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Author Topic: Why does an object require infinite energy to travel at a finite speed?  (Read 18315 times)

Brett

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Brett asked the Naked Scientists:
   
G'day, mate.

An object without zero rest mass gains infinite mass and requires infinite energy to move while travelling at the speed of light, yet light travels at the speed it does even off a small battery. Light speed isn't infinite, so why would an object gain infinite mass and require infinite energy to reach such speeds?

In layman's terms: Why does an object require infinite energy to travel a speed that's not even semi-close to infinite? I'm sure there's a reachable  energy consumption that isn't infinite,

Regards,
Brett

What do you think?
« Last Edit: 10/03/2011 09:30:03 by _system »


 

Offline syhprum

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Mate

I trust special relativity is not too much for a layman as it only requires simple arithmetic.

If we look to the energy of a moving body as we approach light speed we must use this formula

E = mc^2 / ( 1-V^2/c^2 )^.5

Close inspection of this equation reveals that as V approaches c the bottom half of this equation becomes zero hence the energy required becomes infinite.

If you want to know how this equation is derived you will have to study special relativity in more detail but experiment has proved it correct.
« Last Edit: 11/03/2011 06:29:48 by syhprum »
 

Offline jartza

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Frames are kind of squeezed together, when you look at the frames from a distant frame.
Here "frame" means "frame of reference".

For example: Bullet is in a frame only 1 m/s apart from the frame of the rifle that shot the bullet, when you are looking at this shooting event from a frame that is 299999999 m/s apart from the frame where the shooting event happens. 

 

Offline nommiiss

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With out getting into the thick of equations.

Look at it this way… Light speed is a wall that cannot be jumped over if you are on one side of it.

Now the interesting thing about light speed is if you are sitting on the wall and jump over you should be able to travel faster than the speed of light. So theoretically it’s not impossible to go faster.

But an object has to be created at or above the speed of light to go faster than the speed of light…

Now to answer your question:the photons of light require very little energy to travel vast distances because it is created at the speed of light and has no mass (it is light it self…) but if an object with mass is reaching the speed of light from rest it will require an infinite amount of energy as its mass increases infinitely. This is because the amount of energy required to maintaining a object at acceleration increases the faster you move towards light speed and because its mass is increasing too, the amount of energy increases and  this will reach infinity when you hit the speed of light. (The wall ;0)

Its almost like when you accelerate a car, you use more petrol to push it forward and the faster you accelerate the more petrol (energy) you use to move it forward.

So you will need an infinite energy sauce to accelerate to the speed of light. No way around it sorry!

Hope that makes sense.
Simon Brownridge
« Last Edit: 11/03/2011 12:01:29 by nommiiss »
 

Offline lightarrow

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An object without zero rest mass gains infinite mass and requires infinite energy to move while travelling at the speed of light, yet light travels at the speed it does even off a small battery. Light speed isn't infinite, so why would an object gain infinite mass and require infinite energy to reach such speeds?
Your reasoning would be correct, but it hides a subtle assumption: that space and time are independent on each-other. It's not easy to understand why your reasoning it's not correct because of this assumption, you will understand it when you will have studied special relativity.

At low speeds, space and time can be considered as independent, but at high speeds is different.

In practice all this can be seen in this way: suppose that you are in a spaceship travelling very close to c.  You would pass close to the Earth and a fraction of second later you would pass close to the Moon, another fraction of second later you would go out of the solar system, then out of the galaxy, then to the border of the visible universe, then you come back to Earth. All travel time: some fractions of second. Would you still say that "light' speed is not infinite"? Yes, it's not infinite, but *in practice* it is. This "discrepancy" between the finite value of c and the fact that "in practice" is really infinite, is due to the non-independency between space and time.

Said in another way: the definition of speed as space/time is "good" only at low speeds. A better definition would be that of "rapidity" R, which is a quantity used in relativity and it's defined as :

R = artanh(v/c)

v is the speed. Rapidity really goes to infinite when v --> c, so everything becomes more intuitive...
 

Offline yor_on

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As Lightarrow express it :)
Very nice.

SpaceTime is your blob of jello. It has four properties that we can 'see' . Length, width, height and time. Those four mark your position this second relative any other thing you choose to compare yourself too. It doesn't matter if you compare your position relative your home the moon or some galaxy, it's still true that those four marks you out all the way to your death, and for your atoms, even beyond.

When you go very fast you contract that jello, the shape of it change, but it has a limit. That limit is lights speed in a vacuum. You can't 'warp' SpaceTime any more than that and still 'exist' in it. And to 'warp' it that much you need infinite energy, really infinite, and if you consider the way you treat SpaceTime trying to reach that 'speed' contracting it into a 'point', for real as far as you're concerned, then it's no secret any more why it takes so much energy.
 

Offline Bill S

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Quote
When you go very fast you contract that jello, the shape of it change, but it has a limit. That limit is lights speed in a vacuum.

Let's not forget that when "you go very fast", you are going very fast relative to something; which means that you are probably going "very slowly" relative to something else.  This must mean that the vast amount of energy you are using, relative to the first thing, you are not using, relative to the second thing.  ???  
 

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Offline Phractality

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Shrunk
The relativity equations explain it well to a mathematician, but most of us have an instinctive need for picture that matches our experiences. The only picture I can offer is the one that comes from my own model, as follows:

The known particles, like electrons, protons, etc., are composed of more fundamental particles. The most fundamental particles consist of pairs (or perhaps groups) of photons orbiting one another. Since they are photons, they can only move at the speed of light, even when they are locked in orbit around one another. The center of the particle is the center of the orbit. When the particle moves relative to any reference frame, the path of the orbit in that frame is necessarily longer than the path of the center.

For an analogy, consider a bola [thanks, imatfaal, for the correction] (two or more heavy balls tied to the ends of ropes). When you throw a bolero, the balls orbit around the center of the ropes. If you trace the paths of the balls and the center, you will see that the balls travel farther than the center, but in the same amount of time. Obviously, the center of the bola can't move faster than the balls spinning around it.  ::)

The rest mass of the particle is the combined mass of its constituent orbiting photons. I can hear you general relativity people shouting and laughing, "Photons have no mass! Ha, ha!"  :D I'm going to have take a slight detour to satisfy the general relativists before I can resume answering the question.   

I'm not saying GR is wrong; it just uses the same words we learned in high school, but with different meanings. It may be true that, in GR, a photon has no mass; that's because "mass" doesn't mean the same thing in Minkowski space-time as it does in Euclidean space. In Euclidean space, gravity bends the path of light; in Minkowski space-time, the path of light is the definition of a straight line. Near a white dwarf or black hole, the Euclidean space is still there, but things that are spherical in Minkowski space-time are distorted in the Euclidean space. When you see a diagram of a black hole with curvy lines to represent light beams, your actually looking at the black hole in Euclidean space; there is no way to illustrate it in Minkowski space-time unless your visual cortex is wired like a modern computer.

Now, as I was saying: A photon has mass in Euclidean space. In a gravitational field, the force of gravity changes the momentum of the photon. At relativistic speeds, force is not equal to mass times acceleration; instead, force is the rate of change of momentum. The equation, f = dp/dt, works for particles with rest mass as well as for photons, regardless of the velocity. Near the speed of light, dp = mdv + vdm. Mdv = ma, and since dm is not zero at high velocities, f ≠ ma.

To satisfy conservation of momentum and Newton's third law, the force of gravity pulling a photon toward a star must be matched by an equal and opposite force pulling the star toward the photon. So the photon has gravitational mass as well as inertial mass in Euclidean space.

Let's get back to the question, shall we.

The rest mass of the particle is the combined mass of its constituent orbiting photons. To accelerate the particle, you must transform its waveform into a different reference frame. Applying the formulas of special relativity to small increments of velocity, you find that the energy of the orbiting photons is greater in a reference frame that is moving relative to the center of the particle. The greater the velocity difference between particles own reference frame and the moving reference frame, the greater the energy of the orbiting photons. Since acceleration increases the energy of the orbiting photons, it also increases the mass of the particle. The rest mass of the particle remains unchanged because it is the mass measured in reference frame of the particle.

Actually, the picture ain't quite that simple, because the orbiting photons are sometimes moving in the direction of relative motion, sometimes opposite the relative motion, and most of the time at an angle to the relative motion. You have to be pretty good mathematician to prove that the sum of masses of the orbiting photons is always equal to the total mass of the particle. (By the way, I'm not a mathematician.)

And that brings us to the standard explanation of why it takes infinite energy to accelerate a particle to the speed of light. If the center of the particle is moving at the speed of light in a given reference frame, and the particle still has its original rest mass in its own reference frame, then the equations of special relativity can only be satisfied by assuming that the particle has infinite mass. Anyway, how are the photons supposed to orbit? They must take infinite time in the part of their orbit where they move in the direction of relative motion, and zero time coming around the other side of the particle.  :-\

For those of you who are wondering how photons can orbit one another, it’s the Higgs force. I'm working on an explanation of how that works, but it’s not yet posted on my website. Long story short: Dark energy pushes photons less on the side facing one another, but only if they are properly matched for wavelength and aligned for phase, polarity and distance. Then, zero point energy sucks them into a potential well so deep that they become blue shifted and their mass increases by a factor greater than a million to one.

Now, kiddies, you must forget everything I've said because you'll get an F if you mention any of this in your school work. It's pure heresy. Bad thoughts!  [xx(] Nasty! Get them out of your mind, right now!
« Last Edit: 16/03/2011 14:08:14 by Phractality »
 

Offline imatfaal

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It's not heresy, it's wrong.  And I love the bolero analogy - perhaps bolas
 

Offline Phractality

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My legitimate, though admittedly heretical, scientific argument has been censored. I'm having difficulty finding the site's terms of service; I'd like to know, what specific rule did I violate? Is it standard practice, here, to censor views which challenge the scientific establishment? Do you censor everyone who dares to challenge Big Bang or claims that the universe is infinite? Would you have censored Einstein before his theories were widely accepted?
 

Offline Geezer

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Oh, that's one I can answer!

You'll find the AUP here http://www.thenakedscientists.com/forum/index.php?topic=8535.msg99453#msg99453

Pay particular attention to Bullet 5.

"The site is not for evangelising your own pet theory.  It is perfectly acceptable that you should post your own theory up for discussion, but if all you want to do is promote your own idea and are not inviting critical debate about it, then that will not be acceptable.

 

Offline syhprum

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I know that the Americans are very keen on free speech but I find correspondents in publications such as the Scientific American or the New york times are very aggressive and eccentric going on about god and visiting aliens, I wonder how the editors justify their wages ?
 

Offline Geezer

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I wonder how the editors justify their wages ?

Do you mean to say people actually get payed for this crap stuff?
 

Post by jartza click to view.

Offline jartza

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Oh, that's one I can answer!

You'll find the AUP here http://www.thenakedscientists.com/forum/index.php?topic=8535.msg99453#msg99453

Pay particular attention to Bullet 5.

"The site is not for evangelising your own pet theory.  It is perfectly acceptable that you should post your own theory up for discussion, but if all you want to do is promote your own idea and are not inviting critical debate about it, then that will not be acceptable.




Well I was going to say something critical. But the long post has been
deleted. Without a word of explanation.

Geezer you are an asshole.



 

Offline imatfaal

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Jartza - you're out of line.

And the post is still there - it's just been shrunk.  And frankly it was speculative in the extreme and the only place for it was new theories
« Last Edit: 17/03/2011 12:50:56 by imatfaal »
 

Offline BenV

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Imatfaal is right - the post is still there, but as it's speculative and does not provide an accepted answer, it's merely been shrunk - just click "Post by Phractality click to view" to read it.

Jartza - As your post is offensive and completely out of line, it has also been shrunk.  Please edit or remove it now.
« Last Edit: 17/03/2011 13:00:50 by BenV »
 

Offline BenV

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My legitimate, though admittedly heretical, scientific argument has been censored. I'm having difficulty finding the site's terms of service; I'd like to know, what specific rule did I violate? Is it standard practice, here, to censor views which challenge the scientific establishment? Do you censor everyone who dares to challenge Big Bang or claims that the universe is infinite? Would you have censored Einstein before his theories were widely accepted?
As discussed above, it's merely shrunk, rather than censored.

New theories have their own section on this forum.  This is not a judgement on the theories themselves - regarless of whether they turn out to be total rubbish or to overturn all of modern science, we prefer to confine their discussion to there, so as to not distract from the currently accepted answers.
 

Offline syhprum

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I was shocked to see one correspondent refer to another in that manner, I thought this forum was conducted by well maned people.
I trust an apology has been forthcoming.
 

Offline Geezer

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Not yet. Ironically, I was not responsible for shrinking Phractality's post!
 

Post by JP click to view.

Offline JP

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Myself or another mod was responsible for the original shrinking, yet we don't get called names!  I'm jealous, Geezer!

Ben covered the reasons why such posts are shrunk above.  I probably should have deleted the post entirely since it's a direct violation of the forum rules, but I didn't want to be too harsh.
 

Offline jartza

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Not yet. Ironically, I was not responsible for shrinking Phractality's post!

I'm sorry. I'm just frustrated because there isn't too much good scientific discussion around. 
 

Offline yor_on

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I also like the bolas, cool description although giving photons mass, even if in a Euclidean space, was sort of surprising :) I think you can use the idea without having to give them a mass. but the bola has no 'size' and what may 'spin' could be the way 'time' is treated for a photon, or my head of course :)

Because that's one of the things that always surprised me, that something moving as fast as we can measure, still are able to follow a logic mostly applicable at speeds where there still is the possibility of a 'distance'. I know it's only rest mass that can 'experience' those effects as we don't have a description from the photons angle. but we still expect them to have a 'energy', and according to a black hole? 'Energy' has a mass, not moving relativistically any more, but , from our 'frame of reference' actually being at 'rest'. If we accept that there are transformations from matter to radiation to energy, then it's kind of surprising that we have a stage in the middle without 'gravity'. but then again, this is not wholly true, is it :) Photons may show a 'gravity', only depending on 'direction' relative each other, but, and this one rather surprisingly also depending on your definition of a 'system? That last one is especially mysterious I have to admit.

Never the less I'm pretty sure they are without what we call 'mass' although I also see them as containing 'energy'. And they all express themselves under our 'arrow of time', interacting very specifically and logical, allowing us to construct a theory of their 'propagation' although we only can observe their 'interactions'.

Photons are weird :)
« Last Edit: 18/03/2011 03:06:41 by yor_on »
 

Offline Phractality

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Thanks, yor_on, for your well reasoned and constructive response.

Since I don't seem to be welcome, here, I'll copy & paste your response to my own thread on "the lighter side".

I have also copied and pasted my own answer to this question, over there.

A question for the community: Would I be out of line, in the future, if I post a note on mainstream discussions, saying something like, "My own pet theory (model, actually) has an answer to the question under discussion in this thread." Naturally, I would only post such a message where it is appropriate. Would that be considered "evangelizing"?
« Last Edit: 18/03/2011 10:04:58 by Phractality »
 

Offline JP

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A question for the community: Would I be out of line, in the future, if I post a note on mainstream discussions, saying something like, "My own pet theory (model, actually) has an answer to the question under discussion in this thread." Naturally, I would only post such a message where it is appropriate. Would that be considered "evangelizing"?

It depends on how you do it, but generally if you have to ask the question, the answer is probably "yes, it is evangelizing." 

In general, the purposes of the non-new-theories sections of the forum are to ask and answer questions in terms of mainstream science.  Some speculation is allowed, but proposing or promoting (by links or otherwise) completely new theories that stand outside of mainstream science is frowned upon, since that's not the point of the forum.
 

Offline Geezer

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Just to reinforce JP's point - Please understand that the object of this particular forum is to allow those who may have limited scientific knowledge to ask questions. If they receive a barrage of inconsistent answers in response, they are likely to be even more confused than they were before they asked the question.

TNS welcomes spirited debate about new theories that challenge the models that are currently accepted as mainstream science, but to avoid confusion, we try to differentiate New Theories. In general, if a theory is supported by experimental evidence, it is probably considered "mainstream". If there is no experimental evidence, it is probably a "New Theory".

I say "probably" because sometimes it's not that clear. String Theory is one example.

Please do not take my use of bold uppercase blue the wrong way. It was intended to be a bit of Geezer humor  ;D  We try not to take ourselves too seriously here.
 

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