Battery life on VERY fast moving object

[davidjoe]

TL;DR Summary

Effect of time dilation when distance between two objects remains constant

Accepted thinking is that time slows as speed increases, relative to a non-moving reference frame. But supposing that the object approaching C is a ship in rotation around the earth, and on that ship is a laser mounted on a gimbal such that the laser is always pivoting and trained on exactly the same solar panel mounted on a tower, on the North Pole, and the ship is always exactly the same distance from it.

Time passes quickly on earth relative to the ship. Does that laser beam, emitting X amount of energy “per second”, all of which is captured by the mounted panel, transmit a “longer duration” of concentrated energy to the earthbound solar panel than the the duration of the transmission, as measured from the ship?

Intuitively the battery’s power charge is a fixed amount that cannot increase just because it moves faster. What if the ship’s power source for the laser was a 10 minute battery cell, but the solar panel received 30 minutes of beam transmission?

What would that imply for the beam whose wavelength and emission intensity never changed, for a measured 10 minutes, on the ship?

 

[Ibix]

So you have a laser moving in a circle shining at the center of the circle.

Yes, the duration of the illumination as measured by the emitter and receiver will differ. So will the wavelength and frequency due to transverse Doppler. The records of energy transmitted and received would also differ because the recording devices are using different frames and energy is a frame dependent quantity. If the ship emits some total energy $E$ as measured in its frame rest frame then its total energy reduces by $E$. But in the frame where it is moving at $v$ its total energy reduces by $\gamma E$, where $\gamma=\left(1-\frac{v^2}{c^2}\right)^{-1/2}$ is the Lorentz gamma factor. So the total energy received is higher.

The planet sees more energy received because it gets the electrical energy plus the kinetic energy associated with that.

 

[Ibix]

Accepted thinking is that time slows as speed increases, relative to a non-moving reference frame.

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.

 

[PeroK]

Accepted thinking is that time slows as speed increases, relative to a non-moving reference frame.

I would say that this is essentially wrong. Or, at best, misleading. Speed is frame dependent, so no object has an inherent speed.

Also, if you tidy up the wording, it isn't "accepted thinking". It's a clear prediction of the theory of SR (Special Relativity), which is routinely confirmed by experiments and by the syncronization of GPS satellite clocks.

 

[davidjoe]

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? It seems to me the battery’s starting energy is fixed. The solar panel could spin to always face the laser, in which case it really can’t “see” that it is moving at all, and appears to be just like a stationary laser fixed at the same distance. (Think of the fixed video camera inside a rolling car tire).

It occurs to me that this could be recast as an inquiry about trying to have a radioed conversation with someone in close, fast, orbit, whose time has slowed down.

The transmission time from antennae at the pole is never long, and vice versa, because the ship is always near. It’s answering the planet immediately but by the planet’s clock the conversation is exceedingly lengthened. Do the words themselves from the ship stretch out into held note long tones with long gaps between them?

 

[PeroK]

If you imagine the laser producing a pulse of light every $\Delta t$ in its rest frame, then it produces a pulse every $\frac 1 \gamma \Delta t$ in a frame where it is moving. Moreover, you have a thing called the tranverse Doppler effect, that means the energy of each pulse will be reduced (redshifted). So, its power is by no means the same as measured in two different frames.

In general, you are being drawn into arguments that focus on one aspect of the problem. The problem with those arguments in science is that they draw you into false conclusions.

 

[PeroK]

The solar panel could spin to always face the laser, in which case it really can’t “see” that it is moving at all, and appears to be just like a stationary laser fixed at the same distance. (Think of the fixed video camera inside a rolling car tire).

This is false in any physics. Speed is not rate of change of distance(!) Speed is the magnitude of the velocity vector. And, in this case, the laser has a velocity relative to the centre of its circular path. Hence it has a speed relative to the centre of its circular path.

PS or, to be more precise, speed in an inertial reference frame in which the centre of its circular path is at rest.

This observation applies equally in classical, Newtonian physics as it does in SR.

 

[Halc]

Yes, the duration of the illumination as measured by the emitter and receiver will differ. So will the wavelength and frequency due to transverse Doppler.

Transverse Doppler is not a true Doppler effect, which has to do with changing distance between emitter and detector. The transverse effect is purely due to relativistic time dilation, and not something in addition to it. I just wanted to make that clear to the OP.

The records of energy transmitted and received would also differ because the recording devices are using different frames and energy is a frame dependent quantity. If the ship emits some total energy $E$ as measured in its frame rest frame then its total energy reduces by $E$.

Total energy is the same, it's just spread out over a longer time as measured by Earth. Power is reduced by the Lorentz gamma factor, but the duration of the signal is increased by the same factor. Thus the energy of the emitter is the same as the energy at the detector, per energy conservation.

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?

Per the above, it receives the same energy, not more. It gets that energy at lower power, and over a longer time as measured by the receiver.

It occurs to me that this could be recast as an inquiry about trying to have a radioed conversation with someone in close, fast, orbit, whose time has slowed down.

As you describe, the one would have the conversation slowed, low voices, long drawn out words. The 'orbiting' guy (who cannot be conscious at the g forces we're putting on him, but we're ignoring that) would hear the Earth replies 'chipmunked out', higher pitch.

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

Yes, and the opposite for the replies going the other way.

 

[PeroK]

Transverse Doppler is not a true Doppler effect, which has to do with changing distance between emitter and detector. The transverse effect is purely due to relativistic time dilation, and not something in addition to it. I just wanted to make that clear to the OP.

There no such thing as "true" Doppler effect. The transverse Doppler effect is a measureable redshift of the energy of the signal, which is frame invariant. Time dilation is not frame invariant.

 

[Halc]

There no such thing as "true" Doppler effect. The transverse Doppler effect is a measureable redshift of the energy of the signal, which is frame invariant. Time dilation is not frame invariant.

Agree. My term 'true' implies that one is false (sort of like centrifugal force in an inertial frame), which transverse Doppler isn't. I was simply pointing out that it isn't an effect in addiction to the relativistic gamma factor. It is pure time dilation per special relativity.

You correctly point out that Doppler is any change in frequency/wavelength between emitter frame and receiver frame.

I actually always wondered if/how the cops can measure a car speed as it passes transverse to the cop. Sure, it's easy if the car is approaching to or receding directly from the radar gun.
Police and weather radars also use Newtonian physics, and such simple devices have no need for relativistic corrections.

 

[davidjoe]

The radar gun won’t register a meaningful speed at that angle. In theory we always get the benefit of a slower speed read because they don’t set up directly in front of us.

I’m visualizing an LP record, with the laser on the edge pointed at the spindle (earth’s pole mounted receiver) rotating around it. Just another way to picture the same hypothetical.

Beside the panel is a mirror let’s say, and instead of one emitter, beside it, is a twin emitter. One always hits the mirror and one always hits the panel.

If the “record” isn’t spinning at all, a blue beam hits the mirror and is reflected back as a blue beam. (Same wavelength and frequency). But if the record were to be spinning, really at all, the reflected beam is both “redder” and received, with a slight shift of position behind what is expected.

 

[PeroK]

Total energy is the same, it's just spread out over a longer time as measured by Earth. Power is reduced by the Lorentz gamma factor, but the duration of the signal is increased by the same factor. Thus the energy of the emitter is the same as the energy at the detector, per energy conservation.

I think this is wrong, but it is interesting. Instead of circular motion, consider linear motion and the transverse beam. The emission of a light pulse would result in a small recoil of the battery/laser. That would add to the KE of the battery/laser. Hence, not all the energy from the battery would go to the receiver.

In the case of circular motion, there must be a restraining force preventing the radial recoil and some energy from the battery that is not received must be dissipated within that constraint - whatever the mechanism.

In any case, the total energy received is less than the total energy taken from the battery.

 

[Halc]

If the “record” isn’t spinning at all, a blue beam hits the mirror and is reflected back as a blue beam. (Same wavelength and frequency). But if the record were to be spinning, really at all, the reflected beam is both “redder” and received, with a slight shift of position behind what is expected.

If an emitter at the edge or the spindle was to hit a mirror at the other location, reflecting its own signal back to the source, the signal would not be redshifted at all so long as the distance between the two remains constant. So spinning would have no effect on this. You would be firing your laser at a rotating mirror, but even then, the signal will go back to the emitter.

So no redshift for a reflected signal in this scenario, and relative to the rotating frame, I don't even see a shift of position of where the reflected signal returns, although the light bean would not take a straight path relative to such a frame, and thus the direction at which the mirror appears, and the direction the laser must be fired, both change (in opposite directions) due to aberration.

Also note that a spinning solid like a record cannot change angular speed without deformation, per the Ehrenfest 'paradox'.

As for the poor guy suffering the big g forces, we can just put him at sufficient distance (on the order of many light months) that he experiences 1 g of centripetal acceleration when keeping his speed at say 0.8c

 

[davidjoe]

With a solid object like in the “LP record” hypothetical, which is similar in concept to the orbiting satellite, it seems like we get the same result. But it is more difficult for me to imagine the same possible effects of time dilation occurring within a solid object.

 

[PeroK]

With a solid object like in the “LP record” hypothetical, which is similar in concept to the orbiting satellite, it seems like we get the same result. But it is more difficult for me to imagine the same possible effects of time dilation occurring within a solid object.

Time dilation doesn't "occur inside an object". Time dilation is the effect of considering reference frames in relative motion. It's not a physical process. Technically, it is a coordinate effect.

 

[davidjoe]

Time dilation doesn't "occur inside an object". Time dilation is the effect of considering reference frames in relative motion. It's not a physical process. Technically, it is a coordinate effect.

Probably better preposition selections possible, but, then again, if a cable is slinging that satellite around the earth, instead of it moving under its own power, and time is passing more slowly in the satellite, then it is not only dilated for the satellite, but also where it is connected, and necessarily all the way on down, but with greatly diminishing effect, I would think. I do take the point above, about the nasty definitional questions of what is time slowing. But we do envision people aging differently because of the effect, and if that is correct, would there be some logic to the cable having aged differently, in observable ways, along its length.

 

[PeroK]

Probably better preposition selections possible, but, then again, if a cable is slinging that satellite around the earth, instead of it moving under its own power, and time is passing more slowly in the satellite, then it is not only dilated for the satellite, but also where it is connected, and necessarily all the one on down, but with greatly diminishing effect, I would think. I do take the point above, about the nasty definitional questions of what is time slowing.

For circular motion, in general, we are no longer talking about inertial motion, as there is a real centripetal force. Stricly speaking, we are no longer talking about time dilation in the sense of symmetric, reciprocal time dilation between inertial reference frames.

That said, you must stop thinking about time dilation as a physical process. It's purely a coordinate effect. For example, in the rest frame of a high-energy particle at CERN, you are massively length contracted and your heartbeats are massively time dilated. Nothing physical happens to you when we consider you in that reference frame.

There are no nasty definitional issues associated with SR. There is, however, your lack of attention to the basics.

 

[davidjoe]

… Would that mean the orbiting laser emitter, or conversing party, is not actually affected the way I was opining, as it is indeed circular motion?

 

[PeroK]

… Would that mean the orbiting laser emitter, or conversing party, is not actually affected the way I was opining, as it is indeed circular motion?

The solution is that in the rest frame of the experiment:

1) The laser is emitting energy that is less than the energy being used by the battery.

2) Therefore, the total energy received is less than the energy drained from the battery.

3) If you allowed the laser to recoil, it would be fairly obvious that the lost battery energy goes to recoil KE in the laser.

4) If you force the laser to remain in its circular orbit, then the lost energy must be dissipated somehow in the constraining mechanism.

 

[Ibix]

It seems to me the battery’s starting energy is fixed.

It was. Then you accelerated it a lot - that energy is also available for use.

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

Depends on the details of the transmission process. Assuming you've simply heterodyned the sound wave onto a carrier then the received signals would be stretched out and the result would be exactly like listening to a recording played slowly. Digital communications could either work perfectly or break down completely, depending on how different the clock rates are, how tolerant the receiver was of mismatched clock rates, and what it does with it.

Total energy is the same, it's just spread out over a longer time as measured by Earth. Power is reduced by the Lorentz gamma factor, but the duration of the signal is increased by the same factor. Thus the energy of the emitter is the same as the energy at the detector, per energy conservation.

I don't think so. Simple case, imagine that instead of the battery we use a matter/antimatter reactor. The fuel mass is $m/2$ matter and $m/2$ antimatter. In its rest frame after the reaction the energy lost by the ship is $mc^2$, but in a moving frame it's $\gamma mc^2$. Thus there's more energy in the emitted radiation in the frame where the ship is moving. This applies equally to the chemical energy in the battery - essentially, you have the kinetic energy associated with the rest mass loss "extra" compared to the rest frame.

I actually always wondered if/how the cops can measure a car speed as it passes transverse to the cop. Sure, it's easy if the car is approaching to or receding directly from the radar gun.

If you approach me at speed $v$ then the Doppler factor is $(1+v/c)\gamma\approx 1+v/c-v^2/2c^2$, whereas transverse Doppler is $\gamma\approx 1-v^2/2c^2$. That second term is smaller by a factor of $v/2c$, and is not significantly different from zero to the kind of precision traffic radar needs to work.

But if the record were to be spinning, really at all, the reflected beam is both “redder” and received, with a slight shift of position behind what is expected.

It depends who is doing the measuring and who is doing the aiming.

With a solid object like in the “LP record” hypothetical, which is similar in concept to the orbiting satellite, it seems like we get the same result. But it is more difficult for me to imagine the same possible effects of time dilation occurring within a solid object.

Time dilation is not really a thing that "occurs". It's a matter of how you choose to synchronise clocks, so is largely a matter of choice. Note that you are using a rotating reference frame here, though, which has more in common with the differential aging process that is seen in the twin paradox.

 

[davidjoe]

My spectator’s view of these subjects really shows. I don’t even know where to apologize about it the most lol, but I do.

Yes, Ibix, the rotational frame and twin aging paradox, and correcting or synchronizing GPS coordinates and clocks because of satellite speed, this is more familiar.

In that regard, the clocks at the surface versus orbit truly do keep different time, right? You cannot correct and forget. You’d have to correct it infinitely frequently. Every instant, technically, they have experienced and marked a different passage of time and as I understood it, it is because of velocity difference, such that time passage (aging) hyperbolically or exponentially slows toward zero, - at C. To my thinking, the aging process or lack of aging would not be discernible in biological processes, only, but across matter.

Edit: (A photon of light experiences no passage of time no matter how far or long it has been traveling).

*** I’ll edit to add that I have never felt particularly comfortable with aging differentials. Once something is no longer accelerating… ***

 

[davidjoe]

The solution is that in the rest frame of the experiment:

1) The laser is emitting energy that is less than the energy being used by the battery.

2) Therefore, the total energy received is less than the energy drained from the battery.

3) If you allowed the laser to recoil, it would be fairly obvious that the lost battery energy goes to recoil KE in the laser.

4) If you force the laser to remain in its circular orbit, then the lost energy must be dissipated somehow in the constraining mechanism.

Reading “recoil” I have a very unrelated side question for you sometime, if you’re interested. (I’m a long-range competitive marksman and have proposed that if our rifles, which are a form of engine, do recoil before exit, as opposed to the mild force of recentering themselves, which we can easily control, then they are necessarily a form of ventless or impossible rocket, and thus, they don’t, as contrasted with pushing some air out of the muzzle, pre-exit).

 

[A.T.]

if our rifles, which are a form of engine, do recoil before exit, as opposed to the mild force of recentering themselves, which we can easily control, then they are necessarily a form of ventless or impossible rocket,

If you prevent the bullet from leaving the barrel, then you have no net propulsion.

 

[davidjoe]

If an emitter at the edge or the spindle was to hit a mirror at the other location, reflecting its own signal back to the source, the signal would not be redshifted at all so long as the distance between the two remains constant. So spinning would have no effect on this. You would be firing your laser at a rotating mirror, but even then, the signal will go back to the emitter.

I’m not sure how it’s different from the satellite example though, where the same number of pulses, lengthened, and extended to a longer time, were received.

 

[Sagittarius A-Star]

If the ship emits some total energy $E$ as measured in its frame rest frame then its total energy reduces by $E$. But in the frame where it is moving at $v$ its total energy reduces by $\gamma E$, where $\gamma=\left(1-\frac{v^2}{c^2}\right)^{-1/2}$ is the Lorentz gamma factor. So the total energy received is higher.

The planet sees more energy received because it gets the electrical energy plus the kinetic energy associated with that.

The planet doesn't get the kinetic energy part because it receives the light red-shifted.

 

[PeterDonis]

The planet doesn't get the kinetic energy part because it receives the light red-shifted.

Why would the light be redshifted?

 

[Ibix]

The planet doesn't get the kinetic energy part because it receives the light red-shifted.

I presume you agree that the total emitted energy in the planet frame is $\gamma E$. If that isn't absorbed by the planet, where does it go?

 

[Sagittarius A-Star]

Why would the light be redshifted?

Because of the transverse Doppler effect in the receiver's frame. (To my understanding, gravitational time-dilation is neglected in this discussion.)

 

[PeterDonis]

Because of the transverse Doppler effect in the receiver's frame. (To my understanding, gravitational time-dilation is neglected in this discussion.)

Ok. The redshift then also corresponds to a lengthening of the time during which the light is received, compared to the time it takes to emit it. So the redshift does not affect the total energy transferred. It only affects the time taken for the transfer, as seen from the different frames.

 

[Sagittarius A-Star]

Ok. The redshift then also corresponds to a lengthening of the time during which the light is received, compared to the time it takes to emit it. So the redshift does not affect the total energy transferred. It only affects the time taken for the transfer, as seen from the different frames.

The redshift does affect the total energy transferred because of $W=hf$ for each light-pulse ("photon").

It is to be noticed that the energy and the frequency of a light-complex vary according to the same law with the state of motion of the observer.

Source (see §8):
https://en.wikisource.org/wiki/On_the_Electrodynamics_of_Moving_Bodies_(1920_edition)

 

[PeterDonis]

The redshift does affect the total energy transferred because of $W=hf$ for each light-pulse ("photon").

This is the relativity forum, not the QM forum. There is no such thing as "photon" here. (A proper QM analysis would not justify the claim you are making either, but that's a matter for a separate thread in the QM forum.)

If by "light pulse" you mean a classical light pulse, the Doppler effect does not mean what you are claiming it means.

Source (see §8):
https://en.wikisource.org/wiki/On_the_Electrodynamics_of_Moving_Bodies_(1920_edition)

This paper does not justify what you are claiming.

 

[Sagittarius A-Star]

If by "light pulse" you mean a classical light pulse,

Yes.

the Doppler effect does not mean what you are claiming it means.
...
This paper does not justify what you are claiming.

Why? It argues classically.

 

[PeterDonis]

Why? It argues classically.

Sure, Einstein's paper is classical, but just saying "classical" doesn't justify the claim you are making. Go read Einstein's paper carefully. What he means by "the energy and frequency of a light complex" (and note that the "frequency" part is not actually classical, he was smuggling in a quantum concept there, but he doesn't use it anywhere else in the paper so it's not really relevant to this discussion) is not what you would need him to mean to justify your claim.

 

[Ibix]

I think the complete analysis is:

In the frame of the rocket, energy $E$ is emitted in time $\Delta t$, consisting of $f\Delta t$ cycles of coherent radiation. The rocket mass is reduced by $E/c^2$.

In the frame of the planet, energy $\gamma E$ is emitted in time $\gamma\Delta t$, consisting of $(f/\gamma)\gamma\Delta t=f\Delta t$ cycles of coherent radiation. The rocket mass is reduced by $\gamma E/c^2$.

Note that the radiation in the planet frame is redshifted compared to the rocket frame, but the power is the same and the beam duration is longer so the total energy is higher.

 

[Sagittarius A-Star]

Sure, Einstein's paper is classical, but just saying "classical" doesn't justify the claim you are making. Go read Einstein's paper carefully. What he means by "the energy and frequency of a light complex" (and note that the "frequency" part is not actually classical, he was smuggling in a quantum concept there, but he doesn't use it anywhere else in the paper so it's not really relevant to this discussion) is not what you would need him to mean to justify your claim.

Unlike in most of today's derivations of the frequency-Doppler formula, he wasn't smuggling in a quantum concept in §7. He used the Lorentz-transformation for the electromagnetic field components.