Can explosions move faster than the speed of light?

"Nothing travels faster than light, with the possible exception of bad news, which follows its own rules." -Douglas Adams

Every once in a while, a star in our own galaxy can do something to surprise us. Over in the constellation of the Unicorn lived a quiet, run-of-the-mill star named V838 Monocerotis. But in early 2002, it brightened incredibly rapidly, and the before-and-after pictures were rather astonishing.

What was initially thought to be a nova turned out to be much, much more fascinating by time the Hubble Space telescope got around to looking at it in May of 2002.

Warning: what you're about to see may shock you!

By time about four months had passed, this once-compact object now appeared to have an angular diameter of nearly a hundredth of a degree on the sky!

Sure, you say, but that's incredibly tiny. Well, we kept watching it expand, all throughout the year. By September, we were looking at this.

By the end of October, the outer parts of this outburst had expanded even farther.

And finally, by the end of the year (December 2002), the entire original field-of-view was taken up by this massive, expanding cloud of gas!

For something thousands of light-years away to produce something of this size, it had to be expanding very, very quickly. Possibly, according to some estimates, maybe even approaching the speed of light!

But the puzzle got a lot more complicated. Rather than early estimates, which indicated that this star was about 2,000 light-years distant, more detailed models of the outburst combined with new data taken in 2005:

and again in 2006:

Showed that this object -- V838 Monocerotis -- is more like 20,000 to 36,000 light years away!

Does this mean, instead of being near the speed of light, this thing was actually expanding between 10 and 20 times the speed of light? After all, we pretty much watched the expansion unfold, and if we've figured out the distance, the speed is pretty easy to calculate.

And sure enough, those are the numbers we get. But we also know that nothing can move faster than the speed of light! So what's going on here?

You are seeing a phenomenon known as a light echo. What happens is that, sure, you have an event that happens and emits a huge amount of light. The light coming directly from that event reaches you first, as shown in the very first image up top.

But what happens next? The light from other directions travels spherically outward, and does a lot of bouncing around -- and gets absorbed and re-emitted -- by all the gas and dust blown off of the star.

Light that follows the green path takes much, much longer to reach us than light that follows the straight, dotted white line. And light that follows the yellow path takes even longer! While it may not get slowed down as much as in the Sun, where light takes tens of thousands of years to get out, it can still take days or even weeks for the light to get bounced around and sent towards us.

What does all of this mean? That when that bounced-around light finally reaches us, it does so in stages, and the light we receive gives us the optical illusion of faster-than-light expansion!

But everything is actually expanding much slower than light speed; it's just that the initial expansion of this star's outer layers delay the light so significantly that it appears to expand so quickly.

The Universe is a subtle place, and will trick you, unless you pay close attention! So the answer is no, explosions can't move faster than the speed of light. But if you can delay the early bursts of light in the beginning by much more than you delay the later ones, it looks like they do! And that's the explanation behind what we see!

More like this

I'd love to use this as a problem for my honors physics kids, but I don't have any sense of scale in the picture. Is it possible to find/add a scale to the images in this photo?

so the flash of the explosion is like a spherical scan. Could you use that to build a 3D map of the dust around the star?

Truely, truely awesome!

This is incredible, however I wish you'd not say that nothing can move "faster" than light when the correct statement is that nothing with mass can move *as fast as* light - light speed itself is unattainable (so far) by anything with mass.

Never mind Jeff's nit-pick. Brilliant post and i look forward to more in the future. What beautiful images from Hubble. Simply amazing. Gonna be sweet when the JWST gets up there and starts returning data.

@qzl, #2

I'm not sure if you should do what you suggest in this case, because the gas and dust around the star are moving so rapidly.

But, I know that astronomers do exactly what you're suggesting in other situations. Not with a nova-like flash of light, but by using variable stars and correlating the brightness variations from the star with the variations in the light scattered from the dust. This gives you a map of time delay between the star and each point in the cloud.

@Jeff

No, he had it right. There are other things that move as fast as light. Gravity and electro-magnetism for example. As far as we know, nothing can move faster than that. So again, you may play with the wording but his statement is absolutely true.

Should we not also consider the possibility that may be the distance that has been calculated from Earth to the the star may have been miscalculated...?

If the the real distance to the star is much less than the one they are using in their calculations, won't this present the same problem?

This would be a much simpler explanation to this.
As "Occam's razor" state ""the simplest explanation is usually the correct one".

In this case, not even light moves at the speed of light.

Such an excellent article .. it blows my mind .. I usually scan articles .. but was so fascinated had to read every last word.

This explanation is quite reasonable and excellent; unlike your explanation of inflation necessary for the big bang.

"In just a tiny fraction of a second, inflation can take a region the size of a proton and stretch it to be billions of times the size of the visible Universe." Really!

"When inflation occurs, these particle/antiparticle pairs are suddenly ripped apart across the Universe by the exponential expansion." Really! Really!

Inflation of space without particle movement (by definition, not faster than light) is 20th century "phlogiston".

"It depends on what the meaning of "is" is" is politics not science.

"In questions of science, the authority of a thousand astronomers is not worth the humble reasoning of a single individual."

By AngelGabriel (not verified) on 23 Sep 2010 #permalink

@AngelGabriel

"In questions of science, the authority of a thousand astronomers is not worth the humble reasoning of a single individual" is correct, however the quality of the reasoning is called into question when it consists of nothing but an argument from personal incredulity.

@ Ethan: Great post!

How does delaying some of the light make it appear to expand faster? If we see the light that takes an indirect route later than we otherwise would, shouldn't that make the expansion seem slower than it really is not faster?

There must be something I'm not getting about the geometry, because this seems like it'd make it appear to expand SLOWER, not faster.

The light is also travelling outward, not only forward to us. The paths of dust are also travelling outward and that would make it seem to appear faster, not slower. The dust, in light years, IS further away, but we are still able to see it expand outwards.

To me, Ethan's explanation is like a balloon of dust and gas that keeps getting bigger and bigger; but from which only the pinprick of light aimed right at an observer can escape.

Thus as "all the gas and dust (is) blown off of the star"; we initially see nothing but the dead on light. Thus light is bouncing around trapped inside of an expanding balloon of dust and gas for a long time; because the balloon refuses to break (i.e. the light does not reflect towards us).

Now when the (non dead on) light finally starts to leak (i.e. is finally reflected towards us); the ballon bursts forth first at small angles from dead on and then very quickly from large angels from dead on. Thus the expansion of the balloon of gas (i.e. indicated by the reflected light finally aimed right at us) appears to be greater than c.

Hopefully, this explanation is somewhat correct and helpful. If not please clarify.

By AngelGabriel (not verified) on 23 Sep 2010 #permalink

Which physics exactly (e.g. quantum mechanics, general relativity, string theory, particle physics) "credibly" explains the inflationary force?

Is Ethan hedging his bets when he:
1) isolates inflation. Inflation "happened before the big bang". Very tricky.
2) hints at an infinitely old Universe. "it's also possible that the Universe existed for billions of years before inflation". Is this a steady state Universe of a different color?
3) questions the idea of time "It's also conceivable that time didn't have the same meaning that it does now back then." Which physics fundamentally understands time?
4) declares that inflation is unobservable. "inflation prevents us from knowing right now; it wiped out any information about the Universe that existed before inflation!"

Only Ethan's dentist knows, if he is professionally incredulous about the inflation force.

By AngelGabriel (not verified) on 23 Sep 2010 #permalink

It's called a light echo for a reason, it IS moving at the speed of light because it is light. Lighting up dust as it goes.

Prove me wrong. Light is not the fastest phenomena in the universe. This is an example that proves that light is an emanation of an unseen force. It is beyond question that this force is causing the explosion. Light is radiated outward as a result of an emission of energy as the electromagnetic wavefronts are generated. These wavefronts have a finite speed. The force causing the explosion has infinite speed. it is really a question of perspective.

Actually, I think my balloon explanation is misleading on one point. I think that perhaps for a year or more before the explosion of V838 star isvisible, even the image (as in 1989 image)goes invisible in the cloud of gas and dust. Thus there is no pinpoint of light that gets through at the beginning. But otherwise the balloon analogy helps me understand.

By AngelGabriel (not verified) on 23 Sep 2010 #permalink

@tercel #7 - yes, although I'd still suspect that the gas and dust is not moving at anywhere near the speed of light, if at all, and the apparent motion is almost entirely from the wave of light.

@RayTrace. That is a very VERY VERY big (but often common) misrepresentation of what Occams razor actually is. The ACTUAL definition of Occams razor is that the explanation which require the LEAST ANTALOGICAL ASSUMPTIONS is usually the correct answer. You made argument: "should we not also consider the possibility that may be the distance that has been calculated from Earth to the the star may have been miscalculated...?" For that to be true you would have to ASSUME that the leading minds of astronomy fucked up and didn't double check their work to make sure their data was accurate. Since you have to make such an outlandish ASSUMPTION your argument is probably false. Dont worry i'm not tryin to make you feel stupid because alot of people do believe that Occams razor is that SIMPLEST explanation is most likely correct but that's not the true definition. It's the one with the least antalogical assumptions. That's why theist say that accoms razor proves that god is real when in reality the idea of accoms razor was first presented as an argument against the existence of god. Accom himself (the actual scientist who made the argument) was actually an athiest.

And one more thing
@Jeff I know this has already been said but it actually is impossible for anything to move faster than the speed of light. It's actually the speed at which causality occurs in the univers. Have you ever heard that if a human was moving at the speed of light he wouldn't age? That because if he's traveling at the speed of light then causality with actually cease to occur within his own body and he will cease to experience traveling through space and time. There will be no chemical reaction or electical impulses because they just cannot occur at such a speed. It's one of the mysteries of physics. A

Make the nonsense sufficiently complex and it almost sounds reasonable

By Hans Wurst (not verified) on 23 Sep 2010 #permalink

physics can be so confusing...

i thought tachyons moved faster than light. and quantum entanglement of subatomic particles suggests that information on the state of the particles travels instantaneously between them. and perhaps you've heard of the theory of a holographic universe, which says something like the universe being a projection of something else that contains within each individual part the data of the whole? I'm just a humble biochemist, so I can't hope to understand all this metaphysical stuff.

@24: That's precisely how I ended up with 17 shamwows. Damn you complex yet reasonable nonsense, you win again!

(Side note: you know your crappy info-mercial product has hit the big time when its name is featured in google's spell checker.)

@23: Your take on Occam's razor was correct, however the man who is credited with its formulation was actually William of Ockham, a Franciscan friar. Even if he was excommunicated, it was because of heresy, not atheism.

The initial light echo explanation must be wrong. Even if the light takes days to escape the cloud that you suggest is distributed _around_ the star, some other cloud parts would light up with only ligthweek distances from the original source (in which the light would have traveled even less distance).

From the Hubble site you can see that the scale in the picture suggests a 4-6 lightyear distribution. That is based on the _suggestion_ that the cloud that is lighting up from the supernova is spherically distributed around the star.
What actually happends is more likely that the light we see around the star is scattered by a dust clound which is much closer to us than the star. Diffuse scattering is much stronger if the angle towards the observer is low. Thus, the delay between the directly seen light and the indirectly (i.e. scattered light) is, as can be seen, from some weeks to some months. Simple triangulation renders that the dust cloud must be on the order of thousands of light years away from the star. Since we first see the initial ligth from the supernova, the dust must be closer to us.

Another great post.

One thing I found disturbing was the degree of uncertainty for the position of this star. The initial estimates were 2,000 light years, and the latest has it at > 20,000 light years.

I would enjoy a future post on how we know how far away objects are. I assume the methods would be different for things in our solar system, things in our galaxy, things beyond our galaxy.

This explanation of the V838 Nova event is very strange, and a bit difficult to understand.

But it makes sense to this skeptic. Very excellent science.

2,000 versus 20,000 lightyears; astronomers have incorrect distances for many stars. But once a star gets interesting, most of the errors and inconsistencies get hammered.

So... if I'm understanding correctly, the dust cloud was there before the explosion, and is only being illuminated by the explosion rather than being created by the explosion. Is that right? Because it looks more like there's a structure being pushed outward and spread, rather than a "sperical scan" as another poster wrote.

Is this a case of a star progressively shedding its outer layers before blowing up, or is it in a dusty area, or do stars just collect a shell of dust at the outer edges of their solar wind? Or is the cloud simultaneously created and illuminated by the explosion? This last option was how I had always thought of these things, but it doesn't seem you could get a light echo that way.

So much to know, so little time.

- Kevin

By YetAnotherKevin (not verified) on 24 Sep 2010 #permalink

I always hate when discussions get into things about the speed of light. The speed, like the speed of everything (at least everything that can be affecting by part of our physical universe), is variable, which is what would cause this illusion (assuming it is one). I think that is what they were trying to explain. Essentially as the dust cloud got less dense the light was able to reach us with less variance in speed therefore making the expansion as a whole appear to move a lot faster that it really did.

Personally I'm more of a fan of stating that nothing we know of can travel faster than max speed of light rather than just saying nothing period.

As a man of intellect, while not a scientist, there are certain parts of relativity I feel are taken out of context a bit to the point of being misleading. Things such as stating that time would stop if you could travel at the speed of light, which is obviously not exactly true or it wouldn't take time for light to travel from point A to B. In certain ways time would Appear to alter as the object is moving at the same speed as the light we use to see it. For the person moving at such a great speed, there would be an appearance of the warping of the passage of time as things directly in front of them would get close to doubling and things behind them would slow to the point of practically vanishing. You'd have to mark the center of a sphere and draw a line through it from one side to the other and from top to bottom to show it best. The line going across represents the direction the subject is traveling. Any object directing at the end of the line in front would appear to aging 2x as fast, while directly at the back of the line would possibly just disappear. Light coming from directly above or below would be normal speed, though it would slowly start to slow down as it traveled from above/below to behind as the subject passed them by.

To those watching the subject travel away, time would appear to slow down for the subject until it almost appeared to stop. Assuming light cannot travel faster than itself (imagine throwing a baseball at 70mph standing still vs in a train moving 50mph..relatively in regards to myself the baseball is still only moving at 70mph...but relative to someone outside of the train, the baseball would be moving at more like 120mph) It would be an interesting view for an observer in front of the subject.

The general statement of time stopping is given as a way to give an easier, if not wholly accurate, way for the everyday person to understand the general idea. Now I'm sure my explanations are crude and probably not exactly right either (as I said, I'm not a scientist), but the flat statement of 'nothing can travel faster than light' should really be read as either 'nothing yet known' or 'we have yet to find evidence for'. Observing something traveling faster than the light and such that we currently have to use to observe it in the first place, would be tricky to catch.

@23 Austin:

I've also heard it as "the theory with the fewest ad hoc assumptions is probably correct."
My version is "the correct theory is probably the one with the fewest magic dingleberries attached." I wrote this in a humorous piece for Cracked.com and got taken to task for it by a commenter who thought an invisible intelligent designer was the simplest explanation for the origin of matter. Then he called me a shitbag and a brainwashed idiot.
intelligent design,

By feralboy12 (not verified) on 24 Sep 2010 #permalink

As I suspect everyone avoided my discussion. None of you intellectuals can see that some force is causing light to go forth, to emanate. Light does not move without an external force. Light is a messenger. Light comes in many frequencies. Light in an electromagnetic wave front causes a change in the space it interacts, it sends out a code. Do I need to spell it out for you. Light has a finite speed. The force that moves light has infinite speed, it acts instantaneously. I do find the discussions entertaining. But really dark matter, a region of space that our telescopes can not see past. It really is about perspective. There is nothing that light can not reach. You just have to be in the right place.

particals like rain drops colliding in the vacume of space huricane of new matter happens past and present we are the a growing skeleton, dark mater. a bond for anniliated particals to structure.

So, .... how much space/energy does one lb. of light take up?

By Redneckmothr (not verified) on 25 Sep 2010 #permalink

@ Jack Enright,

I love how you say 'prove me wrong' as if thats possible at this point in time. I may as well tell you to prove your right... maybe in 200 years someone will when we hopefully have a better grasp of the inner workings of the universe. Thats assuming we don't destroy ourselves in the meantime. If Iran keeps up their current foreign policy it shouldn't be much longer.

By waffleeater (not verified) on 25 Sep 2010 #permalink

@36:

Well, that depends on which definition you choose you assign to light. One definition says yes while another says no.

I believe a lot of this speculation is based on the Big Bang theory. The Big Bang supposes that matter is lumped together than explodes with Light emanating of course. Actually there was Light in the beginning and matter arose when Light (energy) slowed down. If all you believe that exists is Energy you must have a very shallow life here on Earth. Light is a messenger of a Force. You can designate all kinds of names for this Force. But the Force exists and is undeniable. Just try leaving Planet Earth by jumping. You do not get very far. Gravity is a result of electromagnetic wavefronts. These wavefronts are generated by Light. Light excites matter in its direction of force. Light excites chloroplasts to create sugars. Light makes possible life here on earth. But the speed of Light is finite, however the speed of the Force is infinite and instantaneous.

Jack Enright,

I'll do my best to treat you like an adult, but you need to act like one.
In brief: Scienceblogs is not the community for you, because you are looking for self-gratification which you will never find here.

What you face, right now, is the self-inflicted dilemma faced by blowhards everywhere. The outcome you seek, to Win, is not a choice available to you. Your actual choices are limited to the following, in order of decreasing courage:
1) Own up to the hole you starting digging with your first three words here, and apologize to the community whose standards you have violated;
2) Quietly set down your shovel and walk;
3) Double down and keep digging.
Don't respond to me; I'm done with this.
Address the community, or not; it's up to you.

To the other potential Jacks out there: remember that the best option is actually 0): reflect honestly on your own motivations for participating, and think before you dig.

To Ethan and everyone else: I apologize for prolonging this distraction from interesting science, and I support good-faith dissent, but healthy communities require tending, and I value this one.

By Elmer PhuD (not verified) on 26 Sep 2010 #permalink

in perspective to humans our universe is infinate, partical annihiation paves our residence in space and time.

we need to explore a new reality of phisics, one foot in two feet out ove the box.

By to number 25 bah (not verified) on 26 Sep 2010 #permalink

i apologise 25 bah my computer skills are still in the works, number 42 was ment for you. thanks.

one lb for now,there is no limit in sterile space until an external force is enhanced. please dont quiz.

One point - it is incorrect to say nothing with mass can go the speed of light; light does have mass (it even 'falls in a gravity field) and of course, can and does go the speed of 'light'. The correct and only statement is nothing with rest mass can go the spped of light. That said, some aspects of a light signal does exceed the speed of light (quantum requires this) but that does not violate relativity.

Does the gas produced off of the star effect stars around it? I noticed stars around it turned blue.

How often do these explosions occur?

By Alexander Henderson (not verified) on 27 Sep 2010 #permalink

Should this message arrive at all let me pose for the mathmaticians--:
As far as I read the answer lies in the correct question being asked.
consider that the initial point of the occurrance -has not moved--and then the question should lie in the rate of expansion from that point and as has been been pointed out there is: the resistance to that expansion is a factor in the speed at which we observe the occurrence moving toward earth!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!11

Elmer, conceive this: the speed of light you measure with your human tools is your perspective here on Earth, it is the result of a doppler effect. You merely observe a doppler effect of light passing, you do not perceive the first but the last. You only see the effect of the force which is light as electromagnetic radiation. You have no way of measuring or even comprehending what is ahead of the light. Something must be ahead of the light, at the very beginning. Sort of like a surfer hanging ten on a board just ahead of the wave. Or just go back to chasing rabbits of relativity.

Enjoyed your post and insight. I strongly believe applications in quantum elemental transfer can and do bridge the speed of light constant currently accepted. As found the nova waveform video very good. Within the waveform of energy that comes from Alpha Centuari I believe to have an almost instantaneous present that the gravitational pull of our star (the sun) benifits from and from which certain data transfer andd communication can occur within that brightlight transfer that far exceeds the that commonly utilitied. It is this new technology and math that needs to emerge as a celestrial child being born. Linked to your site via SETI.USA of which I'm a part.Encouraged by your work. I witnessed a major solar regeneration 12-06-2004.

I've spent a lot of time over the last year or too lurking (rarely commenting) in various Climate Science blogs. I wondered if it was just climatologists who had to put up with the contrarian loonies. Clearly, no.

Fascinating stuff, ES. Thanks.

So is the same phenomenon that is responsible for the opaque universe that lasted up until 380,000 years after the big bang? For the big bang it was a ball of radiation, but in this case its dust. Does that change things or is it the same principle?

I have read that our universe is about 13.7 billion years old. Therefore, the time horizon is 13.7 billion light years distance. It has been calculated that our universe is about 173 billion light years across. It is expanding faster than the speed of light. Over billions of years more and more galaxies will disappear outside of the time horizon.

By Dave Tivel (not verified) on 07 Oct 2010 #permalink

Correction to typo above. It has been calculated that our universe is about 153 billion light years across.

By Dave Tivel (not verified) on 08 Oct 2010 #permalink

The circumference is a constant distance from Earth and constantly illuminated. When and where it was illuminated from is irrelevant. If the distance is correct then the expansion is faster than light and should make world headlines. Just because we haven't done or seen something does not make it impossible. Theories can be wrong.

By Faster than light (not verified) on 09 Oct 2010 #permalink

Interesting, but the light echo explanation has some obvious problems - the features of the dust cloud are clearly evolving rapidly.

I even captured the image and layered the frames on top of each other to make sure and it certainly doesn't look like a structure progressively lit up.

The obvious features like the filaments surrounding the hole in the upper right part of the picture for example are expanding at the same rate as the outer rim of the dust cloud. This is inconsistent with the cloud being simply lit up progressively and consistent with it actually expanding.

If it was just lit up the cloud would be static or at least the evolution would be much slower then the growth of the radius of the lit up portion - this is clearly not the case.

Definitely!! In space, anything can travel faster than light because there is no friction or anything else that can cause any hurdle or friction. Moreover, your article has added a lot to my knowledge on this.
http://mojoblast.org/

By Ernest Grote (not verified) on 11 Oct 2010 #permalink

Light does not travel... Light is a chemical reaction process and a bi-product of Universal Respiration...

Many of the problems associated with determining how the universe was created relates to the measurement of light, which is used to measure our distance from other star systems. Current theory regarding the motion of light, supports the speed of light at 186,000 mps. This is highly theoretical! I would like to propose to you that light doesnât move at all like contemporary science tells us. Light as opposed to particles (photons) moving through space, is a chain reaction associated with the motion of electrons and moves at the speed of frequency, which is almost instantaneous! Light is a chemical reaction which would occur at a slightly slower speed but nevertheless, almost instantaneous. In other words, the light which is used to measure whether a star is moving away from a center, is inaccurate as we are seeing this light in almost âreal timeâ!

To read article in its entirety, visit http://tinyurl.com/29uuqrp

Simple, of cause things can travel faster than the speed of light, eg, if I am travelling at the speed of light and throw a ball, for the on-lookers the ball is now travelling faster than the speed of light, for me it is only as fast as I can throw it, it is all relative. All things in front of me would be look sped up, because I am travelling towards the light, so that light is travelling towards me faster than the speed of light, behind me everything looks slower because I am travelling away from it so it takes longer to get to me, so it is travelling slower than the speed of light. It is all relative to the point of origin.

divineadvancedhumanbeings.com

Light does not travel... Light is a chemical reaction process and a bi-product of Universal Respiration...

Many of the problems associated with determining how the universe was created relates to the measurement of light, which is used to measure our distance from other star systems. Current theory regarding the motion of light, supports the speed of light at 186,000 mps. This is highly theoretical! I would like to propose to you that light doesnât move at all like contemporary science tells us. Light as opposed to particles (photons) moving through space, is a chain reaction associated with the motion of electrons and moves at the speed of frequency, which is almost instantaneous! Light is a chemical reaction which would occur at a slightly slower speed but nevertheless, almost instantaneous. In other words, the light which is used to measure whether a star is moving away from a center, is inaccurate as we are seeing this light in almost âreal timeâ!

To read article in its entirety, visit http://tinyurl.com/29uuqrp

A question i need answer for...
If an object travels at the speed of light..then according to special relativity theory..the object would have infinite mass wont it? then this could cause infinite gravity right? according to Newton laws of gravition....then this can attract the est of the bodies in the universe and cause a great disaster right?.. Have i taken something in the wrong sense or are they right?

"If an object travels at the speed of light..then according to special relativity theory..the object would have infinite mass wont it?"

Since it can't travel at the speed of light, this is never going to be a problem.

The speed of objects through space is already taken into account o

@Nish #62: No. The limiting case of infinite energy is for a massive object accelerated _to_ the speed of light. The total energy (rest mass + kinetic) which is sometimes referred to as "relativistic mass", is given by E(tot) = m / sqrt(1 - v^2/c^2). When v=c, you can see that the denominator is zero, so the ratio diverges (i.e., E(tot) -> infinity).

If you try to plug in a value v > c, you end up with E(tot) as a complex (imaginary) value, since the argument to the square root becomes negative.

By Michael Kelsey (not verified) on 11 Sep 2015 #permalink