B Time dilation, relativistic mass and fuel consumption

[PeterDonis]

I think $E = E_0 + E_k = \gamma E_0$ better elucidates the nature of the things than $E = mc^2 + E_k = \gamma mc^2$ does.

Well, then we have a disagreement about pedagogy. I understand such disagreements are fairly common.

I disagree with the notion that how one goes about measuring or calculating these quantities is tantamount to "the physical nature of the things"

I'm not sure why. Ultimately all of physics has to come down to actual measurements we make. The measurements and their results are the bedrock of our understanding. That's how we find out "the physical nature of things"--by making measurements and doing experiments.

measuring mass is measuring the energy in the rest frame!

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.

the thing that's being measured is the sum of all the "internal" energy-contributions. The "mass" doesn't have an independent existence beyond that.

As far as particle physics is concerned, that's an open question; we don't fully understand how mass arises at the fundamental level so we can't say for sure that it all ends up being some kind of internal energy of stuff that has no intrinsic rest mass.

If you're talking about macroscopic objects, without inquiring into their fundamental constituents, what you say is simply false. We don't have any macroscopic objects made solely of radiation (i.e., "stuff" with zero rest mass), which is what they would have to be for your claim to be true of them as you state it.

s your point that our scales use (say) kilograms rather than... (consults Wolfram Alpha)... exajoules?

No, my point is that the devices we use to measure mass, like balances, are different physical devices from the devices we use to measure energy. That has nothing to do with your choice of units. You could label the test masses you use in your balance in GeV for all I care; you're still using a balance instead of measuring capacity to do work.

 

[PainterGuy]

Thank you, @PeroK, @Ibix, @Nugatory, and @Janus.

I'd try to wrap up this discussion as it has been advised to follow a properly structured source to learn the theory. I hope it'd okay if I ask some related questions and make some comments.

For the Earth, he will be burning his engines for even longer. But, also according to the Earth, as he picks up speed, his rocket undergoes time dilation and thus burns fuel at a slower and slower rate. The combination of longer total time, and the decreasing rate of fuel consumption, produces the same answer as to total fuel used to reach 0.99c

Okay. The fuel consumed according to an Earth observer and the pilot is the same, and the rocket's fuel gauge would verify this result. But according to Newtonian calculation more fuel has been consumed. Do you agree with this?We can say that the rocket clock runs fine for the pilot but it's running slow, i.e. time dilated, according to an Earth observer. But at the same time, the pilot finds that the Earth clock is running slower compared to the rocket clock. At the end of day, it would be pilot's clock which was actually running slower. One can say that why an Earth observer's clock is more 'real' than the pilot's, I'd say it's so because at the end of day we observe the universe through Earth's frame of reference or similar frame of reference. So, the pilot experienced a 'temporary illusion' and if the pilot was destined to spend most part of the life from birth to death aboard the rocket then his/her Earth time would be an 'illusion'.

My original question from post #1, Question 1, about a GPS satellite is related here. The satellite clock gets ahead of the Earth clock by 45 microseconds per day. For an Earth observer the satellite clock suffers time contraction but for the satellite observer it's Earth clock which undergoes time dilation. (I hope I'm saying it correctly). But, again, at the end of day, it's the satellite clock which is running faster or has been time contracted.From what I have read (my apologies if I'm not putting it together properly), Einstein originally didn't use the concept of spacetime for his theory in 1905. It was actually Minkowski who gave Einstein's theory a geometric interpretation in terms of four dimensional spacetime. Initially, Einstein didn't like this spacetime interpretation too much but later he adopted it and it was one of the factors along with his desire to incorporate non-inertial frames of reference into his 1905 theory which motivated him to come up with the theory of general relativity. There is a good related discussion here: https://hsm.stackexchange.com/quest...minkowski-spacetime-before-special-relativity

Thanks a lot, as always!

 

[Nugatory]

But according to Newtonian calculation more fuel has been consumed. Do you agree with this?

Sure. The Newtonian calculation is wrong, and it turns out that in this particular example the incorrect result of this incorrect calculation is lower than the correct answer. But there’s nothing especially surprising about an incorrect calculation producing an incorrect answer. Thinking about the Newtonian answer makes about as much sense as thinking about the results you’d get from using a defective calculator - if your calculator doesn’t do arithmetic right you don’t try to explain the fuel consumption using numbers from that calculator, you throw it out and get one that does do arithmetic right.

At the end of day, it would be pilot's clock which was actually running slower.

If you choose to analyze the problem using a frame in which the Earth is at rest, and if we bring the traveler to rest in that frame at the end of journey, and we use the most natural simultaneity convention in that frame to check the two clock readings at the same time so we can see which one is ahead of the other... then yes, the ship clock will have lost some time compared to the Earth clock.

However, that’s a lot of qualifiers. If we use a frame in which the Earth is not at rest (a reasonable choice for anyone who has noticed that the Earth is orbiting the sun, the sun is orbiting the galactic center, and the entire galaxy is moving through intergalactic space) we could easily find that it’s the Earth clock that is behind. Thus...

One can say that why an Earth observer's clock is more 'real' than the pilot's. I’d say it's so because at the end of day we observe the universe through Earth's frame of reference or similar frame of reference

Only if you’re willing to insist that there’s something special about the frame in which the Earth is at rest. “Some similar frame” won’t necessarily produce the same result. (And have you followed the advice earlier in this thread to look at the relativity of simultaneity? You have to understand that before you can make any conclusions about clocks that are not at the the same place at the same time).

 

[Janus]

Thank you, @PeroK, @Ibix, @Nugatory, and @Janus.

I'd try to wrap up this discussion as it has been advised to follow a properly structured source to learn the theory. I hope it'd okay if I ask some related questions and make some comments.
Okay. The fuel consumed according to an Earth observer and the pilot is the same, and the rocket's fuel gauge would verify this result. But according to Newtonian calculation more fuel has been consumed. Do you agree with this?

If you are measuring amount of fuel needed to reach a given velocity, then yes, Relativity predicts you will use more fuel. But, as pointed out by @Nugatory, in our universe, Newtonian physics give you the wrong answer.
However, if you consider things in terms of fuel used for distance traveled, you get a different result. Accelerating at 10 m/s for .95 yrs by Newtonian rules will get you ~0.47 ly from the Earth and moving at 0.99c.
Accelerating at 10m/s for 2.52 yrs ship time, will also get you up to 0.99c, but 5.8 ly from Earth (measured in the Earth frame). So, while you have burned 2.65 times as much fuel, you've gone 12.3 times further from the Earth. In order for you to get 5.8 ly from the Earth accelerating under Newtonian rules, you would have to accelerate for 3.3 yrs. You will have burned 30% more fuel and taken 30% longer (compared to ship time) So if I wanted to get to the nearest star in the shortest amount of ship time, while using less fuel, Relativity is my friend.

We can say that the rocket clock runs fine for the pilot but it's running slow, i.e. time dilated, according to an Earth observer. But at the same time, the pilot finds that the Earth clock is running slower compared to the rocket clock. At the end of day, it would be pilot's clock which was actually running slower. One can say that why an Earth observer's clock is more 'real' than the pilot's, I'd say it's so because at the end of day we observe the universe through Earth's frame of reference or similar frame of reference. So, the pilot experienced a 'temporary illusion' and if the pilot was destined to spend most part of the life from birth to death aboard the rocket then his/her Earth time would be an 'illusion'.

The fact that the pilot measures the Earth clock running slow compared to his is no less real than the fact that the Earth measures his clock running slow. Observing the universe "through Earth's frame of reference" is a convenience for us, and does not establish a universal time frame. Someone in a frame moving at 0.8c relative to the Earth is just as entitled to observe the universe from his frame. If the pilot lives out his whole life in that ship without ever slowing down relative to the Earth, then for him, the Earth really does age less than he does during his life.
If the pilot goes out and then returns, then yes, he will find that he has aged in total less than the Earth has. And while as far as the Earth frame is concerned, this is all due to time dilation, this is not the case for the pilot. For him, the Earth spent a good chunk of his trip aging slower than him( during the outbound and return legs of the trip), and it was only during that period when he was accelerating in order to reverse direction back towards the Earth that the Earth aged faster. His view of Earth aging slow, Earth aging fast, Earth aging slow, is just as valid as the Earth's view of him just aging slow. From another frame, The Earth could have run slow the whole time, while the pilot aged normally for the first half of the trip, and then aged much more slowly than the Earth for the second half, still resulting in less total accumulated time for the pilot than the Earth. There is no one right frame which is the one that actually reflects what is happening.

My original question from post #1, Question 1, about a GPS satellite is related here. The satellite clock gets ahead of the Earth clock by 45 microseconds per day. For an Earth observer the satellite clock suffers time contraction but for the satellite observer it's Earth clock which undergoes time dilation. (I hope I'm saying it correctly). But, again, at the end of day, it's the satellite clock which is running faster or has been time contracted.

No. For the GPS satellite, things are different than that of someone traveling in a straight line relative to the Earth. For now, we will ignore the gravitational time dilation effect, and for argument's sake assume no gravity at all. Just considering the SR effect. The GPS satellite is orbiting the Earth, and thus is traveling in a circle. It is undergoing a centripetal acceleration. This acceleration effects how it measures Earth time, just like the acceleration the pilot underwent during turnaround effected his. So, if yo place a clock circling around another at 0.866c, The central clock will measure the circling clock as ticking 1/2 as fast. The circling clock, will, due to the centripetal acceleration it is under, measure the central clock as ticking twice as fast as itself. The two clocks will agree that the circling clock is the one running slow.
This is what occurs with GPS clocks, If it were just a matter of dealing with the circular motion of the satellite, both surface and satellite would say that the satellite clock runs slower. However once we reintroduce gravity, Gravitational time dilation becomes the stronger effect, and has the GPS clock ticking faster as a whole, with both surface and satellite agreeing as to the magnitude of the difference.

 

[SiennaTheGr8]

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.

As far as particle physics is concerned, that's an open question; we don't fully understand how mass arises at the fundamental level so we can't say for sure that it all ends up being some kind of internal energy of stuff that has no intrinsic rest mass.

If you're talking about macroscopic objects, without inquiring into their fundamental constituents, what you say is simply false. We don't have any macroscopic objects made solely of radiation (i.e., "stuff" with zero rest mass), which is what they would have to be for your claim to be true of them as you state it.

Sure, I should have included the caveat that elementary particles presumably have "intrinsic" rest-energy.

But for a system that's more than an elementary particle, its mass is the sum of the "internal" energy-contributions: that is, the rest-energies of the constituent particles, the particles' kinetic energies (as measured in the system's center-of-momentum frame), and the potential energy associated with the constituents' relative positions (defined as negative for attractive forces and positive for repulsive forces, and with the "zero point" corresponding to the limit where the constituents are infinitely far from each other).

So measuring an object's rest energy (mass) is indeed measuring the sum of its "internal" energy-contributions. The equivalence of mass and rest energy is a hard equivalence. Any statement one might make about a thing's "mass" is nothing more and nothing less than a statement about its "Energieinhalt."

Accordingly, "mass" can't be "converted" into energy because it already is energy (and to be clear, I'm using "energy" here to refer generically to the additive-and-conserved quantity, not as shorthand for an object's "total energy"; language is slippery). Rather, there are physical processes that can convert rest energy into other forms of energy. For a composite system, this often entails the conversion of some of the "internal" potential energy into the kinetic energy of some of the object's constituents, but of course even the "annihilation" of fundamental particles is possible. And if you want to use the "ability to do work" definition of energy, then I'd counter that the rest energy ("mass") of an object sitting on a scale is precisely a measure of the maximum amount of work that the object could do if those aforementioned physical processes went to town on it.

 

[PeterDonis]

I should have included the caveat that elementary particles presumably have "intrinsic" rest-energy.

No, they have intrinsic rest mass (or invariant mass)--at least, as far as we know some of them do. (Some, like photons and gluons, don't.)

But you can't just help yourself to the assumption that those intrinsic rest masses count as energies; that's precisely the point at issue.

for a system that's more than an elementary particle, its mass is the sum of the "internal" energy-contributions: that is, the rest-energies of the constituent particles

You're assuming your conclusion. If rest mass does not count as internal energy for constituent particles (which, as above, you can't assume it does), then rest mass of a composite system is not just the sum of the internal energy contributions.

The rest of your post simply makes the same assumption without argument.

I don't see the point of arguing about this further. We have a difference of opinion about terminology which I don't think is going to be resolved. As long as we each understand the terminology the other is using, we can still communicate about the physics.

 

[SiennaTheGr8]

I don't see the point of arguing about this further. We have a difference of opinion about terminology which I don't think is going to be resolved. As long as we each understand the terminology the other is using, we can still communicate about the physics.

Agreed. Thanks, Peter.

 

[PainterGuy]

Thank you very much!

Now please bear with me.

Only if you’re willing to insist that there’s something special about the frame in which the Earth is at rest. “Some similar frame” won’t necessarily produce the same result. (And have you followed the advice earlier in this thread to look at the relativity of simultaneity? You have to understand that before you can make any conclusions about clocks that are not at the the same place at the same time).

Yes, I personally prefer Earth's frame of reference because it seems more natural and as a novice it seems to help understand it better.

Yes, I did watch a video about "Einstein train simultaneity". This one: youtube.com/watch?v=wteiuxyqtoM

However, if you consider things in terms of fuel used for distance traveled, you get a different result. Accelerating at 10 m/s for .95 yrs by Newtonian rules will get you ~0.47 ly from the Earth and moving at 0.99c.
Accelerating at 10m/s for 2.52 yrs ship time, will also get you up to 0.99c, but 5.8 ly from Earth (measured in the Earth frame). So, while you have burned 2.65 times as much fuel, you've gone 12.3 times further from the Earth. In order for you to get 5.8 ly from the Earth accelerating under Newtonian rules, you would have to accelerate for 3.3 yrs. You will have burned 30% more fuel and taken 30% longer (compared to ship time) So if I wanted to get to the nearest star in the shortest amount of ship time, while using less fuel, Relativity is my friend.

I'm sorry but I'm confused and my head hurts. "2.52 yrs ship time" is dilated according to the reference frame of earth. Therefore, I think, "3.3 yrs" won't be different from "2.52 yrs ship time" once the pilot completes his mission and his mission's duration is checked using Earth's clock; or in other words once the ship time is converted into Earth time using proper factor, it would be same as 3.3 yrs.

"under Newtonian rules, you would have to accelerate for 3.3 yrs. You will have burned 30% more fuel and taken 30% longer (compared to ship time)" - In other words, yes, it would take a Newtonian longer because your clock was running slow. But I don't see how a Newtonian would need to spend more fuel, especially when Newtonian rocket doesn't 'suffer' from any relativistic mass effect, informally speaking, its mass doesn't increase.

Once again, I don't understand why it'd take "30% more fuel" according to Newtonian calculation; in post #53, https://www.physicsforums.com/threa...mass-and-fuel-consumption.984366/post-6299827, @Nugatory confirmed that a Newtonian would say that more fuel has been consumed because Newtonian antiquated model doesn't take into account relativistic effects of mass as it moves.

I understand that the special relativity models the nature more accurately but I'm looking at it from perspective of Newtonian antiquated model. I'm also not focusing on spacetime because even Einstein himself didn't really consider it when he came up with the special theory of relativity. I'm ignoring the general relativity at this stage. Newtonian model uses fixed flow of time and no distinction between rest mass and moving mass.

For him, the Earth spent a good chunk of his trip aging slower than him( during the outbound and return legs of the trip), and it was only during that period when he was accelerating in order to reverse direction back towards the Earth that the Earth aged faster. His view of Earth aging slow, Earth aging fast, Earth aging slow, is just as valid as the Earth's view of him just aging slow.

I googled the effects of acceleration on time and found few things which I didn't know before. I had thought that only when you move fast with respect to an inertial frame, your time gets slow down, i.e. dilated. It looks like acceleration also affects the time in a different manner; I hope it's not a consequence of general relativity because I'm only focusing on special relativity. The theory of general relativity models the acceleration as gravity .

For example, have a look below on the quote. My apologies if it's not entirely accurately but I needed your guidance if it's correct. For example, if a rocket is moving away from Earth to some other planet B. The rocket clock appears to slow down with respect to an Earth observer but a rocket observer notices Earth's clock slowing down. If the rocket is headed directly toward planet B, how would the rocket observer see planet B's clock and how rocket clock appears to planet B observer? I'm assuming rocket is traveling at constant velocity.

According to what is said below, as the rocket accelerates the rocket observer sees Earth clock slowing down more but sees planet B clock moving faster. Is it correct?

"Moving fast only. Actually, just moving at all, though you won't notice it much at low speeds.

Acceleration causes another time effect, which seems different but drops out of the same math. Clocks "above" you, or in the forward direction of acceleration, tick faster. Clocks "below" you tick slower. This happens even when you're rigidly attached to the clock, and both you and the clock are accelerated."
Source: https://qr.ae/T3zzwJ

Well, if you think I'm making no sense then I'd understand if you don't comment.This is an addition to what I said earlier towards the end of my last post.
"In 1908, three years after Einstein first published his special theory of relativity, the mathematician Hermann Minkowski introduced his four-dimensional “spacetime” interpretation of the theory. Einstein initially dismissed Minkowski’s theory, remarking that “since the mathematicians have invaded the theory of relativity I do not understand it myself anymore.” Yet Minkowski’s theory soon found wide acceptance among physicists, including eventually Einstein himself, whose conversion to Minkowski’s way of thinking was engendered by the realization that he could profitably employ it for the formulation of his new theory of gravity. The validity of Minkowski’s mathematical “merging” of space and time has rarely been questioned by either physicists or philosophers since Einstein incorporated it into his theory of gravity. Physicists often employ Minkowski spacetime with little regard to the whether it provides a true account of the physical world as opposed to a useful mathematical tool in the theory of relativity. Philosophers sometimes treat the philosophy of space and time as if it were a mere appendix to Minkowski’s theory. In this critical study, Joseph Cosgrove subjects the concept of spacetime to a comprehensive examination and concludes that Einstein’s initial assessment of Minkowksi was essentially correct."
Source: https://www.palgrave.com/gp/book/9783319726304#aboutBookThe following part is my personal view and I also attempt to explain why I'm finding the special theory of relativity difficult.

As another example, let's consider a thought experiment. If you are asked to go around the Earth at 0.9c speed for one second using fixed amount of fuel. Let's ignore the air friction, gravity, and suppose the rocket starts and end its journey at 0.9c without any acceleration, also ignore centripetal acceleration. The speed of light is 300000 km/s and circumference of Earth is 40075 km. Using Newtonian calculation, in one second you should be able to go around the Earth 6.74 times. A Newtonian standing on Earth would see the rocket going slow, length contracted in the direction of travel but I don't think the Newtonian would be able to notice that the rocket has become more massive. Therefore, after one second the Newtonian would clearly see that the rocket hasn't circled the Earth 6.74 times. If the rocket is taken down once Newtonian clock ticks one second, it would also be noticed that for whatever amount of journey it has covered (which is clearly going to be less than 6.74 times Earth circumference), it has consumed more fuel as it should. Forget what the pilot of rocket has to say about it. Do I make any sense?

Also, for example, in the example shown in the video mentioned above about simultanety, youtube.com/watch?v=wteiuxyqtoM , if there were two light sensors at the ends of train, the person on train would also agree that both flashes occurred at the same time. Yes, if the train is some kind of planet and there was no way of communicating with a person situated outside somewhere above that planet, then the conclusion of person riding the 'train/planet' would be acceptable. Perhaps, the example is a bad example but online tutorials are full of such examples.

In my humble view, the theory of special relativity, is presented more like pure math rather than applied math. Personally, I have nothing against pure math but applied math seems more interesting although the very foundation of applied math is in fact the pure math. I have been looking for a book which presents theories of relativity, especially special relativity, more from 'human' and 'physical' perspective but no success. I will elaborate on it below.

A cathode ray tube takes into account of relativistic effects on length and mass of electrons. An electron has length contraction, time dilation, and its inertial mass increases. I wouldn't really care how I appear to the electron - if it sees me length contracted unicorn or alien then that's not my problem :). Most important to me, as a novice, is to understand how an electron looks as it travels at very high speed. I can imagine later, how the world appears to an electron if it were a living being!

"Cathode ray tube (CRT) televisions create pictures by shooting electrons at a phosphorous screen. These electrons are accelerated to high velocities, near 20- 30% of the speed of light. Remember from special relativity that as a particle approaches speeds near light speed, the energy required to propel the particle is increased. Magnets in the television are responsible for placing the electrons in the correct configuration on the screen. They must account for the relativistic effects on these electrons or the picture created will be out of focus (Akpan, 2015)". Source: https://engagedscholarship.csuohio.edu/cgi/viewcontent.cgi?article=1071&context=tdr "These electrons are moving at roughly a third of the speed of light. This means that engineers had to account for length contraction when designing the magnets that directed the electrons to form an image on the screen. Without accounting for these effects, the electron beam's aim would be off and create unintelligible images." Source: https://www.iflscience.com/physics/4-examples-relativity-everyday-life/amp.html, https://www.quora.com/Is-length-con...chard-Muller-3?ch=12&share=c5c2c623&srid=gk8x . The same goes for the ladder paradox, https://en.wikipedia.org/wiki/Ladder_paradox, if I build a barn and let the ladder move through it at really fast speed, then it's the ladder which contracts in my physical world. The ladder is in my world or the world of barn and ultimately the ladder's movement is not permanent, it has to stop ultimately.

As an another example, the guy gives a very nice introduction to special theory of relativity 'from human point of view', youtube.com/watch?v=umLcFAI5SZg . He won $400000 award for it as well.

Helpful links:
1: http://web.pdx.edu/~egertonr/ph311-12/relativ.htm
2: http://www.exo.net/~pauld/activities/physics/relativitytelevision.htm
3: https://www.iflscience.com/physics/4-examples-relativity-everyday-life/amp.html
4: youtube.com/watch?v=mnJuKXhFaQ8
5: https://physics.stackexchange.com/q...he-speed-of-light-vary-in-non-inertial-frames
6: http://www.alternativephysics.org/book/MuonRelativity.htm
7: https://physics.stackexchange.com/q...ncy-of-speed-of-light-in-gr?noredirect=1&lq=1

 

[jbriggs444]

I googled the effects of acceleration on time and found few things which I didn't know before. I had thought that only when you move fast with respect to an inertial frame, your time gets slow down, i.e. dilated. It looks like acceleration also affects the time in a different manner; I hope it's not a consequence of general relativity because I'm only focusing on special relativity. The theory of general relativity models the acceleration as gravity.

It is an effect seen in general relativity. It is also an effect that can be seen in special relativity if one adopts a particular type of accelerating coordinate system, Rindler coordinates.

If you restrict your attention to inertial frames in special relativity then no such effect exists.

For example, have a look below on the quote. My apologies if it's not entirely accurately but I needed your guidance if it's correct. For example, if a rocket is moving away from Earth to some other planet B. The rocket clock appears to slow down with respect to an Earth observer but a rocket observer notices Earth's clock slowing down. If the rocket is headed directly toward planet B, how would the rocket observer see planet B's clock and how rocket clock appears to planet B observer? I'm assuming rocket is traveling at constant velocity.

According to what is said below, as the rocket accelerates the rocket observer sees Earth clock slowing down more but sees planet B clock moving faster. Is it correct?

"Moving fast only. Actually, just moving at all, though you won't notice it much at low speeds.

Acceleration causes another time effect, which seems different but drops out of the same math. Clocks "above" you, or in the forward direction of acceleration, tick faster. Clocks "below" you tick slower. This happens even when you're rigidly attached to the clock, and both you and the clock are accelerated."
Source: https://qr.ae/T3zzwJ

The writer there is adopting an accelerating coordinate system. You can think about an accelerating coordinate system (one particular accelerating coordinate system anyway) as a sequence of inertial frames anchored to a uniformly accelerating object. Each inertial frame in the sequence is obviously moving slightly faster than the last. Suppose that lay a coordinate system down on this frame. You have two clocks whose relative tick rates you want to consider. The clocks are at some distance from one another in the direction of the acceleration. Each time you change inertial frames, you change relativity of simultaneity. That leads to an asymmetry in the calculated relative rates of the two clocks.

Using accelerated coordinate systems does not do anything physical, of course. Coordinate systems are just doodles on pieces of paper. Doodles cannot do anything physical.

 

[PeroK]

@PainterGuy you are wasting your time on Quora. Unless you already understanding the subject it's impossible to sort the good answers from the nonsense.

Why not give Morin's book a try?

 

[Janus]

Thank you very much!

Now please bear with me.
Yes, I personally prefer Earth's frame of reference because it seems more natural and as a novice it seems to help understand it better.

You can choose to work from whatever frame you find most convenient. It's jut important to realize that this choice of frame is not any more valid in terms of what "really" happens than any other.

Yes, I did watch a video about "Einstein train simultaneity". This one: youtube.com/watch?v=wteiuxyqtoM
I'm sorry but I'm confused and my head hurts. "2.52 yrs ship time" is dilated according to the reference frame of earth. Therefore, I think, "3.3 yrs" won't be different from "2.52 yrs ship time" once the pilot completes his mission and his mission's duration is checked using Earth's clock; or in other words once the ship time is converted into Earth time using proper factor, it would be same as 3.3 yrs.

In a Newtonian universe, it would take 3.3 yrs to reach the destination according to both Earth and ship. In our Relativistic universe is takes 2.52 yrs by ship time, and 6.7 yrs Earth time. So the 3.3 yrs under Newton is different than both the Earth time and Ship time under Einstein.

"under Newtonian rules, you would have to accelerate for 3.3 yrs. You will have burned 30% more fuel and taken 30% longer (compared to ship time)" - In other words, yes, it would take a Newtonian longer because your clock was running slow. But I don't see how a Newtonian would need to spend more fuel, especially when Newtonian rocket doesn't 'suffer' from any relativistic mass effect, informally speaking, its mass doesn't increase.

Once again, I don't understand why it'd take "30% more fuel" according to Newtonian calculation; in post #53, https://www.physicsforums.com/threa...mass-and-fuel-consumption.984366/post-6299827, @Nugatory confirmed that a Newtonian would say that more fuel has been consumed because Newtonian antiquated model doesn't take into account relativistic effects of mass as it moves.

As far as the pilot is concerned, there is no relativistic mass increase to take into account. What he does know is that as he feeds X amount of fuel per second(by his clock) into his engines, it produces a proper acceleration of 10m/sec. Thus if he stood on a scale, it would register just a tad bit more than it would on Earth. This is the same for the pilot in a Newtonian universe or Relativistic one. And the amount of fuel per second they are feeding into the engine to produce that acceleration will be the same in each case. The difference is that one pilot feeds fuel into the engine for only 2.52 yrs(Relativistic Universe) and the other for 3.3 yrs (Newtonian universe) Now according to the Newtonian pilot he would be moving at ~3.5c relative to the Earth after that time, and the Relativistic pilot would be moving at 0.99c relative to the Earth. The Newtonian pilot would also say that he was 5.8 ly from Earth, and the Relativistic pilot would measure that same distance as being just under 0.82 ly.

I understand that the special relativity models the nature more accurately but I'm looking at it from perspective of Newtonian antiquated model. I'm also not focusing on spacetime because even Einstein himself didn't really consider it when he came up with the special theory of relativity. I'm ignoring the general relativity at this stage. Newtonian model uses fixed flow of time and no distinction between rest mass and moving mass.

Why would you wnat to look at it from a perspective that has turned out to be incorrect? Time doesn't have a "fixed flow". Trying to "shoe horn" Relativity into a Newtonian viewpoint isn't going to lead to any understanding of the theory.

I googled the effects of acceleration on time and found few things which I didn't know before. I had thought that only when you move fast with respect to an inertial frame, your time gets slow down, i.e. dilated. It looks like acceleration also affects the time in a different manner; I hope it's not a consequence of general relativity because I'm only focusing on special relativity. The theory of general relativity models the acceleration as gravity .

For example, have a look below on the quote. My apologies if it's not entirely accurately but I needed your guidance if it's correct. For example, if a rocket is moving away from Earth to some other planet B. The rocket clock appears to slow down with respect to an Earth observer but a rocket observer notices Earth's clock slowing down. If the rocket is headed directly toward planet B, how would the rocket observer see planet B's clock and how rocket clock appears to planet B observer? I'm assuming rocket is traveling at constant velocity.

At constant speed, and after you factor out the propagation time delays (Doppler effect), The rocket sees Planet B's clock as running slow, and Planet B sees The rocket clock as running slow.

According to what is said below, as the rocket accelerates the rocket observer sees Earth clock slowing down more but sees planet B clock moving faster. Is it correct?

"Moving fast only. Actually, just moving at all, though you won't notice it much at low speeds.

Acceleration causes another time effect, which seems different but drops out of the same math. Clocks "above" you, or in the forward direction of acceleration, tick faster. Clocks "below" you tick slower. This happens even when you're rigidly attached to the clock, and both you and the clock are accelerated."
Source: https://qr.ae/T3zzwJ

This excerpt would apply to a ship is activelyaccelerating towards planet B, and not when it is moving at a constant speed. In other words, If you start accelerating towards Planet B, while you are accelerating, the clock at planet B will run fast according to you. Once you stop accelerating and begin coasting at a constant speed The clock at B will run slow according to you.
One thing that this excerpt doesn't mention, is that the rate at which the clocks "above" you run fast and the ones below one run slow depends both on the magnitude of the acceleration and and how far "above" or "below" you they are. The more the separation in either direction, the greater the difference in tick rate.
Thus the further way planet B is when you start accelerating towards it, the faster it clocks tick compared to your own.
One thing to keep in mind is that time dilation due to acceleration is only measured by the accelerating observer. Anyone in an inertial frame would just measure an accelerating clock as ticking at a rate that depends only on its relative velocity.

Well, if you think I'm making no sense then I'd understand if you don't comment.This is an addition to what I said earlier towards the end of my last post.
"In 1908, three years after Einstein first published his special theory of relativity, the mathematician Hermann Minkowski introduced his four-dimensional “spacetime” interpretation of the theory. Einstein initially dismissed Minkowski’s theory, remarking that “since the mathematicians have invaded the theory of relativity I do not understand it myself anymore.” Yet Minkowski’s theory soon found wide acceptance among physicists, including eventually Einstein himself, whose conversion to Minkowski’s way of thinking was engendered by the realization that he could profitably employ it for the formulation of his new theory of gravity. The validity of Minkowski’s mathematical “merging” of space and time has rarely been questioned by either physicists or philosophers since Einstein incorporated it into his theory of gravity. Physicists often employ Minkowski spacetime with little regard to the whether it provides a true account of the physical world as opposed to a useful mathematical tool in the theory of relativity. Philosophers sometimes treat the philosophy of space and time as if it were a mere appendix to Minkowski’s theory. In this critical study, Joseph Cosgrove subjects the concept of spacetime to a comprehensive examination and concludes that Einstein’s initial assessment of Minkowksi was essentially correct."
Source: https://www.palgrave.com/gp/book/9783319726304#aboutBookThe following part is my personal view and I also attempt to explain why I'm finding the special theory of relativity difficult.

As another example, let's consider a thought experiment. If you are asked to go around the Earth at 0.9c speed for one second using fixed amount of fuel. Let's ignore the air friction, gravity, and suppose the rocket starts and end its journey at 0.9c without any acceleration, also ignore centripetal acceleration. The speed of light is 300000 km/s and circumference of Earth is 40075 km. Using Newtonian calculation, in one second you should be able to go around the Earth 6.74 times. A Newtonian standing on Earth would see the rocket going slow, length contracted in the direction of travel but I don't think the Newtonian would be able to notice that the rocket has become more massive.

A "Newtonian" (someone living in a Newtonian universe) would measure none of this, As time dilation and length contraction are not a part of Newtonian Physics.
Since you are ignoring air friction, gravity and the centripetal acceleration, the the "fixed amount of fuel" you would need to maintain that 0.9c is zero, so I don't even see the point of mentioning fuel, unless it is the fuel needed to reach 0.9 c in the first place.

Therefore, after one second the Newtonian would clearly see that the rocket hasn't circled the Earth 6.74 times.

If the rocket is traveling at 0.9c, then it makes 6.74 trips around the Earth in one second Earth time, reagardless of whether you take the Newtonian or Relativistic view.

If the rocket is taken down once Newtonian clock ticks one second, it would also be noticed that for whatever amount of journey it has covered (which is clearly going to be less than 6.74 times Earth circumference), it has consumed more fuel as it should. Forget what the pilot of rocket has to say about it. Do I make any sense?

No, you are not making any sense. Either the ship is moving at 0.9c relative to the Earth, in which case it would take more fuel to reach that speed according to Relativity than Newton, Or the ship has a fixed fuel supply, in which case it would not quite as high a speed under Relativity than it does according to Newton. You seem to want to "double up" on the effects.

Also, for example, in the example shown in the video mentioned above about simultanety, youtube.com/watch?v=wteiuxyqtoM , if there were two light sensors at the ends of train, the person on train would also agree that both flashes occurred at the same time. Yes, if the train is some kind of planet and there was no way of communicating with a person situated outside somewhere above that planet, then the conclusion of person riding the 'train/planet' would be acceptable. Perhaps, the example is a bad example but online tutorials are full of such examples.

Putting light sensors at the ends of the Train would make no difference. You could place observers all along the length of the train, and they they would all conclude the the flashes occurred at different times.
Here are events according to the Embankment frame:
Ends of train reach red dots, flashes are emitted simultaneously. They reach the embankment observer simultaneously and the train observer at different times.

Same events according to Train frame.

The first thing you might notice is that the train no longer fits exactly between the red dots. In the first animation, it is the train moving relative to the frame, so it is length contracted, and it is the length contracted train that fits in between the dots. In the train's frame, the train is its proper length and it is the embankment that is length contracted. The train ends cannot be at the red dots at the same time. The right end of the train reaches the right dot before the left end of the train reach the left dot. Thus the events that initiate the flashes cannot occur at the same time. However, you will still note that in this frame the flashes still reach the embankment observer simultaneously. You can also see that in both animations, the right flash hits the train observer when he is about 3 ties past the embankment observer, and the left flash reaches him when he is about even with the right dot.
The second animation are the sequence of events, according to anyone at rest with respect to the train frame. It doesn't matter where you are are on the train or where or how many sensors you have.
In my humble view, the theory of special relativity, is presented more like pure math rather than applied math. Personally, I have nothing against pure math but applied math seems more interesting although the very foundation of applied math is in fact the pure math. I have been looking for a book which presents theories of relativity, especially special relativity, more from 'human' and 'physical' perspective but no success. I will elaborate on it below.

A cathode ray tube takes into account of relativistic effects on length and mass of electrons. An electron has length contraction, time dilation, and its inertial mass increases. I wouldn't really care how I appear to the electron - if it sees me length contracted unicorn or alien then that's not my problem :). Most important to me, as a novice, is to understand how an electron looks as it travels at very high speed. I can imagine later, how the world appears to an electron if it were a living being!

"Cathode ray tube (CRT) televisions create pictures by shooting electrons at a phosphorous screen. These electrons are accelerated to high velocities, near 20- 30% of the speed of light. Remember from special relativity that as a particle approaches speeds near light speed, the energy required to propel the particle is increased. Magnets in the television are responsible for placing the electrons in the correct configuration on the screen. They must account for the relativistic effects on these electrons or the picture created will be out of focus (Akpan, 2015)". Source: https://engagedscholarship.csuohio.edu/cgi/viewcontent.cgi?article=1071&context=tdr "These electrons are moving at roughly a third of the speed of light. This means that engineers had to account for length contraction when designing the magnets that directed the electrons to form an image on the screen. Without accounting for these effects, the electron beam's aim would be off and create unintelligible images." Source: https://www.iflscience.com/physics/4-examples-relativity-everyday-life/amp.html, https://www.quora.com/Is-length-con...chard-Muller-3?ch=12&share=c5c2c623&srid=gk8x . The same goes for the ladder paradox, https://en.wikipedia.org/wiki/Ladder_paradox, if I build a barn and let the ladder move through it at really fast speed, then it's the ladder which contracts in my physical world. The ladder is in my world or the world of barn and ultimately the ladder's movement is not permanent, it has to stop ultimately.

But, again, If you really want to grasp Relativity, you have to accept, that according to the ladder, it is the barn that length contracts, and this is just an "physically real" as your view that the ladder contracts. While it is perfectly fine to work from the frame of the Barn, because that is the frame you are at rest to, it is important to keep in mind that there is nothing special about that choice that makes this view any better than any other.
In the earlier example of how much fuel you burn while traveling to a distant star at constant acceleration, you could work it out from the Earth frame, but it is pretty involved, having to deal with a changing velocity with its resulting changing time dilation for the ship etc. It is easier to work out from the pilot frame. Both approaches give the same answer, so it makes sense to use the simpler one.
Also, when you ignore how events appear from other frame, you are ignoring a good part of the theory and what Relativity tells us about the very nature of time.

 

[Herman Trivilino]

Therefore, I think, "3.3 yrs" won't be different from "2.52 yrs ship time" once the pilot completes his mission and his mission's duration is checked using Earth's clock; or in other words once the ship time is converted into Earth time using proper factor, it would be same as 3.3 yrs.

The facts contradict what you're thinking. When a person's age changes from 20 years to 50 years, he becomes 30 years older. No amount of converting can change that.

 

[PeterDonis]

Therefore, I think, "3.3 yrs" won't be different from "2.52 yrs ship time" once the pilot completes his mission and his mission's duration is checked using Earth's clock; or in other words once the ship time is converted into Earth time using proper factor, it would be same as 3.3 yrs.

You are wrong.

First, to be perfectly clear: the pilot himself ages 2.52 years during the trip. The amount that he ages doesn't magically change when he reaches his destination and finds that the destination clocks, which are synchronized with Earth clocks and not his ship's clock, read something different.

Second, if we assume that there are clocks at his destination that are synchronized with Earth clocks, then those clocks will not show 3.3 years of elapsed time. They will show more. As @Janus said in post #61, the destination clocks will show 6.7 years of elapsed time.

So the Newtonian numbers are just wrong. They don't tell you anything correct about what happens. Your best bet is to forget the Newtonian numbers and the Newtonian calculations entirely, since all they're doing is giving you bad information that is hindering your understanding.

 

[PainterGuy]

Hi,

I wanted to understand it a little better before I respond to any of the replies. I was working on it today but came across a point which I couldn't understand. I'd really appreciate if you could guide me. Thank you.

Suppose there is a rectangular box moving straight in space at constant velocity of say 150000000 m/s. In other words, it's an inertial frame of reference for anyone inside the box. The length of box is 600000000 meters. The width and height are not really important here so you can suppose any reasonable values for them. Please note that the speed in light i vacuum is taken to be 300000000 m/s.

I can understand that why the propagation of any wave which requires a medium, such as sound, is not affected by the uniform motion of box in space. For example, if you have two sensors at the opposite ends of box and a sound is produced in the middle of box, both sensors would register the same time when the sound wave reaches them.

Light does not need any medium to propagate. Suppose a laser pulse of an infinitesimal duration is produced in both directions. It is also assumed that the pulse does not undergo any diffraction - the pulse remains collimated. In my opinion, if it was an absolute rest inertial frame of reference, both pulses would hit the sensors at the time. The pulses would reach the sensors/detectors after one second because laser source is in the middle - 300000000 meters from both ends. I know what I'm saying is wrong because there doesn't exist any absolute rest frame of reference.

But this is the point which is troubling me. I suspect that even for the given frame of reference which is moving at constant velocity of 150000000 m/s in space, the sensors would still detect the same time for the arrival of pulses but I don't understand why and how.

If the box is moving from left to right, then the left detector would have moved 150000000 meters toward the light pulse therefore the left detector should register pulse arrival first; after 0.5 second. On the other hand, the right detector would have actually moved away from the pulse. The right detector would register the arrival after 1 second.

Where am I going wrong?

 

[Janus]

Hi,

I wanted to understand it a little better before I respond to any of the replies. I was working on it today but came across a point which I couldn't understand. I'd really appreciate if you could guide me. Thank you.

Suppose there is a rectangular box moving straight in space at constant velocity of say 150000000 m/s. In other words, it's an inertial frame of reference for anyone inside the box. The length of box is 600000000 meters. The width and height are not really important here so you can suppose any reasonable values for them. Please note that the speed in light i vacuum is taken to be 300000000 m/s.

I can understand that why the propagation of any wave which requires a medium, such as sound, is not affected by the uniform motion of box in space. For example, if you have two sensors at the opposite ends of box and a sound is produced in the middle of box, both sensors would register the same time when the sound wave reaches them.

Light does not need any medium to propagate. Suppose a laser pulse of an infinitesimal duration is produced in both directions. It is also assumed that the pulse does not undergo any diffraction - the pulse remains collimated. In my opinion, if it was an absolute rest inertial frame of reference, both pulses would hit the sensors at the time. The pulses would reach the sensors/detectors after one second because laser source is in the middle - 300000000 meters from both ends. I know what I'm saying is wrong because there doesn't exist any absolute rest frame of reference.

But this is the point which is troubling me. I suspect that even for the given frame of reference which is moving at constant velocity of 150000000 m/s in space, the sensors would still detect the same time for the arrival of pulses but I don't understand why and how.

If the box is moving from left to right, then the left detector would have moved 150000000 meters toward the light pulse therefore the left detector should register pulse arrival first; after 0.5 second. On the other hand, the right detector would have actually moved away from the pulse. The right detector would register the arrival after 1 second.

Where am I going wrong?

For anyone at rest with respect to the box the light pulses would hit the detectors at the same time. For someone for which the box is moving from left to right, the light hits the left detector first and then the right detector
We are back to the relativity of simultaneity.

 

[PainterGuy]

For anyone at rest with respect to the box the light pulses would hit the detectors at the same time. For someone for which the box is moving from left to right, the light hits the left detector first and then the right detector
We are back to the relativity of simultaneity.

Yes, Sir, you are right but, to me, the situation is somewhat different.

Let me change the version to explain myself. Suppose instead of the detectors there are reflectors. Once the pulse hits reflector, it reflects back to the person who is also standing in the middle. Yes, in such a case, the person would SEE/OBSERVE both pulses reaching his eyes at the same time. From my earlier statement, when the left reflector moves 150000000 meters toward the pulse, at the same time the observer moves away 150000000 meters toward the right so the effect gets cancelled. I hope you can understand what I'm trying to say. I already had this point in mind when I made my previous posting and that was the reason I employed detectors instead of reflectors.

The detectors are only there to register the arrival time of pulses. In other words, repeating what I said earlier in previous positing, one detector would register the pulse 0.5 seconds before the other.

Could you please guide me with this? Thanks.

 

[PeterDonis]

Suppose instead of the detectors there are reflectors. Once the pulse hits reflector, it reflects back to the person who is also standing in the middle. Yes, in such a case, the person would SEE/OBSERVE both pulses reaching his eyes at the same time.

Yes. Now work out how this whole process looks to an observer watching the ship go by from left to right at half the speed of light. As @Janus has told you, that observer will see the light pulse hitting the left mirror first. But he will also see that pulse take longer to get back to the person in the center of the ship, because that person is moving to the right and so is the reflected pulse. And the observer watching the ship go by will see the light pulse hitting the right mirror second, but he will also see that pulse not take as long to get back to the person at the center of the ship, because that reflected pulse is moving to the left and the person is moving to the right. So in the end that observer will agree that both pulses return to the person in the center of the ship at the same time.

The detectors are only there to register the arrival time of pulses.

"The arrival time of pulses" registered by the detectors depends on how their clocks are synchronized. And so that time does not tell you any "absolute time". It only tells you the time according to one particular way of synchronizing clocks. You have specified that the detector clocks are synchronized according to the time in the inertial frame in which the ship is at rest. So that's the "time" the detectors will show. See below.

one detector would register the pulse 0.5 seconds before the other.

No, it wouldn't. Both detectors would register the same time, because you specified that the detector clocks are synchronized according to the ship's rest frame.

The observer watching the ship go by from left to right at half the speed of light will calculate that the times according to his rest frame, in which the ship is moving left to right at half the speed of light, are different: the time according to his rest frame for the pulse hitting the left detector is earlier than the time according to his rest frame for the pulse hitting the right detector. But he will not claim, based on this calculation, that the detector clocks themselves will register these times. He knows they won't, because he knows that the detector clocks are not synchronized according to his rest frame.

 

[PainterGuy]

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.

 

[PeterDonis]

Both detectors are in the same frame of reference

No. Both detectors are at rest relative to each other, and to the person in the center of the ship. That does not mean they are "in" one particular frame of reference. You can use any frame of reference you like to describe them and their motion. They are "in" all frames of reference. They just aren't at rest in all of them; they're only at rest in one.

I don't even understand what it has to do with the synchronization of clocks.

Because synchronization of clocks determines what readings the clocks will register at particular events. The detector clocks being synchronized in the rest frame of the ship (which is also their own rest frame) means that if the person at the center of the ship, equidistant from the two detectors, sends out two light pulses at the same instant, one towards each detector, the two detector clocks will register the same reading when they receive the pulses. Each detector receiving a pulse is an event: it's a direct physical happening. And so is the detector's clock registering a particular reading--meaning showing a particular arrangement of hands on its face or a particular set of digits on its display, depending on what kind of clock it is. You can't change what happens at particular events by changing reference frames, so all reference frames must agree on what readings the two detector clocks display when the pulses reach them.

Both clocks would be affected by the same time dilation

Not according to the ship and the person in the ship. To the person in the ship, the detector clocks, which are at rest relative to him, are not time dilated at all. It is the clocks belonging to the observer watching the ship go by that are dilated according to the person in the ship.

perhaps, the clock/detector situated toward the direction of motion, i.e. right detector, gets affected by time dilation more than the left detector.

Nope.

If two persons are located on the same ship moving at uniform speed, their watches would tell the same time.

Yes. And the same applies to two detectors at opposite ends of the same ship, all at rest relative to the ship.

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.

This whole line of thought is a red herring. You should forget all about it.

 

[Herman Trivilino]

Suppose there is a rectangular box moving straight in space at constant velocity of say 150000000 m/s.

Unless you state, or otherwise imply, what it's moving with respect to, this statement is meaningless.

 

[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.

 

[Herman Trivilino]

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.