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Dunbar

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Particles without mass should hypothetically have infinite speed, but experimentally they do not?

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In summary, particles without mass should hypothetically have infinite speed, but experimentally they do not due to the limitations set by the speed of light and the principles of special relativity. While the basic equation of force equals mass times acceleration may suggest that a massless particle would have an infinite speed, this is not the case when considering the more accurate equation of force equals the change in momentum over time. This leads to the conclusion that even with zero mass, a particle can still have non-zero momentum and thus, cannot travel faster than the speed of light.

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Dunbar

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Particles without mass should hypothetically have infinite speed, but experimentally they do not?

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Dunbar said:

Particles without mass should hypothetically have infinite speed, but experimentally they do not?

Why should they have infinite speed?

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Dunbar

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phinds said:Why should they have infinite speed?

Because they have no mass?

I'm aware the particles would blink out of existence instantaneously if they did in fact have infinite speed.

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Dunbar said:Because they have no mass?

I'm aware the particles would blink out of existence instantaneously if they did in fact have infinite speed.

Why does a lack of mass imply infinite speed?

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Dunbar

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phinds said:Why does a lack of mass imply infinite speed?

With lower mass it takes less force to accelerate a particle to higher velocities? With zero mass there is nothing to prevent a particle from instantaneously reaching an infinite speed. Hypothetically?

Experimentally, we have observed that there is indeed a speed limit.

btw, thank you for responding, I greatly appreciate it.

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I'm trying to explain something without math that is trivially easy to explain with math, but the problem you come back to is, where does the math come from?

Basically, the math comes from our(*) having made observations and developed the math (General Relativity) that describes what happens in the real world. It doesn't explain why the observations are what they are.

* Actually "our having made ... " is a bit of a stretch since Einstein didn't get any help from me.

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Drakkith

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Dunbar said:With lower mass it takes less force to accelerate a particle to higher velocities? With zero mass there is nothing to prevent a particle from instantaneously reaching an infinite speed. Hypothetically?

But there is something that prevents a massless particle from reaching an infinite speed...

Experimentally, we have observed that there is indeed a speed limit.

...and this is it. The thing that prevents infinite speed is that there is a speed limit. The rules the universe must follow are set up in such a way as to prevent anything from traveling faster than c.

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The_Duck

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Dunbar said:Particles without mass should hypothetically have infinite speed

If you use special relativity to calculate the speed of a massless particle, you find that massless particles always travel at speed c, the speed of light.

In special relativity there is a sense in which there *are no* speeds greater than c.

Dunbar said:With lower mass it takes less force to accelerate a particle to higher velocities? With zero mass there is nothing to prevent a particle from instantaneously reaching an infinite speed.

If you try to do the calculation using Newtonian mechanics, this is what you would get. But in fact Newtonian mechanics is wrong at large velocities and needs to be replaced with special relativity. In special relativity, forces, accelerations, and speeds work differently from what is intuitive and familiar. It turns out that massless particles can't actually speed up or slow down, and always travel at c, no matter what forces are applied to them.

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Nugatory

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Dunbar said:Particles without mass shouldhypotheticallyhave infinite speed, but experimentally they do not?

That depends on the hypothesis that you're working with. If you start with ##F=ma##, you'll be tempted to set ##m## equal to zero and conclude that any non-zero force leads to an infinite acceleration and hence infinite speed.

However, ##F=ma## is a simplification (used when teaching physics to students who have not yet encountered calculus) of the actual relation, ##F=\frac{\mbox{d}p}{\mbox{d}t}## where ##p## is the momentum. The momentum in turn is connected not to the velocity, but to the total energy, by the relationship ##E^2=(m_0c^2)^2+(pc)^2##, which makes it clear that a massless particle (##m_0=0##) can still have non-zero momentum without infinite velocity.

It's worth noting that ##F=\frac{\mbox{d}p}{\mbox{d}t}## and ##E^2=(m_0c^2)^2+(pc)^2## reduce to the familiar ##F=ma## and ##E_k=mv^2/2## for particles of non-zero mass moving at non-relativistic velocities with constant acceleration. That is, the physics you've already learned isn't wrong, it just doesn't extend to massless particles and relativistic velocities.

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Matterwave

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The_Duck said:If you use special relativity to calculate the speed of a massless particle, you find that massless particles always travel at speed c, the speed of light.

In special relativity there is a sense in which there *are no* speeds greater than c.

Isn't that a postulate of special relativity, rather than something which is calculated?

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Nugatory

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Matterwave said:Isn't that a postulate of special relativity, rather than something which is calculated?

No, the postulate that special relativity makes is that "light is always propagated in empty

space with a definite velocity ##c## which is independent of the state of motion of the emitting body".

The impossibility of traveling faster than ##c## is derived from that postulate and some other even more reasonable assumptions.

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Dunbar

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Nugatory said:The momentum in turn is connected not to the velocity, but to the total energy, by the relationship ##E^2=(m_0c^2)^2+(pc)^2##, which makes it clear that a massless particle (##m_0=0##) can still have non-zero momentum without infinite velocity

Momentum's connection to total energy requires a formula that evokes c? In Newtonian mechanics light has mass, therefore its speed is not a universal limit. Its speed is simply a property of light. A massless particle's speed has no relevance to c in a Newtonian model? So, the simplified formula, ##F=ma##, is the still the most appropriate for massless particles?

(I understand I've probably got this wrong, and ultimately it's all moot; Newton's models aren't supported by observations of relativistic speeds.)

In addition, would I be right in saying: in special relativity a massless particle is traveling at infinite speed in its own frame of reference?

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Nugatory

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Yes... And you might find it interesting to see what that formula says about an object that is at rest (##p=0##).Dunbar said:Momentum's connection to total energy requires a formula that evokes c?

In classical mechanics, there are no massless particles, so classical mechanics says nothing about them. Also in classical mechanics light does not have mass; there's no contradiction here because in classical mechanics light is a wave not a particle, and no one expects a wave to have mass or be subject to forces.In Newtonian mechanics light has mass, therefore its speed is not a universal limit. Its speed is simply a property of light. A massless particle's speed has no relevance to c in a Newtonian model? So, the simplified formula, ##F=ma##, is the still the most appropriate for massless particles?

No. Massless particles don't have a frame of reference at all.In addition, would I be right in saying: in special relativity a massless particle is traveling at infinite speed in its own frame of reference?

One thing that may be confusing you here is our bad habit of talking about "the frame of reference of <something>". Frames don't belong to objects, objects don't own frames, so strictly speaking we shouldn't be using the word "of" here to suggest that the object has its own reference frame. When you see the words "the frame of reference of <something>", you should read that as convenient shorthand for the more precise "a frame in which <something> is at rest". There are no frames in which a massless particle is at rest.

Massless particles are particles that have no rest mass, meaning they do not have any physical mass at rest. Examples of massless particles include photons (particles of light) and gluons (particles that mediate the strong nuclear force).

Yes, according to the theory of relativity, massless particles are able to travel at the speed of light. This is because they have no rest mass and therefore do not experience the effects of time dilation or mass increase as they approach the speed of light.

The universal speed limit, also known as the speed of light, is the maximum speed at which all massless particles and objects with mass can travel. In a vacuum, the speed of light is approximately 299,792,458 meters per second.

Massless particles interact with matter through the fundamental forces of nature, such as electromagnetism and the strong and weak nuclear forces. For example, photons interact with matter through the electromagnetic force, allowing us to see and use light in various technologies.

According to our current understanding of physics, there are no known exceptions to the universal speed limit. All particles and objects, including massless particles, are subject to this limit and cannot travel faster than the speed of light.

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