaced by the equivalent mass

$M=\int_Dd^3x\rho(\overrightarrow{x})$ concentrated at a point $\overrightarrow{x}_0=M^{-1}\int_Dd^3x\overrightarrow{x}\rho(\overrightarrow{x})$

Which we can choose to be at the origin

$\overrightarrow{x}=\overrightarrow{0}$

Sources outside region D the following Newton potential at $\overrightarrow{x}$

$\phi_N(\overrightarrow{x})=-G_N\frac{M}{r}$

Where $G_n=6.673*10^{-11}m^3/KG s^2$ and $r\equiv||\overrightarrow{x}||$

According to Einsteins theory the physical distance of objects in the gravitational field of this mass distribution is described by the line element.

$ds^2=c^2(1+\frac{2\phi_N}{c^2})-\frac{dr^2}{1+2\phi_N/c^2}-r^2d\Omega^2$

Where $d\Omega^2=d\theta^2+sin^2(\theta)d\varphi^2$ denotes the volume element of a 2d sphere

$\theta\in(0,\pi)$ and $\varphi\in(0,\pi)$ are the two angles fully covering the sphere.

The general relativistic form is.

$ds^2=g_{\mu\nu}(x)dx^\mu x^\nu$

By comparing the last two equations we can find the static mass distribution in spherical coordinates.

$(r,\theta\varphi)$

$G_{\mu\nu}=\begin{pmatrix}1+2\phi_N/c^2&0&0&0\\0&-(1+2\phi_N/c^2)^{-1}&0&0\\0&0&-r^2&0\\0&0&0&-r^2sin^2(\theta)\end{pmatrix}$

Now that we have defined our static multi particle field.

Our next step is to define the geodesic to include the principle of equivalence. Followed by General Covariance.

Ok so now the Principle of Equivalence.

You can google that term for more detail

but in the same format as above

$m_i=m_g...m_i\frac{d^2\overrightarrow{x}}{dt^2}=m_g\overrightarrow{g}$

$\overrightarrow{g}-\bigtriangledown\phi_N$

Denotes the gravitational field above.

Now General Covariance. Which use the ds^2 line elements above and the Einstein tensor it follows that the line element above is invariant under general coordinate transformation(diffeomorphism)

$x\mu\rightarrow\tilde{x}^\mu(x)$

Provided ds^2 is invariant

$ds^2=d\tilde{s}^2$ an infinitesimal coordinate transformation

$d\tilde{x}^\mu=\frac{\partial\tilde{x}^\mu}{\partial x^\alpha}dx^\alpha$

With the line element invariance

$\tilde{g}_{\mu\nu}(\tilde{x})=\frac{\partial\tilde{x}^\mu \partial\tilde{x}^\nu}{\partial x^\alpha\partial x^\beta} g_{\alpha\beta}x$

The inverse of the metric tensor transforms as

$\tilde{g}^{\mu\nu}(\tilde{x})=\frac{\partial\tilde{x}^\mu \partial\tilde{x}^\nu}{\partial x^\alpha\partial x^\beta} g^{\alpha\beta}x$

In GR one introduces the notion of covariant vectors $A_\mu$ and contravariant $A^\mu$ which is related as $A_\mu=G_{\mu\nu} A^\nu$ conversely the inverse is $A^\mu=G^{\mu\nu} A_\nu$ the metric tensor can be defined as

$g^{\mu\rho}g_{\rho\nu}=\delta^\mu_\mu$ where $\delta^\mu_nu$=diag(1,1,1,1) which denotes the Kronecker delta.

Finally we can start to look at geodesics.

Let us consider a free falling observer. O who erects a special coordinate system such that particles move along trajectories $\xi^\mu=\xi^\mu (t)=(\xi^0,x^i)$

Specified by a non accelerated motion. Described as

$\frac{d^2\xi^\mu}{ds^2}$

Where the line element ds=cdt such that

$ds^2=c^2dt^2=\eta_{\mu\nu}d\xi^\mu d\xi^\nu$

Now assunme that the motion of O changes in such a way that it can be described by a coordinate transformation.

$d\xi^\mu=\frac{\partial\xi^\mu}{\partial x^\alpha}dx^\alpha, x^\mu=(ct,x^0)$

This and the previous non accelerated equation imply that the observer O, will percieve an accelerated motion of particles governed by the Geodesic equation.

$\frac{d^2x^\mu}{ds^2}+\Gamma^\mu_{\alpha\beta}(x)\frac{dx^\alpha}{ds}\frac{dx^\beta}{ds}=0$

Where the new line element is given by

$ds^2=g_{\mu\nu}(x)dx^\mu dx^\nu$ and $g_{\mu\nu}=\frac{\partial\xi^\alpha}{\partial\xi x^\mu}\frac{\partial\xi^\beta}{\partial x^\nu}\eta_{\alpha\beta}$

and $\Gamma^\mu_{\alpha\beta}=\frac{\partial x^\mu}{\partial\eta^\nu}\frac{\partial^2\xi^\nu}{\partial x^\alpha\partial x^\beta}$

Denote the metric tensor and the affine Levi-Civita connection respectively.

To put bluntly I just described freefall of two particles above a typical planet or star. That description did not require an Ether. Nor did it require force...

The quoted section details the individual EoS. The portion after is freefall matter.

What did I cover...

1) principle of equivalence

2) principle of covariance

3) spacetime geodesic in Newton limit.

4) The equation of state of matter and radiation

5) Levi-Civita_connection

6) parallel transport and its usage to map curvature.

yet the only particle I needed to describe that is motionless baryonic matter.... I did not need a block universe conjecture nor an Eather. The medium already exists (just at extremely low density. ie 10^-29 grams/m^3...) and greater.

What that medium is comprised of requires factoring in the Equations of state and the added degrees of freedom. Though it is your standard model of particles.

Different equations of state influence the stress tensor which influences the metric tensor.

No Ether...

If you wish to do the above in QFT style treatments switch to action vs momentum vectors.

of course if you do that. Using the above you can arrive at the principle of least action . I simply included the principle above without any details.

In simplistic form the principle of least action can be expressed as.

$Action=S=\int_{t_0}^{t_1}[\frac{1}{2}m (\frac{dx}{dt})^2+-mgx]dt$

Between events t_0 and T_1 there is millions of possible paths. Starting and ending at those points. The correct path is the one where the sum of kinetic energy (LHS of the + sign) and potential energy (rhs of the + sign) is lowest.

You can correlate the EoS influence upon the KE term...

edit:::forgot to add an important formula involving the stress tensor

$T^{\mu\nu}=(\rho+p)U^{\mu}U^{\nu}+p\eta^{\mu\nu}$

Now I realize none of the above is easy to understand. However trying to describe the above in terms of an Eather or block universe would only cause additional problems.

Trying to learn GR using ether or block universes will not aid in the above. Your better off simply sticking within GR (albiet the field equations include thermodynamics)

lol from personal experience trying to understand the above using alternative models etc cost me several years. Once I stayed focussed on just GR....

Edited by Mordred
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Sorry but I can't access this link, it seems to want more money or something in the meter.

The link is a Google search result leading to an image of a Google book page. I can still access the page, but it will be better to insert it as an image as you have done before, studiot. Can anyone assist?

As far as block universes. There is two main models. "block universe" and "evolving block universe". The first is problematic as it requires reversible processes...

[snip]

Now I realize none of the above is easy to understand. However trying to describe the above in terms of an Eather or block universe would only cause additional problems.

Trying to learn GR using ether or block universes will not aid in the above. Your better off simply sticking within GR (albiet the field equations include thermodynamics)

lol from personal experience trying to understand the above using alternative models etc cost me several years. Once I stayed focussed on just GR....

I have no intention to quibble with Mordred re his elaborate and pretty impressive calculations and I appreciate his comment that for him to have considered alternative models cost him several years...so why bother to try re-inventing the relativity wheel, so to speak..?

There is one question that I have though. Mordred, you first posted "the biggest problem with block universe is irreversible processes" and now "it requires reversible processes"...why? The model is event-driven, not process-driven, not so? An eternal and deterministic block universe is a collective of all events at all coordinates of space-time. They are all fixed (have occurred) and (theoretically-) accessible by the "reallocation of experiencing one coordinate/event to experiencing another"...so to say.

As far as block universes. There is two main models. "block universe" and "evolving block universe". The first is problematic as it requires reversible processes. The second fixes this using tangent bundle worldlines. However you still run into the "presentism vs eternal arguments".

My understanding thereof is that the "standard" block universe works best as being eternal and deterministic (as in determinism). The alternative is the "growing block universe" which seems to fit better with presentism and/or indeterminism..?

Edited by Memammal
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With new emphasis:

Tim88

A geometric method for solving such applied mathematical questions would [..] be of no interest here, except if that method provides a different explanation for the car example than the two models of reality already under discussion.

OK so you don't want another model when offered, despite asking for one.

But you cannot keep claiming that other models do not exist.

Over and out.

What to make of that?

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You've named the key problem. "deterministic" However deterministic events is also reversible. These type of events the block universe describes rather well. Essentially the block universe can be described by the following.

At any particular moment in time, past or future events can be determined by the time reversible hamiltons.

Now what about the events that aren't deterministic? good example QM and superposition? The uncertainty principle, quantum fluctuations etc.

Now one might argue that this averages out on the macro scale and it does. Right until you include inflation.

Anyways describing our universe evolution by strictly deterministic events was too limited an approach. In steps the evolving block universe.

a simple few sentences can describe this.

The past is already determined and fixed. The future cannot be determined due to quantum fluctuations.

All change occurs in the present.

The papers I've read on the subject. (I still study alternative models. You can often find interesting modelling techniques) tend to get heavily into trying to define presentist, eternalist and probalistic observers. Which becomes quite messy....

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Who said anything about SM particles involvement in the stress tensor being an alternative view to GR.?

That is precisely what GR describes...

As far as block universes. There is two main models. "block universe" and "evolving block universe". The first is problematic as it requires reversible processes. The second fixes this using tangent bundle worldlines. However you still run into the "presentism vs eternal arguments".

the block universe models would just serve to add distraction.

I really don't understand why people can't see the stress tensor involvement in the Einstein field equations. How the stress tensor correlates pressure/mass density to determine the metric tensor.

[..]

lol from personal experience trying to understand the above using alternative models etc cost me several years. Once I stayed focussed on just GR....

The complication of two variants of block universe is useful input; probably it's most useful to keep it generic here without elaborating on variants, in order not to fall in distractions, as you say.

However, I'm very sorry, most of your otherwise very interesting mathematical discussion is really besides the point for the discussion here. [edit:] I doubt that you mean that you really don't understand why Einstein can't see the stress tensor involvement in the Einstein field equations!

Please check out his arguments as summarized in the discussion of which this is a fork, and see if you can offer an alternative to the physical interpretations that are discussed in more detail in this thread.

http://www.scienceforums.net/topic/97105-is-space-time-a-physical-entity-or-a-mathematical-model/page-11#entry944692

http://www.scienceforums.net/topic/97105-is-space-time-a-physical-entity-or-a-mathematical-model/page-11#entry945982

Edited by Tim88
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Yes I read those posts before. You only included two physical interpretations. I'm not going to restrict my discussion to two problematic models simply so you can apply a physical aspect to a model that already details all the physical aspects.

The physical aspects of GR is inherent in the thermodynamics of the standard model of particles. Nothing more.

No ether. No block. No preferred frame.

The math above is right on target from the GR view. You seem to want to restrict yourself to SR historical arguments. However SR (Lorentz,Minskowskii) has a strong reliance on simultaneous events and observers at rest.

The Einstein field equations is where you should be looking to describe the physical hydrodynamic aspects of spacetime.

mass is only one aspect of the stress tensor, you also have flux and vorticity. Your four momentum and 4 vectors are described by the stress tensor.

It is the stress tensor that determines the spacetime geometry.

With the proper applications. One can calculate how every particle species behaves or moves from the EFE. You can calculate nearly every physical characteristic you want. Temperature, pressure, entropy density, chemical potential, wavelength, mass, energy etc

What other physical characteristics are you specifically seeking that isn't included in the above?

I certainly don't require some mythical ether nor block universe to describe how spacetime affected the motion of freefalling particles.

Edited by Mordred
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The past is already determined and fixed. The future cannot be determined due to quantum fluctuations.

All change occurs in the present.

Only that within the "standard" or eternalist block universe the future has the same status as the present and the past in the sense that future events have "already occurred" (thus determined and fixed), but are yet to be experienced (or observed). There can be no change in the status quo apart from the change in a different "now" (location). Quantum fluctuations therefore become illusionary, while inflation simply forms part of that reality..? I intentionally try to keep this as uncomplicated as I possibly can as it then becomes a pretty straightforward model, but perhaps my limited understanding of QM is inhibiting my point of view.

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Bold emphasis mine:

Yes I read those posts before. You only included two physical interpretations. I'm not going to restrict my discussion to two problematic models simply so you can apply a physical aspect to a model that already details all the physical aspects.

The physical aspects of GR is inherent in the thermodynamics of the standard model of particles. Nothing more.

No ether. No block. No preferred frame.

The math above is right on target from the GR view. You seem to want to restrict yourself to SR historical arguments. However SR (Lorentz,Minskowskii) has a strong reliance on simultaneous events and observers at rest.

The Einstein field equations is where you should be looking to describe the physical hydrodynamic aspects of spacetime.

mass is only one aspect of the stress tensor, you also have flux and vorticity. Your four momentum and 4 vectors are described by the stress tensor.

It is the stress tensor that determines the spacetime geometry.

With the proper applications. One can calculate how every particle species behaves or moves from the EFE. You can calculate nearly every physical characteristic you want. Temperature, pressure, entropy density, chemical potential, wavelength, mass, energy etc

What other physical characteristics are you specifically seeking that isn't included in the above?

I certainly don't require some mythical ether nor block universe to describe how spacetime affected the motion of freefalling particles.

What we are discussing here is "the elephant in the room" that you don't see. Your words "spacetime affected" imply your adherence to the block universe (spacetime as a physical entity), which you reject.

Edited by Tim88
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Well I certainly never bothered too much with block universe conjectures. Either way the original block universe model didn't model reality too well.

Is the evolving block universe model any better.? You tell me its incredibly difficult to find decent papers on the subject that has the math formulization.

Words only go so far.

Bold emphasis mine:

What we are discussing here is "the elephant in the room" that you don't see. Your words "spacetime affected" implies your adherence to the block universe (spacetime as a physical entity on its own), and which you reject.

I certainly have no adherence to the block universe. I already pointed out the problems of the block universe. Which you weren't aware of.

Nor were you aware that the block universe was replaced by the evolving block universe.

spacetime is also a generic term that includes the SM particles within its volume.

How do you think the stress tensor causes the spacetime geometry to change without having a source of mass ie particles etc?

It can't you cannot seperate the stress tensor from the metric tensor or the Einstein tensor. What affects one affects them all.

Just like pressure affects temperature and density. They are properties that rely on each other.

Spacetime geometry relies on the stress tensor. The stress tensor relies on the thermodynamics of the SM particles. You can model each seperately but they will affect each other.

Edited by Mordred
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Either you know of a third "model of reality" for SR (and if so, please present it!), or you can watch the "fight" between two known models, and hopefully inject some more stimulating questions!

Special relativity is a model itself - you may be thinking of interpretations or analogies.

The model of special relativity is not very deep once you start to think geometrically, but for sure some of the results are not so intuitive from our everyday Newtonian perspective.

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As far as the quoted section that Ajb quoted. GR is also its own model. The Einstein field equations however is probably the best aporoach to modelling reality in terms of SR. As the EFE and GR include the SR metrics and much more. (thermodynamics)

Edited by Mordred
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As far as block universes. There is two main models. "block universe" and "evolving block universe". The first is problematic as it requires reversible processes. The second fixes this using tangent bundle worldlines. However you still run into the "presentism vs eternal arguments".

You are hinting at space-time cuts. That is making a meaningful cut of space-time into space and time. While this is not a problem locally, doing in globally in a nice way is problematic, unless your space-time has some nice properties - in particular the space-time is globally hyperbolic.

In a loose sense this means that you can cut you space-time into Cauchy surfaces that evolve in time. In particular, all the information about the theory is contained on each surface and you can evolve this. This is needed in the standard formulation of quantum field theory on curved backgrounds (there is some work on space-times that are not globally hyperbolic with in a algebraic framework).

So, I would say that 'pure GR' tells us that the block universe is the 'right' point of view, but as soon as you want other fields about a space-time cut is needed, or at least for now.

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Special relativity is a model itself - you may be thinking of interpretations or analogies.

The model of special relativity is not very deep once you start to think geometrically, but for sure some of the results are not so intuitive from our everyday Newtonian perspective.

[..] Right from the start it was perfectly possible to make sense of relativity by means of Lorentz's ether model.

[..] But in the meantime Minkowski had introduced a new interpretation of the Lorentz transformations [..]

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True GR is typically considered a support of block universe. However only under certain conditions. ie reasonably static.

Take for example freefall particles. Now add vorticity and flux along the freefall path. Can we say this dynamic is reversible?

You are hinting at space-time cuts. That is making a meaningful cut of space-time into space and time. While this is not a problem locally, doing in globally in a nice way is problematic, unless your space-time has some nice properties - in particular the space-time is globally hyperbolic.

In a loose sense this means that you can cut you space-time into Cauchy surfaces that evolve in time. In particular, all the information about the theory is contained on each surface and you can evolve this. This is needed in the standard formulation of quantum field theory on curved backgrounds (there is some work on space-times that are not globally hyperbolic with in a algebraic framework).

So, I would say that 'pure GR' tells us that the block universe is the 'right' point of view, but as soon as you want other fields about a space-time cut is needed, or at least for now.

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Right, so the modern understanding of the Lorentz, or really the Poncare transformations are as isometries of Minkowski space-time. As for any older and no longer used understandings, I know less about.

Lorentz and others who were working with the aether hypothesis tried to understand the invariance of Maxwell's equations in terms of the rest frame of the aether and so on... If there is some notion of the rest frame of the aether - whatever that aether is - then we have a canonical inertial frame to work with (at least ignoring gravity). One could then formulate everything in terms of this rest frame and look at what happens in other (inertial) frames.

But again, our modern understanding is that there is no aether and that field theory is the best understanding we have. There are no true canonical frames to work with and such frames are not needed in modern formulations. You care of course free to pick a frame (inertial or otherwise) to work with, and that is what one usually does in practice. But someone else is free to pick another frame and the physics is not truly dependent on this choice - though the physics may look a bit different at first.

Take for example freefall particles. Now add vorticity and flux along the freefall path. Can we say this dynamic is reversible?

That is a slightly different situation that I was think of - I was thinking of the space-time itself rather than the motion of test particles.

If you are thinking of back reaction then I can imagine that the question of reversibility is more complex. I am not sure.

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Right, so the modern understanding of the Lorentz, or really the Poncare transformations are as isometries of Minkowski space-time. As for any older and no longer used understandings, I know less about.

Lorentz and others who were working with the aether hypothesis tried to understand the invariance of Maxwell's equations in terms of the rest frame of the aether and so on... If there is some notion of the rest frame of the aether - whatever that aether is - then we have a canonical inertial frame to work with (at least ignoring gravity). One could then formulate everything in terms of this rest frame and look at what happens in other (inertial) frames.

But again, our modern understanding is that there is no aether and that field theory is the best understanding we have. There are no true canonical frames to work with and such frames are not needed in modern formulations. You care of course free to pick a frame (inertial or otherwise) to work with, and that is what one usually does in practice. But someone else is free to pick another frame and the physics is not truly dependent on this choice - though the physics may look a bit different at first.

I think that's almost correct. Lorentz and Einstein did not "try" to understand, they understood already Sr and GR in that way; and field theory cannot replace that understanding as already explained in the mother thread. That's why people who were looking for alternatives found refuge in block universe concepts, although probably many don't realize the philosophical consequences.

PS. Note also that "our modern understanding" of philosophy is mostly baseless or based on unscientific arguments. Philosophy is not physics!

Edited by Tim88
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I think that's almost correct.

I like the way you mathematical physics researchers that they are almost right!

Lorentz and Einstein did not "try" to understand, they understood already Sr and GR in that way;

Lorentz for sure tried to understand the mathematics in terms of a aether. Einstein also worked with this idea, but I think he did abandon the idea as it was once understood. I know that Einstein tried to introduce the idea that space-time is the 'aether', but this language did not catch on. For one, we do not think of space-time as being material, so the language is not really correct.

...and field theory cannot replace that understanding as already explained in the mother thread.

I disagree. Field theory, both classical and quantum is the bedrock of modern physics. Field theory gives us the most comprehensive and unified understanding of the Universe.

That's why people who were looking for alternatives found refuge in block universe concepts...

I don't understand your claim here. The block universe is a natural concept in special and general relativity, though as we like dynamics it is common and sometimes necessary to cut space-time into space and time. My own philosophical thoughts here - and many also hold the same thoughts - are that this cut should be avoided. Einstein tells us that space and time should be treated on equal footing.

...although probably many don't realize the philosophical consequences.

This I do agree with. Though, in all honesty, most people working in modern physics are less worried with the philosophical implications than they are with matching theory with observation. Special and general relativity work well and for many people that is enough - also I am not convinced that metaphysics can say a lot more with any confidence.

PS. Note also that "our modern understanding" of philosophy is mostly baseless or based on unscientific arguments. Philosophy is not physics!

Why is one reason I think that one cannot really advance much in metaphysics.

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ajb post#68

................sometimes necessary to cut space-time into space and time. My own philosophical thoughts here - and many also hold the same thoughts - are that this cut should be avoided. Einstein tells us that space and time should be treated on equal footing.

The issue of 'equal footing' is interesting since whilst you can directly plot distance, you cannot plot time.

The method of overcoming this is, of course, to multiply time by a velocity to obtain a distance.

Thus we get to 'ct' as the fourth axis.

However this has some disadvantages, not the least being that there are now two versions of 'spacetime'

one with four distance axes and one with three distance axes and one time axis.

Another disadvantage is that euclidian distance is no longer the sum of the squares of the projections on the axes but has a negative sign in the equation.

This latter can be overcome by the Argand view of the world and multiplying time by ic instead of c and considering the the fourth axis as a rotation from the others.

What implications this has for separation of time and space I'm not sure.

Edited by studiot
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One should use ct as this is what appears in the metric and is essential in the Poincare transformations which mix x and ct.

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One should use ct as this is what appears in the metric and is essential in the Poincare transformations which mix x and ct.

I understand Minkowski (though I don't have original references) originally proposed his 4D world in Argand format since there are only 3 (known) spatial axes not four, so a fourth one must be imaginary.

Using tau = ict allows the standard metric and works well when moving from relativistic kinematics to relativistic mechanics.

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Spacetime without an Eather is a concept that still clings around. Which is, well quite frankly somewhat annoying.

Eather has been searched for in modern times let alone tests like the Michelson-Morley test. That test wasn't nearly as accurate as the modern day tests.

If I recall the degree of accuracy on the modern tests is something along the lines of 10^-18.

Yes historically Lorentz, etc hoped for an Eather but research has gone far beyond those days. Discussing Eather is good only for historical reference.

No test has ever found any sign of Eather.

Now our responsibility on a forum. Isn't to teach outside the box thinking. It is to teach what is in the textbooks. Even if you don't agree with it.

It is irresponsible to use Eather which has never been found. As a training aid to SR or GR. Neither SR nor GR use either the Eather nor the block universe.

Philosophically speaking it would be wrong to teach SR or GR using Eather or block universe. Those ideas are not part of main stream teachings. The former for lack of evidence.

Posting historical thinking isn't evidence....( though its often used as an argument. Point blank. Science has far more modern data than what Lorentz and Minkowskii had.

Quite frankly if relativity doesn't make sense to an OP. Teaching different models outside of SR and GR will only hinder their understanding. NOT AID IT.

(just a side note. I own a 1920 physics textbook. This textbook doesn't cover Eather either. Though it is amusing that they also didn't know about neutrons. The atom was protons and electrons only.)

I'm curious. Why did you only wish to discuss two models. Both of which are outside of mainstream teachings. Yet not wish to discuss the models that run counter to Eather and block universe?

Searching for that elephant?

I posted the modern day solutions. You promptly replied "its not on topic". Yet it is precisely on topic. "Making sense of relativity"......

Edited by Mordred
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Using tau = ict allows the standard metric and works well when moving from relativistic kinematics to relativistic mechanics.

We call this a Wick rotation... it is often used in quantum field theory as analysis works better with a positive definite metric. One then uses what is called analytic continuation - loosely it means that we can rotate between 't' and 'it' (c=1 as ever!). This is generally not okay, but in physics the kinds of functions encountered in quantum field theory are okay for this to make sense.

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-- This is a spin-off of the thread "is space-time a physical entity [..]" --

A lot of people think that special relativity doesn't make sense and that it's hopeless to try to understand it; we are condemned to "shut up and calculate". However, I know of two physical models that can be used to explain the theoretical predictions, and possibly there is another model that I don't know of.

: To be perfectly clear, with "physical models" I here mean two competing hypothetical physical entities that have been proposed to make sense of the phenomena as described by relativity theory.

Right from the start it was perfectly possible to make sense of relativity by means of Lorentz's ether model. That model is quite different from the preceding material ether theories; one may just as well call it physical space. Einstein hoped to get rid of it for philosophical reasons, but others such as Langevin still made use of it[1] and in 1920 Einstein even expanded on the Lorentz ether for general relativity[2].

Is our goal to teach modern relativity as per the OP. Or is it to search for that hidden elephant you mentioned?

If our goal is to teach relativity. Stick to what relativity teaches. Not what the alternative proposals suggest.

( funny How you considered in light of the quoted OP. That posting the GR metrics itself was off topic)??????????

Edited by Mordred
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As this thread is in the philosophy section we should discuss some philosophy...

When people discovered that Maxwell's equations give the speed of electromagnetic radiation as being c, this was interpreted as meaning that Maxwell's equations really only hold in the rest frame of the aether. There was then a lot of theoretical work to understand this, which leads to a more and more 'magical' aether with less and less reasonable properties. The whole idea was to make sense of this canonical inertial frame - the philosophy was that one should have some quasi-mechanical aether and that one must have some singled out inertial frame. A lot of effort in the late 19th was in this direction.

Later, with Einstein and others, it was realised that singling out some canonical rest frame was unnatural and not needed - this is one of the core ideas of special relativity. This was a big philosophical change and the one that meant that the aether was just not needed.

Also, quantum mechanics was developed and the dual nature of light as both particles and waves became apparent. The need to understand light as classical waves in some medium was abandoned. Again, this is a big philosophical change.

Edited by ajb

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