A question about relative time and space.

[JohnSSM]

As I understand it, the person near a black hole will appear to experience time slower than someone who isn't also near a massive object, from their perspective.

As I understand it, the presence of more gravity will slow time as one approaches the presence of gravity.

Does this slow down even the quantum processes? It seems that it must. Chemical reactions, electrical reactions, radiation....wouldnt all those processes also be slowed with the time? I know the person experiences time and it runs the same speed for them, even as they enter gravitational fields which slow the passage of time more and more.

And here is where I get more confused. If space-time are somehow linked together, and gravity is changing time, wouldnt it also be changing space in the same ways? If time is being slowed due to gravity, is space also being "stretched or compressed" due to gravity? The term space-time seems a bit misleading if you can effect changes in one without effecting changes in the other, to me.

How do physicists "see" what is happening to space-time as it nears gravitational fields? TIme is slowing, but what is happening to space?

[ajb]

I assume you are looking for something like 'gravitational length contraction' for the Schwarzschild solution?

 

This is not a natural concept. Because the Schwarzschild solution has time-translation invariance it makes sense to time light pulses, deduce a gravitational Doppler shift and think about and think of a term in the metric as a gravitational time dilation factor.

 

There is nothing similar for time translations.

 

The best you could do is compare short rules moving past each other, but this will give the standard length contraction as expected from special relativity (small rulers mean we can ignore the curvature).

[JohnSSM]

I wasnt looking for anything specific other than my continued (mis)understandings of GR.

And you have not helped me...Ha!

Of course, Im still trying to grasp WHY matter curves spacetime in the first place. It's all just so matter of fact in the stuff I read. Matter curves space, and space then guides matter...but why? Its a pretty big question to leave unanswered, but after reading through lots of stuff for years, I still dont get it.

Then again, yes, I suppose I was looking for some type of space contraction to go along with time dilation. IN terms of space-time, can you curve one without effecting the other or do they follow the same curves? Ive always considered them sharing the same geometry which means you could not effect one without the other. So in my layman's mind, i thought..."If time is changing near sources of gravity, space must also be changing near sources of gravity in some sort of proportional or equal way to that of time"...If that isnt true, then my understandings are wrong. I tried looking for reading material on this subject but didnt find anything that answered that specific question.

Im still trying to grasp it all without understanding the equations.

[ajb]

Of course, Im still trying to grasp WHY matter curves spacetime in the first place. It's all just so matter of fact in the stuff I read. Matter curves space, and space then guides matter...but why?

There is no answer to 'why'. We just know that modeling gravitational phenomena using general relativity agrees with nature well. General relativity gives us the mathematics to describe how matter/energy effect the curvature of space-time. I do not think there is a lot more one can say.

 

Then again, yes, I suppose I was looking for some type of space contraction to go along with time dilation.

Generally there is no such good notion. As I sort of explained.

 

 

IN terms of space-time, can you curve one without effecting the other or do they follow the same curves?

This is poorly phrased. We have space-time in general and we cannot make a cut into space and time that we will all agree on. So I am not sure what your question is asking in general.

 

 

Ive always considered them sharing the same geometry which means you could not effect one without the other.

Without getting technical, this sounds reasonable.

 

 

So in my layman's mind, i thought..."If time is changing near sources of gravity, space must also be changing near sources of gravity in some sort of proportional or equal way to that of time"...If that isnt true, then my understandings are wrong.

The local geometry changes on a general given space-time. This we can measure (again without being technical) by the curvature tensors. One way of doing this is to look at how geodesics converge or diverge.

 

I tried looking for reading material on this subject but didnt find anything that answered that specific question.

I think this is because your question is ill-posed.

 

We do not have a meaningful notion of gravitational length contraction, like we do for time dilation for specific space-times.

 

Im still trying to grasp it all without understanding the equations.

You will only get so far without actually looking at the mathematics. Still, I think some intuitive feeling is possible.

 

Good luck.

[zapatos]

JohnSSM -

 

It might be better to look at it as matter curving space-time, not gravity curving space-time.

 

Then that curvature of space-time caused by matter is what we call gravity; that is, the curvature of space-time is what is responsible for orbits and why time is viewed differently near a large mass.

 

Keep in mind that 'curved space-time' is a description from a model that accurately describes what happens around the presence of matter. No one has ever seen curved space-time; it is just that objects near matter behave as if space-time is curved as described in the model.

[Mordred]

You would be far more accurate in mass curving spacetime. Matter applies to fermionic particles.

 

When you think in terms of Mass-density and keep in mind the definition of mass. (As resistance to inertia) GR becomes easier to understand. However you also have to throw away pop media visualization aids to spacetime curvature and switch your thinking to a geometric distribution of influence. (Ie variation of strength of influence at a given coordinate)

 

Given the above one can recognize that it is the stress energy/momentum term in the Einstein field equation that tells space how to curve.

 

https://en.m.wikipedia.org/wiki/Stress%E2%80%93energy_tensor

Edited May 10, 2016 by Mordred

[mathematic]

 

 

As I understand it, the person near a black hole will appear to experience time slower than someone who isn't also near a massive object, from their perspective.

 

You got it backwards. The person near the black hole experiences time "normally". The distant observer sees things slowing down. For example if an object falls into a black hole, the distant observer will never see the end of the fall - the object falling just seems to get nearer and nearer without entering. Also light from falling objects gets redder.

[JohnSSM]

Thanks for all the responses. A few are from fellas who have heard this question from me a few times over the past couple years, so I appreciate your patience.

At 46 years years old, ive embarked on a psychology degree, so my chances of studying math and physics is dwindling. Ha.

As far as my "why" question goes, it just seems so amazing to me that folks have the geometric math to explain and predict gravity, but they dont obsess to know what is creating the effect that their math predicts. As Mordred says, mass curves spacetime, and my very natural follow up question is "how does mass curve spacetime?" Must there not be some mechanism?

I really tried to wrap my head around the notion of relativity, but I havent found any explanations for how those relative effects of motion and time could create a force that acts upon the physical world in a real and measurable way. I guess, to me, relativity is an observer effect, and how could the observer effect create a force that effects the observer in a real way in the form of gravitation?

I suppose, with the kinda obviousness of asking that question, that I cant find more folks asking it or discussing it.

For Mordred and AJ specifically, did you ever wonder why? Even in your early years when you first heard about GR and gravity and the theory? DId you ever wonder how or why mass curves spacetime?

I think im feeling lonely in these thoughts...I cant be the only one who has questioned this...Than again, I am a rare dude. ha

[Mordred]

I don't need to wonder why mass curves spacetime. If you think carefully about my last post the clues are provided.

 

First define mass.

 

Then define what is truly meant by spacetime curvature. (Mathematically)

Remember space is just volume, spacetime is simply any metric system that involves volume and time as a coordinate.

 

Then look at the diagonal terms under the stress tensor. (rho,p,p,p)

 

[latex]T_{\mu\nu}=\begin{pmatrix}-\rho&0&0&0\\0&p&0&0\\0&0&p&0\\0&0&0&p\end{pmatrix}[/latex]

 

You have mass density and various types of pressure relations.

 

So lets use a simplified analogy.

 

Two particles that interact with each other (attraction) has binding energy. That binding energy is related as a resistance to inertia. (Mass)

 

So lets say we have a Higgs field. This field supplies a binding energy to Say just the w+ bosons. The more w+ bosons you have in a unit volume the more mass that volume has.

(This applies to all fields, electromagnetic, strong and albeit via the Higgs field the weak force)

 

Now recall that neither mass, nor energy exists on its own. These two terms are properties. In order to measure a property you need to measure a particle or object.

 

Now if you think about binding energy and mass being related, then realize that spacetime metrics is a coordinate system. Time dilation and length contraction becomes easier to understand.

 

For gravity you can use a field of test particles. Each coordinate being the location of a test particle.

Then add your mass influence upon that field. Voila the measured amount of influence upon each test particle will have a curved distribution in strength of attraction. As we're using coordinates (ct,x,y,z) this means spacetime is curved due to mass( resistance to Inertia). ( keep in mind the equivalence principle).

 

It might help to also understand that all interactions are usually described by a coordinate system.

 

For example when you measure a frequency we use the x,y coordinates.

X being the amplitude, y being the period or wavelength...

 

Spacetime curvature is no difference, we simply add the z, coordinate but as time also varies we need a time coordinate.

 

An analogy I often found useful is to think of a massless field of test particles. As there is no mass there is no resistance to inertia. Everything moves at c...

 

Now add mass via some binding energy you have resistance to inertia so those particles can no longer travel at c. To get to coordinate b from a will take more time. Now given the above this quoted section should make more sense

 

Lorentz transformation.

First two postulates.

1) the results of movement in different frames must be identical

2) light travels by a constant speed c in a vacuum in all frames.

Consider 2 linear axes x (moving with constant velocity and \acute{x} (at rest) with x moving in constant velocity v in the positive \acute{x} direction.

Time increments measured as a coordinate as dt and d\acute{t} using two identical clocks. Neither dt,d\acute{t} or dx,d\acute{x} are invariant. They do not obey postulate 1.

A linear transformation between primed and unprimed coordinates above

in space time ds between two events is ( this below doesnt have curvature as SR assumes Euclidean)

[latex]ds^2=c^2t^2=c^2dt-dx^2=c^2\acute{t}^2-d\acute{x}^2[/latex]

Invoking speed of light postulate 2.

[latex]d\acute{x}=\gamma(dx-vdt), cd\acute{t}=\gamma cdt-\frac{dx}{c}[/latex]

Where[latex] \gamma=\frac{1}{\sqrt{1-(\frac{v}{c})^2}}[/latex]

Time dilation

dt=proper time ds=line element

since[latex] d\acute{t}^2=dt^2[/latex] is invariant.

an observer at rest records consecutive clock ticks seperated by space time interval dt=d\acute{t} she receives clock ticks from the x direction separated by the time interval dt and the space interval dx=vdt.

[latex]dt=d\acute{t}^2=\sqrt{dt^2-\frac{dx^2}{c^2}}=\sqrt{1-(\frac{v}{c})^2}dt[/latex]

so the two inertial coordinate systems are related by the lorentz transformation

[latex]dt=\frac{d\acute{t}}{\sqrt{1-(\frac{v}{c})^2}}=\gamma d\acute{t}[/latex]

 

 

Here is the coordinate transformation in Lorentz.

[latex]\acute{t}=\frac{t-vx/c^2}{\sqrt{1-v^2/c^2}}[/latex]

[latex]\acute{x}=\frac{x-vt}{\sqrt{1-v^2/c^2}}[/latex]

[latex]\acute{y}=y[/latex]

[latex]\acute{z}=z[/latex]

Edited May 11, 2016 by Mordred

[JohnSSM]

That was most helpful! The explanation did hit a few different light bulbs and I hope what you said is accurate because im excited to get it.

I must say, what I see is a field that guides this process. Its not just "mass" in your example, that creates curved space. Its the wbosons within mass or matter which interact with the higgs field, changing it's inertia and making it seem like spacetime is curved. I mean, that makes total friggin sense and I dont know why someone hasnt said it like that before. Truly. I can find a lot of writting that describes the higgs field interaction and one of them compares the higgs boson to a snobbish waiter making its way through a crowd.

I never would have used the fabric of spacetime analogy. Its simple enough to say that some of the quantum particles in mass create "drag" within a certain field, changing the inertia, and yes, direction of objects which are allready moving. That's essentially how you steer a canoe and i think most people would get it. The fabric is simply there to create the same types of curves that are created when moving objects encounter drag from different direction. The fabric is only a model to recreate what those curves end up being. I totally get it.

It cant be that easy. Did i lose it?

None the less, it does seem that a field is key to GR and gravity, not just mass or inertia with certain particles.. The field is necessary. Thats new news to me.

Ive looked at these things many times. I know it represents a tensor field. Do the four columns and rows have some unmarked significance ive never realized? What do those 16 numbers relate to? I have no idea what Im looking at.

[Mordred]

Keep in mind I posted a single field example above. When it comes to mass you must involve all fields and their coupling constants that are present.

 

For example you can have electromagnetic mass or mass due to the strong force interaction.

 

The stress energy tensor is the term that describes the energy and momentum relations in the EFE.

Tensors take some considerable time to learn.

Each position has its own unique derivative. Which will depend on what that is being related to ie the curvature tensor.

 

I'll dig up some examples once I unpack my textbooks( just finished moving)

 

However in the meantime this article may help.

 

http://www.google.ca/url?q=http://mathreview.uwaterloo.ca/archive/voli/2/olsthoorn.pdf&sa=U&ved=0ahUKEwjY1ceOqdHMAhVU3WMKHegsCW8QFggUMAE&sig2=cKOZEEemRIw0wylOMc0lYQ&usg=AFQjCNEOA2zinwqJc_O4wdiLvAirH1GfqQ

Edited May 11, 2016 by Mordred

[JohnSSM]

Is that it? You allready mentioned that the weak force uses the higgs field. So it's the influence of 3 fields on various particles. I can handle that.

[Mordred]

The diagonal term is detailed somewhat in equation 5.4. I have a better breakdown in one of my textbooks

Is that it? You allready mentioned that the weak force uses the higgs field. So it's the influence of 3 fields on various particles. I can handle that.

Sort of the weak force is mediated by

The w+,w- and z bosons. Those bosons interact with the Higgs field which has four components. [latex] \phi_1,\phi_2,\phi_3,\phi_4[/latex]

 

The interaction essentially uses up the last three components leaving the first. This results in the non zero Higgs field

 

Now look at the interactions of Say a photon compared to a neutrino.

 

https://en.m.wikipedia.org/wiki/Photon

 

keep in mind the photon mediates the electromagnetic field but does not have a charge. (No binding energy) or doesn't couple to the electromagnetic field.

 

Neutrinos interact with the weak force via the weak gauge bosons. So indirectly they gain mass via the Higgs field but in an indirect manner.

The majority of the mass of objects is electromagnetic mass. Ie your table. The strong force loses strength as a function of radius extremely quickly so it's influence is limitted to within composite particles. Ie protons and neutrons.

 

Inertial mass is essentially energy gained due to inertia which also correlates to a mass gain.

 

So when your calculate say the mass of a proton, what your calculating is how strong the particle couples to its interaction field. For a proton 1% roughly is the Higgs field the other 99% is its coupling strength to the strong force.

 

Now if gravity is a force then the mediator boson would be the graviton.

 

However gravity may very well be just the result of curvature relations. We still don't know for sure as we can't fully quantize gravity at the particle level. It's influence one particle to another is too weak

Edited May 11, 2016 by Mordred

[ajb]

...did you ever wonder why?

The closest to an answer why is the mathematics of general relativity. I cannot think of a deeper meaningful answer.

[Mordred]

A handy statement was made in this Master-Geodesic article.

 

Geometry=energy.

 

http://www.google.ca/url?q=http://www.physics.usyd.edu.au/~luke/research/masters-geodesics.pdf&sa=U&ved=0ahUKEwjJkf3tuNHMAhVB52MKHVpUAtwQFggRMAA&sig2=FXfhVBHku5zK1fjW-tkXWw&usg=AFQjCNEr4WEHhcvoL-LVhqBLVIcgBRFdkQ

 

Its an excellent article but takes a bit to understand the math behind it.

 

An old relativity perspective is the

 

"River model of blackholes". This particular article provides me numerous clues when I was first studying relativity.

 

http://www.google.ca/url?q=http://arxiv.org/pdf/gr-qc/0411060&sa=U&ved=0ahUKEwiz1KubvNHMAhUD4WMKHXNRD0MQFggZMAI&sig2=KMwrVt094ZmEpor3wKz94w&usg=AFQjCNFI8GTbcqya0j0qAbhzraDu9VmS6w

Here is the River model of space.

 

http://www.google.ca/url?q=https://arxiv.org/pdf/1204.0419&sa=U&ved=0ahUKEwiR0Iaxv9HMAhUT42MKHYPbBg0QFggRMAA&sig2=U3lt-9TLseeVW-NNxLJLZA&usg=AFQjCNE5KQpW-SbSZ4Sqg_jkHLGfemxynQ

 

Keep in mind these papers are helpful but do not imply an eather

Edited May 11, 2016 by Mordred

[JohnSSM]

I dunno about this guy...He says "Furthermore, the force we know as gravity results from the bending and stretching of the geometry of spacetime by its energetic contents" and "gravity makes curved lines straight!"

Did someone forget to tell him about the binding energy and the dragging effect of field interactions?

[Mordred]

I dunno about this guy...He says "Furthermore, the force we know as gravity results from the bending and stretching of the geometry of spacetime by its energetic contents" and "gravity makes curved lines straight!"

 

Did someone forget to tell him about the binding energy and the dragging effect of field interactions?

The latter part is describing null geodesics which apply to photons. Photons don't interact with gravity.

 

Look at the interactions list on the wiki page I posted earlier. Massless particles aren't dragged per se.

 

Geodesic relations can be tricky when verbally describing them.

 

For example wiki describes it as

 

"Certain types of world lines are called geodesics of the spacetime straight lines in the case of Minkowski space and their closest equivalent in the curved spacetime of general relativity."

 

That description applies to geodesics in general. There being three main types.

 

https://en.m.wikipedia.org/wiki/Spacetime#Spacetime_intervals_in_flat_space

 

PS another thing to keep in mind is often verbal descriptions can be misleading and can vary upon coordinate systems being described.

 

An excellent article describing numerous artifacts of coordinates is the lecture notes by Mathius Blau.

 

http://www.blau.itp.unibe.ch/newlecturesGR.pdf "Lecture Notes on General Relativity" Matthias Blau

 

This last link is roughly 900 pages, but details numerous coordinates. In many ways it's near a textbook in style.

Edited May 11, 2016 by Mordred

[JohnSSM]

Hmmm...the fact that light is massless but is also effected by gravity kinda stumps the original idea i had. I knew it was too easy. ha

[studiot]

 

Hmmm...the fact that light is massless but is also effected by gravity kinda stumps the original idea i had. I knew it was too easy. ha

 

 

 

Here is another view of 'curvature'.

 

First consider the usual x,y,z axes for space and then t for time.

 

We expect the numbers along the space (and time) axes to be distributed evenly and regularly.

That is we expect them to be linearly distributed.

 

and indeed they are in special relativity, which introduces spacetime.

 

Spacetime is 'flat' which is another way of saying the numbers are distributed evenly and regularly or in a linear fashion.

So is ordinary 'space'.

 

Now introduce another entity that has some non linear effect across the axes already defined (ie space, and time)

 

For instance mass.

We know one representation of this effect is a force which varies non linearly with the square of the distance.

 

Another interpretation is that the mathematical system of space plus mass exhibits 'curvature', because of the mass.

It does not mean there is a further axis in which space 'bends'.

The curvature is the nonlinearity coming out when we create mathematical objects (systems) that combine the space and the additional effect eg mass.

 

 

This is exactly what Mordred posted earlier

 

 

Then define what is truly meant by spacetime curvature. (Mathematically)

Remember space is just volume, spacetime is simply any metric system that involves volume and time as a coordinate.

 

Then look at the diagonal terms under the stress tensor. (rho,p,p,p)

 

 

You have mass density and various types of pressure relations.

 

 

The non-linearity introduced by adding the density (rho) term to the mathematical system (called a tensor) is reflected in (or develops) a non linearity in the rest of the system, that was linear without it.

 

A tensor is simply a way to collect all (or at least as many as desirable) of the properties of interest into one basket as possible.

[Markus Hanke]

Im still trying to grasp it all without understanding the equations.

 

 

In my humble opinion, which may or may not turn out to be helpful to you, it is best to find a perspective on relativity which is both geometric and physical.

 

Consider the following simple scenario : let's say you take into your hand a bunch of very fine coffee grounds, and form that into a perfectly spherical ball. Let us further assume that the particles that ball is composed of do not interact with each other in any way ( that is of course an idealisation, but you probably get the idea that this is merely an analogy to demonstrate a principle ). You now release that ball of test particles ( coffee grounds ), and observe how it behaves under a number of conditions.

 

In the most trivial case, you perform this experiment very far away from any source of gravity. What happens ? The answer is that nothing happens - the ball remains stationary with respect to any ( close by ) reference point you choose, and neither its volume nor its shape change in any way. This corresponds to the case of a spacetime that is approximately flat.

 

In the next scenario, you release the ball of test particles in the exterior vacuum somewhere in the vicinity of a source of gravity, such as a planet or a star, again assuming that no influence other than gravity is present here. What happens now ? As time goes by, you will notice the ball starting to move towards the centre of the source of gravity; as the ball approaches the central mass, you will also notice that its shape begins to change - it becomes elongated along the direction of motion, and "squeezed" perpendicularly to it. However, if you perform a measurement of its volume ( by whichever means you choose ), you will - perhaps counterintuitively so - find that the volume of the ball does not change, meaning the deformation of its shape is not arbitrary, but is such that its volume remains unaffected. That is the situation in vacuum.

 

In the last scenario, you place the ball in the interior of a source of gravity. Strictly speaking we would need to find a way for the ball not to be affected by the mass/energy itself, or else we would no longer be dealing with free fall. You can create such an approximate situation by - for example - drilling a very narrow shaft through your planet. What happens now ? Once again, the ball of test particles will move towards the centre of the source of gravity, and once again its shape will deform. However, this time you would find that both shape and volume of your ball of test particles changes as it freely falls. This is the situation in the interior of mass-energy distributions ( as opposed to the exterior vacuum ).

 

All of these are empirical findings about how test particles ( specifically a spherical collection of them ) will behave under the influence of gravity. To understand how this is connected to General Relativity, just put some simple mathematics around it. Specifically, let us look at the volume of our ball of test particles. In scenario (1) there is no gravity, so nothing at all happens. This is trivial, so will ignore it. In scenario (2) - the vacuum case outside a source of gravity - we find that the volume of the ball remains constant; we slightly rephrase this and state that the rate at which the volume of a ball of test particles begins to change as we release it, is zero. In mathematical notation :

 

[latex]\displaystyle{\left ( \frac{\ddot{V}}{V} \right )_{t=0}=0}[/latex]

 

General Relativity uses the languages of tensors to express this very same idea - the mathematical object which describes the rate at which a small ball of test particles begins to change its volume is called the Ricci tensor; using this, we can write the above simply as

 

[latex]\displaystyle{R_{\mu \nu}=0}[/latex]

 

These are precisely the Einstein field equations in vacuum, and their meaning is very simple - if you take a ball of test particles and allow it to fall freely in vacuum, the rate of change of its volume is zero, i.e. its volume remains constant. Note that this says nothing about the shape of the ball, only about its volume, so this equation doesn't mean we are in a flat spacetime - quite the contrary, as the ball will be deformed as it falls.

 

In scenario (3), the ball is in the interior of an energy-momentum distribution. In this case, both shape and volume of the ball change over time, and hence we find that the rate at which the volume begins to change is no longer zero, but rather

 

[latex]\displaystyle{\left ( \frac{\ddot{V}}{V} \right )_{t=0}=-\frac{1}{2}\left ( \rho + P_x+P_y+P_z \right )}[/latex]

 

This means that the rate at which the ball changes its volume is proportional to the energy density at its centre, plus the pressure in the x direction at that point, plus the pressure in the y direction, plus the pressure in the z direction. Expressed in the language of tensors, this reads as

 

[latex]\displaystyle{R_{\mu \nu}=\kappa\left ( T_{\mu \nu}-\frac{1}{2}Tg_{\mu \nu} \right )}[/latex]

 

These are precisely the full Einstein field equations, and their meaning - in geometric and physical terms - is as given above. The form I am giving the equations in looks different than what most textbooks will write, but they are exactly equivalent ( my form follows from the usual form via an operation called trace-reversal ).

 

So, if you wish to understand the meaning of the Einstein equations, just think about small balls of test particles in free fall - and that is all there really is to it. Of course, while this is easy to grasp conceptually, performing any actual calculations with this is fiendishly difficult, since the various tensors used in the equation follow from the metric in non-linear and non-trivial ways.

 

Perhaps the above may be helpful to you.

Edited May 14, 2016 by Markus Hanke

[MigL]

Hi Markus.

Nice explanation of the EFEs.

Have never seen them explained so simply before.

( still remember your GR stickies on that other 'forum' )

[Markus Hanke]

Hi Markus.

Nice explanation of the EFEs.

Have never seen them explained so simply before.

( still remember your GR stickies on that other 'forum' )

 

 

Thank you