Time dilation, relativistic mass and fuel consumption

[Janus]

Thank you.

I'm really sorry but I cannot still understand where I'm going wrong. Both detectors are in the same frame of reference so I don't even understand what it has to do with the synchronization of clocks. Both clocks would be affected by the same time dilation because they both are on the same ship (or, box) and should read the same time. Or, perhaps, the clock/detector situated toward the direction of motion, i.e. right detector, gets affected by time dilation more than the left detector. The ship is moving from left to right.

If two persons are located on the same ship moving at uniform speed, their watches would tell the same time. Yes, for accuracy, they could use atomic clock watches.

As I said earlier, if it was any other wave requiring a medium for propagation, then both detectors should register the same time of arrival. But light doesn't require a medium.

You still aren't getting the gist of the relativity of simultaneity.
You have three clocks in a row with one halfway between the other two. It emits a light pulse which is reflected back to it.
For these clocks and anyone at rest with respect to them, this is what occurs.

(while there appears to be a slight delay before the light pulse is reflected, that is just because you don't see the reflected pulses until they clear the clocks.)
Here we assume that the clocks are all synchronized in this frame. The first pulse leaves the middle clock when all the clocks read the same strikes the two clocks simultaneously wile all the clocks read the same, and is reflected back to return to the central clock while all three clocks read the same.

Now the same clocks, and same light pulses, with the difference that the clock have a relative motion with respect to the frame we are examining the events from.

The first light pulse leaves the center clock when it reads the same time as in the first animation. The clocks and the distance between them is length contracted and all three clocks are time dilated by the same amount. The left clock runs into the pulse first, and then it catches up with the right clock. The light leaves the central clock when it reads the same as it did in the first animation. Both the left and right clocks show the same readings as they did in the first animation when the light reaches them. However, these means that they do not at any time read the same time at the same time. The reflected pulses leave the left clock first, but still arrive at the central clock at the same time (and the central clock's reading of the time of this event agrees with the first animation.)
Thus for this frame the three clocks are never in sync. They tick at the same rate, but the left clock always leads the central clock and the right clocks always lags.

It doesn't matter whether you consider the three clocks as moving or the observer in the second animation.
If you were to give the observer in the second animation an identical set up of clocks, he would determine that his clock were all in sync. However, an observer at rest with respect to the first set of clocks would say that the other observer's clocks as being out of sync.

This is not a matter of one of the observer's view be the "right" one, while the other view is "illusion" either. Both observer's version of "reality" is equally valid.

 

[PainterGuy]

Thank you very much for your help, time and patience.

I'm still struggling with it but it looks like I could at least see a part of the problem what I'm having trouble with. I'll return to it later.

I have another related question. I'm going to use a variation of my earlier statement from post #64.

Suppose there is a rectangular ship moving straight in space at constant velocity of say 150000000 m/s relative to another inertial frame of reference. In other words, it's an inertial frame of reference for anyone inside the box. The length of ship is 600000000 meters (two times the distance traveled by light in one second).

Suppose the width and height are both 300000000 meters. Please note that the speed of light in vacuum is taken to be 300000000 m/s.

Suppose a laser pulse of an infinitesimal duration is produced widthwise or heightwise in both directions by a source which is located in the middle. Please have a look on the attachment. In my opinion, if it was an absolute rest inertial frame of reference, both pulses would hit the marks labelled 'x'.

Would the pulse hit the mark x or y? I think it should hit the mark labelled y because the ship is moving toward the right and as the pulse takes some time to get to the mark, the mark would have moved. I hope you get the point.

If you say that the pulse should hit mark x then wouldn't it imply that the speed of ship add a rightward speed component to the light?

Thanks a lot!

PS: Edited after @PeterDonis pointed out the the error.

 

[PeterDonis]

if it was an absolute rest inertial frame of reference

There is no such thing. You are not going to get anywhere if you keep trying to use concepts that simply aren't valid in relativity. You can reason to valid conclusions from invalid premises.

Would the pulse hit the mark x or y?

x

If you say that the pulse should hit mark y

I assume you mean "if you say that the pulse should hit mark x" here.

wouldn't it imply that the speed of ship add a rightward speed component to the light?

In the frame in which the ship as a whole is moving to the right, the light pulses also will move to the right, as well as up or down. But this doesn't change the speed of the light pulses; it only changes their direction. Velocity vectors don't add in relativity the way they do in Newtonian physics.

You are taking a lot of time and effort over very basic SR problems that are treated in many SR textbooks. Have you tried to work through a basic SR textbook, such as Taylor & Wheeler's Spacetime Physics? If you haven't, you might want to try it.

Also, the setup you are describing in your latest post is basically a light clock with the light pulses moving perpendicular to the direction of relative motion of the clock and the observer. (All you would need to do would be to put a mirror at point x in the ship to reflect the light pulse back.) You should be able to find plenty of resources online that analyze light clocks (including a number of previous threads here on PF).

 

[PainterGuy]

Thank you!

So, the motion of ship does change the direction of light pulses.

There is no such thing. You are not going to get anywhere if you keep trying to use concepts that simply aren't valid in relativity. You can reason to valid conclusions from invalid premises.

Sorry, really poor way of communicating but I did say in my earlier statement that "I know what I'm saying is wrong because there doesn't exist any absolute rest frame of reference".

You are taking a lot of time and effort over very basic SR problems that are treated in many SR textbooks. Have you tried to work through a basic SR textbook, such as Taylor & Wheeler's Spacetime Physics? If you haven't, you might want to try it.

Well, you could classify me as a silly person but that's fine. :)

I remember that you recommended this book earlier as well in this thread and @PeroK recommended Morin's book. In the past I did try two books on this subject and after reading a chapter or two it didn't make any sense to me. I will let you the know titles of those books later. Those were paperbacks. Many of sources I have been to say the things similarly but they use different wording and diagrams. For example, my earlier related query about detectors and arrival of pulses was more about the one-way speed of light which could not calculated and I only came to know about this "one-way speed of light" today and am still reading about it. But I could not phrase it better and is was considered to be more about the synchronization of clock.

Thanks a lot!

 

[PeterDonis]

I did say in my earlier statement that "I know what I'm saying is wrong because there doesn't exist any absolute rest frame of reference".

You said it, but you didn't abide by it in your reasoning in post #72.

If you really do understand that there is no absolute frame of reference, then you need to actually use that information in your reasoning. That means that whenever you find yourself reasoning on the basis of some particular frame being "absolute", you should stop that chain of reasoning right there. Then go back, start again from the beginning, and force yourself to not reason as if any frame is absolute.

 

[SiennaTheGr8]

I second the recommendations that OP consult a textbook. Taylor & Wheeler is my top choice, though Morin is particularly strong with the relativity of simultaneity: https://scholar.harvard.edu/files/david-morin/files/cmchap11.pdf

 

[Janus]

Thank you!

So, the motion of ship does change the direction of light pulses.
Sorry, really poor way of communicating but I did say in my earlier statement that "I know what I'm saying is wrong because there doesn't exist any absolute rest frame of reference".

You said that, but then defaulted to using a absolute rest frame in your analysis. For example, you say:

Suppose there is a rectangular ship moving straight in space at constant velocity of say 150000000 m/s relative to another inertial frame of reference.

The word "relative" is important here, Because it make no difference if you swap the roles of the inertial frames. In other words, the above statement is exactly equivalent to:
"Suppose there is an inertial frame of reference moving straight in space at constant velocity of say 150000000 m/s relative to a rectangular ship ."

The results do not depend on which of the two we consider as "moving".

The pulse hits the "x" in both cases.

As for:

If you say that the pulse should hit mark x then wouldn't it imply that the speed of ship add a rightward speed component to the light?

While it true, that from this "other" frame of reference the light has to travel a longer diagonal path to hit the "x", its speed along that path remains c.
So, for example, let's say that the "height" of the box is 0.149896229 m, and there is a mirror at "x". For someone at rest with respect to the box, the pulse travels straight up to x and reflects straight back, taking 1 nanosecond for the entire trip. For the inertial frame with a 0.5c relative velocity to the box, the pulse has to travel on a diagonal for both legs at c, and takes ~1.155 nanoseconds to return to the emitter.
If we were to increase the relative velocity between the two to 0.866c, you get a 2 to 1 ratio, like this:

Here we give both frames their own light clock. The light clock that is at rest with the animation frame ticks twice while the "moving" clock ticks once. The red numbers tick off nanoseconds. The expanding circle shows how both pulses travel at c with respect to the frame of reference.
If we switch frames to one in which the "moving" clock is at rest with respect to the animation, it would be the one ticking off 2 nanoseconds for every 1 nanosecond ticked off by the other clock. Note that we change nothing concerning the motion of the light clocks themselves, we just switched to view where the clock shown moving to the right stays at the middle of the animation, and the other clock moves off to the left.

 

[Mister T]

So, the motion of ship does change the direction of light pulses.

Let's take an example at speeds low enough that the Newtonian approximation can be used. I'm in an airplane cruising at an altitude of 30 000 ft moving at a speed of 500 mi/h relative to the ground. I take a small ball out of my pocket and toss it upward so that it goes vertically upward and then returns to my hand. To me the ball moves along a straight line.

Suppose you are on a far-away mountain peak with a super telescope. You have it pointed at the airplane and you can see me through the window. You will see the ball follow a parabolic trajectory, not a straight line, because in the fraction of a second that it takes the ball to go up and back down the airplane will have moved a significant distance in horizontal line.

So which is true? The path of the ball follows a straight line or it follows a parabola? You see, the answer depends on how you view the path. It is not correct to say that the ball travels in a parabola because it's moving, the reason being that to a people aboard the airplane the ball is not affected by the airplane's motion.

 

[jbriggs444]

So, the motion of ship does change the direction of light pulses.

It may be worth looking at the manner in which the light pulses are generated. How are they aimed? What mechanism is used to ensure that the pulses are launched "vertically" rather than at an angle?

One standard way of doing this is to put a flashlight at the bottom end of a narrow blackened tube. All frames can agree that the tube is vertical. But not all frames will agree that light pulses that emerge from the tube were traveling vertically while in the tube. The tube may be regarded as moving while the pulses are rising. Or it may be regarded as stationary. The description depends on the frame you choose.

Same for a moving machine gun. Everyone will agree that the gun is pointed vertically upward. But not everyone will agree that the bullets are moving vertically within the barrel. The barrel may be regarded as moving while the bullets are being fired. Or it may be regarded as being stationary. Pick a frame, pick a description.

Edit: To go a step further, it will turn out that the mechanism is irrelevant. No matter what mechanism one uses, the predicted results will be consistent no matter what frame is used to make the prediction. It is just that the "flashlight and blackened tube" is a particularly simple mechanism for producing a collimated beam. Simple and easy to analyze.

 

[PainterGuy]

Thank you very much, everyone. I'm grateful of your help and patience.

In the past I did try two books on this subject and after reading a chapter or two it didn't make any sense to me. I will let you the know titles of those books later. Those were paperbacks.

Actually there are three books: Simply Einstein : Relativity Demystified by Richard Wolfson, Relativity in Illustrations by Jacob Schwartz, The Einstein Theory of Relativity by Lillian Lieber. To be honest, as I said earlier, I tried to read a chapter or two but it didn't work for me. It might be that at that time I didn't ask anyone the related questions from the book.

I feel that this is the first time that the special relativity is making some sense to me.

@Janus, thank you for your post.

In other words, from an observer's perspective aboard the ship, the light only takes 0.5 seconds to get to mark x because the person in the ship only sees light traveling the distance of 15x10^7 m or '0.5c' sec.

From outside the ship a stationary observer would say that the light should take 0.70712 seconds because it has the distance of 212132034.4 meter to cover. Therefore, the stationary observer concludes that the ship's clock is running slow.

In the frame in which the ship as a whole is moving to the right, the light pulses also will move to the right, as well as up or down. But this doesn't change the speed of the light pulses; it only changes their direction. Velocity vectors don't add in relativity the way they do in Newtonian physics.

Continuing from post #72.

Would it be wrong to say that the motion of ship adds a horizontal component (in direction of motion) to the speed of light from reference frame of stationary observer outside the ship? Repeating it: Suppose there is a rectangular ship moving straight in space at constant velocity of say 150000000 m/s relative to another inertial frame of reference. The length of ship is 600000000 meters (two times the distance traveled by light in one second). If light pulse is produced horizontally in direction of ship's motion then for a stationary observer outside the ship sees the pulse covering distance of 'c' sec +'0.5c' sec='1.5c' sec (m/s * sec = m) but for stationary observer it takes 1.5 seconds and stationary observer would also notice that the ship observer has the clock running slow therefore for the same distance of '1.5c' sec, the ship clock ticks only 1 second and hence the ship observer would observe the pulse moving at the speed of light.

I have a related question about Michelson Morley experiment.

Why is the length contraction really necessary to explain Michelson Morley experiment result? I understand that Lorentz came up with the length contraction hypothesis to save the aether theory. (I have some questions about Lorenz aether theory but it'd better to start a separate thread for that.) The problem with me is that I don't think that the experiment needs any length contraction or any relativity related explanation; simple Newtonian explanation should work fine when no aether is assumed.

In the experiment the following times were calculated where 'c' is speed of light, 'v' is orbiting speed of Earth around the sun, and 'd' is length of both arms.

t_total_1 for longitudinal arm = 2dc/(c^2 - v^2)
t_total_2 for transverse arm = 2d/sqrt(c^2 - v^2)

From the equation, it could be seen that t_total_1 would be greater than t_total_2.

Earth is an inertial frame of reference therefore if "v" is removed, we are left with t_total_1=t_total_2. In my view, the aether was the only reason "v" was introduced in the equation. It was assumed that the distance along the direction of longitudinal mirror would take larger time because

Helpful link:
youtube.com/watch?v=JKoz28zSzqw

 

[PeterDonis]

Would it be wrong to say that the motion of ship adds a horizontal component (in direction of motion) to the speed of light from reference frame of stationary observer outside the ship?

Not the way you mean. As I said before, velocities don't add in SR the way they do in Newtonian physics. The speed of light is always c, in every frame. The observer sees the light beam inside the ship moving at c in his frame. He sees it moving in a different direction, in his frame, than the ship observer does in the ship frame. But both of them see the speed of the light as the same: c.

 

[A.T.]

The problem with me is that I don't think that the experiment needs any length contraction or any relativity related explanation; simple Newtonian explanation should work fine when no aether is assumed.

The Michelson–Morley experiment is consistent with the Emission Theory, but that theory is disproven by other observations:

https://en.wikipedia.org/wiki/Emission_theory

 

[Janus]

Thank you very much, everyone. I'm grateful of your help and patience.
Actually there are three books: Simply Einstein : Relativity Demystified by Richard Wolfson, Relativity in Illustrations by Jacob Schwartz, The Einstein Theory of Relativity by Lillian Lieber. To be honest, as I said earlier, I tried to read a chapter or two but it didn't work for me. It might be that at that time I didn't ask anyone the related questions from the book.

I feel that this is the first time that the special relativity is making some sense to me.

@Janus, thank you for your post.

In other words, from an observer's perspective aboard the ship, the light only takes 0.5 seconds to get to mark x because the person in the ship only sees light traveling the distance of 15x10^7 m or '0.5c' sec.

From outside the ship a stationary observer would say that the light should take 0.70712 seconds because it has the distance of 212132034.4 meter to cover. Therefore, the stationary observer concludes that the ship's clock is running slow.

View attachment 257691Continuing from post #72.

Would it be wrong to say that the motion of ship adds a horizontal component (in direction of motion) to the speed of light from reference frame of stationary observer outside the ship? Repeating it: Suppose there is a rectangular ship moving straight in space at constant velocity of say 150000000 m/s relative to another inertial frame of reference. The length of ship is 600000000 meters (two times the distance traveled by light in one second). If light pulse is produced horizontally in direction of ship's motion then for a stationary observer outside the ship sees the pulse covering distance of 'c' sec +'0.5c' sec='1.5c' sec (m/s * sec = m) but for stationary observer it takes 1.5 seconds and stationary observer would also notice that the ship observer has the clock running slow therefore for the same distance of '1.5c' sec, the ship clock ticks only 1 second and hence the ship observer would observe the pulse moving at the speed of light.

View attachment 257698

The pulse would take 4 sec according to the "stationary" observer to go from left to right end, if we assume no length contraction of the ship. The pulse moves at c, the right end has a "head start" of 2 light sec, and move to the right at 0.5c
It would take 1 1/3 sec for the pulse to go back from right end to return to the source, total round trip time 5 1/3 second. For someone in the box, the pulse takes 2 sec each way, for a round trip time of 4 sec.
At 0.5 c, the time dilation would have a clock in the box tick 0.866 as fast according to stationary observer, 0.866 times 5.33 = 4.62 seconds, not 4 seconds. The box observer and "stationary observer would disagree as to how much time ticked away for the Box clock.

If we go back to the light clock example and add a second light clock that is parallel to the line of travel, then you get this without length contraction. The horizontal pulse doesn't even reach the mirror before the vertical pulse has made a round trip. But if I am traveling with that rightward moving clock, I would measure both pulses taking equal times to make their round trips.

But if we add length contraction, then according to the "stationary" observer, the box is only 1.732 light sec long. The pulse moving to the right takes 3.464 sec to reach the right end, and going the other way ~1.1547 sec. Total round trip time is ~4.619 sec. It still takes 4 secs round trip according to the the box observer.
0.866 times 4.619 = 4 sec (allowing for rounding). Box and "stationary" observer agree as to how much time ticks off for the box clock.
Adding length contraction to our light clock set up gives:

If we place clocks at the both ends of the box, and synchronized according to the box frame, if the pulse leaves the left end when the clock reads 12:00:00, it will reach the right end when the clock there( and thus both clocks) reads 12:00:02
The stationary observer has to agree to this: light leaves left clock when it reads 12:00:00 and arrives at right clock when that clock reads 12:00:00
But we also know that it takes 3.464 sec for the pulse to traverse from end to end of the box according to the stationary observer. Due to time dilation he will measure both clocks as ticking off 3 sec during that time. thus for the right clock to read 12:00:02 when the pulse arrives, the right clock had to read 11:59:59 when the pulse left the other end. According the stationary observer, the right clock lags 1 sec behind the left clock, while according to the box observer, the two clocks always read the same.

 

[PainterGuy]

Not the way you mean. As I said before, velocities don't add in SR the way they do in Newtonian physics.

Did I add the velocities the Newtonian way? I'm asking you this for confirmation because I myself am not sure if I added the velocities.

I wanted to know that if some pages of a book are freely available on Google Books, would it be okay if I make a PDF by using some of those available pages and attach it here? Could you please let me know?

The Michelson–Morley experiment is consistent with the Emission Theory, but that theory is disproven by other observations:

https://en.wikipedia.org/wiki/Emission_theory

Thank you for mentioning it. Yes, it has been disproven. The following is an excerpt.

Emission Theories
A very different hypothesis was put forward by Walter Ritz and others. They proposed that the speed of light is c relative to the source of the light instead of relative to the ether. This is admittedly strange behavior for waves; it is more characteristic of particles. However, Ritz managed to construct an "emission theory" in which electromagnetic waves behave in this peculiar fashion. Einstein himself, before he developed special relativ- ity, apparently leaned toward the emission theory.

An emission theory readily explains the result of the Michelson- Morley experiment. Inasmuch as the light source in the experiment was always at rest with respect to the interferometer, the speed of light is always the same and no change in the fringe pattern is to be expected as the interferometer is rotated.

The emission theory has been directly disproven in an experiment by T. Alvager et al. that detected the high-frequency radiation (gamma rays) emitted in the decay of rapidly moving neutral particles called pions. If the speed of light were c relative to the source, then (according to Galilean relativity) the laboratory speed of a gamma ray emitted in the direction of the pion's velocity should be greater than c while that of a gamma ray emitted in the opposite direction should be less than c. No such difference in the speeds was observed.
Source: Understanding Relativity by Leo Sartori, https://books.google.com/books?id=9aMwDwAAQBAJ , page #41

I'm still not able to find any answer to the query about Michelson Morley experiment from post #80. Repeating the main part: Why is the length contraction really necessary to explain Michelson Morley experiment result? I understand that Lorentz came up with the length contraction hypothesis to save the aether theory. The problem with me is that I don't think that the experiment needs any length contraction or any relativity related explanation; simple Newtonian explanation should work fine when no aether is assumed. Light for both arms travel the same distance even when Earth's motion around its orbit is considered, therefore the split light from both arms should reach at the same time.

I think the following excerpt from Wikipedia article on Michelson Morley experiment is saying the same thing. The apparatus and Earth are comoving frames of reference therefore the null result is a natural outcome but if there was a relative motion between the apparatus and lab/earth then one needs to use length contraction/time dilation.

"This allows a more elegant and intuitive explanation of the Michelson–Morley null result. In a comoving frame the null result is self-evident, since the apparatus can be considered as at rest in accordance with the relativity principle, thus the beam travel times are the same. In a frame relative to which the apparatus is moving, the same reasoning applies as described above in "Length contraction and Lorentz transformation", except the word "aether" has to be replaced by "non-comoving inertial frame" - https://en.wikipedia.org/wiki/Michelson–Morley_experiment#Special_relativity

If we place clocks at the both ends of the box, and synchronized according to the box frame, if the pulse leaves the left end when the clock reads 12:00:00, it will reach the right end when the clock there( and thus both clocks) reads 12:00:02
The stationary observer has to agree to this: light leaves left clock when it reads 12:00:00 and arrives at right clock when that clock reads 12:00:00
But we also know that it takes 3.464 sec for the pulse to traverse from end to end of the box according to the stationary observer. Due to time dilation he will measure both clocks as ticking off 3 sec during that time. thus for the right clock to read 12:00:02 when the pulse arrives, the right clock had to read 11:59:59 when the pulse left the other end. According the stationary observer, the right clock lags 1 sec behind the left clock, while according to the box observer, the two clocks always read the same.

I'm grateful of you. I'm sorry but I needed to confirm something. Did you mean to say "arrives at right clock when that clock reads 12:00:02"?

According to the stationary observer outside the ship, "it takes 3.464 sec". It's 3 seconds from 11:59:59 to 12:00:02 so how do we account for the remaining "0.464" portion of second?

Thank you!

 

[A.T.]

Why is the length contraction really necessary to explain Michelson Morley experiment result?

As already explained, that experiment alone doesn't imply relativity. But you need a theory that explains all experiments.

 

[PeterDonis]

if some pages of a book are freely available on Google Books, would it be okay if I make a PDF by using some of those available pages and attach it here?

The fact that you can view the pages on Google Books does not mean you can freely copy them. The best way to provide a reference is using a link. It's also helpful to include the name of the book and the chapter/section/pages you are referencing.

 

[PeterDonis]

Did I add the velocities the Newtonian way?

You added velocities in a way that led you to say that the speed of the light emitted inside the ship, in the frame in which the ship is moving, is larger than c. I don't know whether you would call that the "Newtonian" way or not, but any way that doesn't tell you that the speed of light is c in every frame is the wrong way.

 

[PeterDonis]

Why is the length contraction really necessary to explain Michelson Morley experiment result?

Because without it the result would have been different. More generally, because in any result in which anyone of length contraction, time dilation, and relativity of simultaneity are involved, all three of them are going to be necessary to explain the result. Those three things always go together in SR, because they are all inevitable consequences of the Lorentz transformations.

 

[PeterDonis]

The problem with me is that I don't think that the experiment needs any length contraction or any relativity related explanation; simple Newtonian explanation should work fine when no aether is assumed.

No, it won't, because in Newtonian physics the speed of the light will vary with the motion of the source for the same reason that the speed of a bullet fired from a rifle is different in a frame in which the rifle is moving than in a frame in which the rifle is at rest. You don't need light to be a wave and invoke a wave medium; you can consider light the way Newton did, to be made of tiny particles, and still derive a prediction from Newtonian physics for the Michelson-Morley experiment that is contradicted by the actual results.

 

[Ibix]

I'm still not able to find any answer to the query about Michelson Morley experiment from post #80. Repeating the main part: Why is the length contraction really necessary to explain Michelson Morley experiment result?

It isn't. However, any theory that can explain Michelson-Morley cannot explain at least one other experimental result - except relativity, which explains every experiment we've ever done. For example, naive Newtonian physics explains Michelson-Morley by letting the speed of light vary. But that's inconsistent with light being a wave in a medium - unless you propose something like emission theory, which then fails experimental test as your quote shows.

You can't consider the experiments individually. Each one eliminates some theories, but it's only when you look at them all together that you know all the tests a theory must meet.

 

[Orodruin]

No, it isn't. You don't measure energy on a balance. To measure the energy corresponding to the rest mass of something, you would have to find a way to convert that rest mass into energy, i.e., something that can do work. A mass sitting at rest can't do any work.

By this argumentation, an atomic clock and a mechanical clock measure physically different things. There are many measuring devices that we accept as measuring things that are based on intrinsic theory assumptions and relations from theory. By measuring the resistance to acceleration in the rest frame, you are measuring the energy in the rest frame intrinsically. This is the essence of the mass-energy equivalence - the inertia in the rest frame is the energy in the rest frame.

 

[Janus]

Did I add the velocities the Newtonian way? I'm asking you this for confirmation because I myself am not sure if I added the velocities.

I wanted to know that if some pages of a book are freely available on Google Books, would it be okay if I make a PDF by using some of those available pages and attach it here? Could you please let me know?
Thank you for mentioning it. Yes, it has been disproven. The following is an excerpt.

Emission Theories
A very different hypothesis was put forward by Walter Ritz and others. They proposed that the speed of light is c relative to the source of the light instead of relative to the ether. This is admittedly strange behavior for waves; it is more characteristic of particles. However, Ritz managed to construct an "emission theory" in which electromagnetic waves behave in this peculiar fashion. Einstein himself, before he developed special relativ- ity, apparently leaned toward the emission theory.

An emission theory readily explains the result of the Michelson- Morley experiment. Inasmuch as the light source in the experiment was always at rest with respect to the interferometer, the speed of light is always the same and no change in the fringe pattern is to be expected as the interferometer is rotated.

The emission theory has been directly disproven in an experiment by T. Alvager et al. that detected the high-frequency radiation (gamma rays) emitted in the decay of rapidly moving neutral particles called pions. If the speed of light were c relative to the source, then (according to Galilean relativity) the laboratory speed of a gamma ray emitted in the direction of the pion's velocity should be greater than c while that of a gamma ray emitted in the opposite direction should be less than c. No such difference in the speeds was observed.
Source: Understanding Relativity by Leo Sartori, https://books.google.com/books?id=9aMwDwAAQBAJ , page #41

I'm still not able to find any answer to the query about Michelson Morley experiment from post #80. Repeating the main part: Why is the length contraction really necessary to explain Michelson Morley experiment result? I understand that Lorentz came up with the length contraction hypothesis to save the aether theory. The problem with me is that I don't think that the experiment needs any length contraction or any relativity related explanation; simple Newtonian explanation should work fine when no aether is assumed. Light for both arms travel the same distance even when Earth's motion around its orbit is considered, therefore the split light from both arms should reach at the same time.

I think the following excerpt from Wikipedia article on Michelson Morley experiment is saying the same thing. The apparatus and Earth are comoving frames of reference therefore the null result is a natural outcome but if there was a relative motion between the apparatus and lab/earth then one needs to use length contraction/time dilation.

"This allows a more elegant and intuitive explanation of the Michelson–Morley null result. In a comoving frame the null result is self-evident, since the apparatus can be considered as at rest in accordance with the relativity principle, thus the beam travel times are the same. In a frame relative to which the apparatus is moving, the same reasoning applies as described above in "Length contraction and Lorentz transformation", except the word "aether" has to be replaced by "non-comoving inertial frame" - https://en.wikipedia.org/wiki/Michelson–Morley_experiment#Special_relativity
I'm grateful of you. I'm sorry but I needed to confirm something. Did you mean to say "arrives at right clock when that clock reads 12:00:02"?

Yes, that was a typo and should have been 12:00:02

According to the stationary observer outside the ship, "it takes 3.464 sec". It's 3 seconds from 11:59:59 to 12:00:02 so how do we account for the remaining "0.464" portion of second?

Thank you!

That 3.364 sec is according to the "stationary" observer's clock. the 3 sec is time ticked off by the Box clocks according to the same observer. Since the clocks in the box run slow by a factor of 0.866 according to him, due to time dilation, in 3.364 secs by his clock, he would record the box clocks as advancing by 3.364 x 0.866 = 3 sec.

Ergo, if by his clock the pulse leave the left end of the box when his own clock reads 12:00:00, then it arrives at the right end of the clock when his clock reads 12:00:03.364. In that same time, according to him, the left clock in the box goes from reading 12:00:00 to reading 12:00:03, and the right clock goes from reading 11:59:59 to 12:00:02.

 

[PainterGuy]

The problem with me is that I don't think that the experiment needs any length contraction or any relativity related explanation; simple Newtonian explanation should work fine when no aether is assumed. Light for both arms travel the same distance even when Earth's motion around its orbit is considered, therefore the split light from both arms should reach at the same time.

Because without it the result would have been different. More generally, because in any result in which anyone of length contraction, time dilation, and relativity of simultaneity are involved, all three of them are going to be necessary to explain the result. Those three things always go together in SR, because they are all inevitable consequences of the Lorentz transformations.

I'm sorry that I missed a very important point about the constancy of speed of light. I should have mentioned it. Lorentz came up with the length contraction hypothesis to explain the null result of Michelson Morley experiment and in the historical context he was trying to save or modify the aether theory where Lorentz had assumed a completely stationary aether and a medium of propagation for light and all other matter, including earth, moving relative to the stationary aether. (Note: Fresnel had assumed an almost stationary aether with partial drag, and Stokes had assumed aether with complete drag). For instance, if it had been assumed that light has a constant speed and doesn't require a medium then at least Michelson Morley experiment could have been explained without any length contraction hypothesis. But I do agree that they needed a complete theory to explain the results of all related experiments.

From today's perspective, one only needs to assume that the speed of light is constant, and both Earth and apparatus are co-moving frames of reference and stationary with respect to each to explain the null result.

By the way, since we are at it, "The more important fundamental laws and facts of physical reality have all been discovered and they are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote ... Our future discoveries must be looked for in the 6th place of decimals." - Albert Michelson, 1899I think this is the time I get back to discussion about main question in post #64 which temporarily ended with @Janus post #71.

Point Arena, California, and Washington D.C., DC, lie almost along a straight line. Suppose there is a huge laser tower somewhere in Kansas. Both Point Arena and Washington D.C. are equal distances from the tower. There are also two detector towers - one in Point Arena and another in Washington D.C. and as soon as they receive the laser pulse, time is registered on digital clocks.

All the clocks in three regions are synchronized with NIST-F2, https://en.wikipedia.org/wiki/NIST-F2.

The Earth goes around the sun at speed of 200 kilometers per second. One can ignore the rotational speed which is 460 meters per second at the equator.

Light speed is 300000 kilometers per second and the distance between two cities is almost 4839.3 km. The distance of each city from central tower in Kansas is 2419.7 km.

Washington D.C. is moving away from the laser pulse and Point Arena moving toward it.

It would take the pulse:
300000t = 2419.7 + 200t => t=8071.06 us for Washington D.C
300000t + 200t= 2419.7 => t = 8060.3 us for Point Arena

The clocks should show the difference of 10.76 us. It doesn't contradict the constancy of speed of light.

Do you agree with it? (I suspect that you are going to say that the clocks would register the same time!)

Thank you for your time and patience!

 

[Nugatory]

Washington D.C. is moving away from the laser pulse and Point Arena moving toward it...The clocks should show the difference of 10.76 us. It doesn't contradict the constancy of speed of light.

Do you agree with it? (I suspect that you are going to say that the clocks would register the same time!)

You suspect right.

Using the frame in which the transmitter and the two receivers are at rest, nothing is moving towards or away from the laser pulse, so the travel time to both clocks is the same and both clocks record the same arrival time, which we’ll call T. Using that frame the two detection events are simultaneous - they both happened at the same time T according to our synchronized clocks.

Using the frame in which the earth, the transmitter, and the two receivers are moving to the east the two detection events are not simultaneous because (as you say) the eastern detector is moving away from the laser pulse while the the western one is moving towards it. However, using this frame the clocks are not synchronized - they do not both read the same at the same time. The pulse reaches the western clock when it reads T but because the clocks are not synchronized the eastern clock reads something less than T. A bit later the pulse reaches the eastern clock, and by then it has advanced so that it reads T.

So no matter which frame we use, we agree that both clocks read T when the pulse reaches them. It has to be this way, because we could (for example) wire the clocks to set off a bomb if a light pulse reaches then when they read T - and all frames have to agree about how the clocks are wired and whether the bomb explodes or not.

Using one frame we say that both light flashes covered the same distance in the same time so arrived at the receivers simultaneously when both read T.

Using the other frame we say that the light flashes traveled different distances so arrived at the receivers at different times. However, the clocks aren’t synchronized so they don’t both read T at the same time; they do however both read T at the two different times that the two pulses reach them.

 

[Nugatory]

All the clocks in three regions are synchronized with NIST-F2,

You might not have noticed that synchronizing the clocks with NIST requires doing something similar to your thought experiment.

How do we set the three clocks to agree with the NIST clock? We broadcast a signal from the NIST lab saying “right now the NIST clock reads $Q$”, and when the operator at each clock receives this signal they set their clock to $Q+D/c$ where $D$ is the distance to the NIST lab. This works because the “NIST clock reads Q” message takes time $D/c$ to travel the distance $D$; therefore the NIST clock reads $Q+D/c$ when the message is received.

Think about it for a moment and you’ll see that this procedure only synchronizes the clocks in the frame in which they are all at rest. In any other frame the distance traveled by the message is not (because as you said above, some of the clocks are moving towards the signal and some are moving away) $D$ so the message travel time is not $D/c$.

 

[PainterGuy]

Using the frame in which the earth, the transmitter, and the two receivers are moving to the east the two detection events are not simultaneous because (as you say) the eastern detector is moving away from the laser pulse while the the western one is moving towards it. However, using this frame the clocks are not synchronized - they do not both read the same at the same time. The pulse reaches the western clock when it reads T but because the clocks are not synchronized the eastern clock reads something less than T. A bit later the pulse reaches the eastern clock, and by then it has advanced so that it reads T.

So no matter which frame we use, we agree that both clocks read T when the pulse reaches them.

Thank you very much. I believe the part quoted above embodies the troubling point.

I'm sorry that it's become frustrating but honestly I'm trying hard in my capacity and circumstances.

In my view, what you are saying is that the clocks are not synchronized and that's the reason they register different arrival times for the pulses.

Let's look at it differently. The clocks in Point Arena, Kansas, and Washington D.C. are synchronized and at any moment they read the same time. Would it now make the arrival time for both detectors same? Suppose there are stopwatches at both receiving towers in Point Arena and Washington D.C. and it has been decided that the pulses of infinitesimal duration would be emitted from the laser tower in Kansas exactly at 12:00 PM and at the same exact moment stopwatches start counting. Well, Sir, would you say that the stopwatches should show the same count at the arrival of pulses for both towers? In my view, as I said in my previous post, the stopwatches count should show the difference of 10.76 us.

If you still say that the stopwatches count should read the same then I suspect that the motion of emitting tower has something to do with it. Thanks.

 

[Ibix]

In my view, what you are saying is that the clocks are not synchronized and that's the reason they register different arrival times for the pulses.

No. What he is saying is that different frames disagree on whether the clocks are synchronised. One frame was used in designing the synchronisation process, the frame in which the clocks are at rest. This frame sees the clocks as synchronised. All other frames see the clocks as out of sync, but the pulses arriving at unequal times in exactly the right way that the clocks happen to read the same times when the pulses arrive.

There is no way to create "synchronised clocks" that does not involve choosing a frame. Other frames will say you did not synchronise them correctly.

 

[Nugatory]

In my view, what you are saying is that the clocks are not synchronized and that's the reason they register different arrival times for the pulses.

By “arrival time” do you mean the number on the face of the clock when the pulse reaches it? That will be the same in all frames, and it will be the number that I called $T$ in post #94.

Let's look at it differently. The clocks in Point Arena, Kansas, and Washington D.C. are synchronized and at any moment they read the same time.

The clocks are synchronized in the frame in which they are at rest. They are not synchronized in a frame in which they are moving. Therefore the statement “at any given moment they read the same time” is correct only in the frame in which they are at rest.

 

[Janus]

Thank you very much. I believe the part quoted above embodies the troubling point.

I'm sorry that it's become frustrating but honestly I'm trying hard in my capacity and circumstances.

In my view, what you are saying is that the clocks are not synchronized and that's the reason they register different arrival times for the pulses.

Let's look at it differently. The clocks in Point Arena, Kansas, and Washington D.C. are synchronized and at any moment they read the same time. Would it now make the arrival time for both detectors same? Suppose there are stopwatches at both receiving towers in Point Arena and Washington D.C. and it has been decided that the pulses of infinitesimal duration would be emitted from the laser tower in Kansas exactly at 12:00 PM and at the same exact moment stopwatches start counting. Well, Sir, would you say that the stopwatches should show the same count at the arrival of pulses for both towers? In my view, as I said in my previous post, the stopwatches count should show the difference of 10.76 us.

If you still say that the stopwatches count should read the same then I suspect that the motion of emitting tower has something to do with it. Thanks.

You keep wanting to default back to "absolute" time. There is no one "correct" answer as to whether the clocks are synchronized. In the "ground frame" they are. For someone with a relative motion with respect to the Earth, they are not. The stop watches always read the same time in the ground frame, but are always 10.76 us out of sync in the other. when you say that the stop watches stat counting when the Kansas clock reads 12:00:00, this is only true for the ground frame, For our other frame, one of those clocks starts counting before the Kansas clock reads 12:00:00, and the other starts ticking later. And if we were to add another observer, moving in the opposite direction relative to the Earth, he would say that the order in which the two stopwatches start their counts would reverse. All observers agree as what the stopwatches read when the ligt reaches them, but they do not agree as whether the stopwatches all simultaneously read the same.

 

[PeterDonis]

The clocks in Point Arena, Kansas, and Washington D.C. are synchronized and at any moment they read the same time.

Wrong!

You left out the key qualifier: in which frame? There is no such thing as clocks being "synchronized" or "not synchronized" without specifying a frame. There is no such thing as a "moment" without specifying a frame. There is no such thing as "the same time" without specifying a frame.

Read those statements again and again and again and again and again, until they sink in. You have kept a bunch of people occupied for a hundred posts now because you keep on making the same mistake. You are never going to get anywhere until you stop making it. And if you make it again in this thread I am going to close the thread because there will be no point in continuing.

 

[PainterGuy]

And if you make it again in this thread I am going to close the thread because there will be no point in continuing.

I'm sorry and I do agree with you. It has become frustrating as I said in my previous post. I'd try to avoid any question about the simultaneity. I've a question which seems important to me but if you think it shouldn't have been asked, you can always delete it, or, worse, close the thread. Thank you.A spaceship is moving toward right at uniform speed of 0.5c and at time t1 it emits a light pulse of an infinitesimal duration. The light travels at constant speed of 300000 km/s.

After 1 second, at time t2, the ship notices the distance traveled by pulse is 300000 km. Meanwhile, the ship has also moved the distance of 150000 km toward the moving pulse. Therefore the distance between ship and trailing edge of the pulse should have been 150000 km BUT it is NOT.

For the ship to observe that the light has moved away 300000 km instead of 150000 km, some things need to change in the formula speed=distance/time. Ignoring length contraction of the ship, time slowdown should occur.

The pulse was generated at time t1 and then by time t2 it had traveled the distance of 300000 km. The difference between t2 and t1 is 1 second. For the ship to calculate the traveled distance by pulse to be 300000 km, the pulse should have actually moved the distance of 300000+150000 km after it was generated. But in ship's frame of reference it has traveled only 300000 km and this would require ship's clock running 1/1.5=0.67 times slower. Informally speaking, for light pulse's 1 second the ship clock has only ticked 0.67 seconds, and when ship clock ticks 1 second, the light pulse clock actually ticks 1.5 second.

I understand that what I'm saying above is nothing less than mumbo jumbo but let's hope that one can guide me to identify the root of my misconceptions. Thanks a lot.

 

[PeterDonis]

I've a question which seems important to me but if you think it shouldn't have been asked

That's not the problem. Asking the question, in itself, is fine. What is not fine is continuing to ask the same question, making the same mistake, even after the question has been repeatedly answered and the mistake has been repeatedly pointed out. It's like you haven't read a single thing anyone else has said in this thread for a hundred posts.

let's hope that one can guide me to identify the root of my misconceptions

If what has already been said in this thread hasn't done that, I'm not sure what else could be done. However, I'll give it one more try. In what I'll quote from you below, I'm going to make bolded additions to show you the key things you left out; leaving those things out, repeatedly, even after it's been repeatedly explained to you that you can't, is the mistake you keep making. I'll also strike through statements you make that cannot be made consistent with your other statements, and replace them with bolded additions giving the correct statements.

A spaceship is moving toward right at uniform speed of 0.5c relative to a chosen inertial frame, which we'll call Frame A, and at time t1 relative to Frame A it emits a light pulse of an infinitesimal duration. The light travels at constant speed of 300000 km/s relative to Frame A.

As has been repeatedly pointed out, "time", "distance" and "speed" have no meaning except relative to a particular frame. So you have to specify the frame whenever you specify a time, distance, or speed.

After 1 second, at time t2 by the ship's clock, the ship notices the distance traveled by pulse is 300000 km relative to its own rest frame, which is a different frame from Frame A; we'll call this frame Frame S.

Note carefully the bolded additions; they are the only way to make your statement about the distance "the ship notices" correct. Notice also that time t2 here is by the ship's clock; it is not time according to Frame A. Again, that is the only way to make your statement correct. And that is why the "meanwhile" is struck through and corrected in the very next quote:

Meanwhile, After 1 second relative to Frame A, the ship has also moved the distance of 150000 km toward the moving pulse relative to Frame A. Therefore the distance between ship and trailing edge of the pulse should have been is 150000 km relative to Frame A BUT it is NOT.

Note carefully the strikethroughs and corrections. Note also how the two different distances, 150000 km and 300000 km, are relative to different frames. That's why they're numerically different.

For the ship to observe that the light has moved away 300000 km instead of 150000 km, some things need to change in the formula speed=distance/time. Ignoring length contraction of the ship, time slowdown should occur.

This all has to be simply discarded; there is no way to make it correct and no corresponding correct statement to put in its place. It is all simply wrong and you should forget it entirely.

The pulse was generated at time t1 relative to Frame A and then by time t2 relative to Frame A it had traveled the distance of 300000 km relative to Frame A. The difference between t2 and t1 is 1 second relative to Frame A.

Again note that the frame has to be specified.

For the ship to calculate the traveled distance by pulse to be 300000 km, the pulse should have actually moved the distance of 300000+150000 km after it was generated. But in ship's frame of reference it has traveled only 300000 km and this would require ship's clock running 1/1.5=0.67 times slower. Informally speaking, for light pulse's 1 second the ship clock has only ticked 0.67 seconds, and when ship clock ticks 1 second, the light pulse clock actually ticks 1.5 second.

Same comment here as two quotes above.

I am closing the thread at this point as I see no reason to repeat anything any further. You have more than enough information here and in previous posts.