Ah, I think I had vaguely heard about him. You do see some scientists get weird in later life. It can be more than a bit sad. Sometimes it has medical underpinnings. If not, usually it is when they get involved in something outside their expertise. Age sometimes comes with very unwelcome issues.
You could even say they don‘t realize they’ll need to slow down when entering a new frame of reference.
The answer as to how GPS works is here :- GPS, Relativity, and pop-Science Mythology (and the next chapter).
Which equations do you want me to use? If I use the Lorentz transforms, they will limit my speed to that of just below c. They were designed to do just that. The equations I should be using are the classical velocity equations. A spaceship which carries its own propulsion unit (ie a rocket motor) can accelerate until its fuel runs out, so if it can carry enough fuel, it can accelerate past c. A Bussard Ramjet will do the job nicely. See :- Problems with Relativity
Francis Vaughan, the clocks do not have to be brought together, my question is, what, consistent with the theory, determines which clock works the faster, and why that one?
Use SRT to discover which clock is running faster, and why that one, not the other.
I do not want t know which one is observed to be running slow, I want to know which is actually slow. Einstein said that theses effects are real - not observed or imaginary.
Do I detect a slur in your sentence :- “I assume your Professor Dingle…” He is not my Professor Dingle, he is THE Professor Dingle,
Herbert Dingle
Neither are.
Since they are not in the same reference frame it makes no sense to ask the question. Now this is the point where a lot of people get upset. This is because from a very basic philosophical or religious point of view their minds demand a universal single truth of state. The idea that there isn’t a single true flow of time, gets people very wound up, and if they can’t past this notion, you can’t get any further.
Someone who came to a fundamental religious viewpoint, especially one containing some elements of a neo-Platonic view would probably have an great deal of trouble reconciling the received truth of their chosen religion with relativity.
Demanding a single true flow of time is a not a valid argument here. That is one of personal faith, not science. This the same as demanding a single true reference frame. You can demand from a viewpoint of personal faith or philosophy all you like. Doesn’t make it true.
I gave the answer much earlier in the thread. Everything in the universe moves at the speed of causality. At rest you move at one second per second in time. If you are in motion you exchange some of the motion in the time direction with motion in space, so that the total speed is always the speed of causality. From here you can pretty much derive all of special relativity. Two clocks, each moving in space have different reference frames. There is no one universally true reference frame in this question, so the question of which one is actually slow is a non-question. The only way to decide which clock has lost or gained is to place the two clocks in the same reference frame.
In all honesty I thought it was a problem you had been set in an undergraduate physics course by your then teacher. I have no previous knowledge of Dingle.
I have a question related to this thread but not exactly on point. If it’s too off-topic, I’m happy to start a new thread, but I think it’s a question with a straightforward answer.
The GPS satellites are in a variety of orbits – not different altitudes, but different orbital paths. Is this one of the reasons why they have to account for relativistic time effect? In a way, it’s true what tomh says – it doesn’t matter if they GPS satellites stay in sync with the time on Earth, as long as they are in sync with each other (I mean, other than wanting them to have the correct time, and being able to check that). But, will their varying orbital paths put them out of sync with each other?
Again, see “Doppler Effect” as mentioned above.
A passenger on the train hears the train whistle at a particular frequency.
A person outside the train as it passes by hears a different frequency.
They give different answers, so which one is “correct”?
Both.
Yes, it does. They’ve got different relative velocities to each other and this should pop up in their clocks as well, though there’s also going to be some natural drift between clocks in any event.
The amount of correction from relativity in GPS isn’t exactly small, either. It amounts to ~10km per day according to theory, which would be noticeable inside a day for things like long haul flights and ocean navigation.
Noticing that sort of thing that would make somebody rich and famous if it turned out relativity didn’t work. That’s the part that CTers don’t really get. There’s more benefit to being the contrarian - and having the numbers to back it up - than otherwise. The problem is that pesky qualifier. There have to be numbers that back it up in the real world.
Thanks! So, even if the GPS controllers didn’t care about syncing with ground time, they would still have to correct for relativistic effects in order to keep the satellites in sync with each other. tomh4040, any comment on that? Or, do you just deny that they would fall out of sync with each other?
Depends what you mean by “have to account for relativistic effects”. The orbits require different relativistic correction that includes accounting for the eccentricity of the orbit’s effect on the relativistic correction. The different orbits also pass over an oblate Earth (aka quadrupole potential), and that oblateness causes very fine errors in the correction that are apparently too small to worry normal receivers.
OTOH, ultra precise applications, such as location accuracy to millimetres, or time accuracy enough to time pulsars winding down, may even see the effects of other planets perturbing the clocks.
This is my go to article on all things GPS and relativity.:
Note, they’d have to correct for normal clock drift as well. And there’d still be other effects like signal multi-pathing and atmospheric losses.
Even if the satellites were somehow magically sync’ed up perfectly at all times, receiver stations on the ground can still get different timings from the satellites from the state of the atmosphere below the satellites themselves.
tom, I challenge you to perform an experiment disproving relativity.
The question is valid. It is very simple :- Which clock, according to the theory of relativity is running slow? If the theory is sound, that question aught to elicit a simple answer.
Einstein said that these effects were real, so “one clock appears to run slower…” is not a valid answer. Neither is talking about changing reference frames. Either one clock is running slower than the other or it is not.
Rick Jay, answer professor Dingle’s question.
Look, I’m really sorry, but you are just not getting it. I guess that is the entire point. Einstein said the effects are real. Correct. He also said there is no preferred frame of reference. There is no contradiction. You are stuck with a mindset that simply can’t grasp the idea that there isn’t a single frame of reference. I can’t help that.
You are demanding an answer that does not fit with reality. The framework you are demanding an answer in is simply one in your mind.
Until you get the idea of no distinguished frame of reference you are lost.
Francis Vaughan. I know all about frames of reference, I know that the clocks are in different frames. That does not preclude answering the question by using the rules of relativity. So according to the theory, which clock is it (and why that one)?
The theory of relativity says neither. You continue to demand a different answer, but there isn’t one. “Neither” is the answer relativity provides. It isn’t me, it is what the theory demands is the answer. There is no preferred reference frame. The statement alone demands that the answer is neither. If you understand about reference frames you should understand this. That you continue to demand a different answer simply indicates that you don’t understand relativity. I can’t help that either.
I’m just playing along here, and it’s pretty obvious to me that the answer is “neither,” as well. Why this is unacceptable to our esteemed poster, I don’t know. But thanks for fighting the good fight guys – Lord knows I lack the patience to do so.
Francis (I am typing your name quite frequently, so I hope you don’t mind me shortening it).
Yo referred to PubMed Central for a treatise on GPS, and in it I found this
“The Sagnac effect is very important in making such comparisons, as it can amount to hundreds of nanoseconds, depending on the geometry. In 1984 GPS satellites 3, 4, 6, and 8 were used in simultaneous common view between three pairs of earth timing centers, to accomplish closure in performing an around-the-world Sagnac experiment. The centers were the National Bureau of Standards (NBS) in Boulder, CO, Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig, West Germany, and Tokyo Astronomical Observatory (TAO). The size of the Sagnac correction varied from 240 to 350 ns.”
“240 to 350ns”? Shouldn’t that be “0 to 207ns”? The effect is supposed to be due to Earth’s rotation, meaning it should be zero at the poles. And how did it get up to 350ns when 207.4ns represents the maximum possible which is at the equator?
Tom.
One would need to look at the full geometry. The satellites are in orbit, so rotating about the Earth as well. It isn’t just the geometry of the earth stations that may need to be taken into account here.
Not a problem.
I’m timing out for today. Well past time to be asleep here.
Apparently you don’t, or at least, you’re completely failing to grasp the fundamental role of reference frames in special relativity.
The question is meaningless without the specification of a reference frame; it falsely implies either that a reference frame is irrelevant, or that there is some implicit preferred reference frame. It is foundational to relativity that neither is true. It’s really very simple: describe the reference frame you’re in in terms of the observed velocity of the first clock, v1, and the observed velocity of the second clock, v2, and I’ll tell you which one is running slower, and by how much. Without that qualification, the question has no meaning.
You are equally confused in describing your hypothetical spaceship with the exhaust being used as a frame of reference, claiming that you’re free to use that since all frames of reference “are equal”. That’s not what special relativity says and that wording is subject to a contrarian misinterpretation. What special relativity says is that all inertial reference frames are equivalent in terms of how the laws of physics are observed within them. It does not say that measurements between co-moving frames of reference will always be the same, because those will depend on the relative velocity observed.
In this case, you’re free to choose the rocket exhaust as your frame of reference, but you then have to understand what you’re measuring. The fuel is accelerating along with the rocket, and at any instant in time, the rocket will always be observed to be traveling at a constant velocity of precisely 3000 m/s away from that frame of reference. Because of that, what you’re actually measuring is velocity in proper time, or proper velocity, just like measurements taken on the spaceship itself would show. It’s only from a frame of reference detached from the ship itself, such as earth or beings on Alpha Centauri, that one observes that ship can only asymptotically approach light speed, that time dilates and approaches zero as v approaches c, and that from this frame of reference the trip takes many years.
There also appear to be a great many other things where you could benefit from doing some reading instead of making uninformed claims, such as how particle accelerators work and how GPS works. I note also that when presented with evidence such as the kinetic energy graph in my post #48, you just ignore it, which makes me wonder if you’re even interested in educating yourself with facts.