Battery life on VERY fast moving object

[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.

 

[davidjoe]

Speed, above, by me has been about a fraction if C. C is a certain distance per second, with seconds being accepted as a unit that is definite on earth. It’s not that it’s an absolute quantity, more that I’m just not interspersing different frames into the hypothetical.

 

[PeterDonis]

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

@PAllen's response is a good one, but I would add that there is no reference frame that is "absolute" in the sense you are implying here. There is no reference frame in which time, distance, speed, etc. are the "true" ones, "unaffected by dilation" or anything else.

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?

Because there is no such thing as "a 1 kilometer length" without it being relative to something. For example, if you put out a 1 kilometer long ruler and say that is "a 1 kilometer length", then you are measuring lengths relative to that ruler, which means relative to that ruler's rest frame. (And even that assumes that the ruler can be treated as a rigid body, which will not be true for all possible states of motion of the ruler or all possible spacetime geometries--if the ruler is being subjected to forces or is free-falling in a curved spacetime, it will not be a perfect rigid body.) There is no way to define "a 1 kilometer length" without choosing something tangible to refer it to.

once you knew that your clock was not synchronized with earth, you would have no idea by how much this was the case

Sure you can. You can determine your orbital parameters around Earth, and use that to compute the difference in clock rates. Indeed, that is exactly how GPS works: the orbital parameters of each GPS satellite are known with high precision, and that enables their clock rates relative to Earth clocks to be calculated with high precision--which in turn enables the signals from the satellites to be used by Earthbound GPS receivers to calculate position and time with high precision.

 

[PeterDonis]

C is a certain distance per second, with seconds being accepted as a unit that is definite on earth.

"Distance" in SI units is defined in terms of the speed of light having the defined value of 299,792,458 and the SI second defined in terms of a cesium hyperfine transition; there is no independent unit of "distance" in SI units.

In "natural" units, which are often used in relativity (I use them all the time when posting calculations here), $c$ is defined to be $1$.

 

[PeroK]

Speed, above, by me has beta about a fraction if C. C is a certain distance per second, with seconds being accepted as a unit that is definite on earth. It’s not that it’s an absolute quantity, more that I’m just not interspersing different frames into the hypothetical.

As you sit at your desk typing in your posts, what is your definite speed? How do you measure it?

 

[davidjoe]

As you sit at your desk typing in your posts, what is your definite speed? How do you measure it?

For me, measurement would be from the “birds eye” view, centering over my head, and I could draw larger and larger circles (going higher) to determine when I moved, relative to still things. Until the circle is continent size, I’m not seeing movement, then it’s tiny movement, then orbital movement and so on…

 

[PeroK]

For me, measurement would be from the “birds eye” view, centering over my head, and I could draw larger and larger circles (going higher) to determine when I moved, relative to still things. Until the circle is continent size, I’m not seeing movement, then it’s tiny movement, then orbital movement and so on…

Hmm? Legal arguments, it seems, are very different from mathematical arguments!

 

[PeterDonis]

For me, measurement would be from the “birds eye” view, centering over my head, and I could draw larger and larger circles (going higher) to determine when I moved, relative to still things.

What are "still things"? You're still assuming that something can be "still" in an absolute sense. It can't. There is no such thing. All motion is relative.

Until the circle is continent size, I’m not seeing movement, then it’s tiny movement, then orbital movement and so on…

What you actually mean here is: you are not moving relative to the Earth (at least not when you are sitting typing your posts at a desk--you would be if you were typing them on a bus or train en route between stops). But you are moving relative to the sun, and relative to the center of the Milky Way galaxy, and...

In other words, all motion is relative. There is no absolute sense in which you, or anything else, are "moving" or "still".

 

[davidjoe]

Hmm? Legal arguments, it seems, are very different from mathematical arguments!

I could say an accelerometer would tell me if I moved, but it’s not going to tell me speed. If I knew size of other things in the concentric circles, I could deduce my speed, relative to them.

I do get the point about “relative to other objects” being a way to describe my speed. But, technically, if I’m looking down at me, (a camera) and the earth I see moving around the sun, but all objects are removed, I still see the earth circling, and I didn’t need the other objects to determine that.

 

[PeterDonis]

I could say an accelerometer would tell me if I moved

No, it tells you whether or not you are being subjected to a force. An accelerometer attached to you as you sit at your desk, at rest relatve to the Earth, reads nonzero. (Nowadays smartphones make it easy to test this.)

I do get the point about “relative to other objects” being a way to describe my speed.

Then why do you insist on backing away from the point immediately?

But, technically, if I’m looking down at me, (a camera) and the earth I see moving around the sun, but all objects are removed, I still see the earth circling, and I din’t need the other objects to determine that.

Yes, you do--you need the camera. You are assuming that the camera is "at rest". But that's relative. Relative to the Earth, it's the camera that is moving and the Earth that is at rest.

In other words, no, you still have not truly grasped what "all motion is relative" means, because you are failing to account for the camera as an "object" like everything else.

 

[davidjoe]

How do you type so fast.

Relative to me.

 

[PeroK]

I could say an accelerometer would tell me if I moved, but it’s not going to tell me speed. If I knew size of other things in the concentric circles, I could deduce my speed, relative to them.

I do get the point about “relative to other objects” being a way to describe my speed. But, technically, if I’m looking down at me, (a camera) and the earth I see moving around the sun, but all objects are removed, I still see the earth circling, and I din’t need the other objects to determine that.

My point was that fundamentally we are talking at cross purposes. To take an analogy. The law is to some extent arbitrary, but a specific legal framework has been laid down. It's no good if someone comes along and wants to have their own personal definition of legal terms and what the law means.

Likewise, we can't have a sensible, practical discussion about physics without using an established common set of definitions and terminology. And, the onus is on you to learn and adopt the standard definitions of things like velocity and speed and reference frames. We can't discuss physics using your "homespun" definitions of things. That doesn't work at all and leads nowhere.

 

[davidjoe]

I think an accelerometer does not detect force, just movement. If I attached one to the base of the Empire State Building and then shoved on it, there’s force but no movement.

 

[davidjoe]

My point was that fundamentally we are talking at cross purposes. To take an analogy. The law is to some extent arbitrary, but a specific legal framework has been laid down. It's no good if someone comes along and wants to have their own personal definition of legal terms and what the law means.

Likewise, we can't have a sensible, practical discussion about physics without using an established common set of definitions and terminology. And, the onus is on you to learn and adopt the standard definitions of things like velocity and speed and reference frames. We can't discuss physics using your "homespun" definitions of things. That doesn't work at all and leads nowhere.

I do like what you are saying here.

I would say that complying with one law should not put one in the position of breaking another. Rarely, it can though, but usually not because laws are proscriptive. Feds say no MJ, state allows RX, what’s a doctor to do. But usually gets straightened out immediately if it does.

Physics seems to challenge me. For example. Can’t explain the speed of galactic motion - invent dark matter to explain it.

 

[PeroK]

Physics seems to challenge me. For example. Can’t explain the speed of galactic motion - invent dark matter to explain it.

That's an open question. Before Newton, Kepler's laws were known as an observable phenomeon by had no theory to explain them. Newton invented the force of gravity to explain them. This replaced "the hand of God"!

Now, galaxy rotational dynamics are an observable phenomenon. There are at least two theories put forward to explain them. Dark matter is one and MOND is another. This is the way science works.

 

[Sagittarius A-Star]

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.

A precondition that you can understand it is, that you first fully understand the relativistic calculation of the Sagnac-effect with respect to the rotating reference frame and the calculation of the Ehrenfest-"paradox".

Links:

1. http://www.physicsinsights.org/sagnac_1.html
2. https://en.wikipedia.org/wiki/Ehrenfest_paradox

Not everything what you don't fully understand must be incorrect.
Non-inertial (i.e. rotating) reference frames maybe more complicated than you think they are.

 

[jbriggs444]

I think an accelerometer does not detect force, just movement. If I attached one to the base of the Empire State Building and then shoved on it, there’s force but no movement.

They detect [non-gravitational] net force^(*). They are designed to be insensitive to stress, such as someone pushing on one side while the Empire State Building resists on the other.

[This is in contrast to a bathroom scale which is designed to be sensitive to the stress of feet pushing down on one side and the floor up on the other]

If you have attached an accelerometer to the base of the Empire State Building, it will detect a net force of magnitude $mg$ directed upward despite the lack of movement or acceleration relative to the local rest frame of West 34th Street.

You may have noticed that West 34th Street is not in free fall.

(*) To be pedantic, an accelerometer measures the stresses that are created in supporting a test mass. That test mass is buried inside the device and held approximately stationary by materials that can report their internal stress in some way (piezoelectric, piezoresistive or capacitive for instance). If you know the stress on the support material, you know the force on the test mass. If you know the force on the test mass, you know its acceleration. Since it is held approximately in place, the acceleration of the test mass matches the acceleration of the accelerometer. Which is what you wanted to know.

If the mass of the accelerometer as a whole is known then its acceleration relative to a free fall frame will be proportional to the non-gravitational net force on the accelerometer. In this situation, a measurement of acceleration and a measurement of non-gravitational external net force are one and the same thing. It is just a matter of how you calibrate the dial.

 

[PeroK]

You may have noticed that West 34th Street is not in free fall.

Wall Street was in free fall in 1929, but perhaps not West 34th Street.

 

[Nugatory]

I think an accelerometer does not detect force, just movement. If I attached one to the base of the Empire State Building and then shoved on it, there’s force but no movement.

Someone in free fall (and reasonably nearby) will find that the Empire State Building, foundations and all, is accelerating at 1g while they are at rest and their accelerometer is reading zero, no force because they’re free-falling. On what basis do you justify the claim that your perspective (no movement relative to you and the surface of the earth) is more “real” then the free-faller’s perspective (earth and building are moving towards them?

Before you answer, I’m going to add one more thing: the person you are trying to convince is an astronomer on Mars, sitting peacefully in their easy chair and watching through a telescope - so as far as they are concerned the free-faller and the surface of the earth are both moving.

 

[davidjoe]

I’m just the interested man on the street, guys, don’t judge me too harshly. I hadn’t realized Peter and PeroK weren’t the same author above, quoting me that fast, for a few minutes lol.

A true outsider’s perspective is interesting sometimes, maybe in my case concerning what is or isn’t as difficult to accept, or to grasp.

I think the YouTube sound bites by about 5-10 physicists or pop physics personas are for views yes, but also possibly an “inside baseball” pump the brakes message to academia saying hey, look where this is leading, especially in the logical extreme of this or that, subject.

Mass going to infinity, for example. Doesn’t matter how small the mass is, it goes to infinity. It receives “energy” going to infinity, to keep accelerating, and converts that energy toward infinite mass, just because it’s going faster. Common folk tend to reject infinity as part of, or the outcome of an equation. Strictly speaking, the tiniest fraction of it, is it.

Theories that support infinite universes, again, I would wonder what being observed can lead one to think there are infinite universes. 10 to the 500th power of string theories. As an outsider, one thing I don’t see is much public criticism of another’s ideas, in the field. Not saying it doesn’t happen. I’m just wondering how they get the momentum they do, such as string theory did.

 

[jbriggs444]

Mass going to infinity, for example. Doesn’t matter how small the mass is, it goes to infinity.

It does not. Mass (in the modern accepted meaning) does not increase with velocity at all. We do not use relativistic mass. We use rest mass. Also known as invariant mass. And call it "mass". See our Insight article here.

In the modern terminology, "mass" is the energy (divided by c²) of an object in a frame of reference where it is at rest.

A slightly more general definition is that the "mass" of an object is the magnitude of its energy-momentum four-vector. That is to say, $m^2 = E^2/c^4 - p^2/c^2$. For something at rest, $p=0$ and $E=mc^2$. In the case of anything moving at light speed, $E = pc$ and $m=0$.

It receives “energy” going to infinity, to keep accelerating

Yes. If mass is constant, energy increases without bound as speed increases toward $c$. The Bertozzi experiment is a good demonstration. And interesting to watch.

Common folk tend to reject infinity as part of, or the outcome of an equation. Strictly speaking, the tiniest fraction of it, is it.

Common people who have not taken a course in real analysis have a rather lacking understanding of infinite quantities.

Theories that support infinite universes...

Are not on topic in this thread.

More generally, if your mission is to kvetch about physics, you need to find some scholarly references. Or another forum.