I Battery life on VERY fast moving object

[davidjoe]

With respect to laser pulses, the effect of red shift, and of the satellite’s pulses emitting toward the fixed receiver from its changing coordinates in orbit, as it moves in orbit at a significant portion of C does explain the distortion and impossibility of a contemporaneous, normal conversation through radio waves, which are experiencing a similar effect to the laser’s pulses.

If the same satellite in orbit was tethered to the receiver tower by a taut, copper cable and the mode of conversation was not radio or light wave transmission, but carried by electrical impulse, one aspect of the original hypothetical that changes is that the satellite’s transmission signal is now confined and does not spread out along the curved path of the satellite, as it travels to the receiver. It’s a straight line transmission.

Does this confinement of electrical current to the wire, which on one end is moving with the satellite at relativistic speed, but on the opposite end is comparatively still, change anything in the analyses of the conversation’s distortion?

The cable if examined in isolation, and assuming it does not experience dilation or aging at different rates along its length, in a sense really does not “know” that it is moving, when only it is examined, again in complete isolation. The given is that a hard limit on the transmission of information, the speed of causality, is C, of course.

 

[PeroK]

The cable if examined in isolation and it does not experience dilation or aging at different rates along its length, in a sense really does not “know” that it is moving, if only it is examined in complete isolation.

The cable will definitely know its moving. In fact, no cable could realistically sustain the centripetal force required to keep an object moving in a circular path at relativistic speed. Even before you get to relativistic speeds, the tension required would exceed what is physically possible.

 

[davidjoe]

The cable will definitely know its moving. In fact, no cable could realistically sustain the centripetal force required to keep an object moving in a circular path at relativistic speed. Even before you get to relativistic speeds, the tension required would exceed what is physically possible.

That is true, but, … theoretically, for relativistic discussion. I’ve seen the spinning puppet in space where all surrounding objects are removed one by one, whose arms do rise. It’s hard to contradict that. But, I don’t know about electricity being impeded by centripetal force…

 

[Sagittarius A-Star]

Compared to a stationary laser equally distant but still, with an identical 10 minute battery, if the planet receives more energy, and/or a longer duration of impulse than the battery is rated to be able to produce, Is this problematic?

For the following answer I assume, that the usable electric energy in the battery is neglectable small compared the the rest-energy of the rocket, so that the laser emission does not significantly change the velocity of the rocket.

The planet receives the laser energy for a duration, that is $\gamma$ times longer than 10 minutes.
But the received power is by the same factor smaller. So the total received energy is not affected by the motion of the battery.

Edit:
But the received energy is by the same factor smaller. So the total received energy is smaller.

Do the words themselves from the ship stretch out into held note long tones with long gaps between them?

Yes.

 

[Ibix]

It’s a straight line transmission.

The wire will be curved, in fact. But time dilation is time dilation and it doesn't care whether you're signalling in a wire or in free space. If the ship signals constantly for one minute while it has a time dilation factor of ten relative to the planet frame, the planet frame will see the transmission taking ten minutes, and it will take ten minutes to receive.

 

[Ibix]

Yes.

Broadly I agree, but I would just repeat what I said before, that what you hear depends a lot on your transmission mode and how resilient your receivers are to the signal timing. Assuming a simple analogue signal it would just sound like playing a cassette tape slow, as you say, although you'd have to retune the receiver because the carrier wave would also redshifted by a factor of ten. Digital could sound quite different depending on how the electronics deals with the slow bit rate and slow on/off transitions, even after you've allowed for the carrier wave frequency change.

 

[davidjoe]

The wire will be curved, in fact. But time dilation is time dilation and it doesn't care whether you're signalling in a wire or in free space. If the ship signals constantly for one minute while it has a time dilation factor of ten relative to the planet frame, the planet frame will see the transmission taking ten minutes, and it will take ten minutes to receive.

I have heard explanations that photons do not “age” or experience time, and why that is, such that a 14B year old photon captured by Hubble “thinks” it just left and further we have probably all seen them slow to either capturable in slow motion or visible-in-real time, in certain mediums. The “speed of light” is extremely slow traveling through those mediums.

I am starting to get that the disparity is - as measured, at two independent locations, but in trying to test this little bit, how that works out, exactly with the complication of a link between them, seems like very fertile subject matter ground.

If I was looking down at that wire from above, similar to how we would look down at the radiation waves, emitting, traversing, and being received, I’m expecting that I’d see, if I could see charge flowing, that it would appear to traverse the wire at a constant rate. Probably true in both directions. Probably similar. I don’t know that this is correct though.

But if I looked down at a train approaching a station and were able to see its horn blast’s waves, I could see them bunch up into what amounts to higher frequency at the station due to the Doppler effect. It makes sense in the space between earth and a satellite. Logic suggests it must happen regardless of medium, so then it must occur in the wire as well as Ibix notes. The problem is the wire is fixed length and unlike the train and station, the source and receiver’s distance remains the same.

It’s harder to envision for me, as a result. It’s like envisioning a garden hose of fixed volume, where water is forced in at a very high rate and pressure, but comes out the other end, extremely slowly, over a very long time, as if it was compressed and with more being stored in the hose than its dimensional capacity permits.

 

[PeroK]

There's nothing like a bit of home-spun physics every now and then!

 

[davidjoe]

There's nothing like a bit of home-spun physics every now and then!

I have read somewhere that the frames must be independent. It was left as a just because, proposition. The lawyer in me is curious if that was because picturing a link, leads to questions, with answers, that lead to more questions, without answers.

I’m a lawyer, though a “but why”, kind of guy, too.

 

[Ibix]

I have heard explanations that photons do not “age” or experience time,

For one, don't talk about photons. They're incredibly subtle things and you will almost inevitably mislead yourself trying to think about them without a solid grounding in the maths of quantum field theory. There's a reason I've been talking about light pulses in this thread - it's all classical physics.

Second, proper time isn't defined along null worldlines, but light can clearly change with time, losing or gaining intensity or reflecting off things. It's overly simplistic to say it doesn't age.

The “speed of light” is extremely slow traveling through those mediums.

There's an important distinction between the constant $c$ and the speed at which light travels. The former is the same everywhere; the latter can change and is only equal to $c$ in vacuum. It's the constant $c$ that is relevant to relativity.

I’m expecting that I’d see, if I could see charge flowing, that it would appear to traverse the wire at a constant rate.

Almost certainly not. One end of the wire is moving at near $c$ in a circle, so the signal can make very little inward progress. Near the center the wire is practically stationary and the inward progress of electrical signals can be as high as normal.

Note that electrical signals are not the same as flows of charge. Electrons in wires move at far less than walking pace, but the light comes on near instantly when you flip the switch.

It’s harder to envision for me, as a result. It’s like envisioning a garden hose of fixed volume, where water is forced in at a very high rate and pressure, but comes out the other end, extremely slowly, over a very long time, as if it was compressed and with more being stored in the hose than its dimensional capacity permits.

Analogy is a bad way to do physics, which is why we use maths. Frankly, you're going to struggle to understand physics at the level you are asking about unless you learn the maths.

If you look back over this thread you will see that I didn't do the maths and got the wrong answer. When I did do the maths I worked out where I'd gone wrong. Even with my experience in relativity theory (I can pass for an expert in a bad light) my intuition misled me - as yours will. And you can't fall back on the maths as I did. You don't really need anything tougher than Pythagoras' theorem, although some calculus helps a lot.

 

[davidjoe]

Photons indeed, I hear you. No time passes in their frame at C, therefore possibly, no distance, could have been traveled, either.

 

[Sagittarius A-Star]

in their frame at C

Such a frame does not exist, because light moves at speed $c$ with reference to each inertial frame.

 

[davidjoe]

Such a frame does not exist, because light moves at speed $c$ with reference to each inertial frame.

I might have worded it better by saying if they travel at C and they measure no time passing, a nullity for them, they don’t perceive a distance traveled, either, distance being speed X time.

 

[Sagittarius A-Star]

I might have worded it better by saying if they travel at C and they measure no time passing, a nullity for them, they don’t perceive a distance traveled, either, distance being speed X time.

Such a measurement is not possible. For measuring time, you need a clock. For measuring distance, you need a ruler. Both have mass and therefore cannot move at the speed of light.

 

[Ibix]

No time passes in their frame at C, therefore possibly, no distance, could have been traveled, either.

There is a flaw in the chain of logic used to reach this view: it turns out you need two vectors that are each timelike, spacelike and null all at once. This is a self-contradiction, and reasoning from there is meaningless. That's how you end up with zen-sounding statements about how light moves without moving in no time - it genuinely is nonsense.

You cannot even define proper time for a pulse of light - it simply doesn't make sense. It's not that they experience zero time, it's that "experience" simply isn't a concept that applies. (And not merely because only humans experience, yadda yadda - because the concept of "time for a pulse of light" is a contradiction in terms.)

 

[davidjoe]

There is a flaw in the chain of logic used to reach this view: it turns out you need two vectors that are each timelike, spacelike and null all at once. This is a self-contradiction, and reasoning from there is meaningless. That's how you end up with zen-sounding statements about how light moves without moving in no time - it genuinely is nonsense.

You cannot even define proper time for a pulse of light - it simply doesn't make sense. It's not that they experience zero time, it's that "experience" simply isn't a concept that applies. (And not merely because only humans experience, yadda yadda - because the concept of "time for a pulse of light" is a contradiction in terms.)

I absolutely follow what you are saying and wonder if there is some intentional mystification of physics, especially in what I would call popular culture theoretical physics, going on. By this I do mean the zen like statements, and or focusing on paradoxical or apparently paradoxical aspects of physics.

Unrelated question, but do you think the popular (high viewership) personalities in physics and astrophysics really do dig into the math and/or push intellectual boundaries? I do realize this is very generally asked, I just don’t want to name specific individuals.

I do credit them for intriguing many and provoking thought processes in their general consumption releases. But for example, you would never glean that a photon is a controversial subject at all, from simply reading and watching current discussions about it, where it’s dealt with as a mundane, pat, known quantity.

 

[Drakkith]

I absolutely follow what you are saying and wonder if there is some intentional mystification of physics, especially in what I would call popular culture theoretical physics, going on. By this I do mean the zen like statements, and or focusing on paradoxical or apparently paradoxical aspects of physics.

Yes, pop-sci is generally oversimplified and overly focused on the 'big flashy stuff' like you say. Articles and videos are also almost always written/produced by someone who isn't and expert in the topic area, and even the ones that are authored by an expert are still usually oversimplified so that people can understand it.

Unrelated question, but do you think the popular (high viewership) personalities in physics and astrophysics really do dig into the math and/or push intellectual boundaries? I do realize this is very generally asked, I just don’t want to name specific individuals.

In their day-to-day work, sure. In their videos, articles, and other types of communication, no.

 

[Nugatory]

I absolutely follow what you are saying and wonder if there is some intentional mystification of physics, especially in what I would call popular culture theoretical physics, going on. By this I do mean the zen like statements, and or focusing on paradoxical or apparently paradoxical aspects of physics.

It’s not intentional mystification, it is the undesired but unavoidable consequence of not using math to describe things that can only be precisely described by math.

Unrelated question, but do you think the popular (high viewership) personalities in physics and astrophysics really do dig into the math and/or push intellectual boundaries? I do realize this is very generally asked, I just don’t want to name specific individuals.

Look at their CV. No one gets a physics PhD or a tenure-track position in a physics department without having really dug into the math and making some original contribution.

But for example, you would never glean that a photon is a controversial subject at all, from simply reading and watching current discussions about it, where it’s dealt with as a mundane, pat, known quantity.

Photons are not a controversial subject, just one that is impossible to discuss clearly without math. But the populizers are not trying to mislead, they’re doing the best they can with inadequate descriptive tools.

 

[PeterDonis]

No time passes in their frame at C, therefore possibly, no distance, could have been traveled, either.

if they travel at C and they measure no time passing, a nullity for them, they don’t perceive a distance traveled, either, distance being speed X time.

Neither of these statements are correct.

 

[davidjoe]

Neither of these statements are correct.

I know, rulers and clocks can’t reach C . Very, very literal construction guys, but I think if I were to take photons out of the statement, and just utilize people instead, which otherwise do perceive the passage of time and distance, it would be “fair” or fairer at least, to say that they, with anything else, would no longer perceive the passage of any time or distance at C. Realizing that it will be said they cannot reach C, I’ll go ahead and agree in advance, though it’s still a true statement the perception of time or distance travelled would stop at that point, and slow, to very nearly stop, extremely close to it.

I’m soft in understanding on the subject of the boundaries of reference frames. CERN for example is intuitively clear acceleration and velocity, relative to us. It’s less clear to me, after that and on large scales.

Math as a representation of relationships and a prediction of positions isn’t inherently problematic for me, I don’t shy away from it, but I don’t use it daily, and haven’t formally honestly since the 90’s. But, I notice from several posts that the plural is maths, now, and that does make me feel old, as that word usage is peculiar to me and would have been unacceptable as the plural of math was math, as of my last course, about 1992. Can I ask if 52 is on average, about a generation or more older than most members here?

 

[PeterDonis]

Very, very literal construction guys

No, it's physics. Your dismissive attitude here is not going to get you anywhere. Physics is not done by waving your hands. It's done by understanding its laws.

I think if I were to take photons out of the statement, and just utilize people instead, which otherwise do perceive the passage of time and distance, it would be “fair” or fairer at least, to say that they, with anything else, would no longer perceive the passage of any time or distance at C.

No, you wouldn't, because people cannot move at C. People are timelike objects; photons are lightlike objects. Those are two physically different kinds of things, and concepts like "perceive the passage of time and distance" only apply to timelike objects. They do not apply to lightlike objects. That is the physics; that is what the laws of relativity say. You can either accept that and try to understand it, or dismiss it and end up having your thread closed.

Realizing that it will be said they cannot reach C, I’ll go ahead and agree in advance, though it’s still a true statement the perception of time or distance travelled would stop at that point

No, it is not a true statement, it's a false one. You really, really, really need to learn what the laws of relativity actually say instead of continuing to make baseless wrong claims.

and slow, to very nearly stop, extremely close to it.

This is not correct either. The correct statement is that "rate of time flow" as you are using the term here has no physical meaning. You, right now, are moving at 0.9999999c relative to cosmic ray particles reaching Earth. Is your time slowed? No. That is the physics. The "time dilation" of you relative to the cosmic ray particles is just a coordinate artifact.

I’m soft in understanding on the subject of the boundaries of reference frames.

Then you should definitely not be making such confident statements about what you think relativity says. You should not be making statements at all.

Can I ask if 52 is on average, about a generation or more older than most members here?

I can't speak for other members, but you are younger than me by a number of years. And my last formal course in anything, including math, was about four years before your last one.

 

[PAllen]

unacceptable as the plural of math was math, as of my last course, about 1992. Can I ask if 52 is on average, about a generation or more older than most members here?

My last math course was in 1973 and I am a couple of decades older than you.

 

[renormalize]

But, I notice from several posts that the plural is maths, now, and that does make me feel old, as that word usage is peculiar to me and would have been unacceptable as the plural of math was math, as of my last course, about 1992.

https://www.thesaurus.com/e/grammar/math-vs-maths/
"The only difference between math and maths is where they’re used. Math is the preferred term in the United States and Canada. Maths is the preferred term in the United Kingdom, Ireland, Australia, and other English-speaking places."

 

[davidjoe]

No, it's physics. Your dismissive attitude here is not going to get you anywhere. Physics is not done by waving your hands. It's done by understanding its laws.


No, you wouldn't, because people cannot move at C. People are timelike objects; photons are lightlike objects. Those are two physically different kinds of things, and concepts like "perceive the passage of time and distance" only apply to timelike objects. They do not apply to lightlike objects. That is the physics; that is what the laws of relativity say. You can either accept that and try to understand it, or dismiss it and end up having your thread closed.


No, it is not a true statement, it's a false one. You really, really, really need to learn what the laws of relativity actually say instead of continuing to make baseless wrong claims.


This is not correct either. The correct statement is that "rate of time flow" as you are using the term here has no physical meaning. You, right now, are moving at 0.9999999c relative to cosmic ray particles reaching Earth. Is your time slowed? No. That is the physics. The "time dilation" of you relative to the cosmic ray particles is just a coordinate artifact.


Then you should definitely not be making such confident statements about what you think relativity says. You should not be making statements at all.


I can't speak for other members, but you are younger than me by a number of years. And my last formal course in anything, including math, was about four years before your last one.

I’m not trying to be argumentative with you, but this excerpt is literally Microsoft Bing’s first hit on the subject, highlights are not mine.

 

[davidjoe]

This is the article.

 

[PeterDonis]

I’m not trying to be argumentative with you, but this is excerpt is literally Microsoft Bing’s first hit on the subject, highlights are not mine.

I'm not trying to be argumentative with you either, but you should know that doing random Internet searches is not a good way to learn physics. You need to be learning from textbooks and peer-reviewed papers.

This is the article.

Nothing you provided gives a link to any article.

 

[PAllen]

I’m not trying to be argumentative with you, but this excerpt is literally Microsoft Bing’s first hit on the subject, highlights are not mine.


View attachment 342883

Bing is a search engine. It finds nonsense just as easily as good science. Actually, it is skewed towards bad science, since there is more of this on the internet, so its weighting ends up favoring bad science.

The above statements are a mixture of just wrong and totally meaningless.

 

[Nugatory]

I’m not trying to be argumentative with you, but this is excerpt is literally Microsoft Bing’s first hit on the subject, highlights are not mine.

Not everything you find on the internet is correct, and not everything correct is highly ranked by the search engines. In this case Bing is serving highly ranked incorrect content.

 

[davidjoe]

I don’t know enough to disagree with you, I only know I’m not saying something that I have not understood, from other sources.

 

[Drakkith]

I know, rulers and clocks can’t reach C . Very, very literal construction guys, but I think if I were to take photons out of the statement, and just utilize people instead, which otherwise do perceive the passage of time and distance, it would be “fair” or fairer at least, to say that they, with anything else, would no longer perceive the passage of any time or distance at C. Realizing that it will be said they cannot reach C, I’ll go ahead and agree in advance, though it’s still a true statement the perception of time or distance travelled would stop at that point, and slow, to very nearly stop, extremely close to it.

Some issues: Reference frames are relative. If something is moving at .5c relative to us, then we are moving at 0.5c relative to it. So statements about what light may or may not being doing in a reference frame moving at c relative to us would force us to be moving at c relative to light. Which introduces some problems to which the only solution that is self-consistent is that light cannot be assigned a reference frame and any talk of the passage of time for objects moving at c is meaningless.

I don’t know enough to disagree with you, I only know I’m not saying something that I have not understood, from other sources.

Any source that talks about light as having a reference frame is wrong. It doesn't and any attempt to do so introduces severe problems.

 

[PeterDonis]

I don’t know enough to disagree with you

Indeed.

I only know I’m not saying something that I have not understood, from other sources.

You might want to read our rules on acceptable sources, which are under "Acceptable Sources" on this page:

https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/

No source you have referenced is acceptable according to our guidelines.

 

[Sagittarius A-Star]

I don’t know enough to disagree with you, I only know I’m not saying something that I have not understood, from other sources.

Here is a good source:
http://www.scholarpedia.org/article/Special_relativity

 

[davidjoe]

Here is a good source:
http://www.scholarpedia.org/article/Special_relativity

Thank you, I’ll print this at the office and look forward to reading it. I do hope members realize that I was merely reprising that passage in response to the comment on my basis for my prior comments, and not as an advocate for its truth in comparison to the veracity of other resources. I’ll add that positions in that excerpt do seem to be commonly held views often reproduced in whole or part, and certainly I over years have had enough exposure to them to be assuming it was accepted thought, when it evidently is not at all, and is actually considered to be inaccurate, and as said I openly do not have reason to disagree.

I have tried to do the opposite of confidently staking out the truth of any positions let alone novel ones, by saying several times already in my short experience here, that I am not in this field, I’ve been an attorney since 1997 (not a natural science field) and my thoughts are expressions and discussion based only on what I have gleaned is the current thought, from consumer grade, readily and widely accessible sources, with my own inferences drawn from them, and characterized that way. I certainly didn’t believe them (such as the excerpt on experiencing time stoppage at C above) to be either controversial or wrong, and I do appreciate that, now. It is a valuable lesson and well taken.

 

[Sagittarius A-Star]

Thank you, I’ll print this at the office and look forward to reading it.

I think this is a good idea. I like this text. However, please be aware, that Wolfgang Rindler used in the chapter about relativistic mechanics the "relativistic mass", which is today considered an out-dated terminology.

A WORD OF CAUTION: there is a school of thought (mainly among particle physicists who, after all, are the main consumers of collision mechanics) who reject the concept of relativistic mass altogether. Wherever we have an $m_u$, they would replace it by $E/c^2$ ; our $m_0$ becomes their $m$, simply called the mass; and our $E=m_uc^2$ becomes their $E=\gamma(u)mc^2$. This has nothing to do with physics. It is simply a choice between two alternative conventions

Source:
http://www.scholarpedia.org/article/Special_relativity:_mechanics#The_equivalence_of_mass_and_energy

A discussion of it:
https://edisciplinas.usp.br/pluginfile.php/7731007/mod_resource/content/1/Rindler-et-al-1990.pdf

 

[jbriggs444]

widely accessible sources, with my own inferences drawn from them

A serious and, perhaps, unavoidable problem with widely accessible sources is that in order to be accessible and understandable without careful definitions and mathematics, things are simplified. Often oversimplified. Explained with heavy use of analogy.

If the idea is to provide a bit of flavor, some amusement and awestruck wonder, this is no problem. The audience gets what they came to see.

However, oversimplification and analogy does not work as a basis from which to reason further. It is unreliable and utterly worthless as a jumping off point for an actual understanding. It is just one more layer to unlearn before an actual education can begin. You cannot trust the conclusions you reach by reasoning further from what you think you have learned in a popular video.

 

[Sagittarius A-Star]

Effect of time dilation when distance between two objects remains constant

For the following I assume, that the usable electric energy in the battery is neglectable small compared the the rest-energy of the rocket, so that the laser emission does not significantly change the velocity of the rocket.

The rocket moved momentarily with $v$ in $x$-direction and emits a laser pulse in $y$-direction towards the planet (transversal Doppler shift in the receiver's frame).

The 4-momentum of the laser pulse in the (unprimed) planet's frame is is $\mathbf P = \begin{pmatrix} p_{ct} \\ p_x \\ p_y \\ p_z \end{pmatrix} = {E \over c^2} \begin{pmatrix} c \\ 0 \\ c \\ 0 \end{pmatrix}$

Lorentz-transformation into the (primed) rocket's frame:

$p'_{ct} = \gamma (p_{ct} - {v \over c} p_x) = \gamma {E \over c} = c\delta m$
$p'_{x} = \gamma (p_{x} - {v \over c} p_{ct}) = -\gamma {E \over c^2}v$
$p'_{y} = p_{y} = {E \over c}$
$p'_{z} = p_{z} = 0$

$\Rightarrow {E \over c^2} = {1 \over \gamma} \delta m$ (=redshift)

Here $\delta m$ is the (rest-)mass-decrease of the battery and $E$ the received energy from the laser-pulse.

 

[Drakkith]

I have tried to do the opposite of confidently staking out the truth of any positions let alone novel ones, by saying several times already in my short experience here, that I am not in this field, I’ve been an attorney since 1997 (not a natural science field) and my thoughts are expressions and discussion based only on what I have gleaned is the current thought, from consumer grade, readily and widely accessible sources, with my own inferences drawn from them, and characterized that way. I certainly didn’t believe them (such as the excerpt on experiencing time stoppage at C above) to be either controversial or wrong, and I do appreciate that, now. It is a valuable lesson and well taken.

Learning physics without looking at the actual math and accepted rules of the theory is like using various web articles and videos about to learn about the law versus actually reading the laws from their official sources. It's fine if you want a summarized overview of what things are likely to be, but I bet you wouldn't be surprised to find a great many of the details wrong or omitted.

 

[davidjoe]

Note that some care is needed with this statement. It's not really correct. A better way to put it is that clocks in motion with respect to sn inertial reference frame tick slowly as measured by clocks at rest in that frame. Thay avoids nasty definitional questions around what "time slowing" might actually mean and grounds everything in physical measurements.

The sentence as written happens to work out in the case in this thread because one clock is moving in a circle at constant speed and one is inertial, but it's not a good general description.

Following up, my understanding is the relativistic speed of the satellite could separate two synchronized clocks, one in the satellite, and one on the surface.

Is speed also relative, as time is, affecting the calculation of orbital speed? For example if the satellite is in low earth orbit, say 150 miles up, seeking to be accelerated to 4 circumferential revolutions per second under ground control, as determined by interrupting say 2 perpendicular beams along its path, equidistant, to level out at 8 interruptions per second, then the satellite levels out at roughly 4/7 C.

4/7 C is a relativistic speed. If the control of the orbiting satellite is not ground based, but instead is performed from the satelite wherby it accelerates and decelerates so as to level out and maintain breaking those two light beams eight times per second according to its clock, to cover the distance required to put its speed at 4/7 C, then its speed won’t be the same as if measured from earth, right? (because the clocks are keeping time differently)

In the original hypothetical 10 minutes (600 seconds) in orbit could equal 30 minutes 1,800 seconds) passing on the ground.

The battery whose life was 10 minutes could be explained to extend to 30 minutes of weaker emission as measured on the ground through red shift but, if both the ground sensors and the ship experience the ship breaking the light beam eight times every second to achieve 4/7 C, how does this reconcile with three times as many seconds passing on the ground?

 

[Drakkith]

4/7 C is a relativistic speed. If the control of the orbiting satellite is not ground based, but instead is performed from the satelite wherby it accelerates and decelerates so as to level out and maintain breaking those two light beams two times per second according to its clock, to cover the distance required to put its speed at 4/7 C, then its speed won’t be the same as if measured from earth, right? (because the clocks are keeping time differently)

Hmm. I wonder how length contraction works into this?

 

[jbriggs444]

For example if the satellite is in low earth orbit, say 150 miles up, seeking to be accelerated to 4 circumferential revolutions per second under ground control, as determined by interrupting say 2 perpendicular beams along its path, equidistant, to level out at 8 interruptions per second, then the satellite levels out at roughly 4/7 C.

So we have a satellite that is orbitting the earth 4 times a second. Meanwhile, light can orbit the earth about 7 times a second. So yes, this is 4/7 C -- as measured from the inertial rest frame of the earth.

4/7 C is a relativistic speed. If the control of the orbiting satellite is not ground based, but instead is performed from the satelite wherby it accelerates and decelerates so as to level out and maintain breaking those two light beams eight times per second according to its clock, to cover the distance required to put its speed at 4/7 C, then its speed won’t be the same as if measured from earth, right? (because the clocks are keeping time differently)

At any instant, the speed of the Earth in the instantaneous rest frame of the satellite will match the speed of the satellite in the rest frame of the Earth. That is 4/7 C.

Things get sticky when you try to shift from the inertial frame where the satellite is momentarily at rest to an accelerating frame where the satellite is continuously at rest. Any such accelerating frame (there is some freedom in choosing how to set one up) is going to be wonky in some way. For instance, if you assume an isotropic speed of light and try to synchronize clocks all the way around the orbital path of the satellite, you'll find that the satellite clock is out of synch with itself.

This is at the heart of the Ehrenfest paradox.

Since length contraction, time dilation and relativity of simultaneity are features that arise when comparing coordinates between inertial frames of reference, it ought to be no surprise that they stop working as expected when blindly applied between an inertial and a non-inertial frame.

It turns out that there is no problem applying the time dilation formula to Earth clocks to compute the elapsed proper time on the satellite. If an orbit takes $\frac{1}{4}$ second as judged by Earth and if the time dilation factor is $\sqrt{1-v^2/c^2}$ for $v=\frac{4}{7}c$ then I make it about 0.2 seconds per "orbit" as measured on the satellite clock. [Elapsed proper time is a direct physical measurable. Not just a convention that is affected by choice of coordinate system]

I am taking "orbit" to mean a low altitude circular equatorial trajectory starting above Quito Equador and then arriving back there again a bit later.

 

[davidjoe]

I follow the paradox. While clocks’ recordation of time will differ from each other due to one traveling at relativistic speed, an object as this satellite can only be moving at one true speed at a given instant.

Two calculated speeds cannot both be correct, to the extent they differ, but the satellite and the earth must agree on their count of how many times the satellite has broken the light beams. Divergence here in the count, I think is an impossibility. The light beams are the control in hypothetical. If two different speeds are calculated based on the passage of two different periods of time as measured by different clocks, then at least one of them cannot be correct.

My thought is the earth clock would support speed of 4/7 C, with 8 beams per second being broken. The satellite’s clock necessarily varies from the earth clock, and if used to calculate speed, produces a different speed, which is the incorrect one.

 

[jbriggs444]

I follow the paradox. While clocks’ recordation of time will differ from each other due to one traveling at relativistic speed, an object as this satellite can only be moving at one true speed at a given instant.

There is no such thing as "one true speed". There are only relative speeds.

Two calculated speeds cannot both be correct

Certainly they can both be correct. Because they are not measures of the same thing.

to the extent they differ, but the satellite and the earth must agree on their count of how many times the satellite has broken the light beams.

Yes. Over any trajectory, the number of passings over Quito Equador is an invariant physical observable.

The coordinate distance covered during the trajectory and the coordinate time elapsed during the trajectory are relative to a coordinate system. If you want to call the ratio of those two quantities "speed", then the speed of the satellite or of the Earth beneath will depend on a choice of coordinate system.

 

[davidjoe]

The coordinate distance covered during the trajectory and the coordinate time elapsed during the trajectory are relative to a coordinate system. If you want to call the ratio of those two quantities "speed", then the speed of the satellite or of the Earth beneath will depend on a choice of coordinate system.

4/7 C is a certain and definite number of kilometers per second. It’s approximately 4/7 of 300,000 kilometers per second.

If the circumferential revolutions were a given distance, such that breaking the light beams 8 times per earth second means the satellite is traveling at 4/7 C, and satellite achieves that and maintains it, but its clock is no longer synchronized with earth’s, so that it does not register 8 beams broken per (earth) second, and it uses its clock to attempt to determine its speed along the circumferential path, then isn’t it going to calculate a speed that is not 4/7 C, the stipulated speed that it is going when breaking 8 beams per second? If this is true, then is that calculated speed incorrect?

 

[Ibix]

4/7 C is a certain and definite number of kilometers per second. It’s approximately 4/7 of 300,000 kilometers per second.

If the circumferential revolutions were a given distance, such that breaking the light beams 8 times per earth second means the satellite is traveling at 4/7 C, and satellite achieves that and maintains it, but its clock is no longer synchronized with earth’s, so that it does not register 8 beams broken per (earth) second, and it uses its clock to attempt to determine its speed along the circumferential path, then isn’t it going to calculate a speed that is not 4/7 C, the stipulated speed that it is going when breaking 8 beams per second? If this is true, then is that calculated speed incorrect?

I've missed a few posts here and might have slightly lost the thread of this, but I think the issue is that the quantity you are thinking of as "the speed of the satellite" is the speed measured in the Earth frame. To get that you need to divide the distance travelled by the satellite as measured by the Earth divided by the time taken as measured by the Earth. Dividing the distance measured by the Earth by the time taken as measured by the satellite gives you a meaningless number.

You may want to know the speed of the Earth as measured by the satellite. That is where a lot of complications come in, fundamentally because you can't measure distance travelled through space without defining "space". There is no unique definition of the term in relativity. For inertial observers there is only one sane way of defining it, so there's a straightforward answer to what it means for the Earth to measure distances. But the satellite is not inertial, and there are quite a lot of issues in defining space in a way that won't cause odd behaviour in your calculations. You can come up with more than one number, and all of them will be loaded with caveats and assumptions.

 

[davidjoe]

I appreciate your reply, both content and the fact of it, as well as the fact that so many others have. I believe it is largely true that there are no new thoughts under the sun and likely much of my opining is neither new nor interesting.

Ibix, your reply does anticipate my points and is subtle and nuanced in the word choice of “meaningless”, (as opposed to “incorrect”) and as a lawyer I appreciate that. It tends to remove the implication of an expectation that the basic formula for deriving speed as distance over time, ought to apply to objects at relativistic speed, recasting it as an of course relativistic speed objects carrying a clock can’t calculate their speed with the clock, even if they are certain of it, from hypotheticals such as breaking a beam.

And they could be certain of their speed from breaking a beam with the following givens, a) they are constrained to a precise orbit of known distance, similar to the defined path of a SCSC, b) the beam itself that they cross carries a transmission of the time on earth, and c) they know how far the beam has travelled from it source to their interception (say 100 miles).

It was agreeable above to the poster and mentor I believe, that the satellite or ship and the earth will always agree on the count of crossings of a beam, or Quito there is no inherent divergence. It is a given that normally, one can determine the speed of a car for example, either from inside the car, or from outside of it, equally well, several different ways such as Doppler, known intervals and triangulation, and the quantities can agree.

Not so with objects at relativistic speed.

I cannot yet discern if the thinking is that the well publicized attention grabbing headlines and implications of SR and GR are by and large wrong, or right, or a qualified right and otherwise misleading, or, it’s a case by case analysis.

One of the things that seems intentionally designed to keep the public in a state of confusion is what I would call embedded contradictions. Maybe it’s simply the case of everybody in the classroom talking at once.

I can listen to or read physicists explain how nothing with mass could ever go the speed of light. It would require infinite energy.

In the context of a different discussion altogether, the same, or equally accomplished physicists will readily accede or even espouse that the entire universe is simply energy. Matter is simply another form of energy. Indeed if matter with mass were more like the solids we associate with it prevalently, instead of just energy packages, then it’s far more difficult to accept compression such that everything was in a singularity.

In fact physicists are seemingly certain even what we consider to be matter is basically nearly empty space, with merely almost ephemeral bound sub particles of energy.

But, as soon as we start talking about SR, massive objects are not a thing at all like energetic waves, all of which traverse the at the speed of light for infinity, as far as we can prove, using no more energy than they were born with.

Again, the same physicists, and probably all physicists actually will say that matter can be transformed into energy and vice versa. Matter is just an efficient packaging of energy. There is not even a universally accepted or inherent distinction between them, I’m aware of. If the mass of an object can change from speed, and approach infinity, (consider that) this undermines a distinction, but if there is less distinction between mass and energy, there is less reason to assume such results occur. No one, was legitimately, really and truly concerned, that the SCSC would create an object with so much mass its gravity would destroy the earth, were they?

Any of us could probably write out 100 contradictions, major ones. Ibix your reference to arriving at more than one number, with caveats and assumptions, this illustrates the point that we are not capturing what transpires yet, right, because to the degree they differ, they cannot all be correct.

 

[PeterDonis]

the basic formula for deriving speed as distance over time, ought to apply to objects at relativistic speed, recasting it as an of course relativistic speed objects carrying a clock can’t calculate their speed with the clock, even if they are certain of it, from hypotheticals such as breaking a beam.

You keep using the word "speed" as if it were an absolute quantity. It's not. That is one of the main points of relativity. You can use standard techniques to measure your speed relative to something else using your clock. You just have to use the correct relativistic math to analyze your data.

It is a given that normally, one can determine the speed of a car for example, either from inside the car, or from outside of it, equally well, several different ways such as Doppler, known intervals and triangulation, and the quantities can agree.

Not so with objects at relativistic speed.

Why not? You can do the same things you just described with objects moving at relativistic speed relative to some known object or objects. Again, you just have to use the correct relativistic math to analyze your data. This is a solved problem and has been for decades.

Ibix your reference to arriving at more than one number, with caveats and assumptions, this illustrates the point that we are not capturing what transpires yet, right, because to the degree they differ, they cannot all be correct.

Nonsense. Numbers that represent different observables can of course be different and still all be correct. That is all that is going on here. Things like "speed", "length", and "time" are not absolutes; "speed", "length", and "time" relative to you are different observables from "speed", "length", and "time" relative to me, if I am moving relative to you. So the fact that we get different numbers for these observables is no problem at all; quite the contrary, it is necessary.

In the particular case @Ibix was talking about, there is no such thing as a unique "rest frame" for an object. There are always multiple different coordinate conventions you can choose, and those conventions affect the numbers that you get when you do various calculations. However, none of this will change invariants, quantities that do not depend on your choice of coordinate system. For example, the quantity "time elapsed on your clock between you leaving Earth and you arriving at Alpha Centauri on Universal Spaceways Flight 265" will be the same regardless of anyone's choice of coordinates. And those invariants are where the actual physics lies.

 

[PAllen]

It tends to remove the implication of an expectation that the basic formula for deriving speed as distance over time, ought to apply to objects at relativistic speed,

There is a term in relativity for the notion of change of distance per some inertial frame divided by proper time per some observer (timelike world line). It is called celerity, and it has no upper bound in special relativity (it can be arbitrarily superliminal). It is a completely different quantity than relative velocity, which, in SR may be defined as between a momentarily comoving inertial frame for some arbitrary observer, and some other inertial frame (e.g. earth). This quantity is always subluminal, this is the only form of relative velocity commonly used in special relativity. This quantity (relative velocity) is also always the same in magnitude but opposite in direction depending on which frame you use as the 'base'.

 

[PeterDonis]

I cannot yet discern if the thinking is that the well publicized attention grabbing headlines and implications of SR and GR are by and large wrong, or right, or a qualified right and otherwise misleading, or, it’s a case by case analysis.

Actual physics is not "attention grabbing headlines". It's building models that make accurate predictions. The actual models in SR and GR make accurate predictions. A good everyday example is GPS: if the GPS in your smartphone is consistently accurate, you are proving the accuracy of the predictions of SR and GR constantly every day.

You say you are a lawyer, and you appear to be taking a lawyer's viewpoint on this, as if you were trying to catch physicists in a lie the way you would try to catch a hostile witness. Physics doesn't work like that. The actual content of physics is not the "attention grabbing headlines" or the pop science books and articles and videos, even when Nobel Prize winning physicists write or produce them. The actual content of physics is the models that make accurate predictions, and the only way to learn them properly is to look at the actual papers and textbooks that describe the models and their experimental support.

 

[davidjoe]

Peter, wouldn’t there be a reference frame where nothing at all impacts the time a clock keeps? Not dilation from “speed” or gravity, or rotation of earth, or anything else? Speed as determined there, by such a clock would be nominal speed, for lack of a better term. I would think that at the macro scale by volume, this is normally the condition a clock would randomly be in. I get that distance has to be ascertained. I think where we might disagree is that you need to compare that quantity relative to some other object. Why would it not be possible to simply say that an object covers a 1 kilometer length without deviating, so as to trigger an accelerometer, per second, according to a clock that is unaffected by any form of dilation?

I think one or two posting above, but at least me, considered that once you knew that your clock was not synchronized with earth, you would have no idea by how much this was the case, absent some extraordinary mechanisms to ascertain it (which I inserted into the hypo). Therefore, you could not use any correction formula.

 

[PAllen]

Peter, wouldn’t there be a reference frame where nothing at all impacts the time a clock keeps?

Nothing at all ever impacts the time a clock keeps (if it is an "ideal clock"). This is referred to as the clock hypothesis. All clock differences in relativity (special or general) are differences between clocks, neither of which is considered wrong. Consider, for comparison, odometers on a flat surface. Different paths will measure different distances but neither odometer would be considered to be impacted or altered by its path.