B Time dilation, relativistic mass and fuel consumption

[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.