Light Speed Motor Scooter: Newsletter Challenge (07/10/07)

Neither will indicate an increase in mass.

The relativistic mass increases with the velocity and kinetic energy of an object in motion, but the invariant mass doesn't change.

How can the scooter which provides its own energy from the battery and the Streetcar which uses an eternal source both maintain the same mass?

Fyz

The problem with this question is that mass is not properly defined here and this may lead to interpretations like ve9gfi's above.

However, one can argue that if the mass of a moving object is measured by a stationary observer, it must be the relativistic (or moving) mass that is measured and not the invariant rest mass.

Given this definition of mass, my answer is: the scooter's moving mass will decrease and and the streetcar's moving mass will increase. I will hold my arguments for the answers until later, for if I'm right, giving it now would spoil an excellent challenge for the rest!

Is something to with the the scooter's energy source being on-board and the streetcar's being off-board (for want of a better expression)?

Since energy and mass are interchangeable, and the scooter is using up energy to gain speed, it must (apparantly) lose mass. The streetcar however is gaining speed, but paying the price from an external energy source, so overall its (apparant) mass must have increased.

rest mass + rest energy + speed energy - losses =>

Scooter

RM = constant
RE = reduces
SE = increases
L = increases

RE = SE + L

Streetcar

RM = constant
RE = constant
SE = increases
L = increases

Not a very coherent explanation - I can kinda see what I mean, but not sure I have the vocab to explain what I see! Am I close?

I'm sure that's the same as I tried at #4 .

It was #4 that reminded me that a streetcar is a tram (English-American translation failed when reading the question) - but I didn't read the rest of your post in the same way...but then I don't really know what I'm on...oh...it's a chair!

And mine's not about the electrons, but toal energy balance - which is probably just a different way of looking at so...

...I'll get me coat!

I was finkin the batteries had finite mass....finite energy...couldn't reach c cos it didn't have enough ....

Cheque please.........

Hi Kris - "I was finkin the batteries had finite mass....finite energy...couldn't reach c cos it didn't have enough ...."

I do not understand your equation Kris - what is cos(it)? I thought we long abandoned ict...

Anyway, this is the typical excellent challenge: short, sweet and challenging, but vague enough to stir controversy and with more than one feasible answer!

Jorrie

Not my line of thinking at all! At least you admit you're a fink

Jorrie, and ER,

The sun must be shining on me this morning. So far I've had Fyz(elsewhere), Jorrie, and ER posting great comments.When I have eventually reduced all of CR4s finest to making jokes I shall wade back in with something like a formula and be hailed as a serious minded genius. Academic awards will fall upon my head like morning dew.This is a perfect question for assault and battery with humour. I currently have a mental image of Jorrie on a photon*, ER on a super-charged (vintage) Blackpool Tram , and Fyz on a MagLev train (with precisely stated characteristics), all zooming forward** like an Editors cut of 2001.

*Being the acknowledged CR4 expert in this area , Jorrie may opt for some sort of quantum wave type thing instead. The photon was merely a suggestion.

** you may define 'forward' as you wish

Now I'm worried - how did you find out about my love of vintage public transport vehicles?

I have a memory like a sponge dear. Dense at times , often leaky , and occasionally festering. The opening of the upgraded museum should be interesting. Some major work has gone on at the site. Next time I'm in London I'll pass by to see how it's going.

Also, Jorrie, there is the question of where the energy for propulsion is coming from. Are the bodies converting (losing) mass in mass-to-energy conversion? Not as simple a question as it might appear!

I doubt. The conservation of energy still holds in the relativistic world.

Since E = mc^2 it will remain mc^2 whether is moving or not (the scooter I mean).

So, the scooter mass will be constant, since it drives on the on-board battery and the street car mass will increase, since it has a power input from the overhead and the tracks.

Hi Daniel, you wrote: "I doubt. The conservation of energy still holds in the relativistic world."

Yea, but not inside the scooter - what about losses to the environment?

Energy is obviously conserved in the 'total system', whatever that may mean...

Jorrie

hi Jorrie

I tend to agree with you about the final outcomes in relative masses of both: scooter's to decrease and streetcar's to increase.

Whereas there will have to be frictional energy losses in both cases, the compensatory sources to fill out these energy losses are different: in house in the case of scooter and external one in the case of streetcar. On this account, there will have to be a net mass loss in the case of scooter "system" to attain the final momentum that results in speeds approaching that of light speeds. However, in the case of streetcar, the "system" is externally compensated to cover such losses. the final momentum attained

will need to have gained mass conversion from gain in speed, adding to the net overall mass of streetcar "system" to go up.

m_rel=m₀/(1-v²/c²)^1/2

I can't see how the scooter mass will decrease

A discharged battery has less mass than a charged one. m=e/c^2

It's probably easier to think about in the case of nuclear fission where we are used to the idea of mass loss as energy is created.

Where would you get a power cord long enough to keep that high powered battery charged? Or do you ride at light speed one way and never return?

I'm guessing that the street car is powered off cables , so is this all about the effect of moving electrons at high speed or something ? More a kind of ' what happens to a battery when moving fast ? ' sort of thing. Maybe it's mass will have to go to 0 as it tries for infinite Energy.

The streetcar must be powerd by a solar panel and have neons underneath and around the exhaust to increase the speed.

What will happen if the solar powered streetcar move towards or away from the light source?

My guess is the Scooter - for no reason at all.

This sort of thing shows the ultimate stupidity of taking e=mc^2 to the point where it obviously makes no sense.

As the scooter approaches C , some point on the wheels will reach C, and thus according to the slavish view that Einstein can do no wrong (except believe in god, another argument), those points on the wheels will reach infinite mass, and thus probably cause another big bang.

I refuse to believe that increased speed = increased mass. Mass is matter, and going faster doesn't magically create more atoms.

Hi Spartacus, you wrote: "This sort of thing shows the ultimate stupidity of taking e=mc^2 to the point where it obviously makes no sense".

This famous equation that you quoted does not actually come into question here, since it is a static equation. The moving energy equation is:

e = mc²/√(1-v²/c²).

Some people call the quantity m/√(1-v²/c²) the 'moving mass' or 'relativistic mass', but it is actually avoided in contemporary science circles. It is basically the relativistic kinetic energy added to the rest energy of a mass.

You are right about the wheels, but for the purpose of this teaser, one must ignore that - imagine the scooter and tram on skids...

Jorrie

Gentlemen, aren't you both forgetting something? - special relativity shows how object 1 at velocity c-delta relative to object 2 at c-delta is moving slower than c relative to the frame in which the velocity of object 2 is measured - and these measures all look sensible from any of the frames of reference. (Jorrie might wish to translate?)

Fyz

Hi Fyz, you said: "- special relativity shows how object 1 at velocity c-delta relative to object 2 at c-delta is moving slower than c relative to the frame in which the velocity of object 2 is measured -"

Sorry, don't follow your drift, because I interpret the velocities of the objects as both relative to the same stationary observer. So where are the relative speeds coming in?

Jorrie

Hi Jorrie

Spartacus wrote: "As the scooter approaches C, some point on the wheels will reach C"; you replied: "You are right about the wheels".

Clearly, if the scooter is moving at C-delta relative to the reference frame, the tops of the wheels are moving at C-delta relative to the scooter. But, as you well know, contrary to what Spartacus wrote, every part of the wheel will go be moving slower than C relative to the reference frame (however small delta may be).

Regards

Fyz

Hi Fyz

You are also right about the wheels.

I agree that the top of the wheels can never reach c, just approach it...

Jorrie

Both the motor scooter and the streetcar will have apparent increases in mass according to the Special Theory of relativity. The closer to the velocity of light, the more rapidly the apparent mass increases, tending to infinite as the velocity approaches the speed of light.

This has to happen, or it would be possible for the vehicles to exceed the velocity of light, which is a physical limit. This is really an energy concept rather than a mass concept. The apparent relativistic mass increase is a way to relate the fact that the energy of something approaching the velocity of light is very high, and tending to infinity as the velocity increases, which means that it would take an infinite amount of energy to propel even a very small particle mass to the speed of light, which, of course, cannot happen.

According to relativity, any object approaching light-speed approaches infinite mass.

If the imaginary streetcar behaves differently due to its electrical connections that's beyond MY imagination. - RPM

One thing missing so far in this discussion is the effect of the speed of light travel upon the streetcar's power source, assuming it is designed like the normal streetcar which gets its power from overhead wires, and not an onboard solar cell as someone suggested. Also, just for the purpose of discussion, we will accept that the battery contains sufficient charge to power the scooter to lightspeed (ROFLMAO).

OK, <snicker> I just couldn't type that with a straight face. <giggle> <chortle>

Ahem. Of course Spartacus is right the whole thing is ludicrous, but so are many other assumptions, so let's play the game.

English Rose surmised, based on Jorrie's enigmatic answer, the scooter could be seen as losing relativistic mass, since its energy source is onboard, and the streetcar would gain mass, since its energy source is external. I hope I got that right, in a nutshell, anyway.

There is at least one problem with this that I can see right away. If the streetcar is traveling towards its energy source, and we know that electrical energy in wires travels at approximately the speed of light, or so I was told in my Physics classes, then, yes the streetcar will pick up energy, and therefore, relativistic mass. However, if the streetcar is going away from its energy source at the speed of light, it cannot receive any energy, which is also traveling at the speed of light in the same direction, just like a missile which travels at Mach 1 cannot catch a fighter jet also travelling at Mach 1 if fired from behind. In this case, I believe the streetcar will reach some equilibrium where it will just receive enough energy while travelling at sub-lightspeed to maintain its speed and not convert any more energy to relativistic mass, so its relativistic mass should stay constant, while the scooter continues to lose relativistic mass as its onboard energy source is depleted.

However, I am not so sure that ER's (and Jorrie's if it is the same as ER's) answer is entirely correct, even disregarding the whole trolley power source direction issue. If e = m*c², and "c" is a constant, not a variable, and "m" is relativistic mass, then "e" is directly proportional to 'm". As they both approach the speed of light and they are being fed energy to do so (whether or not it is internal or external I believe makes no difference, except as I noted above), they both convert energy to relativistic mass at the same rate, and should, therefore gain the same amount of "m" for a given change in energy, "e", if you disregard losses.

Maybe I missed something, and maybe I can't have my cake and eat it, too (meaning that if I am right about the first bit, I am probably wrong about the second and vice versa!). Besides, does the potential energy of the battery really count towards relativistic mass, ER (and Jorrie?)? Why should the scooter's relative mass, "m", be reduced? It seems like it should increase as PE converts to KE, which in turn converts to "m" as mentioned in the last paragraph. If anything, the streetcar's larger rest mass would require more energy to overcome the losses due to inertia, but then again, we are neglecting these losses, as the approaching lightspeed "barrier" would tend to make them meaningless.

Hi STL.

I think we must take the fact that the scooter and the streetcar can approach the speed of light as a given, however improbable it may be in reality.

BTW, since when do electrons flow at or near the speed of light in a wire? [Edit: I see you have cleared this one up before I posted this comment] It's only a signal that can approach the speed of light. Individual electrons travel at mundane speeds in a wire, I think...

Makes me think of the physics prof. asking his students: if we stack all the volumes of Physics Review Letters end to end as they appear, can the speed at which the stack grows ever exceed the speed of light? The answer is 'obviously' yes.

Lastly, yes I think ER and myself are saying the same thing and as such I think ER is right!

Jorrie

"BTW, since when do electrons flow at or near the speed of light in a wire? [Edit: I see you have cleared this one up before I posted this comment]"

Well, you must have misread my posting, because I never said, nor would have said, that electrons flow at or near the speed of light in a wire. I did NOT edit my post afterwards, so my original statement stands, "electrical energy in wires travels at approximately the speed of light", not free electrons. If you wish to call that a signal, that's OK with me, but doesn't a signal imply data or some value, such as voltage, rather than simply a physical phenomena such as energy? I guess that depends on your definition. Hams often refer to a signal, when discussing the strength of their RF energy transmission, even if it has no intelligence, e.g. pure carrier wave, so I will accept that definition as well.

Since you "came out" that you and ER are saying the same thing, how do you address my concern for the direction of the streetcar versus the flow of the energy "signal" that powers it? Don't I have a valid point? (Note: "direction" meaning away from or towards it's source, not to be confused with AC vs. DC as the Guest suggested)

Hi STL, yea, I slightly misread your initial posting on the "speed of energy in wires". Only after I posted my comment, I saw that your next post clarified the issue completely.

I guess one can think of a light beam (say laser) that transfers power to the streetcar. Heading away from the transmitter at speeds approaching c will redshift the light to almost non-existence. In the other direction it will become near infinitely intense. So yes, direction will matter (but then, just feed the line from both ends?)

With that said, I think it will be near impossible to transfer energy from overhead wires to any device with 'brushes' that moves near the speed of light relative to the wire, irrespective of the direction relative to the generator. The teaser's intention is clearly to ignore such practicalities and assume that it can work.

Jorrie

"So yes, direction will matter (but then, just feed the line from both ends?)"

Oh, yeah, duh. Parallel power source. That's why you get the Big Buicks! (No, not a typo! <grin>)

Silly question ... if the street car or moped had a head light would the light from said light "pile up" in front of said vehicle? Also would a tail light leave behind a trail of photons that are not moveing (speed of light - speed of light should = 0)

Reading carefully, STL Engineer (in 13) did NOT state that electrons travel at the speed of light in a conductor... we all know the physical electrons only travel mere centimeters per second in a conductor... what he said was "we know that electrical ENERGY in wires travels at APPROXIMATELY the speed of light..." which is true, at least insofar as the speed of light in THAT particular medium would be.

Most of the input, here, leaves me a bit perturbed ... banging about inside that same old cardboard box(!) There must be SUM1 else, who, having read some Brian Greene (etc) , is wondering about those "other dimensions", and how one or more of them might render our own concepts of 'speed' and intersteller space travel essentially meaningless. Who said that "nothing can exceed the speed of light?"

Just because we can't SEE it happening doesn't mean it isn't going-on all around us all the time! As has been expressed by greater minds than my own: (paraphrasing, here) "We ain't seeing those other dimensions and phenomena because we don't know how to look for them yet!"

My answer is: we chose the wrong vehicles to try this experiment!

"My answer is: we chose the wrong vehicles to try this experiment!"

OK, how about a Kawasaki ZX-10R Ninja and an F-22 Raptor? <pant, drool,....>

You're getting close... (grin!)... Picture now, the 12th generation "F-22-Omega", tapping into the energy of the Higgs Field (providing the outward push that is accelerating the expansion of *our* universe). Riding a wave of this force that is 10¹⁰⁰ more powerful than the force that Einstein had calculated as a "Cosmological Constant", while rapaciously gorging on the microwave energy that pervades this known universe (using its wing-like "intakes" ... and, naturally, at a rate accelerating with its own) ... our pilot enters a realm that approximates something more akin to what Ellie (Jodie Foster's character) experienced in 'Contact' than anything that any human has yet been exposed to ... apologies and *exception* given to any of you who have been abducted and taken for a ride (by aliens, of course). In THIS scenario, no craft would exhibit any noticible/measurable change in its mass. How can you either see, or measure something that you can't observe for any measurable amount of time? {BTW; even when we DO figure out a way to track it ... a couple generations later ... we find that nothing truly changes except our perceptions thereof!}

Some inherent dilemmas:

The scooter derives energy from an internal chemical reaction which does not result in a change in mass, just a variation in internal chemisty. The postulate that mass increases as matter approaches the speed of light indicates the scooter, containing the same atoms it started with, but some different molecules, would increase in mass.

The streetcar receives energy generated by an external source, delivered via a wire paralleling travel. Electorns enter (via wire) and leave (via rail) the streetcar at the same rate, avoiding increasing its mass. The type and source of energy - AC or DC, ahead or behind the trolley - affect the result. With DC supplied from behind, as the car approaches C, it will equal the electrons' velocity in the wire, essentially ceasing power transfer. If DC and the electrons and car travel opposite directions, the electrons' velocity relative to the car would approach 2C - Albert E might be concerned. Seems like AC would fluctuate between nothing and too much.

A wheel (steel or rubber) is challenged to get either vehicle to the speed of light, since as it rotates, the angular velocity vector constantly changes direction. Relative to the vehicle, when contacting the ground or rail, it's traveling the same forward speed as the vehicle, but at the top of its travel, it moves twice a fast as the vehicle, or 2C. Einstein would predict a blowout.

Guest #14, the points you raise in your first two paragraphs are very similar to mine, with two exceptions:

1. Electrical energy in a wire is not transferred by free flow of electrons in a conductor. Although there is a small amount of free electron "drift", it in no way accounts for the much larger transfer of charge in electric current. Rather it is the jumping and bumping of electrons, displacing other electrons that causes the transfer of electrical charge, and therefore electrical energy. Sort of like the balls in the ubiquitous desktop ballistic pendulum which transfer mechanical energy when one ball strikes the end, causing a ball at the other end to swing, while the balls in the middle do not move significantly. Some physicists say that it is not the negatively charged electrons moving, but the flow of positively charged "holes" in the opposite direction that is the real current, and helps to justify the notion of current flowing from positive to negative. Electric current also flows at approximately the speed of light, while the flow of "free" electrons is not nearly so fast.

2. Your rationale behind the difference in the source of energy being AC or DC making a difference strikes me as a bit odd. Energy must travel from it source to its load or some other transfer point. DC is simply a current that maintains a constant voltage or EMF, while AC has a fluctuating and reversing voltage, normally following a sine wave or nearly so, although some sources may be closer to a square wave. Since it does this 60 times per second in the USA (50 Hz in some other countries) the time period of voltage in each direction is relatively long as compared to the speed with which the energy travels, and can be thought of as two energy pulse, positive and negative, which are both used by the load. Either way, the energy still travels in the same direction, from source to load. Electrical Energy cannot and does not travel from its load, where it is used up by conversion to heat or mechanical energy, back to its source simply because the voltage has reversed! If that was true, where does the energy going back to the source originate? At the load? Surely, this is begging the question.

Your last paragraph is pretty much the same point made by Spartacus in an earlier posting, and that I agreed with, that the concept of the wheeled vehicles approaching the speed of light is somewhat ludicrous due to the mechanics of its wheels, but accepted only for the purpose of discussion of the other issues.

"Electric current also flows at approximately the speed of light, while the flow of "free" electrons is not nearly so fast."

Hi STL Engineer,

Technically, there is a difference between powering streetcars with AC or DC. Practically, they are powered with HV DC.

DC electric current in conductors has an incredible low speed - a few milimeters per second. Only in vacuumed tubes electrons have higher speed but much lower than c anyway. The definition of 1Amp = 1C/s is not referring to an actual flow of electrons all along a conductor but at the transfer of 1 coulomb of electricity through a cross section of the conductor in any given point of its length! You see the difference? Speed is about space/time but DC is about transfer through a very thin wall. In vacuum tubes it is correct to speak about speed because there is a distance to be run and almost all electrons leaving the cathode are reaching the anode. The issue is about transferring the energy of the generator to the load which is still much under c. If DC would be a true flow of electrons, than a moving load on a long overhead line (i.e. the streetcar) should encounter real problems in absorbing part of the generator's energy even at a few meters/second velocity because of the backlash of electrons in trolleys. But think about the rail gun: it can accelerate a conductive projectile up to supersonic speeds. The speed limit is imposed only by friction and electrical contact efficiency.

AC is a different story. The best analogy is sonicity (mechanical energy transmitted through compressible fluids). The energy is transfered through waves and in this case it is important where the cross-sectional wall is placed along a conductor in order to absorb or reflect the energy. The impedance is the mathematical expression of energy transfer. In RF industry, it is well known that impedance is a function of transmission line length. In terms of speed of energy transfer, again, is very low. For this reason, coax cables cut at multiples of lambda/4 are used as delay lines for RF signals!

However, the original question is of that category in which a lot of simplifications are taken for the sake of a concept. So we have to forget about many details discussed so far.

My solution:the relativistic mass of the scooter remains constant while that of the street car is increasing when reaching relativistic speeds. Relativity has brilliantly unified two laws of conservation: conservation of mass and conservation of energy. In both cases (scooter and streetcar) the electrical generator is loosing mass in order to convert it into kinetic energy. The difference is that in scooter's case the generator's mass is part of vehicle's mass while in the street car case, the generator is loosing mass as well but is linked to the static coordinate system. The increase in scooter's relativistic mass is compensated by the decrease in battery's mass. The street car is gaining relativistic mass from the static coordinate system. We may consider the streetcar as an open system (exchanging energy with the environment) and the scooter as a closed system. The scooter is not a rocket!

Blah, blah....nothing new here. But you do make some misleading and contradictory statements:

"DC electric current in conductors has an incredible low speed - a few milimeters per second."

"Speed is about space/time but DC is about transfer through a very thin wall."

Make up your mind! Seems like you yourself got current flow and electron flow confused.

I myself pointed out the difference between the transfer of electrons and the transfer of charge, or energy. So why are you calling me to task for that?

"In terms of speed of energy transfer, again, is very low." Uhhhh...what?

Why do you write out "lambda"? Is that just to show-off your knowledge of the Greek alphabet? If you are going to write out a word anyway, why not use the word "wavelength" which is what "lambda" symbolizes. Better yet, why not use the symbol tool on the reply box toolbar? It has the character you want, "λ" and then there is no mistake if you meant the upper case lambda or the lower case lambda! (Λ or λ). Say "quarter wavelength" or "λ/4", but don't say "lambda/4"! That's just dumb!

NO comments... Nobody's perfect.

I liked your post ! It maybe just came across a bit wrong because it was addressed to STL and implied he didn't understand. I'm sure you both know the stuff and it's just one of those 'doesn't-come-over-in-writing' type things.

Kris: thank you very much.

I repent for wrongly addressing my comment to STL. Could you believe that initially I wanted to write "lambda/four"? At least I learned how to use the toolbar for symbols.

If someone is more interested in the true speed of propagation of electromagnetic energy and free electrons in DC and AC long circuits, you may read the following:

http://www.cartage.org.lb/en/themes/sciences/physics/Electromagnetism/Electrostatics/ElectricCurrent/Mysteryofelectric/Mysteryofelectric.htm

from which I quote: "It means that when 1V voltage is put on both ends of 1m long copper wire, the velocity of free electrons to length direction is 4.62 mm/s. It seems amazingly slow but since electric charge of electrons is -1.6e-19c, 12.6A electric current flows in the 0.5mm copper wire with this speed."

More related data for AC - audio is given by:

http://www.st-andrews.ac.uk/~jcgl/Scots_Guide/audio/skineffect/page2.htm

and finally a very interesting Physics article on DC conduction:

http://sites.huji.ac.il/science/stc/staff_h/Igal/Research%20Articles/Pointing-AJP.pdf

Regards,

Michael

Your welcome Michael. The links look interesting but I'll have to check them late ( in a slight hurry here).

Cheers,

Kris

"The concept of the wheeled vehicles approaching the speed of light is somewhat ludicrous due to the mechanics of its wheels"

There is no theoretical contradiction here - if the vehicle travels at (say) 0.75*c relative to our "stationary" observer, the velocity of the top and bottom of the wheel would be +/-0.75*c relative to the vehicle, but the velocity of the top of the wheel is still well sub-c relative to the "stationary" observer; for myself, I blame Lorentz, if that's not too much of a contraction .

Of course this can only be a hypothetical experiment - if the wheel was 2-metres in diameter, it would be rotating at 5-million rev/sec ** when it reached c/10 - I know of no material that could survive even 5-thousand rev/sec.

**I did hear there were staffing problems in the church, but that's an unbelievable level of staff turnover.

"I know of no material that could survive even 5-thousand rev/sec."

Sure there is! It's called unobtainium.

"There is no theoretical contradiction here - if the vehicle travels at (say) 0.75*c relative to our "stationary" observer, the velocity of the top and bottom of the wheel would be +/-0.75*c relative to the vehicle, but the velocity of the top of the wheel is still well sub-c relative to the "stationary" observer"

OK, maybe I am just a dumb engineer , but if we had wheels made out of "unobtainium", and the top of the wheel is travelling, even instantaneously, at +.75*c relative to the vehicle travelling at +.75*c and on a parallel vector, then the top of the wheel should be travelling at +1.50*c relative to the "stationary" observer, right? However, we all "know", according to Herr Doctor Einstein, that is not possible, since matter and energy cannot travel faster than the speed of light, or so I have been told. Seems like a contradiction to me. I guess that part of the wheel changes to photons WRT the observer, with the difference being an increase (or decrease?) in relativistic mass, then back again to matter on a continuous cycle? Huh, ....what? Hmmm, how would this affect the moment of inertia of the wheel?

Boy am I confused!

Boy, this is some thread - an element that will survive extraordinary stress, and an unprecedentedly large number!

Not dumb - but contentious and cantankerous maybe...

But in this area, I'd say you were ill informed.

Did you look up Lorentz contraction? It's as good a place to start as any. The reasons are twofold however:

Viewed from the stationary frame,
a) time in the moving frame is slowed down, and
b) physical lengths are contracted
both these effects contribute to the result - that that a forward velocity measured from the moving frame looks like a markedly smaller delta of forward velocity when viewed from the stationary frame.

Various people have written books on the topic - but SFIK, Einstein's explanations have yet to be bettered (I think that Jorrie follows the general texts much better than I, so he's more likely to know that sort of thing than I)

Fyz

Hi Fyz,

Your post sounds right, but what a weird looking wheel that will be!

Tom

Hi Tom

I think early galaxies (including quasars) are probably as close as you can get to such a wheel. But they don't just look weird...

Fyz

Hi STL.

The Lorentz transformation that Fyz mentioned earlier saved the day for 'Herr Doctor Einstein'.

I used this figure in my eBook to show the effects of time dilation and length contraction graphically:

Figure 2.4

It was drawn for a velocity of 0.4c relative to the reference frame (x,ct). The moving frame (x',ct') attains oblique axes, apparently 'shrinking' both distance and time as viewed by the reference frame's observers.

This causes the relativistic addition of velocities rule:

where v₁ will be the scooter's velocity relative to the rest frame (the ground), v₂=v₁ is the wheel's top end velocity relative to the scooter and v the resultant velocity of the wheel's top as observed in the rest frame. You will find that your example of v₁ = v₂ = 0.75c gives a resultant of v = 0.96c.

To an observer on the ground, the scooter appears to be Lorentz contracted to ~0.66 of its original horizontal length and the top of the wheels to 0.28 of their original lengths. The contraction factor on the wheels varies from no contraction where it touches the ground, to 0.28 at the top - if one could see them, they would be weird looking wheels...

Remember that these contractions are not 'real' - they are just the way that things moving at relativistic speeds are being measured.

Jorrie

Aha, I see.

I still don't get the reference to "staffing problems in the church".

Sorry, I was having an off-moment - it was horribly corny - rev(erends) and turn(ing)over.

Fyz

The motor scooter. The street car is energized from overhead wire at rest. For the wire to be at rest, it must be collocated with the point of reference. Therefore point of reference, along with the wire must be travelling at speed approaching speed of light--they and the observer will both increase but not observably. The motorcycle does not have the constraints as do the streetcar, therefore increase in mass is observable from a "static" point of reference.

Face it.. a scooter?? it's just not going to handle....

A Lambretta is bad enough...and even when I'd tuned mine up it never got anywhere near light speed....70mph down hill with a tail wind was best!

Mind it might have handled better if my brother hadn't run it into a wall...

Can anyone answer where the extra mass comes from?

The laws of conservation of matter & energy render the std argument about c=infinite speed and at c m=infinite invalid.

I don't care if we are burping hacks out of our universities by the dozens who buy it, the relativistic theories don't cover where the increased mass comes from w/out violating the conservation laws. Saying that c is infinite is like insisting that a bumble bee and the F-4 cannot fly. Obviously there is something wrong with the math.

Hi Spartacus, you wrote: "Can anyone answer where the extra mass comes from?"

In the case of the streetcar, the overhead lines pump extra energy into the car in the form of kinetic energy of movement.

This energy is not really mass, but since energy and mass are interchangeable, some people talk about a moving mass that is larger than the rest mass - hence, the 'extra mass' is coming from the electric lines.

Also see my previous reply on e=mc^2.

Jorrie

hmmm this just begs the question:

are mass and matter the same thing? to my understanding, there is a relationship between them but the two terms are not exactly interchangeable. an object is made of matter and has mass, but is mass actually matter?

as to the challenge question, i say they both will increase in mass regardless of the energy delivery system.

Spartacus:

The objects behave as though they have vastly increased mass. However, with regard to gravitation, their impact is only their rest mass, which is THE mass.

This all comes about because of using Newtonian equations such as K.E. = (1/2)(m)(v^2). As v approaches c, the kinetic energy becomes enormous and it APPEARS that the mass increased dramatically. We measure v and know what it is, so the only other apparent thing to have gone up must be the mass, if you look at it this way.

In fact, the mass is the same but the relativistic kinetic energy went way up very dramtically confusing everyone trying to look at it from the point of view of Newtonian physics.

It is probably unfortunate that the term relativistic mass was ever created because it does cause a lot of confusion. A better term is relativistic KINETIC ENERGY, because that is what we are really talking about.

c is NOT infinite. The very basis of relativity is that c is constant no matter the coordinate system used by any observer. All observers speeding along in various coordinate systems will ALWAYS observe the speed of light to be the same and constant in all directions.

Conservation of energy is not violated. You accelerate a particle to relativistic speeds using a lot of energy, and when you deaccelerate it, you can get all of the energy back.

Hi edykes@cvtv, you wrote: "The objects behave as though they have vastly increased mass. However, with regard to gravitation, their impact is only their rest mass, which is THE mass."

It depends on how one defines 'their impact', I suppose.

Very fast, horizontally moving particles 'falls' more towards a massive object than what a Newtonian calculation, using their gravitational mass equalling their inertial mass would suggest.

Jorrie

Jorrie:

You are correct. I was way out in space in some black hole when I wrote that.

The warping of space-time (i.e., gravity) is a function of total energy equivalence, not just rest mass (or energy equivalence of the rest mass).

The rest mass is the mass. However, relativistic effects depend on the total energy.

Thank you for noting this. I don't want to be part of the global disinformation brigade!

Since electricity travels around the earth approximately 7.5 times in one second. Maybe it catches up and uses the electrons it already missed. That would make it a time machine and not a street car!!!

Once again, the constraints of the challenge are made for us to come up with an answer that comes from the impossible. IF these things were possible( which they are not), a theoretical answer would be impossible to prove correct or incorrect. The peripheral and intangible proofs of possiblity for a scooter and a streetcar running under electrical power and reaching sub light speed is either a ploy to distract us from the pure mathmatical quandry it purports to be or is a hidden artifice that is known only to the challenger, whose first word (of the challenge question) gives us the first clue as to where the answer lies.....

The both would certainly get smaller. The velocity would tear them both apart.

The one true question is....

If we were to ask Albert Einstein this question, what would his answer be?

Only then, can we approach the subject clearly.

Guest suggested we ask Albert. My guess is that he would have said: "it depends..."

Or he might'a said .......

"Read my new Book"

hmmm.

Nah , surely not ?

How about ....

"Well I remember what yo'all did LAST time I told you secret stuff"

Hallo everybody...

As we give energy to the electric car from outside (via electric cables or lasers or whatever) as the vehicle approaches the speed of light it demands even more and more energy in order to further increase its speed (even for a small amount)... So it seems to increase its "moving mass", as the energy that WE GIVE to it's a measure (for us) to consider this mass increase...

But the scooter carries its own saurce of energy: a "magical battery" with infinite capability of supplying energy... In this case we don't give energy from the outside... So we don't have a measure to estimate this increase of mass... So, I think that we assume that the scooter's "moving mass" remains unchangeable...

The scooter has an internal power source so electrons are exchanged within the unit (no gain in mass). The streetcar receives external electrons so it has an increase in mass. But; I assume that both are not black bodies so there will be a loss from radiation of photons. If the vehicles travelled in an atmosphere, friction of the streetcar would be greater due to aerodynamics so it would reach a higher terminal temperature.

It's the streetcar. Electrons have a greater mass.

DD

The scooter is increasing its velocity by using stored chemical potential energy that can reasonably be considered part of the initial mass of the scooter. The transformation from chemical potential to kinetic energy does not add to the total energy in the scooter "system," thus the mass of the scooter does not increase as it increases its speed -- in fact the opposite occurs due to heat losses in bearings, electrical field leakage, drag and heat generation/dissipation in the batteries. Probably other things too.

The energy used to increase the velocity of the streetcar is coming in from outside the control volume enclosing the streetcar and thus on the well-tested assumption that energy has mass, is increasing the mass of the streetcar. Special relativity predicts the proportion of mass increase associated with a particular relative velocity increase, and these predictions have been well correlated with results from experiments in high-energy particle physics.

mass will mot change in any case, only waight will change depend on gravity.

It seems to me we have a real world example of the street car case. Particle accelerators can accelerate an electron to very high velocities approaching the speed of light. This seems to me a case of an object being accelerated by an outside energy source to significant fractions of c. If I'm not mistaken relativistic effects (like an increase in observed mass) can be measured in these instances.

On the scooter side of things, I would think a fusion powered "ram jet" that uses interstellar hydrogen would be an analogous system.

I believe mass is going to increase in both systems.

The only true answer is "no one knows" b/c everything I have read here is speculative and theoretical.

I'm troubled by a common question regarding near-speed-of-light travel. If you are in a car going at the speed of light and you turn the headlights on, what happens? Well, from the car's perspective or the driver's, the lights turn on, but if you are stationary (whatever that means), the driver can't move--he would appear frozen--so his hand can't reach the light switch or turn it on. Electricity doesn't quite move at the speed of light, if I recall correctly, so driving an object electrically to near the speed of light would result in a point where, from the stationary observer's POV, the electricity would no longer be moving through the wires, the object would falter and slow to a speed less than the speed of electrical travel, speed up again, etc. Mass at the speed of light is infinite, but at a speed less than the speed of light, it would be proportionately greater for the street car than for the motorcycle, assuming the street car was more massive to begin with. That seems like an awfully simple solution. Am I understanding the queston properly? To the cyclist and the streetcar conductor, nothing would appear to have changed, but to an observer at rest, the masses of the devices would be approaching infinity.

.. mass increases to infinity as speed approaches C ? well that means we better stay outta the sunshine eh?

scientists get tangled...need to watch star trek more studiously..

i say both units would arrive the same way 2 different weight objects would fall.. and crash with different force..

but that's assuming a lot ...

Jsta cat

Watching from a reference point independent of the physical bodies of these both items approaching (but not really there!) I would say an increase of mass in equal proportion will be observed.

However, the increase of individual masses will still be in exactly same proportion as it was when they started off from zero velocity from the point of reference.

Therefore, the observed ratio of their masses will indicate that their masses have increased but to the same extent.

I believe that will be the case.

As I said before it's all a matter of special relativity:

As the energy comes from INSIDE the vehicle (and NOT from outside by us) there is no way (for us) to verify an increase of the mass of the scooter... We see only a scooter travelling near the speed of light and that's all...

But, in the case of the electric car, WE give the energy from OUTSIDE... In this way, of course, WE have the way to observe an increase of the mass of the vehicle because WE have to give a continuously increased force (or energy) from outside in order to further increase it's speed (and in relativistic speeds this external energy becomes extremely large)... So, the fact that we have to give an increased external force (or energy) is translated (by us) as that the body (electric car) has become more massive...

As a result we'll observe an increased mass for the car but not for the scooter...

Hi G.K, you wrote: "As the energy comes from INSIDE the vehicle (and NOT from outside by us) there is no way (for us) to verify an increase of the mass of the scooter..."

A stationary observer can measure the relativistic mass-energy of the scooter indirectly by means of momentum changes. Just let it crash into a heavy stationary and fairly pliable object (sponge, gel, or whatever) of known mass. When the scooter stops relative to and inside the object, measure the momentum change, the temperature change and any friction components of the object. You can now calculate the relativistic mass-energy that the scooter had before the impact.

Same for the streetcar if you wish.

Jorrie

Hi, Jorrie...

Of course the mass of the scooter has, also, objectively increased near the speed of light... But I supposed that we dont make any other measurement (or experiment) in order to verify whether or not the mass of the scooter has increased... If someone doesn't know what Einstein had said about the change of the mass in relativistic speeds, he couldn't know what has happened to the mass of the scooter (by just looking at it running)... Of course, it's always possible to take other "measurements" and come to a conclusion that the mass of the scotter has actually increased...

But in the case of the electric car is very obvious for an observer that its mass is, continuously, increased...

Maybe I misunderstood the question... Maybe it's not what an observer presume, but what is realy happening... If it's not the "obvious" answer that the mass of both two vehicles has increased, then there must be a "trap"...

I gave such an answer because of the question that says:

"which one (or both) will indicate that its mass has increased?"

Notice the world "INDICATE"...

The "trick" to this question is the the equivalence of mass and energy. The proper mass (once called rest mass) of the streetcar will not change, but its momentum will increase toward infinity. That is what a stationary observer would normally measure, e.g., by erecting a nice brick wall in front of the streetcar. The so-called relativistic mass increase would come from the energy supplied by the overhead electric wires. However, following the collision with the brick wall, if we sweep up all the pieces and weigh them (allowing time for cooling), we find we still have the proper mass.

The motor scooter, however, is a different story. It will lose proper mass as its battery chemicals react to give up energy. Since the battery will not recharge during the collision with the brick wall, that mass (energy) is gone.

Imagine there is a passenger on the streetcar as its relativistic mass approaches infinity and that passenger shines a flashlight out toward the side. Will that light "escape" the infinite mass?

No, the mass of the trolly at the speed of light will prevent the photons from the flashlight from escaping the trolley. The passenger (to a stationary observer) would be frozen in time and space--a feature of an event horizon. His finger might be on the switch, but it will never move. The flashlight will remain dark through all eternity. From an intermediate point of view, an observer traveling parallel to the trolley, but slightly slower, the photons will escape the flashlight and then be bent drastically backward forming a kind of wake (like the sonic boom of a jet breaking the sound barrier) behind it in its path. When the intermediate observer is left behind by the trolley as it accelerates to the speed of light relative to intermediate observor, this wake will close behind the trolley, once again leaving behind an event horizon upon which nothing appears to be in motion.

I have kind of a crazy theory of the cavitation universe--that objects beyond the blackness in the night sky--on the surface of the bubble--are traveling faster than the speed of light relative to us, that light can't enter the universe (or any other kind of information) from the "pre-big-bang" area beyond the bubble skin because either we or the objects beyond the darkness are in a black hole. If the limits of the visible universe can be seen as retreating from us at the speed of light, it has, in effect, pulled its wake into its structure, so the most we can know about the universe is what objects looked like just as they breached or broached the speed of light. When we are able to refine our vision to the point of seeing these objects (mostly quarks, I suppose) at the distance of 8 or 16 billion light years, they will appear to be stationary and all quantum movement will be absent. The universe is a flat beer. No foam. The fact that distant objects in the known universe are accelerating away from us indicates to me that we are outside of the black hole, that the black hole is very near and so massive that it has pulled its wake in behind it--that's why the universe appears to be all around us instead of an object retreating in a single direction. Over time, the darkness will be increasingly pocked with objects going relativistic--stars, quarks, dark matter--whatever. At some point its powerful tidal forces will begin to stretch our local space and ourselves. It might happen trillions of years from now or a week from tuesday. It might be happening right now. Next time you have a pulled muscle, you might be about to be dragged into a black hole. The universal temperature--supposedly the remnant of the radiation from the big bang--might actually be radiation from objects disappearing through the surface of the universal singularity. It's the same from every direction because every direction is actually one single point whose wake has been distorted into a sphere that appears to surround us. The universe is a singularity whose ___ is nowhere and whose event horizon is everywhere. Fill in the blank and win a Nobel Prize.

Oh, wow! So, our solar system, our galaxy, and our universe, might just be tiny little points in some giant's hand! ......and my little pinkie might just contain billions and billions of smaller universes.

Hey, don't Bogart that joint! "Pass de' doobie by de' left hand side".

I remember discussions like this from my college days, fueled by too much alcohol, marijuana, peyote, magic mushrooms, or other mind-bending substance. In fact, there was so much grass smoked in my fraternity house, I like to paraphrase Bill Clinton, when he discussed his own personal marijuana use:

I never smoked marijuana, but I did inhale!

The streetcar can't be powered externally. It would have to be powered by batteries or an onboard generator. A stationary generator would slow to glacial (pre-global warming) speed, cranking out an electron every week or two. Even a slower generator that is still on the trolley's trajectory would suffer this kind of relativistic problem, only less so. The generator would have to be moving at the same rate as the trolley to continue powering it. Whether the generator is onboard the trolley or not isn't relevant--it has to be moving at the same speed and therefore is essentially part of the trolley structure even if only cables connect them (other parts of the trolley are connected with bolts, rivets, and so forth--a cable is just a more flexible version of a rivet in this situation. How is the generator generating power? Is there a way to generate power without loss of mass in the form of stack gases? Doesn't even plutonium generate gases as it deteriorates?

Some batteries, mainly wet cells, generate a gaseous byproduct as they free electrons. This would reduce the mass of the scooter over time, but far less than the losses from the trolley/generator complex. I presume that these vehicles are coursing through empty space or they would have burned to gasses themselves long before approaching lightspeed. What happens to a gas traveling through empty space? Eventually it would probably dissipate, but it would always be moving at the same rate of speed (if you take into account the vectors of all the molecules in the cloud) as when it was released. But other than their meagre gravitational pull, I don't see how these molecules could affect the scooter or the trolley.

You could detect the masses of the trolley and the scooter by their gravitational effect on the observer. To the observer, their masses would appear to be warping time-space to the extent that at lightspeed, they would turn the universe into a singularity (that's what happens when you have infinite mass, right?). I'm not convinced that the universe isn't already a singularity. I see things traveling at the speed of light all the time. Hint: When it's really dark, I have to turn on a flashlight to see them.

I've always thought of the universe (ours and anyone else's) as a perturbation.

Sort of like (by 'eck what a good phrase!) the bubbles you get when you stir a liquid...the big bang was the bubble being formed by the localised loss in pressure (cavitation) caused by the stirring. It would be intersting to 'see' if the universe collapses in the same way as a cavitation bubble.

Sorry, slightly sideways ramble - I take your point on the practicalities of supply electricity to the streetcar. We just ignored that to answer the bare question at the start. It's good to see the next levels of discussion.

Hi ER, you wrote in reply to rbixby: "I take your point on the practicalities of supply electricity to the streetcar. We just ignored that to answer the bare question at the start."

STL and myself did 'cross words' on this before, but I do not think the issue was completely settled. Consider this:

Power a DC overhead cable from both ends, i.e., control it to have a certain electrical potential above ground, like a bus bar. Now power an electrical car from it by a 'slip connection', like in most streetcars or trams. Given enough power, why would the car not be able to draw energy from this cable, even at a speed that is a significant portion of the speed of light?

For the difference between the streetcar and the scooter to become measurable, it is not really necessary to 'approach the speed of light', as stated in the challenge. A 'mere' 20% of the speed of light will be more than enough to measure the difference (streetcar gaining ~4% mass-energy and the scooter losing a lot due to the inevitable losses, which is not made up from an outside source).

Jorrie

didn't somebody already address all this, way up the threads? Something about colocation? I think that meant, in a manner of speaking?

It would seem that having a power source BEHIND the streetcar would be pointless. But the electrons would be unable to return to the source--the battery ahead of the streetcar, so you put another battery behind it so that electrons have a sink.

I'm trying to thought-experiment what happens to something traveling toward me at the speed of light when I am also traveling toward it at the speed of light. It seems like we could not be in the same universe, so electrons couldn't flow from one to the other.

This really opens up a can of worms. The positive line in forward direction would be unable to accept electrons, so how could it be positive? The negative line in the backward direction would have no available electrons, so how could it be negative? Could a stream of electrons arriving at the streetcar at a rate that should be twice the speed of light make a right angle turn, flow through a coil, take another right angle turn, and then proceed to a battery from which they did not emerge? I don't see how there could be a potential between the power lines. Could someone explain this to a poor layman?

The question is flawed and therefore unanswerable: there is no point of reference at rest by definition of the special theory of relativity

Guest wrote: "there is no point of reference at rest by definition of the special theory of relativity".

Not quite true. Einstein's Special Theory allows one to choose any inertially moving point as a "reference at rest". Earth's center of mass is such a point. Fixed points on the surface are not quite that (due to Earth's rotation), but close enough for all practical purposes.

Jorrie

Hi Jorrie,

What's your background ? You certainly seem to have an in depth understanding of this subject.

Hi Guest.

Professional engineer (aerospace) and self-taught (amateur) relativist-cum-cosmologist, whatever that may mean...

Jorrie

"relativist-cum-cosmologist"

Is that anything like a "relative who is a cosmetologist"?, cause I got this niece who does great hair, makeup, and manicures....

ROFL

I'm really grateful for your patience and in-depth knowledge of the subject. It's a treat to spend time in the company of learned people.

I think if one light beam is closing on an electromagnetic field coming from the opposite direction at some large fraction of the speed of light, from the reference point of either, the other will appear at rest, frozen in time. So electricity could not reach the trolley from a stationary generator either the front or the back. We could set up an infinite number of induction coils alongside the track using nuclear fuel to generate powerful magnetic fields that could either be used inside the trolley to generate electricity or could be used as external propulsion as in a rail gun. To induce 60-cycle current in a trolley passing at the speed of light, you would need induction coils 3100 miles long. We could use metalic hydrogen from the heart of Jupiter. It would save weight and it's free.

This really is a classic gedanken question, meant to be performed only in our minds without regard to practical limitations and intended to illustrate a particular point or two. Since relativity says that no object having proper mass can be accelerated to the speed of light in vacuo, we might as well consider a speed of 0.2c where we could, in principle, measure the effects without worrying about extraneous matters.

The question, then, is to compare the relativistic mass of an object being accelerated by an external energy source with that of an object being accelerated by an on-board energy source. Relativistic mass is an unclear term but we need only think about the total energy of the objects in this question (that is, the proper mass energy equivalence plus the energy of motion).

The streetcar receives energy from an external source and that adds to its total energy. Its relativistic mass increases.

The motorscooter only exchanges mass for energy. It always has exactly what it started with. Its relativistic mass stays the same.

My apologies for the somewhat glib sleight of hand with the mass-energy equivalence, but I don't like to try to type equations.

I think that most of the thought experiments ignored the issue of the source of the energy needed to accelerate an object with mass to .2c, but due to my limited imagination, I was always forced to imagine a rocket ship, which exchanges mass for energy. Blame it on Heinlein. So you're saying that the rocket would not experience the relativistic increase in mass because it is self-propelled. But the objects inside the rocket ship are not self propelled, are they? Is Captain Kirk exchanging mass for energy? No, he's just sitting there in his Eames chair watching Klingons on his giant screen TV. So Kirk becomes massy. Would the increase in mass of these objects be perfectly balanced by the decrease in mass of the dilithium crystals? Could we say that the battery is losing mass, but the drive train is gaining mass? Could we see it as a transfer of mass from objects involved in filling up the other objects in the system with energy? And then when you decelerate, you are once again shedding mass in the reactor core, but Captain Kirk is shedding mass as well. Where does it go? Heinlein said the best way to handle a long intersteller trip would be to accelerate at 1g to the halfway point in the journey, they turn the rocket around and decelerate at 1g until you reach your destination, moving at a manageable speed. So that is the kind of trip I am thinking about. I've never done the math, but he seemed to think that a trip to a nearby star would appear to the ship's company to last a matter of a very short time. 32 feet per second squared adds up fast.

Hi Rbixby,

It helps to think of energy rather than mass, and it helps to think of closed systems rather than individual objects. So, the rocket, with Kirk and his ever-changing toupee, can be thought of as a closed system, only provided we imagine some non-exhaust propulsion system (maybe a quantum tractor beam powered by dilithium crystals?). If there is no interaction with the surroundings, there will be no energy exchange and the energy of the closed system stays constant. Now, within that system, the dilithium crystals lose energy and the Kirk person gains energy. So, it greatly depends on how you define the system.

If the rocket ship should, perchance, strike a cleverly cloaked Klingon battleship, all of Kirk's energy would be transferred to the nearest bulkhead. Seriously, it's not really any different from the added energy you have while riding in your car. You gain it from your gas tank/engine when you accelerate and give it up to your brake rotors when you stop.

There is an argument that shows that the closed system energy must remain constant, or decrease. If it were to increase, then we could simply built a low friction track, accelerate our motor scootor on it, and run Tokyo off the excess energy.