# Why does it require an infinite amount of energy to reach the speed of light?

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mucker
I don't need equations, I would just like to pose a question which contradicts the above statement (I know I am wrong btw, I want to see where I am going wrong).

My understanding of space (not near any gravity and therefore no spacetime curvature) is that a body in motion will continue to move at said speed unless acted on by another force. So let's use an example. Let's say I am moving at 10mph through space but I want to reach the speed of light. (Now I'm going to use fictious numbers and equations to keep the math simple). Let's say in my spaceship I fire off my rockets to increase the speed, which requires 5 amount of newtons (or whatever else the metric is for force – it doesn't really matter for the point I'll make). And that 5 amount of newtons increases my speed by 10mph, so I'm now I'm going at 20mph. At this point I stop the rockets and i continue indefinitely at 20mph. So I now apply another 5 newtons to reach 30mph, and so on until I reach the speed of light. This does not require an infinite amount of energy.

Now I know the above is wrong (for many reasons) but bear with me for a minute. So from E=mc2 (I think) it states that the reason we can’t reach the speed of light is because as you get closer to the speed of light your mass increases, and therefore requires infinitely more energy – I get that. But the first issue I have here is that I thought speed was all relative. So in my example above I know that I am wrong when I keep saying my speed in increasing. But if my 30mph is the equivalent of being still in space, then how can my ship gain mass when increasing in speed? and therefore need infinitely more energy if speed is relative? To demonstrate more, imagine nothing is close by to judge our relative speed to it. To put it another it seems that speed is relative to everything but not light. I have come to the conclusion that when we say we can’t reach the speed of light that maybe it actually means the acceleration to the speed of light - because to reach the speed of light (relative to another body) we’d have to accelerate at an insane amount (which would require a lot of energy). So my question is, is it more accurate when we say “it requires an infinite amount of energy to reach the speed of light” to change that to “it requires an infinite amount of energy to reach the speed of light”

Or have I completely missed the point? Where I am coming from is that there is no speed in space unless it’s relative to another object. The other thing that is weird, is that, if light speed is always constant how can light still travel at said speed if I were to speed up just half the speed of light in the same direction as the light beam? I should perceive the light traveling at half the speed of light but I know (from reading up on GR) that light is always the speed no matter the reference frame. The explanation to this is that apparently that time is slowed down the faster you move – but again, I thought speed was relative.

goganesyan and Delta2

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First, you need to start studying SR systematically. Posing questions like this that are a mixture of fact, fiction, popular science and your own misconceptions thrown in will get you nowhere.

The first chapter of Morin's book is online here:

https://scholar.harvard.edu/files/david-morin/files/relativity_chap_1.pdf

My personal recommendation is Helliwell's book:

A massive object cannot move at the speed of light (as measured in an inertial reference frame) even if an infinite amount of energy is available. (By infinite here I'm using the more precise mathematical idea of unbounded or unlimited, rather than infinite as some ill-defined number.)

The why follows from the postulates of SR and is explained in a methodical way in the above textbooks.

rudransh verma, sysprog, Omega0 and 3 others
A postulate of special relativity is that the speed of light is the same in all inertial frames of reference. Thus you cannot travel at the speed of light because you cannot be stationary with respect to light and have it doing light speed at the same time. All of the "reasons you can't get to the speed of light" follow from that postulate and the contradiction it implies for an observer traveling at that speed.

sysprog, FactChecker and Dale
mucker
First, you need to start studying SR systematically. Posing questions like this that are a mixture of fact, fiction, popular science and your own misconceptions thrown in will get you nowhere.
I told you in the other thread I am going to study it. In the meantime though you could just point out where I am going wrong instead telling my I am wrong. I am not looking for the math yet (I know that is beyone me yet), what I asking for is for someone to just say if my interpretations are wrong or right so I stay on the right track.

A postulate of special relativity is that the speed of light is the same in all inertial frames of reference. Thus you cannot travel at the speed of light because you cannot be stationary with respect to light and have it doing light speed at the same time. All of the "reasons you can't get to the speed of light" follow from that postulate and the contradiction it implies for an observer traveling at that speed.
The reason I brought this up is in relation to time travel. I've seen many times all over the Internet hat FTL implies time travel. But in all explanations (even hypothetically), everyone talks about mass increasing as you get faster and time slowing down around you, and infinite energy being required -but if speed is relative then how can you even make these statements? Maybe my linking of this to E=mc2 is wrong, but you know what conversations I am referring to right? The time travel stuff.

Now, I don't want to go off topic and talk about time travel, the point I am making is that where did the idea come from that you to FTL you need an infinite amount of energy, if we know that we can never reach it? I mean these discussions are wide spread, I even remember them in high school

Delta2
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I told you in the other thread I am going to study it. In the meantime though you could just point out where I am going wrong instead telling my I am wrong.
My suggestion is to start now.

Assume everything you wrote is wrong and start again.

hutchphd, DaveE, phinds and 2 others
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For example, when you fire your rockets how do you know you are speeding up and not slowing down?

mucker
For example, when you fire your rockets how do you know you are speeding up and not slowing down?
Did you not see the bit where I said I know I was wrong in that regard? I was trying to show that the statements I read about reaching the speed of light don't make sense if speed is relative. So the scenario I painted (imo) was the only way I could refer to speed not being relative but then I acknowledge that the scenario is wrong.

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Did you not see the bit where I said I know I was wrong in that regard? I was trying to show that the statements I read about reaching the speed of light don't make sense if speed is relative. So the scenario I painted (imo) was the only way I could refer to speed not being relative but then I acknowledge that the scenario is wrong.
Who cares whether they don't make sense? Given they didn't come from a reliable source.

Once something is sufficiently messy and erroneous I have trouble knowing where to start.

robphy
mucker
Who cares whether they don't make sense? Given they didn't come from a reliable source.
Let me see if I can find it. It was a while since I read so maybe I repeating it back wrong...

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Let's say in my spaceship I fire off my rockets to increase the speed, which requires 5 amount of newtons (or whatever else the metric is for force – it doesn't really matter for the point I'll make). And that 5 amount of newtons increases my speed by 10mph, so I'm now I'm going at 20mph. At this point I stop the rockets and i continue indefinitely at 20mph. So I now apply another 5 newtons to reach 30mph
Let me try to directly answer why this argument does not work.

Your goal is to exceed the speed of light as measured in some particular frame of reference. For instance, in the rest frame of an unaccelerated stay-at-home fellow named Orville. (Thinking Orville for origin).

You fire your thrusters for one second and increase your speed by 10 mph. Orville now sees you moving at 10 mph.

You fire your thrusters for another second and increase your speed by 10 mph relative to your previous 10 mph frame. Does Orville measure the same 10 mph increase in speed? No, he does not.

When you measure your speed change, you are using standards of length, time and simultaneity particular to your new 10 mph frame. When Orville measures your speed change, he is using standards of length, time and simultaneity particular to his original frame. The two measurements are not guaranteed to match.

There is a simple formula for how one can add a velocity measured in one frame to that frame's velocity measured in another frame and get a velocity measured in that other frame. It is called the relativistic velocity addition formula.

[It might help to think of this as a "velocity composition formula" instead. It is hard arguing with the seemingly inescapable thought that velocities should add linearly. One needs to keep straight that you cannot simply add a velocity relative to this frame and a velocity relative to that frame and expect to get a result that is meaningful. So a useful mental trick is to think of it as composing, not adding]

As it turns out, when you get close to the speed of light and add 10 mph to your speed, Orville will measure a speed increase that is much smaller. Your new velocity after a finite speed increase will always be less than the speed of light. The formula guarantees it.

Edit: In case you were interested in the experimental result rather than the sort of theoretical handwaving above, the Bertozzi experiment is a very good view.

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LBoy, russ_watters, sysprog and 2 others
mucker
And just for the record, I have tried learning SR and GR. In fact I've tried it several times (not through uni but the Internet). This time I've decided to do it seriously so have enrolled for a physics degree but it only starts next month. The problem I have found with learning SR and GR is that you have to know other foundation stuff first like calculus for example, then maybe Newtonian mechanics. I might be wrong in this last regard but what I've found is that within the first few paragraphs it starts going into maths I don't understand so I can't progress any further. I only have a high school level of maths and never did calculus. So I've realized I need to get the math in order first before I can grasp SR dn GR properly, so the degree I am looking covers all that...

But I don't need to understand the math to work out that something doesn't sound right. Take my previous post for example - I raised it because accelerating to Earth is clearly what was happening and so the Equivelence Principle contradicted itself (as it appeared to me). It obviously was not the case, but it was my perception of what acceleration is which was wrong - so my logic was good. It turned out that it's because I was using coordinate accelleration instead of proper acceleration. I didn't know there were two types. So you don't need all the math to understand some parts of it - but by Dale explaining to me that I was using the wrong type of acceleration suddenly it made sense.

Dale and Delta2
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Let's say in my spaceship I fire off my rockets to increase the speed, which requires 5 amount of newtons (or whatever else the metric is for force – it doesn't really matter for the point I'll make). And that 5 amount of newtons increases my speed by 10mph, so I'm now I'm going at 20mph. At this point I stop the rockets and i continue indefinitely at 20mph. So I now apply another 5 newtons to reach 30mph, and so on until I reach the speed of light. This does not require an infinite amount of energy.

Let's also say that a space tanker-ship fills your fuel tank after each burn, so that burns are identical.

Now the thing is that burn #33 increases speed by 10 mph, compared to speed after burn #32 , but not compared to speed after burn #31. The latter is less than 10 mph.

I mean, when you change your speed by 10 mph, a few objects change their speed by 10 mph according to you, while other objects change their speed less than 10 mph according to you.

The faster the object is according to you, the less its speed changes according to you.

mucker
So I just did a search for time travel and the first thing that came up was a paragraph like so: (and this is the general gist of what I was saying above about reaching the speed of light - the description is always the same)

Thanks to Einstein, we know that the faster you go, the slower time passes--so a very fast spaceship is a time machine to the future. Five years on a ship traveling at 99 percent the speed of light (2.5 years out and 2.5 years back) corresponds to roughly 36 years on Earth. When the spaceship returned to Earth, the people onboard would come back 31 years in their future

The explanation for why time slows down is that as you approach the speed of light, time slows down for you relative to objects moving slower, is this correct?

mucker
And here is the other quote I was reffering to:

According to Einstein's general theory of relativity, as an object moves faster, its mass increases, while its length contracts. At the speed of light, such an object has an infinite mass, while its length is 0 — an impossibility. Thus, no object can reach the speed of light, the theory goes.
This is the bit I don't get if speed is relative. As an example, let's use the same scenario in my post above. As I move away from Earth and get closer to the speed of light my mass increases. But this is only from Earth reference frame perspective. If another object was flying at the same speed as me (alongside me) we'd both see each other as having no speed. So my mass wouldn't increase from this other object's perspective, so how can my mass be different to these two observers at the same time?

so how can my mass be different to these two observers at the same time?
It isn't. Your relativistic mass is different, not your mass (a.k.a. rest mass or invariant mass). If that seems confusing, it is. That's a big part of why the concept of relativistic mass was deprecated in professional circles decades ago. Popsci can't seem to let go of it, though...

That said, there's nothing wrong with frame dependent quantities. If I'm sitting in a car the person next to me would say my kinetic energy is zero. A pedestrian might well disagree.

LBoy
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I don't need equations,
This already excludes any understanding of physics. If you don't need (or want) equations (math) you don't need to waste your time in trying to understand any modern physics, including special (let alone general) relativity.

pinball1970, rsk, sysprog and 6 others
This already excludes any understanding of physics.
I think there's an implicit "yet" after the "no equations" - OP is signed up to start a physics degree next month.

Grasshopper, SiennaTheGr8, Delta2 and 1 other person
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For this question there are several different equivalent ways of seeing the fact that you cannot travel at c.

My least favorite is, unfortunately, the one that is most commonly given in pop-sci sources. That is the “relativistic mass” argument, basically as you approach c in some frame your “relativistic mass” diverges to infinity. I dislike this explanation because “relativistic mass” is a useless concept for the reasons you stated among others. Please, if you gain nothing else from this reply, at least learn to ignore any source that uses relativistic mass. Serious sources abandoned the concept 60 or 70 years ago or more (its problems were recognized by Einstein late in his career even earlier), so sources that use it are either not serious or are outdated. “Relativistic mass” is now a hallmark of a source to ignore.

My favorite approach is the momentarily co-moving inertial frame. Any massive object has a momentarily co-moving inertial frame. In that frame the speed of light is c and the speed of the object is 0. So you cannot even approach c from your perspective and that translates to never reaching c from another perspective.

Another good approach is the relativistic velocity addition approach mentioned above. Each time you try to add 10 mph from your frame you actually add a bit less in a fixed inertial frame.

Another good approach is the mass approach, but it requires four-vectors. Once you learn four-vectors you will find that any object with mass (real invariant mass, not relativistic mass) has a timelike four-momentum. And any object with a timelike four-momentum has a timelike four-velocity, which means a velocity less than light.

russ_watters, sysprog, jbriggs444 and 1 other person
Please, if you gain nothing else from this reply, at least learn to ignore any source that uses relativistic mass.
That may be a bit strong - older respectable sources use it (for example the Feynman lectures equations 15.1 and 15.10). But certainly any modern source (as you note, pretty much anything younger than Feynman) should be treated with suspicion if it uses relativistic mass.

SiennaTheGr8
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Instead of using relativistic mass, just use energy, and everything is fine. The mathematics that describes relativistic physics, which we are not allowed to use to explain the issue in the best understandable way, tells us that you need an infinite energy to accelerate a massive body/particle from rest to the speed of light ("rest" and "speed of light" relative to an arbitrary (inertial) frame of reference). There is no need for relativistic mass at all.

LBoy, Omega0 and Dale
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That may be a bit strong - older respectable sources use it (for example the Feynman lectures equations 15.1 and 15.10). But certainly any modern source (as you note, pretty much anything younger than Feynman) should be treated with suspicion if it uses relativistic mass.
I stand by it. I would look for the best modern sources. Generally they will be better than older respectable sources in terms of pedagogy even than a master teacher like Feynman. The modern authors may not rise to Feynman’s mastery, but they have the advantage of Feynman’s genius as well as an additional half-century of pedagogical experience and scientific progress to draw on.

weirdoguy and Ibix
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At this point I stop the rockets and i continue indefinitely at 20mph. So I now apply another 5 newtons to reach 30mph
This is not how physics works. In particular, velocity addition is not linear in relativity.

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This already excludes any understanding of physics. If you don't need (or want) equations (math) you don't need to waste your time in trying to understand any modern physics, including special (let alone general) relativity.
I think there can be some unusual people that can have very good qualitative understanding of physics with little to no quantitative understanding.

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The last historical figure of this kind that comes to my mind is Faraday. Geniuses of this caliber are very rare. We normal mortals have to use math to talk about and understand physics.

LBoy, dextercioby, Grasshopper and 2 others
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I think there can be some unusual people that can have very good qualitative understanding of physics with little to no quantitative understanding.
This understanding would have to take some form. You can see how that would work in art, music, chess, or mathematics for example. People with no formal training who can just do stuff.

I can see that in experimental physics or amateur electronics, for example. Faraday's understanding came from that practical sides of things, which led to some significant theoretical insights.

But, if someone simply claims to understand physics at some intuitive level and throws some buzz words around as evidence, then I'd be less than impressed.

vanhees71
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But, if someone simply claims to understand physics at some intuitive level and throws some buzz words around as evidence, then I'd be less than impressed
Yes well the qualitative understanding of OP doesn't seem so good but maybe you could help him develop his qualitative understanding instead of just saying "Go get a book and read it all from the very beginning". I myself don't know relativity so I just can't help him.

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Yes well the qualitative understanding of OP doesn't seem so good but maybe you could help him develop his qualitative understanding instead of just saying "Go get a book and read it all from the very beginning". I myself don't know relativity so I just can't help him.
If I wanted to learn the piano, I would listen to my piano teacher. I wouldn't clatter the keys at random and demand an analysis of why that isn't music.

My physics knowldege is all self-taught, so I'm not suggesting anything I didn't do myself. If that's too austere, then too bad. I don't know how else to learn physics.

Motore, goganesyan, phinds and 3 others
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If I wanted to learn the piano, I would listen to my piano teacher. I wouldn't clatter the keys at random and demand an analysis of why that isn't music.

My physics knowldege is all self-taught, so I'm not suggesting anything I didn't do myself. If that's too austere, then too bad. I don't know how else to learn physics.
Ehm , I know you have helped many people in these forums, I cannot judge my self the qualitative understanding of the OP (since I don't know relativity myself) but is it that bad, like playing random keys at piano? random relativity concepts and random words put together?

Mentor
I've seen many times all over the Internet hat FTL implies time travel.
There's more to it than that, although the general conclusion is correct: Any FTL travel or even just signalling allows us to create casality paradoxes, such as allowing you to have your grandfather killed, thereby preventing your own birth. Google for "tachyonic anti-telephone" - the wikipedia article is pretty good.
But in all explanations (even hypothetically), everyone talks about mass increasing as you get faster and time slowing down around you....
That is one of the more common incorrect things you'll read on the internet. Your best bet will be to try to forget everything that you've read about "mass increasing" and "time slowing down"; both are dangerously misleading descriptions.

Now consider a rocket that can accelerate itself from zero to .8c (relative to someone who is at rest relative to the rocket before we fire the engines, and remains at rest). Say that rocket is already moving at .2c relative to us, and we want to fire its engines to goose its speed from .2c to c relative to us.... But the velocity addition rule tells us that although the speed of the rocket increases from 0 to .8c relative to someone initially at rest relative to the rocket, the final speed of the rocket relative to us is not ##.2c+.8c## but something less. No matter how much fuel we pump through the motors, no matter how much we increase the speed of the rocket relative to its previous seed, we can never get it up ##c## relative to us.

vanhees71
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but is it that bad, like playing random keys at piano? random relativity concepts and random words put together?
Yes.
However also more forgiveable as there are so many bad sources out there. Sometimes I think the only thing we do here is take people who have been sent down the wrong road by bad popularizations and try to point them in the right direction.

Motore, phinds, vanhees71 and 2 others
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The need of infinite energy to reach light speed can look a bit more intuitive if you notice that it also takes an infinite energy to stop something that has a nonzero mass and is moving towards you with speed ##c##. Therefore, even a single electron can have effects similar to nuclear explosion or worse if it's moving fast enough (in Earth's reference frame) and collides with Earth. No energy is lost irreversibly when accelerating an object to higher and higher speeds.

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takes an infinite energy to stop something that has a nonzero mass and is moving towards you with speed ##c##.
Since nothing with a non-zero invariant mass can be moving toward you at ##c##, this doesn't seem to help much.

My math teachers worked hard to get us to avoid the word "infinity" and to instead use euphemisms such as "increasing without bound". That prevents one from falling into the trap of talking about the situation "at infinity".

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My math teachers worked hard to get us to avoid the word "infinity" and instead using euphemisms such as "increasing without bound". That prevents one from falling into the trap of talking about the situation "at infinity".
Usually I ignore that complaint from my math teachers because usually it doesn’t matter. This is one place where they get their vindication.

Nugatory and jbriggs444
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Since nothing with a non-zero invariant mass can be moving toward you at ##c##, this doesn't seem to help much.
The main idea I wanted to demonstrate with that, was that if you accelerate an object with a constant power of 1.0 kilowatts, its speed will increase slower and slower when approaching light speed but the dangerousness of colliding with it still increases linearly. It removes the false idea that accelerating something towards light speed is a bottomless drain where you can put a lot of energy and cause only a tiny effect with it.

rsk