Can someone explain Einstein's relativity theory?

[OsiriS^]

I've read a piece on his theory and I'm having a little difficulty understanding it. I've used the famous E = MC^2 in calculations before but I want to have more understanding of the theory behind it.

Any info would be great.

 

[dextercioby]

I've read a piece on his theory and I'm having a little difficulty understanding it. I've used the famous E = MC^2 in calculations before but I want to have more understanding of the theory behind it.

Any info would be great.

I'm afraid it cannot be explained in one post from a frum...I would advise you to read the famous book:"A brief History of time" by Stephen Hawking.
You'll understand many things.

Daniel.

 

[marlon]

I've read a piece on his theory and I'm having a little difficulty understanding it. I've used the famous E = MC^2 in calculations before but I want to have more understanding of the theory behind it.

Any info would be great.

Check out the text "string theory part 1" on page three in my journal. There is a short paragraphe on General Relativity. Ofcourse it is very introductory, but it sets the tone. Firther on i suggest you check the info on the web entry for further reliable references. The answer to your question cannot be given in a few posts. First question should be : "why the name RELATIVITY theory". What does relativity mean. The answer is in my text...

regards
marlon

here is the link https://www.physicsforums.com/journal.php?s=&action=view&journalid=13790&perpage=10&page=3

 

[theriddler876]

hmnnnn well einstein said something like " you sit next to a girl for an hour and it seems like a mintue, you sit on a hot stove for a minute, and it seems like an hour, that's relativity"

 

[NeutronStar]

Einstein based his special theory of relativity on two postulates:

The First Postulate

The laws of physics are the same in all inertial systems¹. There are no preferred inertial systems, or reference frames². When inertial reference-frames move with constant speed with respect to one another the laws of physics will be the same in both reference-frames.

The Second Postulate

The phenomenon of light is correctly described by Maxwell's equations. In other words, all observers will measure³ the speed of light in a vacuum to be a constant value c in all inertial systems.

Conclusions to the Special Theory of Relativity

Once given the above two postulates as premises, the theory of special theory of relativity pretty much falls out from normal intuitive reasoning. I won't go into the actual conclusions, other than to say that once you've accepted these postulates the rest of Relativity is fairly easy⁴ to deduce and accept.

Footnotes:

1. Inertial systems are reference frames that move uniformly and without rotation.

2. A reference frame is just another name for an inertial system.

3. Note that this postulate does not actually say that the speed of light is c in all reference frames, but rather it only requires that the speed of light is measured as c in all reference frames. This is a technicality that most physicists never seem to want to talk about. This is because for physicists, "to measure is to be". In other words, as far as physicists are concerned what you see is what you get, or only observables matter. They typically aren't interested in discussing the ontological implications of fundamental measurements.

4. While the conclusions are fairly easy to deduce, the postulates are not without contradiction with respect to these conclusions. For example, Postulate One states that the laws of physics are the same in all inertial frames. Yet, one of the conclusions of special relativity is that time passes at different rates in different inertial frames thus contradicting the first postulate that states that the laws of physics are the same in all inertial frames. The twin brother's paradox proves this inconsistency between the theory and its postulates. The twin that ages less may have undergone an acceleration, however, his or her clock continues to run more slowly relative to the non-accelerated sibling even after the acceleration has ceased. Therefore, the twin who has undergone a change in an inertial frame has also undergone a change in his or her fundamental laws of physics (i.e. time passes at a different rate for that twin than for the first twin) So the theory does seem to be in direct contradiction with its very own postulates.

Personal Comment

It is not my intention to discredit Special Relativity in any way by stating the above facts. Special Relativity has indeed panned out quite nicely as a mathematical framework making unprecedented confirmed predictions. The mere fact that the theory itself seems to be in direct contradiction with one of the postulates from which is was deduced does not in any way prove, or even suggest, that the theory is incorrect (i.e. the postulates themselves are not really a part of the theory, they were merely stated as a basis for deducing the theory. Therefore the theory is not actually in contradiction with itself.) It does, however, cause one to ponder how a postulate can lead intuitively to a conclusion which denies the very postulate that gave birth to it.

 

[dextercioby]

Einstein based his special theory of relativity on two postulates:

The First Postulate

The laws of physics are the same in all inertial systems¹. There are no preferred inertial systems, or reference frames². When inertial reference-frames move with constant speed with respect to one another the laws of physics will be the same in both reference-frames.

The Second Postulate

The phenomenon of light is correctly described by Maxwell's equations. In other words, all observers will measure³ the speed of light in a vacuum to be a constant value c in all inertial systems.

Conclusions to the Special Theory of Relativity

Once given the above two postulates as premises, the theory of special theory of relativity pretty much falls out from normal intuitive reasoning. I won't go into the actual conclusions, other than to say that once you've accepted these postulates the rest of Relativity is fairly easy⁴ to deduce and accept.

Footnotes:

1. Inertial systems are reference frames that move uniformly and without rotation.

2. A reference frame is just another name for an inertial system.

3. Note that this postulate does not actually say that the speed of light is c in all reference frames, but rather it only requires that the speed of light is measured as c in all reference frames. This is a technicality that most physicists never seem to want to talk about. This is because for physicists, "to measure is to be". In other words, as far as physicists are concerned what you see is what you get, or only observables matter. They typically aren't interested in discussing the ontological implications of fundamental measurements.

4. While the conclusions are fairly easy to deduce, the postulates are not without contradiction with respect to these conclusions. For example, Postulate One states that the laws of physics are the same in all inertial frames. Yet, one of the conclusions of special relativity is that time passes at different rates in different inertial frames thus contradicting the first postulate that states that the laws of physics are the same in all inertial frames. The twin brother's paradox proves this inconsistency between the theory and its postulates. The twin that ages less may have undergone an acceleration, however, his or her clock continues to run more slowly relative to the non-accelerated sibling even after the acceleration has ceased. Therefore, the twin who has undergone a change in an inertial frame has also undergone a change in his or her fundamental laws of physics (i.e. time passes at a different rate for that twin than for the first twin) So the theory does seem to be in direct contradiction with its very own postulates.

Personal Comment

It is not my intention to discredit Special Relativity in any way by stating the above facts. Special Relativity has indeed panned out quite nicely as a mathematical framework making unprecedented confirmed predictions. The mere fact that the theory itself seems to be in direct contradiction with one of the postulates from which is was deduced does not in any way prove, or even suggest, that the theory is incorrect (i.e. the postulates themselves are not really a part of the theory, they were merely stated as a basis for deducing the theory. Therefore the theory is not actually in contradiction with itself.) It does, however, cause one to ponder how a postulate can lead intuitively to a conclusion which denies the very postulate that gave birth to it.

Where did u get the "fotnotes"?Check this one out:

2. A reference frame is just another name for an inertial system.

I THINK THAT WIPES OUT 10 YEARS OF MR EINSTEIN'S WORK...And did a hella of a favor to QFT...


Daniel.

 

[Doc Al]

4. While the conclusions are fairly easy to deduce, the postulates are not without contradiction with respect to these conclusions. For example, Postulate One states that the laws of physics are the same in all inertial frames. Yet, one of the conclusions of special relativity is that time passes at different rates in different inertial frames thus contradicting the first postulate that states that the laws of physics are the same in all inertial frames. The twin brother's paradox proves this inconsistency between the theory and its postulates. The twin that ages less may have undergone an acceleration, however, his or her clock continues to run more slowly relative to the non-accelerated sibling even after the acceleration has ceased. Therefore, the twin who has undergone a change in an inertial frame has also undergone a change in his or her fundamental laws of physics (i.e. time passes at a different rate for that twin than for the first twin) So the theory does seem to be in direct contradiction with its very own postulates.

This is nonsense.

 

[Galileo]

For example, Postulate One states that the laws of physics are the same in all inertial frames. Yet, one of the conclusions of special relativity is that time passes at different rates in different inertial frames thus contradicting the first postulate that states that the laws of physics are the same in all inertial frames.

No, time passes at a different rate in an inertial frame that is moving with a constant velocity with respect to your inertial frame.
The first postulate simply says that if you view the situation from the other reference frame, the physical description is exactly identical.

 

[JesseM]

Einstein based his special theory of relativity on two postulates:

The First Postulate

The laws of physics are the same in all inertial systems¹. There are no preferred inertial systems, or reference frames². When inertial reference-frames move with constant speed with respect to one another the laws of physics will be the same in both reference-frames.

The Second Postulate

The phenomenon of light is correctly described by Maxwell's equations. In other words, all observers will measure³ the speed of light in a vacuum to be a constant value c in all inertial systems.

Conclusions to the Special Theory of Relativity

Once given the above two postulates as premises, the theory of special theory of relativity pretty much falls out from normal intuitive reasoning. I won't go into the actual conclusions, other than to say that once you've accepted these postulates the rest of Relativity is fairly easy⁴ to deduce and accept.

Footnotes:

1. Inertial systems are reference frames that move uniformly and without rotation.

2. A reference frame is just another name for an inertial system.

3. Note that this postulate does not actually say that the speed of light is c in all reference frames, but rather it only requires that the speed of light is measured as c in all reference frames. This is a technicality that most physicists never seem to want to talk about. This is because for physicists, "to measure is to be". In other words, as far as physicists are concerned what you see is what you get, or only observables matter. They typically aren't interested in discussing the ontological implications of fundamental measurements.

4. While the conclusions are fairly easy to deduce, the postulates are not without contradiction with respect to these conclusions. For example, Postulate One states that the laws of physics are the same in all inertial frames. Yet, one of the conclusions of special relativity is that time passes at different rates in different inertial frames thus contradicting the first postulate that states that the laws of physics are the same in all inertial frames.

No. If you are traveling at velocity v in my frame, I will see your clock slowed by a factor $$1/(1 - v^2/c^2)$$; in your frame, you will see me traveling at velocity v, and you will also see my clock slowed by a factor of $$1/(1 - v^2/c^2)$$. So in each frame, a clock traveling at v is slowed by the same factor, thus the laws concerning time dilation work the same way in both frames.

The twin brother's paradox proves this inconsistency between the theory and its postulates. The twin that ages less may have undergone an acceleration, however, his or her clock continues to run more slowly relative to the non-accelerated sibling even after the acceleration has ceased.

No, in the traveling twin's frame it doesn't run more slowly once the acceleration has ceased. After the acceleration has ceased, and the twin is returning to Earth at constant velocity, the traveling twin's clock is running slow in the earth-twin's frame, and the earth-twin's clock is running slow in the traveling twin's frame. In both frames, though, you can predict that the traveling twin's clock will be behind the earth-twin's clock when they meet; in the traveling twin's frame, this is because at the moment the acceleration stopped, his clock was way behind the earth-twin's clock at the same moment, so that even though his clock is "catching up" to the Earth twin's clock (since the earth-twin's clock is ticking more slowly in his frame), it still will be behind the earth-twin's clock at the moment their paths cross. In the earth-twin's frame the analysis would be different--at the moment the acceleration stopped, he would also say that the traveling twin's clock is behind his own, but by a smaller factor; but since the traveling twin's clock ticks more slowly in his frame, the difference between their clocks would increase rather than decrease. But things will work out so that each frame will have exactly the same prediction about how much the traveling twin's clock will be behind the earth-twin's clock at the moment they meet.

 

[s3nn0c]

In my opinion, one of the best popular explanations of the theory of relativity was written by Brian Greene in his "The fabric of the cosmos" book.

 

[JesseM]

Where did u get the "fotnotes"?Check this one out:

2. A reference frame is just another name for an inertial system.

I THINK THAT WIPES OUT 10 YEARS OF MR EINSTEIN'S WORK...And did a hella of a favor to QFT...


Daniel.

Actually, this footnote, along with the rest of his post up to footnote 4, is correct. The statement that the laws of physics work the same way in all reference frames is only true if you assume that we're only talking about the reference frames of observers who are moving inertially (ie moving at constant velocity relative to other inertial observers, not accelerating).

 

[dextercioby]

Actually, this footnote, along with the rest of his post up to footnote 4, is correct. The statement that the laws of physics work the same way in all reference frames is only true if you assume that we're only talking about the reference frames of observers who are moving inertially (ie moving at constant velocity relative to other inertial observers, not accelerating).

Nope,notice the degree of generality.He said "reference frame=inertial frame" ,but he didn't say the key words:"in SR".

Again,i'm convinced thatwas balloney.Either he invented the footnotes or took'em from a crack-pot source...


Daniel.

 

[JesseM]

Nope,notice the degree of generality.He said "reference frame=inertial frame" ,but he didn't say the key words:"in SR".

Even in SR, you can have accelerated reference frames, you just can't assume the laws of physics work the same way in these frames. But in context, I think that footnote wasn't talking about SR in general, it was just qualifying a statement he made in the first postulate, namely "There are no preferred inertial systems, or reference frames". So in that context, the footnote need not have meant "whenever a physicist uses the words 'reference frame' they always just mean an inertial system"--it could have just meant "when I use the word 'reference frame' in my statement of the first postulate, I'm just using it to mean an inertial system".

 

[NeutronStar]

--it could have just meant "when I use the word 'reference frame' in my statement of the first postulate, I'm just using it to mean an inertial system".

That's precisely what I meant to convey in that footnote. Sorry if it was taken to imply some kind of blanket definition for the term. That wasn't my intent. I probably should have added something like "when speaking in terms of SR, the term reference frame is generally taken to mean Inertial system.

Sorry for the confusion. Ironically I put in the footnote to avoid confusion and it seems to have backfired.

I probably should have also clarified that my original post refers only to SR. I assumed that since GR requires additional postulates, such as the equivalency of acceleration and a gravitational field, it wouldn't be necessary to mention the distinction.

 

[ohwilleke]

I've read a piece on his theory and I'm having a little difficulty understanding it. I've used the famous E = MC^2 in calculations before but I want to have more understanding of the theory behind it.

Any info would be great.

Special relativity is much, much easier conceptually than general relativity. In special relativity you are basically talking about a small number of equations (the Lorentz transformations), in ordinary every day algebra like the rest of physics, that insure consistency in cases where there are high velocity motion while maintaining the speed of light in a vacuum as a constant.

General relativity is much deeper. To be crude to the point of being inaccurate but heuristically useful, general relativity explains gravity by explaining how mass-energy and its pressure and motion (customarily broken out into ten numerical quantities) affect the curvature of space. General relativity does so using "tensors" (which are basically matrixes from linear algebra), most notably the "Ricci Tensor" and the "Stress Energy" tensor (which contains the ten numbers describing the mass alluded to above).

Tensor math is good, because it through the form of the equations make it obvious that there can be no preferred reference frame, but to actually calculate them without major assumptions concerning how you choose your reference frame and symmetry is extremely difficult.

Among the major qualitative predictions of general relativity are that:

(1) E=mc^2
(2) Light is deflected by gravity.
(3) Gravity is a quadradic function of velocity. A first order term depends on mass (with various other assumptions in place), a second order term depends on velocity, and a third order term depends on the square of velocity. This creates effects such as "frame dragging" and an altered expected precession of Mercury.
(4) Gravity is capable of being so great that light cannot escape, creating a black hole.
(5) The equations of GR can be generalized to the universe as a whole with certain simplifying assumptions. This generalization leads to our notions of how much matter, dark matter, and dark energy is necessary to have a universe consistent with data on the Hubble constant, other data and the equations of general relativity. The fact that there appears to be "dark energy" in the universe can be explained through a disputed term in the equations of general relativity called the cosmological constant, which has little or no impact on events at the galactic scale and below.

A nice primer is here: http://math.ucr.edu/home/baez/einstein/einstein.html

The real short version of GR (from the Baez primer):

We promised to state Einstein's equation in plain English, but have not done so yet. Here it is:

Given a small ball of freely falling test particles initially at rest with respect to each other, the rate at which it begins to shrink is proportional to its volume times: the energy density at the center of the ball, plus the pressure in the direction at that point, plus the pressure in the direction, plus the pressure in the direction.

The reader who already knows general relativity may be somewhat skeptical of this claim. After all, Einstein's equation in its usual tensorial form is really a bunch of equations: the left and right sides of equation (1) are matrices. It is hard to believe that the single equation (2) captures all that information. It does, though, as long as we include one bit of fine print: in order to get the full content of the Einstein equation from equation (2), we must consider small balls with all possible initial velocities -- i.e., balls that begin at rest in all possible local inertial reference frames.

Before we begin, it is worth noting an even simpler formulation of Einstein's equation that applies when the pressure is the same in every direction:

Given a small ball of freely falling test particles initially at rest with respect to each other, the rate at which it begins to shrink is proportional to its volume times: the energy density at the center of the ball plus three times the pressure at that point.

Equation (8) here: http://math.ucr.edu/home/baez/einstein/node10.html is the Einstein Equation.

 

[NeutronStar]

No, in the traveling twin's frame it doesn't run more slowly once the acceleration has ceased.

I don't see how that can be correct?

Say we have three twins, A, B, and C.

Twin A stays on earth. Twin B and C both take off in rockets (separate rockets).

To keep things as simple as possible imagine that both rockets take off in the same general direction and accelerate to something close to the speed of light side-by-side. They both cease to accelerate at precisely the same time, still being side-by-side. Then they travel along for some extended period of time until twin B decides to decelerate and then re-accelerated to return back to earth.

When twin B gets back to Earth he or she will be younger than twin A by say, x amount of time.

In the meantime, twin C is still just drifting along at close to the speed of light at a constant velocity. Finally, after some arbitrary time twin C decides to decelerate and then re-accelerate back toward earth. (Note that in this experiment both rocket pilots experience precisely the same amount of acceleration)

Now when twin C returns to Earth he or she will be younger than twin A by y amount of time.

If acceleration was the only deciding factor for time dilation then x=y. In other words, twin B and C are precisely the same age. I don’t believe that this is what SR predicts. I believe that it predicts that B will even be younger than C. In other words, x will not be equal to y.

Therefore, time dilation must have been occurring during the non-accelerated part of the trip. This must necessarily be the case since twin B and C both experienced precisely the same amount of acceleration.

Is this right or wrong? I'm open to criticism?

 

[JesseM]

I don't see how that can be correct?

Say we have three twins, A, B, and C.

Twin A stays on earth. Twin B and C both take off in rockets (separate rockets).

To keep things as simple as possible imagine that both rockets take off in the same general direction and accelerate to something close to the speed of light side-by-side. They both cease to accelerate at precisely the same time, still being side-by-side. Then they travel along for some extended period of time until twin B decides to decelerate and then re-accelerated to return back to earth.

When twin B gets back to Earth he or she will be younger than twin A by say, x amount of time.

In the meantime, twin C is still just drifting along at close to the speed of light at a constant velocity. Finally, after some arbitrary time twin C decides to decelerate and then re-accelerate back toward earth. (Note that in this experiment both rocket pilots experience precisely the same amount of acceleration)

Now when twin C returns to Earth he or she will be younger than twin A by y amount of time.

If acceleration was the only deciding factor for time dilation then x=y. In other words, twin B and C are precisely the same age. I don’t believe that this is what SR predicts. I believe that it predicts that B will even be younger than C. In other words, x will not be equal to y.

Therefore, time dilation must have been occurring during the non-accelerated part of the trip. This must necessarily be the case since twin B and C both experienced precisely the same amount of acceleration.

Is this right or wrong? I'm open to criticism?

I didn't say that time dilation only occurs during acceleration--in fact I said that in the traveling twin's frame, the clock of the Earth twin is running slow (this would be true in both the outbound frame and the inbound frame).

The thing to keep in mind is that different reference frames define simultaneity differently. If I am moving away from the Earth at constant velocity, and my clock was synchronized with clocks on Earth when I left, then in my reference frame the Earth clocks are all running slow, so my clock will keep getting further and further ahead of what the Earth clock reads "at the same moment" in my reference frame. But then if I accelerate so I am now traveling towards the earth, I will have a new reference frame, and this reference frame defines simultaneity differently than my old one, so that now the Earth clock is far ahead of what my clock reads "at the same moment". The earth-clocks will still be ticking slower than my clock in this reference frame, so my clock will be catching up to the Earth clock, but the Earth clock was far enough ahead when I first entered this frame that when I arrive at Earth my clock will still be behind.

If you find this hard to understand, we could try plugging some numbers into your scenario above to show exactly how this works, and why the time difference between the clocks of A and B will be smaller than the time difference between the clocks of A and C when they reunite.

 

[Janus]

I don't see how that can be correct?

Say we have three twins, A, B, and C.

Twin A stays on earth. Twin B and C both take off in rockets (separate rockets).

To keep things as simple as possible imagine that both rockets take off in the same general direction and accelerate to something close to the speed of light side-by-side. They both cease to accelerate at precisely the same time, still being side-by-side. Then they travel along for some extended period of time until twin B decides to decelerate and then re-accelerated to return back to earth.

When twin B gets back to Earth he or she will be younger than twin A by say, x amount of time.

In the meantime, twin C is still just drifting along at close to the speed of light at a constant velocity. Finally, after some arbitrary time twin C decides to decelerate and then re-accelerate back toward earth. (Note that in this experiment both rocket pilots experience precisely the same amount of acceleration)

Now when twin C returns to Earth he or she will be younger than twin A by y amount of time.

If acceleration was the only deciding factor for time dilation then x=y. In other words, twin B and C are precisely the same age. I don’t believe that this is what SR predicts. I believe that it predicts that B will even be younger than C. In other words, x will not be equal to y.

Therefore, time dilation must have been occurring during the non-accelerated part of the trip. This must necessarily be the case since twin B and C both experienced precisely the same amount of acceleration.

Is this right or wrong? I'm open to criticism?

The problem you are having is that you aren't taking the Relativity of Simultaneity into account. Clocks that are simultaneous as measured in one frame will not be simultaneous in another frame that is moving with respect to the first, if the clocks are separated along the axis of relative motion. So, for instance, if there were clocks at Earth, the point where B turns around and the point that C turns around that are sychronized in the Earth frame, according to B and C, the clocks at the turn around points will read later
than the Earth clock while B & C are moving away from the Earth. Since the distance of separation affects how much the Clocks are out of sync, the clock at C's turn around will read later than the one at B's turnaround.

When B turns around he changes frames of reference. (now heading towards Earth). In this new reference frame it is the Earth clock that reads the later time. Thus, according to B, the Earth clock now reads later than his own (Before he made the change of frame the Eart clock read Earlier than his own). When he returns to Earth he will find that the Earth clock will still read more than his own. (even though the Earth clock ran slower than his own during th return trip). IOW, his Earth twin will be older than him.

When C turns around, he is much further from Earth, thus from his new frame, the Earth clock reads much later. Again, when he returns to Earth, he will find that much more time has passed on Earth for him than it did for B, who made the shorter trip.

 

[jdavel]

Neut,


"While the conclusions are fairly easy to deduce, the postulates are not without contradiction with respect to these conclusions."

Nonsense. The theory IS the postulates, and there are no contradictions among them and the conclusions to which they lead.

Consider another possibility: You don't know what you're talking about!

 

[NeutronStar]

I didn't say that time dilation only occurs during acceleration--

I'm sorry for misunderstanding you. I thought you said,…

No, in the traveling twin's frame it doesn't run more slowly once the acceleration has ceased.

That sounded to me like you were saying that time dilation ceases to occur once the acceleration has ceased

If you find this hard to understand, we could try plugging some numbers into your scenario above to show exactly how this works, and why the time difference between the clocks of A and B will be smaller than the time difference between the clocks of A and C when they reunite.

I never said that I find it hard to understand. Nor did I ever say that I don’t believe that it happens. I've taken modern physics and I've gone through all the calculations and the Minkowski diagrams. All I'm saying is that time does indeed flow differently in different inertial frames. I believe that Relativity actually bears this out.

The problem you are having is that you aren't taking the Relativity of Simultaneity into account.

I never even mentioned simultaneity. Neither was that concept important to the experiment that I spoke of. Never once did I talk about what might be happening "simultaneously" between the twins during the experiment.

"While the conclusions are fairly easy to deduce, the postulates are not without contradiction with respect to these conclusions."

Nonsense. The theory IS the postulates, and there are no contradictions among them and the conclusions to which they lead.

Consider another possibility: You don't know what you're talking about!

Actually you're right. Technically the postulate merely states that the laws of physics are the same in all inertial frames. And I suppose that is true.

What isn't the same is the actual physics.

In other words, imagine that two observers are in frame A. They both age by the same amount. One of the observers goes off into frame B. When they return to frame A they did not age as much as the observer that remained in frame A. Therefore the only possible conclusion is that time flows more slowly in frame B.

If time flows more slowly in frame B then the physics of frame be is different from that from A. However, the laws of physics may remain the same within that frame. So I suppose it isn't a contradiction of the postulate after all.

I kind of fell into the trap of thinking that the laws of physics and the actual physics were basically the same thing. They're not.

So you're right. Technically, Special Relativity doesn't contradict it's postulates after all.

 

[JesseM]

I'm sorry for misunderstanding you. I thought you said,…

No, in the traveling twin's frame it doesn't run more slowly once the acceleration has ceased.

That sounded to me like you were saying that time dilation ceases to occur once the acceleration has ceased

I was responding to your statement "The twin that ages less may have undergone an acceleration, however, his or her clock continues to run more slowly relative to the non-accelerated sibling even after the acceleration has ceased." The traveling twin's clock doesn't run more slowly in his own frame--the earth twin's clock runs slower, because he is the one who is moving in this frame. Again, time dilation works the same way in every frame--any clock moving at velocity v in a given frame ticks more slowly by a factor of $$\sqrt{1 - v^2/c^2}$$.

The problem is you are talking as if "time dilation" is something objective, when in fact it never is--whether a clock shows time dilation depends on which frame you're in.

I never said that I find it hard to understand. Nor did I ever say that I don’t believe that it happens. I've taken modern physics and I've gone through all the calculations and the Minkowski diagrams. All I'm saying is that time does indeed flow differently in different inertial frames. I believe that Relativity actually bears this out.

It depends what you mean by "time flows differently". Of course it flows differently in the sense that each observer sees the other one's clock slowing down. But it doesn't flow differently in the sense that there is some objective truth about which clock is "really" ticking more slowly, and your discussion of the twin paradox suggested you thought otherwise.

I never even mentioned simultaneity. Neither was that concept important to the experiment that I spoke of. Never once did I talk about what might be happening "simultaneously" between the twins during the experiment.

I didn't say you had mentioned it, but I brought it up because I think it is quite important in understanding the experiment--it shows why, even though the traveling twin sees the Earth's clock ticking slower as he returns, he still predicts that his clock will be behind the Earth clock when he arrives, because at the moment he began the trip back, the Earth clock was far ahead of his clock in his frame, so even though his clock is ticking faster the whole trip back it still won't have caught up by the time he returns. And the phrase "at the moment he began the trip back" in that last sentence depends on understanding how he defines simultaneity in his frame.

Actually you're right. Technically the postulate merely states that the laws of physics are the same in all inertial frames. And I suppose that is true.

What isn't the same is the actual physics.

In other words, imagine that two observers are in frame A. They both age by the same amount. One of the observers goes off into frame B. When they return to frame A they did not age as much as the observer that remained in frame A. Therefore the only possible conclusion is that time flows more slowly in frame B.

No, you could analyze this problem equally well from the perspective of frame B, and from that perspective time is flowing more slowly in frame A. You would get the same predictions either way--that's a direct consequence of the fact that the laws of physics must be the same in all inertial frames (I don't know what you think you mean when you say the laws of physics could be the same in all frames and yet 'actual' physics could be different--that's obvious nonsense).

 

[Janus]

I never even mentioned simultaneity. Neither was that concept important to the experiment that I spoke of. Never once did I talk about what might be happening "simultaneously" between the twins during the experiment.

No, you didn't mention it, and that's the problem. Taking the Relativity of Simultaneity into account isimportant to understanding what happens according to twins B and C.

 

[jdavel]

JesseM

"...even though the traveling twin sees the Earth's clock ticking slower as he returns...

Careful there! As the traveller returns, the doppler effect causes him to see the Earth's clock running faster than his, not slower.

 

[NeutronStar]

The problem is you are talking as if "time dilation" is something objective, when in fact it never is--.

Excuse me?

The fact that the returned twin is younger than the original twin isn't objective?

Yes, I most certainly hold that "time dilation" is objective. Please correct me if I'm wrong but isn't that also the conclusion of Special Relativity?

Time dilation really does occur. That is to say that it objectively occurs. It's not just some optical illusion during the trip. The returning twin really is younger objectively upon return. It's a "real" objective phenomenon.

So yes, I'm absolutely talking as if "time dilation" is something objective.

 

[JesseM]

JesseM

"...even though the traveling twin sees the Earth's clock ticking slower as he returns...

Careful there! As the traveller returns, the doppler effect causes him to see the Earth's clock running faster than his, not slower.

OK, I was using "sees" to mean what events are simultaneous in his reference frame, not the delayed image he gets from light signals.

 

[JesseM]

Excuse me?

The fact that the returned twin is younger than the original twin isn't objective?

Sure, but the returned twin did not stick to a single reference frame.

Yes, I most certainly hold that "time dilation" is objective. Please correct me if I'm wrong but isn't that also the conclusion of Special Relativity?

It's not objective in the sense that as long as two observers are traveling at constant velocity, there is no objective truth about whose clock is running slower. If you calculate things in A's frame then B's clock is running slower, while if you calculate things in B's frame then A's clock is running slower. Regardless of which frame you use, you'll get the same predictions about the readings on their respective clocks at the moment their paths cross.

Time dilation really does occur. That is to say that it objectively occurs. It's not just some optical illusion during the trip. The returning twin really is younger objectively upon return. It's a "real" objective phenomenon.

Yes, of course the twin's clock will show less time elapsed when he returns. But during either the outbound leg or the inbound leg, when he was moving inertially, there is no objective truth about whether his clock or the Earth's clock was running slower for the duration of that leg of the trip. You can calculate the results of the entire experiment from any of the three inertial reference frames--the Earth's rest, the outbound rest frame, or the inbound rest frame, and in each case you will get the same prediction about what each twin's clock read when the traveling twin returned to earth. For example, in the outbound rest frame, you'd calculate that before the twin accelerated it was the earth-twin's clock that was running slower, but after the twin accelerates he will now be moving even faster than the Earth in this frame, so his clock will run slower than the earth-twin's clock (which is still running slow in this frame) during the second leg of the trip. In the inbound reference frame the opposite would be true--the earth-twin's clock would run at the same slow rate for the whole time, while the traveling twin's clock would run even slower during the first leg of the trip, then it'd run at normal speed after accelerating.

 

[NeutronStar]

Sure, but the returned twin did not stick to a single reference frame.

I'm afraid that I don't understand what that as to do with the price of bananas. I never claimed that the returned twin stuck to a single reference frame. I did, however, maintain that twin A remained in a single reference frame, and that is very important to my argument.

It's not objective in the sense that as long as two observers are traveling at constant velocity, there is no objective truth about whose clock is running slower.

But I just proved that there is objective truth to this. My experiment proves it beyond a shadow of a doubt. Assuming my experiment holds water with respect to the calculations of SR, but I'm pretty sure that it does.

If you calculate things in A's frame then B's clock is running slower, while if you calculate things in B's frame then A's clock is running slower.

I'm not the slightest bit worried about calculating things in different frames. My experiment does not require intermediate results or predictions. I'm only interested in the beginning and the end results of the experiment, and I can measure all of that in frame A.

Yes, of course the twin's clock will show less time elapsed when he returns. But during either the outbound leg or the inbound leg, when he was moving inertially, there is no objective truth about whether his clock or the Earth's clock was running slower for the duration of that leg of the trip.

Again, I'm not the slightest bit interested about what happens during any particular leg of any trip. The sole conclusion of my experiment is to say nothing more than time must have been dilated during the non-accelerating part of the trip. That's the only conclusion that I'm interested in, and my experiment proves that.

Also, I want to point out again that I'm not claiming that time doesn't dilate during acceleration. I'm really not concerned about that. I'm only interested in showing that time must have been dilated during the non-accelerating part of the trip That's really all I need to show to claim that physics is behaving differently in different inertial frames even though the laws of physics may appear to be unaffected within that frame.

I'm totally confident that my conclusions are correct and in agreement with SR.

 

[JesseM]

I'm afraid that I don't understand what that as to do with the price of bananas. I never claimed that the returned twin stuck to a single reference frame.

And I didn't say you had. The point is that for any two inertial reference frames, there is no objective truth about whose clocks are running slower.

But I just proved that there is objective truth to this. My experiment proves it beyond a shadow of a doubt.

No, your logic makes no sense. There are three frames here, and there is no reason to say that time "objectively" runs slower in anyone of them.

I'm not the slightest bit worried about calculating things in different frames. My experiment does not require intermediate results or predictions. I'm only interested in the beginning and the end results of the experiment, and I can measure all of that in frame A.

But the beginning and end results can also be measured from frame B or frame C, and you'll get the same predictions. Any physical situation can be analyzed from any frame you choose, without your ever having to switch to a different frame.

gain, I'm not the slightest bit interested about what happens during any particular leg of any trip. The sole conclusion of my experiment is to say nothing more than time must have been dilated during the non-accelerating part of the trip. That's the only conclusion that I'm interested in, and my experiment proves that.

But it doesn't prove that time was objectively running slower in anyone inertial reference frame, so it doesn't conflict with any of the postulates of relativity as you argued earlier. There is still a complete symmetry between the perspectives of the three different inertial reference frames--each frame says that the clocks in the other frames are running slower than its own clocks.

Also, I want to point out again that I'm not claiming that time doesn't dilate during acceleration. I'm really not concerned about that. I'm only interested in showing that time must have been dilated during the non-accelerating part of the trip That's really all I need to show to claim that physics is behaving differently in different inertial frames even though the laws of physics may appear to be unaffected within that frame.

Which frame, in particular, do you think is behaving differently? Do you think the inbound frame is behaving differently than the Earth frame, for example? I can assure you that no matter which you pick, there is no difference, each frame says that a clock at rest in that frame ticks at the normal rate, and clocks in another frame moving at velocity v relative to it are time-dilated by a factor of $$\sqrt{1 - v^2/c^2}$$.

 

[Janus]

I'm not the slightest bit worried about calculating things in different frames. My experiment does not require intermediate results or predictions. I'm only interested in the beginning and the end results of the experiment, and I can measure all of that in frame A.

SR.

Again, that's a problem. If you really want to grasp what SR is about, you need to consider what happens according to all the frames.

 

[NeutronStar]

Again, that's a problem. If you really want to grasp what SR is about, you need to consider what happens according to all the frames.

What ever gave you the idea that I'm trying to grasp what SR is all about? I already know what SR is all about. I'm simply pointing out the fact that time must necessarily flow at different rates for different inertial frames. I don't think that SR denies this, on the contrary, the twin brothers paradox confirms it! If this wasn't true then time dilation would indeed just be an illusion and not at all objective. But it is objective.

Forget about all the gory details. Look at it this way. In a lab there are two black boxes. One is marked A and the other marked B. You put objects into box A and bring them back out again and there is no apparent change. Put them into box B and bring them back out again and apparently they haven't aged as much. What's the conclusion? The physics in box B is acting differently from the physics in box A.

It's pretty simple and straight-forward if you ask me.

Now send physicists into each of these boxes to perform experiments. When they come back out they confirm that all of the laws of physics are valid in both boxes. However, even though the laws of physics are the same in box B it should be quite obvious that the actual physics behaves differently relative to the physics that occurs in box A.

So physics is not the same in all inertial frames even though the laws of physics may appear to be the same within the frames individually. That's the only conclusion possible.

Nothing I have said here conflicts with SR in any way. At first glance it appears to conflict with the first postulate, but I was wrong about that because the first postulate merely says that the laws of physics are the same in all inertial systems. It doesn't make any claim that the actual physics is the same. In fact, the transformation equations of SR show quantitatively that the actual physics isn't the same in different inertial frames!

My mistake earlier was that I was confusing the laws of physics with actual physics. The first postulate of relativity doesn't say that the actual physics is the same in all inertial frames, it simply says that the laws must be the same. And that indeed is true. So I need to retract my statement that SR is in contradiction with one of its postulates. That's wasn't technically correct. :yuck:

 

[JesseM]

What ever gave you the idea that I'm trying to grasp what SR is all about? I already know what SR is all about. I'm simply pointing out the fact that time must necessarily flow at different rates for different inertial frames. I don't think that SR denies this, on the contrary, the twin brothers paradox confirms it! If this wasn't true then time dilation would indeed just be an illusion and not at all objective. But it is objective.

Time does flow differently in different inertial frames, in the sense that within each frame, clocks in the other frame are running slower. However, there is no objective truth about whose clocks are really running slower. Do you disagree with this last part?

 

[russ_watters]

What ever gave you the idea that I'm trying to grasp what SR is all about? I already know what SR is all about.

No offense, but the part you keep saying you want to ignore is the key part of the theory - if you don't grasp that by ignoring it you aren't addressing SR, you don't grasp SR.

I'm simply pointing out the fact that time must necessarily flow at different rates for different inertial frames. I don't think that SR denies this, on the contrary, the twin brothers paradox confirms it! If this wasn't true then time dilation would indeed just be an illusion and not at all objective. But it is objective.

The point of the twins paradox is it confirms the fact that SR is symmetrical - the twins don't experience the same passage of time because their paths are not symmetrical.

The fact that either twin can be picked, randomly, to accelerate to meet the other twin and the results will be the same (ie, the twin chosen to experience the acceleration will be the one showing less time at the end) shows that SR is, indeed, consistent and the laws of the universe are universal.

 

[NeutronStar]

Time does flow differently in different inertial frames, in the sense that within each frame, clocks in the other frame are running slower. However, there is no objective truth about whose clocks are really running slower. Do you disagree with this last part?

Yes, I disagree with your statement; "...there is no objective truth about whose clocks are really running slower".

I think it's quite obvious when the twins get back together that the younger twin was the one whose clock ran slower. There can be no denial of this since that is the twin that is younger upon return. What else would cause this effect if it wasn't objectively true? Really.

 

[RandallB]

Forget about all the gory details. Look at it this way. In a lab there are two black boxes. One is marked A and the other marked B. You put objects into box A and bring them back out again and there is no apparent change. Put them into box B and bring them back out again and apparently they haven't aged as much. What's the conclusion? The physics in box B is acting differently from the physics in box A.

It's pretty simple and straight-forward if you ask me.

Sure that is simple; but don't leave out the most important little detail.
When you opened box B, the twin Clock you put in there WAS NOT THERE!
It is now miles, Km's or Light years away and still speeding away from your lab.
At best you might see a series of clocks chasing after it. You will of course see time directly viewed on those clocks as running faster than your lab clock. Yes I said FASTER - but don't concern yourself with that until your ready to work with the words synchronized and simultaneity.
The only way you can see the original twin clock again is if someone somewhere moves it over to box C. So when you open box C (yes it's clocks zipping by in the other direction appear to be running fast), when you can extract the returning twin clock it will be well behind the lab clock because the rate of time in both box B and C is slow as measured by your lab clock.

Now to confirm that speed makes all the difference put an extra lab clock in box D where it will travel after the clock that continues in box B at 3 times the speed in box B to catch up with it. (Note: vB + vB + vB = 3vB is not correct) When it catches up it will be even more behind the time on the traveling clock than the returning clock was behind the lab clock.

This is all true only because SR and "the laws of physics and the actual physics" is the same in every reference frame.

Note: The time dilation your looking for has nothing to do with doppler effect or acceleration. When working SR it is best to use 'Black Hole' accelerations that only take a very short time to get to the speed you want. In GR the time change on the accelerated clock is ZERO for just a second, which you can discard. thus you can consider the time in the frame your measuring based only on speed.

Work those out and let us know if ready to look at simultaneity.

 

[NeutronStar]

The fact that either twin can be picked, randomly, to accelerate to meet the other twin and the results will be the same.

I'm sorry russ, but what you've said here simply isn't true. If you pick the twin in frame A to accelerate back to meet the other twin, then twin A would need to undergo more acceleration, and travel at a greater speed than the other twin in order to catch up to the other twin.

So there is an absolute difference in which twin you pick to accelerate.

It's not totally symmetric as you claim.