Time and General Relativity help?

[electronicmatt]

Hi, I am new here, I am no physicist and I'll admit have not read much on physics, but I do have a keen interest and a deep wanting to know answers and understand how and why things are the way they are. lately I've been reading a lot about General and Special Relativity, and time, I've always wondered about time and what it really is, I will think for hours and hours about it!

Similar things may have been posted here before but I am not sure, I feel that time does not exist in the way some people think it does, there is not a flow or arrow of time, just the movement of mater in a three dimensional space, time is just an illusion of flow, when matter moves from one point in space to another, time appears to have passed but it has not, all that has happened is matter has moved from one point to another, time is just a numerical order of this motion, numerical in the sense that we reference that motion to time frames ie: a ticking clock etc...

I could be completely wrong, (and I do not fully understand e=mc2) but am I wrong in saying that e=mc2 explains that certain things happen but not truly why they happen?? ... I came up with this idea which could be nonsense, when matter moves faster and faster towards the speed of light, say for example a human, if it were possible, the human would appear to age slower because all the matter of the human is already moving so fast, the atomic structure of the human matter would be limited by the already great motion of the human.

The same effect but in reverse when an atomic clock is slowed by gravity, the atomic structure of the matter which makes up the clock is being limited by the force of gravity, and time appears to move faster if you take the clock into space, with reference to Earth time, it's not time that's changing it's the gravitational limiting effect on sub atomic matter.

Therefore I am wondering does gravity not just affect (and be affected by) large bodies of mass, but it is directly connected to the sub atomic level, pushing and pulling every atom.

Am I talking nonsense or is there something in this?

 

[PeterDonis]

Hi, electronicmatt, and welcome to PF!

I've always wondered about time and what it really is, I will think for hours and hours about it!

You do realize the irony here, right?

there is not a flow or arrow of time, just the movement of mater in a three dimensional space, time is just an illusion of flow, when matter moves from one point in space to another, time appears to have passed but it has not, all that has happened is matter has moved from one point to another, time is just a numerical order of this motion, numerical in the sense that we reference that motion to time frames ie: a ticking clock etc...

You should check out the papers of Julian Barbour: he has worked out this kind of viewpoint in great detail:

http://www.platonia.com/papers.html

The paper on "the emergence of time" is probably the best place to start:

http://www.platonia.com/barbour_emergence_of_time.pdf

am I wrong in saying that e=mc2 explains that certain things happen but not truly why they happen??

One piece of advice for future reference: try to keep to one subject/question per thread. This is really a separate subject/question from the above and should have its own thread. (Same for your third question about gravity below.)

To answer your question, science can't really explain "why" things happen, in the sense that science does not give us "final" explanations that can never be improved on. There is always more to learn.

when matter moves faster and faster towards the speed of light, say for example a human, if it were possible, the human would appear to age slower

This is true; it's just straightforward relativistic time dilation.

because all the matter of the human is already moving so fast, the atomic structure of the human matter would be limited by the already great motion of the human.

But this part has nothing to do with the above. Relativistic time dilation is a purely kinematic effect: that is, it happens to every kind of object, regardless of its composition, because it is due to the nature of spacetime itself, not due to the nature of the object.

when an atomic clock is slowed by gravity, the atomic structure of the matter which makes up the clock is being limited by the force of gravity

No, this is not how gravitational time dilation works. It is a different effect from time dilation due to relative velocity, but it is also due to the nature of spacetime itself, not the nature of any particular object.

does gravity not just affect (and be affected by) large bodies of mass, but it is directly connected to the sub atomic level, pushing and pulling every atom.

In principle, gravity affects everything, even individual atoms; but the gravitational forces between individual atoms are way, way too weak for us to measure. The atomic structure of matter is governed by electromagnetic forces between atoms, and by the strong (and to some extent the weak) nuclear force between quarks in atomic nuclei.

As for the gravitational effects of a large mass, in General Relativity these are modeled as spacetime curvature, i.e., as I said above, gravity is a property of spacetime, not matter. Spacetime affects atoms just as it affects everything else, but its effect is not modeled as "pushing and pulling"; objects moving solely under the influence of gravity feel no force at all.

 

[electronicmatt]

Hi PeterDonis, thank you for the reply, I am not sure of the correct manner to reply with the quoting? do i re-quote your sections?

Did not realize the irony at the top, may be that shows I am too daft to even begin to understand any of this, but I want to!

I shall read this papers of Julian Barbour, thank you.

The reason I asked or wrote about multiple things was becasue I thought they were all tied in together.

I want to understand relativistic time dilation, I kind of do but also do not, I think I have a very weird or difficult way of thinking about things and but can visualize the way things work in my head.

Could you explain how gravitational time dilation works simply? I have read so much about it but still fail to grasp it!

The experiment where two clocks were synchronised, one was put on a plane and flown around the Earth twice, then compared to the time of the clock on earth, I thought velocity and gravity both affect the clocks?

 

[phinds]

Velocity and gravity DO both affects clocks. The GPS system works on exactly that basis. There have to be adjustments for both the speed of the GPS satellites and the fact that they are further out of Earth's gravitational well.

 

[electronicmatt]

Velocity and gravity DO both affects clocks. The GPS system works on exactly that basis. There have to be adjustments for both the speed of the GPS satellites and the fact that they are further out of Earth's gravitational well.

How does the gravitational well actually affect the clock though? is gravity actually affecting the subatomic level of the clock or something else, this is what I can not get my head around

In my mind I visualize every atom as being affected by motion, if an atom was moving at 99.9% the speed of light it's internal structure would have practically no more (and I do not know what it's called) but allowance to move inside.

 

[phinds]

How does the gravitational well actually affect the clock though? is gravity actually affecting the subatomic level of the clock or something else, this is what I can not get my head around

In my mind I visualize every atom as being affected by motion, if an atom was moving at 99.9% the speed of light it's internal structure would have practically no more (and I do not know what it's called) but allowance to move inside.

As Peter repeated stated, the atomic makeup of an object is utterly irrelevant to time dilation of either sort.

All motion is relative. It is completely meaningless to say that something is moving at ANY speed unless you specify what it is moving relative to.

Gravitational time dilation, and again I'm just repeating what Peter already told you, is due to spacetime curvature.

Relativistic time dilation is due to spacetime paths differing between objects. Read about the twin paradox.

You, right now as you read this, are moving at 99.99999% of c from the frame of reference of an accelerated particle at CERN. You are massively time dilated and length contracted from that reference frame. Do you feel any different?

 

[electronicmatt]

As Peter repeated stated, the atomic makeup of an object is utterly irrelevant to time dilation of either sort.

All motion is relative. It is completely meaningless to say that something is moving at ANY speed unless you specify what it is moving relative to.

Gravitational time dilation, and again I'm just repeating what Peter already told you, is due to spacetime curvature.

Relativistic time dilation is due to spacetime paths differing between objects. Read about the twin paradox.

You, right now as you read this, are moving at 99.99999% of c from the frame of reference of an accelerated particle at CERN. You are massively time dilated and length contracted from that reference frame. Do you feel any different?

I still don't really understand, I am angry at myself for not being able to understand.

I understand about speed and being relative to something else, but I really want to understand why Gravitational time dilation happens.

 

[Dale]

Forum member A.T. has some visualizations that may help. He may post a link, or you can search for his posts.

The key to understanding SR and GR is to think geometrically. Relativity is about understanding space and time as two parts of a combined geometry called spacetime, where the amount of time that passes on a clock is given by the "length" of the clock's line in spacetime.

Once you have that idea in place then gravitational time dilation is easy to understand by analogy. Consider two latitude lines on a sphere. As they each go 1° west, the line closer to the equator will traverse a larger distance. In the analogy, the longer distance is a longer time, so the line further from the equator is time dilated.

 

[electronicmatt]

Forum member A.T. has some visualizations that may help. He may post a link, or you can search for his posts.

The key to understanding SR and GR is to think geometrically. Relativity is about understanding space and time as two parts of a combined geometry called spacetime, where the amount of time that passes on a clock is given by the "length" of the clock's line in spacetime.

Once you have that idea in place then gravitational time dilation is easy to understand by analogy. Consider two latitude lines on a sphere. As they each go 1° west, the line closer to the equator will traverse a larger distance. In the analogy, the longer distance is a longer time, so the line further from the equator is time dilated.

Thank you for that, that does help :) I like to think visually and analogies do help a lot!

So a clock in a deep gravitation well is in a more stretched spacetime than a clock further away from Earth which is in more contracted spacetime?

I think where my misunderstanding comes from is the fact I can't accept that time really flows in a direction, I just can't see that time really exists at all, and I was trying to tie this and gravity together, and may be quantum gravity.

 

[Dale]

Thank you for that, that does help :) I like to think visually and analogies do help a lot!

So a clock in a deep gravitation well is in a more stretched spacetime than a clock further away from Earth which is in more contracted spacetime?

I am glad that it helped. Regarding "stretched" or "compressed" I would probably not use those words. After all, you wouldn't consider one latitude line to be stretched and another to be compressed. They simply are different lengths. But despite that wording it sounds like you get the gist of the analogy.

I think where my misunderstanding comes from is the fact I can't accept that time really flows in a direction, I just can't see that time really exists at all, and I was trying to tie this and gravity together, and may be quantum gravity.

Frankly, I find that most questions or statements which use the word "really" are useless. Time, whether it "really actually truly exists" or not, is useful. It allows you to accurately predict the outcome of experiments, which is all that the scientific method demands.

I would recommend setting aside this line of thought until after you learn relativity, as it will not be helpful.

 

[TumblingDice]

I understand about speed and being relative to something else, but I really want to understand why Gravitational time dilation happens.

There are some great folks here that can answer questions to help guide you towards understanding the theories. Successful theories often include mathematical models that consistently provide accurate results and have never been disproved. But, they do not explain "why". People can interpret what the models imply, yet different people can (and do) suggest different interpretations...

I'm going to speak a little loosely to keep to the important principles, hoping for Peter, Dale or another knowledgeable member to correct any mistakes.

In the case of gravitational time dilation, I believe Albert Einstein provided at least two mathematical models that can calculate gravitational time dilation. Let's start with Special Relativity circa 1905. This was based on the laws of physics acting consistently for ALL inertial (non-accelerating) frames, and the speed of light being the same for all inertial frames no matter what their relative speed or the relative speed of the light source. This is where E=mc^2 was derived. It is also where time dilation, and other variants and invariants were mathematically postulated/predicted for observers in different inertial frames. In SR, rather than an invariant time interval between two events, there is an invariant spacetime interval. You can find the formulas for these calculations in Wiki. But, SR only addressed inertial frames without gravity. (An over-simplification, but true at the time.)

Around 1907 Einstein introduced the Equivalence Principle, as a consequence of SR in accelerated reference frames. The EP said that for the most part, it isn't possible for an observer to detect any difference between the effects of gravity as opposed to if they were in an enclosed lab that was accelerating at a constant rate. So with parts of SR combined with the EP, time dilation could be already be modeled and should be observed in a gravitational field just as it is between observers in relative motion. This is entirely based on the equivalence principle where gravity can be treated as an accelerating frame.

The EP was a first step along the path to General Relativity. Where SR doesn't include gravity, GR embraces and integrates it. GR involves a deeper more complicated set of maths and models that include what's termed a "metric tensor". The tensor includes a component to account for gravitation - it's actually an energy value, but remember, gravity is directly related to mass and e=mc^2. So mass and energy can be combined into one component.

Unlike SR and the EP, in GR time dilation is considered to be a difference in the passage of proper time at different positions as described by a metric tensor of spacetime. So - different maths/models - same consistent, quality, verified predictions.

And just like classical physics and Newtonian gravitational theory, neither SR nor GR are perfect. Their maths can introduce singularities (just a word that means the mathematics break down at these points). It would indeed be difficult to begin to feel assured of "why" gravity causes time dilation, or any other questions seeking why.

So if you want to understand gravitational time dilation, you might want to begin understanding time dilation in SR, and proceed to the EP. I think the math and understanding is easier than diving into GR, and beginning with SR/EP is well worth the value you'll carry forward.

 

[PeterDonis]

I am not sure of the correct manner to reply with the quoting? do i re-quote your sections?

Normally it's enough to just quote the particular statement(s) you are responding to, as I just did above. If responding to an extended argument, I usually try to pick out a short excerpt that captures the essence of the argument, and quote that.

The experiment where two clocks were synchronised, one was put on a plane and flown around the Earth twice, then compared to the time of the clock on earth, I thought velocity and gravity both affect the clocks?

They do. The Wikipedia article on this experiment gives a good overview:

http://en.wikipedia.org/wiki/Hafele–Keating_experiment

Note particularly the "results" table; as you can see, it includes both gravitational and "kinematic" (i.e., relative velocity) effects.

 

[A.T.]

I like to think visually and analogies do help a lot!

Here are some links with visualisations:

http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

http://www.relativitet.se/spacetime1.html
http://www.adamtoons.de/physics/gravitation.swf
http://www.relativitet.se/Webtheses/tes.pdf

But I don't think they will help you with your philosophical questions about time being "real", and why nature is the way it is. Relativity also doesn't offer any underlying mechanism on how time dilation affects individual processes. It simply predicts that all processes will slow down, so we can just as well say that time itself slows down.

 

[electronicmatt]

Thank you for all the replies, after more reading, I now think that I understand Gravitational time dilation, if I was some how onboard a satellite looking at a clock that was synced the same as one on Earth before it was flown into orbit it would appear normal, but if I could look at a clock back down on Earth from the satellite it would appear to run slower, relative to me and my clock in the satellite, then the reverse if I was on Earth looking up at a clock on the satellite, because the spacetime is longer on Earth and shorter at the satellite, is this correct?

 

[A.T.]

Thank you for all the replies, after more reading, I now think that I understand Gravitational time dilation, if I was some how onboard a satellite looking at a clock that was synced the same as one on Earth before it was flown into orbit it would appear normal, but if I could look at a clock back down on Earth from the satellite it would appear to run slower, relative to me and my clock in the satellite, then the reverse if I was on Earth looking up at a clock on the satellite,

Yes. Satellite in orbit might not be the best example, because it also involves kinematic time dilation from relative movement. But assuming a very high orbit it works like you said.

...because the spacetime is longer on Earth and shorter at the satellite, is this correct?

You can interpret it geometrically as: Distances between ticks along the time dimension are longer, so clocks at different elevations traverse different number of ticks.

 

[nomadreid]

I am post this questioning this question here rather than as a new thread, since my question is related to the discussion here. The papers by Julian Barbour (linked to above) are very interesting, but in those papers there remains one question to which I do not find the answer, although perhaps I have overlooked it. It is the following: in the standard responses to the question as to why time is considered a fourth dimension, the four-vector of Minkowski space (ct, r) is cited. c is considered just a constant, so time becomes the fourth dimension. However, ct is not a temporal co-ordinate: it is a spatial coordinate. So, unless one wants to say that time is in some way really space... (Alternatively, one could use the four vector as (t, r/c), but then one has the parallel problem of having four time coordinates, and again one would have to say that space is a kind of spatial coordinate, also unsatisfactory.) Hence, something seems to be missing in this answer as to why time is a fourth dimension. Could someone fill in the blanks here? Thanks.

 

[A.T.]

Hence, something seems to be missing in this answer as to why time is a fourth dimension. Could someone fill in the blanks here?

Because it turned out to be a useful mathematical concept.

 

[nomadreid]

Because it turned out to be a useful mathematical concept.

Could you be a bit more specific? (You may assume that I have a mathematical background.) That is, without going around in a circle? I know that the Minkowski 4-vector is a useful tool, obviously, but none of its coordinates are actually time (unless you select "natural units", which hand-waves the problem away). In other words, "ct" could be perhaps called another dimension, but how does that allow you to label "t" another dimension?

 

[A.T.]

I know that the Minkowski 4-vector is a useful tool

And that's all that matters to physics.

...really space...

...actually time...

All those "really" and "actually" qualifiers don't matter much in physics.

..could be perhaps called...

And neither do naming conventions.

 

[Last_Exile]

I think that it would be appropriate to offer an alternative explanation of time dilation which is not based on curvature of spacetime but on quantum field theory.

Reference:http://www.quantum-field-theory.net/

I'm not saying one is right and the other wrong - just being open-minded about alternatives.

 

[nomadreid]

to A.T. : First, my use of "really" and "actually" were only stylistic fillers, and have no reference to any supposed "reality". [I would even go so far as to say that (a slight modification of) Tegmark's position that physics is just applied mathematics is reasonable, but I am not trying to get into a philosophical debate.] As far as your statement that labels are irrelevant here, I take this to mean that you would have no problem with labeling ct as "time". I would be interested in knowing whether any other contributors to this forum are in complete agreement with this.

 

[PeterDonis]

ct is not a temporal co-ordinate: it is a spatial coordinate.

No, it isn't. Whether a coordinate is temporal or spatial isn't determined by its units; it's determined by how it appears in the metric. The $ct$ coordinate appears in the metric the same way $t$ does: its square has the opposite sign to the squares of the other three coordinates. That makes it temporal. (The reason $ct$ is used instead of $t$ is to make it explicit that the units of all the terms appearing in the metric have to be the same; most people, including me, just use units in which $c = 1$, which is more convenient for calculation but doesn't explicitly show how the units of all the terms are the same.)

 

[nomadreid]

Thanks, PeterDonis. That point of view (that temporal and spatial are attributes of the metric) is one that I had not considered, and it makes sense. I shall now let that soak in.

 

[electronicmatt]

Yes. Satellite in orbit might not be the best example, because it also involves kinematic time dilation from relative movement. But assuming a very high orbit it works like you said.


You can interpret it geometrically as: Distances between ticks along the time dimension are longer, so clocks at different elevations traverse different number of ticks.

What if the universe was timeless, like I described in my first post, just say the universe was timeless how would General Relativity function with regards to time dilation (difference in clocks)?

 

[PeterDonis]

say the universe was timeless how would General Relativity function with regards to time dilation (difference in clocks)?

The same. "Timelessness" in the sense of your OP has nothing to do with "time" in the sense of "time dilation" in GR. Even on the "timeless" viewpoint (as laid out, for example, in Julian Barbour's papers), you still end up with a 4-dimensional spacetime that obeys the Einstein Field Equation, and there are still clocks that can register different readings depending on which path through spacetime they follow. The only difference is in how you get there from other more fundamental principles.

 

[PeterDonis]

I think that it would be appropriate to offer an alternative explanation of time dilation which is not based on curvature of spacetime but on quantum field theory.

Reference:http://www.quantum-field-theory.net/

I don't see anything here about time dilation. Anyway, the standard view among physicists is basically that "curvature of spacetime" is just the classical limit of whatever turns out to be the correct quantum theory of gravity. So explaining time dilation using quantum field theory *is* explaining it using curvature of spacetime.

 

[pervect]

Could you be a bit more specific? (You may assume that I have a mathematical background.) That is, without going around in a circle? I know that the Minkowski 4-vector is a useful tool, obviously, but none of its coordinates are actually time (unless you select "natural units", which hand-waves the problem away). In other words, "ct" could be perhaps called another dimension, but how does that allow you to label "t" another dimension?

Let's try the short version first:

We can no longer write the group structure of space-time as the tensor product of a "space" group and a "time group" in relativity, hence we are forced to combine them together into a single conceptual entity, "space-time".

A longer version:

The Lorentz transform of special relativity we have

t' = γ (t - vx/c^2), x' = γ(x-vt)

t' is not the same as t, or even γt, it differs by the offset vx/c^2. Mathematically, this is consistent with space-time being a 4 dimensional vector space, and inconsistent with a view of time being different from space - as you can't add together two fundamentally different things, but we are required by the Lorentz transform to "add" time and space.

The more precise way of saying this is that the group structure of the Lorentz transform is the Lorentz group. There's a different more general view where we add in space and time translations and call the group structure of space-time the Poincare group, this is part of the Ehrlanger program.

For comparison purposes , before SR we used the Galillean transformation to change between frames

t' = t
x' = x-vt

Here t' is the same as t, so we can treat the time dimenson as separate. Mathematically we'd say that the group structure is the tensor product of the Euclidean group E(3) for space and a 1-d group for time. I believe this would be compactly written as E(3) x E(1), or if you prefer R(3) x R(1) or even E(3) x R(1).

See
http://en.wikipedia.org/w/index.php?title=Minkowski_space&oldid=613199758
and
http://en.wikipedia.org/w/index.php?title=Euclidean_space&oldid=609105409

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