SR and the earth, sun, and galaxy.

In summary: The first paragraph is explaining what inertia is and how it affects an object. The second paragraph is explaining how time is measured on Earth. The third paragraph is asking if different reference frames can affect the calculation of the age of something. The fourth paragraph is asking if the age of something can be calculated using different reference frames. The fifth paragraph is explaining that if the galaxies, our sun, the earth, etc, are moving at speeds which are large enough of fractions of c, then the age differences between them can be calculated.
  • #1
aychamo
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First of all let me say Hello! as this is my first post. I am a biologist, and have been reading over the very basics of SR for a little while and have a lot of questions on the implications of the theory.

I had been asking my questions primarily at a different forum, one that wasn't directed towards physics so I figured this would be a better place for me to ask my questions and hopefully receive responses that I can comprehend.

This was my last post at the forum, with a lot of the questions I had. We had previously been discussing an example of I was on an airplane traveling at 300mph, and then we talked about if I was on an airplane traveling .865c.

In the first paragraph, if it is not clear, I am wanting to understand what exactly is meant by an "inertial reference frame."

--

Hmm. I think the key to me understanding this is realizing what an "inertial reference frame" is. I know inertia, in the most basic sense, is an objects resistance to movement. So is the inertial reference frame the observer that isn't moving? I mean, the one that isn't traveling at speeds a fraction of c? The one on earth.

I realize the person on Earth is the inertial reference frame, but in the advanced calculations, since the Earth is rotating around the sun, it is undergoing constant acceleration. Is this ever a factor?

In addition to the above paragraph, could this be what makes us "realize" time as we do? Obviously, a second is a unit of time that we arbitrarily invented, and now it "is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. (some website from Google)".

But with us rotating around the sun, it seems the sun would be the inertial reference frame (ignoring the wobble from planets) and that we on Earth would be undergoing (I guess) constant acceleration. The speed of the Earth around the sun is very fast, I'm sure. I'm sure over 30,000 mph. I don't have the data to do the division to see what factor of c that is, but I'm sure it's a decent factor (I'm sure less than .05c though), but much greater than the example of the airplane.

Using what I've learned from you guys here and probably poor logic of my own, I would say the entire earth, and presumably everything on it has aged less than the sun (I know the sun existed before earth). Since the Earth (and everything on it) is undergoing the constant acceleration, and the sun, relative to us, is static, the Earth would have aged slower than the sun. Would this be a factor in calculating the age of the sun? Or is the age of the sun calculated by other means (fuel left in it)?

But if any of the above has merit, then wouldn't we have to take it back a step further and look at the Earth revolving around the sun, which is moving around in our galaxy? And even further, assuming a singularity-type-entity that the big bang came from, our entire galaxy is moving away from the point of the big bang at probably a very fast speed, so we'd age less than the point from which we all came from. Which I guess makes sense, that would make us younger than the universe's existence?

If the Milky Way ages less than the singularity from which we came from, and, uh oh, my mind is locking up I can't see the answer here, but, oh wait no that's wrong. If it were the opposite, that would mean we've been around longer than the universe existed. Hmm. Wait, this last part about our galaxy and the singularity-type-entity we came from really isn't an issue because the singularity exploded, (I'm frowning now), and doesn't exist anymore for us to use as an inertial reference frame.

But as I asked above with more complicated calculations with Einstein's SR, since all the galaxies in the universe are moving away from a central point (or each other? but couldn't you have two moving in somewhat parallel?) could the age differences be calculated using different reference frames?

I'm sure they (you guys, the physicists who know this stuff) have methods for calculating the ages of galaxies, etc. Or for knowing that something is x light years away. I guess my question is if SR theory is used in addition to conventional methods, like to check for differences in ages. I guess this is also all hinged on whether or not the galaxies, our sun, the earth, etc, is moving at speeds which are large enough of a fraction of c to make a difference when calculating ages. It seems to me that even if it's a small part of c, in a time frame of 11 billion years, that it could have an effect. Even my original question/example with a 300 mph airplane would show differences over 11 billion years (although everyone would die from the airplane's disgusting food -- my apologies if anyone is an airplane food chef!)

This is amazing stuff. Really, congratulations to you guys for devoting so much time to studying and understanding this stuff.

Thank you anyone in advance for reading this, and for any reply you may give me. I am enjoying learning the basics of this subject. I know the time you put in a reply may seem to be worthless, but the knowledge that I and others gain is priceless.

--Aychamo

NOTE: I found a figure that says the Earth moves about 66,000 mile per hour around the sun. That is 66,000 mi/hr / 60 min/hr / 60 sec/min = 18.33 miles per second. The speed of light is 186,000 miles/second. So the 18.33 (repeating) / 186,000 means the Earth is moving at 9.85 * 10^-5c. Pretty insignificant, but still 220 times more significant than an airplane moving at 300 mph. I don't know the math, but over 4.5 billion years that is bound to have some effect. I cannot find figures for the sun's speed in revolving about in the Milky Way (I actually don't like the candy bar).
 
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  • #2
Originally posted by aychamo
...I know inertia, in the most basic sense, is an objects resistance to movement.

Actually inertia in terms of mass is resistence to "change in" motion. The Newtonian concept of inertia is that things unacted on by ordinary forces remain in constant motion states. In relativity it is that things unacted on by real forces, i.e. four-vector forces, remain in geodesic motion states.

So is the inertial reference frame the observer that isn't moving?

It isn't accelerating.

I mean, the one that isn't traveling at speeds a fraction of c? The one on earth.

The velocity one observer has with respect to another has nothing to do with whether either of them are in inertial states of motion. As long as their velocities are constants and one can neglect gravitation then both of their frames are inertial.

I realize the person on Earth is the inertial reference frame, but in the advanced calculations, since the Earth is rotating around the sun, it is undergoing constant acceleration. Is this ever a factor?

If your worried about precision to nanoseconds in typical calculations then yes, but in the 0.865c scenarios one usually neglects such small effects.

I don't have the data to do the division to see what factor of c that is, but I'm sure it's a decent factor (I'm sure less than .05c though), but much greater than the example of the airplane.

The airplane clocks weren't compared to a clock held stationary with respect to the sun, but either way the speed of the Earth with respect to the sun is [tex]9.9x10^{-5}c[/tex], and [tex]\gamma[/tex] is 1.000004.

Using what I've learned from you guys here and probably poor logic of my own, I would say the entire earth, and presumably everything on it has aged less than the sun (I know the sun existed before earth).

Actually compared to the SR time dilation of the Earth the sun's own gravitational time dilation of its own matter is significant.

But if any of the above has merit, then wouldn't we have to take it back a step further and look at the Earth revolving around the sun, which is moving around in our galaxy?

These are still small effects.

And even further, assuming a singularity-type-entity that the big bang came from, our entire galaxy is moving away from the point of the big bang at probably a very fast speed, so we'd age less than the point from which we all came from.

The big bang isn't motion of matter away from a center point within our universe. It is an expansion of space itself. There is no one single point within our universe that can be said to be the center of the explosion. The dynamics you want to consider here are general relativistic, not special at all. For example, instead of inertial frames, commoving frames are of interest.

could the age differences be calculated using different reference frames?

The age of the universe refers to the time elapsed for a commoving frame since big bang.

I guess my question is if SR theory is used in addition to conventional methods, like to check for differences in ages.

When it is significant.

The speed of light is 186,000 miles/second. So the 18.33 (repeating) / 186,000 means the Earth is moving at 9.85 * 10^-5c. Pretty insignificant, but still 220 times more significant than an airplane moving at 300 mph.

But a comparison wasn't being made to a clock held stationary with respect to the sun.
 
  • #3


Originally posted by DW

The age of the universe refers to the time elapsed for a commoving frame since big bang.

I agree, but lately I've wondered if it isn't impossible to define precisely. Comoving frames differ depending on how low or high they are in gravitational potential. I used to imagine there was a universal time (since the bang) that all comoving observers could agree on, now it seems there would at best be only a rough approximate agreement. Or?

Originally posted by DW

The big bang isn't motion of matter away from a center point within our universe. It is an expansion of space itself. There is no one single point within our universe that can be said to be the center of the explosion.

Again I agree, or have gathered the same impression from reading what cosmologists have to say.
The conventional scientific view is that we didnt all come from a point anywhere. The presumed spatial flatness implies that the initial singularity was infinite in spatial extent. So space was already infinite in all directions when it began expanding.

the alternative view, of a finite closed universe begun at a point, has become a minority view---has become marginalized in the past 5 years or so. Maybe some time it will come back in fashion---Ned Wright had something to say about this at his website last time I looked, some tentative evidence of small positive curvature. But the majority view seems to simply be "flat or flat enough for government work". Which means an spatially infinite beginning. Do you have the same impression?
------------------------------
"Actually compared to the SR time dilation of the Earth the sun's own gravitational time dilation of its own matter is significant."

that reminds me, apparently there are or were two time standards: one an imaginary clock at the center of the Earth and another at the center of the sun-----no clock on the surface of the Earth keeps standard time. Something about rotation. Also the atomic clocks in GPS satellites do not keep surface time but speed up and slow down along the satellites elliptical orbits as their altitudes change (among other things) so their time signals must be corrected using General Relativity (among other considerations). Strange thought, or strange to me anyway.
 
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  • #4
Marcus: I agree, but lately I've wondered if it isn't impossible to define precisely. Comoving frames differ depending on how low or high they are in gravitational potential. I used to imagine there was a universal time (since the bang) that all comoving observers could agree on, now it seems there would at best be only a rough approximate agreement. Or?

I've always wondered whether the CMBR could be used as a frame of reference for all observers. As the Universe expands with time, the temperature of the CMBR decreases. I suppose that wouldn't be a very practical measure of time as the CMBR wouldn't change significantly over our lifetimes. But it's just a thought. Also, our motion wrt the CMBR has been measured to be around 370 km/s. Can the CMBR be used as an absolute frame of reference with regard to motion?
 
  • #5
Originally posted by Jimmy
I've always wondered whether the CMBR could be used as a frame of reference for all observers. As the Universe expands with time, the temperature of the CMBR decreases. I suppose that wouldn't be a very practical measure of time as the CMBR wouldn't change significantly over our lifetimes. But it's just a thought. Also, our motion wrt the CMBR has been measured to be around 370 km/s. Can the CMBR be used as an absolute frame of reference with regard to motion?

Originally posted by Jimmy


Can the CMBR be used as an absolute frame of reference with regard to motion?




Quantum Mechanics will always be within a reduced Dimensional field .
 
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  • #6


Originally posted by marcus
I agree, but lately I've wondered if it isn't impossible to define precisely. Comoving frames differ depending on how low or high they are in gravitational potential. I used to imagine there was a universal time (since the bang) that all comoving observers could agree on, now it seems there would at best be only a rough approximate agreement. Or?

All comoving frame observers in a Robertson-Walker universe agree on this time. They are not at different "gravitational potentials".

Ned Wright had something to say about this at his website last time I looked, some tentative evidence of small positive curvature. But the majority view seems to simply be "flat or flat enough for government work". Which means an spatially infinite beginning. Do you have the same impression?

I believe it will be found to be closed curved. Right now there isn't a great weight of evidence for which side of asymtoticaly flat it actually is.
 
  • #7


Originally posted by DW
All comoving frame observers in a Robertson-Walker universe agree on this time. They are not at different "gravitational potentials".
...

I realize that about a Robertson-Walker universe
but that is where matter is spread out uniformly.
And the moment you have galaxies in the universe it is no longer
exactly R-W.

So a comoving clock somewhere deep in Andromeda's potential-well
will be ticking more slowly than a comoving clock halfway between us and Andromeda.

which will be ticking more slowly than a comoving clock completely out of the Local Group altogether, not near any cluster

once I raised this issue with a gravity expert (i.e. a relativist or GR person) and whether you could slice spacetime cleverly into a foliation that would define a universal time, and he gave me some arguments that you could not-----and that, if I understand what he said, the R-W universal time is just a rough approximation to an ideal which does not exist

it is still a beautiful idea to be at rest with respect to the Hubble flow or, in other words, with respect to the CM Background. and that all those observers at rest wrt Background could agree down on the atomic clock age of the universe, down to the tick.
 
  • #8
Originally posted by aychamo
I am a biologist,

In the field of biology, have you ever heard of the term "thermodynamic time"?
 
  • #9
Time "Rate" FASTER on Earth than Sun!

aychamo:

The idea that because the Earth is moving (whatever that means), that its time "rate" , (arguing on the ideas of Special Relativity) must be slowed relative to the Sun is erroneous. The opposite is in fact the case.

As a matter of fact there is "point" where a kind of "balance" occurs between the time "rate" decreasing effect of Special Relativity (SR), and the time "rate" increasing effect of "increasing" gravitational potential (ie: General Relativity, GR) as an orbit's (assume circular for simplicity) radius increases.

This balance occurs at a satellite orbit (either natural or man-made satellites, the maths doesn't know any difference) altitude of half the radius of the "central attractor" (eg: this would be the Sun when considering the Earth's orbit around it, or the earth, if considering an earth-tied artificial satellite). At this point the time "rate" changes of GR are exactly equal and opposite those attributable to SR. So, for example, an atomic clock in a satellite circularly orbiting the Earth at half its radius (around 2,000 miles) would exhibit the same time "rate" as identical atomic clocks at the geographic poles.

See:
http://gijxixj.home.att.net/Relativity/GrSrTpSatExplns.htm#FreelyOrbitingSatellites [Broken]

for more along these lines. (Hope you enjoy the guitar music ;-). It plays fitfully whilst it loads, at least on a slow connection, volume control at TOP of web-page, where you can also mute it when the endless repetition p**s you off too much ;-).

Dennis Revell
 
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  • #10
Satellites in low Earth orbit travel at 16,500mph. At that speed, time dilation in gps satellites is about 7,000 nanoseconds (seven millionths of a second) per day (and then there is the general relativity time dilation which is 45,000 nanoseconds per day in the opposite direction). That works out to about 2.5 seconds per thousand years or just over one year over the life of the universe.

I got the dilation values off the net and I really hate math, so I won't try to calculate the actual values for the Earth going around the sun. But it'll be within an order of magnitude or two of what I just gave you. Not real significant on the galactic timescale.
 
  • #11
Actually russ, the formula(e) for circular orbits is(are) quite simple:

The ratio of satellite time to planet or star time (actually planet/star time at its geographical poles only), for any circular orbit, is given by:

GAMMA = 1/ SQRT [ 1 + GM/c²{2/R - 3/r} ]

where G = Newton's Gravitational constant, M = mass of the planet/star, c = speed of light, R = planet/star radius, r = radius of orbit.

If this equation hasn't already got a name, why don't I modestly call it the Revell equation. ;-) In terms of the speed v of a circularly orbiting satellite, which speed is fixed by G, M, and r, this becomes:

GAMMA = 1/ SQRT [ 1 + {2h/R - 1}v²/c² ]

here h = satellite altitude (ie: h = r - R).

Btw, GPS satellites do not orbit at 16,500 mph. The formula relating satellite speed to altitude (for circular orbits) is quite simply, and strictly:

v = SQRT [GM/(R + h)], symbols same meanings as given above, so you can work it out for any (circular) situation. Interestingly for h = 0, v² becomes GM/R, which is half of the (escape velocity)², or half of vesc², so the simplest version of expression for GAMMA becomes:

GAMMA = 1/ SQRT [ 1 + {vesc²/c²}{1 - 3R/2r} ]

... unless I made a mishtake somewhere (couldn't be bothered double checking it ;-).
 
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  • #12
Hi, how are you? I am a programmer, not Physic major. I just read Physic to exercise my bored brain. I did some SR reading, but not GR yet. So, I am really a layman.

I am very interested in this formula regarding time difference between two objects orbiting the same star.

Is there a book that shows the derivation of this formula?

Also, since the object in the Sun does not orbit the Sun, will this formula need to be adjusted to that?
 
  • #13
Sammywu:

The formula/e for circular orbits is/are given in the immediately preceding post to yours. Take your pick but version 2 or 3 are probably most appropriate.

Take ver. 3: GAMMA = 1/ SQRT [ 1 + {v²esc/c²}{1 - 3R/2r} ]. If you know the escape velocity of the star (given, in case you don't, by v²esc = 2GM/R, all symbols usual meanings), then you can apply it in turn to as many orbit radii (r) as you like, the ratios will give the relative plod of time from orbit to orbit. The smaller the value of GAMMA, the more the "time-rate" of a satellite is "speeded up". Each individual GAMMA gives the time plod difference between an individual satellite and the geographical poles of the star/planet. ( and ... duh ... this is a slippery slope I'm sliding down ... )

You could even account for all (reasonably sized circular) orbits by plotting the graph of GAMMA versus r, for any given planet/star, or indeed for a completely imaginary one. ;-)

Well, the proof is from General Relativity, so prepare for a long haul. ;-) The "finale" of this, as far as the information you requested is concerned, can be found as Eq. (392) from Pauli's "Theory of Relativity", Dover paperback edition:

T' = T/SQRT(-g44) = T/SQRT[1 + 2Ø/c²] ... ... (392)

Here Ø is the potential, and in the case you're interested in, it is the gravitational potential. For a circularly orbiting satellite you just add the centrifugal potential of -½v² to the gravitational potential to get the overall potential of (Øgrav - ½v²).

and no doubt, you can find simlilar in many other places, and Einstein's original 1916 paper. But I "like" this equation, very reminiscent of the Special Relativity Lorentz Transformation. For the closest I've found to the "real McCoy", look HERE.


Also see http://gijxixj.home.att.net/Relativity/GrSrTpSatExplns.htm#FreelyOrbitingSatellites [Broken] for more, but I should warn you there are huge mistakes there. ;-) (I'm just waiting for a professional relativist to point them out to me. ;-)





If you're not confused, you don't understand the problem.
 
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  • #14
Before I get too crazy and confused, let me propose an imaginary experiment.

Let me put a space station in a remote space area far away from all gravities. Now a rocket passes by the station; at the event, you can synchronize their clocks, and we will ignite a propeller attched to the rocket pointing perpendicular to the rocket instead of parallel. This propeller will continuously generate a calculated acceleration and make the rocket go thru a circle and back to the station again at the sam speed so that we can synchronize and compare their clocks without any ambiguity again.

You can see we now generate a artificial gravity on this rocket. According to the GR and SR effects you people proposed, will they exactly cancel out each other and their clocks shall match?

Or does the gravity have different effect from a propeller generated artificial gravity?

At the same time, I have proposed a twin paradox that could be realized without gravity and infinite acceleration, which I can not comprehend just as DR. Does this really mean that twin paradox is really meaningless?

Does this click? Please help.

Thanks
 
  • #15
Another questions:

Simply when applying this GR effect to some observers, there are three different kind of observers:

1. The one orbiting around the planet or sun in a circular constant speed.

2. The one free falling.

3. The one stands on the surface of the planet and supposed the planet is not spining by itself, this person actually felt two forces: the gravity that pull him down and the ground support that push him up and they cancel each other.

How do their clocks tick differently?

Thanks
 
  • #16
Another experiment:

You sent a rocket out of the space station that I put in the space in the previous experiment. Of course, we will give it some push for a certain amount of time until it reaches a certain speed. Let it fly for a certain time in constant speed. Then at one point, we ignite its returning propeller until it reverses its velocity ( I assume velocity is the vector one. If I am wrong, forgive the layman. ) Let it fly for a certain time and then start its bracking propeller so that it will undergo acceleration until it stops at the space station. Again we can synchronize their clocks at two events without ambiguity. Could you tell me what is their clock difference in certain formula? Keep the thought simple, you can either assume you are the clock at the station or or the clock at the rocket and give me your answer as you like. just make it clear what is T and T' in your answer.
 
  • #17
Originally posted by Sammywu
Before I get too crazy and confused, let me propose an imaginary experiment.

Let me put a space station in a remote space area far away from all gravities. Now a rocket passes by the station; at the event, you can synchronize their clocks, and we will ignite a propeller attched to the rocket pointing perpendicular to the rocket instead of parallel. This propeller will continuously generate a calculated acceleration and make the rocket go thru a circle and back to the station again at the sam speed so that we can synchronize and compare their clocks without any ambiguity again.

You can see we now generate a artificial gravity on this rocket. According to the GR and SR effects you people proposed, will they exactly cancel out each other and their clocks shall match?

No, the clocks won't match. Since the Rocket from its perpective is always accelerating towards the station it will perceive the station clock as running fast. The station will simply preceive the rocket clock as running slow due to its relative velocity. (The rocket's acceleration will only affect the rocket's clock in as far as it affects the rocket's relative velocity.
 
  • #18
Janus, Thank you for your reply. Just one thing I would like to make clear. The rocket passed right by the station and retruned through the station again after a circle. The station is not in the center of the circle. Also, the station is light enough so its gravity shall be neglegible.

If you still maintain your answer, where did the GR effect that proposed by other people go? It seems that only SR is making an effect here.

Thank you very much. Would you might shed some lights to the other two questions?
 
  • #19
Originally posted by Sammywu
Janus, Thank you for your reply. Just one thing I would like to make clear. The rocket passed right by the station and retruned through the station again after a circle. The station is not in the center of the circle. Also, the station is light enough so its gravity shall be neglegible.

If you still maintain your answer, where did the GR effect that proposed by other people go? It seems that only SR is making an effect here.

Thank you very much. Would you might shed some lights to the other two questions?

Strictly speaking, you don't need to invoke GR for this problem, just SR as it applies to acceleration.

From the perspective of the station this is simple. you only need to take into account the ship's relative velocity.

From the ship's perspective, dealing with its acceleration is a bit more difficult. (The time dilation the ship measures on the station's clock will vary by not only the postion of the station with respect to the accleration but also its relative distance.)

For instance, while the ship is next to the station, the acceleration of the ship is away from the station like this:

<-------Ship Station.

During this part of the circular path the effect seen by the ship is that the station clock runs slow both due the relative motion and the acceleration the ship experiences. since the distance between ship and station is small, the second effect will be small.

During another part of the path the acceleration of the ship will point towards the station like this:

Ship------->______Station

The relative motion effect will be the same. But now the ship will see the station clock as running fast due to the acceleration. But now that the ship is far away from the station, this effect will be considerable. (Enough to overwhelm the relative motion effect. )

The upshot is that the rocket will measure more total time as passing on the station clock when it come back around.

You really only need to invoke GR if you want to consider the spaceship as being your "at rest" frame during the whole time. Then you have to explain the motion of the station(and the force felt by the passengers of the ship as being due to a gravitational field.

Then you factor in the the gravitational time dilation due to the relative postions of the ship and station in the field.
 
  • #20
Janus, Thank you for you reply. I am still not clear. Let me make a wild guess.

The GR effect seems to me is a compensation for the potential energy lost. I need to auume an observer rest at the infinite far away from the start, i.e the center of the gravity source. This observer will run a slowest clock compared with all other clocks cuaght in the vincinity of the gravity, i. e. their potential energy is negative as -GMm/R, referred as EP hereafter. Let's keep it simple for now, assuming them as rest without movement. This GR effect formulate their clock as T/sqrt(1+2EP), knowing EP as negative. This will show that the smaller is R, the higher is the T.

Now let's assume the object in vincinity is moving, then all we need to do is add the SR effect, which is oppsite to the GR figure in sign, back to the object.

If this is correct, we then equate the clock in the infinitely far away to the center of the gravity source. Here is what bother me. How could you simply equate a clock so far to the clock in the gravity center?

Do i do it right? If it's complete baloney, please let me know. If I capture it, please correct me any place I am wrong.

Now, If it somehow captures our mainstream scientist, I will ask another question. Back to the mass-energy equation, my impresion is the mass is really how an outsider measure the internal dynamic of an enclosed confinement ( simply said, box ). Einstein has shown how to derive the mass of photon in the way in SR. Now, gravity potential energy, actually all potential energy, bother me. If I can confine two masses, M and m, and keep them in a certain distance inside that confiement, what will be the mass when we measure it. Could it be M+m-GMm/Rc**2?

Thanks
 
  • #21
Er, Sammyu, isn't what you're talking about exactly the scenario given in http://gijxixj.home.att.net/Relativity/Image1.gif [Broken]?

Btw, neither propellers (nor jet engines) work in space. ;-)

Janus, your explanation seems awfully complicated. Surely it doesn't really matter that the station is not at the centre of the space-ship's circular path because it's in the same reference frame as the centre of that circular path.
 
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  • #22
Dear Janus,

When digesting your answers more, I realized that gravity is not the same as a true force in this model.

Because the experiment I gave showed clearly the spaceship has a slower clock than the station, from your answer. Even though from a relative motion point of view, if disreagrding the acceleration, they look symmetric to each other.

While applying gravity and my artifical gravity actually generate two opposite effects. So, gravity is apparently different from the artificial gravity I created with the material-antimaterial propeller, which as I know could be the most efficient propeller thereotically.

The better way to interprete this seems to be taht the gravity is purely a curvature of the space, from lots of people saying, which I had problem to grasp in the past. Now it seems clearer to me what that really means and why Einstein needed to say that. I need sometimes to further digest the idea.

Thank you for tolerating the layman here.

Well, I am still interested in knowing your response to my interpretation of compensation for potential energy and whether the mass measurement will be different by an outside observer when a box containing two masses in certain distance. If you are willing to tolerate me more. Thanks
 
  • #23
Janus,

I think I got closer to the core of the problem.

I modify my experiment to make me comfortable with no ambiguity. My station could have attached a tunnel to the center of the circle. In this way, I am certain the center is at the same reference frame as Gixxie said. I know for you this is unnecessary.

Now, the next thing, I want to talk about is the absoluteness of acceleration. It always bother me when it was said who is feeling the acceleration. Now I found a scientific way without ambiguity to check who is under influence of true acceleration. It's from Einstein any way. I just did not understood it. Simple, whoever see the light bent is under the true accelaration. Most of time, we will not able to see the curve of loght but in an astronomical scale, this effect could become clear.

Back to my experiment, the spaceship will see the light bent. The space staion and the center will not see the light bent.

In a gravity field, the free fall observers and the orbiting observers will not see the light bent because the light is bent together with them. Or, in a different words, all of the three: free falling objects, orbiting objects and light are under the gravity influence.

The objects on the planet, assuming no planet spin, will see light bent, because they are not moving together with light by gavity. So, it has the same clock as the infinite observer, or the center observer in Physicists' textbook. The force acting on them are the electromagnectic forces exercised by the push of the outer electrons in the ground serface. As I remember, somebody has said, all contact push forces actually base on the outer electron push force. Or simply, the ground support force that keep the observers in standing.

The three models: PE compensation, space curvature and absolute acceleration examined by light bent all seem to be able to explain somethings and might have more foundamental implcation embeded.

For one, now we can clearly see gravity is a fake force-- my own term. You people might not agree with that. ElectroMaganetic force seem to be a real force. I am not sure about weak and strong forces.
Does this seem to deviate from the mainstream?

Now what I need to do is putting some math. in, so I can derive a common formula for he GR effect and SR effect in these models. And hopefully that will come out to agree with yours.
 
  • #24
Dennis, Sorry, I have misspelled your name. Also, I did not notice you are the same person.

About the propeller, maybe a thruster will be more acceptable to you.

Any way, geting back to this topic. I have to take one statement back. The free falling clock might be different from the orbiting clock. Even though they both see the light straight, so, they are under the influence of the same fraudulent force, the gravity. But the orbiting object has an initial speed and the free falling does not. Let's worry that later.

Now, back to my imginary experiment, the formula between the space station clock Tst and the spaceship's clock Tship shall be Tst=Tship*1/sqrt(1-v^2/c^2). Since only SR is neededin the evaluation of their relationship and Tship has a slower clock. And do not forget, you can compare their clocks after one circle without ambiguity. It's real effect. The person in the spaceship will be younger.

Now, reversing that back to the relationship between the Sun and the Earth, Tearth=Tsun*1/sqrt(1-v^2/c^2). The particles in the Sun shall experience slower clock than the Earth clock, assuming there is no spin in both sun and Earth. The Earth is orbiting around the Sun under the fraudulent force. Borrowing your derivation, -v^2/c^2 = 2EP = -GMsun/R, here R is the distance between the Sun and the Earth.

Now, let's look at the spin at the Earth. You probably can assume polar bears are not under any spin effect and need no adjustment compared with the Earth's clock.

My friend supplied me these figures, about 6,000,000m for Earth's radius, 9.8 m/sec2 for gravity experienced in the surface of the Earth. With that figure, I found an object to orbit around Earth's surface, you might call that escape velocity, I can't remember why, requires about 7,800 m/sec ( I did the calculation in the office and can't remember the exact figure. Any way, it's high school math. by v^2/g=r.) The spinning speed at the Equator would be very small, like 34 m.sec maybe. Any way, the person on the Earth's surface could be considered standing firm supported by the ground force. This means you can treat that clock just like the Earth clock. I might show you how to adjust that next time.

Now, Let's denote Ts as the clock of a satellite orbiting around the Earth at the height of H. By the GR effect I just learned from you, Ts=Tearth*1/sqrt(1-v^2/c^2). Here -v^2/c^2 probably is 2PE which you already derived. 2PE=-2GM/(r+H), here r is the radius of the Earth, not the distance between the Sun and the Earth.

It does not seem to me I need any SR effect, did I miss something?

Thank you for your and Janus's help.
 
  • #25
Question About Gravity

Hi,

I was wondering:

if two objects traveling in a parallel paths near each other, were to approach the speed of light, would the gravitational force attracting the two objects approach infinity? Or would the gravitational force between the two objects remain unchanged? In other words, does the gravitational force of an object increase to infinity as it's velocity approaches the speed of light? I was under the impression that the gravitational force of an object remains unchanged as it approaches the speed of light, otherwise, any object approaching the speed of light would be crushed to a point under it's own gravity, instead of a two dimensional plane under Lorentz contraction. I could be wrong, could someone clarify for me? Thanks!

Best Regards,

Edwin
 
  • #26
Edwin,

That's a very interesting question. Maybe I will spend some times thinking about that too.

Any way, the reason I got back here is that I found I got another question answered, probably. The inertial reference frame that bothered me and most people is apparently the frame that light is not bent. Now, we have a physical way to measure which one is the inertial reference frame.

When I thought that through, I will elaborate. Otherwise, for now, it's enough for me. We might be able to discuss whether there is a truly preferred frme or not.
 
  • #27


Originally posted by Edwin
Hi,

I was wondering:

if two objects traveling in a parallel paths near each other, were to approach the speed of light, would the gravitational force attracting the two objects approach infinity? Or would the gravitational force between the two objects remain unchanged? In other words, does the gravitational force of an object increase to infinity as it's velocity approaches the speed of light? I was under the impression that the gravitational force of an object remains unchanged as it approaches the speed of light, otherwise, any object approaching the speed of light would be crushed to a point under it's own gravity, instead of a two dimensional plane under Lorentz contraction. I could be wrong, could someone clarify for me? Thanks!
If you were sitting on (or in) either object, the other would appear "stationary" - not moving , except towards you. The gravitational force (between your object and the other one) that you would measure would be the same, whether you observed the quasar 3C273 (an arbitrary, distant point of reference) traveling at 0 m/s or 200 million m/s. The usual caveats apply.

Perhaps you are interested in what you would observe if you were a distant observer?
 
  • #28
Edwin, My attemp to answer your question might not be authetic. Do not take me as your final answer.

I see your point. Let me elaborate. You need to assume another observer that is static. So, to the observer, their mass were increased, so their gravity attraction shall be increased to the observer. Now, if there was nothing holding them afar. They will be socked to each other, of course. But what will be the clocks and space measured to themselves and the static observer? Note one thing, the distance should be observed unchanged by either the moving observer or static observer, because the length contraction occurred on the dimention of movement.

If they are held afar by something, the question will be what force is required to break down the holding architect.

Here, of course we are assuming no acceleration is involved.

Well, I can't get the answer yet. Just trying to clarify your question behind your statements took me some analysis.
 
  • #29
Gravitational Question

Thankyou for your help guys. I am interested both the observations of distant observers as well as the observer on the masses themselves. I have been reading up on relativity, and have not found a specific answer yet, either, but will continue to search. I think it is that General Relativity does not treat gravity as a true force, but describes the affects of gravity in terms of curved space-time and manifolds. Suppose that our two objects traveling near each other are spheres, the idea that the dimensions of the two spherical masses do not contract but in the direction of travel would make me wonder as to whether the gravitational force is homogenous in three spatial dimensions x, y, and z the two masses. What do you think. Would the gravitation forces appear to be homogenous to some third stationary observer on some planet? Would the gravitational force between the two objects appear to be homogenous(equal in strength in all directions) to the observer riding along on one the two objects?

Inquisitively,

Edwin
 
  • #30
Edwin, Nereid,

I have no answer for Edwin's question. I can only make his puzzling a little clearer.

There is a hidden paradox in the situation.

Since the distance between the two objects does not contract and the time takes two objects to hit each other is independent upon the Masses. So, the increase of mass measurement by the static observer will be irrelevant. The time taken for the two objects colliding will be the saem by both moving observers and static observer. This contradicts SR's theory of time dilation supposed to be observed by the static observer.

The next case, if we carefully manufacture the holding bar between the two objects so that it can only stands the force of Gm0*m0/R^2. The moving observers shall not see the bar broken. By the static observer, the mass increase will make higher arracting force and will break the holding bar.

Again, we , the nonbelievers, prevail. Albert lost. Take one step back, can we explain the constant light speed phenomenon without Albert's SR? NO. Maybe we shall listen to what Albert wants to say about it. Janus, would you mind representing Albert again?

Another question, if the two objects actually are two electrons, when we add electromagnectic force here. How does that play? I always have problems with Albert's imagination when he says about that infinite current. I tried to decipher that mystery with just two electrons. Did anyones do this already?

Now let me get back my unfinished work on the free falling object in the gravity. It appeared to me, at the initial point, when the free falling object was let go, it shall have a difference in time measurement difference with the pass by orbiting object. With its falling continued, it shall have a different time measurement against the orbiting object. Its velocity ( which one is the scalor one, velocity or speed? ) will increase but less than the orbiting object's velocity until it reach the center of star.

Let me stop here, because i thought of two interesting imaginary experiment.

I can actually extend my imaginary experiment with one more spaceship B, naming the original one A. While the spaceship A passes the station, B will leave the station. With precise control, B will work like the shadow of A on the diameter of the circle that A will move around. If you are familiar with the coircular motion and the oscillation, you know what I am talking about. A and B will meet at the other end of the diameter according to classical theory, another event without ambiguity. Coming back, they will meet with the station agin. What will be the clock difference among the threes?

Another one. making a device like a donut with a connecting tunnel through one of the diameters. With an open end at the joint of the tunnel and the donut, you can shoot an object in with certain speed. Put a comparable significant mass in the middle; now this is a artificial Sun experiment that you can let objects orbiting through the donut and objects falling through the tunnel. You can perform a true comparison of clocks between free falling objects and orbiting objects.
 
  • #31
Just one thing. My imaginary two masses in a closed box might not be imaginary. Browsing Physic World, notice a double pulsar being viewed now, that could be an arena for two masses in an enclosed box.
 
  • #32
Back to my free fall object issue. My calculation was a litle rusty. I need to correct the calculation of those formula. I wonder why nobody caught it and corrected me. Now, I have to spend long words for just calculation. Ek=(1/2)*mv^2. Ep=-GMm/R. E=Ek+Ep=-(1/2)GMm/R. and v^2=GM/R=-2E/m. Let's denote F=E/m. F is not the potential energy but rather the field, Is it that how you call it? Tst=Tship*(1/sqrt(1-v^2/c^2)). In reverse, Tearth=Tsun*(1/sqrt(1-v^2/c^2))=Tsun*(1/sqrt(1+2F/c^2)).

Please help me to check my math. If I am still wrong, correct it for me.

Back to my experiment, the one with staion timed by Ts, the orbiting ship timed by Ta and the straight moving ship timed by Tb. We already know Ta. The only question is Tb. Let's use Ts as a standard parameter; you can make Tb as a function of Ts. Make integration of Tb along the path with Ts as the parameter. Can anyone do the math? I believe this will bring us to the GR effect when we equate Tsun=Ta and Tearth=Tb.

Let's go back to the three models I proposed, The second saying that gravity is a fraudulent force and just the space curvature ( inward though ) is really the same as the third that uses light path as a check for who is under true acceleration. Is it? Maybe not. for now, let's assume they are. The first one will completely match this one, result wise. If yiur calculation showed that they are different, please let me know.

If this proved correct, this seems to be a complete model that we can deduce GR from SR. So GR does not exclude SR, GR is an extention of SR. Without SR, GR has no wher to be born.

This seems to resolve our question. Actually this poses more question. If this is true, does that imply any length dilation and mass measurement issue here in GR? Did GR textbook mention anything like that?

Where does my two stars in one box fit?

Does GR help us to resolve Edwin's paradox?
 
  • #33
Back to Edwin's question.

Now, I remember this is really the part of SR's Electrodynamic analysis.

The question actually arised from a phenomenon. Two static free electrons will exercise electric force between them. While two constantly moving electrons ( or current ) will exercise not only electric force but also magnetic force between them. This is a paradox itself. In Newtonian's world, movement is relative. From the view-points of the moving electrons, they are static. There should not be additional force observed.

That's why the question of two electrons came to my mind immediately. I think.

Many people here have studied that part of SR. I think Lawrenzian force came out from that part also. Hope I use the right term. . I can't find my SR book. Anyone want to help Edwin to understand this part. Nereid, David, how about you?
 
  • #34


Originally posted by Edwin
Hi,

I was wondering:

if two objects traveling in a parallel paths near each other, were to approach the speed of light, would the gravitational force attracting the two objects approach infinity? Or would the gravitational force between the two objects remain unchanged? In other words, does the gravitational force of an object increase to infinity as it's velocity approaches the speed of light?
Since the second question is easier to answer I''l respond to that one first. Yes. The gravitational force is a function of velocity. The gravitational force on a particle in free fall is given by

[tex]G_{\mu} = \frac {1}{2} m g_{\alpha \beta, \mu} v^{\alpha} v^{\beta}[/tex]

where

[tex] g_{\alpha \beta}[/tex]

are the gravitational potentials, also known as the components of the metric tensor and

[tex]g_{\alpha \beta, \mu}[/tex]

is the partial derivative of the potential with respect to mu. There are ten independant gravitational potentials in GR as opposed to the one in Newtonian gravity. The Newtonian gravitational potential is defined as

[tex] \Phi = \frac{c^2}{2} (g_{00}-1)[/tex]

The mass of the particle with proper mass m0 is given by

[tex]m = \gamma m_{0} = m_{0} \frac {dt}{d\tau}[/tex]

The mass is not only a function of speed but a function of the gravitational potential as well. For detailed defintions and proof of these relations see
http://www.geocities.com/physics_world/gr/grav_force.htm

As the speed increases then the gravitational force goes to infinity. However since the mass increases as well the particle will actually slow down in cases such as a falling towards a black hole or in a uniform gravitational field.

Note: The gravitational force has a relative existence. Einstein's Equivalence Principle states that at any point in spacetime the force my be transformed away at that point. For the falling particle - the particle may be considered to be a rest at the origin of a locally inertial frame. At the origin of this frame the gravitational force is zero. However the tidal force may not be zero as is the case of tidal forces, which cannot be transformed away.
 
  • #35
Thanks!

Thankyou everybody for your help. I really appreciate it.

Best Regards,

Edwin
 
<h2>1. What is the relationship between Special Relativity and the Earth, Sun, and Galaxy?</h2><p>Special Relativity (SR) is a theory developed by Albert Einstein that describes the relationship between space and time. It explains how objects in motion appear differently to different observers and how the laws of physics are the same for all observers. This theory is applicable to all objects in the universe, including the Earth, Sun, and Galaxy.</p><h2>2. How does Special Relativity affect our understanding of the Earth's orbit around the Sun?</h2><p>Special Relativity predicts that objects in motion experience time dilation, which means time passes slower for objects in motion compared to those at rest. This means that the Earth's orbit around the Sun is slightly affected by time dilation, causing the Earth's clock to run slower than a clock on the Sun. However, this effect is very small and not noticeable in our daily lives.</p><h2>3. Can Special Relativity explain the movement of galaxies in the universe?</h2><p>Yes, Special Relativity can explain the movement of galaxies in the universe. According to the theory, the speed of light is constant for all observers, regardless of their motion. This means that the light from distant galaxies may appear to be redshifted or blueshifted, depending on the relative motion between the observer and the galaxy. This phenomenon is known as the Doppler effect and is explained by Special Relativity.</p><h2>4. How does Special Relativity affect our understanding of the shape of the Earth?</h2><p>Special Relativity has no direct impact on our understanding of the shape of the Earth. However, it does explain the concept of the curvature of space-time, which is essential in understanding the shape of the universe. The Earth's curvature is a result of the gravitational force exerted by the Sun, which is explained by Einstein's theory of General Relativity.</p><h2>5. Can Special Relativity explain the concept of time travel?</h2><p>Special Relativity allows for the possibility of time travel, but it is highly theoretical and has not been proven to be possible. According to the theory, time travel would require an object to travel at speeds close to the speed of light or to be in the presence of a massive object, such as a black hole. However, there are many paradoxes and complications that arise with the concept of time travel, and it remains a topic of ongoing research and debate among scientists.</p>

1. What is the relationship between Special Relativity and the Earth, Sun, and Galaxy?

Special Relativity (SR) is a theory developed by Albert Einstein that describes the relationship between space and time. It explains how objects in motion appear differently to different observers and how the laws of physics are the same for all observers. This theory is applicable to all objects in the universe, including the Earth, Sun, and Galaxy.

2. How does Special Relativity affect our understanding of the Earth's orbit around the Sun?

Special Relativity predicts that objects in motion experience time dilation, which means time passes slower for objects in motion compared to those at rest. This means that the Earth's orbit around the Sun is slightly affected by time dilation, causing the Earth's clock to run slower than a clock on the Sun. However, this effect is very small and not noticeable in our daily lives.

3. Can Special Relativity explain the movement of galaxies in the universe?

Yes, Special Relativity can explain the movement of galaxies in the universe. According to the theory, the speed of light is constant for all observers, regardless of their motion. This means that the light from distant galaxies may appear to be redshifted or blueshifted, depending on the relative motion between the observer and the galaxy. This phenomenon is known as the Doppler effect and is explained by Special Relativity.

4. How does Special Relativity affect our understanding of the shape of the Earth?

Special Relativity has no direct impact on our understanding of the shape of the Earth. However, it does explain the concept of the curvature of space-time, which is essential in understanding the shape of the universe. The Earth's curvature is a result of the gravitational force exerted by the Sun, which is explained by Einstein's theory of General Relativity.

5. Can Special Relativity explain the concept of time travel?

Special Relativity allows for the possibility of time travel, but it is highly theoretical and has not been proven to be possible. According to the theory, time travel would require an object to travel at speeds close to the speed of light or to be in the presence of a massive object, such as a black hole. However, there are many paradoxes and complications that arise with the concept of time travel, and it remains a topic of ongoing research and debate among scientists.

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