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Maxila


There is a staggering amount of evidence proving time is relative, dependent on the magnitude of gravity and velocity to the frame of observation. In general dilated time will be observed from a rest frame observing a frame experiencing greater gravity and/or a sufficiently greater velocity.

The question I’d like to ask and discuss is; “why does gravity and velocity dilate time”? I am most interested to learn if there is any generally accepted scientific theories or explanations. I am not aware of such an explanation, if this is the case I’m am interested in other reasonable ideas.

Maxila

P.S. The purpose of this thread is to expand my understanding and learn from others. Some of you may know I've had some speculative thoughts on this subject; it is not my intent to discuss those thoughts in this thread; I want to learn and get different perspectives from others.
mathman
I can't tell what kind of answer you are looking for. The effects you are asking about come out of General Relativity. Why is a difficult question to answer - the effects just result from the theory.
mudderrunner
I think a classic example is when you have a guy on a train with a clock and a guy on the ground next to the train tracks with a clock. You already know that the train is moving relative to the guy on the ground and the guy on the ground is moving relative to the guy on the train. And you already know that relative to each observer the other clock is going slower.

The reason for this:

you are the guy on the ground. The train is going by at 80% c (so the effect of time dilation is noticed). In your frame of reference light moves the same speed no matter where you look (next to you or on the train). Imagine the clocks worked because they had mirrors inside that counted how many times a beam of light bounced back and forth and then ticked after a certain number of bounces. In the clock next to you the light is just going up and down, as it bounces off the mirrors. But the light in the train clock is different. The light bounces off the mirrors but due to the motion of the train the light also has to travel a distance to the left (assuming the train is headed to your left). So the distance the light in the clock travels in longer. And since the speed of light is a constant it takes a longer period of time for the light to bounce off each mirror making the clock run slower.

hope that made sense. There are probably plenty of more descriptive versions of the same example on the web. That was just describing time dilation caused by special relativity, not gravitational time dilation in general relativity.
Trout
QUOTE (Maxila+Nov 23 2010, 07:07 PM)


The question I’d like to ask and discuss is; “why does gravity and velocity dilate time”?

The answer can be found in books, studying a book on relativity would most definitely answer your questions. Anyways, here it goes:

1. Time dilation due to relative speed (SR)

Einstein showed very early on that time dilation due to relative speed is a consequence of the Lorentz transforms:

x'=g(x-vt)
t'=g(t-vx/c^2)

Re-written in differential form


dx'=g(dx-vdt)
dt'=g(dt-vdx/c^2)

Here dx, dx'=space interval between two events in frames S, respectively S'
dt,dt' time interval between two events in frams S, respectively S'

He set to determine the relationship between dt' and dt when the events are located at the same location, say dx'=0.

dx'=0 means dx-vdt=0, i.e. dx=vdt

Substituting in dt'=g(dt-vdx/c^2) he obtained:

dt'=g(dt-v^2/c^2*dt)=dt/g=dt*sqrt(1-(v/c)^2)

Written as :

dt=dt'/sqrt (1-(v/c)^2) the relation is the famous "time dilation". The physical explanation is that relative motion changes our perspective about lengths and time

Indeed, if we want to find out the relationship between two rods of lengths dx and dx' (in S and S' respectively) we need to mark the endpoints of the rod simultaneously in one frame (say S'), i.e. we need to make dt'=0 in


dx'=g(dx-vdt)
dt'=g(dt-vdx/c^2)

This produces dt=vdx/c^2 . Substituted in the first expression:

dx'=g(dx-v^2/c^2*dx)=dx/g=dx*sqrt(1-(v/c)^2) i.e. the famous "length contraction" formula


2. Time dilation in gravitational fields (GR)

In the presence of the gravitational fields we need to start from the solutions of Einstein Field Equations. One such solution is given by Schwarzschild:

(c*d\tau)^2=(1-2m/r)(c*dt)^2-dr^2/(1-2m/r) (in its simplest form).

If the events have no spatial separation (the case we want to study), then make dr=0 and you obtain:

c*d\tau=c*dt*sqrt(1-2m/r) i.e.

d\tau=dt*sqrt(1-2m/r)

The time dilation formula in GR, due to the presence of gravitational fields.
Maxila
Trout:

You put a good deal effort in that explanation, and I did learn something. I am weak in the mathematics; however I've been working on that but I was only able to understand some not all of your maths. Thank you.

mudderrunner:

No matter what I have read similar, or know, seeing it in different perspectives helps to get a deeper understanding. I am familiar with the reason why time "needs" to be relative and I wasn't clear enough in my question.

Both of you:

Specifically I was trying to understand what common trait or mechanism do gravity and velocity possess that cause them to change the flow of time to observers of other frames? Is it know, or an understood mechanic of the process that causes time to be relative?

I have played with relativistic calculators that calculate time dilation and length contraction due to velocity, relative to the earth. I noticed there might be an inverse relationship between gamma and length contraction. (i.e. gamma = 4, length contraction = 1/4)? I haven't not found a gravitational time dilation calculator and I don't trust my math skills enough to play around with it on my own.

As far as I know length contraction is a phenomena unique to velocity and not present in gravitational time dilation (please correct me if I am wrong)? My curiosity is to understand the common thread between velocity and gravity that cause them to effect time?

Trout, you mentioned the answer might be contained in books if you know of one that addresses this specific question I would appreciate it if you could post the name. Preferably one that is light on math and offers a good conceptual understanding.

Thank you everyone,

Maxila
Trout
QUOTE (Maxila+Nov 24 2010, 06:38 PM)
Trout:

You put a good deal effort in that explanation, and I did learn something. I am weak in the mathematics; however I've been working on that but I was only able to understand some not all of your maths. Thank you.

mudderrunner:

No matter what I have read similar, or know, seeing it in different perspectives helps to get a deeper understanding. I am familiar with the reason why time "needs" to be relative and I wasn't clear enough in my question.

Both of you:

Specifically I was trying to understand what common trait or mechanism do gravity and velocity possess that cause them to change the flow of time to observers of other frames? Is it know, or an understood mechanic of the process that causes time to be relative?

I have played with relativistic calculators that calculate time dilation and length contraction due to velocity, relative to the earth. I noticed there might be an inverse relationship between gamma and length contraction. (i.e. gamma = 4, length contraction = 1/4)? I haven't not found a gravitational time dilation calculator and I don't trust my math skills enough to play around with it on my own.


Trout, you mentioned the answer might be contained in books if you know of one that addresses this specific question I would appreciate it if you could post the name. Preferably one that is light on math and offers a good conceptual understanding.

Thank you everyone,

Maxila

The common mechanism is the relative view of nature. Different frames, be they in relative motion or located at different values of a gravitational potential measure time and space differently. This is why it is called the theory of "relativity"
A good book would be Feynman's Lectures. It is fantastic, buy it and READ it. Even better, enroll in a class.

QUOTE

As far as I know length contraction is a phenomena unique to velocity and not present in gravitational time dilation (please correct me if I am wrong)? My curiosity is to understand the common thread between velocity and gravity that cause them to effect time?


This is false. Start again with the Schwarzschild solution but in a slightly different form:

ds^2=dr^2/(1-2m/r)-(1-2m/r)(cdt)^2

Make dt=0 (mark the endpoints of the rod simultaneously). Then:

ds^2=dr^2/(1-2m/r)

so:

ds=dr/sqrt(1-2m/r)

This is the (lesser known) length contraction in gravitational fields. It is really more complicated than that but it is sufficiently accurate.
Maxila
QUOTE (Trout+Nov 24 2010, 01:51 PM)
The common mechanism is the relative view of nature. Different frames, be they in relative motion or located at different values of a gravitational potential measure time and space differently. This is why it is called the theory of "relativity"
A good book would be Feynman's Lectures. It is fantastic, buy it and READ it. Even better, enroll in a class.



This is false. Start again with the Schwarzschild solotion but in a slightly different form:

ds^2=dr^2/(1-2m/r)-(1-2m/r)(cdt)^2

Make dt=0 (mark the endpoints of the rod simultaneously). Then:

ds^2=dr^2/(1-2m/r)

so:

ds=dr/sqrt(1-2m/r)

This is the (lesser known) length contraction in gravitational fields. It is really more complicated than that but it is sufficiently accurate.


I've read a few books and articles about time and relativity.

I do understand that time is relative to motion and gravitational potential. That the relativity of time is more then an observation or view, it is physically relative also. In other words if a person were to experience significant time dilation relative to the earth, due to gravity or motion they would have aged less then if they remained on Earth.

What I am trying to understand is: If I were to observe from Earth, two different people experiencing identical time intervals relative from my frame of reference, one dilated by motion the other by gravity. We can say person A's time is dilated due to gravity, while person B's time is identically dilated due to their motion, from my frame of reference. What common thread between person A and B, causes me to observe the identical time dilation from my frame? Further if I could bring them back to Earth under identical conditions, I assume they both would have physically experienced the identical amount of time too?

I wanted to make my question more detailed; however because I am not good enough at the math, I did not. If anyone is interested, using a relativity calculator I was able to determine that a speed of 86.60254038 % of c would allow me to observe, from Earths frame, 1 second of time for every two seconds of Earth time. I don't know what amount of mass and distance from that mass, is necessary to observe an identical ratio of time?

Because gravity and motion appear to be different phenomena and yet they are similar in their ability to effect time, I want to try and understand what common thread they both possess that effects time?

One additional question, does G force from acceleration have any effect on time independent of motion? I am asking because of Einstein’s elevator thought experiment? I recall that he said someone inside would not be able to differentiate 1G of gravity from 1g of acceleration. I wondered if that G force had any basis in time dilation?

P.S. I read the additional information in your edit after I made my post. I was fascinated to read that there's is a form of gravitational length contraction. Does the "Feynman's Lectures" book discuss it?
brucep
QUOTE (Maxila+Nov 24 2010, 08:18 PM)

I've read a few books and articles about time and relativity.

I do understand that time is relative to motion and gravitational potential. That the relativity of time is more then an observation or view, it is physically relative also. In other words if a person were to experience significant time dilation relative to the earth, due to gravity or motion they would have aged less then if they remained on Earth.

What I am trying to understand is: If I were to observe from Earth, two different people experiencing identical time intervals relative from my frame of reference, one dilated by motion the other by gravity. We can say person A's time is dilated due to gravity, while person B's time is identically dilated due to their motion, from my frame of reference. What common thread between person A and B, causes me to observe the identical time dilation from my frame? Further if I could bring them back to Earth under identical conditions, I assume they both would have physically experienced the identical amount of time too?

I wanted to make my question more detailed; however because I am not good enough at the math, I did not. If anyone is interested, using a relativity calculator I was able to determine that a speed of 86.60254038 % of c would allow me to observe, from Earths frame, 1 second of time for every two seconds of Earth time. I don't know what amount of mass and distance from that mass, is necessary to observe an identical ratio of time?

Because gravity and motion appear to be different phenomena and yet they are similar in their ability to effect time, I want to try and understand what common thread they both possess that effects time?

One additional question, does G force from acceleration have any effect on time independent of motion? I am asking because of Einstein’s elevator thought experiment? I recall that he said someone inside would not be able to differentiate 1G of gravity from 1g of acceleration. I wondered if that G force had any basis in time dilation?

P.S. I read the additional information in your edit after I made my post. I was fascinated to read that there's is a form of gravitational length contraction. Does the "Feynman's Lectures" book discuss it?

Remember what I showed you about gamma.

v^2 = 2M/r

so for

gamma = 1 / (1-v^2) ^1/2

you can substitute the curvature component of the metric, 2M/r, for velocity squared.

gamma = 1 / (1-2M/r)^1/2

This means that there is a relative velocity which corresponds with a position in the gravitational field. For example I'll chose the position in the gravitational field to be r = 4M [twice the distance r = 2M] and M_meter [mass in geometric units].

v^2 = 2M/4M = 1/2

v = (1/2)^1/2 = .707106781 [this is a fraction of c=1 the speed of light] so I can just say .707106781c.

I'm glad you went away from asking 'why' because I think the 'why' of this natural phenomena is beyond our ability to quantify. So the gist of this answer was

v^2 = 2M/r
brucep
QUOTE (brucep+Nov 24 2010, 10:45 PM)
Remember what I showed you about gamma.

v^2 = 2M/r

so for

gamma = 1 / (1-v^2) ^1/2

you can substitute the curvature component of the metric, 2M/r, for velocity squared.

gamma = 1 / (1-2M/r)^1/2

This means that there is a relative velocity which corresponds with a position in the gravitational field. For example I'll chose the position in the gravitational field to be r = 4M [twice the distance r = 2M] and M_meter [mass in geometric units].

v^2 = 2M/4M = 1/2

v = (1/2)^1/2 = .707106781 [this is a fraction of c=1 the speed of light] so I can just say .707106781c.

I'm glad you went away from asking 'why' because I think the 'why' of this natural phenomena is beyond our ability to quantify. So the gist of this answer was

v^2 = 2M/r

Just to make it clearer the velocity I derived is the velocity of an object orbiting at r_shell = 4M.
Maxila
QUOTE (brucep+Nov 24 2010, 05:45 PM)

I'm glad you went away from asking 'why' because I think the 'why' of this natural phenomena is beyond our ability to quantify. So the gist of this answer was v^2 = 2M/r



No offense but I hope you are wrong. Even if we are far from understanding it now, I hope physicists can eventually discover what is the mechanism by which gravity and motion dilate time. Personally to me, Relativity seems unfinished without that part of the puzzle answered.

Changing the subject, I want to publicly thank you for helping me understand a bit of Physics math. I've got a long , long way to go ;however when I research a web page looking something up, I can often understand some of the simpler maths, that I didn't understand before. I'm taking it slow but it nice to see some progress. THANK YOU!

P.S. I sent you an email with some questions on a few things I was unsure of.
JTsang
Here is a different answer, not in today's physics:

It's the Energy ---- actually Momentum, if you have some GR ----- that associate with the time.

In other word, Time or RateOfTime = F[ Energy&Momentum(s) ]

Take for example
1. a "fast moving" muon last longer.
2. a heavier mass slow down the time.

The actual physics and it's math ? just look up what I wrote in this forum & elsewhere under my name.
flyingbuttressman
QUOTE (JTsang+Nov 26 2010, 12:47 AM)
The actual physics and it's math ?

Is this a question?
The answer is no.
JTsang
QUOTE (flyingbuttressman+Nov 26 2010, 04:50 AM)
Is this a question?
The answer is no.

That's funny. in fact

Time or RateOfTime = F[ Energy&Momentum(s) ]
is a simplified representation of a equation called "E's Field Eq".
brucep
QUOTE (Maxila+Nov 26 2010, 03:43 AM)

No offense but I hope you are wrong. Even if we are far from understanding it now, I hope physicists can eventually discover what is the mechanism by which gravity and motion dilate time. Personally to me, Relativity seems unfinished without that part of the puzzle answered.

Changing the subject, I want to publicly thank you for helping me understand a bit of Physics math. I've got a long , long way to go ;however when I research a web page looking something up, I can often understand some of the simpler maths, that I didn't understand before. I'm taking it slow but it nice to see some progress. THANK YOU!

P.S. I sent you an email with some questions on a few things I was unsure of.

Happy Thanksgiving friend.

I know how you feel. The 'why' is more philosophical for me. I don't think the great theoretical models attempt to answer that question. Maybe somebody could convince me otherwise based on my possible erroneous personal definition of 'why'. Trout showed you how the models describe the phenomena. Maybe spacetime geometry is adequate 'why'. I tend to think that's just the way it is'. IE being good enough for me.
Lunarlanding
QUOTE (Maxila+Nov 24 2010, 08:18 PM)



What I am trying to understand is: If I were to observe from Earth, two different people experiencing identical time intervals relative from my frame of reference, one
dilated by motion the other by gravity. .....
What common thread between person A and B, causes me to observe the identical time dilation from my frame?



Maxila; you have a good question...

To find out where the grav. time dilation equals the SR (velocity) time dialtion simply set the two equations equal to each other and solve for velocity:

You will find that the velocity at which they are equal is at the escape velocity of the gravitational well.

More specifically, for exactness....
We usually refer to "clock rate" being changed, rather than time itself.
Using t( ) as the "clock rate"... and t( )/t(o) as the ratio of the dilated clock with respect to the undilated clock rate in your frame, t(o).

...and starting with the usual eqns:

Grav. time dilation, t(g)/t(o) = sqrt(1-(2GM/Rc^2))
(notice I left the constants in there so you can recognize that the gravitational POTENTIAL, GM / R, is part of the equation).

And for the SR clock rate with velocity v:
t(v)/t(o)= sqrt(1-v^2/c^2)

Setting them equal to each other:

t(g)/t(o) = t(v)/t(o)

sqrt(1-(2GM/Rc^2)) = sqrt(1-v^2/c^2)

And solving for Velocity:

v = sqrt(2GM/R)

Well what do you know; that is just the escape velocity of a particle (clock) constrained in a planet's gravitational field. smile.gif

IOW, the time dilation of a clock in a gravitational well is equal to that of its escape velocity from that position in the gravity well.

Thus, simply subtituting the escape velocity for v in the kinematic (SR) time dilation formula transforms it into the gravitational Time dilation .


This informal proceedure may give you a better understanding of the "common thread" (as you call it) between the gravitational and kinematic time dilations.

If you think this is coincidence, its probably not. The relation can be thought of classically through conservation of energy considerations, revealing
that in some respects energy dynamics have a temporal effect.


Lunar
enord
me stupid= maybe some ado with birth .........of whatever, by whomever or whatever might be sympethatic?
Maxila
QUOTE (Lunarlanding+Nov 26 2010, 01:40 PM)
Well what do you know; that is just the escape velocity of a particle (clock) constrained in a planet's gravitational field. smile.gif

IOW, the time dilation of a clock in a gravitational well is equal to that of its escape velocity from that position in the gravity well.

Thus, simply subtituting the escape velocity for v in the kinematic (SR) time dilation formula transforms it into the gravitational Time dilation .


This informal  proceedure may give you a better understanding of the "common thread" (as you call it) between the gravitational and kinematic time dilations.

If you think this is coincidence, its probably not.  The relation can be thought of  classically through conservation of energy considerations, revealing
that in some respects  energy dynamics have a temporal effect.
 

Lunar


Thank you Lunar, that information was fascinating for me to learn.

QUOTE
Using t( ) as the "clock rate"... and t( )/t(o) as the ratio of the dilated clock with respect to the undilated clock rate in your frame, t(o).


I've only recently started to attempt to understand a bit of this math and I am uncertain of myself in applying what I "think" I know. I have a question on the section I quoted above. Would t()/t(o) be the same thing as gamma or the Lorentz factor, I think it may be, but I'm not sure? Again I am very uncertain of myself because it is so new to me but it looks like you are writing coordinate time / proper time?

Thank you for you help.

Maxila
brucep
QUOTE (Maxila+Nov 27 2010, 01:58 AM)

Thank you Lunar, that information was fascinating for me to learn.



I've only recently started to attempt to understand a bit of this math and I am uncertain of myself in applying what I "think" I know. I have a question on the section I quoted above. Would t()/t(o) be the same thing as gamma or the Lorentz factor, I think it may be, but I'm not sure? Again I am very uncertain of myself because it is so new to me but it looks like you are writing coordinate time / proper time?

Thank you for you help.

Maxila

This is what Lunar said:

"Using t( ) as the "clock rate"... and t( )/t(o) as the ratio of the dilated clock with respect to the undilated clock rate in your frame, t(o)."

That's another way to express the ratio dTau/dt = (1-v^2)^1/2

Lunar wrote it:

t( )/t(o) = sqrt(1-v^2) [same thing].

gamma is the inverse ratio t(o)/t( ) = 1/sqrt(1-v^2)

or

dt/dTau = (1-v^2)^-1/2

If you think about it you'll see why gamma is a useful relativistic expression. For instance momentum.

p = mv

The relativistic momentum becomes

p_relativistic = (1-v^2)^-1/2(mv) = gamma(mv)

For small velocity the Newtonian p = mv works fine but when velocity becomes relativistic you need to use p = gamma(mv). In the weak gravitational field and for non-relativistic velocity the Newtonian expressions are a very close approximation but for the strong field and relativistic velocity you have to use relativity theory. gamma is the relativistic factor. For low velocity gamma is very close to 1 but as you approach the speed of light gamma becomes a very large number without bound.
boit
Being also mathematicaly challenged, i'll seek some clarification with the bare minimum of maths. If a rocket leaving at escape velocity shines a beam of light from a head lamp for just one second, what will be the length of that beam of light? Will it be eleven kilometer less of a light second? Relative to an observer on earth that is.
Maxila
QUOTE (brucep+Nov 26 2010, 09:40 PM)
This is what Lunar said:

"Using t( ) as the "clock rate"... and t( )/t(o) as the ratio of the dilated clock with respect to the undilated clock rate in your frame, t(o)."

That's another way to express the ratio dTau/dt = (1-v^2)^1/2

Lunar wrote it:

t( )/t(o) = sqrt(1-v^2) [same thing].

gamma is the inverse ratio t(o)/t( ) = 1/sqrt(1-v^2)

or

dt/dTau = (1-v^2)^-1/2

If you think about it you'll see why gamma is a useful relativistic expression. For instance momentum.

p = mv

The relativistic momentum becomes

p_relativistic = (1-v^2)^-1/2(mv) = gamma(mv)

For small velocity the Newtonian p = mv works fine but when velocity becomes relativistic you need to use p = gamma(mv). In the weak gravitational field and for non-relativistic velocity the Newtonian expressions are a very close approximation but for the strong field and relativistic velocity you have to use relativity theory. gamma is the relativistic factor. For low velocity gamma is very close to 1 but as you approach the speed of light gamma becomes a very large number without bound.



Thanks Bruce, I see I didn't read that sentence carefully enough. Am I using the terms correctly to say that dTau/dt is proper time / coordinate time?

I sorry to be redundant in my questions. I often double and triple check information that is new to me. It's a personality flaw.

Maxila
AlexG
boit, do you mean that the light shines for one second of ship's time?

Here's a guess, with no calculation at all. Relative to the observer on earth, the ship will be higher in the gravitational field, and so will have a lower time dilation, and will be travelling at 25,300 mph, and so will have a higher time dilation. There must be a point where the two cancel each other out. At that point, the beam of light shining for one second 300,000,000 meters long, as measured by the earth observer.
brucep
QUOTE (Maxila+Nov 27 2010, 05:24 AM)


Thanks Bruce, I see I didn't read that sentence carefully enough. Am I using the terms correctly to say that dTau/dt is proper time / coordinate time?

I sorry to be redundant in my questions. I often double and triple check information that is new to me. It's a personality flaw.

Maxila

You're not redundant. You're using the terms perfectly. You have good personal skills and use them well. I like to be sure what I'm saying also.
Trout
QUOTE (AlexG+Nov 27 2010, 05:41 AM)
boit, do you mean that the light shines for one second of ship's time?

Here's a guess, with no calculation at all.  Relative to the observer on earth, the ship will be higher in the gravitational field, and so will have a lower time dilation, and will be travelling at 25,300 mph, and so will have a higher time dilation.  There must be a point where the two cancel each other out.  At that point, the beam of light shining for one second  300,000,000 meters long, as measured by the earth observer.

1. If the ship shines the light for one second in ship's time the length of the pulse in ship's frame is exactly one light second, there is no GR time dilation.

2. If the ship shines the light one second in the Earth's frame, then there is a kinematic effect due to the relative velocity equal to sqrt(1-(v/c)^2) and a gravitational effect (see my earlier post) due to gravitational potential difference equal to sqrt(1-r_s/r) where r_s is the Schwarzschild radius and r is the Schwarzschild radial distance. The net effect can be shown to be:

d\tau/dt=sqrt(1-r_s/r)*sqrt[1-(v/c)^2/(1-r_s/r)^2] so :

d\tau<dt

In other words, the proper time in the rocket frame is always smaller than the coordinate time dt in the Earth frame (remember the twins "paradox"). For case 2, the light beam will tend to be shorter than 1 light second.

As an aside, the above explanation shows why the GPS clocks need to be set at a higher rate than the Earth bound clocks. Setting the GPS frequency higher forces them to count the same amount of time as the Earth bound clocks, i.e. synchronizes them. Otherwise , GPS would not work.
boit
Thank you guys for your answers. I had imagined a second by the earthbound observer but i discounted gravity. Far off in space, will the stationary observer calculate a distance exactly eleven kilometers short of a light second? That is if the spaceship flashes light in one second by the stationary observer's clock.
Trout
QUOTE (boit+Nov 27 2010, 05:46 PM)
Thank you guys for your answers. I had imagined a second by the earthbound observer but i discounted gravity. Far off in space, will the stationary observer calculate a distance exactly eleven kilometers short of a light second? That is if the spaceship flashes light in one second by the stationary observer's clock.

You have few ideas but fixed. Where does the 11km come from?
Maxila
QUOTE (Lunarlanding+Nov 26 2010, 01:40 PM)


IOW, the time dilation of a clock in a gravitational well is equal to that of its escape velocity from that position in the gravity well.



I don't know too much about the force of gravity. Is the force gravity exerts on matter linear with the axis being towards the center of a gravity well?
boit
QUOTE (Trout+Nov 27 2010, 09:04 PM)
You have few ideas but fixed. Where does the 11km come from?

The same spacecraft that achieved escape velocity. I am assuming it is coasting at that speed indefinately (that is unless another force compells it to act otherwise). I have more ideas that am not really fixated with. Say it is a monochromatic and there is another observer ahead that is stationary relative to the first observer. My guess it he will see the light blueshifted but the flash will last less than a second, a thirty thousandth of a second less thereabouts. Or is it not as simple as that? Stop me if i start getting into your nerves. My apologies.
Trout
QUOTE (boit+Nov 27 2010, 06:41 PM)
The same spacecraft that achieved escape velocity. I am assuming it is coasting at that speed indefinately (that is unless another force compells it to act otherwise). I have more ideas that am not really fixated with. Say it is a monochromatic and there is another observer ahead that is stationary relative to the first observer. My guess it he will see the light blueshifted but the flash will last less than a second, a thirty thousandth of a second less thereabouts. Or is it not as simple as that? Stop me if i start getting into your nerves. My apologies.

I have already answered this question in an earlier post to Maxilla. Why don't you read a book or take a class? Too lazy?
brucep
QUOTE (boit+Nov 27 2010, 06:41 PM)
The same spacecraft that achieved escape velocity. I am assuming it is coasting at that speed indefinately (that is unless another force compells it to act otherwise). I have more ideas that am not really fixated with. Say it is a monochromatic and there is another observer ahead that is stationary relative to the first observer. My guess it he will see the light blueshifted but the flash will last less than a second, a thirty thousandth of a second less thereabouts. Or is it not as simple as that? Stop me if i start getting into your nerves. My apologies.

Hi boit

The speed of light is independent of the speed of the emitter and or the receiver [most amazing result in the universe in my opinion]. But that only describes the speed of light not the distance the light travels. For your problem the light would arrive in less than a second because the emitter movement reduces the distance the light has to travel to the receiver.
boit
QUOTE (brucep+Nov 28 2010, 12:12 AM)
Hi boit

The speed of light is independent of the speed of the emitter and or the receiver [most amazing result in the universe in my opinion]. But that only describes the speed of light not the distance the light travels. For your problem the light would arrive in less than a second because the emitter movement reduces the distance the light has to travel to the receiver.

Thanks brucep. You've helped me evaluate my comprehension skills. @Trout. Sorry, i see i was getting into your nerves. I usually try to search this forum before starting a topic or asking a question since i believe much has been covered and i have repeating stuff as much as you do. Am not lazy. I don't know if a pinned FAQs will be a good idea here.
Trout
QUOTE (boit+Nov 28 2010, 05:19 AM)
Thanks brucep. You've helped me evaluate my comprehension skills. @Trout. Sorry, i see i was getting into your nerves. I usually try to search this forum before starting a topic or asking a question since i believe much has been covered and i have repeating stuff as much as you do. Am not lazy. I don't know if a pinned FAQs will be a good idea here.

If you aren't lazy why don't you read a book (I recommended an excellent one to Maxila) or take a class?
boit
QUOTE (Trout+Nov 28 2010, 08:21 AM)
If you aren't lazy why don't you read a book (I recommended an excellent one to Maxila) or take a class?

It is from reading books that we come up with these questions. Don't you think. You obviously don't have teaching skills. Allowing students to ask questions, no matter how stupid the guestion my seem, is part of learning process. I'll be careful to add the words ''Trout may abstain from answering this question''. I wouldn't ask my computer geek friend to block your posts though cause i trully try to learn from them. I now know how to square negative numbers, see:)
Trout
QUOTE (boit+Nov 28 2010, 05:31 AM)
It is from reading books that we come up with these questions. Don't you think. You obviously don't have teaching skills. Allowing students to ask questions, no matter how stupid the guestion my seem, is part of learning process. I'll be careful to add the words ''Trout may abstain from answering this question''.

Based on the stupidity of your questions I have a hard time believing that you read any books.

QUOTE
I wouldn't ask my computer geek friend to block your posts though cause i trully try to learn from them.


If you did, you would have decided to take a class by now. Yet, you prefer to troll the forum. Much easier.


QUOTE (->
QUOTE
I wouldn't ask my computer geek friend to block your posts though cause i trully try to learn from them.


If you did, you would have decided to take a class by now. Yet, you prefer to troll the forum. Much easier.


I now know how to square negative numbers, see:)


You do? How much is -3^3?
boit
How much is -3 cubed? Would that be -27? Yes, negative twenty seven smile.gif
Trout
QUOTE (boit+Nov 28 2010, 10:46 AM)
How much is -3 cubed? Would that be -27? Yes, negative twenty seven smile.gif

good, and -3^2?
boit
QUOTE (Trout+Nov 28 2010, 06:23 PM)
good, and -3^2?

Easy. -9 rolleyes.gif
Trout
QUOTE (boit+Nov 28 2010, 04:11 PM)
Easy. -9 rolleyes.gif

You finally learned.
boit
QUOTE (Trout+Nov 28 2010, 07:12 PM)
You finally learned.

Auuuiii! I've passed. Thank you very much. Now about those books you recommended, I'll check in the local library next time I venture out. Enrolling in an evening class would be great but too bad there aren't any around. In a short while I'll be posting in the puzzling questions sections. Check it for troll like theme and I'll weed it out pronto. rolleyes.gif
JTsang
QUOTE (JTsang+Nov 26 2010, 04:47 AM)
Here is a different answer, not in today's physics:

It's the Energy ---- actually Momentum, if you have some GR ----- that associate with the time.

In other word, Time or RateOfTime = F[ Energy&Momentum(s) ]

Take for example
1. a "fast moving" muon last longer.
2. a heavier mass slow down the time.

The actual physics and it's math ? just look up what I wrote in this forum & elsewhere under my name.

Why resort to slave when there's a slave master ? Even though GR is not a complete theory, SR is just way inferior .

The twisted version of the field equation holds some interesting hints:
1) All dimensions are renamed to Time instead of Xs, a change in name, to encourage reader NOT to identify any dimension as "spatial" .... indeed, this is generalized coordinates.
2) Generalized Momentum is used to replace mass, energy or momentum.

The equation clearly implies the Time structure is a function of Momentum(s)... now consider give a different name to left-right , front-back, top-bottom ...... as t1, t2, t3 axis.

So, how to use it ?

Take the case of clock.

Case A: circular high obit.
Case C: circular very low obit, just above ground.
Case B: elliptic obit from high to low.
Case D: ground station.

Keep in mind: there's no more concept of "energy" , it's all about G Momentum.

neglect effect of planet, for those caesium clocks,
Reader simply look at their relative (Total Momentum)^2 = Sum( p^2) :
Case A > Case B > Case C > Case D
That is how those clock related.

Note:
(Total Momentum)^2 = Sum( p^2) was commonly presented in most textbook as
E^2 = M^2 * C^4
Lunarlanding
QUOTE (JTsang+Nov 29 2010, 05:18 PM)


Keep in mind: there's no more concept of "energy" , it's all about G Momentum.




Not necesarily, JT; that's only true for clocks with relative Velocity, and doesn't take into account stationary clocks in different gravitational potentials; the time difference is related to the gravitational potential (or energy) difference.

QUOTE

neglect effect of planet, for those caesium clocks,


Cannot be neglected , sorry.

You mis-understood the OP's question. Its NOT about what relates time dilation between two clocks in relative motion; rather its about what relates time dilation between kimematic time dilation and gravitational time dilation.

Lunar
Maxila
QUOTE (Lunarlanding+Nov 29 2010, 01:43 PM)

You mis-understood the OP's question. Its NOT about what relates time dilation between two clocks in relative motion; rather its about what relates time dilation between kimematic time dilation and gravitational time dilation.

Lunar


That is my question and I would add; by what common process or function, (for lack of a better term) do they manipulate time?

Lunar, based on what you told me about dilation being equal for a point in a gravity well to the escape velocity of that point in the gravity well (I hope I understood you correctly). I have a question, is the force gravity exerts linear, with its axis being towards the center of the gravity well?

The reason I asked is to clarify my understanding of the common thread. A linear (directional force) exerted on matter by gravity, and an equal amount of linear force (resulting in velocity) that can offset the gravitational force?

I'm not sure if I structured that sentence clearly enough so I'm going to make an analogy:

If I placed a bowling ball on the surface of the Earth. Gravity is excreting force on it in a single axis towards the center of the gravity well. An amount of force equal to the escape velocity of the ball is required to counter that gravitational force. If that ball was in a vacuum, away from any gravity wells, traveling at the escape velocity it needed to escape Earths surface, its clock would be running the same rate as a clock on Earth surface? Also if my velocity relative to the ball was zero, the amount of force needed to bring the ball to my relative velocity (zero), without accelerating myself, is also equal to the force that could accelerate the ball to its escape velocity from the Earths surface (lets assume there is no atmosphere)?

Addendum:

I wanted to add what I am finding so fascinating. I never gave it much thought before; reading another thread made me understand weight and mass are not the same thing. Gravity give us weight and escape velocity counters that weight, and If I understood Lunar's post correctly time dilation is equal for the force of a gravity well and it's corresponding escape velocity.
Lunarlanding
QUOTE (Maxila+Nov 27 2010, 06:37 PM)


I don't know too much about the force of gravity. Is the force gravity exerts on matter linear with the axis being towards the center of a gravity well?


Hi Maxila....glad to see you are getting something out of this...

Its not about gravitational "force", Max.
Its about gravitational potential.

Force of gravity = GMm / R^2

Gravitational potential = GM / R

So to answer your question directly....looking at the above equations....
The 'force' of gravity goes as the inverse square of distance, R (above the planet's surface); and it acts radially toward the center of mass;

and the gravitational potential falls off linearly with distance; (R = distance to center of mass)

However, in dealing with time dilation we look at the Grav. potential.

Again; the fact that escape velocity is the velocity at which kinematic time dilation equals grav. time dilation is not coincidental.
In terms of the derivations, both gravitational T. D. and the escape velocity equations have as their basis gravitational potential (energy)....so its not entirely unexpected...

It is good to remember that to derive the escape velocity eqn. we set the kinetic energy of the particle's velocity against the gravitational energy of the planet.

IOWs, an object must do work against the planet's grav. potential energy to escape the constraint of the planet's field. In that sense you could look at force, but otherwise it is easier to consider the off-setting energies.
more on that later.

Sorry, I missed that post, earlier...
PS. I'll address your other question above (about the counteracting attributes that 'connect' the two forms of Time dilation) when I have more time....

It is a fascinating topic and glad you are getting something out of it.

Lunar
Maxila
QUOTE (Lunarlanding+Nov 29 2010, 07:39 PM)

It is good to remember that to derive the escape velocity eqn. we set the kinetic energy of the particle's velocity against the gravitational energy of the planet.

IOWs, an object must do work against the planet's grav. potential energy to escape the constraint of the planet's field. In that sense you could look at force, but otherwise it is easier to consider the off-setting energies.
more on that later.


I may be using the term force incorrectly, I was also thinking of it as interchangeable with energy.

I was visualizing gravity adding energy to matter by exerting a linear force giving it weight. If the surface of the earth didn't stop that matter from falling, the result of that linear force would be velocity instead of weight. Add an identical amount of energy, by way of a linear force, to that identical matter in a vacuum, and the result is velocity instead of weight.

I don't know if it is correct, but the connection I was making is the main difference between gravity and velocity is the mass of a gravitational well usually thwarts velocity and results in matter having weight. But if both velocity and gravity applying a linear force to matter with the same energy potential it results in the same time dilation. In one potential energy (gravity) movement is thwarted by other matter resulting in weight, the other potential energy is free to move in the form of velocity. IOW's, it appears you have energy potential by way of a directional force, one thwarted (gravity) results in weight, the other free to move results in velocity?

Even if I totally confused this, you have been great in trying to help me understand more then I know before, please be patient and I'll work to understand it correctly.
mudderrunner
QUOTE (Maxila+Nov 24 2010, 01:38 PM)
Specifically I was trying to understand what common trait or mechanism do gravity and velocity possess that cause them to change the flow of time to observers of other frames? Is it know, or an understood mechanic of the process that causes time to be relative?

The commonality is everything except for the fact that in a gravitational field, space is curved. So in other words, the only difference is that space is curved in a gravity field. This curvature makes things seem a lot different but time dilation works the same in gravity as it does in flat space.

In flat space:
If you are traveling in uniform motion, a clock in your frame of reference does not run fast or slow. If you accelerate away from the clock then that clock will run slow from your frame of reference.

In curved space:
If you are traveling in uniform motion (in free fall), a clock in your frame of reference does not run fast or slow. If you accelerate away from the clock (clock continues to free fall, you land on the surface of earth) then that clock will run slow from your frame of reference.
Maxila
QUOTE (mudderrunner+Nov 30 2010, 12:24 AM)
The commonality is everything except for the fact that in a gravitational field, space is curved. So in other words, the only difference is that space is curved in a gravity field. This curvature makes things seem a lot different but time dilation works the same in gravity as it does in flat space.

In flat space:
If you are traveling in uniform motion, a clock in your frame of reference does not run fast or slow. If you accelerate away from the clock then that clock will run slow from your frame of reference.

In curved space:
If you are traveling in uniform motion (in free fall), a clock in your frame of reference does not run fast or slow. If you accelerate away from the clock (clock continues to free fall, you land on the surface of earth) then that clock will run slow from your frame of reference.



This was very good additional information to read, thank you.

I have a few questions on this part:

QUOTE
If you accelerate away from the clock (clock continues to free fall, you land on the surface of earth) then that clock will run slow from your frame of reference.


Wouldn't this depend on the velocity of the clock because you are now deeper in the gravity well then the clock?

Within the curved space of a gravity well, does velocity need to exceeded escape velocity of a point in the gravity well for moving clock would run slower; or would any velocity greater then a rest frame of that point in a gravity well make the moving clock run slower? (I may have answered this question with a recollection I read that atomic clocks have been shown to run slower on board jet aircraft?)
mudderrunner
QUOTE (Maxila+Nov 30 2010, 12:58 PM)
This is because you are now deeper in the gravity well then the clock, correct?

Even in curved space of gravity, once velocity exceeded the escape velocity of a point in the gravity well, the moving clock would run slower, then a stationary one at that point in the gravity well, correct?

It is because you are in accelerated motion when standing on the surface of earth while the clock, which is still in free fall (say it went down a really deep well or something), is in uniform motion. So it is equivalent to being in the middle of flat space where you suddenly accelerate away from the clock. From your frame of reference the clock starts running slower and slower as you continue to accelerate away.

a different situation would be two clock in different places. One is at the top of a mountain and the other at the bottom. Gravity is slightly stronger at the bottom of the mountain. Another way to say this is that space is more curved at the bottom of the mountain. So a clock sitting on the ground at the bottom of the mountain is actually accelerating a bit faster then the clock sitting on the ground at the top of the mountain. Therefore the bottom clock will run slower in the top clocks frame of reference while the top clock will run faster from the bottom clocks frame of reference.

So whenever there are two clocks and at least one is accelerating, the one that is accelerating faster will always be the one running slower. It doesn't matter if this acceleration is in curved space (sitting on the ground) or in flat space (turning on the rockets that are attached to a space ship away from massive objects).
boit
I am glad that the post above clears the air for those that refute relativity. Here we see the inhabitants of earth noticing a spaceship's clock running slow while the crew in the spaceship see the clocks on earth running faster. The anti-relativity forum says the crew also sees the earth's clock running slower too thereby rendering it impossible to determine who is actually time dilating and which twin will actually be younger. Now i think if you notices someone clock running faster, it is probably yours that is actually running slower.
Maxila
QUOTE (mudderrunner+Nov 30 2010, 01:22 PM)
A different situation would be two clock in different places. One is at the top of a mountain and the other at the bottom. Gravity is slightly stronger at the bottom of the mountain. Another way to say this is that space is more curved at the bottom of the mountain. So a clock sitting on the ground at the bottom of the mountain is actually accelerating a bit faster then the clock sitting on the ground at the top of the mountain. Therefore the bottom clock will run slower in the top clocks frame of reference while the top clock will run faster from the bottom clocks frame of reference.



In the past I never could make a satisfactory connection in my mind to the "elevator thought experiment" and the curved space-time of gravity. This paragraph made that connection click for me.
mudderrunner
QUOTE (boit+Nov 30 2010, 01:42 PM)
I am glad that the post above clears the air for those that refute relativity. Here we see the inhabitants of earth noticing a spaceship's clock running slow while the crew in the spaceship see the clocks on earth running faster. The anti-relativity forum says the crew also sees the earth's clock running slower too thereby rendering it impossible to determine who is actually time dilating and which twin will actually be younger. Now i think if you notices someone clock running faster, it is probably yours that is actually running slower.

the problem that the anti-relativity forumites have is understanding the difference between special and general relativity. They understand special relativity enough to know that clocks moving relative to you are running slow, and that this effect is reciprocal so that from the other clocks frame of reference.. a clock that you're holding is running slower. However, they don't understand that this reciprocation only applies in "special" circumstances, meaning that it only occurs when both frames of reference are moving in uniform motion. Special relativity is special because it only applies to the special case of uniform motion.

The twin paradox on the other hand has one frame of reference in uniform motion (earth) and another in accelerated frame of reference (space ship). So the reciprocation does not apply. The circumstances are more "general" in this case because they encumpass all frames of reference, not just uniform motion but acceleration as well. Therefore general relativity must be consulted.
mudderrunner
QUOTE (Maxila+Nov 30 2010, 02:04 PM)

In the past I never could make a satisfactory connection in my mind to the "elevator thought experiment" and the curved space-time of gravity. This paragraph made that connection click for me.

I'm glad that helped. Gotta love those satisfying little epiphanies. They are one of my favorite things in life.
Confused1
Post superceded by Brucep's next post.

brucep
QUOTE (Maxila+Nov 30 2010, 07:04 PM)

In the past I never could make a satisfactory connection in my mind to the "elevator thought experiment" and the curved space-time of gravity. This paragraph made that connection click for me.

I'm not to sure why acceleration is being associated with different clock rates. If it's being thought of as the cause of different clock rates then that is wrong. It's relative velocity in SR and spacetime curvature in GR

dTau = (1-v^2)^1/2 dt

and

dTau = (1-2M/r)^1/2 dt

http://en.wikipedia.org/wiki/Twin_paradox

this section:

Difference in elapsed time as a result of differences in twins' spacetime paths.

...... where the following relations hold between V, a and T_a:

v = a T_a / [1+(a T_a)^2]^1/2

This is the instantaneous velocity along the accelerating twins path with respect to time. Any difference in clock rates are due to relative velocity not acceleration.

and

a T_a = v / (1-v^2)^1/2

I think it was rpenner who straightened this out for me. It's easy to get caught in that trap. NA pointed out that my explanation didn't jive with rpenner and after further review I learned something. The jist of the explanation is good, I think. Maybe rpenner can find the post. It would be a good post to put in a FAQ.
mudderrunner
QUOTE (brucep+Nov 30 2010, 06:40 PM)
I'm not to sure why acceleration is being associated with different clock rates. If it's being thought of as the cause of different clock rates then that is wrong. It's relative velocity in SR and spacetime curvature in GR

acceleration is what GR is all about. And gravity, while it doesn't cause acceleration, obfuscates what acceleration is. So GR is also a theory of gravity by default.

acceleration causes time dilation. You just have to understand the equivalence principle to know how to identify acceleration in curved space. And since acceleration is absolute it does not cause a reciprocal time dilation such as the case between two objects in uniform motion (SR).
brucep
QUOTE (mudderrunner+Dec 1 2010, 12:10 AM)
acceleration is what GR is all about. And gravity, while it doesn't cause acceleration, obfuscates what acceleration is. So GR is also a theory of gravity by default.

acceleration causes time dilation. You just have to understand the equivalence principle to know how to identify acceleration in curved space. And since acceleration is absolute it does not cause a reciprocal time dilation such as the case between two objects in uniform motion (SR).

No it doesn't. I actually know what GR says about it.
mudderrunner
QUOTE (brucep+Nov 30 2010, 07:19 PM)
No it doesn't. I actually know what GR says about it.

QUOTE
It's relative velocity in SR and spacetime curvature in GR


then why does acceleration matter with respect to time dilation in flat space?
NoCleverName
QUOTE (mudderrunner+Nov 30 2010, 08:10 PM)
And since acceleration is absolute

No it isn't; if it were then (its integral) speed would be absolute, too.
mudderrunner
QUOTE (NoCleverName+Nov 30 2010, 07:31 PM)
No it isn't; if it were then (its integral) speed would be absolute, too.

Uniform motion is relative, acceleration is absolute.

you can never tell how fast you're going when in uniform motion because it's relative.

you always know when you're in acceleration and with some details you can always calculate how much you're accelerating. This is because acceleration is absolute. It isn't relative.
brucep
QUOTE (mudderrunner+Dec 1 2010, 12:29 AM)


then why does acceleration matter with respect to time dilation in flat space?

It only matters because the acceleration is changing instantaneous velocity over time.

In GR

g-shell = local gravitational acceleration [tidal acceleration]

g_shell = M/r^2(1-2M/r)^-1/2 = (M/r^2)gamma

g_shell is a derivative of dr_shell / dt_shell = .....

the ratio of clock rates

dTau/dt = (1-2M/r)^1/2

2M/r is the curvature component and responsible for gravitational time dilation. When 2M/r is a very small number [r is very large]

dTau/dt = ~1

It's easy to get these terms mixed up when thinking about the equivalence principle.
mudderrunner
QUOTE (brucep+Nov 30 2010, 08:01 PM)
It only matters because the acceleration is changing instantaneous velocity over time. In GR

exactly. And this causes non-inertial motion rather then inertial motion. This is why the twin from the space craft (twin paradox) is younger and never the other way around. It's because of acceleration. It provides an absolute frame of reference.

I guess you can argue that acceleration is a different type of velocity and uniform motion is another type. So you can then argue that velocity is what ultimately causes time dilation. But that doesn't make my statement false. Acceleration does cause time dilation.

I'd rather not get into the math cause I don't care for it. So forgive me for not replying to the rest.
brucep
QUOTE (mudderrunner+Dec 1 2010, 01:12 AM)
exactly. And this causes non-inertial motion rather then inertial motion. This is why the twin from the space craft (twin paradox) is younger and never the other way around. It's because of acceleration. It provides an absolute frame of reference.

I guess you can argue that acceleration is a different type of velocity and uniform motion is another type. So you can then argue that velocity is what ultimately causes time dilation. But that doesn't make my statement false. Acceleration does cause time dilation.

I'd rather not get into the math cause I don't care for it. So forgive me for not replying to the rest.

I don't have to argue about anything. If you look at what I wrote down you could actually learn something. Acceleration doesn't cause time dilation.
NoCleverName
QUOTE (mudderrunner+Nov 30 2010, 08:39 PM)
with some details you can always calculate how much you're accelerating. This is because acceleration is absolute. It isn't relative.

yuk, yuk ... and with some details you can always tell how fast you are going, too. Right.

Better tell Einstein he was wrong when he thought acceleration was relative, too.
brucep
QUOTE (NoCleverName+Dec 1 2010, 12:31 AM)
No it isn't; if it were then (its integral) speed would be absolute, too.

The absolute for him is that with an accelerometer you can proof motion.
mudderrunner
QUOTE (NoCleverName+Nov 30 2010, 08:24 PM)
yuk, yuk ... and with some details you can always tell how fast you are going, too. Right.


only if that detail is the frame of reference from which you're doing the measurement.

QUOTE
Better tell Einstein he was wrong when he thought acceleration was relative, too.


He says it's not.

QUOTE (->
QUOTE
Better tell Einstein he was wrong when he thought acceleration was relative, too.


He says it's not.

I don't have to argue about anything. If you look at what I wrote down you could actually learn something. Acceleration doesn't cause time dilation.

likewise, so we're at a stalemate. I don't want to get into the math, and you don't want to get into the verbal explanation.
brucep
QUOTE (mudderrunner+Dec 1 2010, 01:48 AM)
only if that detail is the frame of reference from which you're doing the measurement.



He says it's not.


likewise, so we're at a stalemate. I don't want to get into the math, and you don't want to get into the verbal explanation.

Look at the formulas and find out you're wrong. Good reason not to look for somebody uninterested in learning but only interested in being right. Don't bring up these theoretical models if you don't understand them. We're not at stalemate you're just wrong.
NoCleverName
Time dilation is an outcome of special relativity. SR deals only with uniform, unaccelerated motion. Only in GR did Einstein come to grips with acceleration ... but it's true that the "twins paradox" glosses over the implied acceleration that must have occurred in order for there to be a velocity difference between the two. It appears that this acceleration is not critical for time dilation to work ... but the math is beyond me. biggrin.gif
mudderrunner
QUOTE (NoCleverName+Nov 30 2010, 08:55 PM)
Time dilation is an outcome of special relativity. SR deals only with uniform, unaccelerated motion. Only in GR did Einstein come to grips with acceleration ... but it's true that the "twins paradox" glosses over the implied acceleration that must have occurred in order for there to be a velocity difference between the two. It appears that this acceleration is not critical for time dilation to work ... but the math is beyond me. biggrin.gif

It's not an outcome of special relativity. It's an outcome of relative motion, which SR describes.

the acceleration in the twin paradox is what causes the twin from the space ship to be younger and never the other way around. It provides an absolute frame of reference with respect to time dilation. So it's certainly not "glossed over". It is integral to the outcome.

true, acceleration isn't required for time dilation. As I said before you can make the argument that acceleration (non-uniform motion) and uniform motion are both types of motion, and that time dilation is ultimately caused by motion. But this doesn't mean that my statement was incorrect. Acceleration does cause time dilation.

QUOTE (brucep+Nov 30 2010, 08:54 PM)
Look at the formulas and find out you're wrong. Good reason not to look for somebody uninterested in learning but only interested in being right. Don't bring up these theoretical models if you don't understand them. We're not at stalemate you're just wrong.

likewise about my verbal explanations. I raised significant points that you're neglecting.

Don't get cranky. It's just a stalemate. If I wanted to be right I wouldn't agree to disagree. You, on the other hand, are not.
Maxila
QUOTE (brucep+Nov 30 2010, 06:40 PM)
I'm not to sure why acceleration is being associated with different clock rates. If it's being thought of as the cause of different clock rates then that is wrong. It's relative velocity in SR and spacetime curvature in GR


Hi Bruce:

I tend to turn everything into a mental image, when muddrunner said the clock at the bottom of the mountain was "accelerating faster" I visualized it having more potential energy as Lunar had explained, not moving or accelerating.

What I find interesting is the potential energy is directional to the center of the gravity-well and time dilation for velocity is directional too.

Please point out if I seem to have interpreted anything else wrong. I want to be sure my base understanding is not flawed.
brucep
QUOTE (mudderrunner+Dec 1 2010, 02:05 AM)
It's not an outcome of special relativity. It's an outcome of relative motion, which SR describes.

the acceleration in the twin paradox is what causes the twin from the space ship to be younger and never the other way around. It provides an absolute frame of reference with respect to time dilation. So it's certainly not "glossed over". It is integral to the outcome.

true, acceleration isn't required for time dilation. As I said before you can make the argument that acceleration (non-uniform motion) and uniform motion are both types of motion, and that time dilation is ultimately caused by motion. But this doesn't mean that my statement was incorrect. Acceleration does cause time dilation.


likewise about my verbal explanations. I raised significant points that you're neglecting.

Don't get cranky. It's just a stalemate. If I wanted to be right I wouldn't agree to disagree. You, on the other hand, are not.

I could care less you don't understand the physics but that's no reason others should. The fact is you're wrong and it's not a matter of opinion. You're insisting that the cause of the time dilation is the acceleration. That's not what the science says regardless of what you believe. Enough said on my part.
Trout
QUOTE (mudderrunner+Dec 1 2010, 12:10 AM)

acceleration causes time dilation. You just have to understand the equivalence principle to know how to identify acceleration in curved space. And since acceleration is absolute it does not cause a reciprocal time dilation such as the case between two objects in uniform motion (SR).

No, the "Clock Hypothesis" (and the very precise tests this hypothesis was subjected to) show that your claim is wrong.

Now, the principle of equivalence applies in very small regions in GR whereas gravitational time dilation has been predicted and observed over huge distances (see Vessot's experiment, GPS, etc).
brucep
QUOTE (Maxila+Dec 1 2010, 03:02 AM)
Hi Bruce:

I tend to turn everything into a mental image, when muddrunner said the clock at the bottom of the mountain was "accelerating faster" I visualized it having more potential energy as Lunar had explained, not moving or accelerating.

What I find interesting is the potential energy is directional to the center of the gravity-well and time dilation for velocity is directional too.

Please point out if I seem to have interpreted anything else wrong. I want to be sure my base understanding is not flawed.

The only thing that makes him wrong is the insistence that the difference in clock rates is due to acceleration. He needs to do what I suggested for you and learn some dimensional analysis. If it was due to gravitational acceleration Newton would have discovered it

Newton

g = m/r^2

Einstein

g_shell = gamma(M/r^2)

Time dilation

dTau/dt = (1-v^2)^1/2

dTau/dt = (1-2M/r)^1/2

Gee

v^2 = 2M/r

relative velocity = curvature component of the metric.
mudderrunner
QUOTE (Maxila+Nov 30 2010, 10:02 PM)
Hi Bruce:

I tend to turn everything into a mental image, when muddrunner said the clock at the bottom of the mountain was "accelerating faster" I visualized it having more potential energy as Lunar had explained, not moving or accelerating.

What I find interesting is the potential energy is directional to the center of the gravity-well and time dilation for velocity is directional too.

Please point out if I seem to have interpreted anything else wrong. I want to be sure my base understanding is not flawed.

the clock on top of the mountain would have more potential energy, but this is a newtonian explanation, which says that gravity is a force. You will have a very difficult time understanding gravitational time dilation with a newtonian frame of mind because gravitational time dilation is a consequence of general relativity, which states that gravity is not a force.

Gravity does not have potential energy because it's not a force. It's just curved space.

if an asteroid were moving with a constant velocity (uniform motion, no force is being applied) towards the earth, as it gets closer it will start moving faster, but this is NOT acceleration. It is constant velocity in curved space. It seems to get faster because the warping of space is gradually increasing as the asteroid nears the earth. There is no force involved. The asteroid isn't gaining kinetic energy. How do we know that it's not accelerating? Because the asteroid is weightless. It is only when a force resists it's free fall (uniform motion) that the asteroid attains weight. It's the same thing that happens when an asteroid in flat space encounters a force, it attains weight. You can always tell when something is accelerating because it will have weight.

So in both cases a force is being applied to an object in uniform motion. This causes acceleration. The asteroid that is headed toward earth and encounters a force in the opposite direction is still plummeting toward earth but it is actually accelerating in the opposite direction. As the force gets stronger the asteroid slows it decent which means it is accelerating faster and faster in the opposite direction. It is curved space which makes it seem as though it is not. Finally the asteroid hits earth. The electromagnetic force of earth's surface is strong enough to stop the asteroid which actually means it applies a greater force which makes it accelerate more.

Another dynamic is that the curvature of space increases as the asteroid approaches earth. So it would take less force for a mountain top to accelerate the asteroid to the point of appearing to 'stop' then it would for the valley below. This is apparent by the larger energy of an impact in the valley relative to one at the mountain top (neglecting atmospheric friction). ...because the asteroid is going faster by the time it hits the valley (uniform motion in greater curved space) as opposed to when it reaches the mountain top (uniform motion in lessor curved space).




QUOTE (Trout+Nov 30 2010, 11:02 PM)
No, the "Clock Hypothesis" (and the very precise tests this hypothesis was subjected to) show that your claim is wrong.

Now, the principle of equivalence applies in very small regions in GR whereas gravitational time dilation has been predicted and observed over huge distances (see Vessot's experiment, GPS, etc).

I have complete understanding of that clock hypothesis and it does not show that my claim was wrong. The clock hypothesis basically points out that acceleration is a change in motion over a period of time. If you take away time then all you have is motion. This is like taking a cross section of a acceleration. And then they basically prove that ultimately, time dilation is caused by motion. It doesn't need change in motion over a period of time. If you think this contradicts me then you haven't been reading carefully. I've actually stated this exact same thing. Acceleration is basically a type of motion and motion is what causes time dilation (ask and I will gladly repost the ~2 statements of mine that concurred).

What the hypothesis also says, and what you've also failed to understand, is that acceleration does affect time dilation because it changes the state of motion. Time dilation is obviously different when an object is going fast then when an object is going slow. So when an object changes from fast to slow (or vice versa) then this changes time dilation.

QUOTE (clock hypothesis+)
So the clock postulate says that the rate of an accelerated clock doesn't depend on its acceleration.  But note: the clock postulate does not say that the rate of timing of a moving clock is unaffected by its acceleration.  The timing rate will certainly be affected if the acceleration changes the clock's speed of movement, because its speed determines how fast it counts out its time (i.e. by the factor γ).


think about it. If you accelerate away from a clock in space, time dilation will occur. I said time dilation causes acceleration. If acceleration didn't occur then neither would time dilation because you can't have relative motion in this case without acceleration.

in every other case, since acceleration is a type of motion, it's like saying wheat bread causes allergies when technically it is the gluten in the wheat bread. This doesn't mean that saying "wheat bread causes allergies" is incorrect. Likewise, acceleration causes time dilation.

...semantics.

QUOTE (brucep+Nov 30 2010, 10:50 PM)
I could care less you don't understand the physics but that's no reason others should. The fact is you're wrong and it's not a matter of opinion. You're insisting that the cause of the time dilation is the acceleration. That's not what the science says regardless of what you believe. Enough said on my part.

you're mad cause I wont look at your math. I'm apathetic since you wont look at my verbal explanation. You say I'm wrong, I say you're wrong. Again, stalemate. Stop having a hissy fit.

QUOTE (brucep+Nov 30 2010, 11:07 PM)
The only thing that makes him wrong is the insistence that the difference in clock rates is due to acceleration. He needs to do what I suggested for you and learn some dimensional analysis. If it was due to gravitational acceleration Newton would have discovered it

gravity doesn't cause things to acceleration.
Trout
QUOTE (mudderrunner+Dec 1 2010, 04:42 AM)


What the hypothesis also says, and what you've also failed to understand, is that acceleration does affect time dilation because it changes the state of motion. Time dilation is obviously different when an object is going fast then when an object is going slow. So when an object changes from fast to slow (or vice versa) then this changes time dilation.



What in "The clock hypothesis states that the tick rate of a clock when measured in an inertial frame depends only upon its velocity relative to that frame, and is independent of its acceleration or higher derivatives." didn't you understand?
mudderrunner
QUOTE (Trout+Dec 1 2010, 12:59 AM)
What in "The clock hypothesis states that the tick rate of a clock when measured in an inertial frame depends only upon its velocity relative to that frame, and is independent of its acceleration or higher derivatives." didn't you understand?

that makes perfect sense. I agree. It goes right along with what I said. Did you happen to click the link for a more in-depth description or did you read that one statement and assume you knew what it meant? Here is the link.

The key phrase is "inertial frame depends only upon its velocity relative to that frame" ... they are describing acceleration in terms of a single moment in time, which negates time and leaves just velocity because you can't have change in velocity without time.

Here is what you need to concentrate on when you read the more in-depth description:

QUOTE
So this says that an accelerating clock will count out its time in such a way that at any one moment, its timing has slowed by a factor (γ) that only depends on its current speed; its acceleration has no effect at all.


and my statements have been compatible to this.

QUOTE (->
QUOTE
So this says that an accelerating clock will count out its time in such a way that at any one moment, its timing has slowed by a factor (γ) that only depends on its current speed; its acceleration has no effect at all.


and my statements have been compatible to this.

I guess you can argue that acceleration is a different type of velocity and uniform motion is another type. So you can then argue that velocity is what ultimately causes time dilation. But that doesn't make my statement false. Acceleration does cause time dilation.


QUOTE (mudderrunner+)
true, acceleration isn't required for time dilation. As I said before you can make the argument that acceleration (non-uniform motion) and uniform motion are both types of motion, and that time dilation is ultimately caused by motion. But this doesn't mean that my statement was incorrect. Acceleration does cause time dilation.
brucep
QUOTE (mudderrunner+Dec 1 2010, 04:42 AM)
the clock on top of the mountain would have more potential energy, but this is a newtonian explanation, which says that gravity is a force. You will have a very difficult time understanding gravitational time dilation with a newtonian frame of mind because gravitational time dilation is a consequence of general relativity, which states that gravity is not a force.

Gravity does not have potential energy because it's not a force. It's just curved space.

if an asteroid were moving with a constant velocity (uniform motion, no force is being applied) towards the earth, as it gets closer it will start moving faster, but this is NOT acceleration. It is constant velocity in curved space. It seems to get faster because the warping of space is gradually increasing as the asteroid nears the earth. There is no force involved. The asteroid isn't gaining kinetic energy. How do we know that it's not accelerating? Because the asteroid is weightless. It is only when a force resists it's free fall (uniform motion) that the asteroid attains weight. It's the same thing that happens when an asteroid in flat space encounters a force, it attains weight. You can always tell when something is accelerating because it will have weight.

So in both cases a force is being applied to an object in uniform motion. This causes acceleration. The asteroid that is headed toward earth and encounters a force in the opposite direction is still plummeting toward earth but it is actually accelerating in the opposite direction. As the force gets stronger the asteroid slows it decent which means it is accelerating faster and faster in the opposite direction. It is curved space which makes it seem as though it is not. Finally the asteroid hits earth. The electromagnetic force of earth's surface is strong enough to stop the asteroid which actually means it applies a greater force which makes it accelerate more.

Another dynamic is that the curvature of space increases as the asteroid approaches earth. So it would take less force for a mountain top to accelerate the asteroid to the point of appearing to 'stop' then it would for the valley below. This is apparent by the larger energy of an impact in the valley relative to one at the mountain top (neglecting atmospheric friction). ...because the asteroid is going faster by the time it hits the valley (uniform motion in greater curved space) as opposed to when it reaches the mountain top (uniform motion in lessor curved space).





I have complete understanding of that clock hypothesis and it does not show that my claim was wrong. The clock hypothesis basically points out that acceleration is a change in motion over a period of time. If you take away time then all you have is motion. This is like taking a cross section of a acceleration. And then they basically prove that ultimately, time dilation is caused by motion. It doesn't need change in motion over a period of time. If you think this contradicts me then you haven't been reading carefully. I've actually stated this exact same thing. Acceleration is basically a type of motion and motion is what causes time dilation (ask and I will gladly repost the ~2 statements of mine that concurred).

What the hypothesis also says, and what you've also failed to understand, is that acceleration does affect time dilation because it changes the state of motion. Time dilation is obviously different when an object is going fast then when an object is going slow. So when an object changes from fast to slow (or vice versa) then this changes time dilation.


you're mad cause I wont look at your math. I'm apathetic since you wont look at my verbal explanation. You say I'm wrong, I say you're wrong. Again, stalemate. Stop having a hissy fit.


gravity doesn't cause things to acceleration.

Dummy. I looked at your verbal explanation and that's why I felt the need to correct your nonsense. Clearly a waste of my time. Remaining ignorant is a choice. There is no rebuttal for the clock hypothesis since it isn't a matter of individual opinion.
mudderrunner
QUOTE (brucep+Dec 1 2010, 01:35 AM)
Dummy. I looked at your verbal explanation and that's why I felt the need to correct your nonsense. Clearly a waste of my time. Remaining ignorant is a choice. There is no rebuttal for the clock hypothesis since it isn't a matter of individual opinion.

good thing I didn't post a rebuttal to the clock hypothesis, genius lol.
Trout
QUOTE (mudderrunner+Dec 1 2010, 06:34 AM)
that makes perfect sense. I agree. It goes right along with what I said.


But this is not what you said. This is why I corrected you. Here is what you REALLY said:

QUOTE
acceleration causes time dilation. You just have to understand the equivalence principle to know how to identify acceleration in curved space. And since acceleration is absolute it does not cause a reciprocal time dilation such as the case between two objects in uniform motion (SR).



QUOTE (->
QUOTE
acceleration causes time dilation. You just have to understand the equivalence principle to know how to identify acceleration in curved space. And since acceleration is absolute it does not cause a reciprocal time dilation such as the case between two objects in uniform motion (SR).



Did you happen to click the link for a more in-depth description or did you read that one statement and assume you knew what it meant? Here is the link.

The key phrase is "inertial frame depends only upon its velocity relative to that frame" ... they are describing acceleration in terms of a single moment in time, which negates time and leaves just velocity because you can't have change in velocity without time.

Here is what you need to concentrate on when you read the more in-depth description:



and my statements have been compatible to this.

QUOTE (mudderrunner+)
I guess you can argue that acceleration is a different type of velocity and uniform motion is another type. So you can then argue that velocity is what ultimately causes time dilation. But that doesn't make my statement false. Acceleration does cause time dilation.


QUOTE (mudderrunner+)
true, acceleration isn't required for time dilation. As I said before you can make the argument that acceleration (non-uniform motion) and uniform motion are both types of motion, and that time dilation is ultimately caused by motion. But this doesn't mean that my statement was incorrect. Acceleration does cause time dilation.

Yes, I know it very well, I wrote quite a bit of stuff on this subject. Time dilation does not depend of the acceleration but can be influenced by acceleration (especially in flat spacetime, in curved spacetime things are a lot more complicated, I have already posted the derivation starting from the Schwarzschild metric). Now, I would have bought your claim if :

-you phrased it correctly (you did not)

-you did not link it with the equivalence principle (I noticed that you glossed over my criticism of your fumble on the subject).
mudderrunner
QUOTE (Trout+Dec 1 2010, 02:16 AM)
But this is not what you said. This is why I corrected you. Here is what you REALLY said:





I have no idea what issue you have with what I've said. You're being vague. Do you want me to explain why the equivalence principle is important to identifying acceleration in curved space? I'll gladly explain. Just let me know.

QUOTE

Yes, I know it very well, I wrote quite a bit of stuff on this subject. Time dilation does not depend of the acceleration but can be influenced by acceleration (especially in flat spacetime, in curved spacetime things are a lot more complicated, I have already posted the derivation starting from the Schwarzschild metric). Now, I would have bought your claim if :

-you phrased it correctly (you did not)

-you did not link it with the equivalence principle (I noticed that you glossed over my criticism of your fumble on the subject).


It is phrased correctly. The problem is that you're extracting a meaning that was never intended. Acceleration does cause time dilation. It's true. I didn't say that acceleration is the only cause or that velocity/uniform motion don't cause time dilation. That would be completely false not to mention completely ignorant of SR. Stop reading into things.

Everything I say is with consideration of the equivalence principle. It would be difficult to talk about general relativity otherwise. What exactly do you need me to link to the EP? Tell me and I'll gladly make it explicit.
mudderrunner
Trout, take another look at that quote that you're confused about.

QUOTE (mudderrunner+)
acceleration causes time dilation. You just have to understand the equivalence principle to know how to identify acceleration in curved space. And since acceleration is absolute it does not cause a reciprocal time dilation such as the case between two objects in uniform motion (SR).


you realize that the third sentence is saying that time dilation occurs between two objects in uniform motion, right? This implies that constant velocity is also a cause of time dilation. Not just acceleration. I'm pointing this out because you bolded the first two sentences. Isolating them makes it seem like I'm saying that acceleration is the sole cause of time dilation. And that is obviously just being taken out of context.
Trout
QUOTE (mudderrunner+Dec 1 2010, 07:49 AM)
I have no idea what issue you have with what I've said. You're being vague.





I am not vague, I bolded the text I am having issue with. You claimed several times that acceleration causes time dilation.

QUOTE
Do you want me to explain why the equivalence principle is important to identifying acceleration in curved space? I'll gladly explain. Just let me know.


No, spare me. You clearly did not understand my contention.

QUOTE (->
QUOTE
Do you want me to explain why the equivalence principle is important to identifying acceleration in curved space? I'll gladly explain. Just let me know.


No, spare me. You clearly did not understand my contention.

IAcceleration does cause time dilation. It's true.


See?

QUOTE
Everything I say is with consideration of the equivalence principle. It would be difficult to talk about general relativity otherwise. What exactly do you need me to link to the EP? Tell me and I'll gladly make it explicit.


I explained to yo that the EP does not apply for large domains. The gravitational time dilation has been observed for VERY large domains. So, you cannot invoke it in order to explain how "acceleration causes time dilation". I had misgivings giving you the neg but now I feel that it was fully warranted.
mudderrunner
QUOTE (Trout+Dec 1 2010, 09:40 AM)
I am not vague, I bolded the text I am having issue with. You claimed several times that acceleration causes time dilation.



No, spare me. You clearly did not understand my contention.



See?

Why haven't you responded to my defense that acceleration causes time dilation? You clearly just avoided this entire explanation. So until you respond to it then I have no reason to defend myself again.

QUOTE (mudderrunner+)
think about it. If you accelerate away from a clock in space, time dilation will occur. I said time dilation causes acceleration. If acceleration didn't occur then neither would time dilation because you can't have relative motion in this case without acceleration.

in every other case, since acceleration is a type of motion, it's like saying wheat bread causes allergies when technically it is the gluten in the wheat bread. This doesn't mean that saying "wheat bread causes allergies" is incorrect. Likewise, acceleration causes time dilation.


QUOTE
I explained to yo that the EP does not apply for large domains. The gravitational time dilation has been observed for VERY large domains. So, you cannot invoke it in order to explain how "acceleration causes time dilation". I had misgivings giving you the neg but now I feel that it was fully warranted.


given that acceleration does cause time dilation (see above), the only thing I said was that the EP helps to identify acceleration in curved space. Which it does.

so again, you seem to be reading into things.

how do you feel about that neg now? Not that I care. I gave you a pos just because.
Trout
QUOTE (mudderrunner+Dec 1 2010, 03:44 PM)
Why haven't you responded to my defense that acceleration causes time dilation? You clearly just avoided this entire explanation. So until you respond to it then I have no reason to defend myself again.



given that acceleration does cause time dilation (see above), the only thing I said was that the EP helps to identify acceleration in curved space. Which it does.

so again, you seem to be reading into things.

how do you feel about that neg now? Not that I care. I gave you a pos just because.

I feel that you have done everything to deserve the neg.
mudderrunner
QUOTE (Trout+Dec 1 2010, 10:47 AM)
I feel that you have done everything to deserve the neg.

since you ignored half of what I said (case-in-point) and misunderstood the rest I can understand how you'd think so.

If anything came out of this it is that I helped you understand the clock hypothesis.

take care.
boit
If I understand you guys correctly, acceleration is absolute only if you take the frame into consideration. Meaning if we are inside a lift (elevator) that accidentaly snapped its cable and went into free fall, I'll not notice that anyone of you, the unfortunate occupants of that lift, accelerating. If someone shoots down a bungee cable and i make a grab for it, i'll experience a force upwards and hence will be accelerating up. I'll experience weight. Ultimately it is not you guy going don at approx. Ten meters per second every second but its me going up at negative ten meters per second squared. Have i got it finaly?
brucep
QUOTE (Trout+Dec 1 2010, 03:47 PM)
I feel that you have done everything to deserve the neg.

Obstinate = uneducable = muddledrunner. The physics is clear and easy to understand.
mudderrunner
QUOTE (boit+Dec 1 2010, 11:11 AM)
If I understand you guys correctly, acceleration is absolute only if you take the frame into consideration. Meaning if we are inside a lift (elevator) that accidentaly snapped its cable and went into free fall, I'll not notice that anyone of you, the unfortunate occupants of that lift, accelerating. If someone shoots down a bungee cable and i make a grab for it, i'll experience a force upwards and hence will be accelerating up. I'll experience weight. Ultimately it is not you guy going don at approx. Ten meters per second every second but its me going up at negative ten meters per second squared. Have i got it finaly?

yes, I think so. And as per the equivalence principle, the equivalent situation would be you in a ship in flat space accelerated by rockets at 10m/s/s. You will have the same weight, the same feeling of acceleration. They are the same situation.
brucep
QUOTE (mudderrunner+Dec 1 2010, 04:01 PM)
since you ignored half of what I said (case-in-point) and misunderstood the rest I can understand how you'd think so.

If anything came out of this it is that I helped you understand the clock hypothesis.

take care.

That conclusion is ignorant. Dream on Muddledrunner. laugh.gif
mudderrunner
QUOTE (brucep+Dec 1 2010, 11:17 AM)
Obstinate = uneducable = muddledrunner.

I see you've stumbled upon the lessor known, unequivalence principle.

tongue.gif
brucep
QUOTE (mudderrunner+Dec 1 2010, 04:22 PM)
I see you've stumbled upon the lessor known, unequivalence principle.

tongue.gif

It would do you some good to actually look at the physics instead of making a bad conclusion based on what you think. You're not stupid just obstinate. But if you continue you'll be orbiting the dunce stool.
mudderrunner
QUOTE (brucep+Dec 1 2010, 11:27 AM)
It would do you some good to actually look at the physics instead of making a bad conclusion based on what you think. You're not stupid just obstinate. But if you continue you'll be orbiting the dunce stool.

sore stalemater.
boit
QUOTE (mudderrunner+Dec 1 2010, 07:20 PM)
yes, I think so. And as per the equivalence principle, the equivalent situation would be you in a ship in flat space accelerated by rockets at 10m/s/s. You will have the same weight, the same feeling of acceleration. They are the same situation.

Thanks. Now I can enjoy reading on. I hate to be left far behind. I may need help with the maths though, I haven't attempted them yet. smile.gif
Ed Wood
I see the argument for speed vs. acceleration and thought I would jump in.

Acceleration and relative acceleration are the same thing 'sort of'

Acceleration happens when an object changes its velocity.

Relative acceleration is unrealized acceleration between 2 or more objects/ reference frames or the the potential for acceleration to occur this potential is for lack of a better term stored in time.

There could be an argument that relative acceleration is a difference in distance in the dimension of time. I am not prepared to make that argument yet but I think it is makeable.
brucep
QUOTE (mudderrunner+Dec 1 2010, 04:31 PM)
sore stalemater.

The physic is clear and your personal trial and error methods of explaining time dilation have been wrong. You can't understand the derivations so you ask Trout and I to muddle through your attempts to hide the error. The science is clear but you don't understand it so you claim a stalemate which would require Trout and I to justify your ignorance and boneheaded obstinate disregard for the scientific literature. Your need to be right is disrespectful to the scientific literature just like so many dorks posting in this forum. The fact that you claimed an epiphany proofs you hadn't researched this subject before and you still are lost in the woods now.
mudderrunner
QUOTE (brucep+Dec 1 2010, 01:51 PM)
The physic is clear and your personal trial and error methods of explaining time dilation have been wrong. You can't understand the derivations so you ask Trout and I to muddle through your attempts to hide the error. The science is clear but you don't understand it so you claim a stalemate which would require Trout and I to justify your ignorance and boneheaded obstinate disregard for the scientific literature. Your need to be right is disrespectful to the scientific literature just like so many dorks posting in this forum. The fact that you claimed an epiphany proofs you hadn't researched this subject before and you still are lost in the woods now.

I didn't claim an epiphany. That was Maxila.

Nor did I post a rebuttal to the clock hypothesis like you said before. You're all mixed up.
Maxila
Hi Mudderrunner:

I've followed this thread since my last post, I have re-read some of the posts a few times, and I've read the links in the posts.

You have helped me in my understanding, I have also found some of your comments a bit confusing.

It may have been my error of interpretation; however I did get the impression you were stating acceleration caused time dilation, which was not, and is not my understanding. The link you posted reaffirmed my understanding in that acceleration effects time dilation but was not the cause. If I may use your analogy:


(Quote) Mudderrunner
QUOTE
in every other case, since acceleration is a type of motion, it's like saying wheat bread causes allergies when technically it is the gluten in the wheat bread. This doesn't mean that saying "wheat bread causes allergies" is incorrect. Likewise, acceleration causes time dilation.


It's logical that acceleration or deceleration has to be part of any change in velocity, it is the "wheat bread"; however the "gluten" is relative velocity which determines time dilation as I still understand it.

I also found part of the following paragraph to be inconsistent with what "I think" I know.

(Quote) Mudderrunner
QUOTE (->
QUOTE
in every other case, since acceleration is a type of motion, it's like saying wheat bread causes allergies when technically it is the gluten in the wheat bread. This doesn't mean that saying "wheat bread causes allergies" is incorrect. Likewise, acceleration causes time dilation.


It's logical that acceleration or deceleration has to be part of any change in velocity, it is the "wheat bread"; however the "gluten" is relative velocity which determines time dilation as I still understand it.

I also found part of the following paragraph to be inconsistent with what "I think" I know.

(Quote) Mudderrunner
I have complete understanding of that clock hypothesis and it does not show that my claim was wrong. The clock hypothesis basically points out that acceleration is a change in motion over a period of time.{ If you take away time then all you have is motion. This is like taking a cross section of a acceleration. And then they basically prove that ultimately, time dilation is caused by motion. It doesn't need change in motion over a period of time. If you think this contradicts me then you haven't been reading carefully. I've actually stated this exact same thing. Acceleration is basically a type of motion and motion is what causes time dilation (ask and I will gladly repost the ~2 statements of mine that concurred).


I posted the whole paragraph so as the highlighted part in bold could be read in context. As I understand it "motion" is a change of position over time. If you take away time you can't have motion. As far as I can see motion is what effects time and acceleration is an effect of a change in motion.

(Quote) Mudderrunner
QUOTE
“the clock on top of the mountain would have more potential energy, but this is a newtonian explanation, which says that gravity is a force. You will have a very difficult time understanding gravitational time dilation with a newtonian frame of mind because gravitational time dilation is a consequence of general relativity, which states that gravity is not a force.”


Here you responded to my thought about potential energy being greater as you go deeper in a gravity well. This is based on my understanding of Lunarlandings posts which I hope i got right. I want to clarify the explanation of my thought and feel free to provide any insights you see fit.

The connection I made between velocity and gravity regarding time dilation was on the surface of the Earth I have weight, potential energy and motion in a directional vector to the center of the gravity well. I am not certain but I thought at the top of a mountain my weight would be slightly less, so when motionless at that point I had less potential energy to the gravity well. In either case if I were able to fall , free of resistence towards the gravity well, my weight would be converted, via acceleration to velocity.

The connection I made was weight is potential energy (velocity) towards the center of a gravity well and motion is potential energy via directional velocity. They are two forms of directional potential energy.

If got that wrong I hope others can explain where I erred?

Maxila

P.S. I have no intention of insulting or you. I am only trying to point out the difficulties I am having with some of your comments so perhaps you may address them.
brucep
QUOTE (mudderrunner+Dec 1 2010, 07:14 PM)
I didn't claim an epiphany. That was Maxila.

Nor did I post a rebuttal to the clock hypothesis like you said before. You're all mixed up.

I'm mixed up? laugh.gif laugh.gif It's to bad you can't read the simple formulas I wrote down to help you understand. It wasn't like you had to follow a complete derivation. I didn't write it down because I figured you couldn't. But I did expect you to be able to read what I did write down. Seemed like you had a general idea what is going on other than to insist acceleration is the cause of time dilation. Oh well maybe you'll get it at a later date when the need to be right subsides and allows you to review the subject in a reasonable way.
brucep
QUOTE (Maxila+Dec 1 2010, 07:36 PM)
Hi Mudderrunner:

I've followed this thread since my last post, I have re-read some of the posts a few times, and I've read the links in the posts.

You have helped me in my understanding, I have also found some of your comments a bit confusing.

It may have been my error of interpretation; however I did get the impression you were stating acceleration caused time dilation, which was not, and is not my understanding. The link you posted reaffirmed my understanding in that acceleration effects time dilation but was not the cause. If I may use your analogy:


(Quote) Mudderrunner


It's logical that acceleration or deceleration has to be part of any change in velocity, it is the "wheat bread"; however the "gluten" is relative velocity which determines time dilation as I still understand it.

I also found part of the following paragraph to be inconsistent with what "I think" I know.

(Quote) Mudderrunner


I posted the whole paragraph so as the highlighted part in bold could be read in context. As I understand it "motion" is a change of position over time. If you take away time you can't have motion. As far as I can see motion is what effects time and acceleration is an effect of a change in motion.

(Quote) Mudderrunner


Here you responded to my thought about potential energy being greater as you go deeper in a gravity well. This is based on my understanding of Lunarlandings posts which I hope i got right. I want to clarify the explanation of my thought and feel free to provide any insights you see fit.

The connection I made between velocity and gravity regarding time dilation was on the surface of the Earth I have weight, potential energy and motion in a directional vector to the center of the gravity well. I am not certain but I thought at the top of a mountain my weight would be slightly less, so when motionless at that point I had less potential energy to the gravity well. In either case if I were able to fall , free of resistence towards the gravity well, my weight would be converted, via acceleration to velocity.

The connection I made was weight is potential energy (velocity) towards the center of a gravity well and motion is potential energy via directional velocity. They are two forms of directional potential energy.

If got that wrong I hope others can explain where I erred?

Maxila

P.S. I have no intention of insulting or you. I am only trying to point out the difficulties I am having with some of your comments so perhaps you may address them.

It's a good idea to study the classical non-relativistic theories but not when you're trying to understand relativistic phenomena. Potential energy isn't very well defined in GR [at least at the level I've studied which is an undergraduate introduction developed by Edwin Taylor and John Wheeler]. Basically time dilation is a consequence of spactime geometry in GR and SR [the special case for a more general gravitational theory where the effect of gravity can be ignored]. I always like saying that. Interesting how the special case came first. The cart before the horse but historically it needed to happen that way. Science, and especially physics, is great stuff.
mudderrunner
QUOTE (Maxila+Dec 1 2010, 02:36 PM)
Hi Mudderrunner:

I've followed this thread since my last post, I have re-read some of the posts a few times, and I've read the links in the posts.

You have helped me in my understanding, I have also found some of your comments a bit confusing.

It may have been my error of interpretation; however I did get the impression you were stating acceleration caused time dilation, which was not, and is not my understanding. The link you posted reaffirmed my understanding in that acceleration effects time dilation but was not the cause. If I may use your analogy:


(Quote) Mudderrunner


It's logical that acceleration or deceleration has to be part of any change in velocity, it is the "wheat bread"; however the "gluten" is relative velocity which determines time dilation as I still understand it.

It wasn't your impression. It's true. I did state that acceleration causes time dilation. And it seems you've figured out why I said that. Simply put, motion is the cause of time dilation and acceleration is made of motion. So just like wheat bread causes allergies, acceleration causes time dilation.

and also, like I said before, in the situation where there are two clocks in the same frame of reference, there can be no time dilation between them without acceleration to cause a different frame of reference between them. So in this sense acceleration is absolutely required for time dilation to occur.

QUOTE
I also found part of the following paragraph to be inconsistent with what "I think" I know.

(Quote) Mudderrunner


I posted the whole paragraph so as the highlighted part in bold could be read in context. As I understand it "motion" is a change of position over time. If you take away time you can't have motion. As far as I can see motion is what effects time and acceleration is an effect of a change in motion.


That's a great point. That quote of mine is not clear. Let me post an excerpt from the clock hypothesis reference (linky), and then I'll explain it in my own way and see of it doesn't help.

QUOTE (->
QUOTE
I also found part of the following paragraph to be inconsistent with what "I think" I know.

(Quote) Mudderrunner


I posted the whole paragraph so as the highlighted part in bold could be read in context. As I understand it "motion" is a change of position over time. If you take away time you can't have motion. As far as I can see motion is what effects time and acceleration is an effect of a change in motion.


That's a great point. That quote of mine is not clear. Let me post an excerpt from the clock hypothesis reference (linky), and then I'll explain it in my own way and see of it doesn't help.

It's just a postulate!  This is just like the fact that even though a 1000-sided polygon looks pretty much like a circle, a small piece of a circle can't always be treated as an infinitesimal straight line: after all, no matter how small the circular arc is, it will always have the same radius of curvature, whereas a straight line has an infinite radius of curvature.


and actually the whole paragraph that this came from might be good to read too.

My explanation: If you stop all forces acting on an accelerating object, it will suddenly have a constant velocity. That velocity is what existed during that moment of acceleration. Stopping the force is sort of like doing an autopsy on a part of a stretch of acceleration to find out what's inside. This implies that each moment of acceleration is composed of a velocity. And so that 'velocity moment' can be used to calculate time dilation. Using another 'velocity moment' of the same accelerating object will result in a different time dilation because the velocity will be different.

QUOTE
(Quote) Mudderrunner


Here you responded to my thought about potential energy being greater as you go deeper in a gravity well. This is based on my understanding of Lunarlandings posts which I hope i got right. I want to clarify the explanation of my thought and feel free to provide any insights you see fit.

The connection I made between velocity and gravity regarding time dilation was on the surface of the Earth I have weight, potential energy and motion in a directional vector to the center of the gravity well. I am not certain but I thought at the top of a mountain my weight would be slightly less, so when motionless at that point I had less potential energy to the gravity well. In either case if I were able to fall , free of resistence towards the gravity well, my weight would be converted, via acceleration to velocity.

The connection I made was weight is potential energy (velocity) towards the center of a gravity well and motion is potential energy via directional velocity. They are two forms of directional potential energy.

If got that wrong I hope others can explain where I erred?

Maxila


You're correct that the higher you are (further away from the source of gravity) the less you weigh. But Imagine holding a heavy object 2 feet off the ground and dropping it. Now compare that with dropping the same object off a tall building. The higher the object is held, the more potential it has for a greater release of energy.

This is how gravity works in newtonian physics. But it's not how it works in general relativity. In GR a stationary object is actually accelerating and an accelerating object in free fall is actually in uniform motion. So kinetic and potential energy get jumbled up. You wouldn't say that an accelerating object has zero kinetic energy, yet that's what is done with newtonian physics in a gravity field.

QUOTE (->
QUOTE
(Quote) Mudderrunner


Here you responded to my thought about potential energy being greater as you go deeper in a gravity well. This is based on my understanding of Lunarlandings posts which I hope i got right. I want to clarify the explanation of my thought and feel free to provide any insights you see fit.

The connection I made between velocity and gravity regarding time dilation was on the surface of the Earth I have weight, potential energy and motion in a directional vector to the center of the gravity well. I am not certain but I thought at the top of a mountain my weight would be slightly less, so when motionless at that point I had less potential energy to the gravity well. In either case if I were able to fall , free of resistence towards the gravity well, my weight would be converted, via acceleration to velocity.

The connection I made was weight is potential energy (velocity) towards the center of a gravity well and motion is potential energy via directional velocity. They are two forms of directional potential energy.

If got that wrong I hope others can explain where I erred?

Maxila


You're correct that the higher you are (further away from the source of gravity) the less you weigh. But Imagine holding a heavy object 2 feet off the ground and dropping it. Now compare that with dropping the same object off a tall building. The higher the object is held, the more potential it has for a greater release of energy.

This is how gravity works in newtonian physics. But it's not how it works in general relativity. In GR a stationary object is actually accelerating and an accelerating object in free fall is actually in uniform motion. So kinetic and potential energy get jumbled up. You wouldn't say that an accelerating object has zero kinetic energy, yet that's what is done with newtonian physics in a gravity field.

P.S. I have no intention of insulting or you. I am only trying to point out the difficulties I am having with some of your comments so perhaps you may address them.


no need to worry.

QUOTE (brucep+Dec 1 2010, 03:20 PM)
I'm mixed up? laugh.gif  laugh.gif It's to bad you can't read the simple formulas I wrote down to help you understand. It wasn't like you had to follow a complete derivation. I didn't write it down because I figured you couldn't. But I did expect you to be able to read what I did write down. Seemed like you had a general idea what is going on other than to insist acceleration is the cause of time dilation. Oh well maybe you'll get it at a later date when the need to be right subsides and allows you to review the subject in a reasonable way.

I never said, "acceleration is the cause of time dilation". I said it causes time dilation.

nor was I the one that claimed an epiphany.

nor did I post a rebuttal to the clock hypothesis.

nor do I like green eggs and ham... this is starting to sound like verse out of a dr seuss book.
brucep
QUOTE (mudderrunner+Dec 1 2010, 12:10 AM)
acceleration is what GR is all about. And gravity, while it doesn't cause acceleration, obfuscates what acceleration is. So GR is also a theory of gravity by default.

acceleration causes time dilation. You just have to understand the equivalence principle to know how to identify acceleration in curved space. And since acceleration is absolute it does not cause a reciprocal time dilation such as the case between two objects in uniform motion (SR).

You said it a bunch of times. Along with a bunch of other nonsense. The above is especially a stupid post. You need to quit lying and pay attention to what Trout and I've written done. You lie again and I'm going to suggest you take a little vacation from spewing nonsense.
mudderrunner
QUOTE (brucep+Dec 1 2010, 05:23 PM)
You said it a bunch of times. Along with a bunch of other nonsense. The above is especially a stupid post. You need to quit lying and pay attention to what Trout and I've written done. You lie again and I'm going to suggest you take a little vacation from spewing nonsense.

you obviously don't understand the difference between

"acceleration is the cause of time dilation" (did not say)

and

"acceleration causes time dilation" (did say)

maybe you're too busy trying to think of ways to insult me.
NoCleverName
QUOTE (mudderrunner+Dec 1 2010, 06:31 PM)
maybe you're too busy trying to think of ways to insult me.

Maybe you shouldn't try to school people who have the odd graduate degree in the subject at hand.

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