Thread: speed of light, acceleration, and the human body.

1. speed of light, acceleration, and the human body.

Here's an odd ball question for you...

if there was a ship capable of eventually reaching light speed, could a human widthstand the g-forces needed to gain light speed in his/her lifetime? or would it take too long to reach light speed to do so with out hitting killer G forces.

2. Order of Kilopi
Join Date
Jul 2005
Posts
9,761
I take it you're asking us to assume that relativity doesn't apply?
In which case, we could reach lightspeed easily. Light travels at 300,000,000 m.s-1; the acceleration due to gravity is about 10 m.s-2. So that means we could reach lightspeed in 30,000,000 s, accelerating at 1g: one year.

Relativity means that we can never reach lightspeed, but can get pretty close to it for a fairly short elapsed time aboard our spaceship. After one year accelerating at 1g, we've reached 0.75 lightspeed; at two years, 0.96; five years, 0.9999; ten years, 0.99999999. (Unfortunately, after ten years of acceleration, 9,000 years would have passed at home on Earth.)

Grant Hutchison

3. Also humans could withstand huge Acceleration Forces if you just immerse them in a gel or liquid which is the same density as the human body. (Like water)

4. Order of Kilopi
Join Date
Jul 2005
Posts
9,761
Originally Posted by max8166
Also humans could withstand huge Acceleration Forces if you just immerse them in a gel or liquid which is the same density as the human body. (Like water)
It certainly would help, but you'd also need to fill the lungs and other air cavities with this liquid, so it would get technically tricky to do in a survivable way.
And, at the extreme, there would be a limit to acceleration set by the difference in density of the various tissues. Under very high acceleration, the relative bouyancy forces within the tissues would start to pull them apart: your skeleton would be dragged downwards, and your fat shoved upwards.

Grant Hutchison

5. Originally Posted by grant hutchison
... your skeleton would be dragged downwards, and your fat shoved upwards.
May your consumption during the holidays accelerate none of you forwad too much.

6. Order of Kilopi
Join Date
Nov 2003
Posts
6,197
Originally Posted by grant hutchison
Relativity means that we can never reach lightspeed, but can get pretty close to it for a fairly short elapsed time aboard our spaceship. After one year accelerating at 1g, we've reached 0.75 lightspeed; at two years, 0.96; five years, 0.9999; ten years, 0.99999999. (Unfortunately, after ten years of acceleration, 9,000 years would have passed at home on Earth.)

Grant Hutchison
In special relativity the spaceship observer would see the earth clock slow down, so he would see little time pass on earth. The earth clock would not be seen to speed up as in your example.

7. Order of Kilopi
Join Date
Jul 2005
Posts
9,761
Originally Posted by Sam5
In special relativity the spaceship observer would see the earth clock slow down, so he would see little time pass on earth. The earth clock would not be seen to speed up as in your example.
Fair enough.
But our observer aboard ship has no way to get back into the same inertial reference frame as Earth without finding that 9000 years have elapsed on Earth.

Grant Hutchison

8. Order of Kilopi
Join Date
Nov 2003
Posts
6,197
Originally Posted by grant hutchison
Fair enough.
But our observer aboard ship has no way to get back into the same inertial reference frame as Earth without finding that 9000 years have elapsed during her 10 years of acceleration.

Grant Hutchison
Not so. Simply rotate the ship 180 degrees and it will slow down at 1 g and gradually head back toward the earth at 1 g. While everyone on the earth experiences 1 g. The ship observer sees the earth clocks running slow the whole time.

9. Order of Kilopi
Join Date
Jul 2005
Posts
9,761
Originally Posted by Sam5
Not so. Simply rotate the ship 180 degrees and it will slow down at 1 g and gradually head back toward the earth at 1 g. While everyone on the earth experiences 1 g. The ship observer sees the earth clocks running slow the whole time.
Not so. The deceleration shifts the line of simultaneity for the ship across a wide span of time on the Earth (the span determined by the distance from the Earth at the time of deceleration). If the ship were to accelerate for 10 years (shipboard) and then come to a stop (relative to Earth) on a dime, the observer would find that my 9000 years had passed on Earth.

Grant Hutchison

10. Order of Kilopi
Join Date
Nov 2003
Posts
6,197
Originally Posted by grant hutchison
Not so. The deceleration shifts the line of simultaneity for the ship across a wide span of time on the Earth (the span determined by the distance from the Earth at the time of deceleration). If the ship were to accelerate for 10 years (shipboard) and then come to a stop (relative to Earth) on a dime, the observer would find that my 9000 years had passed on Earth.

Grant Hutchison
Nope, that's not in SR theory. The observer sees the other clock always slowing down, both coming and going. He never sees the clock speed up.

11. Order of Kilopi
Join Date
Jul 2005
Posts
9,761
Originally Posted by Sam5
Nope, that's not in SR theory.
It is. The business of acceleration and deceleration is easily derived from the Lorentz transformations, and comes out as I've described.
Are you proposing that the "twin paradox" does not result in shorter elapsed time for the traveller?

Grant Hutchison

12. Order of Kilopi
Join Date
Nov 2003
Posts
6,197
Originally Posted by grant hutchison
It is. The business of acceleration and deceleration is easily derived from the Lorentz transformations, and comes out as I've described.
Are you proposing that the "twin paradox" does not result in shorter elapsed time for the traveller?

Grant Hutchison
In this thought experiment, the acceleration on the rocket is the same as the acceleration on the earth people. The motion is relative and the acceleration is the same.

There is no observer seeing a clock speed up in SR theory.

13. Order of Kilopi
Join Date
Jul 2005
Posts
9,761
Originally Posted by Sam5
In this thought experiment, the acceleration on the rocket is the same as the acceleration on the earth people. The motion is relative and the acceleration is the same.
So are you claiming that no time difference is incurred in the twin paradox?

Originally Posted by Sam5
There is no observer seeing a clock speed up in SR theory.
I can only suggest you do one or more of the following:
1) Draw yourself a space-time diagram in which the simultaneity lines are plotted for the accelerating/decelerating traveller and the stay-at-home observer. This makes the location and cause of the increased observed clock rate very clear.
2) Invest in a copy of Time and the Space Traveller, which walks through the same construction.
3) Move to the ATM section, where people may be prepared to discuss this in more detail.

Grant Hutchison

14. Order of Kilopi
Join Date
Nov 2003
Posts
6,197
Originally Posted by grant hutchison
So are you claiming that no time difference is incurred in the twin paradox?

I can only suggest you do one or more of the following:
1) Draw yourself a space-time diagram in which the simultaneity lines are plotted for the accelerating/decelerating traveller and the stay-at-home observer. This makes the location and cause of the increased observed clock rate very clear.
2) Invest in a copy of Time and the Space Traveller, which walks through the same construction.
3) Move to the ATM section, where people may be prepared to discuss this in more detail.

Grant Hutchison
No, I think you are thinking of the basic theme of “Planet of the Apes,” where the earth ages while the rocket travels, but that’s not SR theory. That’s a science fiction movie plot.

This is SR theory:

http://www.fourmilab.ch/etexts/einstein/specrel/www/

No clock is observed to speed up in SR theory. It is you who should go to the ATM section.

15. Order of Kilopi
Join Date
Nov 2003
Posts
6,197
What you are doing is switching back and forth between two different clocks that one observer is observing. You judge the “10 years” by the rocket observer watching his own clock, then you have that same observer say that 9,000 years have passed on earth during his own 10 years. But that requires an earth clock speed-up as seen by the rocket observer, yet there is no observer-observed clock speedup in SR theory.

16. Sam5,

In the classic version of the twin paradox, the symmetry between the two twins is broken by the fact that only one, the one who turns around, actually experiences *proper acceleration*. The one who stays behind does not, never feels a force. The other twin does. The turn-around twin sees the other one accelerate, but that's purely a coordinate acceleration, due to his own real proper acceleration. He would agree the other twin was following geodesics, *zero proper acceleration*.

It is during that burst of acceleration that the turn-around twin sees the clock of the other speed up. In the classic formulation with an instant turn around, that speed up is an instantaneous jump way ahead. The relative clock rate is infinite for zero time, and the clock jumps ahead some finite value proportional to the distance between the two twins. That is the simplest way to do it, mathematically, and that's the way it will be intially taught usually.

I'm pretty sure you know that, and this objection of yours is due to sematic quibble of whether one is doing "pure SR" in the above, or is one doing GR. I got into that myself, here.

The modern view is true GR is about those space-times that arise from solutions to the EFE, the gravitational field equations, and *NOT from space-times that arise from non-inertial coordinate transforms*, such as that of the twin who turns around.

In this view, GR is "tidal gravity", space-times with *non-constant* curvature. Now, curvature is tensor, a rather complex one, and a constant curvature can be all sorts of complex things. Rindler, due to constant proper acceleration is a very simple constant curvature. Born (coriolis frame) is constant as well, but it has a gravitomagnetic component. And constant curvature does not mean 'g', or even B_g is constant with position nor time. It means free-fallers are globally inertial, seeing a flat global metric.

Any constant curvature metric can transformed away to zero *globally* by the appropriate free-fall transform, and you're back to the flat (0 curvature) metric of SR. So, in this view, SR applies in the domain of constant curvature metrics. Any coordinate transform to the frame of an accelerating observer is simply a constant-curvature transform.

Only gravity, only the stress-energy tensor, can make variable curvature metrics, and the modern view is that is what GR is.

-Richard

17. Order of Kilopi
Join Date
Jul 2005
Posts
9,761
Richard:
Originally Posted by publius
I'm pretty sure you know that, and this objection of yours is due to sematic quibble of whether one is doing "pure SR" in the above, or is one doing GR.
If Sam5 is merely quibbling over the applicability of SR to accelerating objects, then of course I must withdraw my suggestion that he move to the ATM section.
However, when he writes:
Originally Posted by Sam5
Simply rotate the ship 180 degrees and it will slow down at 1 g and gradually head back toward the earth at 1 g. While everyone on the earth experiences 1 g. The ship observer sees the earth clocks running slow the whole time.
he appears to be going rather farther, and denying the simultaneity shifts that resolve the twin paradox.

So it would be very useful if Sam5 could answer the question I've asked him twice already:
Originally Posted by grant hutchison
Are you proposing that the "twin paradox" does not result in shorter elapsed time for the traveller?
Grant Hutchison

18. Grant,

Yes, he needs to answer that question. I'm giving Sam5 the maximum benefit of the doubt. He may be of the opinion that it requires GR to "save" SR from the twin paradox, but there's some wiggle room in the meaning of "save" here.

There is no paradox there at all, and SR does just fine, of course. If Sam5 holds that SR truly fails the twin paradox, and therefore SR is wrong, and GR is required to "save the day", so to speak, then that is wrong.

However, if by "saving" he means that GR is required to see what happens from the accelerating twin's perspective (that is when you go to Rindler, or whatever metric is required to describe the proper acceleration profile that effects the turn around), but the simple inertial SR result as calculated from any non-accelerating frame comparing the two world lines when they cross again is valid, then that is a "semantic quibble", I suppose.

In this "semantic quibble" view, SR would apply only in 0 curvature, and anything with non-zero curvature is GR. However, the "real GR is tidal gravity" view is it GR is only variable curvature.

From some of Sam5's other posts, he seems to be of the opinion that it is only clocks that are affected by both relative motion and gravity, not "time itself", so we'll have to wait and hope he clarifies exactly what he is trying to say, here.

-Richard

19. Order of Kilopi
Join Date
Nov 2003
Posts
6,197
Originally Posted by grant hutchison
Richard:If Sam5 is merely quibbling over the applicability of SR to accelerating objects, then of course I must withdraw my suggestion that he move to the ATM section.

However, when he writes:he appears to be going rather farther, and denying the simultaneity shifts that resolve the twin paradox.

Grant Hutchison
Hi Grant,

Have you read Einstein’s resolution of the 1905 clock paradox in his 1918 paper “Dialog über Einwände gegen die Relativitätistheorie”? The English translation is published in Volume 7 of “The Collected Papers of Albert Einstein.” Have you read it? In Wolfgang Pauli’s 1921 book, he mentioned that article as Einstein’s own solution to the paradox, and in the 1918 article Einstein says that paper contains his own solution.

20. Order of Kilopi
Join Date
Nov 2002
Posts
6,235
Why do I have the feeling of Deja vu?

21. As I see it, it's not a semantic quibble-- Sam5 is materially disputing the perfectly correct (and useful) analysis by Grant. He is of course incorrect in asserting that "no clock can appear to move fast" relative to yours, and indeed this betrays a complete lack of understanding of the role of the de-simultanization (to coin a word) that Grant discussed (and so also of SR in general), but what is more interesting is the basis he is using for doing this. If Earth had no gravity of its own, then we have the pure twin paradox, and it's not at all clear what Sam5 would claim is happening to clocks in that case. But he is saying that Earth does have a 1g gravity, and that this somehow induces the same effect on clocks that the 1g acceleration of the traveller does. That is a drastic oversimplification of the way acceleration works in both SR and GR, and is also quite incorrect, but the question is, why is this incorrect? In Grant's analysis, the time differential appears because the 1g acceleration of the traveller is not symmetric-- if the traveller switched to -1g to return, he would not make a symmetrical return trip-- the return would take much longer than the outbound trip. But this isn't Sam5's point, he is simply saying that both have a 1g acceleration the whole time. Of course, even though there's a 1g acceleration in the Earth frame, we know its effects are so small that SR will still work quite well. I think part of the problem is that Sam5 is forgetting the traveler must also escape Earth's gravity if one is going to include that in the problem. Whatever the reason, we know from a basic understanding of SR and GR that Grant is right and Sam5 is not.

At the end of the day, though, there is still something interesting in Sam5's observation-- for both the traveller and the stay-at-home twin, a 1g acceleration is a relevant number somehow. But it is only for the traveller that this acceleration has any significant effect. That is somewhat interesting to muse on. I think the bottom line must be that in GR, 1g is only significant when compared to something that is actually allowed to fall for the whole time, so if we were comparing to an inertial faller, then we would have to compare similar effects to what the traveller is experiencing. Ironically, it is precisely because the stay-at-home twin is accelerated in the gravity field, and not inertial, that the consequences of that acceleration are negligible when compared to the traveller. But I'm not sure if the issue is that some things are cancelling out for the stay-at-home twin, or if it is that we must also consider that the traveler is escaping through the Earth's gravity as well, as I said before. Maybe both ways of looking at it are relevant, but the bottom line is, gravity as weak as the Earth's does not alter time in any remotely significant way, whereas a 1g acceleration into space for 5 years certainly does a spectacular twist on time.

22. Order of Kilopi
Join Date
Nov 2003
Posts
6,197
Originally Posted by publius

However, if by "saving" he means that GR is required to see what happens from the accelerating twin's perspective

-Richard
Hi Richard,

I addressed Grant because in Post #2 he introduced a 1g acceleration in the rate of the "traveling twin", while the earth twin also experiences a 1g acceleration. So there is no extra "acceleration" experienced by either twin. Thus we have SR, not GR, and we have both twins seeing each other's clocks slow down at the same rate, while they don't see their own clocks slow down, and of course in SR the motion is "relative" and not "absolute", so both twins see each other as "traveling" while they see themselves as not "traveling".

23. Order of Kilopi
Join Date
Nov 2003
Posts
6,197
Originally Posted by Tensor
Why do I have the feeling of Deja vu?
Hi, I see the whole gang has arrived.

24. Originally Posted by Sam5
Hi Richard,

I addressed Grant because in Post #2 he introduced a 1g acceleration in the rate of the "traveling twin", while the earth twin also experiences a 1g acceleration. So there is no extra "acceleration" experienced by either twin. Thus we have SR, not GR, and we have both twins seeing each other's clocks slow down at the same rate, while they don't see their own clocks slow down, and of course in SR the motion is "relative" and not "absolute", so both twins see each other as "traveling" while they see themselves as not "traveling".
Aha. I didn't notice this. You're comparing earth's *gravity* of 1g with the accelerating twin's 1g. I didn't even see that. By "earth's acceleration", I was thinking of the coordinate acceleration the turn-around twin would see in his own frame, as earth slowed, stopped, and started moving back toward him.

I wasn't realizing you were trying to compare earth's own gravity here. Ken saw that right off, I see.

Well, Sam, you are wrong, big time.

-Richard

25. Originally Posted by Ken G

At the end of the day, though, there is still something interesting in Sam5's observation-- for both the traveller and the stay-at-home twin, a 1g acceleration is a relevant number somehow. But it is only for the traveller that this acceleration has any significant effect.

I'm musing and pondering on that right now..... I need to take my Saturday night bath, and I'll ponder on that there.

Some intial thoughts. It's not the "force we feel" that determines clock rate, but the *potential* (the metric is actually a tensor potential, and a tensor potential is a lot more than a simple scalar, or even vector potential, but in the weak field limit, the g_00 of this potential is the simple scalar Newtonian potential plus 1. In Schwarzchild, it is exactly the Newtonian inverse square potential +1, but this does not hold in the general case of non-spherical masses and everything else).

Rindler is a very different potential than 1/r^2. The clock rate increases without limit the higher you go, while with inverse square, it simply increases to a limiting value of 1. So, sitting there accelerating at 1g, resisting Earth's rough Schwarzchild field, your clock rate is not that much slower than someone 100 LY away. In (1g) Rindler, there would be a big difference in clock rates over 100 LY. {EDIT: I wrote AU, but LY makes the difference very dramatic between just about reasonable acceleration}

So we can chaulk this up to the difference between "tidal gravity" and the coordinate transform psuedo gravity of Rindler.

It's not the force you feel, but the darn metric, and that can make 1g be very different depending on what sort of space-time you're in.

-Richard

26. Order of Kilopi
Join Date
Nov 2003
Posts
6,197
Originally Posted by Ken G
He is of course incorrect in asserting that "no clock can appear to move fast" relative to yours,
Huh? I never said that. Both observers see the other observer's clock "move fast" and they see themselves as not moving.

But he is saying that Earth does have a 1g gravity, and that this somehow induces the same effect on clocks that the 1g acceleration of the traveller does.
Yes, if we are going to talk about "acceleration" as being the cause of just one of the clocks really slowing down, since Grant has provided us with a definition of 1g for the "traveler" and of course we have 1g for the "earth" twin. So we have SR, not GR.

I think part of the problem is that Sam5 is forgetting the traveler must also escape Earth's gravity if one is going to include that in the problem.
Lol, you are trying to squeeze in some extra acceleration. Sounds like you are going for a GR solution to an SR paradox.

At the end of the day, though, there is still something interesting in Sam5's observation-- for both the traveller and the stay-at-home twin, a 1g acceleration is a relevant number somehow. But it is only for the traveller that this acceleration has any significant effect.
In SR, both are relative travelers. There are no "absolute" travelers in SR. There is no single "traveler" in SR. There are two relative travelers. See the SR statement:

”The introduction of a ‘luminiferous ether’ will prove to be superfluous inasmuch as the view here to be developed will not require an ‘absolutely stationary space’ provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place.”

And also:

“Let us take a system of co-ordinates in which the equations of Newtonian mechanics hold good. In order to render our presentation more precise and to distinguish this system of co-ordinates verbally from others which will be introduced hereafter, we call it the ‘stationary system’.”

In other words, in the theory, both systems are viewed by their own observers as being “stationary.” There is no absolute space or absolute motion. All motion is relative in the theory. That means both relatively moving observers are equally correct in calling their own system the “stationary” one.

The thought experiments about the "earth" and human "twins" were added later to make the "earth" seem like something that is really big, solid, and "stationary". But there is no "earth" or "stationary" point in space in SR theory. The motion is only "relative".

That is somewhat interesting to muse on.
That's why I brought it up. I didn't bring it up to cause any trouble. I'm a mainstream kind of guy myself.

Ironically, it is precisely because the stay-at-home twin is accelerated in the gravity field, and not inertial, that the consequences of that acceleration are negligible when compared to the traveller.
There actually is no "stay at home" twin in SR theory. Both "observers" stay with their own clocks in their own "systems". There is no earth. They always see the other "system" as the one that "moves". But they don't see their own "system" as moving. So both are "stay at home" in their own system.

But I'm not sure if the issue is that some things are cancelling out for the stay-at-home twin, or if it is that we must also consider that the traveler is escaping through the Earth's gravity as well, as I said before. Maybe both ways of looking at it are relevant, but the bottom line is, gravity as weak as the Earth's does not alter time in any remotely significant way, whereas a 1g acceleration into space for 5 years certainly does a spectacular twist on time.
Actually, I think that a rocket acceleration of only 1g off the surface of the earth would cause the rocket to just hover over the earth but not move away from the earth. It would be a big waste of fuel.

27. Originally Posted by publius
So we can chaulk this up to the difference between "tidal gravity" and the coordinate transform psuedo gravity of Rindler.

It's not the force you feel, but the darn metric, and that can make 1g be very different depending on what sort of space-time you're in.
Ah, thank you for really bringing this right into focus. You are right that we typically imagine the Rindler metric (or its equivalent SR application of a continuous Lorentz transform) when we think of 1g acceleration, so it tends to bias us (Sam5 included here) into imagining that all 1g accelerations are created equal. That is precisely the error that Sam5 is making, and that I was not seeing in those clear terms.

28. Originally Posted by Sam5
Huh? I never said that. Both observers see the other observer's clock "move fast" and they see themselves as not moving.
I really think you want to reconsider that post, both in regard to your own posts so far on this thread (#14: "no clock is observed to speed up in SR theory"?), and the concept of time dilation.

Yes, if we are going to talk about "acceleration" as being the cause of just one of the clocks really slowing down, since Grant has provided us with a definition of 1g for the "traveler" and of course we have 1g for the "earth" twin. So we have SR, not GR.
I'm at a complete loss as to how you can both assert that there's a 1g acceleration for us here on Earth, and that this is not a GR statement. How can you possibly believe those two claims are compatible?

In SR, both are relative travelers. There are no "absolute" travelers in SR. There is no single "traveler" in SR. There are two relative travelers.
Can we at least agree that one is in a rocket capable of 1g acceleration, and the other is pulling weeds in their garden? If we can, then I will define the rocketeer as the "traveler", and why this is a real difference will emerge shortly. As for there not being an absolute reference frame, I think you may assume that all posters on this thread are perfectly well aware of this and that this has nothing whatever to do with the error in your claims.
But there is no "earth" or "stationary" point in space in SR theory. The motion is only "relative".
Yes, but acceleration is not relative in SR-- as you yourself prescribed, the "stationary" frames must be ones in which Newton's laws hold good! Were you not paying attention to your own quoted material?

That's why I brought it up. I didn't bring it up to cause any trouble. I'm a mainstream kind of guy myself.
And I must thank you, because it has allowed publius to explain to me (and perhaps others) exactly where you went astray, in terms that I found enlightening. That is no doubt the very purpose of this forum-- stir something up, and see what gets learned!

There actually is no "stay at home" twin in SR theory.
As per my above statements, yes there is. The "stay at home" twin is the one for whom Newton's physics will work fine, and the traveller is the one for whom they will not, without including "ficticious" gravity that is not in Newton's theory (and is part of what is meant to be excluded in the statement "Newtonian mechanics hold good.")
Actually, I think that a rocket acceleration of only 1g off the surface of the earth would cause the rocket to just hover over the earth but not move away from the earth. It would be a big waste of fuel.
This is not the conventional usage of a 1g acceleration, though it is the general usage of a phrase like "pulling 1g". It's not always obvious which meaning is intended, but in this case, it is.

29. Order of Kilopi
Join Date
Nov 2003
Posts
6,197
Originally Posted by Ken G
I really think you want to reconsider that post, both in regard to your own posts so far on this thread (#14: "no clock is observed to speed up in SR theory"?), and the concept of time dilation.
I'm talking about a speed up in tick rate, not a speed up in motion. No clock in SR is seen to tick faster than normal. They are only seen to slow down their tick rates with increasing relative velocity or return to a normal tick rate as the relative velocity slows down. No clock in SR is seen to or said to tick faster than normal. And both relatively moving observers see each other's clocks ticking more slowly during the relative motion. I'm talking about the 1905 SR theory.

30. Order of Kilopi
Join Date
Nov 2003
Posts
6,197
Originally Posted by publius
Aha. I didn't notice this. You're comparing earth's *gravity* of 1g with the accelerating twin's 1g. I didn't even see that. By "earth's acceleration", I was thinking of the coordinate acceleration the turn-around twin would see in his own frame, as earth slowed, stopped, and started moving back toward him.

I wasn't realizing you were trying to compare earth's own gravity here. Ken saw that right off, I see.

Well, Sam, you are wrong, big time.

-Richard

Richard, you are the one who has been saying that acceleration due to motion causes a clock rate slowdown, You have said that's what causes the "moving clock" to slow down its tick rate. And we all know that an atomic clock in an increased gravity field, a strong gravity field, experiences a tick rate slowdown. So you are saying there is an equivalence between acceleration due to motion and acceleration due to gravity, as far as the tick rates of atomic clocks are concerned.
Last edited by Sam5; 2006-Dec-17 at 05:45 AM.

Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•