[Vorador (OP)]

Hi,

I wanted to know where exactly this conclusion of SR follow from?
The most popular explanation given for this is by invoking the relativistic mass equation, (an infinite mass would require an infinite amount of energy to be accelerated, thus v=c=impossible!) but I don't think that is strictly correct because SR works for speeds comparable but less than c. So it seems self-contradictory to insert v=c in the theory's equations.

So here am I left wondering, what exactly is there in SR that prohibits a massive object moving at c?

Thank you very much for your time!

[Bill S]

So it seems self-contradictory to insert v=c in the theory's equations.

Hi Vorador, Welcome.

The scientists on the Forum will undoubtedly give you a better explanation, but my understanding is that v=c is included simply as an example of the limit which cannot be reached for the reason you quoted in your post.  Relativistic calculations stop just before v=c is reached, except when photons are involved.

[JP]

Hi Vorador,

Bill is correct.  To be a bit more technical, when scientists say that an object with mass requires an infinite amount of energy to reach the speed of light, what they mean is that if you tell me how close you want to get to the speed of light, I can tell you how much energy it requires.  If you keep increasing your speed closer and closer to the speed of light, the amount of energy increases without an upper limit.  In mathematics, this formally means that in the limit as you approach the speed of light, the amount of energy required diverges to infinity.

Saying "it would take an infinite amount of energy to reach the speed of light" is somewhat misleading (since you can never reach that speed), but it's shorthand for the above concept of limits.

[lightarrow]

... because SR works for speeds comparable but less than c.

This is not true; SR gives the correct relation between momentum p and energy E even for objects moving at c, for example photons, as Bill S wrote. The relation, valid for all speeds and all masses is:

E² = (cp)² + (mc²)²

but if an object moves at c, its mass m is zero.

If instead you put a mass m different than zero, you discover that E should be infinite, since:

E = mc²/sqrt[1 - (v/c)²]

for a non zero mass object moving at speed v; an infinite value for an object's energy is a nonsense in physics, unless interpreted, in this case, in the sense explained by JP.

[Vorador (OP)]

Oh, I see.

Can we use this limits concept to extrapolate how a photon might "experience" the relativistic effects of time dilation, length contraction etc? I'm asking this because the internet is full of pages talking about the "perspective of a photon" and I'm not sure how correct these extrapolations are..

Thank you, lightarrow, Bill and JP for your informative posts! I appreciate it.

[JP]

Good question.  This gets asked a lot and posted on the internet a lot.  It's a very common mistake that you can simply take the limit as speed goes to the speed of light for a massive object and get the effects experienced by a photon.  Often times people say that a photon is "timeless" or "experiences zero length" because the equations show that in the limit, but this is wrong.

The problem here is that the equations for length contraction and time dilation require that no matter how something is moving, it will always measure all light as moving at the speed of light with respect to itself.  As a consequence, measurements of time and distance must vary between different objects depending on relative motion.  Light obviously cannot travel at the speed of light with respect to itself, so these equations explicitly do not apply to light!

[Vorador (OP)]

That's what I thought. Thanks a lot, JP, for illuminating this.

Just one more question: You said that it's a common mistake that we can simply take the limit as speed goes to the speed of light; what exactly is the mistake here? That we can take the limit as speeds approach closer and closer to the speed of light but not exactly at the speed of light (I hope that made any sense..) ?

[JP]

Like I said above, those equations (length contraction and time dilation) don't even make sense for light, since they've been derived by assuming that the object you're applying them to sees all light as traveling at the speed of light with respect to itself.  If you think about the "point of view" of a photon of light, it will obviously be standing still with respect to itself, and this violates the above assumption (it isn't moving with respect to itself), so these equations don't apply to light at all. 

[Vorador (OP)]

I understand that. I was asking this for a massive object (I'm sorry I should've made that clear).

[yor_on]

Two ways to see it. As a car accelerating, where the 'speed limit' is just under 'c', or if you like, always accelerating but never reaching 'c'. The other, more applicable is that light defines a limit for how fast anything seems to propagate, relative a observer. The last one do not discuss mass, just a speed limit for the 'fastest' thing we know, lights speed in a vacuum. Mass is unable to touch that speed limit as long as it is mass, but as soon as it transform into radiation it automatically will be of that speed, without acceleration involved.

The most fascinating thing about lights propagation is that all measuring a same light must reach the same definition, 'c', no matter different 'relative uniform motions' versus each other.

[lean bean]

SR and GR are tools used because of their predictive power, the assumption for both that the speed of light is the same for all observers is a postulation.
Why use the theories ? Because up to now nothing as shown them to be wrong in their predictive properties for the ‘working‘ of nature.
The equations are designed around (or derived from) the postulates of the theories.

[Vorador (OP)]

Thanks guys, but I am aware of that much. I'm not completely new to SR, it's just one of those question that I always took for granted before and just realized I didn't really understand the reason why it had to be so. I still don't completely understand it, but I'm getting there, thanks to you guys. Thanks to everyone, really!

This thread can be locked if the moderators feel like it.

[yor_on]

Well, it is weird. That car won't find a greater resistance, or friction, accelerating, or a new locally defined mass/energy (assuming measuring in intervals of uniform motion), through some experiment inside measuring, but 'c' must always be out of reach for it. And I doubt TNS will close this thread Maybe someone has a better definition, explaining it all.

http://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor
http://en.wikipedia.org/wiki/Theoretical_motivation_for_general_relativity#Stress-energy_tensor
http://math.ucr.edu/home/baez/gr/stress.energy.html
=

Accelerations will give you a locally definable energy, if I define that rocket as being 'at rest' in a acceleration. If you set a light bulb in the middle of that rocket it will, depending on where you stand relative the 'rest frames' direction of acceleration, either give you a blue or a red shift. And if we assume that the acceleration is a constant uniform one, you will then find that you, being 'down' in the gravity well, opposite the rockets direction accelerating, must see a blue shift. And moving towards the 'front' of that direction, looking back at that light bulb, a red shift.

But If the rocket stops accelerating, being in a uniform motion, in between accelerations, the light bulb will neither red or blue shift. So where did the energy go? Your speed is the same as just before ending that acceleration. You can test it on Earth. Just pick another frame of reference in space, not 'at rest' with Earth, to define a speed and a 'direction', then move around that light bulb and see if it will red/blue shift

[JP]

I understand that. I was asking this for a massive object (I'm sorry I should've made that clear).

Ah--well, there are two issues here.  From a theoretical standpoint, what I said about the "point of view of light" holds for anything that you would assume to be moving at the speed of light.  Special relativity describes observations and is derived from postulates that assume that every observer sees light as always moving at the speed of light.  If an observer (massive object) were moving at the speed of light, then any photons moving in the same direction as the observer would appear to be stationary.  This would contradict the postulates of special relativity, so it can't describe objects moving at the speed of light. 

The problem with simply looking at the equations and assuming that speed goes to the speed of light in some sort of limiting case is that you're jumping from cases where the observer sees all light (in vacuum) as moving at the speed of light (anything with v<c) to a case where suddenly light can be stationary to the observer (v=c).  So while this limit can be done mathematically, this is a case where the v->c limit does not model anything physical.

[Vorador (OP)]

Thank you so much, JP! I really really appreciate it!